Subgroups — C₅₃×#61972 #27269484

Order 13568.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3327	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3312	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3308	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3277	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3111	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#559	C₂²	1	1	yes	characteristic
39	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#556	—	2	1	no	—
41	C₅₃×#556	C₂²	1	1	yes	characteristic
42	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#555	—	2	1	no	—
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#552	—	2	1	no	—
46	C₅₃×#552	C₂²	1	1	yes	characteristic
47	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#548	C₂²	1	1	yes	characteristic
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic
55	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#547	—	2	1	no	—
57	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#538	—	2	1	no	—
64	C₅₃×#538	—	2	1	no	—
65	C₅₃×#533	—	2	1	no	—
66	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#532	C₂²	1	1	yes	characteristic
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#529	—	2	1	no	—
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₅₃×#529	C₂²	1	1	yes	characteristic
72	C₅₃×#529	C₂²	1	1	yes	characteristic
73	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
75	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#518	—	2	1	no	—
78	C₄×#41×C₅₃	—	2	1	no	—
79	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
80	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic
84	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic
87	C₅₃×#495	C₂²	1	1	yes	characteristic
88	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic
91	C₅₃×#489	C₂²	1	1	yes	characteristic
92	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#488	C₂²	1	1	yes	characteristic
94	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic
99	C₅₃×#481	C₂²	1	1	yes	characteristic
100	C₅₃×#480	C₂²	1	1	yes	characteristic
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#478	C₂²	1	1	yes	characteristic
107	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#469	C₂²	1	1	yes	characteristic
115	C₅₃×#468	C₂²	1	1	yes	characteristic
116	C₅₃×#468	C₂²	1	1	yes	characteristic
117	C₅₃×#468	C₂²	1	1	yes	characteristic
118	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#466	C₂²	1	1	yes	characteristic
121	C₅₃×#465	C₂²	1	1	yes	characteristic
122	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#464	C₂²	1	1	yes	characteristic
124	C₅₃×#464	C₂²	1	1	yes	characteristic
125	C₅₃×#464	C₂²	1	1	yes	characteristic
126	C₅₃×#464	C₂²	1	1	yes	characteristic
127	C₅₃×#464	C₂²	1	1	yes	characteristic
128	C₅₃×#464	C₂²	1	1	yes	characteristic
129	C₅₃×#464	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×#464	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#463	C₂²	1	1	yes	characteristic
141	C₅₃×#463	C₂²	1	1	yes	characteristic
142	C₅₃×#463	C₂²	1	1	yes	characteristic
143	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#460	C₂²	1	1	yes	characteristic
152	C₅₃×#460	C₂²	1	1	yes	characteristic
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#450	C₂²	1	1	yes	characteristic
162	C₅₃×#450	C₂²	1	1	yes	characteristic
163	C₅₃×#450	C₂²	1	1	yes	characteristic
164	C₅₃×#449	C₂²	1	1	yes	characteristic
165	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic
168	C₅₃×#448	C₂²	1	1	yes	characteristic
169	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic
171	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#440	C₂²	1	1	yes	characteristic
178	C₅₃×#440	C₂²	1	1	yes	characteristic
179	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#435	C₂²	1	1	yes	characteristic
188	C₅₃×#435	C₂²	1	1	yes	characteristic
189	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#418	C₂²	1	1	yes	characteristic
199	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
201	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	—	2	1	no	—
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	#137×C₅₃	—	4	2	no	—
216	#137×C₅₃	—	4	2	no	—
217	#137×C₅₃	—	4	2	no	—
218	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
219	C₂×Q₁₆×C₅₃	—	4	2	no	—
220	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	—	4	2	no	—
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×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×D₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	—	2	1	no	—
252	C₄⋊Q₈×C₅₃	—	2	1	no	—
253	C₄⋊Q₈×C₅₃	—	2	1	no	—
254	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	#127×C₅₃	C₂³	1	1	yes	characteristic
258	#126×C₅₃	—	2	1	no	—
259	#126×C₅₃	—	2	1	no	—
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#126×C₅₃	—	2	1	no	—
266	#126×C₅₃	—	2	1	no	—
267	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#125×C₅₃	—	2	1	no	—
270	#125×C₅₃	—	2	1	no	—
271	#125×C₅₃	—	2	1	no	—
272	#125×C₅₃	—	2	1	no	—
273	#125×C₅₃	—	2	1	no	—
274	#125×C₅₃	C₂³	1	1	yes	characteristic
275	#125×C₅₃	C₂³	1	1	yes	characteristic
276	#125×C₅₃	C₂³	1	1	yes	characteristic
277	#124×C₅₃	—	2	1	no	—
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	—	2	1	no	—
284	#124×C₅₃	—	2	1	no	—
285	#124×C₅₃	—	2	1	no	—
286	#124×C₅₃	C₂³	1	1	yes	characteristic
287	#124×C₅₃	C₂³	1	1	yes	characteristic
288	#124×C₅₃	C₂³	1	1	yes	characteristic
289	#124×C₅₃	C₂³	1	1	yes	characteristic
290	#124×C₅₃	C₂³	1	1	yes	characteristic
291	#124×C₅₃	C₂³	1	1	yes	characteristic
292	#124×C₅₃	C₂³	1	1	yes	characteristic
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
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	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	—	2	1	no	—
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	—	2	1	no	—
316	C₂²⋊Q₈×C₅₃	—	2	1	no	—
317	C₂²⋊Q₈×C₅₃	—	2	1	no	—
318	C₂²⋊Q₈×C₅₃	—	2	1	no	—
319	C₂²⋊Q₈×C₅₃	—	2	1	no	—
320	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
325	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	—	2	1	no	—
329	#121×C₅₃	—	2	1	no	—
330	#121×C₅₃	—	2	1	no	—
331	#121×C₅₃	—	2	1	no	—
332	#121×C₅₃	—	2	1	no	—
333	#121×C₅₃	—	2	1	no	—
334	#121×C₅₃	—	2	1	no	—
335	#121×C₅₃	—	2	1	no	—
336	#121×C₅₃	C₂³	1	1	yes	characteristic
337	#121×C₅₃	C₂³	1	1	yes	characteristic
338	#121×C₅₃	C₂³	1	1	yes	characteristic
339	#121×C₅₃	C₂³	1	1	yes	characteristic
340	#121×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
349	C₄×Q₈×C₅₃	—	2	1	no	—
350	C₄×Q₈×C₅₃	—	2	1	no	—
351	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
352	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
357	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
358	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
360	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
361	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
363	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
374	C₄×D₄×C₅₃	—	2	1	no	—
375	C₄×D₄×C₅₃	—	2	1	no	—
376	C₄×D₄×C₅₃	—	2	1	no	—
377	C₄×D₄×C₅₃	—	2	1	no	—
378	C₄×D₄×C₅₃	—	2	1	no	—
379	C₄×D₄×C₅₃	—	2	1	no	—
380	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
381	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
382	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
383	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
385	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
387	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
388	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
389	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
391	#117×C₅₃	—	2	1	no	—
392	#117×C₅₃	—	2	1	no	—
393	#117×C₅₃	—	2	1	no	—
394	#117×C₅₃	—	2	1	no	—
395	#117×C₅₃	—	2	1	no	—
396	#117×C₅₃	—	2	1	no	—
397	#117×C₅₃	—	2	1	no	—
398	#117×C₅₃	—	2	1	no	—
399	#117×C₅₃	—	2	1	no	—
400	#117×C₅₃	—	2	1	no	—
401	#117×C₅₃	—	2	1	no	—
402	#117×C₅₃	D₄	1	1	yes	characteristic
403	#117×C₅₃	D₄	1	1	yes	characteristic
404	#117×C₅₃	D₄	1	1	yes	characteristic
405	#117×C₅₃	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
409	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
410	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₄²×C₅₃	—	2	1	no	—
417	C₂×C₄²×C₅₃	—	2	1	no	—
418	C₂×C₄²×C₅₃	—	2	1	no	—
419	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
421	C₂×C₄²×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	#107×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	C₄⋊C₈×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	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×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	#103×C₅₃	C₂³	1	1	yes	characteristic
456	#103×C₅₃	C₂³	1	1	yes	characteristic
457	#103×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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×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	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	#97×C₅₃	C₂³	1	1	yes	characteristic
481	#97×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂⁴×C₅₃	—	2	1	no	—
485	C₂⁴×C₅₃	—	2	1	no	—
486	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	4	2	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	4	no	—
494	C₂×Q₈×C₅₃	—	2	1	no	—
495	C₂×Q₈×C₅₃	—	2	1	no	—
496	C₂×Q₈×C₅₃	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	2	2	no	—
500	C₂×Q₈×C₅₃	—	2	2	no	—
501	C₂×Q₈×C₅₃	—	4	1	no	—
502	C₂×Q₈×C₅₃	—	4	1	no	—
503	C₂×Q₈×C₅₃	—	4	1	no	—
504	C₂×Q₈×C₅₃	—	4	1	no	—
505	C₂×Q₈×C₅₃	—	4	1	no	—
506	C₂×Q₈×C₅₃	—	4	1	no	—
507	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
513	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	1	no	—
526	C₂×D₄×C₅₃	—	4	1	no	—
527	C₂×D₄×C₅₃	—	4	1	no	—
528	C₂×D₄×C₅₃	—	4	1	no	—
529	C₂×D₄×C₅₃	—	4	1	no	—
530	C₂×D₄×C₅₃	—	4	4	no	—
531	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	2	1	no	—
542	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	2	1	no	—
544	C₂²×C₄×C₅₃	—	2	1	no	—
545	C₂²×C₄×C₅₃	—	2	1	no	—
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
553	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
554	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	Q₁₆×C₅₃	—	2	2	no	—
562	Q₁₆×C₅₃	—	2	2	no	—
563	Q₁₆×C₅₃	—	2	2	no	—
564	Q₁₆×C₅₃	—	4	1	no	—
565	Q₁₆×C₅₃	—	4	1	no	—
566	Q₁₆×C₅₃	—	4	1	no	—
567	Q₁₆×C₅₃	—	4	1	no	—
568	Q₁₆×C₅₃	—	4	1	no	—
569	Q₁₆×C₅₃	—	4	1	no	—
570	SD₁₆×C₅₃	—	2	2	no	—
571	SD₁₆×C₅₃	—	2	2	no	—
572	SD₁₆×C₅₃	—	2	2	no	—
573	SD₁₆×C₅₃	—	4	1	no	—
574	SD₁₆×C₅₃	—	4	1	no	—
575	SD₁₆×C₅₃	—	4	1	no	—
576	SD₁₆×C₅₃	—	4	1	no	—
577	SD₁₆×C₅₃	—	4	1	no	—
578	SD₁₆×C₅₃	—	4	1	no	—
579	SD₁₆×C₅₃	—	4	1	no	—
580	SD₁₆×C₅₃	—	4	1	no	—
581	SD₁₆×C₅₃	—	4	1	no	—
582	D₈×C₅₃	—	4	1	no	—
583	D₈×C₅₃	—	4	1	no	—
584	D₈×C₅₃	—	4	1	no	—
585	M₁₆×C₅₃	—	4	1	no	—
586	M₁₆×C₅₃	—	4	1	no	—
587	M₁₆×C₅₃	—	4	1	no	—
588	M₁₆×C₅₃	—	4	1	no	—
589	C₂×C₈×C₅₃	—	4	1	no	—
590	C₂×C₈×C₅₃	—	4	1	no	—
591	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₄⋊C₄×C₅₃	—	2	1	no	—
600	C₄⋊C₄×C₅₃	—	2	1	no	—
601	C₄⋊C₄×C₅₃	—	2	1	no	—
602	C₄⋊C₄×C₅₃	—	2	1	no	—
603	C₄⋊C₄×C₅₃	—	2	1	no	—
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	—	2	1	no	—
628	C₄⋊C₄×C₅₃	—	2	1	no	—
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₅₃	—	2	1	no	—
685	C₄²×C₅₃	—	2	1	no	—
686	C₄²×C₅₃	—	2	1	no	—
687	C₄²×C₅₃	—	2	1	no	—
688	C₄²×C₅₃	—	2	1	no	—
689	C₄²×C₅₃	—	2	1	no	—
690	C₄²×C₅₃	—	2	1	no	—
691	C₄²×C₅₃	—	2	1	no	—
692	C₄²×C₅₃	—	2	1	no	—
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
697	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
700	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	—	2	1	no	—
708	C₂³×C₅₃	—	2	1	no	—
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	4	2	no	—
711	C₂³×C₅₃	—	4	2	no	—
712	C₂³×C₅₃	—	8	1	no	—
713	C₂³×C₅₃	—	8	1	no	—
714	C₂³×C₅₃	—	8	1	no	—
715	C₂³×C₅₃	—	8	1	no	—
716	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
717	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
718	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
719	Q₈×C₅₃	—	2	1	no	—
720	Q₈×C₅₃	—	2	1	no	—
721	Q₈×C₅₃	—	2	1	no	—
722	Q₈×C₅₃	—	2	1	no	—
723	Q₈×C₅₃	—	2	1	no	—
724	Q₈×C₅₃	—	2	1	no	—
725	Q₈×C₅₃	—	2	1	no	—
726	Q₈×C₅₃	—	2	1	no	—
727	Q₈×C₅₃	—	2	1	no	—
728	Q₈×C₅₃	—	2	1	no	—
729	Q₈×C₅₃	—	2	1	no	—
730	Q₈×C₅₃	—	4	1	no	—
731	Q₈×C₅₃	—	4	2	no	—
732	Q₈×C₅₃	—	4	2	no	—
733	Q₈×C₅₃	—	4	2	no	—
734	Q₈×C₅₃	—	8	1	no	—
735	Q₈×C₅₃	—	8	1	no	—
736	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
737	D₄×C₅₃	—	2	2	no	—
738	D₄×C₅₃	—	2	2	no	—
739	D₄×C₅₃	—	2	1	no	—
740	D₄×C₅₃	—	2	1	no	—
741	D₄×C₅₃	—	2	1	no	—
742	D₄×C₅₃	—	2	1	no	—
743	D₄×C₅₃	—	2	1	no	—
744	D₄×C₅₃	—	2	1	no	—
745	D₄×C₅₃	—	2	1	no	—
746	D₄×C₅₃	—	2	1	no	—
747	D₄×C₅₃	—	4	1	no	—
748	D₄×C₅₃	—	4	2	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	4	2	no	—
751	D₄×C₅₃	—	4	2	no	—
752	D₄×C₅₃	—	4	2	no	—
753	D₄×C₅₃	—	4	2	no	—
754	D₄×C₅₃	—	8	1	no	—
755	D₄×C₅₃	—	8	1	no	—
756	D₄×C₅₃	—	8	1	no	—
757	D₄×C₅₃	—	8	1	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	—	8	1	no	—
760	C₂×C₄×C₅₃	—	2	2	no	—
761	C₂×C₄×C₅₃	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	2	1	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	2	1	no	—
772	C₂×C₄×C₅₃	—	2	1	no	—
773	C₂×C₄×C₅₃	—	2	1	no	—
774	C₂×C₄×C₅₃	—	2	1	no	—
775	C₂×C₄×C₅₃	—	2	1	no	—
776	C₂×C₄×C₅₃	—	2	1	no	—
777	C₂×C₄×C₅₃	—	2	1	no	—
778	C₂×C₄×C₅₃	—	2	1	no	—
779	C₂×C₄×C₅₃	—	4	1	no	—
780	C₂×C₄×C₅₃	—	4	1	no	—
781	C₂×C₄×C₅₃	—	4	1	no	—
782	C₂×C₄×C₅₃	—	4	1	no	—
783	C₂×C₄×C₅₃	—	4	1	no	—
784	C₂×C₄×C₅₃	—	4	2	no	—
785	C₂×C₄×C₅₃	—	4	2	no	—
786	C₂×C₄×C₅₃	—	4	2	no	—
787	C₂×C₄×C₅₃	—	4	2	no	—
788	C₂×C₄×C₅₃	—	4	2	no	—
789	C₂×C₄×C₅₃	—	4	2	no	—
790	C₂×C₄×C₅₃	—	4	2	no	—
791	C₂×C₄×C₅₃	—	4	2	no	—
792	C₂×C₄×C₅₃	—	8	1	no	—
793	C₂×C₄×C₅₃	—	8	1	no	—
794	C₂×C₄×C₅₃	—	8	1	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
803	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
805	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
806	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
808	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
810	C₈×C₅₃	—	2	1	no	—
811	C₈×C₅₃	—	2	1	no	—
812	C₈×C₅₃	—	2	1	no	—
813	C₈×C₅₃	—	2	1	no	—
814	C₈×C₅₃	—	2	1	no	—
815	C₈×C₅₃	—	2	1	no	—
816	C₈×C₅₃	—	2	1	no	—
817	C₈×C₅₃	—	2	1	no	—
818	#61972	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
819	C₂²×C₅₃	—	2	1	no	—
820	C₂²×C₅₃	—	2	1	no	—
821	C₂²×C₅₃	—	2	1	no	—
822	C₂²×C₅₃	—	2	1	no	—
823	C₂²×C₅₃	—	2	1	no	—
824	C₂²×C₅₃	—	2	1	no	—
825	C₂²×C₅₃	—	2	1	no	—
826	C₂²×C₅₃	—	2	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	4	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	4	1	no	—
836	C₂²×C₅₃	—	4	1	no	—
837	C₂²×C₅₃	—	4	1	no	—
838	C₂²×C₅₃	—	4	1	no	—
839	C₂²×C₅₃	—	16	2	no	—
840	C₂²×C₅₃	—	16	2	no	—
841	C₂²×C₅₃	#575	1	2	yes	—
842	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
843	C₄×C₅₃	—	2	1	no	—
844	C₄×C₅₃	—	2	1	no	—
845	C₄×C₅₃	—	2	1	no	—
846	C₄×C₅₃	—	2	1	no	—
847	C₄×C₅₃	—	2	1	no	—
848	C₄×C₅₃	—	2	1	no	—
849	C₄×C₅₃	—	2	1	no	—
850	C₄×C₅₃	—	2	2	no	—
851	C₄×C₅₃	—	2	1	no	—
852	C₄×C₅₃	—	2	1	no	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	2	1	no	—
855	C₄×C₅₃	—	4	1	no	—
856	C₄×C₅₃	—	4	1	no	—
857	C₄×C₅₃	—	4	1	no	—
858	C₄×C₅₃	—	4	1	no	—
859	C₄×C₅₃	—	4	1	no	—
860	C₄×C₅₃	—	4	1	no	—
861	C₄×C₅₃	—	4	1	no	—
862	C₄×C₅₃	—	4	1	no	—
863	C₄×C₅₃	—	4	1	no	—
864	C₄×C₅₃	—	4	1	no	—
865	C₄×C₅₃	—	4	1	no	—
866	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
867	C₄×C₅₃	#585	1	1	yes	characteristic
868	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3402	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3377	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3371	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3327	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3323	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3312	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3308	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3277	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3256	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3215	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3117	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3111	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3108	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
897	C₂×#464	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
899	C₂×C₅₃	—	2	2	no	—
900	C₂×C₅₃	—	4	1	no	—
901	C₂×C₅₃	—	4	1	no	—
902	C₂×C₅₃	—	8	1	no	—
903	C₂×C₅₃	—	8	1	no	—
904	C₂×C₅₃	—	8	1	no	—
905	C₂×C₅₃	—	8	1	no	—
906	C₂×C₅₃	#3488	1	1	yes	characteristic
907	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
908	C₂×C₅₃	#3586	1	1	yes	characteristic
909	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
913	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
915	#559	C₂²×C₅₃	1	1	yes	characteristic
916	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#556	—	2	1	no	—
918	#556	C₂²×C₅₃	1	1	yes	characteristic
919	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#555	—	2	1	no	—
921	#552	—	2	1	no	—
922	#552	—	2	1	no	—
923	#552	C₂²×C₅₃	1	1	yes	characteristic
924	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#551	—	2	1	no	—
926	#551	—	2	1	no	—
927	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
928	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#548	C₂²×C₅₃	1	1	yes	characteristic
930	#548	C₂²×C₅₃	1	1	yes	characteristic
931	#548	C₂²×C₅₃	1	1	yes	characteristic
932	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#547	—	2	1	no	—
934	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#546	—	2	1	no	—
936	#546	C₂²×C₅₃	1	1	yes	characteristic
937	#546	C₂²×C₅₃	1	1	yes	characteristic
938	D₄²	C₂²×C₅₃	1	1	yes	characteristic
939	#542	—	2	1	no	—
940	#538	—	2	1	no	—
941	#538	—	2	1	no	—
942	#533	—	2	1	no	—
943	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#532	C₂²×C₅₃	1	1	yes	characteristic
945	#529	—	2	1	no	—
946	#529	—	2	1	no	—
947	#529	C₂²×C₅₃	1	1	yes	characteristic
948	#529	C₂²×C₅₃	1	1	yes	characteristic
949	#529	C₂²×C₅₃	1	1	yes	characteristic
950	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
953	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
954	#518	—	2	1	no	—
955	C₄×#41	—	2	1	no	—
956	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
957	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#497	C₂²×C₅₃	1	1	yes	characteristic
961	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#496	C₂²×C₅₃	1	1	yes	characteristic
964	#495	C₂²×C₅₃	1	1	yes	characteristic
965	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#490	C₂²×C₅₃	1	1	yes	characteristic
968	#489	C₂²×C₅₃	1	1	yes	characteristic
969	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#488	C₂²×C₅₃	1	1	yes	characteristic
971	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#482	C₂²×C₅₃	1	1	yes	characteristic
976	#481	C₂²×C₅₃	1	1	yes	characteristic
977	#480	C₂²×C₅₃	1	1	yes	characteristic
978	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#478	C₂²×C₅₃	1	1	yes	characteristic
984	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#469	C₂²×C₅₃	1	1	yes	characteristic
992	#468	C₂²×C₅₃	1	1	yes	characteristic
993	#468	C₂²×C₅₃	1	1	yes	characteristic
994	#468	C₂²×C₅₃	1	1	yes	characteristic
995	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#466	C₂²×C₅₃	1	1	yes	characteristic
998	#465	C₂²×C₅₃	1	1	yes	characteristic
999	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#464	C₂²×C₅₃	1	1	yes	characteristic
1001	#464	C₂²×C₅₃	1	1	yes	characteristic
1002	#464	C₂²×C₅₃	1	1	yes	characteristic
1003	#464	C₂²×C₅₃	1	1	yes	characteristic
1004	#464	C₂²×C₅₃	1	1	yes	characteristic
1005	#464	C₂²×C₅₃	1	1	yes	characteristic
1006	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#463	C₂²×C₅₃	1	1	yes	characteristic
1018	#463	C₂²×C₅₃	1	1	yes	characteristic
1019	#463	C₂²×C₅₃	1	1	yes	characteristic
1020	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#460	C₂²×C₅₃	1	1	yes	characteristic
1029	#460	C₂²×C₅₃	1	1	yes	characteristic
1030	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#450	C₂²×C₅₃	1	1	yes	characteristic
1039	#450	C₂²×C₅₃	1	1	yes	characteristic
1040	#450	C₂²×C₅₃	1	1	yes	characteristic
1041	#449	C₂²×C₅₃	1	1	yes	characteristic
1042	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#448	C₂²×C₅₃	1	1	yes	characteristic
1045	#448	C₂²×C₅₃	1	1	yes	characteristic
1046	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#447	C₂²×C₅₃	1	1	yes	characteristic
1048	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#440	C₂²×C₅₃	1	1	yes	characteristic
1055	#440	C₂²×C₅₃	1	1	yes	characteristic
1056	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#435	C₂²×C₅₃	1	1	yes	characteristic
1065	#435	C₂²×C₅₃	1	1	yes	characteristic
1066	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#418	C₂²×C₅₃	1	1	yes	characteristic
1076	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1080	C₅₃	#61972	1	1	yes	characteristic, direct product factor, Sylow
1081	C₂×#41	—	2	1	no	—
1082	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
1083	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂²×D₄	—	2	1	no	—
1091	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1093	#137	—	4	2	no	—
1094	#137	—	4	2	no	—
1095	#137	—	4	2	no	—
1096	AGL(1,ℤ/8)	—	4	2	no	—
1097	C₂×Q₁₆	—	4	2	no	—
1098	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×SD₁₆	—	4	2	no	—
1108	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₄⋊Q₈	—	2	1	no	—
1130	C₄⋊Q₈	—	2	1	no	—
1131	C₄⋊Q₈	—	2	1	no	—
1132	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1133	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1134	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1135	#127	C₂³×C₅₃	1	1	yes	characteristic
1136	#126	—	2	1	no	—
1137	#126	—	2	1	no	—
1138	#126	—	2	1	no	—
1139	#126	—	2	1	no	—
1140	#126	—	2	1	no	—
1141	#126	—	2	1	no	—
1142	#126	—	2	1	no	—
1143	#126	—	2	1	no	—
1144	#126	—	2	1	no	—
1145	#126	—	2	1	no	—
1146	#126	—	2	1	no	—
1147	#125	—	2	1	no	—
1148	#125	—	2	1	no	—
1149	#125	—	2	1	no	—
1150	#125	—	2	1	no	—
1151	#125	—	2	1	no	—
1152	#125	C₂³×C₅₃	1	1	yes	characteristic
1153	#125	C₂³×C₅₃	1	1	yes	characteristic
1154	#125	C₂³×C₅₃	1	1	yes	characteristic
1155	#124	—	2	1	no	—
1156	#124	—	2	1	no	—
1157	#124	—	2	1	no	—
1158	#124	—	2	1	no	—
1159	#124	—	2	1	no	—
1160	#124	—	2	1	no	—
1161	#124	—	2	1	no	—
1162	#124	—	2	1	no	—
1163	#124	—	2	1	no	—
1164	#124	C₂³×C₅₃	1	1	yes	characteristic
1165	#124	C₂³×C₅₃	1	1	yes	characteristic
1166	#124	C₂³×C₅₃	1	1	yes	characteristic
1167	#124	C₂³×C₅₃	1	1	yes	characteristic
1168	#124	C₂³×C₅₃	1	1	yes	characteristic
1169	#124	C₂³×C₅₃	1	1	yes	characteristic
1170	#124	C₂³×C₅₃	1	1	yes	characteristic
1171	#124	C₂³×C₅₃	1	1	yes	characteristic
1172	#124	C₂³×C₅₃	1	1	yes	characteristic
1173	#123	—	2	1	no	—
1174	#123	—	2	1	no	—
1175	#123	—	2	1	no	—
1176	#123	—	2	1	no	—
1177	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	—	2	1	no	—
1185	#123	—	2	1	no	—
1186	C₂²⋊Q₈	—	2	1	no	—
1187	C₂²⋊Q₈	—	2	1	no	—
1188	C₂²⋊Q₈	—	2	1	no	—
1189	C₂²⋊Q₈	—	2	1	no	—
1190	C₂²⋊Q₈	—	2	1	no	—
1191	C₂²⋊Q₈	—	2	1	no	—
1192	C₂²⋊Q₈	—	2	1	no	—
1193	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	—	2	1	no	—
1198	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1200	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	#121	—	2	1	no	—
1206	#121	—	2	1	no	—
1207	#121	—	2	1	no	—
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	—	2	1	no	—
1214	#121	C₂³×C₅₃	1	1	yes	characteristic
1215	#121	C₂³×C₅₃	1	1	yes	characteristic
1216	#121	C₂³×C₅₃	1	1	yes	characteristic
1217	#121	C₂³×C₅₃	1	1	yes	characteristic
1218	#121	C₂³×C₅₃	1	1	yes	characteristic
1219	#120	—	2	1	no	—
1220	#120	—	2	1	no	—
1221	#120	—	2	1	no	—
1222	#120	—	2	1	no	—
1223	C₄×Q₈	—	2	1	no	—
1224	C₄×Q₈	—	2	1	no	—
1225	C₄×Q₈	—	2	1	no	—
1226	C₄×Q₈	—	2	1	no	—
1227	C₄×Q₈	—	2	1	no	—
1228	C₄×Q₈	—	2	1	no	—
1229	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
1230	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1231	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1232	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1233	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1234	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1235	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1236	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×D₄	—	2	1	no	—
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	—	2	1	no	—
1245	C₄×D₄	—	2	1	no	—
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	—	2	1	no	—
1258	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1259	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1260	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1261	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1262	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	#117	—	2	1	no	—
1270	#117	—	2	1	no	—
1271	#117	—	2	1	no	—
1272	#117	—	2	1	no	—
1273	#117	—	2	1	no	—
1274	#117	—	2	1	no	—
1275	#117	—	2	1	no	—
1276	#117	—	2	1	no	—
1277	#117	—	2	1	no	—
1278	#117	—	2	1	no	—
1279	#117	—	2	1	no	—
1280	#117	D₄×C₅₃	1	1	yes	characteristic
1281	#117	D₄×C₅₃	1	1	yes	characteristic
1282	#117	D₄×C₅₃	1	1	yes	characteristic
1283	#117	C₂³×C₅₃	1	1	yes	characteristic
1284	C₂×C₄⋊C₄	—	2	1	no	—
1285	C₂×C₄⋊C₄	—	2	1	no	—
1286	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1287	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1288	C₂×C₂²⋊C₄	—	2	1	no	—
1289	C₂×C₂²⋊C₄	—	2	1	no	—
1290	C₂×C₂²⋊C₄	—	2	1	no	—
1291	C₂×C₂²⋊C₄	—	2	1	no	—
1292	C₂×C₂²⋊C₄	—	2	1	no	—
1293	C₂×C₂²⋊C₄	—	2	1	no	—
1294	C₂×C₄²	—	2	1	no	—
1295	C₂×C₄²	—	2	1	no	—
1296	C₂×C₄²	—	2	1	no	—
1297	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1298	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1299	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1300	#107	C₂³×C₅₃	1	1	yes	characteristic
1301	#107	C₂³×C₅₃	1	1	yes	characteristic
1302	#107	C₂³×C₅₃	1	1	yes	characteristic
1303	#107	C₂³×C₅₃	1	1	yes	characteristic
1304	#106	C₂³×C₅₃	1	1	yes	characteristic
1305	#106	C₂³×C₅₃	1	1	yes	characteristic
1306	#106	C₂³×C₅₃	1	1	yes	characteristic
1307	#106	C₂³×C₅₃	1	1	yes	characteristic
1308	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1309	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1311	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1312	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1313	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1314	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1315	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1316	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1318	#103	C₂³×C₅₃	1	1	yes	characteristic
1319	#103	C₂³×C₅₃	1	1	yes	characteristic
1320	#103	C₂³×C₅₃	1	1	yes	characteristic
1321	#103	C₂³×C₅₃	1	1	yes	characteristic
1322	#103	C₂³×C₅₃	1	1	yes	characteristic
1323	#103	C₂³×C₅₃	1	1	yes	characteristic
1324	#103	C₂³×C₅₃	1	1	yes	characteristic
1325	#103	C₂³×C₅₃	1	1	yes	characteristic
1326	#103	C₂³×C₅₃	1	1	yes	characteristic
1327	#103	C₂³×C₅₃	1	1	yes	characteristic
1328	#103	C₂³×C₅₃	1	1	yes	characteristic
1329	#103	C₂³×C₅₃	1	1	yes	characteristic
1330	#103	C₂³×C₅₃	1	1	yes	characteristic
1331	#103	C₂³×C₅₃	1	1	yes	characteristic
1332	#103	C₂³×C₅₃	1	1	yes	characteristic
1333	#103	C₂³×C₅₃	1	1	yes	characteristic
1334	#103	C₂³×C₅₃	1	1	yes	characteristic
1335	#103	C₂³×C₅₃	1	1	yes	characteristic
1336	#102	C₂³×C₅₃	1	1	yes	characteristic
1337	#102	C₂³×C₅₃	1	1	yes	characteristic
1338	#102	C₂³×C₅₃	1	1	yes	characteristic
1339	#102	C₂³×C₅₃	1	1	yes	characteristic
1340	#102	C₂³×C₅₃	1	1	yes	characteristic
1341	#102	C₂³×C₅₃	1	1	yes	characteristic
1342	#102	C₂³×C₅₃	1	1	yes	characteristic
1343	#102	C₂³×C₅₃	1	1	yes	characteristic
1344	#102	C₂³×C₅₃	1	1	yes	characteristic
1345	#102	C₂³×C₅₃	1	1	yes	characteristic
1346	#102	C₂³×C₅₃	1	1	yes	characteristic
1347	#102	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1351	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1353	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1354	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1355	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1356	#97	C₂³×C₅₃	1	1	yes	characteristic
1357	#97	C₂³×C₅₃	1	1	yes	characteristic
1358	#97	C₂³×C₅₃	1	1	yes	characteristic
1359	#97	C₂³×C₅₃	1	1	yes	characteristic
1360	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1361	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1362	C₂⁴	—	2	1	no	—
1363	C₂⁴	—	2	1	no	—
1364	#41	—	2	2	no	—
1365	#41	—	4	2	no	—
1366	#41	—	4	1	no	—
1367	#41	—	4	1	no	—
1368	#41	—	4	1	no	—
1369	#41	—	4	1	no	—
1370	#41	—	4	1	no	—
1371	#41	—	4	4	no	—
1372	C₂×Q₈	—	2	1	no	—
1373	C₂×Q₈	—	2	1	no	—
1374	C₂×Q₈	—	2	1	no	—
1375	C₂×Q₈	—	2	1	no	—
1376	C₂×Q₈	—	2	1	no	—
1377	C₂×Q₈	—	2	2	no	—
1378	C₂×Q₈	—	2	2	no	—
1379	C₂×Q₈	—	4	1	no	—
1380	C₂×Q₈	—	4	1	no	—
1381	C₂×Q₈	—	4	1	no	—
1382	C₂×Q₈	—	4	1	no	—
1383	C₂×Q₈	—	4	1	no	—
1384	C₂×Q₈	—	4	1	no	—
1385	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1386	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1387	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1388	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1389	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1390	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1391	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×D₄	—	2	1	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	—	2	1	no	—
1400	C₂×D₄	—	2	1	no	—
1401	C₂×D₄	—	2	1	no	—
1402	C₂×D₄	—	2	1	no	—
1403	C₂×D₄	—	2	1	no	—
1404	C₂×D₄	—	4	1	no	—
1405	C₂×D₄	—	4	1	no	—
1406	C₂×D₄	—	4	1	no	—
1407	C₂×D₄	—	4	1	no	—
1408	C₂×D₄	—	4	4	no	—
1409	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1410	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1411	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1412	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1415	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1416	C₂²×C₄	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	—	2	1	no	—
1423	C₂²×C₄	—	2	1	no	—
1424	C₂²×C₄	—	2	1	no	—
1425	C₂²×C₄	—	2	1	no	—
1426	C₂²×C₄	—	2	1	no	—
1427	C₂²×C₄	—	2	1	no	—
1428	C₂²×C₄	—	2	1	no	—
1429	C₂²×C₄	—	2	1	no	—
1430	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1431	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1432	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1433	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1434	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1435	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1436	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1437	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1439	Q₁₆	—	2	2	no	—
1440	Q₁₆	—	2	2	no	—
1441	Q₁₆	—	2	2	no	—
1442	Q₁₆	—	4	1	no	—
1443	Q₁₆	—	4	1	no	—
1444	Q₁₆	—	4	1	no	—
1445	Q₁₆	—	4	1	no	—
1446	Q₁₆	—	4	1	no	—
1447	Q₁₆	—	4	1	no	—
1448	SD₁₆	—	2	2	no	—
1449	SD₁₆	—	2	2	no	—
1450	SD₁₆	—	2	2	no	—
1451	SD₁₆	—	4	1	no	—
1452	SD₁₆	—	4	1	no	—
1453	SD₁₆	—	4	1	no	—
1454	SD₁₆	—	4	1	no	—
1455	SD₁₆	—	4	1	no	—
1456	SD₁₆	—	4	1	no	—
1457	SD₁₆	—	4	1	no	—
1458	SD₁₆	—	4	1	no	—
1459	SD₁₆	—	4	1	no	—
1460	D₈	—	4	1	no	—
1461	D₈	—	4	1	no	—
1462	D₈	—	4	1	no	—
1463	M₁₆	—	4	1	no	—
1464	M₁₆	—	4	1	no	—
1465	M₁₆	—	4	1	no	—
1466	M₁₆	—	4	1	no	—
1467	C₂×C₈	—	4	1	no	—
1468	C₂×C₈	—	4	1	no	—
1469	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1470	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1471	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1472	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1473	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1474	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1475	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1476	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	2	1	no	—
1496	C₄⋊C₄	—	2	1	no	—
1497	C₄⋊C₄	—	2	1	no	—
1498	C₄⋊C₄	—	2	1	no	—
1499	C₄⋊C₄	—	2	1	no	—
1500	C₄⋊C₄	—	2	1	no	—
1501	C₄⋊C₄	—	2	1	no	—
1502	C₄⋊C₄	—	2	1	no	—
1503	C₄⋊C₄	—	2	1	no	—
1504	C₄⋊C₄	—	2	1	no	—
1505	C₄⋊C₄	—	2	1	no	—
1506	C₄⋊C₄	—	2	1	no	—
1507	C₄⋊C₄	—	2	1	no	—
1508	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1509	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1510	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1511	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1512	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1513	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1514	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1515	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1516	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1517	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1518	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1519	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	—	2	1	no	—
1545	C₂²⋊C₄	—	2	1	no	—
1546	C₂²⋊C₄	—	2	1	no	—
1547	C₂²⋊C₄	—	2	1	no	—
1548	C₂²⋊C₄	—	2	1	no	—
1549	C₂²⋊C₄	—	2	1	no	—
1550	C₂²⋊C₄	—	2	1	no	—
1551	C₂²⋊C₄	—	2	1	no	—
1552	C₂²⋊C₄	—	2	1	no	—
1553	C₂²⋊C₄	—	2	1	no	—
1554	C₂²⋊C₄	—	2	1	no	—
1555	C₂²⋊C₄	—	2	1	no	—
1556	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1557	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1558	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1559	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1560	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1561	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1562	C₄²	—	2	1	no	—
1563	C₄²	—	2	1	no	—
1564	C₄²	—	2	1	no	—
1565	C₄²	—	2	1	no	—
1566	C₄²	—	2	1	no	—
1567	C₄²	—	2	1	no	—
1568	C₄²	—	2	1	no	—
1569	C₄²	—	2	1	no	—
1570	C₄²	—	2	1	no	—
1571	C₄²	—	2	1	no	—
1572	C₄²	—	2	1	no	—
1573	C₄²	—	2	1	no	—
1574	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1575	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1576	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1577	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1578	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1579	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1580	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1581	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1582	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1583	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1584	C₂³	—	2	1	no	—
1585	C₂³	—	2	1	no	—
1586	C₂³	—	2	1	no	—
1587	C₂³	—	2	1	no	—
1588	C₂³	—	4	2	no	—
1589	C₂³	—	4	2	no	—
1590	C₂³	—	8	1	no	—
1591	C₂³	—	8	1	no	—
1592	C₂³	—	8	1	no	—
1593	C₂³	—	8	1	no	—
1594	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1595	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1596	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1597	Q₈	—	2	1	no	—
1598	Q₈	—	2	1	no	—
1599	Q₈	—	2	1	no	—
1600	Q₈	—	2	1	no	—
1601	Q₈	—	2	1	no	—
1602	Q₈	—	2	1	no	—
1603	Q₈	—	2	1	no	—
1604	Q₈	—	2	1	no	—
1605	Q₈	—	2	1	no	—
1606	Q₈	—	2	1	no	—
1607	Q₈	—	2	1	no	—
1608	Q₈	—	4	1	no	—
1609	Q₈	—	4	2	no	—
1610	Q₈	—	4	2	no	—
1611	Q₈	—	4	2	no	—
1612	Q₈	—	8	1	no	—
1613	Q₈	—	8	1	no	—
1614	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1615	D₄	—	2	2	no	—
1616	D₄	—	2	2	no	—
1617	D₄	—	2	1	no	—
1618	D₄	—	2	1	no	—
1619	D₄	—	2	1	no	—
1620	D₄	—	2	1	no	—
1621	D₄	—	2	1	no	—
1622	D₄	—	2	1	no	—
1623	D₄	—	2	1	no	—
1624	D₄	—	2	1	no	—
1625	D₄	—	4	1	no	—
1626	D₄	—	4	2	no	—
1627	D₄	—	4	2	no	—
1628	D₄	—	4	2	no	—
1629	D₄	—	4	2	no	—
1630	D₄	—	4	2	no	—
1631	D₄	—	4	2	no	—
1632	D₄	—	8	1	no	—
1633	D₄	—	8	1	no	—
1634	D₄	—	8	1	no	—
1635	D₄	—	8	1	no	—
1636	D₄	—	8	1	no	—
1637	D₄	—	8	1	no	—
1638	C₂×C₄	—	2	2	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	2	1	no	—
1643	C₂×C₄	—	2	1	no	—
1644	C₂×C₄	—	2	1	no	—
1645	C₂×C₄	—	2	1	no	—
1646	C₂×C₄	—	2	1	no	—
1647	C₂×C₄	—	2	1	no	—
1648	C₂×C₄	—	2	1	no	—
1649	C₂×C₄	—	2	1	no	—
1650	C₂×C₄	—	2	1	no	—
1651	C₂×C₄	—	2	1	no	—
1652	C₂×C₄	—	2	1	no	—
1653	C₂×C₄	—	2	1	no	—
1654	C₂×C₄	—	2	1	no	—
1655	C₂×C₄	—	2	1	no	—
1656	C₂×C₄	—	2	1	no	—
1657	C₂×C₄	—	4	1	no	—
1658	C₂×C₄	—	4	1	no	—
1659	C₂×C₄	—	4	1	no	—
1660	C₂×C₄	—	4	1	no	—
1661	C₂×C₄	—	4	1	no	—
1662	C₂×C₄	—	4	2	no	—
1663	C₂×C₄	—	4	2	no	—
1664	C₂×C₄	—	4	2	no	—
1665	C₂×C₄	—	4	2	no	—
1666	C₂×C₄	—	4	2	no	—
1667	C₂×C₄	—	4	2	no	—
1668	C₂×C₄	—	4	2	no	—
1669	C₂×C₄	—	4	2	no	—
1670	C₂×C₄	—	8	1	no	—
1671	C₂×C₄	—	8	1	no	—
1672	C₂×C₄	—	8	1	no	—
1673	C₂×C₄	—	8	1	no	—
1674	C₂×C₄	—	8	1	no	—
1675	C₂×C₄	—	8	1	no	—
1676	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1677	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1678	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1679	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1680	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1681	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1682	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1683	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1684	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1685	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1686	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1687	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1688	C₈	—	2	1	no	—
1689	C₈	—	2	1	no	—
1690	C₈	—	2	1	no	—
1691	C₈	—	2	1	no	—
1692	C₈	—	2	1	no	—
1693	C₈	—	2	1	no	—
1694	C₈	—	2	1	no	—
1695	C₈	—	2	1	no	—
1696	C₂²	—	2	1	no	—
1697	C₂²	—	2	1	no	—
1698	C₂²	—	2	1	no	—
1699	C₂²	—	2	1	no	—
1700	C₂²	—	2	1	no	—
1701	C₂²	—	2	1	no	—
1702	C₂²	—	2	1	no	—
1703	C₂²	—	2	1	no	—
1704	C₂²	—	4	1	no	—
1705	C₂²	—	4	1	no	—
1706	C₂²	—	4	1	no	—
1707	C₂²	—	4	1	no	—
1708	C₂²	—	4	1	no	—
1709	C₂²	—	4	1	no	—
1710	C₂²	—	4	1	no	—
1711	C₂²	—	4	1	no	—
1712	C₂²	—	4	1	no	—
1713	C₂²	—	4	1	no	—
1714	C₂²	—	4	1	no	—
1715	C₂²	—	4	1	no	—
1716	C₂²	—	16	2	no	—
1717	C₂²	—	16	2	no	—
1718	C₂²	C₅₃×#575	1	2	yes	—
1719	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1720	C₄	—	2	1	no	—
1721	C₄	—	2	1	no	—
1722	C₄	—	2	1	no	—
1723	C₄	—	2	2	no	—
1724	C₄	—	2	1	no	—
1725	C₄	—	2	1	no	—
1726	C₄	—	2	1	no	—
1727	C₄	—	2	1	no	—
1728	C₄	—	2	1	no	—
1729	C₄	—	2	1	no	—
1730	C₄	—	2	1	no	—
1731	C₄	—	2	1	no	—
1732	C₄	—	4	1	no	—
1733	C₄	—	4	1	no	—
1734	C₄	—	4	1	no	—
1735	C₄	—	4	1	no	—
1736	C₄	—	4	1	no	—
1737	C₄	—	4	1	no	—
1738	C₄	—	4	1	no	—
1739	C₄	—	4	1	no	—
1740	C₄	—	4	1	no	—
1741	C₄	—	4	1	no	—
1742	C₄	—	4	1	no	—
1743	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1744	C₄	C₅₃×#585	1	1	yes	characteristic
1745	C₂	—	2	2	no	—
1746	C₂	—	4	1	no	—
1747	C₂	—	4	1	no	—
1748	C₂	—	8	1	no	—
1749	C₂	—	8	1	no	—
1750	C₂	—	8	1	no	—
1751	C₂	—	8	1	no	—
1752	C₂	C₅₃×#3488	1	1	yes	characteristic
1753	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1754	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3514	C₂	semidirect
2. C₅₃×#3482	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3401	C₂	semidirect
5. C₅₃×#3377	C₂	semidirect
6. C₅₃×#3371	C₂	semidirect
7. C₅₃×#3327	C₂	semidirect
8. C₅₃×#3323	C₂	semidirect
9. C₅₃×#3312	C₂	semidirect
10. C₅₃×#3310	C₂	semidirect
11. C₅₃×#3308	C₂	semidirect
12. C₅₃×#3306	C₂	semidirect
13. C₅₃×#3277	C₂	semidirect
14. C₅₃×#3275	C₂	semidirect
15. C₅₃×#3270	C₂	semidirect
16. C₅₃×#3270	C₂	semidirect
17. C₅₃×#3266	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3256	C₂	semidirect
20. C₅₃×#3252	C₂	semidirect
21. C₅₃×#3250	C₂	semidirect
22. C₅₃×#3219	C₂	semidirect
23. C₅₃×#3215	C₂	semidirect
24. C₅₃×#3211	C₂	semidirect
25. C₅₃×#3117	C₂	semidirect
26. C₅₃×#3111	C₂	semidirect
27. C₅₃×#3108	C₂	semidirect
28. C₅₃×#3040	C₂	semidirect
29. C₅₃×#3037	C₂	semidirect
30. C₂×C₅₃×#464	C₂	semidirect
31. C₅₃×#2989	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
33. C₂×#137×C₅₃	C₂²	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
36. C₂²×Q₁₆×C₅₃	C₂²	semidirect
39. C₅₃×#557	C₂²	semidirect
42. C₅₃×#556	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
51. D₄×Q₈×C₅₃	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
57. C₅₃×#547	C₂²	semidirect
66. C₅₃×#533	C₂²	semidirect
73. C₅₃×#529	C₂²	semidirect
74. C₅₃×#529	C₂²	semidirect
80. C₄×#41×C₅₃	C₂²	semidirect
81. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
82. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
84. C₅₃×#497	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
88. C₅₃×#495	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
94. C₅₃×#488	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#484	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#479	C₂²	semidirect
103. C₅₃×#479	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#479	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#477	C₂²	semidirect
110. C₅₃×#476	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
112. C₅₃×#470	C₂²	semidirect
113. C₅₃×#470	C₂²	semidirect
118. C₅₃×#468	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
130. C₅₃×#464	C₂²	semidirect
131. C₅₃×#464	C₂²	semidirect
132. C₅₃×#464	C₂²	semidirect
133. C₅₃×#464	C₂²	semidirect
134. C₅₃×#464	C₂²	semidirect
135. C₅₃×#464	C₂²	semidirect
136. C₅₃×#464	C₂²	semidirect
137. C₅₃×#464	C₂²	semidirect
138. C₅₃×#464	C₂²	semidirect
139. C₅₃×#464	C₂²	semidirect
143. C₅₃×#463	C₂²	semidirect
144. C₅₃×#463	C₂²	semidirect
145. C₅₃×#463	C₂²	semidirect
146. C₅₃×#463	C₂²	semidirect
147. C₅₃×#462	C₂²	semidirect
148. C₅₃×#462	C₂²	semidirect
149. C₅₃×#462	C₂²	semidirect
150. C₅₃×#461	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#451	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#451	C₂²	semidirect
159. C₅₃×#451	C₂²	semidirect
160. C₅₃×#451	C₂²	semidirect
165. C₅₃×#449	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
176. C₅₃×#441	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×Q₁₆×C₅₃	C₂²	semidirect
182. C₄×Q₁₆×C₅₃	C₂²	semidirect
183. C₄×SD₁₆×C₅₃	C₂²	semidirect
184. C₄×SD₁₆×C₅₃	C₂²	semidirect
185. C₅₃×#436	C₂²	semidirect
186. C₅₃×#436	C₂²	semidirect
189. C₅₃×#435	C₂²	semidirect
190. C₅₃×#435	C₂²	semidirect
191. C₅₃×#432	C₂²	semidirect
192. C₅₃×#432	C₂²	semidirect
193. C₅₃×#431	C₂²	semidirect
194. C₅₃×#423	C₂²	semidirect
195. C₅₃×#423	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#419	C₂²	semidirect
199. C₅₃×#417	C₂²	semidirect
200. C₅₃×#417	C₂²	semidirect
201. C₂×#103×C₅₃	C₂²	semidirect
818. #61972	C₅₃	direct (N × H)
868. #3514	C₂×C₅₃	semidirect
869. #3482	C₂×C₅₃	semidirect
870. #3402	C₂×C₅₃	semidirect
871. #3401	C₂×C₅₃	semidirect
872. #3377	C₂×C₅₃	semidirect
873. #3371	C₂×C₅₃	semidirect
874. #3327	C₂×C₅₃	semidirect
875. #3323	C₂×C₅₃	semidirect
876. #3312	C₂×C₅₃	semidirect
877. #3310	C₂×C₅₃	semidirect
878. #3308	C₂×C₅₃	semidirect
879. #3306	C₂×C₅₃	semidirect
880. #3277	C₂×C₅₃	semidirect
881. #3275	C₂×C₅₃	semidirect
882. #3270	C₂×C₅₃	semidirect
883. #3270	C₂×C₅₃	semidirect
884. #3266	C₂×C₅₃	semidirect
885. #3265	C₂×C₅₃	semidirect
886. #3256	C₂×C₅₃	semidirect
887. #3252	C₂×C₅₃	semidirect
888. #3250	C₂×C₅₃	semidirect
889. #3219	C₂×C₅₃	semidirect
890. #3215	C₂×C₅₃	semidirect
891. #3211	C₂×C₅₃	semidirect
892. #3117	C₂×C₅₃	semidirect
893. #3111	C₂×C₅₃	semidirect
894. #3108	C₂×C₅₃	semidirect
895. #3040	C₂×C₅₃	semidirect
896. #3037	C₂×C₅₃	semidirect
897. C₂×#464	C₂×C₅₃	semidirect
898. #2989	C₂×C₅₃	semidirect
909. C₂×#137	C₂²×C₅₃	semidirect
910. C₂×#137	C₂²×C₅₃	semidirect
911. C₂×#137	C₂²×C₅₃	semidirect
913. C₂²×Q₁₆	C₂²×C₅₃	semidirect
916. #557	C₂²×C₅₃	semidirect
919. #556	C₂²×C₅₃	semidirect
924. #552	C₂²×C₅₃	semidirect
928. D₄×Q₈	C₂²×C₅₃	semidirect
932. #548	C₂²×C₅₃	semidirect
934. #547	C₂²×C₅₃	semidirect
943. #533	C₂²×C₅₃	semidirect
950. #529	C₂²×C₅₃	semidirect
951. #529	C₂²×C₅₃	semidirect
957. C₄×#41	C₂²×C₅₃	semidirect
958. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
959. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
961. #497	C₂²×C₅₃	semidirect
962. #497	C₂²×C₅₃	semidirect
965. #495	C₂²×C₅₃	semidirect
966. #491	C₂²×C₅₃	semidirect
969. #489	C₂²×C₅₃	semidirect
971. #488	C₂²×C₅₃	semidirect
972. #485	C₂²×C₅₃	semidirect
973. #484	C₂²×C₅₃	semidirect
974. #483	C₂²×C₅₃	semidirect
978. #479	C₂²×C₅₃	semidirect
979. #479	C₂²×C₅₃	semidirect
980. #479	C₂²×C₅₃	semidirect
981. #479	C₂²×C₅₃	semidirect
982. #479	C₂²×C₅₃	semidirect
984. #478	C₂²×C₅₃	semidirect
985. #478	C₂²×C₅₃	semidirect
986. #477	C₂²×C₅₃	semidirect
987. #476	C₂²×C₅₃	semidirect
988. #470	C₂²×C₅₃	semidirect
989. #470	C₂²×C₅₃	semidirect
990. #470	C₂²×C₅₃	semidirect
995. #468	C₂²×C₅₃	semidirect
996. #467	C₂²×C₅₃	semidirect
999. #465	C₂²×C₅₃	semidirect
1006. #464	C₂²×C₅₃	semidirect
1007. #464	C₂²×C₅₃	semidirect
1008. #464	C₂²×C₅₃	semidirect
1009. #464	C₂²×C₅₃	semidirect
1010. #464	C₂²×C₅₃	semidirect
1011. #464	C₂²×C₅₃	semidirect
1012. #464	C₂²×C₅₃	semidirect
1013. #464	C₂²×C₅₃	semidirect
1014. #464	C₂²×C₅₃	semidirect
1015. #464	C₂²×C₅₃	semidirect
1016. #464	C₂²×C₅₃	semidirect
1020. #463	C₂²×C₅₃	semidirect
1021. #463	C₂²×C₅₃	semidirect
1022. #463	C₂²×C₅₃	semidirect
1023. #463	C₂²×C₅₃	semidirect
1024. #462	C₂²×C₅₃	semidirect
1025. #462	C₂²×C₅₃	semidirect
1026. #462	C₂²×C₅₃	semidirect
1027. #461	C₂²×C₅₃	semidirect
1030. #452	C₂²×C₅₃	semidirect
1031. #452	C₂²×C₅₃	semidirect
1032. #452	C₂²×C₅₃	semidirect
1033. #451	C₂²×C₅₃	semidirect
1034. #451	C₂²×C₅₃	semidirect
1035. #451	C₂²×C₅₃	semidirect
1036. #451	C₂²×C₅₃	semidirect
1037. #451	C₂²×C₅₃	semidirect
1042. #449	C₂²×C₅₃	semidirect
1043. #449	C₂²×C₅₃	semidirect
1046. #448	C₂²×C₅₃	semidirect
1048. #446	C₂²×C₅₃	semidirect
1049. #446	C₂²×C₅₃	semidirect
1050. #442	C₂²×C₅₃	semidirect
1051. #441	C₂²×C₅₃	semidirect
1052. #441	C₂²×C₅₃	semidirect
1053. #441	C₂²×C₅₃	semidirect
1056. #440	C₂²×C₅₃	semidirect
1057. #440	C₂²×C₅₃	semidirect
1058. C₄×Q₁₆	C₂²×C₅₃	semidirect
1059. C₄×Q₁₆	C₂²×C₅₃	semidirect
1060. C₄×SD₁₆	C₂²×C₅₃	semidirect
1061. C₄×SD₁₆	C₂²×C₅₃	semidirect
1062. #436	C₂²×C₅₃	semidirect
1063. #436	C₂²×C₅₃	semidirect
1066. #435	C₂²×C₅₃	semidirect
1067. #435	C₂²×C₅₃	semidirect
1068. #432	C₂²×C₅₃	semidirect
1069. #432	C₂²×C₅₃	semidirect
1070. #431	C₂²×C₅₃	semidirect
1071. #423	C₂²×C₅₃	semidirect
1072. #423	C₂²×C₅₃	semidirect
1073. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1074. #419	C₂²×C₅₃	semidirect
1076. #417	C₂²×C₅₃	semidirect
1077. #417	C₂²×C₅₃	semidirect
1078. C₂×#103	C₂²×C₅₃	semidirect
1080. C₅₃	#61972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3514	2
C₅₃×#3482	2
C₅₃×#3402	2
C₅₃×#3401	2
C₅₃×#3377	2
C₅₃×#3371	2
C₅₃×#3327	2
C₅₃×#3323	2
C₅₃×#3312	2
C₅₃×#3310	2
C₅₃×#3308	2
C₅₃×#3306	2
C₅₃×#3277	2
C₅₃×#3275	2
C₅₃×#3270	2
C₅₃×#3266	2
C₅₃×#3265	2
C₅₃×#3256	2
C₅₃×#3252	2
C₅₃×#3250	2
C₅₃×#3219	2
C₅₃×#3215	2
C₅₃×#3211	2
C₅₃×#3117	2
C₅₃×#3111	2
C₅₃×#3108	2
C₅₃×#3040	2
C₅₃×#3037	2
C₂×C₅₃×#464	2
C₅₃×#2989	2
#61972	53

Subgroups — C53×#61972 #27269484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61972 #27269484