Subgroups — C₅₃×#61141 #27268653

Order 13568.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3321	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3317	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3312	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3309	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3308	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#553	C₂²	1	1	yes	characteristic
43	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#552	C₂²	1	1	yes	characteristic
46	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#551	—	2	1	no	—
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#550	C₂²	1	1	yes	characteristic
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#548	C₂²	1	1	yes	characteristic
52	C₅₃×#548	C₂²	1	1	yes	characteristic
53	C₅₃×#547	—	2	1	no	—
54	C₅₃×#547	C₂²	1	1	yes	characteristic
55	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#546	—	2	1	no	—
57	C₅₃×#546	—	2	1	no	—
58	C₅₃×#546	—	2	1	no	—
59	C₅₃×#546	C₂²	1	1	yes	characteristic
60	C₅₃×#546	C₂²	1	1	yes	characteristic
61	D₄²×C₅₃	—	2	1	no	—
62	D₄²×C₅₃	C₂²	1	1	yes	characteristic
63	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#532	—	2	1	no	—
65	C₅₃×#532	C₂²	1	1	yes	characteristic
66	C₅₃×#529	—	2	1	no	—
67	C₅₃×#529	—	2	1	no	—
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#525	—	2	1	no	—
70	C₅₃×#525	—	2	1	no	—
71	C₅₃×#525	C₂²	1	1	yes	characteristic
72	C₅₃×#525	C₂²	1	1	yes	characteristic
73	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
75	C₄×#41×C₅₃	—	2	1	no	—
76	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
77	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₄×C₅₃	—	2	1	no	—
79	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
80	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#435	C₂²	1	1	yes	characteristic
163	C₅₃×#435	C₂²	1	1	yes	characteristic
164	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
173	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#416	C₂²	1	1	yes	characteristic
183	C₅₃×#416	C₂²	1	1	yes	characteristic
184	C₅₃×#416	C₂²	1	1	yes	characteristic
185	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
200	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	—	2	1	no	—
205	C₂×#41×C₅₃	—	2	1	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	—	2	1	no	—
208	C₂×#41×C₅₃	—	2	4	no	—
209	C₂×#41×C₅₃	—	2	4	no	—
210	C₂×#41×C₅₃	—	4	2	no	—
211	C₂×#41×C₅₃	—	4	2	no	—
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²×D₄×C₅₃	—	2	1	no	—
223	C₂²×D₄×C₅₃	—	2	1	no	—
224	C₂²×D₄×C₅₃	—	2	1	no	—
225	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
226	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂³×C₄×C₅₃	—	2	1	no	—
229	C₂³×C₄×C₅₃	—	2	1	no	—
230	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
232	#135×C₅₃	—	2	4	no	—
233	#135×C₅₃	—	4	2	no	—
234	#135×C₅₃	—	4	2	no	—
235	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×M₁₆×C₅₃	—	4	2	no	—
248	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂²×C₈×C₅₃	—	4	2	no	—
253	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
260	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
261	C₄⋊Q₈×C₅₃	—	2	1	no	—
262	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
265	#127×C₅₃	—	2	1	no	—
266	#127×C₅₃	C₂³	1	1	yes	characteristic
267	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#126×C₅₃	—	2	1	no	—
270	#126×C₅₃	—	2	1	no	—
271	#126×C₅₃	—	2	1	no	—
272	#126×C₅₃	—	2	1	no	—
273	#125×C₅₃	—	2	1	no	—
274	#125×C₅₃	—	2	1	no	—
275	#125×C₅₃	—	2	1	no	—
276	#125×C₅₃	C₂³	1	1	yes	characteristic
277	#125×C₅₃	C₂³	1	1	yes	characteristic
278	#124×C₅₃	—	2	1	no	—
279	#124×C₅₃	—	2	1	no	—
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	C₂³	1	1	yes	characteristic
284	#124×C₅₃	C₂³	1	1	yes	characteristic
285	#123×C₅₃	—	2	1	no	—
286	#123×C₅₃	—	2	1	no	—
287	#123×C₅₃	—	2	1	no	—
288	#123×C₅₃	—	2	1	no	—
289	#123×C₅₃	—	2	1	no	—
290	#123×C₅₃	—	2	1	no	—
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	—	2	1	no	—
293	#123×C₅₃	—	2	1	no	—
294	#123×C₅₃	—	2	1	no	—
295	#123×C₅₃	—	2	1	no	—
296	#123×C₅₃	—	2	1	no	—
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	—	2	1	no	—
300	C₂²⋊Q₈×C₅₃	—	2	1	no	—
301	C₂²⋊Q₈×C₅₃	—	2	1	no	—
302	C₂²⋊Q₈×C₅₃	—	2	1	no	—
303	C₂²⋊Q₈×C₅₃	—	2	1	no	—
304	C₂²⋊Q₈×C₅₃	—	2	1	no	—
305	C₂²⋊Q₈×C₅₃	—	2	1	no	—
306	C₂²⋊Q₈×C₅₃	—	2	1	no	—
307	C₂²⋊Q₈×C₅₃	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	#121×C₅₃	—	2	1	no	—
317	#121×C₅₃	—	2	1	no	—
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	—	2	1	no	—
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	—	2	1	no	—
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	—	2	1	no	—
329	#121×C₅₃	C₂³	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	C₂³	1	1	yes	characteristic
332	#121×C₅₃	C₂³	1	1	yes	characteristic
333	#121×C₅₃	C₂³	1	1	yes	characteristic
334	#121×C₅₃	C₂³	1	1	yes	characteristic
335	#121×C₅₃	C₂³	1	1	yes	characteristic
336	#121×C₅₃	C₂³	1	1	yes	characteristic
337	#120×C₅₃	—	2	1	no	—
338	#120×C₅₃	—	2	1	no	—
339	#120×C₅₃	—	2	1	no	—
340	#120×C₅₃	—	2	1	no	—
341	#120×C₅₃	—	2	1	no	—
342	#120×C₅₃	—	2	1	no	—
343	#120×C₅₃	—	2	1	no	—
344	#120×C₅₃	—	2	1	no	—
345	C₄×Q₈×C₅₃	—	2	1	no	—
346	C₄×Q₈×C₅₃	—	2	1	no	—
347	C₄×Q₈×C₅₃	—	2	1	no	—
348	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	—	2	1	no	—
361	C₄×D₄×C₅₃	—	2	1	no	—
362	C₄×D₄×C₅₃	—	2	1	no	—
363	C₄×D₄×C₅₃	—	2	1	no	—
364	C₄×D₄×C₅₃	—	2	1	no	—
365	C₄×D₄×C₅₃	—	2	1	no	—
366	C₄×D₄×C₅₃	—	2	1	no	—
367	C₄×D₄×C₅₃	—	2	1	no	—
368	C₄×D₄×C₅₃	—	2	1	no	—
369	C₄×D₄×C₅₃	—	2	1	no	—
370	C₄×D₄×C₅₃	—	2	1	no	—
371	C₄×D₄×C₅₃	—	2	1	no	—
372	C₄×D₄×C₅₃	—	2	1	no	—
373	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
374	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
375	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
376	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
382	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
385	#117×C₅₃	—	2	1	no	—
386	#117×C₅₃	—	2	1	no	—
387	#117×C₅₃	—	2	1	no	—
388	#117×C₅₃	—	2	1	no	—
389	#117×C₅₃	—	2	1	no	—
390	#117×C₅₃	—	2	1	no	—
391	#117×C₅₃	—	2	1	no	—
392	#117×C₅₃	—	2	1	no	—
393	#117×C₅₃	—	2	1	no	—
394	#117×C₅₃	C₂³	1	1	yes	characteristic
395	#117×C₅₃	C₂³	1	1	yes	characteristic
396	#117×C₅₃	C₂³	1	1	yes	characteristic
397	#117×C₅₃	C₂³	1	1	yes	characteristic
398	#117×C₅₃	C₂³	1	1	yes	characteristic
399	#117×C₅₃	C₂³	1	1	yes	characteristic
400	#117×C₅₃	C₂³	1	1	yes	characteristic
401	#117×C₅₃	C₂³	1	1	yes	characteristic
402	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
404	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
405	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
407	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
408	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
413	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
414	C₂×C₄²×C₅₃	—	2	1	no	—
415	C₂×C₄²×C₅₃	—	2	1	no	—
416	C₂×C₄²×C₅₃	—	2	1	no	—
417	C₂×C₄²×C₅₃	—	2	1	no	—
418	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
419	#107×C₅₃	C₂³	1	1	yes	characteristic
420	#107×C₅₃	C₂³	1	1	yes	characteristic
421	#107×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#106×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	#106×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	#103×C₅₃	C₂³	1	1	yes	characteristic
436	#103×C₅₃	C₂³	1	1	yes	characteristic
437	#103×C₅₃	C₂³	1	1	yes	characteristic
438	#103×C₅₃	C₂³	1	1	yes	characteristic
439	#103×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×C₅₃	C₂³	1	1	yes	characteristic
474	#102×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
483	#97×C₅₃	C₂³	1	1	yes	characteristic
484	#97×C₅₃	C₂³	1	1	yes	characteristic
485	#97×C₅₃	C₂³	1	1	yes	characteristic
486	#97×C₅₃	C₂³	1	1	yes	characteristic
487	C₂⁴×C₅₃	—	2	1	no	—
488	C₂⁴×C₅₃	—	2	1	no	—
489	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
490	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
491	#41×C₅₃	—	2	2	no	—
492	#41×C₅₃	—	2	2	no	—
493	#41×C₅₃	—	2	2	no	—
494	#41×C₅₃	—	2	2	no	—
495	#41×C₅₃	—	2	2	no	—
496	#41×C₅₃	—	2	2	no	—
497	#41×C₅₃	—	2	2	no	—
498	#41×C₅₃	—	2	2	no	—
499	#41×C₅₃	—	2	2	no	—
500	#41×C₅₃	—	2	2	no	—
501	#41×C₅₃	—	2	2	no	—
502	#41×C₅₃	—	4	4	no	—
503	#41×C₅₃	—	4	4	no	—
504	#41×C₅₃	—	4	1	no	—
505	#41×C₅₃	—	4	1	no	—
506	#41×C₅₃	—	4	1	no	—
507	#41×C₅₃	—	4	1	no	—
508	#41×C₅₃	—	4	4	no	—
509	#41×C₅₃	—	4	4	no	—
510	#41×C₅₃	—	4	4	no	—
511	#41×C₅₃	#41	1	4	yes	complemented
512	C₂×Q₈×C₅₃	—	2	1	no	—
513	C₂×Q₈×C₅₃	—	2	1	no	—
514	C₂×Q₈×C₅₃	—	2	1	no	—
515	C₂×Q₈×C₅₃	—	2	1	no	—
516	C₂×Q₈×C₅₃	—	2	2	no	—
517	C₂×Q₈×C₅₃	—	2	2	no	—
518	C₂×Q₈×C₅₃	—	4	1	no	—
519	C₂×Q₈×C₅₃	—	4	1	no	—
520	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
522	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
523	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	2	no	—
526	C₂×D₄×C₅₃	—	2	2	no	—
527	C₂×D₄×C₅₃	—	2	1	no	—
528	C₂×D₄×C₅₃	—	2	1	no	—
529	C₂×D₄×C₅₃	—	2	1	no	—
530	C₂×D₄×C₅₃	—	2	1	no	—
531	C₂×D₄×C₅₃	—	2	1	no	—
532	C₂×D₄×C₅₃	—	2	1	no	—
533	C₂×D₄×C₅₃	—	2	1	no	—
534	C₂×D₄×C₅₃	—	2	1	no	—
535	C₂×D₄×C₅₃	—	2	1	no	—
536	C₂×D₄×C₅₃	—	2	1	no	—
537	C₂×D₄×C₅₃	—	2	1	no	—
538	C₂×D₄×C₅₃	—	2	1	no	—
539	C₂×D₄×C₅₃	—	2	1	no	—
540	C₂×D₄×C₅₃	—	2	1	no	—
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	1	no	—
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	2	1	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	4	1	no	—
547	C₂×D₄×C₅₃	—	4	1	no	—
548	C₂×D₄×C₅₃	—	4	2	no	—
549	C₂×D₄×C₅₃	—	4	4	no	—
550	C₂×D₄×C₅₃	—	4	4	no	—
551	C₂×D₄×C₅₃	—	4	4	no	—
552	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
553	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
554	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
555	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
556	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	—	2	1	no	—
561	C₂²×C₄×C₅₃	—	2	2	no	—
562	C₂²×C₄×C₅₃	—	2	2	no	—
563	C₂²×C₄×C₅₃	—	2	2	no	—
564	C₂²×C₄×C₅₃	—	2	2	no	—
565	C₂²×C₄×C₅₃	—	2	1	no	—
566	C₂²×C₄×C₅₃	—	2	1	no	—
567	C₂²×C₄×C₅₃	—	2	1	no	—
568	C₂²×C₄×C₅₃	—	2	1	no	—
569	C₂²×C₄×C₅₃	—	2	1	no	—
570	C₂²×C₄×C₅₃	—	2	1	no	—
571	C₂²×C₄×C₅₃	—	2	1	no	—
572	C₂²×C₄×C₅₃	—	2	1	no	—
573	C₂²×C₄×C₅₃	—	2	1	no	—
574	C₂²×C₄×C₅₃	—	2	1	no	—
575	C₂²×C₄×C₅₃	—	2	1	no	—
576	C₂²×C₄×C₅₃	—	2	1	no	—
577	C₂²×C₄×C₅₃	—	2	1	no	—
578	C₂²×C₄×C₅₃	—	2	1	no	—
579	C₂²×C₄×C₅₃	—	2	1	no	—
580	C₂²×C₄×C₅₃	—	2	1	no	—
581	C₂²×C₄×C₅₃	—	2	1	no	—
582	C₂²×C₄×C₅₃	—	4	4	no	—
583	C₂²×C₄×C₅₃	—	4	4	no	—
584	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
585	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
586	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
587	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
588	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
589	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
590	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
591	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
592	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
597	Q₁₆×C₅₃	—	2	2	no	—
598	Q₁₆×C₅₃	—	4	1	no	—
599	Q₁₆×C₅₃	—	4	1	no	—
600	SD₁₆×C₅₃	—	2	2	no	—
601	SD₁₆×C₅₃	—	2	2	no	—
602	SD₁₆×C₅₃	—	4	1	no	—
603	SD₁₆×C₅₃	—	4	1	no	—
604	SD₁₆×C₅₃	—	4	1	no	—
605	SD₁₆×C₅₃	—	4	1	no	—
606	D₈×C₅₃	—	2	2	no	—
607	D₈×C₅₃	—	4	1	no	—
608	D₈×C₅₃	—	4	1	no	—
609	M₁₆×C₅₃	—	4	1	no	—
610	M₁₆×C₅₃	—	4	1	no	—
611	M₁₆×C₅₃	—	4	1	no	—
612	M₁₆×C₅₃	—	4	1	no	—
613	C₂×C₈×C₅₃	—	2	2	no	—
614	C₂×C₈×C₅₃	—	2	2	no	—
615	C₂×C₈×C₅₃	—	2	2	no	—
616	C₂×C₈×C₅₃	—	2	2	no	—
617	C₂×C₈×C₅₃	—	4	1	no	—
618	C₂×C₈×C₅₃	—	4	1	no	—
619	C₂×C₈×C₅₃	—	4	1	no	—
620	C₂×C₈×C₅₃	—	4	1	no	—
621	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
622	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
623	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
624	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
625	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
626	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
627	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
628	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	—	2	1	no	—
631	C₄⋊C₄×C₅₃	—	2	1	no	—
632	C₄⋊C₄×C₅₃	—	2	1	no	—
633	C₄⋊C₄×C₅₃	—	2	1	no	—
634	C₄⋊C₄×C₅₃	—	2	1	no	—
635	C₄⋊C₄×C₅₃	—	2	1	no	—
636	C₄⋊C₄×C₅₃	—	2	1	no	—
637	C₄⋊C₄×C₅₃	—	2	1	no	—
638	C₄⋊C₄×C₅₃	—	2	1	no	—
639	C₄⋊C₄×C₅₃	—	2	1	no	—
640	C₄⋊C₄×C₅₃	—	2	1	no	—
641	C₄⋊C₄×C₅₃	—	2	1	no	—
642	C₄⋊C₄×C₅₃	—	2	1	no	—
643	C₄⋊C₄×C₅₃	—	2	1	no	—
644	C₄⋊C₄×C₅₃	—	2	1	no	—
645	C₄⋊C₄×C₅₃	—	2	1	no	—
646	C₄⋊C₄×C₅₃	—	2	1	no	—
647	C₄⋊C₄×C₅₃	—	2	1	no	—
648	C₄⋊C₄×C₅₃	—	2	1	no	—
649	C₄⋊C₄×C₅₃	—	2	1	no	—
650	C₄⋊C₄×C₅₃	—	2	1	no	—
651	C₄⋊C₄×C₅₃	—	2	1	no	—
652	C₄⋊C₄×C₅₃	—	2	1	no	—
653	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
654	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
655	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
656	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
657	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
658	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
659	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
660	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
661	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
662	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
663	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
664	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	—	2	1	no	—
676	C₂²⋊C₄×C₅₃	—	2	1	no	—
677	C₂²⋊C₄×C₅₃	—	2	1	no	—
678	C₂²⋊C₄×C₅₃	—	2	1	no	—
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
682	C₂²⋊C₄×C₅₃	—	2	1	no	—
683	C₂²⋊C₄×C₅₃	—	2	1	no	—
684	C₂²⋊C₄×C₅₃	—	2	1	no	—
685	C₂²⋊C₄×C₅₃	—	2	1	no	—
686	C₂²⋊C₄×C₅₃	—	2	1	no	—
687	C₂²⋊C₄×C₅₃	—	2	1	no	—
688	C₂²⋊C₄×C₅₃	—	2	1	no	—
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	—	2	1	no	—
693	C₂²⋊C₄×C₅₃	—	2	1	no	—
694	C₂²⋊C₄×C₅₃	—	2	1	no	—
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
700	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
703	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
704	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
705	C₄²×C₅₃	—	2	1	no	—
706	C₄²×C₅₃	—	2	1	no	—
707	C₄²×C₅₃	—	2	1	no	—
708	C₄²×C₅₃	—	2	1	no	—
709	C₄²×C₅₃	—	2	1	no	—
710	C₄²×C₅₃	—	2	1	no	—
711	C₄²×C₅₃	—	2	1	no	—
712	C₄²×C₅₃	—	2	1	no	—
713	C₄²×C₅₃	—	2	1	no	—
714	C₄²×C₅₃	—	2	1	no	—
715	C₄²×C₅₃	—	2	1	no	—
716	C₄²×C₅₃	—	2	1	no	—
717	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
718	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
719	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
720	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
721	C₂³×C₅₃	—	2	2	no	—
722	C₂³×C₅₃	—	2	2	no	—
723	C₂³×C₅₃	—	2	1	no	—
724	C₂³×C₅₃	—	2	2	no	—
725	C₂³×C₅₃	—	2	1	no	—
726	C₂³×C₅₃	—	2	1	no	—
727	C₂³×C₅₃	—	2	1	no	—
728	C₂³×C₅₃	—	4	1	no	—
729	C₂³×C₅₃	—	4	1	no	—
730	C₂³×C₅₃	—	4	1	no	—
731	C₂³×C₅₃	—	4	2	no	—
732	C₂³×C₅₃	—	4	2	no	—
733	C₂³×C₅₃	—	4	2	no	—
734	C₂³×C₅₃	—	4	2	no	—
735	C₂³×C₅₃	—	8	1	no	—
736	C₂³×C₅₃	—	8	1	no	—
737	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
738	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
739	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
740	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
741	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
742	Q₈×C₅₃	—	2	1	no	—
743	Q₈×C₅₃	—	2	1	no	—
744	Q₈×C₅₃	—	2	1	no	—
745	Q₈×C₅₃	—	2	1	no	—
746	Q₈×C₅₃	—	2	1	no	—
747	Q₈×C₅₃	—	2	1	no	—
748	Q₈×C₅₃	—	2	1	no	—
749	Q₈×C₅₃	—	4	2	no	—
750	Q₈×C₅₃	—	4	2	no	—
751	Q₈×C₅₃	—	4	2	no	—
752	Q₈×C₅₃	—	8	1	no	—
753	Q₈×C₅₃	C₂×#41	1	2	yes	—
754	D₄×C₅₃	—	2	4	no	—
755	D₄×C₅₃	—	2	2	no	—
756	D₄×C₅₃	—	2	2	no	—
757	D₄×C₅₃	—	2	1	no	—
758	D₄×C₅₃	—	2	1	no	—
759	D₄×C₅₃	—	2	1	no	—
760	D₄×C₅₃	—	2	1	no	—
761	D₄×C₅₃	—	2	1	no	—
762	D₄×C₅₃	—	2	1	no	—
763	D₄×C₅₃	—	2	1	no	—
764	D₄×C₅₃	—	4	1	no	—
765	D₄×C₅₃	—	4	1	no	—
766	D₄×C₅₃	—	4	2	no	—
767	D₄×C₅₃	—	4	2	no	—
768	D₄×C₅₃	—	4	2	no	—
769	D₄×C₅₃	—	4	2	no	—
770	D₄×C₅₃	—	4	2	no	—
771	D₄×C₅₃	—	4	2	no	—
772	D₄×C₅₃	—	4	2	no	—
773	D₄×C₅₃	—	4	2	no	—
774	D₄×C₅₃	—	4	2	no	—
775	D₄×C₅₃	—	4	2	no	—
776	D₄×C₅₃	—	4	2	no	—
777	D₄×C₅₃	—	4	2	no	—
778	D₄×C₅₃	—	4	2	no	—
779	D₄×C₅₃	—	4	2	no	—
780	D₄×C₅₃	—	8	1	no	—
781	D₄×C₅₃	—	8	1	no	—
782	D₄×C₅₃	—	8	1	no	—
783	D₄×C₅₃	—	8	1	no	—
784	D₄×C₅₃	—	8	1	no	—
785	D₄×C₅₃	C₂×#41	1	2	yes	—
786	C₂×C₄×C₅₃	—	2	2	no	—
787	C₂×C₄×C₅₃	—	2	2	no	—
788	C₂×C₄×C₅₃	—	2	1	no	—
789	C₂×C₄×C₅₃	—	2	2	no	—
790	C₂×C₄×C₅₃	—	2	2	no	—
791	C₂×C₄×C₅₃	—	2	2	no	—
792	C₂×C₄×C₅₃	—	2	2	no	—
793	C₂×C₄×C₅₃	—	2	4	no	—
794	C₂×C₄×C₅₃	—	2	1	no	—
795	C₂×C₄×C₅₃	—	2	1	no	—
796	C₂×C₄×C₅₃	—	2	1	no	—
797	C₂×C₄×C₅₃	—	2	1	no	—
798	C₂×C₄×C₅₃	—	2	1	no	—
799	C₂×C₄×C₅₃	—	2	1	no	—
800	C₂×C₄×C₅₃	—	2	1	no	—
801	C₂×C₄×C₅₃	—	2	1	no	—
802	C₂×C₄×C₅₃	—	2	1	no	—
803	C₂×C₄×C₅₃	—	2	1	no	—
804	C₂×C₄×C₅₃	—	2	1	no	—
805	C₂×C₄×C₅₃	—	2	1	no	—
806	C₂×C₄×C₅₃	—	2	1	no	—
807	C₂×C₄×C₅₃	—	2	1	no	—
808	C₂×C₄×C₅₃	—	2	1	no	—
809	C₂×C₄×C₅₃	—	2	1	no	—
810	C₂×C₄×C₅₃	—	2	1	no	—
811	C₂×C₄×C₅₃	—	2	1	no	—
812	C₂×C₄×C₅₃	—	2	1	no	—
813	C₂×C₄×C₅₃	—	4	1	no	—
814	C₂×C₄×C₅₃	—	4	1	no	—
815	C₂×C₄×C₅₃	—	4	2	no	—
816	C₂×C₄×C₅₃	—	4	2	no	—
817	C₂×C₄×C₅₃	—	4	2	no	—
818	C₂×C₄×C₅₃	—	4	2	no	—
819	C₂×C₄×C₅₃	—	4	2	no	—
820	C₂×C₄×C₅₃	—	4	2	no	—
821	C₂×C₄×C₅₃	—	4	2	no	—
822	C₂×C₄×C₅₃	—	4	2	no	—
823	C₂×C₄×C₅₃	—	4	2	no	—
824	C₂×C₄×C₅₃	—	4	2	no	—
825	C₂×C₄×C₅₃	—	4	2	no	—
826	C₂×C₄×C₅₃	—	4	2	no	—
827	C₂×C₄×C₅₃	—	4	2	no	—
828	C₂×C₄×C₅₃	—	8	1	no	—
829	C₂×C₄×C₅₃	—	8	1	no	—
830	C₂×C₄×C₅₃	—	8	1	no	—
831	C₂×C₄×C₅₃	—	8	1	no	—
832	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
833	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
834	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
835	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
836	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
837	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
838	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
839	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
840	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
841	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
842	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
843	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
844	C₈×C₅₃	—	2	1	no	—
845	C₈×C₅₃	—	2	1	no	—
846	C₈×C₅₃	—	2	1	no	—
847	C₈×C₅₃	—	2	1	no	—
848	C₈×C₅₃	—	2	1	no	—
849	C₈×C₅₃	—	2	1	no	—
850	C₈×C₅₃	—	2	1	no	—
851	C₈×C₅₃	—	2	1	no	—
852	#61141	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
853	C₂²×C₅₃	—	2	1	no	—
854	C₂²×C₅₃	—	2	1	no	—
855	C₂²×C₅₃	—	2	1	no	—
856	C₂²×C₅₃	—	2	1	no	—
857	C₂²×C₅₃	—	2	1	no	—
858	C₂²×C₅₃	—	2	1	no	—
859	C₂²×C₅₃	—	2	1	no	—
860	C₂²×C₅₃	—	2	1	no	—
861	C₂²×C₅₃	—	2	1	no	—
862	C₂²×C₅₃	—	2	1	no	—
863	C₂²×C₅₃	—	2	2	no	—
864	C₂²×C₅₃	—	2	1	no	—
865	C₂²×C₅₃	—	2	1	no	—
866	C₂²×C₅₃	—	2	1	no	—
867	C₂²×C₅₃	—	4	4	no	—
868	C₂²×C₅₃	—	4	1	no	—
869	C₂²×C₅₃	—	4	1	no	—
870	C₂²×C₅₃	—	4	1	no	—
871	C₂²×C₅₃	—	4	1	no	—
872	C₂²×C₅₃	—	4	1	no	—
873	C₂²×C₅₃	—	4	1	no	—
874	C₂²×C₅₃	—	4	1	no	—
875	C₂²×C₅₃	—	4	1	no	—
876	C₂²×C₅₃	—	4	1	no	—
877	C₂²×C₅₃	—	4	1	no	—
878	C₂²×C₅₃	—	4	1	no	—
879	C₂²×C₅₃	—	8	2	no	—
880	C₂²×C₅₃	—	8	4	no	—
881	C₂²×C₅₃	—	8	4	no	—
882	C₂²×C₅₃	#546	1	2	yes	—
883	C₂²×C₅₃	#575	1	2	yes	—
884	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
885	C₄×C₅₃	—	2	1	no	—
886	C₄×C₅₃	—	2	1	no	—
887	C₄×C₅₃	—	2	1	no	—
888	C₄×C₅₃	—	2	1	no	—
889	C₄×C₅₃	—	2	1	no	—
890	C₄×C₅₃	—	2	1	no	—
891	C₄×C₅₃	—	2	2	no	—
892	C₄×C₅₃	—	2	1	no	—
893	C₄×C₅₃	—	2	1	no	—
894	C₄×C₅₃	—	4	1	no	—
895	C₄×C₅₃	—	4	1	no	—
896	C₄×C₅₃	—	4	1	no	—
897	C₄×C₅₃	—	4	1	no	—
898	C₄×C₅₃	—	4	1	no	—
899	C₄×C₅₃	—	4	1	no	—
900	C₄×C₅₃	—	4	1	no	—
901	C₄×C₅₃	—	4	1	no	—
902	C₄×C₅₃	—	4	1	no	—
903	C₄×C₅₃	—	4	1	no	—
904	C₄×C₅₃	—	4	1	no	—
905	C₄×C₅₃	#546	1	2	yes	—
906	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
907	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
908	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
909	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
910	#3321	C₂×C₅₃	1	1	yes	characteristic, complemented
911	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
912	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
913	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
914	#3317	C₂×C₅₃	1	1	yes	characteristic, complemented
915	#3316	C₂×C₅₃	1	1	yes	characteristic, complemented
916	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
917	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
918	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
919	#3312	C₂×C₅₃	1	1	yes	characteristic, complemented
920	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
921	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
922	#3309	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#3308	C₂×C₅₃	1	1	yes	characteristic, complemented
924	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#3135	C₂×C₅₃	1	1	yes	characteristic, complemented
927	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#3054	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#3050	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
935	#2943	C₂×C₅₃	1	1	yes	characteristic, complemented
936	C₂×#435	C₂×C₅₃	1	1	yes	characteristic, complemented
937	#2896	C₂×C₅₃	1	1	yes	characteristic, complemented
938	C₂×#416	C₂×C₅₃	1	1	yes	characteristic, complemented
939	C₂×C₅₃	—	2	2	no	—
940	C₂×C₅₃	—	2	2	no	—
941	C₂×C₅₃	—	4	1	no	—
942	C₂×C₅₃	—	4	1	no	—
943	C₂×C₅₃	—	4	1	no	—
944	C₂×C₅₃	—	4	2	no	—
945	C₂×C₅₃	—	8	1	no	—
946	C₂×C₅₃	—	8	1	no	—
947	C₂×C₅₃	—	8	1	no	—
948	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
949	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
950	C₂×C₅₃	#3584	1	1	yes	characteristic
951	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
952	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
953	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
954	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#553	C₂²×C₅₃	1	1	yes	characteristic
962	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#552	—	2	1	no	—
964	#552	C₂²×C₅₃	1	1	yes	characteristic
965	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#551	—	2	1	no	—
967	#551	—	2	1	no	—
968	#550	C₂²×C₅₃	1	1	yes	characteristic
969	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
970	#548	C₂²×C₅₃	1	1	yes	characteristic
971	#548	C₂²×C₅₃	1	1	yes	characteristic
972	#547	—	2	1	no	—
973	#547	C₂²×C₅₃	1	1	yes	characteristic
974	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#546	—	2	1	no	—
976	#546	—	2	1	no	—
977	#546	—	2	1	no	—
978	#546	C₂²×C₅₃	1	1	yes	characteristic
979	#546	C₂²×C₅₃	1	1	yes	characteristic
980	D₄²	—	2	1	no	—
981	D₄²	C₂²×C₅₃	1	1	yes	characteristic
982	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#532	—	2	1	no	—
984	#532	C₂²×C₅₃	1	1	yes	characteristic
985	#529	—	2	1	no	—
986	#529	—	2	1	no	—
987	#529	—	2	1	no	—
988	#525	—	2	1	no	—
989	#525	—	2	1	no	—
990	#525	C₂²×C₅₃	1	1	yes	characteristic
991	#525	C₂²×C₅₃	1	1	yes	characteristic
992	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	C₄×#41	—	2	1	no	—
995	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
996	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	C₂×C₄×D₄	—	2	1	no	—
998	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
999	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#435	C₂²×C₅₃	1	1	yes	characteristic
1082	#435	C₂²×C₅₃	1	1	yes	characteristic
1083	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#416	C₂²×C₅₃	1	1	yes	characteristic
1102	#416	C₂²×C₅₃	1	1	yes	characteristic
1103	#416	C₂²×C₅₃	1	1	yes	characteristic
1104	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1117	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	C₅₃	#61141	1	1	yes	characteristic, direct product factor, Sylow
1123	C₂×#41	—	2	1	no	—
1124	C₂×#41	—	2	1	no	—
1125	C₂×#41	—	2	1	no	—
1126	C₂×#41	—	2	1	no	—
1127	C₂×#41	—	2	1	no	—
1128	C₂×#41	—	2	4	no	—
1129	C₂×#41	—	2	4	no	—
1130	C₂×#41	—	4	2	no	—
1131	C₂×#41	—	4	2	no	—
1132	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂²×D₄	—	2	1	no	—
1143	C₂²×D₄	—	2	1	no	—
1144	C₂²×D₄	—	2	1	no	—
1145	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
1146	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂³×C₄	—	2	1	no	—
1149	C₂³×C₄	—	2	1	no	—
1150	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1152	#135	—	2	4	no	—
1153	#135	—	4	2	no	—
1154	#135	—	4	2	no	—
1155	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1162	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×M₁₆	—	4	2	no	—
1168	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂²×C₈	—	4	2	no	—
1173	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1181	C₄⋊Q₈	—	2	1	no	—
1182	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1183	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1184	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1185	#127	—	2	1	no	—
1186	#127	C₂³×C₅₃	1	1	yes	characteristic
1187	#126	—	2	1	no	—
1188	#126	—	2	1	no	—
1189	#126	—	2	1	no	—
1190	#126	—	2	1	no	—
1191	#126	—	2	1	no	—
1192	#126	—	2	1	no	—
1193	#125	—	2	1	no	—
1194	#125	—	2	1	no	—
1195	#125	—	2	1	no	—
1196	#125	C₂³×C₅₃	1	1	yes	characteristic
1197	#125	C₂³×C₅₃	1	1	yes	characteristic
1198	#124	—	2	1	no	—
1199	#124	—	2	1	no	—
1200	#124	—	2	1	no	—
1201	#124	—	2	1	no	—
1202	#124	—	2	1	no	—
1203	#124	C₂³×C₅₃	1	1	yes	characteristic
1204	#124	C₂³×C₅₃	1	1	yes	characteristic
1205	#123	—	2	1	no	—
1206	#123	—	2	1	no	—
1207	#123	—	2	1	no	—
1208	#123	—	2	1	no	—
1209	#123	—	2	1	no	—
1210	#123	—	2	1	no	—
1211	#123	—	2	1	no	—
1212	#123	—	2	1	no	—
1213	#123	—	2	1	no	—
1214	#123	—	2	1	no	—
1215	#123	—	2	1	no	—
1216	#123	—	2	1	no	—
1217	#123	—	2	1	no	—
1218	#123	—	2	1	no	—
1219	C₂²⋊Q₈	—	2	1	no	—
1220	C₂²⋊Q₈	—	2	1	no	—
1221	C₂²⋊Q₈	—	2	1	no	—
1222	C₂²⋊Q₈	—	2	1	no	—
1223	C₂²⋊Q₈	—	2	1	no	—
1224	C₂²⋊Q₈	—	2	1	no	—
1225	C₂²⋊Q₈	—	2	1	no	—
1226	C₂²⋊Q₈	—	2	1	no	—
1227	C₂²⋊Q₈	—	2	1	no	—
1228	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1229	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1230	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1231	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1232	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1233	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1234	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1235	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1236	#121	—	2	1	no	—
1237	#121	—	2	1	no	—
1238	#121	—	2	1	no	—
1239	#121	—	2	1	no	—
1240	#121	—	2	1	no	—
1241	#121	—	2	1	no	—
1242	#121	—	2	1	no	—
1243	#121	—	2	1	no	—
1244	#121	—	2	1	no	—
1245	#121	—	2	1	no	—
1246	#121	—	2	1	no	—
1247	#121	—	2	1	no	—
1248	#121	—	2	1	no	—
1249	#121	C₂³×C₅₃	1	1	yes	characteristic
1250	#121	C₂³×C₅₃	1	1	yes	characteristic
1251	#121	C₂³×C₅₃	1	1	yes	characteristic
1252	#121	C₂³×C₅₃	1	1	yes	characteristic
1253	#121	C₂³×C₅₃	1	1	yes	characteristic
1254	#121	C₂³×C₅₃	1	1	yes	characteristic
1255	#121	C₂³×C₅₃	1	1	yes	characteristic
1256	#121	C₂³×C₅₃	1	1	yes	characteristic
1257	#120	—	2	1	no	—
1258	#120	—	2	1	no	—
1259	#120	—	2	1	no	—
1260	#120	—	2	1	no	—
1261	#120	—	2	1	no	—
1262	#120	—	2	1	no	—
1263	#120	—	2	1	no	—
1264	#120	—	2	1	no	—
1265	C₄×Q₈	—	2	1	no	—
1266	C₄×Q₈	—	2	1	no	—
1267	C₄×Q₈	—	2	1	no	—
1268	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1271	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1272	C₄×D₄	—	2	1	no	—
1273	C₄×D₄	—	2	1	no	—
1274	C₄×D₄	—	2	1	no	—
1275	C₄×D₄	—	2	1	no	—
1276	C₄×D₄	—	2	1	no	—
1277	C₄×D₄	—	2	1	no	—
1278	C₄×D₄	—	2	1	no	—
1279	C₄×D₄	—	2	1	no	—
1280	C₄×D₄	—	2	1	no	—
1281	C₄×D₄	—	2	1	no	—
1282	C₄×D₄	—	2	1	no	—
1283	C₄×D₄	—	2	1	no	—
1284	C₄×D₄	—	2	1	no	—
1285	C₄×D₄	—	2	1	no	—
1286	C₄×D₄	—	2	1	no	—
1287	C₄×D₄	—	2	1	no	—
1288	C₄×D₄	—	2	1	no	—
1289	C₄×D₄	—	2	1	no	—
1290	C₄×D₄	—	2	1	no	—
1291	C₄×D₄	—	2	1	no	—
1292	C₄×D₄	—	2	1	no	—
1293	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1294	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1295	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1296	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1297	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1298	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1299	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1300	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1303	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1304	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1305	#117	—	2	1	no	—
1306	#117	—	2	1	no	—
1307	#117	—	2	1	no	—
1308	#117	—	2	1	no	—
1309	#117	—	2	1	no	—
1310	#117	—	2	1	no	—
1311	#117	—	2	1	no	—
1312	#117	—	2	1	no	—
1313	#117	—	2	1	no	—
1314	#117	C₂³×C₅₃	1	1	yes	characteristic
1315	#117	C₂³×C₅₃	1	1	yes	characteristic
1316	#117	C₂³×C₅₃	1	1	yes	characteristic
1317	#117	C₂³×C₅₃	1	1	yes	characteristic
1318	#117	C₂³×C₅₃	1	1	yes	characteristic
1319	#117	C₂³×C₅₃	1	1	yes	characteristic
1320	#117	C₂³×C₅₃	1	1	yes	characteristic
1321	#117	C₂³×C₅₃	1	1	yes	characteristic
1322	C₂×C₄⋊C₄	—	2	1	no	—
1323	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1324	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1325	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1326	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1327	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1328	C₂×C₂²⋊C₄	—	2	1	no	—
1329	C₂×C₂²⋊C₄	—	2	1	no	—
1330	C₂×C₂²⋊C₄	—	2	1	no	—
1331	C₂×C₂²⋊C₄	—	2	1	no	—
1332	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1333	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1334	C₂×C₄²	—	2	1	no	—
1335	C₂×C₄²	—	2	1	no	—
1336	C₂×C₄²	—	2	1	no	—
1337	C₂×C₄²	—	2	1	no	—
1338	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1339	#107	C₂³×C₅₃	1	1	yes	characteristic
1340	#107	C₂³×C₅₃	1	1	yes	characteristic
1341	#107	C₂³×C₅₃	1	1	yes	characteristic
1342	#107	C₂³×C₅₃	1	1	yes	characteristic
1343	#107	C₂³×C₅₃	1	1	yes	characteristic
1344	#107	C₂³×C₅₃	1	1	yes	characteristic
1345	#106	C₂³×C₅₃	1	1	yes	characteristic
1346	#106	C₂³×C₅₃	1	1	yes	characteristic
1347	#106	C₂³×C₅₃	1	1	yes	characteristic
1348	#106	C₂³×C₅₃	1	1	yes	characteristic
1349	#106	C₂³×C₅₃	1	1	yes	characteristic
1350	#106	C₂³×C₅₃	1	1	yes	characteristic
1351	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1353	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1354	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1355	#103	C₂³×C₅₃	1	1	yes	characteristic
1356	#103	C₂³×C₅₃	1	1	yes	characteristic
1357	#103	C₂³×C₅₃	1	1	yes	characteristic
1358	#103	C₂³×C₅₃	1	1	yes	characteristic
1359	#103	C₂³×C₅₃	1	1	yes	characteristic
1360	#103	C₂³×C₅₃	1	1	yes	characteristic
1361	#103	C₂³×C₅₃	1	1	yes	characteristic
1362	#103	C₂³×C₅₃	1	1	yes	characteristic
1363	#103	C₂³×C₅₃	1	1	yes	characteristic
1364	#103	C₂³×C₅₃	1	1	yes	characteristic
1365	#103	C₂³×C₅₃	1	1	yes	characteristic
1366	#103	C₂³×C₅₃	1	1	yes	characteristic
1367	#103	C₂³×C₅₃	1	1	yes	characteristic
1368	#103	C₂³×C₅₃	1	1	yes	characteristic
1369	#103	C₂³×C₅₃	1	1	yes	characteristic
1370	#103	C₂³×C₅₃	1	1	yes	characteristic
1371	#103	C₂³×C₅₃	1	1	yes	characteristic
1372	#103	C₂³×C₅₃	1	1	yes	characteristic
1373	#103	C₂³×C₅₃	1	1	yes	characteristic
1374	#103	C₂³×C₅₃	1	1	yes	characteristic
1375	#102	C₂³×C₅₃	1	1	yes	characteristic
1376	#102	C₂³×C₅₃	1	1	yes	characteristic
1377	#102	C₂³×C₅₃	1	1	yes	characteristic
1378	#102	C₂³×C₅₃	1	1	yes	characteristic
1379	#102	C₂³×C₅₃	1	1	yes	characteristic
1380	#102	C₂³×C₅₃	1	1	yes	characteristic
1381	#102	C₂³×C₅₃	1	1	yes	characteristic
1382	#102	C₂³×C₅₃	1	1	yes	characteristic
1383	#102	C₂³×C₅₃	1	1	yes	characteristic
1384	#102	C₂³×C₅₃	1	1	yes	characteristic
1385	#102	C₂³×C₅₃	1	1	yes	characteristic
1386	#102	C₂³×C₅₃	1	1	yes	characteristic
1387	#102	C₂³×C₅₃	1	1	yes	characteristic
1388	#102	C₂³×C₅₃	1	1	yes	characteristic
1389	#102	C₂³×C₅₃	1	1	yes	characteristic
1390	#102	C₂³×C₅₃	1	1	yes	characteristic
1391	#102	C₂³×C₅₃	1	1	yes	characteristic
1392	#102	C₂³×C₅₃	1	1	yes	characteristic
1393	#102	C₂³×C₅₃	1	1	yes	characteristic
1394	#102	C₂³×C₅₃	1	1	yes	characteristic
1395	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1396	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1397	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1398	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1399	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1400	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1401	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1402	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1403	#97	C₂³×C₅₃	1	1	yes	characteristic
1404	#97	C₂³×C₅₃	1	1	yes	characteristic
1405	#97	C₂³×C₅₃	1	1	yes	characteristic
1406	#97	C₂³×C₅₃	1	1	yes	characteristic
1407	C₂⁴	—	2	1	no	—
1408	C₂⁴	—	2	1	no	—
1409	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1410	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1411	#41	—	2	2	no	—
1412	#41	—	2	2	no	—
1413	#41	—	2	2	no	—
1414	#41	—	2	2	no	—
1415	#41	—	2	2	no	—
1416	#41	—	2	2	no	—
1417	#41	—	2	2	no	—
1418	#41	—	2	2	no	—
1419	#41	—	2	2	no	—
1420	#41	—	2	2	no	—
1421	#41	—	2	2	no	—
1422	#41	—	4	4	no	—
1423	#41	—	4	4	no	—
1424	#41	—	4	1	no	—
1425	#41	—	4	1	no	—
1426	#41	—	4	1	no	—
1427	#41	—	4	1	no	—
1428	#41	—	4	4	no	—
1429	#41	—	4	4	no	—
1430	#41	—	4	4	no	—
1431	#41	#41×C₅₃	1	4	yes	complemented
1432	C₂×Q₈	—	2	1	no	—
1433	C₂×Q₈	—	2	1	no	—
1434	C₂×Q₈	—	2	1	no	—
1435	C₂×Q₈	—	2	1	no	—
1436	C₂×Q₈	—	2	2	no	—
1437	C₂×Q₈	—	2	2	no	—
1438	C₂×Q₈	—	4	1	no	—
1439	C₂×Q₈	—	4	1	no	—
1440	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1441	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1442	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1443	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1444	C₂×D₄	—	2	1	no	—
1445	C₂×D₄	—	2	2	no	—
1446	C₂×D₄	—	2	2	no	—
1447	C₂×D₄	—	2	1	no	—
1448	C₂×D₄	—	2	1	no	—
1449	C₂×D₄	—	2	1	no	—
1450	C₂×D₄	—	2	1	no	—
1451	C₂×D₄	—	2	1	no	—
1452	C₂×D₄	—	2	1	no	—
1453	C₂×D₄	—	2	1	no	—
1454	C₂×D₄	—	2	1	no	—
1455	C₂×D₄	—	2	1	no	—
1456	C₂×D₄	—	2	1	no	—
1457	C₂×D₄	—	2	1	no	—
1458	C₂×D₄	—	2	1	no	—
1459	C₂×D₄	—	2	1	no	—
1460	C₂×D₄	—	2	1	no	—
1461	C₂×D₄	—	2	1	no	—
1462	C₂×D₄	—	2	1	no	—
1463	C₂×D₄	—	2	1	no	—
1464	C₂×D₄	—	2	1	no	—
1465	C₂×D₄	—	2	1	no	—
1466	C₂×D₄	—	4	1	no	—
1467	C₂×D₄	—	4	1	no	—
1468	C₂×D₄	—	4	2	no	—
1469	C₂×D₄	—	4	4	no	—
1470	C₂×D₄	—	4	4	no	—
1471	C₂×D₄	—	4	4	no	—
1472	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1475	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1476	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1477	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1478	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1480	C₂²×C₄	—	2	1	no	—
1481	C₂²×C₄	—	2	2	no	—
1482	C₂²×C₄	—	2	2	no	—
1483	C₂²×C₄	—	2	2	no	—
1484	C₂²×C₄	—	2	2	no	—
1485	C₂²×C₄	—	2	1	no	—
1486	C₂²×C₄	—	2	1	no	—
1487	C₂²×C₄	—	2	1	no	—
1488	C₂²×C₄	—	2	1	no	—
1489	C₂²×C₄	—	2	1	no	—
1490	C₂²×C₄	—	2	1	no	—
1491	C₂²×C₄	—	2	1	no	—
1492	C₂²×C₄	—	2	1	no	—
1493	C₂²×C₄	—	2	1	no	—
1494	C₂²×C₄	—	2	1	no	—
1495	C₂²×C₄	—	2	1	no	—
1496	C₂²×C₄	—	2	1	no	—
1497	C₂²×C₄	—	2	1	no	—
1498	C₂²×C₄	—	2	1	no	—
1499	C₂²×C₄	—	2	1	no	—
1500	C₂²×C₄	—	2	1	no	—
1501	C₂²×C₄	—	2	1	no	—
1502	C₂²×C₄	—	4	4	no	—
1503	C₂²×C₄	—	4	4	no	—
1504	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1505	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1506	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1507	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1508	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1509	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1510	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1511	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1512	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1513	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1514	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1515	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1516	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1517	Q₁₆	—	2	2	no	—
1518	Q₁₆	—	4	1	no	—
1519	Q₁₆	—	4	1	no	—
1520	SD₁₆	—	2	2	no	—
1521	SD₁₆	—	2	2	no	—
1522	SD₁₆	—	4	1	no	—
1523	SD₁₆	—	4	1	no	—
1524	SD₁₆	—	4	1	no	—
1525	SD₁₆	—	4	1	no	—
1526	D₈	—	2	2	no	—
1527	D₈	—	4	1	no	—
1528	D₈	—	4	1	no	—
1529	M₁₆	—	4	1	no	—
1530	M₁₆	—	4	1	no	—
1531	M₁₆	—	4	1	no	—
1532	M₁₆	—	4	1	no	—
1533	C₂×C₈	—	2	2	no	—
1534	C₂×C₈	—	2	2	no	—
1535	C₂×C₈	—	2	2	no	—
1536	C₂×C₈	—	2	2	no	—
1537	C₂×C₈	—	4	1	no	—
1538	C₂×C₈	—	4	1	no	—
1539	C₂×C₈	—	4	1	no	—
1540	C₂×C₈	—	4	1	no	—
1541	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1542	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1543	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1544	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1545	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1546	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1547	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1548	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1549	C₄⋊C₄	—	2	1	no	—
1550	C₄⋊C₄	—	2	1	no	—
1551	C₄⋊C₄	—	2	1	no	—
1552	C₄⋊C₄	—	2	1	no	—
1553	C₄⋊C₄	—	2	1	no	—
1554	C₄⋊C₄	—	2	1	no	—
1555	C₄⋊C₄	—	2	1	no	—
1556	C₄⋊C₄	—	2	1	no	—
1557	C₄⋊C₄	—	2	1	no	—
1558	C₄⋊C₄	—	2	1	no	—
1559	C₄⋊C₄	—	2	1	no	—
1560	C₄⋊C₄	—	2	1	no	—
1561	C₄⋊C₄	—	2	1	no	—
1562	C₄⋊C₄	—	2	1	no	—
1563	C₄⋊C₄	—	2	1	no	—
1564	C₄⋊C₄	—	2	1	no	—
1565	C₄⋊C₄	—	2	1	no	—
1566	C₄⋊C₄	—	2	1	no	—
1567	C₄⋊C₄	—	2	1	no	—
1568	C₄⋊C₄	—	2	1	no	—
1569	C₄⋊C₄	—	2	1	no	—
1570	C₄⋊C₄	—	2	1	no	—
1571	C₄⋊C₄	—	2	1	no	—
1572	C₄⋊C₄	—	2	1	no	—
1573	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1574	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1575	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1576	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1577	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1578	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1579	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1580	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1581	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1582	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1583	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1584	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1585	C₂²⋊C₄	—	2	1	no	—
1586	C₂²⋊C₄	—	2	1	no	—
1587	C₂²⋊C₄	—	2	1	no	—
1588	C₂²⋊C₄	—	2	1	no	—
1589	C₂²⋊C₄	—	2	1	no	—
1590	C₂²⋊C₄	—	2	1	no	—
1591	C₂²⋊C₄	—	2	1	no	—
1592	C₂²⋊C₄	—	2	1	no	—
1593	C₂²⋊C₄	—	2	1	no	—
1594	C₂²⋊C₄	—	2	1	no	—
1595	C₂²⋊C₄	—	2	1	no	—
1596	C₂²⋊C₄	—	2	1	no	—
1597	C₂²⋊C₄	—	2	1	no	—
1598	C₂²⋊C₄	—	2	1	no	—
1599	C₂²⋊C₄	—	2	1	no	—
1600	C₂²⋊C₄	—	2	1	no	—
1601	C₂²⋊C₄	—	2	1	no	—
1602	C₂²⋊C₄	—	2	1	no	—
1603	C₂²⋊C₄	—	2	1	no	—
1604	C₂²⋊C₄	—	2	1	no	—
1605	C₂²⋊C₄	—	2	1	no	—
1606	C₂²⋊C₄	—	2	1	no	—
1607	C₂²⋊C₄	—	2	1	no	—
1608	C₂²⋊C₄	—	2	1	no	—
1609	C₂²⋊C₄	—	2	1	no	—
1610	C₂²⋊C₄	—	2	1	no	—
1611	C₂²⋊C₄	—	2	1	no	—
1612	C₂²⋊C₄	—	2	1	no	—
1613	C₂²⋊C₄	—	2	1	no	—
1614	C₂²⋊C₄	—	2	1	no	—
1615	C₂²⋊C₄	—	2	1	no	—
1616	C₂²⋊C₄	—	2	1	no	—
1617	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1618	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1619	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1620	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1621	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1622	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1623	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1624	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1625	C₄²	—	2	1	no	—
1626	C₄²	—	2	1	no	—
1627	C₄²	—	2	1	no	—
1628	C₄²	—	2	1	no	—
1629	C₄²	—	2	1	no	—
1630	C₄²	—	2	1	no	—
1631	C₄²	—	2	1	no	—
1632	C₄²	—	2	1	no	—
1633	C₄²	—	2	1	no	—
1634	C₄²	—	2	1	no	—
1635	C₄²	—	2	1	no	—
1636	C₄²	—	2	1	no	—
1637	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1638	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1639	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1640	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1641	C₂³	—	2	2	no	—
1642	C₂³	—	2	2	no	—
1643	C₂³	—	2	1	no	—
1644	C₂³	—	2	2	no	—
1645	C₂³	—	2	1	no	—
1646	C₂³	—	2	1	no	—
1647	C₂³	—	2	1	no	—
1648	C₂³	—	4	1	no	—
1649	C₂³	—	4	1	no	—
1650	C₂³	—	4	1	no	—
1651	C₂³	—	4	2	no	—
1652	C₂³	—	4	2	no	—
1653	C₂³	—	4	2	no	—
1654	C₂³	—	4	2	no	—
1655	C₂³	—	8	1	no	—
1656	C₂³	—	8	1	no	—
1657	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1658	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1659	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1660	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1661	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1662	Q₈	—	2	1	no	—
1663	Q₈	—	2	1	no	—
1664	Q₈	—	2	1	no	—
1665	Q₈	—	2	1	no	—
1666	Q₈	—	2	1	no	—
1667	Q₈	—	2	1	no	—
1668	Q₈	—	2	1	no	—
1669	Q₈	—	4	2	no	—
1670	Q₈	—	4	2	no	—
1671	Q₈	—	4	2	no	—
1672	Q₈	—	8	1	no	—
1673	Q₈	C₂×#41×C₅₃	1	2	yes	—
1674	D₄	—	2	4	no	—
1675	D₄	—	2	2	no	—
1676	D₄	—	2	2	no	—
1677	D₄	—	2	1	no	—
1678	D₄	—	2	1	no	—
1679	D₄	—	2	1	no	—
1680	D₄	—	2	1	no	—
1681	D₄	—	2	1	no	—
1682	D₄	—	2	1	no	—
1683	D₄	—	2	1	no	—
1684	D₄	—	4	1	no	—
1685	D₄	—	4	1	no	—
1686	D₄	—	4	2	no	—
1687	D₄	—	4	2	no	—
1688	D₄	—	4	2	no	—
1689	D₄	—	4	2	no	—
1690	D₄	—	4	2	no	—
1691	D₄	—	4	2	no	—
1692	D₄	—	4	2	no	—
1693	D₄	—	4	2	no	—
1694	D₄	—	4	2	no	—
1695	D₄	—	4	2	no	—
1696	D₄	—	4	2	no	—
1697	D₄	—	4	2	no	—
1698	D₄	—	4	2	no	—
1699	D₄	—	4	2	no	—
1700	D₄	—	8	1	no	—
1701	D₄	—	8	1	no	—
1702	D₄	—	8	1	no	—
1703	D₄	—	8	1	no	—
1704	D₄	—	8	1	no	—
1705	D₄	C₂×#41×C₅₃	1	2	yes	—
1706	C₂×C₄	—	2	2	no	—
1707	C₂×C₄	—	2	2	no	—
1708	C₂×C₄	—	2	1	no	—
1709	C₂×C₄	—	2	2	no	—
1710	C₂×C₄	—	2	2	no	—
1711	C₂×C₄	—	2	2	no	—
1712	C₂×C₄	—	2	2	no	—
1713	C₂×C₄	—	2	4	no	—
1714	C₂×C₄	—	2	1	no	—
1715	C₂×C₄	—	2	1	no	—
1716	C₂×C₄	—	2	1	no	—
1717	C₂×C₄	—	2	1	no	—
1718	C₂×C₄	—	2	1	no	—
1719	C₂×C₄	—	2	1	no	—
1720	C₂×C₄	—	2	1	no	—
1721	C₂×C₄	—	2	1	no	—
1722	C₂×C₄	—	2	1	no	—
1723	C₂×C₄	—	2	1	no	—
1724	C₂×C₄	—	2	1	no	—
1725	C₂×C₄	—	2	1	no	—
1726	C₂×C₄	—	2	1	no	—
1727	C₂×C₄	—	2	1	no	—
1728	C₂×C₄	—	2	1	no	—
1729	C₂×C₄	—	2	1	no	—
1730	C₂×C₄	—	2	1	no	—
1731	C₂×C₄	—	2	1	no	—
1732	C₂×C₄	—	2	1	no	—
1733	C₂×C₄	—	4	1	no	—
1734	C₂×C₄	—	4	1	no	—
1735	C₂×C₄	—	4	2	no	—
1736	C₂×C₄	—	4	2	no	—
1737	C₂×C₄	—	4	2	no	—
1738	C₂×C₄	—	4	2	no	—
1739	C₂×C₄	—	4	2	no	—
1740	C₂×C₄	—	4	2	no	—
1741	C₂×C₄	—	4	2	no	—
1742	C₂×C₄	—	4	2	no	—
1743	C₂×C₄	—	4	2	no	—
1744	C₂×C₄	—	4	2	no	—
1745	C₂×C₄	—	4	2	no	—
1746	C₂×C₄	—	4	2	no	—
1747	C₂×C₄	—	4	2	no	—
1748	C₂×C₄	—	8	1	no	—
1749	C₂×C₄	—	8	1	no	—
1750	C₂×C₄	—	8	1	no	—
1751	C₂×C₄	—	8	1	no	—
1752	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1753	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1754	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1755	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1756	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1757	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1758	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1759	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1760	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1761	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1762	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1763	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1764	C₈	—	2	1	no	—
1765	C₈	—	2	1	no	—
1766	C₈	—	2	1	no	—
1767	C₈	—	2	1	no	—
1768	C₈	—	2	1	no	—
1769	C₈	—	2	1	no	—
1770	C₈	—	2	1	no	—
1771	C₈	—	2	1	no	—
1772	C₂²	—	2	1	no	—
1773	C₂²	—	2	1	no	—
1774	C₂²	—	2	1	no	—
1775	C₂²	—	2	1	no	—
1776	C₂²	—	2	1	no	—
1777	C₂²	—	2	1	no	—
1778	C₂²	—	2	1	no	—
1779	C₂²	—	2	2	no	—
1780	C₂²	—	2	1	no	—
1781	C₂²	—	2	1	no	—
1782	C₂²	—	2	1	no	—
1783	C₂²	—	2	1	no	—
1784	C₂²	—	2	1	no	—
1785	C₂²	—	2	1	no	—
1786	C₂²	—	4	4	no	—
1787	C₂²	—	4	1	no	—
1788	C₂²	—	4	1	no	—
1789	C₂²	—	4	1	no	—
1790	C₂²	—	4	1	no	—
1791	C₂²	—	4	1	no	—
1792	C₂²	—	4	1	no	—
1793	C₂²	—	4	1	no	—
1794	C₂²	—	4	1	no	—
1795	C₂²	—	4	1	no	—
1796	C₂²	—	4	1	no	—
1797	C₂²	—	4	1	no	—
1798	C₂²	—	8	2	no	—
1799	C₂²	—	8	4	no	—
1800	C₂²	—	8	4	no	—
1801	C₂²	C₅₃×#546	1	2	yes	—
1802	C₂²	C₅₃×#575	1	2	yes	—
1803	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1804	C₄	—	2	1	no	—
1805	C₄	—	2	1	no	—
1806	C₄	—	2	1	no	—
1807	C₄	—	2	1	no	—
1808	C₄	—	2	2	no	—
1809	C₄	—	2	1	no	—
1810	C₄	—	2	1	no	—
1811	C₄	—	2	1	no	—
1812	C₄	—	2	1	no	—
1813	C₄	—	4	1	no	—
1814	C₄	—	4	1	no	—
1815	C₄	—	4	1	no	—
1816	C₄	—	4	1	no	—
1817	C₄	—	4	1	no	—
1818	C₄	—	4	1	no	—
1819	C₄	—	4	1	no	—
1820	C₄	—	4	1	no	—
1821	C₄	—	4	1	no	—
1822	C₄	—	4	1	no	—
1823	C₄	—	4	1	no	—
1824	C₄	C₅₃×#546	1	2	yes	—
1825	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1826	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1827	C₂	—	2	2	no	—
1828	C₂	—	2	2	no	—
1829	C₂	—	4	1	no	—
1830	C₂	—	4	1	no	—
1831	C₂	—	4	1	no	—
1832	C₂	—	4	2	no	—
1833	C₂	—	8	1	no	—
1834	C₂	—	8	1	no	—
1835	C₂	—	8	1	no	—
1836	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1837	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1838	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3475	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3321	C₂	semidirect
4. C₅₃×#3320	C₂	semidirect
5. C₅₃×#3319	C₂	semidirect
6. C₅₃×#3318	C₂	semidirect
7. C₅₃×#3317	C₂	semidirect
8. C₅₃×#3316	C₂	semidirect
9. C₅₃×#3315	C₂	semidirect
10. C₅₃×#3314	C₂	semidirect
11. C₅₃×#3313	C₂	semidirect
12. C₅₃×#3312	C₂	semidirect
13. C₅₃×#3311	C₂	semidirect
14. C₅₃×#3310	C₂	semidirect
15. C₅₃×#3309	C₂	semidirect
16. C₅₃×#3308	C₂	semidirect
17. C₅₃×#3307	C₂	semidirect
18. C₅₃×#3306	C₂	semidirect
19. C₅₃×#3135	C₂	semidirect
20. C₅₃×#3091	C₂	semidirect
21. C₅₃×#3091	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#3054	C₂	semidirect
24. C₅₃×#3050	C₂	semidirect
25. C₅₃×#3035	C₂	semidirect
26. C₅₃×#3002	C₂	semidirect
27. C₅₃×#3002	C₂	semidirect
28. C₅₃×#2943	C₂	semidirect
29. C₂×C₅₃×#435	C₂	semidirect
30. C₅₃×#2896	C₂	semidirect
31. C₂×C₅₃×#416	C₂	semidirect
35. C₂×#135×C₅₃	C₂²	semidirect
36. C₂×#135×C₅₃	C₂²	semidirect
37. C₂²×M₁₆×C₅₃	C₂²	semidirect
38. C₂³×C₈×C₅₃	C₂²	semidirect
39. C₅₃×#556	C₂²	semidirect
40. C₅₃×#555	C₂²	semidirect
41. C₅₃×#554	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
46. C₅₃×#552	C₂²	semidirect
55. C₅₃×#547	C₂²	semidirect
63. C₅₃×#533	C₂²	semidirect
73. C₅₃×#525	C₂²	semidirect
74. C₅₃×#525	C₂²	semidirect
77. C₄×#41×C₅₃	C₂²	semidirect
80. C₂×#117×C₅₃	C₂²	semidirect
81. C₂×#117×C₅₃	C₂²	semidirect
82. C₅₃×#491	C₂²	semidirect
83. C₅₃×#491	C₂²	semidirect
84. C₅₃×#490	C₂²	semidirect
85. C₅₃×#490	C₂²	semidirect
86. C₅₃×#489	C₂²	semidirect
87. C₅₃×#489	C₂²	semidirect
88. C₅₃×#489	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#485	C₂²	semidirect
91. C₅₃×#485	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#484	C₂²	semidirect
95. C₅₃×#484	C₂²	semidirect
96. C₅₃×#483	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#481	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#480	C₂²	semidirect
105. C₅₃×#480	C₂²	semidirect
106. C₅₃×#479	C₂²	semidirect
107. C₅₃×#479	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#478	C₂²	semidirect
110. C₅₃×#477	C₂²	semidirect
111. C₅₃×#476	C₂²	semidirect
112. C₅₃×#475	C₂²	semidirect
113. C₅₃×#474	C₂²	semidirect
114. C₅₃×#470	C₂²	semidirect
115. C₅₃×#470	C₂²	semidirect
116. C₅₃×#469	C₂²	semidirect
117. C₅₃×#469	C₂²	semidirect
118. C₅₃×#468	C₂²	semidirect
119. C₅₃×#468	C₂²	semidirect
120. C₅₃×#468	C₂²	semidirect
121. C₅₃×#468	C₂²	semidirect
122. C₅₃×#467	C₂²	semidirect
123. C₅₃×#467	C₂²	semidirect
124. C₅₃×#466	C₂²	semidirect
125. C₅₃×#466	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
128. C₅₃×#465	C₂²	semidirect
129. C₅₃×#465	C₂²	semidirect
130. C₅₃×#464	C₂²	semidirect
131. C₅₃×#464	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#462	C₂²	semidirect
135. C₅₃×#461	C₂²	semidirect
136. C₅₃×#460	C₂²	semidirect
137. C₅₃×#459	C₂²	semidirect
138. C₅₃×#452	C₂²	semidirect
139. C₅₃×#452	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#451	C₂²	semidirect
143. C₅₃×#451	C₂²	semidirect
144. C₅₃×#450	C₂²	semidirect
145. C₅₃×#450	C₂²	semidirect
146. C₅₃×#449	C₂²	semidirect
147. C₅₃×#449	C₂²	semidirect
148. C₅₃×#449	C₂²	semidirect
149. C₅₃×#449	C₂²	semidirect
150. C₅₃×#448	C₂²	semidirect
151. C₅₃×#448	C₂²	semidirect
152. C₅₃×#447	C₂²	semidirect
153. C₅₃×#447	C₂²	semidirect
154. C₅₃×#442	C₂²	semidirect
155. C₅₃×#442	C₂²	semidirect
156. C₅₃×#441	C₂²	semidirect
157. C₅₃×#441	C₂²	semidirect
158. C₅₃×#440	C₂²	semidirect
159. C₅₃×#440	C₂²	semidirect
160. C₅₃×#440	C₂²	semidirect
161. C₅₃×#440	C₂²	semidirect
164. C₅₃×#435	C₂²	semidirect
165. C₅₃×#435	C₂²	semidirect
166. C₅₃×#435	C₂²	semidirect
167. C₅₃×#435	C₂²	semidirect
168. C₅₃×#435	C₂²	semidirect
169. C₅₃×#435	C₂²	semidirect
170. C₅₃×#427	C₂²	semidirect
171. C₅₃×#427	C₂²	semidirect
172. C₅₃×#427	C₂²	semidirect
173. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
174. C₅₃×#419	C₂²	semidirect
175. C₅₃×#419	C₂²	semidirect
176. C₅₃×#418	C₂²	semidirect
177. C₅₃×#418	C₂²	semidirect
178. C₅₃×#417	C₂²	semidirect
179. C₅₃×#417	C₂²	semidirect
180. C₅₃×#417	C₂²	semidirect
181. C₅₃×#417	C₂²	semidirect
185. C₅₃×#416	C₂²	semidirect
186. C₅₃×#416	C₂²	semidirect
187. C₅₃×#416	C₂²	semidirect
188. C₅₃×#416	C₂²	semidirect
189. C₅₃×#416	C₂²	semidirect
190. C₅₃×#416	C₂²	semidirect
191. C₅₃×#416	C₂²	semidirect
192. C₅₃×#416	C₂²	semidirect
193. C₅₃×#416	C₂²	semidirect
194. C₅₃×#416	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
196. C₂×#103×C₅₃	C₂²	semidirect
197. C₂×#103×C₅₃	C₂²	semidirect
198. C₂×#102×C₅₃	C₂²	semidirect
199. C₂×#102×C₅₃	C₂²	semidirect
200. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
201. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
202. C₂×#97×C₅₃	C₂²	semidirect
511. #41×C₅₃	#41	semidirect
852. #61141	C₅₃	direct (N × H)
908. #3475	C₂×C₅₃	semidirect
909. D₄×#41	C₂×C₅₃	semidirect
910. #3321	C₂×C₅₃	semidirect
911. #3320	C₂×C₅₃	semidirect
912. #3319	C₂×C₅₃	semidirect
913. #3318	C₂×C₅₃	semidirect
914. #3317	C₂×C₅₃	semidirect
915. #3316	C₂×C₅₃	semidirect
916. #3315	C₂×C₅₃	semidirect
917. #3314	C₂×C₅₃	semidirect
918. #3313	C₂×C₅₃	semidirect
919. #3312	C₂×C₅₃	semidirect
920. #3311	C₂×C₅₃	semidirect
921. #3310	C₂×C₅₃	semidirect
922. #3309	C₂×C₅₃	semidirect
923. #3308	C₂×C₅₃	semidirect
924. #3307	C₂×C₅₃	semidirect
925. #3306	C₂×C₅₃	semidirect
926. #3135	C₂×C₅₃	semidirect
927. #3091	C₂×C₅₃	semidirect
928. #3091	C₂×C₅₃	semidirect
929. #3076	C₂×C₅₃	semidirect
930. #3054	C₂×C₅₃	semidirect
931. #3050	C₂×C₅₃	semidirect
932. #3035	C₂×C₅₃	semidirect
933. #3002	C₂×C₅₃	semidirect
934. #3002	C₂×C₅₃	semidirect
935. #2943	C₂×C₅₃	semidirect
936. C₂×#435	C₂×C₅₃	semidirect
937. #2896	C₂×C₅₃	semidirect
938. C₂×#416	C₂×C₅₃	semidirect
954. C₂×#135	C₂²×C₅₃	semidirect
955. C₂×#135	C₂²×C₅₃	semidirect
956. C₂²×M₁₆	C₂²×C₅₃	semidirect
957. C₂³×C₈	C₂²×C₅₃	semidirect
958. #556	C₂²×C₅₃	semidirect
959. #555	C₂²×C₅₃	semidirect
960. #554	C₂²×C₅₃	semidirect
962. #553	C₂²×C₅₃	semidirect
965. #552	C₂²×C₅₃	semidirect
974. #547	C₂²×C₅₃	semidirect
982. #533	C₂²×C₅₃	semidirect
992. #525	C₂²×C₅₃	semidirect
993. #525	C₂²×C₅₃	semidirect
996. C₄×#41	C₂²×C₅₃	semidirect
999. C₂×#117	C₂²×C₅₃	semidirect
1000. C₂×#117	C₂²×C₅₃	semidirect
1001. #491	C₂²×C₅₃	semidirect
1002. #491	C₂²×C₅₃	semidirect
1003. #490	C₂²×C₅₃	semidirect
1004. #490	C₂²×C₅₃	semidirect
1005. #489	C₂²×C₅₃	semidirect
1006. #489	C₂²×C₅₃	semidirect
1007. #489	C₂²×C₅₃	semidirect
1008. #489	C₂²×C₅₃	semidirect
1009. #485	C₂²×C₅₃	semidirect
1010. #485	C₂²×C₅₃	semidirect
1011. #485	C₂²×C₅₃	semidirect
1012. #485	C₂²×C₅₃	semidirect
1013. #484	C₂²×C₅₃	semidirect
1014. #484	C₂²×C₅₃	semidirect
1015. #483	C₂²×C₅₃	semidirect
1016. #483	C₂²×C₅₃	semidirect
1017. #482	C₂²×C₅₃	semidirect
1018. #482	C₂²×C₅₃	semidirect
1019. #482	C₂²×C₅₃	semidirect
1020. #482	C₂²×C₅₃	semidirect
1021. #481	C₂²×C₅₃	semidirect
1022. #481	C₂²×C₅₃	semidirect
1023. #480	C₂²×C₅₃	semidirect
1024. #480	C₂²×C₅₃	semidirect
1025. #479	C₂²×C₅₃	semidirect
1026. #479	C₂²×C₅₃	semidirect
1027. #478	C₂²×C₅₃	semidirect
1028. #478	C₂²×C₅₃	semidirect
1029. #477	C₂²×C₅₃	semidirect
1030. #476	C₂²×C₅₃	semidirect
1031. #475	C₂²×C₅₃	semidirect
1032. #474	C₂²×C₅₃	semidirect
1033. #470	C₂²×C₅₃	semidirect
1034. #470	C₂²×C₅₃	semidirect
1035. #469	C₂²×C₅₃	semidirect
1036. #469	C₂²×C₅₃	semidirect
1037. #468	C₂²×C₅₃	semidirect
1038. #468	C₂²×C₅₃	semidirect
1039. #468	C₂²×C₅₃	semidirect
1040. #468	C₂²×C₅₃	semidirect
1041. #467	C₂²×C₅₃	semidirect
1042. #467	C₂²×C₅₃	semidirect
1043. #466	C₂²×C₅₃	semidirect
1044. #466	C₂²×C₅₃	semidirect
1045. #465	C₂²×C₅₃	semidirect
1046. #465	C₂²×C₅₃	semidirect
1047. #465	C₂²×C₅₃	semidirect
1048. #465	C₂²×C₅₃	semidirect
1049. #464	C₂²×C₅₃	semidirect
1050. #464	C₂²×C₅₃	semidirect
1051. #463	C₂²×C₅₃	semidirect
1052. #463	C₂²×C₅₃	semidirect
1053. #462	C₂²×C₅₃	semidirect
1054. #461	C₂²×C₅₃	semidirect
1055. #460	C₂²×C₅₃	semidirect
1056. #459	C₂²×C₅₃	semidirect
1057. #452	C₂²×C₅₃	semidirect
1058. #452	C₂²×C₅₃	semidirect
1059. #452	C₂²×C₅₃	semidirect
1060. #452	C₂²×C₅₃	semidirect
1061. #451	C₂²×C₅₃	semidirect
1062. #451	C₂²×C₅₃	semidirect
1063. #450	C₂²×C₅₃	semidirect
1064. #450	C₂²×C₅₃	semidirect
1065. #449	C₂²×C₅₃	semidirect
1066. #449	C₂²×C₅₃	semidirect
1067. #449	C₂²×C₅₃	semidirect
1068. #449	C₂²×C₅₃	semidirect
1069. #448	C₂²×C₅₃	semidirect
1070. #448	C₂²×C₅₃	semidirect
1071. #447	C₂²×C₅₃	semidirect
1072. #447	C₂²×C₅₃	semidirect
1073. #442	C₂²×C₅₃	semidirect
1074. #442	C₂²×C₅₃	semidirect
1075. #441	C₂²×C₅₃	semidirect
1076. #441	C₂²×C₅₃	semidirect
1077. #440	C₂²×C₅₃	semidirect
1078. #440	C₂²×C₅₃	semidirect
1079. #440	C₂²×C₅₃	semidirect
1080. #440	C₂²×C₅₃	semidirect
1083. #435	C₂²×C₅₃	semidirect
1084. #435	C₂²×C₅₃	semidirect
1085. #435	C₂²×C₅₃	semidirect
1086. #435	C₂²×C₅₃	semidirect
1087. #435	C₂²×C₅₃	semidirect
1088. #435	C₂²×C₅₃	semidirect
1089. #427	C₂²×C₅₃	semidirect
1090. #427	C₂²×C₅₃	semidirect
1091. #427	C₂²×C₅₃	semidirect
1092. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1093. #419	C₂²×C₅₃	semidirect
1094. #419	C₂²×C₅₃	semidirect
1095. #418	C₂²×C₅₃	semidirect
1096. #418	C₂²×C₅₃	semidirect
1097. #417	C₂²×C₅₃	semidirect
1098. #417	C₂²×C₅₃	semidirect
1099. #417	C₂²×C₅₃	semidirect
1100. #417	C₂²×C₅₃	semidirect
1104. #416	C₂²×C₅₃	semidirect
1105. #416	C₂²×C₅₃	semidirect
1106. #416	C₂²×C₅₃	semidirect
1107. #416	C₂²×C₅₃	semidirect
1108. #416	C₂²×C₅₃	semidirect
1109. #416	C₂²×C₅₃	semidirect
1110. #416	C₂²×C₅₃	semidirect
1111. #416	C₂²×C₅₃	semidirect
1112. #416	C₂²×C₅₃	semidirect
1113. #416	C₂²×C₅₃	semidirect
1114. #416	C₂²×C₅₃	semidirect
1115. C₂×#103	C₂²×C₅₃	semidirect
1116. C₂×#103	C₂²×C₅₃	semidirect
1117. C₂×#102	C₂²×C₅₃	semidirect
1118. C₂×#102	C₂²×C₅₃	semidirect
1119. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1120. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1121. C₂×#97	C₂²×C₅₃	semidirect
1122. C₅₃	#61141	direct (N × H)
1431. #41	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3475	2
D₄×#41×C₅₃	2
C₅₃×#3321	2
C₅₃×#3320	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3317	2
C₅₃×#3316	2
C₅₃×#3315	2
C₅₃×#3314	2
C₅₃×#3313	2
C₅₃×#3312	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3309	2
C₅₃×#3308	2
C₅₃×#3307	2
C₅₃×#3306	2
C₅₃×#3135	2
C₅₃×#3091	2
C₅₃×#3076	2
C₅₃×#3054	2
C₅₃×#3050	2
C₅₃×#3035	2
C₅₃×#3002	2
C₅₃×#2943	2
C₂×C₅₃×#435	2
C₅₃×#2896	2
C₂×C₅₃×#416	2
#61141	53

Subgroups — C53×#61141 #27268653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61141 #27268653