Subgroups — C₅₃×#61280 #27268792

Order 13568.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3337	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#137×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#559	—	2	1	no	—
28	C₅₃×#557	—	2	1	no	—
29	C₅₃×#556	—	2	1	no	—
30	C₅₃×#556	—	2	1	no	—
31	C₅₃×#556	C₂²	1	2	yes	—
32	C₅₃×#554	C₂²	1	2	yes	—
33	C₅₃×#553	—	2	2	no	—
34	C₅₃×#553	—	2	2	no	—
35	C₅₃×#553	C₂²	1	2	yes	—
36	C₅₃×#553	C₂²	1	2	yes	—
37	C₅₃×#552	C₂²	1	2	yes	—
38	C₅₃×#552	C₂²	1	2	yes	—
39	C₅₃×#552	C₂²	1	2	yes	—
40	C₅₃×#552	C₂²	1	2	yes	—
41	C₅₃×#541	—	2	1	no	—
42	C₅₃×#540	—	2	1	no	—
43	C₅₃×#539	—	2	2	no	—
44	C₅₃×#537	C₂²	1	1	yes	characteristic
45	C₅₃×#537	C₂²	1	1	yes	characteristic
46	C₅₃×#536	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	1	yes	characteristic
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#529	—	2	1	no	—
52	C₅₃×#529	—	2	2	no	—
53	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#520	C₂²	1	1	yes	characteristic
55	C₅₃×#520	C₂²	1	1	yes	characteristic
56	C₅₃×#520	C₂²	1	1	yes	characteristic
57	C₅₃×#520	C₂²	1	1	yes	characteristic
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#501	C₂²	1	2	yes	—
61	C₅₃×#501	C₂²	1	2	yes	—
62	C₅₃×#499	C₂²	1	2	yes	—
63	C₅₃×#499	C₂²	1	2	yes	—
64	C₅₃×#485	C₂²	1	2	yes	—
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#485	C₂²	1	2	yes	—
67	C₅₃×#485	C₂²	1	2	yes	—
68	C₅₃×#485	C₂²	1	2	yes	—
69	C₅₃×#485	C₂²	1	2	yes	—
70	C₅₃×#484	C₂²	1	2	yes	—
71	C₅₃×#484	C₂²	1	2	yes	—
72	C₅₃×#484	C₂²	1	2	yes	—
73	C₅₃×#483	C₂²	1	2	yes	—
74	C₅₃×#483	C₂²	1	2	yes	—
75	C₅₃×#483	C₂²	1	2	yes	—
76	C₅₃×#482	C₂²	1	2	yes	—
77	C₅₃×#482	C₂²	1	2	yes	—
78	C₅₃×#481	C₂²	1	2	yes	—
79	C₅₃×#480	C₂²	1	2	yes	—
80	C₅₃×#479	C₂²	1	2	yes	—
81	C₅₃×#479	C₂²	1	2	yes	—
82	C₅₃×#479	C₂²	1	2	yes	—
83	C₅₃×#479	C₂²	1	2	yes	—
84	C₅₃×#479	C₂²	1	1	yes	characteristic
85	C₅₃×#479	C₂²	1	1	yes	characteristic
86	C₅₃×#478	C₂²	1	1	yes	characteristic
87	C₅₃×#478	C₂²	1	1	yes	characteristic
88	C₅₃×#477	C₂²	1	1	yes	characteristic
89	C₅₃×#476	C₂²	1	1	yes	characteristic
90	C₅₃×#475	C₂²	1	1	yes	characteristic
91	C₅₃×#474	C₂²	1	1	yes	characteristic
92	C₅₃×#470	C₂²	1	2	yes	—
93	C₅₃×#470	C₂²	1	2	yes	—
94	C₅₃×#468	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	—
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#467	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#441	C₂²	1	2	yes	—
101	C₅₃×#440	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#436	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₅₃×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₅₃	C₂²	1	2	yes	—
108	C₅₃×#428	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	1	yes	characteristic
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#428	C₂²	1	2	yes	—
112	C₅₃×#428	C₂²	1	2	yes	—
113	C₅₃×#428	C₂²	1	2	yes	—
114	C₅₃×#428	C₂²	1	2	yes	—
115	C₅₃×#428	C₂²	1	1	yes	characteristic
116	C₅₃×#428	C₂²	1	1	yes	characteristic
117	C₅₃×#427	C₂²	1	1	yes	characteristic
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₅₃×#427	C₂²	1	2	yes	—
120	C₅₃×#427	C₂²	1	2	yes	—
121	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#107×C₅₃	C₂²	1	2	yes	—
123	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×#106×C₅₃	C₂²	1	2	yes	—
125	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
126	C₅₃×#419	C₂²	1	1	yes	characteristic
127	C₅₃×#417	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₅₃×#416	C₂²	1	1	yes	characteristic
130	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#408	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	#137×C₅₃	—	2	4	no	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
142	#131×C₅₃	—	2	4	no	—
143	#131×C₅₃	—	2	4	no	—
144	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	#127×C₅₃	D₄	1	1	yes	characteristic
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	1	no	—
173	#125×C₅₃	C₂³	1	2	yes	—
174	#125×C₅₃	C₂³	1	1	yes	characteristic
175	#125×C₅₃	C₂³	1	1	yes	characteristic
176	#125×C₅₃	C₂³	1	2	yes	—
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	1	no	—
179	#124×C₅₃	—	2	1	no	—
180	#124×C₅₃	D₄	1	1	yes	characteristic
181	#124×C₅₃	D₄	1	1	yes	characteristic
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	1	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	D₄	1	2	yes	—
209	#121×C₅₃	D₄	1	2	yes	—
210	#121×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₅₃	—	2	2	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	1	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	#117×C₅₃	—	2	2	no	—
243	#117×C₅₃	—	2	2	no	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	C₂³	1	2	yes	—
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	2	yes	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
264	C₂×C₄²×C₅₃	—	2	1	no	—
265	C₂×C₄²×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	2	yes	—
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	2	yes	—
275	#107×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#107×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	#106×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	2	yes	—
287	#106×C₅₃	C₂³	1	1	yes	characteristic
288	#106×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	2	yes	—
302	#103×C₅₃	C₂³	1	1	yes	characteristic
303	#103×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	#102×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	#41×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	2	2	no	—
320	#41×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	1	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	2	1	no	—
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	2	no	—
348	C₂²×C₄×C₅₃	—	2	1	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₅₃	—	2	4	no	—
357	SD₁₆×C₅₃	—	2	4	no	—
358	M₁₆×C₅₃	—	2	2	no	—
359	M₁₆×C₅₃	—	2	4	no	—
360	M₁₆×C₅₃	—	2	4	no	—
361	M₁₆×C₅₃	#41	1	4	yes	—
362	C₂×C₈×C₅₃	—	2	2	no	—
363	C₂×C₈×C₅₃	—	2	2	no	—
364	C₂×C₈×C₅₃	—	2	4	no	—
365	C₂×C₈×C₅₃	—	2	4	no	—
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	1	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₄²×C₅₃	—	2	1	no	—
432	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	2	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	—	2	2	no	—
440	C₄²×C₅₃	—	2	1	no	—
441	C₄²×C₅₃	—	2	1	no	—
442	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂³×C₅₃	—	2	1	no	—
447	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
448	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
449	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
450	Q₈×C₅₃	—	2	2	no	—
451	Q₈×C₅₃	—	2	2	no	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	1	no	—
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	2	1	no	—
456	Q₈×C₅₃	—	4	2	no	—
457	Q₈×C₅₃	—	4	2	no	—
458	Q₈×C₅₃	—	8	1	no	—
459	D₄×C₅₃	—	2	4	no	—
460	D₄×C₅₃	—	2	4	no	—
461	D₄×C₅₃	—	2	2	no	—
462	D₄×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	1	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	2	no	—
468	D₄×C₅₃	—	8	2	no	—
469	D₄×C₅₃	—	8	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	2	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	1	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	4	1	no	—
486	C₂×C₄×C₅₃	—	4	1	no	—
487	C₂×C₄×C₅₃	—	4	2	no	—
488	C₂×C₄×C₅₃	—	4	2	no	—
489	C₂×C₄×C₅₃	—	8	1	no	—
490	C₂×C₄×C₅₃	—	8	1	no	—
491	C₂×C₄×C₅₃	—	8	1	no	—
492	C₂×C₄×C₅₃	—	8	2	no	—
493	C₂×C₄×C₅₃	—	8	2	no	—
494	C₂×C₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	—	8	1	no	—
496	C₂×C₄×C₅₃	—	8	2	no	—
497	C₂×C₄×C₅₃	—	8	1	no	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
506	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
507	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
508	C₈×C₅₃	—	2	1	no	—
509	C₈×C₅₃	—	2	1	no	—
510	C₈×C₅₃	—	2	1	no	—
511	C₈×C₅₃	—	2	1	no	—
512	C₈×C₅₃	—	2	2	no	—
513	C₈×C₅₃	C₂×#41	1	4	yes	—
514	#61280	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
515	C₂²×C₅₃	—	2	1	no	—
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	2	no	—
518	C₂²×C₅₃	—	2	2	no	—
519	C₂²×C₅₃	—	2	2	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	2	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	—	4	1	no	—
525	C₂²×C₅₃	—	4	1	no	—
526	C₂²×C₅₃	#547	1	2	yes	—
527	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₅₃	—	2	1	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	1	no	—
531	C₄×C₅₃	—	2	1	no	—
532	C₄×C₅₃	—	2	2	no	—
533	C₄×C₅₃	—	2	2	no	—
534	C₄×C₅₃	—	4	1	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	—	4	2	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	1	no	—
542	C₄×C₅₃	—	4	1	no	—
543	C₄×C₅₃	—	4	1	no	—
544	C₄×C₅₃	—	4	2	no	—
545	C₄×C₅₃	#547	1	2	yes	—
546	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
547	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	#3512	C₂×C₅₃	1	1	yes	characteristic
549	#3507	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3352	C₂×C₅₃	1	2	yes	complemented
551	#3351	C₂×C₅₃	1	2	yes	complemented
552	#3350	C₂×C₅₃	1	2	yes	complemented
553	#3349	C₂×C₅₃	1	2	yes	complemented
554	#3346	C₂×C₅₃	1	2	yes	complemented
555	#3344	C₂×C₅₃	1	2	yes	complemented
556	#3337	C₂×C₅₃	1	2	yes	complemented
557	#3336	C₂×C₅₃	1	2	yes	complemented
558	#3166	C₂×C₅₃	1	1	yes	characteristic, complemented
559	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
564	C₂×#479	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
567	C₄×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#2935	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#2913	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#2912	C₂×C₅₃	1	1	yes	characteristic, complemented
571	C₂×C₅₃	—	2	2	no	—
572	C₂×C₅₃	—	4	2	no	—
573	C₂×C₅₃	—	4	2	no	—
574	C₂×C₅₃	—	8	1	no	—
575	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
576	C₂×C₅₃	#3584	1	1	yes	characteristic
577	C₂×C₅₃	#3586	1	1	yes	characteristic
578	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
579	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
580	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
581	#559	—	2	1	no	—
582	#557	—	2	1	no	—
583	#556	—	2	1	no	—
584	#556	—	2	1	no	—
585	#556	C₂²×C₅₃	1	2	yes	—
586	#554	C₂²×C₅₃	1	2	yes	—
587	#553	—	2	2	no	—
588	#553	—	2	2	no	—
589	#553	C₂²×C₅₃	1	2	yes	—
590	#553	C₂²×C₅₃	1	2	yes	—
591	#552	C₂²×C₅₃	1	2	yes	—
592	#552	C₂²×C₅₃	1	2	yes	—
593	#552	C₂²×C₅₃	1	2	yes	—
594	#552	C₂²×C₅₃	1	2	yes	—
595	#541	—	2	1	no	—
596	#540	—	2	1	no	—
597	#539	—	2	2	no	—
598	#537	C₂²×C₅₃	1	1	yes	characteristic
599	#537	C₂²×C₅₃	1	1	yes	characteristic
600	#536	C₂²×C₅₃	1	1	yes	characteristic
601	#536	C₂²×C₅₃	1	1	yes	characteristic
602	#533	C₂²×C₅₃	1	1	yes	characteristic
603	#532	C₂²×C₅₃	1	1	yes	characteristic
604	#529	—	2	1	no	—
605	#529	—	2	1	no	—
606	#529	—	2	2	no	—
607	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
608	#520	C₂²×C₅₃	1	1	yes	characteristic
609	#520	C₂²×C₅₃	1	1	yes	characteristic
610	#520	C₂²×C₅₃	1	1	yes	characteristic
611	#520	C₂²×C₅₃	1	1	yes	characteristic
612	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
614	#501	C₂²×C₅₃	1	2	yes	—
615	#501	C₂²×C₅₃	1	2	yes	—
616	#499	C₂²×C₅₃	1	2	yes	—
617	#499	C₂²×C₅₃	1	2	yes	—
618	#485	C₂²×C₅₃	1	2	yes	—
619	#485	C₂²×C₅₃	1	2	yes	—
620	#485	C₂²×C₅₃	1	2	yes	—
621	#485	C₂²×C₅₃	1	2	yes	—
622	#485	C₂²×C₅₃	1	2	yes	—
623	#485	C₂²×C₅₃	1	2	yes	—
624	#484	C₂²×C₅₃	1	2	yes	—
625	#484	C₂²×C₅₃	1	2	yes	—
626	#484	C₂²×C₅₃	1	2	yes	—
627	#483	C₂²×C₅₃	1	2	yes	—
628	#483	C₂²×C₅₃	1	2	yes	—
629	#483	C₂²×C₅₃	1	2	yes	—
630	#482	C₂²×C₅₃	1	2	yes	—
631	#482	C₂²×C₅₃	1	2	yes	—
632	#481	C₂²×C₅₃	1	2	yes	—
633	#480	C₂²×C₅₃	1	2	yes	—
634	#479	C₂²×C₅₃	1	2	yes	—
635	#479	C₂²×C₅₃	1	2	yes	—
636	#479	C₂²×C₅₃	1	2	yes	—
637	#479	C₂²×C₅₃	1	2	yes	—
638	#479	C₂²×C₅₃	1	1	yes	characteristic
639	#479	C₂²×C₅₃	1	1	yes	characteristic
640	#478	C₂²×C₅₃	1	1	yes	characteristic
641	#478	C₂²×C₅₃	1	1	yes	characteristic
642	#477	C₂²×C₅₃	1	1	yes	characteristic
643	#476	C₂²×C₅₃	1	1	yes	characteristic
644	#475	C₂²×C₅₃	1	1	yes	characteristic
645	#474	C₂²×C₅₃	1	1	yes	characteristic
646	#470	C₂²×C₅₃	1	2	yes	—
647	#470	C₂²×C₅₃	1	2	yes	—
648	#468	C₂²×C₅₃	1	2	yes	—
649	#468	C₂²×C₅₃	1	2	yes	—
650	#467	C₂²×C₅₃	1	2	yes	—
651	#467	C₂²×C₅₃	1	2	yes	—
652	#465	C₂²×C₅₃	1	2	yes	—
653	#465	C₂²×C₅₃	1	2	yes	—
654	#441	C₂²×C₅₃	1	2	yes	—
655	#440	C₂²×C₅₃	1	2	yes	—
656	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
657	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
658	#436	C₂²×C₅₃	1	2	yes	—
659	#435	C₂²×C₅₃	1	2	yes	—
660	#435	C₂²×C₅₃	1	2	yes	—
661	C₈×D₄	C₂²×C₅₃	1	2	yes	—
662	#428	C₂²×C₅₃	1	2	yes	—
663	#428	C₂²×C₅₃	1	2	yes	—
664	#428	C₂²×C₅₃	1	2	yes	—
665	#428	C₂²×C₅₃	1	2	yes	—
666	#428	C₂²×C₅₃	1	1	yes	characteristic
667	#428	C₂²×C₅₃	1	1	yes	characteristic
668	#428	C₂²×C₅₃	1	1	yes	characteristic
669	#428	C₂²×C₅₃	1	1	yes	characteristic
670	#428	C₂²×C₅₃	1	1	yes	characteristic
671	#427	C₂²×C₅₃	1	1	yes	characteristic
672	#427	C₂²×C₅₃	1	1	yes	characteristic
673	#427	C₂²×C₅₃	1	2	yes	—
674	#427	C₂²×C₅₃	1	2	yes	—
675	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
676	C₂×#107	C₂²×C₅₃	1	2	yes	—
677	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
678	C₂×#106	C₂²×C₅₃	1	2	yes	—
679	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
680	#419	C₂²×C₅₃	1	1	yes	characteristic
681	#417	C₂²×C₅₃	1	1	yes	characteristic
682	#416	C₂²×C₅₃	1	1	yes	characteristic
683	#416	C₂²×C₅₃	1	1	yes	characteristic
684	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
685	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
686	#408	C₂²×C₅₃	1	1	yes	characteristic
687	#408	C₂²×C₅₃	1	1	yes	characteristic
688	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
689	C₅₃	#61280	1	1	yes	characteristic, direct product factor, Sylow
690	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
691	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
694	#137	—	2	4	no	—
695	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
697	#131	—	2	4	no	—
698	#131	—	2	4	no	—
699	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
700	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
701	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
703	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
706	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
712	#127	D₄×C₅₃	1	1	yes	characteristic
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	C₂³×C₅₃	1	2	yes	—
729	#125	C₂³×C₅₃	1	2	yes	—
730	#125	C₂³×C₅₃	1	1	yes	characteristic
731	#125	C₂³×C₅₃	1	1	yes	characteristic
732	#124	—	2	2	no	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	D₄×C₅₃	1	1	yes	characteristic
736	#124	D₄×C₅₃	1	1	yes	characteristic
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
757	#121	—	2	1	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	D₄×C₅₃	1	2	yes	—
764	#121	D₄×C₅₃	1	2	yes	—
765	#121	C₂³×C₅₃	1	2	yes	—
766	#121	C₂³×C₅₃	1	2	yes	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₅₃	1	2	yes	—
796	C₄×D₄	C₂³×C₅₃	1	2	yes	—
797	#117	—	2	2	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	C₂³×C₅₃	1	1	yes	characteristic
803	#117	C₂³×C₅₃	1	1	yes	characteristic
804	#117	C₂³×C₅₃	1	1	yes	characteristic
805	#117	C₂³×C₅₃	1	2	yes	—
806	#117	C₂³×C₅₃	1	2	yes	—
807	#117	C₂³×C₅₃	1	2	yes	—
808	#117	C₂³×C₅₃	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
813	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
819	C₂×C₄²	—	2	1	no	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
822	#107	C₂³×C₅₃	1	1	yes	characteristic
823	#107	C₂³×C₅₃	1	2	yes	—
824	#107	C₂³×C₅₃	1	2	yes	—
825	#107	C₂³×C₅₃	1	2	yes	—
826	#107	C₂³×C₅₃	1	2	yes	—
827	#107	C₂³×C₅₃	1	1	yes	characteristic
828	#107	C₂³×C₅₃	1	2	yes	—
829	#107	C₂³×C₅₃	1	1	yes	characteristic
830	#107	C₂³×C₅₃	1	1	yes	characteristic
831	#107	C₂³×C₅₃	1	2	yes	—
832	#107	C₂³×C₅₃	1	2	yes	—
833	#106	C₂³×C₅₃	1	1	yes	characteristic
834	#106	C₂³×C₅₃	1	2	yes	—
835	#106	C₂³×C₅₃	1	2	yes	—
836	#106	C₂³×C₅₃	1	2	yes	—
837	#106	C₂³×C₅₃	1	2	yes	—
838	#106	C₂³×C₅₃	1	1	yes	characteristic
839	#106	C₂³×C₅₃	1	2	yes	—
840	#106	C₂³×C₅₃	1	1	yes	characteristic
841	#106	C₂³×C₅₃	1	1	yes	characteristic
842	#106	C₂³×C₅₃	1	2	yes	—
843	#106	C₂³×C₅₃	1	2	yes	—
844	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	2	yes	—
850	#103	C₂³×C₅₃	1	2	yes	—
851	#103	C₂³×C₅₃	1	2	yes	—
852	#103	C₂³×C₅₃	1	1	yes	characteristic
853	#103	C₂³×C₅₃	1	1	yes	characteristic
854	#103	C₂³×C₅₃	1	1	yes	characteristic
855	#103	C₂³×C₅₃	1	1	yes	characteristic
856	#103	C₂³×C₅₃	1	2	yes	—
857	#103	C₂³×C₅₃	1	2	yes	—
858	#103	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	1	yes	characteristic
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	1	yes	characteristic
862	#102	C₂³×C₅₃	1	1	yes	characteristic
863	#102	C₂³×C₅₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
868	#97	C₂³×C₅₃	1	2	yes	—
869	C₄×C₈	C₂³×C₅₃	1	2	yes	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	2	2	no	—
874	#41	—	2	2	no	—
875	#41	—	2	2	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
882	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
889	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
890	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
892	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
893	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
894	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
911	Q₁₆	—	2	4	no	—
912	SD₁₆	—	2	4	no	—
913	M₁₆	—	2	2	no	—
914	M₁₆	—	2	4	no	—
915	M₁₆	—	2	4	no	—
916	M₁₆	#41×C₅₃	1	4	yes	—
917	C₂×C₈	—	2	2	no	—
918	C₂×C₈	—	2	2	no	—
919	C₂×C₈	—	2	4	no	—
920	C₂×C₈	—	2	4	no	—
921	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
922	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
998	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
999	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1001	C₂³	—	2	1	no	—
1002	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1003	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1004	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	D₄	—	2	4	no	—
1015	D₄	—	2	4	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	—	8	1	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1060	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1061	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1062	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	C₂×#41×C₅₃	1	4	yes	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	C₅₃×#547	1	2	yes	—
1081	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1082	C₄	—	2	2	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	C₅₃×#547	1	2	yes	—
1100	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1101	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	2	no	—
1105	C₂	—	8	1	no	—
1106	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1107	C₂	C₅₃×#3584	1	1	yes	characteristic
1108	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#3507	C₂	semidirect
3. C₅₃×#3352	C₂	semidirect
4. C₅₃×#3351	C₂	semidirect
5. C₅₃×#3350	C₂	semidirect
6. C₅₃×#3349	C₂	semidirect
7. C₅₃×#3346	C₂	semidirect
8. C₅₃×#3344	C₂	semidirect
9. C₅₃×#3337	C₂	semidirect
10. C₅₃×#3336	C₂	semidirect
11. C₅₃×#3166	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3098	C₂	semidirect
14. C₅₃×#3097	C₂	semidirect
15. C₅₃×#3097	C₂	semidirect
16. C₅₃×#3076	C₂	semidirect
17. C₂×C₅₃×#479	C₂	semidirect
18. C₅₃×#3063	C₂	semidirect
19. C₅₃×#3063	C₂	semidirect
20. C₄×#137×C₅₃	C₂	semidirect
21. C₅₃×#2935	C₂	semidirect
22. C₅₃×#2913	C₂	semidirect
23. C₅₃×#2912	C₂	semidirect
514. #61280	C₅₃	direct (N × H)
549. #3507	C₂×C₅₃	semidirect
550. #3352	C₂×C₅₃	semidirect
551. #3351	C₂×C₅₃	semidirect
552. #3350	C₂×C₅₃	semidirect
553. #3349	C₂×C₅₃	semidirect
554. #3346	C₂×C₅₃	semidirect
555. #3344	C₂×C₅₃	semidirect
556. #3337	C₂×C₅₃	semidirect
557. #3336	C₂×C₅₃	semidirect
558. #3166	C₂×C₅₃	semidirect
559. #3099	C₂×C₅₃	semidirect
560. #3098	C₂×C₅₃	semidirect
561. #3097	C₂×C₅₃	semidirect
562. #3097	C₂×C₅₃	semidirect
563. #3076	C₂×C₅₃	semidirect
564. C₂×#479	C₂×C₅₃	semidirect
565. #3063	C₂×C₅₃	semidirect
566. #3063	C₂×C₅₃	semidirect
567. C₄×#137	C₂×C₅₃	semidirect
568. #2935	C₂×C₅₃	semidirect
569. #2913	C₂×C₅₃	semidirect
570. #2912	C₂×C₅₃	semidirect
689. C₅₃	#61280	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×#3512	2
C₅₃×#3507	2
C₅₃×#3352	2
C₅₃×#3351	2
C₅₃×#3350	2
C₅₃×#3349	2
C₅₃×#3346	2
C₅₃×#3344	2
C₅₃×#3337	2
C₅₃×#3336	2
C₅₃×#3166	2
C₅₃×#3099	2
C₅₃×#3098	2
C₅₃×#3097	2
C₅₃×#3076	2
C₂×C₅₃×#479	2
C₅₃×#3063	2
C₄×#137×C₅₃	2
C₅₃×#2935	2
C₅₃×#2913	2
C₅₃×#2912	2
#61280	53

Subgroups — C53×#61280 #27268792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61280 #27268792