Subgroups — C₅₃×#61982 #27269494

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3308	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3300	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3285	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	2	yes	—
25	C₂×#135×C₅₃	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#557	C₂²	1	1	yes	characteristic
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#556	C₂²	1	2	yes	—
31	C₅₃×#555	—	2	1	no	—
32	C₅₃×#554	—	2	1	no	—
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#552	—	2	1	no	—
36	C₅₃×#552	—	2	1	no	—
37	C₅₃×#552	C₂²	1	1	yes	characteristic
38	C₅₃×#552	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#548	C₂²	1	1	yes	characteristic
41	C₅₃×#548	C₂²	1	1	yes	characteristic
42	C₅₃×#548	C₂²	1	2	yes	—
43	C₅₃×#548	C₂²	1	2	yes	—
44	C₅₃×#547	—	2	1	no	—
45	C₅₃×#547	C₂²	1	2	yes	—
46	C₅₃×#547	C₂²	1	1	yes	characteristic
47	C₅₃×#542	—	2	1	no	—
48	C₅₃×#542	—	2	1	no	—
49	C₅₃×#537	—	2	1	no	—
50	C₅₃×#533	—	2	1	no	—
51	C₅₃×#533	C₂²	1	1	yes	characteristic
52	C₅₃×#533	C₂²	1	1	yes	characteristic
53	C₅₃×#533	C₂²	1	1	yes	characteristic
54	C₅₃×#532	C₂²	1	1	yes	characteristic
55	C₅₃×#532	C₂²	1	1	yes	characteristic
56	C₅₃×#532	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#529	—	2	1	no	—
59	C₅₃×#529	—	2	1	no	—
60	C₅₃×#529	C₂²	1	1	yes	characteristic
61	C₅₃×#529	C₂²	1	1	yes	characteristic
62	C₅₃×#520	—	2	1	no	—
63	C₄×#41×C₅₃	—	2	1	no	—
64	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
65	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
68	C₅₃×#497	C₂²	1	2	yes	—
69	C₅₃×#497	C₂²	1	2	yes	—
70	C₅₃×#495	C₂²	1	2	yes	—
71	C₅₃×#491	C₂²	1	2	yes	—
72	C₅₃×#489	C₂²	1	2	yes	—
73	C₅₃×#488	C₂²	1	2	yes	—
74	C₅₃×#485	C₂²	1	2	yes	—
75	C₅₃×#484	C₂²	1	2	yes	—
76	C₅₃×#480	C₂²	1	2	yes	—
77	C₅₃×#479	C₂²	1	2	yes	—
78	C₅₃×#478	C₂²	1	2	yes	—
79	C₅₃×#477	C₂²	1	1	yes	characteristic
80	C₅₃×#477	C₂²	1	1	yes	characteristic
81	C₅₃×#477	C₂²	1	2	yes	—
82	C₅₃×#477	C₂²	1	1	yes	characteristic
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#470	C₂²	1	2	yes	—
85	C₅₃×#468	C₂²	1	2	yes	—
86	C₅₃×#467	C₂²	1	2	yes	—
87	C₅₃×#467	C₂²	1	2	yes	—
88	C₅₃×#466	C₂²	1	2	yes	—
89	C₅₃×#465	C₂²	1	2	yes	—
90	C₅₃×#464	C₂²	1	2	yes	—
91	C₅₃×#464	C₂²	1	2	yes	—
92	C₅₃×#464	C₂²	1	2	yes	—
93	C₅₃×#464	C₂²	1	2	yes	—
94	C₅₃×#463	C₂²	1	2	yes	—
95	C₅₃×#463	C₂²	1	2	yes	—
96	C₅₃×#462	C₂²	1	1	yes	characteristic
97	C₅₃×#462	C₂²	1	1	yes	characteristic
98	C₅₃×#462	C₂²	1	1	yes	characteristic
99	C₅₃×#462	C₂²	1	1	yes	characteristic
100	C₅₃×#462	C₂²	1	2	yes	—
101	C₅₃×#462	C₂²	1	2	yes	—
102	C₅₃×#462	C₂²	1	1	yes	characteristic
103	C₅₃×#462	C₂²	1	1	yes	characteristic
104	C₅₃×#462	C₂²	1	2	yes	—
105	C₅₃×#461	C₂²	1	1	yes	characteristic
106	C₅₃×#461	C₂²	1	1	yes	characteristic
107	C₅₃×#460	C₂²	1	1	yes	characteristic
108	C₅₃×#460	C₂²	1	1	yes	characteristic
109	C₅₃×#460	C₂²	1	1	yes	characteristic
110	C₅₃×#459	C₂²	1	1	yes	characteristic
111	C₅₃×#452	C₂²	1	2	yes	—
112	C₅₃×#452	C₂²	1	2	yes	—
113	C₅₃×#452	C₂²	1	2	yes	—
114	C₅₃×#452	C₂²	1	2	yes	—
115	C₅₃×#451	C₂²	1	2	yes	—
116	C₅₃×#451	C₂²	1	2	yes	—
117	C₅₃×#449	C₂²	1	2	yes	—
118	C₅₃×#448	C₂²	1	2	yes	—
119	C₅₃×#448	C₂²	1	2	yes	—
120	C₅₃×#446	C₂²	1	2	yes	—
121	C₅₃×#441	C₂²	1	2	yes	—
122	C₅₃×#440	C₂²	1	2	yes	—
123	C₅₃×#440	C₂²	1	2	yes	—
124	C₅₃×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
126	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
127	C₅₃×#435	C₂²	1	2	yes	—
128	C₅₃×#435	C₂²	1	2	yes	—
129	C₈×D₄×C₅₃	C₂²	1	2	yes	—
130	C₅₃×#432	C₂²	1	1	yes	characteristic
131	C₅₃×#432	C₂²	1	1	yes	characteristic
132	C₅₃×#431	C₂²	1	1	yes	characteristic
133	C₅₃×#423	C₂²	1	1	yes	characteristic
134	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
136	C₅₃×#417	C₂²	1	2	yes	—
137	C₅₃×#416	C₂²	1	2	yes	—
138	C₂×#103×C₅₃	C₂²	1	2	yes	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
148	#137×C₅₃	—	4	4	no	—
149	#135×C₅₃	—	4	4	no	—
150	C₂×Q₁₆×C₅₃	—	4	4	no	—
151	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
165	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₅₃	—	2	1	no	—
167	C₄⋊Q₈×C₅₃	—	2	1	no	—
168	C₄⋊Q₈×C₅₃	—	2	1	no	—
169	C₄⋊Q₈×C₅₃	—	2	1	no	—
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
176	#127×C₅₃	C₂³	1	1	yes	characteristic
177	#126×C₅₃	—	2	1	no	—
178	#126×C₅₃	—	2	1	no	—
179	#126×C₅₃	—	2	2	no	—
180	#126×C₅₃	—	2	2	no	—
181	#126×C₅₃	—	2	1	no	—
182	#126×C₅₃	—	2	1	no	—
183	#126×C₅₃	—	2	1	no	—
184	#126×C₅₃	—	2	1	no	—
185	#125×C₅₃	—	2	1	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	—	2	1	no	—
188	#125×C₅₃	—	2	1	no	—
189	#125×C₅₃	—	2	1	no	—
190	#125×C₅₃	—	2	1	no	—
191	#125×C₅₃	—	2	1	no	—
192	#125×C₅₃	C₂³	1	1	yes	characteristic
193	#125×C₅₃	C₂³	1	1	yes	characteristic
194	#124×C₅₃	—	2	1	no	—
195	#124×C₅₃	—	2	1	no	—
196	#124×C₅₃	—	2	2	no	—
197	#124×C₅₃	—	2	2	no	—
198	#124×C₅₃	—	2	1	no	—
199	#124×C₅₃	C₂³	1	2	yes	—
200	#124×C₅₃	C₂³	1	2	yes	—
201	#124×C₅₃	C₂³	1	1	yes	characteristic
202	#124×C₅₃	C₂³	1	1	yes	characteristic
203	#123×C₅₃	—	2	1	no	—
204	#123×C₅₃	—	2	1	no	—
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	1	no	—
208	#123×C₅₃	—	2	1	no	—
209	#123×C₅₃	—	2	1	no	—
210	#123×C₅₃	—	2	1	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	2	no	—
215	C₂²⋊Q₈×C₅₃	—	2	2	no	—
216	C₂²⋊Q₈×C₅₃	—	2	1	no	—
217	C₂²⋊Q₈×C₅₃	—	2	1	no	—
218	C₂²⋊Q₈×C₅₃	—	2	1	no	—
219	C₂²⋊Q₈×C₅₃	—	2	2	no	—
220	C₂²⋊Q₈×C₅₃	—	2	1	no	—
221	C₂²⋊Q₈×C₅₃	—	2	1	no	—
222	C₂²⋊Q₈×C₅₃	—	2	1	no	—
223	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
233	#121×C₅₃	—	2	2	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	1	no	—
236	#121×C₅₃	—	2	1	no	—
237	#121×C₅₃	—	2	1	no	—
238	#121×C₅₃	—	2	1	no	—
239	#121×C₅₃	C₂³	1	1	yes	characteristic
240	#121×C₅₃	C₂³	1	1	yes	characteristic
241	#121×C₅₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₃	—	2	1	no	—
243	C₄×Q₈×C₅₃	—	2	1	no	—
244	C₄×Q₈×C₅₃	—	2	1	no	—
245	C₄×Q₈×C₅₃	—	2	1	no	—
246	C₄×Q₈×C₅₃	—	2	1	no	—
247	C₄×Q₈×C₅₃	—	2	1	no	—
248	C₄×Q₈×C₅₃	—	2	1	no	—
249	C₄×Q₈×C₅₃	—	2	1	no	—
250	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
251	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
261	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	2	no	—
265	C₄×D₄×C₅₃	—	2	2	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	—	2	1	no	—
272	C₄×D₄×C₅₃	—	2	1	no	—
273	C₄×D₄×C₅₃	—	2	1	no	—
274	C₄×D₄×C₅₃	—	2	1	no	—
275	C₄×D₄×C₅₃	—	2	1	no	—
276	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
277	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
278	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
279	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₅₃	C₂³	1	2	yes	—
282	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
285	#117×C₅₃	—	2	1	no	—
286	#117×C₅₃	—	2	2	no	—
287	#117×C₅₃	—	2	1	no	—
288	#117×C₅₃	—	2	1	no	—
289	#117×C₅₃	—	2	1	no	—
290	#117×C₅₃	—	2	1	no	—
291	#117×C₅₃	—	2	1	no	—
292	#117×C₅₃	—	2	1	no	—
293	#117×C₅₃	—	2	1	no	—
294	#117×C₅₃	—	2	1	no	—
295	#117×C₅₃	D₄	1	1	yes	characteristic
296	#117×C₅₃	D₄	1	1	yes	characteristic
297	#117×C₅₃	D₄	1	1	yes	characteristic
298	#117×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
301	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
303	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
304	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₅₃	—	2	1	no	—
307	C₂×C₄²×C₅₃	—	2	1	no	—
308	C₂×C₄²×C₅₃	—	2	1	no	—
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	#107×C₅₃	C₂³	1	2	yes	—
313	#107×C₅₃	C₂³	1	2	yes	—
314	#107×C₅₃	C₂³	1	2	yes	—
315	#106×C₅₃	C₂³	1	2	yes	—
316	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
320	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
321	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
323	#103×C₅₃	C₂³	1	2	yes	—
324	#103×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#103×C₅₃	C₂³	1	2	yes	—
327	#103×C₅₃	C₂³	1	2	yes	—
328	#103×C₅₃	C₂³	1	2	yes	—
329	#103×C₅₃	C₂³	1	2	yes	—
330	#103×C₅₃	C₂³	1	2	yes	—
331	#103×C₅₃	C₂³	1	2	yes	—
332	#103×C₅₃	C₂³	1	2	yes	—
333	#103×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	—
338	#102×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
342	#97×C₅₃	C₂³	1	2	yes	—
343	#97×C₅₃	C₂³	1	2	yes	—
344	C₄×C₈×C₅₃	C₂³	1	2	yes	—
345	#41×C₅₃	—	2	2	no	—
346	#41×C₅₃	—	4	2	no	—
347	#41×C₅₃	—	4	1	no	—
348	#41×C₅₃	—	4	4	no	—
349	#41×C₅₃	—	4	2	no	—
350	#41×C₅₃	—	4	2	no	—
351	#41×C₅₃	—	4	2	no	—
352	#41×C₅₃	—	4	2	no	—
353	#41×C₅₃	—	4	4	no	—
354	C₂×Q₈×C₅₃	—	2	1	no	—
355	C₂×Q₈×C₅₃	—	2	1	no	—
356	C₂×Q₈×C₅₃	—	2	1	no	—
357	C₂×Q₈×C₅₃	—	2	1	no	—
358	C₂×Q₈×C₅₃	—	2	2	no	—
359	C₂×Q₈×C₅₃	—	2	2	no	—
360	C₂×Q₈×C₅₃	—	2	2	no	—
361	C₂×Q₈×C₅₃	—	4	1	no	—
362	C₂×Q₈×C₅₃	—	4	1	no	—
363	C₂×Q₈×C₅₃	—	4	2	no	—
364	C₂×Q₈×C₅₃	—	4	2	no	—
365	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
368	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	1	no	—
373	C₂×D₄×C₅₃	—	2	1	no	—
374	C₂×D₄×C₅₃	—	2	1	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	1	no	—
378	C₂×D₄×C₅₃	—	2	1	no	—
379	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
383	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	Q₁₆×C₅₃	—	2	4	no	—
405	Q₁₆×C₅₃	—	2	4	no	—
406	Q₁₆×C₅₃	—	4	2	no	—
407	Q₁₆×C₅₃	—	4	2	no	—
408	Q₁₆×C₅₃	—	4	2	no	—
409	Q₁₆×C₅₃	—	4	2	no	—
410	SD₁₆×C₅₃	—	2	4	no	—
411	SD₁₆×C₅₃	—	4	2	no	—
412	SD₁₆×C₅₃	—	4	2	no	—
413	SD₁₆×C₅₃	—	4	2	no	—
414	SD₁₆×C₅₃	—	4	2	no	—
415	D₈×C₅₃	—	4	2	no	—
416	M₁₆×C₅₃	—	4	2	no	—
417	C₂×C₈×C₅₃	—	4	2	no	—
418	C₂×C₈×C₅₃	—	4	2	no	—
419	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
422	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	1	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	1	no	—
436	C₄⋊C₄×C₅₃	—	2	1	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	1	no	—
439	C₄⋊C₄×C₅₃	—	2	1	no	—
440	C₄⋊C₄×C₅₃	—	2	1	no	—
441	C₄⋊C₄×C₅₃	—	2	1	no	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	1	no	—
444	C₄⋊C₄×C₅₃	—	2	1	no	—
445	C₄⋊C₄×C₅₃	—	2	1	no	—
446	C₄⋊C₄×C₅₃	—	2	1	no	—
447	C₄⋊C₄×C₅₃	—	2	1	no	—
448	C₄⋊C₄×C₅₃	—	2	1	no	—
449	C₄⋊C₄×C₅₃	—	2	1	no	—
450	C₄⋊C₄×C₅₃	—	2	1	no	—
451	C₄⋊C₄×C₅₃	—	2	1	no	—
452	C₄⋊C₄×C₅₃	—	2	1	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
456	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	1	no	—
472	C₂²⋊C₄×C₅₃	—	2	1	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	1	no	—
476	C₂²⋊C₄×C₅₃	—	2	1	no	—
477	C₂²⋊C₄×C₅₃	—	2	1	no	—
478	C₂²⋊C₄×C₅₃	—	2	1	no	—
479	C₂²⋊C₄×C₅₃	—	2	1	no	—
480	C₂²⋊C₄×C₅₃	—	2	1	no	—
481	C₂²⋊C₄×C₅₃	—	2	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	1	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₅₃	—	2	1	no	—
494	C₄²×C₅₃	—	2	1	no	—
495	C₄²×C₅₃	—	2	1	no	—
496	C₄²×C₅₃	—	2	1	no	—
497	C₄²×C₅₃	—	2	1	no	—
498	C₄²×C₅₃	—	2	1	no	—
499	C₄²×C₅₃	—	2	1	no	—
500	C₄²×C₅₃	—	2	1	no	—
501	C₄²×C₅₃	—	2	1	no	—
502	C₄²×C₅₃	—	2	2	no	—
503	C₄²×C₅₃	—	2	2	no	—
504	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
505	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
507	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
510	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
513	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂³×C₅₃	—	2	2	no	—
515	C₂³×C₅₃	—	2	1	no	—
516	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
518	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
519	Q₈×C₅₃	—	2	1	no	—
520	Q₈×C₅₃	—	2	1	no	—
521	Q₈×C₅₃	—	2	1	no	—
522	Q₈×C₅₃	—	2	2	no	—
523	Q₈×C₅₃	—	2	2	no	—
524	Q₈×C₅₃	—	2	2	no	—
525	Q₈×C₅₃	—	2	2	no	—
526	Q₈×C₅₃	—	2	1	no	—
527	Q₈×C₅₃	—	2	1	no	—
528	Q₈×C₅₃	—	4	1	no	—
529	Q₈×C₅₃	—	4	2	no	—
530	Q₈×C₅₃	—	4	2	no	—
531	Q₈×C₅₃	—	4	2	no	—
532	Q₈×C₅₃	—	4	2	no	—
533	Q₈×C₅₃	—	8	2	no	—
534	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
535	D₄×C₅₃	—	2	2	no	—
536	D₄×C₅₃	—	2	2	no	—
537	D₄×C₅₃	—	2	1	no	—
538	D₄×C₅₃	—	2	2	no	—
539	D₄×C₅₃	—	2	2	no	—
540	D₄×C₅₃	—	2	1	no	—
541	D₄×C₅₃	—	4	1	no	—
542	D₄×C₅₃	—	4	2	no	—
543	D₄×C₅₃	—	4	2	no	—
544	D₄×C₅₃	—	4	2	no	—
545	D₄×C₅₃	—	4	4	no	—
546	D₄×C₅₃	—	4	2	no	—
547	D₄×C₅₃	—	4	2	no	—
548	D₄×C₅₃	—	8	2	no	—
549	D₄×C₅₃	—	8	2	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	2	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	2	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	2	no	—
563	C₂×C₄×C₅₃	—	2	2	no	—
564	C₂×C₄×C₅₃	—	2	2	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	4	1	no	—
571	C₂×C₄×C₅₃	—	4	1	no	—
572	C₂×C₄×C₅₃	—	4	2	no	—
573	C₂×C₄×C₅₃	—	4	2	no	—
574	C₂×C₄×C₅₃	—	4	2	no	—
575	C₂×C₄×C₅₃	—	4	4	no	—
576	C₂×C₄×C₅₃	—	4	2	no	—
577	C₂×C₄×C₅₃	—	4	2	no	—
578	C₂×C₄×C₅₃	—	4	2	no	—
579	C₂×C₄×C₅₃	—	4	2	no	—
580	C₂×C₄×C₅₃	—	8	2	no	—
581	C₂×C₄×C₅₃	—	8	2	no	—
582	C₂×C₄×C₅₃	—	8	2	no	—
583	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
595	C₈×C₅₃	—	2	2	no	—
596	C₈×C₅₃	—	2	2	no	—
597	C₈×C₅₃	—	2	2	no	—
598	C₈×C₅₃	—	2	2	no	—
599	#61982	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
600	C₂²×C₅₃	—	2	1	no	—
601	C₂²×C₅₃	—	2	1	no	—
602	C₂²×C₅₃	—	2	1	no	—
603	C₂²×C₅₃	—	2	1	no	—
604	C₂²×C₅₃	—	2	1	no	—
605	C₂²×C₅₃	—	2	1	no	—
606	C₂²×C₅₃	—	2	1	no	—
607	C₂²×C₅₃	—	2	1	no	—
608	C₂²×C₅₃	—	4	1	no	—
609	C₂²×C₅₃	—	4	2	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	4	1	no	—
613	C₂²×C₅₃	—	4	2	no	—
614	C₂²×C₅₃	#575	1	2	yes	—
615	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₅₃	—	2	1	no	—
617	C₄×C₅₃	—	2	1	no	—
618	C₄×C₅₃	—	2	1	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	2	1	no	—
621	C₄×C₅₃	—	2	1	no	—
622	C₄×C₅₃	—	2	1	no	—
623	C₄×C₅₃	—	2	1	no	—
624	C₄×C₅₃	—	2	1	no	—
625	C₄×C₅₃	—	2	1	no	—
626	C₄×C₅₃	—	2	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	2	no	—
630	C₄×C₅₃	—	4	2	no	—
631	C₄×C₅₃	—	4	1	no	—
632	C₄×C₅₃	—	4	2	no	—
633	C₄×C₅₃	—	4	1	no	—
634	C₄×C₅₃	—	4	1	no	—
635	C₄×C₅₃	—	4	1	no	—
636	C₄×C₅₃	#578	1	2	yes	—
637	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
638	C₄×C₅₃	#585	1	1	yes	characteristic
639	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3402	C₂×C₅₃	1	2	yes	complemented
642	#3377	C₂×C₅₃	1	2	yes	complemented
643	#3315	C₂×C₅₃	1	2	yes	complemented
644	#3308	C₂×C₅₃	1	2	yes	complemented
645	#3300	C₂×C₅₃	1	2	yes	complemented
646	#3285	C₂×C₅₃	1	2	yes	complemented
647	#3270	C₂×C₅₃	1	2	yes	complemented
648	#3269	C₂×C₅₃	1	2	yes	complemented
649	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
650	#3249	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3218	C₂×C₅₃	1	1	yes	characteristic, complemented
653	#3216	C₂×C₅₃	1	1	yes	characteristic, complemented
654	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#3112	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#3104	C₂×C₅₃	1	1	yes	characteristic, complemented
658	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
659	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
660	C₂×#462	C₂×C₅₃	1	1	yes	characteristic, complemented
661	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
662	C₂×C₅₃	—	2	2	no	—
663	C₂×C₅₃	—	4	1	no	—
664	C₂×C₅₃	—	4	1	no	—
665	C₂×C₅₃	—	8	1	no	—
666	C₂×C₅₃	—	8	2	no	—
667	C₂×C₅₃	#3488	1	1	yes	characteristic
668	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
669	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
670	C₂×#137	C₂²×C₅₃	1	2	yes	—
671	C₂×#135	C₂²×C₅₃	1	2	yes	—
672	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	—
673	#557	C₂²×C₅₃	1	1	yes	characteristic
674	#556	—	2	1	no	—
675	#556	C₂²×C₅₃	1	2	yes	—
676	#556	C₂²×C₅₃	1	1	yes	characteristic
677	#555	—	2	1	no	—
678	#554	—	2	1	no	—
679	#553	—	2	1	no	—
680	#553	—	2	1	no	—
681	#552	—	2	1	no	—
682	#552	—	2	1	no	—
683	#552	C₂²×C₅₃	1	1	yes	characteristic
684	#552	C₂²×C₅₃	1	1	yes	characteristic
685	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
686	#548	C₂²×C₅₃	1	1	yes	characteristic
687	#548	C₂²×C₅₃	1	1	yes	characteristic
688	#548	C₂²×C₅₃	1	2	yes	—
689	#548	C₂²×C₅₃	1	2	yes	—
690	#547	—	2	1	no	—
691	#547	C₂²×C₅₃	1	2	yes	—
692	#547	C₂²×C₅₃	1	1	yes	characteristic
693	#542	—	2	1	no	—
694	#542	—	2	1	no	—
695	#537	—	2	1	no	—
696	#533	—	2	1	no	—
697	#533	C₂²×C₅₃	1	1	yes	characteristic
698	#533	C₂²×C₅₃	1	1	yes	characteristic
699	#533	C₂²×C₅₃	1	1	yes	characteristic
700	#532	C₂²×C₅₃	1	1	yes	characteristic
701	#532	C₂²×C₅₃	1	1	yes	characteristic
702	#532	C₂²×C₅₃	1	1	yes	characteristic
703	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
704	#529	—	2	1	no	—
705	#529	—	2	1	no	—
706	#529	C₂²×C₅₃	1	1	yes	characteristic
707	#529	C₂²×C₅₃	1	1	yes	characteristic
708	#520	—	2	1	no	—
709	C₄×#41	—	2	1	no	—
710	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
711	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
712	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
713	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
714	#497	C₂²×C₅₃	1	2	yes	—
715	#497	C₂²×C₅₃	1	2	yes	—
716	#495	C₂²×C₅₃	1	2	yes	—
717	#491	C₂²×C₅₃	1	2	yes	—
718	#489	C₂²×C₅₃	1	2	yes	—
719	#488	C₂²×C₅₃	1	2	yes	—
720	#485	C₂²×C₅₃	1	2	yes	—
721	#484	C₂²×C₅₃	1	2	yes	—
722	#480	C₂²×C₅₃	1	2	yes	—
723	#479	C₂²×C₅₃	1	2	yes	—
724	#478	C₂²×C₅₃	1	2	yes	—
725	#477	C₂²×C₅₃	1	1	yes	characteristic
726	#477	C₂²×C₅₃	1	1	yes	characteristic
727	#477	C₂²×C₅₃	1	1	yes	characteristic
728	#477	C₂²×C₅₃	1	2	yes	—
729	#476	C₂²×C₅₃	1	1	yes	characteristic
730	#470	C₂²×C₅₃	1	2	yes	—
731	#468	C₂²×C₅₃	1	2	yes	—
732	#467	C₂²×C₅₃	1	2	yes	—
733	#467	C₂²×C₅₃	1	2	yes	—
734	#466	C₂²×C₅₃	1	2	yes	—
735	#465	C₂²×C₅₃	1	2	yes	—
736	#464	C₂²×C₅₃	1	2	yes	—
737	#464	C₂²×C₅₃	1	2	yes	—
738	#464	C₂²×C₅₃	1	2	yes	—
739	#464	C₂²×C₅₃	1	2	yes	—
740	#463	C₂²×C₅₃	1	2	yes	—
741	#463	C₂²×C₅₃	1	2	yes	—
742	#462	C₂²×C₅₃	1	1	yes	characteristic
743	#462	C₂²×C₅₃	1	1	yes	characteristic
744	#462	C₂²×C₅₃	1	1	yes	characteristic
745	#462	C₂²×C₅₃	1	2	yes	—
746	#462	C₂²×C₅₃	1	2	yes	—
747	#462	C₂²×C₅₃	1	2	yes	—
748	#462	C₂²×C₅₃	1	1	yes	characteristic
749	#462	C₂²×C₅₃	1	1	yes	characteristic
750	#462	C₂²×C₅₃	1	1	yes	characteristic
751	#461	C₂²×C₅₃	1	1	yes	characteristic
752	#461	C₂²×C₅₃	1	1	yes	characteristic
753	#460	C₂²×C₅₃	1	1	yes	characteristic
754	#460	C₂²×C₅₃	1	1	yes	characteristic
755	#460	C₂²×C₅₃	1	1	yes	characteristic
756	#459	C₂²×C₅₃	1	1	yes	characteristic
757	#452	C₂²×C₅₃	1	2	yes	—
758	#452	C₂²×C₅₃	1	2	yes	—
759	#452	C₂²×C₅₃	1	2	yes	—
760	#452	C₂²×C₅₃	1	2	yes	—
761	#451	C₂²×C₅₃	1	2	yes	—
762	#451	C₂²×C₅₃	1	2	yes	—
763	#449	C₂²×C₅₃	1	2	yes	—
764	#448	C₂²×C₅₃	1	2	yes	—
765	#448	C₂²×C₅₃	1	2	yes	—
766	#446	C₂²×C₅₃	1	2	yes	—
767	#441	C₂²×C₅₃	1	2	yes	—
768	#440	C₂²×C₅₃	1	2	yes	—
769	#440	C₂²×C₅₃	1	2	yes	—
770	#440	C₂²×C₅₃	1	2	yes	—
771	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
772	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
773	#435	C₂²×C₅₃	1	2	yes	—
774	#435	C₂²×C₅₃	1	2	yes	—
775	C₈×D₄	C₂²×C₅₃	1	2	yes	—
776	#432	C₂²×C₅₃	1	1	yes	characteristic
777	#432	C₂²×C₅₃	1	1	yes	characteristic
778	#431	C₂²×C₅₃	1	1	yes	characteristic
779	#423	C₂²×C₅₃	1	1	yes	characteristic
780	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
781	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
782	#417	C₂²×C₅₃	1	2	yes	—
783	#416	C₂²×C₅₃	1	2	yes	—
784	C₂×#103	C₂²×C₅₃	1	2	yes	—
785	C₅₃	#61982	1	1	yes	characteristic, direct product factor, Sylow
786	C₂×#41	—	2	1	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
789	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×#41	C₂³×C₅₃	1	2	yes	—
791	C₂×#41	C₂³×C₅₃	1	2	yes	—
792	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
793	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
794	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
795	#137	—	4	4	no	—
796	#135	—	4	4	no	—
797	C₂×Q₁₆	—	4	4	no	—
798	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
800	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
802	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
803	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
804	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
805	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
806	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
808	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
809	C₂×D₈	C₂³×C₅₃	1	2	yes	—
810	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
811	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
812	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
813	C₄⋊Q₈	—	2	1	no	—
814	C₄⋊Q₈	—	2	1	no	—
815	C₄⋊Q₈	—	2	1	no	—
816	C₄⋊Q₈	—	2	1	no	—
817	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
819	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
820	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
821	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
822	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
823	#127	C₂³×C₅₃	1	1	yes	characteristic
824	#126	—	2	1	no	—
825	#126	—	2	1	no	—
826	#126	—	2	2	no	—
827	#126	—	2	2	no	—
828	#126	—	2	1	no	—
829	#126	—	2	1	no	—
830	#126	—	2	1	no	—
831	#126	—	2	1	no	—
832	#125	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	—	2	1	no	—
836	#125	—	2	1	no	—
837	#125	—	2	1	no	—
838	#125	—	2	1	no	—
839	#125	C₂³×C₅₃	1	1	yes	characteristic
840	#125	C₂³×C₅₃	1	1	yes	characteristic
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	—	2	2	no	—
844	#124	—	2	2	no	—
845	#124	—	2	1	no	—
846	#124	C₂³×C₅₃	1	1	yes	characteristic
847	#124	C₂³×C₅₃	1	1	yes	characteristic
848	#124	C₂³×C₅₃	1	2	yes	—
849	#124	C₂³×C₅₃	1	2	yes	—
850	#123	—	2	1	no	—
851	#123	—	2	1	no	—
852	#123	—	2	1	no	—
853	#123	—	2	1	no	—
854	#123	—	2	1	no	—
855	#123	—	2	1	no	—
856	#123	—	2	2	no	—
857	#123	—	2	2	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	2	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	1	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	2	no	—
867	C₂²⋊Q₈	—	2	2	no	—
868	C₂²⋊Q₈	—	2	1	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
871	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
873	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
874	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	2	no	—
879	#121	—	2	2	no	—
880	#121	—	2	2	no	—
881	#121	—	2	1	no	—
882	#121	—	2	1	no	—
883	#121	—	2	1	no	—
884	#121	—	2	1	no	—
885	#121	—	2	1	no	—
886	#121	C₂³×C₅₃	1	1	yes	characteristic
887	#121	C₂³×C₅₃	1	1	yes	characteristic
888	#121	C₂³×C₅₃	1	2	yes	—
889	C₄×Q₈	—	2	1	no	—
890	C₄×Q₈	—	2	1	no	—
891	C₄×Q₈	—	2	1	no	—
892	C₄×Q₈	—	2	1	no	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	—	2	1	no	—
895	C₄×Q₈	—	2	1	no	—
896	C₄×Q₈	—	2	1	no	—
897	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
898	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
899	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
900	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
903	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
904	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
905	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
906	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
907	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
908	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	—	2	2	no	—
917	C₄×D₄	—	2	2	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	1	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	1	no	—
923	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
924	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
925	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
926	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
928	C₄×D₄	C₂³×C₅₃	1	2	yes	—
929	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
930	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
931	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
932	#117	—	2	1	no	—
933	#117	—	2	1	no	—
934	#117	—	2	1	no	—
935	#117	—	2	1	no	—
936	#117	—	2	2	no	—
937	#117	—	2	1	no	—
938	#117	—	2	1	no	—
939	#117	—	2	1	no	—
940	#117	—	2	1	no	—
941	#117	—	2	1	no	—
942	#117	D₄×C₅₃	1	1	yes	characteristic
943	#117	D₄×C₅₃	1	1	yes	characteristic
944	#117	D₄×C₅₃	1	1	yes	characteristic
945	#117	C₂³×C₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	—	2	1	no	—
947	C₂×C₄⋊C₄	—	2	1	no	—
948	C₂×C₄⋊C₄	—	2	1	no	—
949	C₂×C₄⋊C₄	—	2	1	no	—
950	C₂×C₄⋊C₄	—	2	2	no	—
951	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₂×C₄²	—	2	1	no	—
954	C₂×C₄²	—	2	1	no	—
955	C₂×C₄²	—	2	1	no	—
956	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
957	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
958	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
959	#107	C₂³×C₅₃	1	2	yes	—
960	#107	C₂³×C₅₃	1	2	yes	—
961	#107	C₂³×C₅₃	1	2	yes	—
962	#106	C₂³×C₅₃	1	2	yes	—
963	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
964	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
965	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
966	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
967	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
968	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
969	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
970	#103	C₂³×C₅₃	1	2	yes	—
971	#103	C₂³×C₅₃	1	2	yes	—
972	#103	C₂³×C₅₃	1	2	yes	—
973	#103	C₂³×C₅₃	1	2	yes	—
974	#103	C₂³×C₅₃	1	2	yes	—
975	#103	C₂³×C₅₃	1	2	yes	—
976	#103	C₂³×C₅₃	1	2	yes	—
977	#103	C₂³×C₅₃	1	2	yes	—
978	#103	C₂³×C₅₃	1	2	yes	—
979	#103	C₂³×C₅₃	1	2	yes	—
980	#103	C₂³×C₅₃	1	2	yes	—
981	#102	C₂³×C₅₃	1	2	yes	—
982	#102	C₂³×C₅₃	1	2	yes	—
983	#102	C₂³×C₅₃	1	2	yes	—
984	#102	C₂³×C₅₃	1	2	yes	—
985	#102	C₂³×C₅₃	1	2	yes	—
986	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
987	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
988	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
989	#97	C₂³×C₅₃	1	2	yes	—
990	#97	C₂³×C₅₃	1	2	yes	—
991	C₄×C₈	C₂³×C₅₃	1	2	yes	—
992	#41	—	2	2	no	—
993	#41	—	4	2	no	—
994	#41	—	4	1	no	—
995	#41	—	4	4	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	#41	—	4	2	no	—
999	#41	—	4	2	no	—
1000	#41	—	4	4	no	—
1001	C₂×Q₈	—	2	1	no	—
1002	C₂×Q₈	—	2	1	no	—
1003	C₂×Q₈	—	2	1	no	—
1004	C₂×Q₈	—	2	1	no	—
1005	C₂×Q₈	—	2	2	no	—
1006	C₂×Q₈	—	2	2	no	—
1007	C₂×Q₈	—	2	2	no	—
1008	C₂×Q₈	—	4	1	no	—
1009	C₂×Q₈	—	4	1	no	—
1010	C₂×Q₈	—	4	2	no	—
1011	C₂×Q₈	—	4	2	no	—
1012	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1013	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1014	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1015	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1029	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1030	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1047	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1051	Q₁₆	—	2	4	no	—
1052	Q₁₆	—	2	4	no	—
1053	Q₁₆	—	4	2	no	—
1054	Q₁₆	—	4	2	no	—
1055	Q₁₆	—	4	2	no	—
1056	Q₁₆	—	4	2	no	—
1057	SD₁₆	—	2	4	no	—
1058	SD₁₆	—	4	2	no	—
1059	SD₁₆	—	4	2	no	—
1060	SD₁₆	—	4	2	no	—
1061	SD₁₆	—	4	2	no	—
1062	D₈	—	4	2	no	—
1063	M₁₆	—	4	2	no	—
1064	C₂×C₈	—	4	2	no	—
1065	C₂×C₈	—	4	2	no	—
1066	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1067	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1068	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1069	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	2	no	—
1101	C₄⋊C₄	—	2	2	no	—
1102	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1104	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1105	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1108	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1112	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1135	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1136	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1137	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1138	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1139	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1140	C₄²	—	2	1	no	—
1141	C₄²	—	2	1	no	—
1142	C₄²	—	2	1	no	—
1143	C₄²	—	2	1	no	—
1144	C₄²	—	2	1	no	—
1145	C₄²	—	2	1	no	—
1146	C₄²	—	2	1	no	—
1147	C₄²	—	2	1	no	—
1148	C₄²	—	2	1	no	—
1149	C₄²	—	2	2	no	—
1150	C₄²	—	2	2	no	—
1151	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1152	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1153	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1154	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1155	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1156	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1157	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1158	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1159	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1160	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1161	C₂³	—	2	1	no	—
1162	C₂³	—	2	2	no	—
1163	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1164	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1165	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1166	Q₈	—	2	1	no	—
1167	Q₈	—	2	1	no	—
1168	Q₈	—	2	2	no	—
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	1	no	—
1171	Q₈	—	2	1	no	—
1172	Q₈	—	2	2	no	—
1173	Q₈	—	2	1	no	—
1174	Q₈	—	2	2	no	—
1175	Q₈	—	4	1	no	—
1176	Q₈	—	4	2	no	—
1177	Q₈	—	4	2	no	—
1178	Q₈	—	4	2	no	—
1179	Q₈	—	4	2	no	—
1180	Q₈	—	8	2	no	—
1181	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1182	D₄	—	2	2	no	—
1183	D₄	—	2	2	no	—
1184	D₄	—	2	1	no	—
1185	D₄	—	2	2	no	—
1186	D₄	—	2	1	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	4	1	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	2	no	—
1192	D₄	—	4	4	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	8	2	no	—
1196	D₄	—	8	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	2	no	—
1217	C₂×C₄	—	4	1	no	—
1218	C₂×C₄	—	4	1	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	4	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	2	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	—	4	2	no	—
1227	C₂×C₄	—	8	2	no	—
1228	C₂×C₄	—	8	2	no	—
1229	C₂×C₄	—	8	2	no	—
1230	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1235	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1236	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1237	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1238	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1239	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1240	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1241	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1242	C₈	—	2	2	no	—
1243	C₈	—	2	2	no	—
1244	C₈	—	2	2	no	—
1245	C₈	—	2	2	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	1	no	—
1252	C₂²	—	2	1	no	—
1253	C₂²	—	2	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	C₅₃×#575	1	2	yes	—
1261	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	2	no	—
1276	C₄	—	4	2	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	C₅₃×#578	1	2	yes	—
1283	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1284	C₄	C₅₃×#585	1	1	yes	characteristic
1285	C₂	—	2	2	no	—
1286	C₂	—	4	1	no	—
1287	C₂	—	4	1	no	—
1288	C₂	—	8	1	no	—
1289	C₂	—	8	2	no	—
1290	C₂	C₅₃×#3488	1	1	yes	characteristic
1291	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1292	C₂	C₂×C₅₃×#578	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×#3511	C₂	semidirect
2. C₅₃×#3482	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3377	C₂	semidirect
5. C₅₃×#3315	C₂	semidirect
6. C₅₃×#3308	C₂	semidirect
7. C₅₃×#3300	C₂	semidirect
8. C₅₃×#3285	C₂	semidirect
9. C₅₃×#3270	C₂	semidirect
10. C₅₃×#3269	C₂	semidirect
11. C₅₃×#3252	C₂	semidirect
12. C₅₃×#3249	C₂	semidirect
13. C₅₃×#3247	C₂	semidirect
14. C₅₃×#3218	C₂	semidirect
15. C₅₃×#3216	C₂	semidirect
16. C₅₃×#3212	C₂	semidirect
17. C₅₃×#3116	C₂	semidirect
18. C₅₃×#3112	C₂	semidirect
19. C₅₃×#3104	C₂	semidirect
20. C₅₃×#3037	C₂	semidirect
21. C₅₃×#3035	C₂	semidirect
22. C₂×C₅₃×#462	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
599. #61982	C₅₃	direct (N × H)
639. #3511	C₂×C₅₃	semidirect
640. #3482	C₂×C₅₃	semidirect
641. #3402	C₂×C₅₃	semidirect
642. #3377	C₂×C₅₃	semidirect
643. #3315	C₂×C₅₃	semidirect
644. #3308	C₂×C₅₃	semidirect
645. #3300	C₂×C₅₃	semidirect
646. #3285	C₂×C₅₃	semidirect
647. #3270	C₂×C₅₃	semidirect
648. #3269	C₂×C₅₃	semidirect
649. #3252	C₂×C₅₃	semidirect
650. #3249	C₂×C₅₃	semidirect
651. #3247	C₂×C₅₃	semidirect
652. #3218	C₂×C₅₃	semidirect
653. #3216	C₂×C₅₃	semidirect
654. #3212	C₂×C₅₃	semidirect
655. #3116	C₂×C₅₃	semidirect
656. #3112	C₂×C₅₃	semidirect
657. #3104	C₂×C₅₃	semidirect
658. #3037	C₂×C₅₃	semidirect
659. #3035	C₂×C₅₃	semidirect
660. C₂×#462	C₂×C₅₃	semidirect
661. #2990	C₂×C₅₃	semidirect
785. C₅₃	#61982	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×#3511	2
C₅₃×#3482	2
C₅₃×#3402	2
C₅₃×#3377	2
C₅₃×#3315	2
C₅₃×#3308	2
C₅₃×#3300	2
C₅₃×#3285	2
C₅₃×#3270	2
C₅₃×#3269	2
C₅₃×#3252	2
C₅₃×#3249	2
C₅₃×#3247	2
C₅₃×#3218	2
C₅₃×#3216	2
C₅₃×#3212	2
C₅₃×#3116	2
C₅₃×#3112	2
C₅₃×#3104	2
C₅₃×#3037	2
C₅₃×#3035	2
C₂×C₅₃×#462	2
C₅₃×#2990	2
#61982	53

Subgroups — C53×#61982 #27269494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61982 #27269494