Subgroups — C₅₃×#62217 #27269729

Order 13568.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3515	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3302	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3261	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3083	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#557	—	2	1	no	—
27	C₅₃×#557	C₂²	1	1	yes	characteristic
28	C₅₃×#557	C₂²	1	1	yes	characteristic
29	C₅₃×#556	—	2	1	no	—
30	C₅₃×#556	C₂²	1	2	yes	—
31	C₅₃×#556	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#554	C₂²	1	1	yes	characteristic
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#552	—	2	2	no	—
37	C₅₃×#552	—	2	1	no	—
38	C₅₃×#552	C₂²	1	2	yes	—
39	C₅₃×#552	C₂²	1	2	yes	—
40	C₅₃×#547	C₂²	1	2	yes	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	2	yes	—
43	C₅₃×#542	—	2	1	no	—
44	C₅₃×#541	—	2	2	no	—
45	C₅₃×#541	—	2	1	no	—
46	C₅₃×#541	C₂²	1	2	yes	—
47	C₅₃×#541	C₂²	1	2	yes	—
48	C₅₃×#539	—	2	2	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#533	C₂²	1	1	yes	characteristic
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₂×#125×C₅₃	—	2	1	no	—
55	C₅₃×#520	C₂²	1	2	yes	—
56	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#500	C₂²	1	1	yes	characteristic
59	C₅₃×#499	C₂²	1	2	yes	—
60	C₅₃×#498	C₂²	1	1	yes	characteristic
61	C₅₃×#491	C₂²	1	2	yes	—
62	C₅₃×#487	C₂²	1	1	yes	characteristic
63	C₅₃×#487	C₂²	1	1	yes	characteristic
64	C₅₃×#487	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	1	yes	characteristic
70	C₅₃×#485	C₂²	1	1	yes	characteristic
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×#479	C₂²	1	2	yes	—
76	C₅₃×#479	C₂²	1	2	yes	—
77	C₅₃×#479	C₂²	1	2	yes	—
78	C₅₃×#479	C₂²	1	2	yes	—
79	C₅₃×#479	C₂²	1	2	yes	—
80	C₅₃×#479	C₂²	1	2	yes	—
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#477	C₂²	1	2	yes	—
84	C₅₃×#477	C₂²	1	1	yes	characteristic
85	C₅₃×#477	C₂²	1	1	yes	characteristic
86	C₅₃×#477	C₂²	1	1	yes	characteristic
87	C₅₃×#477	C₂²	1	2	yes	—
88	C₅₃×#476	C₂²	1	1	yes	characteristic
89	C₅₃×#475	C₂²	1	1	yes	characteristic
90	C₅₃×#475	C₂²	1	1	yes	characteristic
91	C₅₃×#474	C₂²	1	1	yes	characteristic
92	C₅₃×#474	C₂²	1	2	yes	—
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#470	C₂²	1	2	yes	—
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#467	C₂²	1	2	yes	—
98	C₅₃×#467	C₂²	1	2	yes	—
99	C₅₃×#467	C₂²	1	2	yes	—
100	C₅₃×#462	C₂²	1	2	yes	—
101	C₅₃×#462	C₂²	1	1	yes	characteristic
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×#462	C₂²	1	2	yes	—
106	C₅₃×#461	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	1	yes	characteristic
108	C₅₃×#452	C₂²	1	2	yes	—
109	C₅₃×#452	C₂²	1	2	yes	—
110	C₅₃×#452	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#441	C₂²	1	2	yes	—
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
116	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₅₃	C₂²	1	2	yes	—
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#433	C₂²	1	2	yes	—
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#427	C₂²	1	2	yes	—
129	C₂×#107×C₅₃	C₂²	1	2	yes	—
130	C₅₃×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#417	C₂²	1	2	yes	—
133	C₅₃×#416	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₅₃	—	2	2	no	—
147	C₄⋊Q₈×C₅₃	—	2	1	no	—
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	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	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	D₄	1	2	yes	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	1	no	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	—	2	1	no	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	2	no	—
179	#125×C₅₃	—	2	2	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	—	2	1	no	—
182	#125×C₅₃	D₄	1	1	yes	characteristic
183	#125×C₅₃	C₂³	1	2	yes	—
184	#125×C₅₃	C₂³	1	2	yes	—
185	#125×C₅₃	C₂³	1	2	yes	—
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	—	2	2	no	—
188	#124×C₅₃	D₄	1	1	yes	characteristic
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	2	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	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
234	C₄×D₄×C₅₃	—	2	2	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	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	2	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄²×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	2	yes	—
270	#107×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	1	yes	characteristic
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×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	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	4	no	—
314	#41×C₅₃	—	4	1	no	—
315	#41×C₅₃	—	4	2	no	—
316	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅₃	—	2	2	no	—
332	C₂²×C₄×C₅₃	—	2	2	no	—
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	1	no	—
335	C₂²×C₄×C₅₃	—	2	2	no	—
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
342	Q₁₆×C₅₃	—	4	2	no	—
343	Q₁₆×C₅₃	—	4	1	no	—
344	Q₁₆×C₅₃	—	4	2	no	—
345	Q₁₆×C₅₃	—	4	1	no	—
346	SD₁₆×C₅₃	—	2	2	no	—
347	SD₁₆×C₅₃	—	2	2	no	—
348	M₁₆×C₅₃	—	4	2	no	—
349	C₂×C₈×C₅₃	—	4	2	no	—
350	C₂×C₈×C₅₃	—	4	2	no	—
351	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₅₃	—	2	2	no	—
358	C₄⋊C₄×C₅₃	—	2	1	no	—
359	C₄⋊C₄×C₅₃	—	2	1	no	—
360	C₄⋊C₄×C₅₃	—	2	2	no	—
361	C₄⋊C₄×C₅₃	—	2	2	no	—
362	C₄⋊C₄×C₅₃	—	2	2	no	—
363	C₄⋊C₄×C₅₃	—	2	2	no	—
364	C₄⋊C₄×C₅₃	—	2	2	no	—
365	C₄⋊C₄×C₅₃	—	2	2	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	1	no	—
375	C₄⋊C₄×C₅₃	—	2	1	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	1	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	1	no	—
417	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₄²×C₅₃	—	2	1	no	—
423	C₄²×C₅₃	—	2	1	no	—
424	C₄²×C₅₃	—	2	1	no	—
425	C₄²×C₅₃	—	2	2	no	—
426	C₄²×C₅₃	—	2	2	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	1	no	—
429	C₄²×C₅₃	—	2	1	no	—
430	C₄²×C₅₃	—	2	2	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₅₃	C₂⁴	1	2	yes	—
437	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂³×C₅₃	—	2	1	no	—
439	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
440	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₅₃	—	2	2	no	—
442	Q₈×C₅₃	—	2	1	no	—
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	2	1	no	—
445	Q₈×C₅₃	—	2	1	no	—
446	Q₈×C₅₃	—	2	1	no	—
447	Q₈×C₅₃	—	2	2	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	2	1	no	—
450	Q₈×C₅₃	—	4	2	no	—
451	Q₈×C₅₃	—	8	1	no	—
452	Q₈×C₅₃	—	8	1	no	—
453	Q₈×C₅₃	—	8	1	no	—
454	Q₈×C₅₃	—	8	2	no	—
455	D₄×C₅₃	—	2	2	no	—
456	D₄×C₅₃	—	2	1	no	—
457	D₄×C₅₃	—	4	2	no	—
458	D₄×C₅₃	—	4	2	no	—
459	D₄×C₅₃	—	4	4	no	—
460	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	1	no	—
463	C₂×C₄×C₅₃	—	2	2	no	—
464	C₂×C₄×C₅₃	—	2	1	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	1	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	4	1	no	—
478	C₂×C₄×C₅₃	—	4	2	no	—
479	C₂×C₄×C₅₃	—	4	4	no	—
480	C₂×C₄×C₅₃	—	4	2	no	—
481	C₂×C₄×C₅₃	—	8	1	no	—
482	C₂×C₄×C₅₃	—	8	2	no	—
483	C₂×C₄×C₅₃	—	8	2	no	—
484	C₂×C₄×C₅₃	—	8	2	no	—
485	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
494	C₈×C₅₃	—	2	1	no	—
495	C₈×C₅₃	—	2	1	no	—
496	C₈×C₅₃	—	2	1	no	—
497	C₈×C₅₃	—	2	2	no	—
498	C₈×C₅₃	—	2	2	no	—
499	C₈×C₅₃	—	2	1	no	—
500	#62217	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂²×C₅₃	—	2	1	no	—
502	C₂²×C₅₃	—	2	2	no	—
503	C₂²×C₅₃	—	2	1	no	—
504	C₂²×C₅₃	—	2	2	no	—
505	C₂²×C₅₃	—	2	2	no	—
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	2	no	—
508	C₂²×C₅₃	—	4	1	no	—
509	C₂²×C₅₃	—	4	1	no	—
510	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₅₃	—	2	1	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	2	no	—
514	C₄×C₅₃	—	2	1	no	—
515	C₄×C₅₃	—	2	2	no	—
516	C₄×C₅₃	—	2	1	no	—
517	C₄×C₅₃	—	2	2	no	—
518	C₄×C₅₃	—	4	1	no	—
519	C₄×C₅₃	—	4	2	no	—
520	C₄×C₅₃	—	4	1	no	—
521	C₄×C₅₃	—	4	2	no	—
522	C₄×C₅₃	—	4	1	no	—
523	C₄×C₅₃	—	4	1	no	—
524	C₄×C₅₃	—	4	2	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	1	no	—
527	C₄×C₅₃	—	4	1	no	—
528	C₄×C₅₃	—	4	2	no	—
529	C₄×C₅₃	#578	1	2	yes	—
530	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	C₄×C₅₃	#585	1	1	yes	characteristic
532	#3555	C₂×C₅₃	1	1	yes	characteristic, complemented
533	#3515	C₂×C₅₃	1	1	yes	characteristic
534	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
535	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
536	#3374	C₂×C₅₃	1	1	yes	characteristic, complemented
537	#3363	C₂×C₅₃	1	1	yes	characteristic, complemented
538	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
539	#3349	C₂×C₅₃	1	2	yes	complemented
540	#3338	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#3336	C₂×C₅₃	1	2	yes	complemented
542	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3315	C₂×C₅₃	1	2	yes	complemented
544	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3302	C₂×C₅₃	1	2	yes	complemented
546	#3261	C₂×C₅₃	1	2	yes	complemented
547	#3249	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3242	C₂×C₅₃	1	2	yes	complemented
549	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3120	C₂×C₅₃	1	2	yes	complemented
551	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3083	C₂×C₅₃	1	2	yes	complemented
553	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
555	C₂×C₅₃	—	4	1	no	—
556	C₂×C₅₃	—	4	2	no	—
557	C₂×C₅₃	—	4	2	no	—
558	C₂×C₅₃	#3489	1	1	yes	characteristic
559	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
560	C₂×C₅₃	#3584	1	1	yes	characteristic
561	#563	—	2	2	no	—
562	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
563	#557	—	2	1	no	—
564	#557	C₂²×C₅₃	1	1	yes	characteristic
565	#557	C₂²×C₅₃	1	1	yes	characteristic
566	#556	—	2	1	no	—
567	#556	C₂²×C₅₃	1	2	yes	—
568	#556	C₂²×C₅₃	1	1	yes	characteristic
569	#554	C₂²×C₅₃	1	1	yes	characteristic
570	#554	C₂²×C₅₃	1	1	yes	characteristic
571	#554	C₂²×C₅₃	1	1	yes	characteristic
572	#553	—	2	1	no	—
573	#552	—	2	2	no	—
574	#552	—	2	1	no	—
575	#552	C₂²×C₅₃	1	2	yes	—
576	#552	C₂²×C₅₃	1	2	yes	—
577	#547	C₂²×C₅₃	1	1	yes	characteristic
578	#547	C₂²×C₅₃	1	2	yes	—
579	#544	C₂²×C₅₃	1	2	yes	—
580	#542	—	2	1	no	—
581	#541	—	2	2	no	—
582	#541	—	2	1	no	—
583	#541	C₂²×C₅₃	1	2	yes	—
584	#541	C₂²×C₅₃	1	2	yes	—
585	#539	—	2	2	no	—
586	#533	C₂²×C₅₃	1	1	yes	characteristic
587	#533	C₂²×C₅₃	1	1	yes	characteristic
588	#533	C₂²×C₅₃	1	1	yes	characteristic
589	#529	—	2	1	no	—
590	#529	C₂²×C₅₃	1	1	yes	characteristic
591	C₂×#125	—	2	1	no	—
592	#520	C₂²×C₅₃	1	2	yes	—
593	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
594	#501	C₂²×C₅₃	1	2	yes	—
595	#500	C₂²×C₅₃	1	1	yes	characteristic
596	#499	C₂²×C₅₃	1	2	yes	—
597	#498	C₂²×C₅₃	1	1	yes	characteristic
598	#491	C₂²×C₅₃	1	2	yes	—
599	#487	C₂²×C₅₃	1	1	yes	characteristic
600	#487	C₂²×C₅₃	1	2	yes	—
601	#487	C₂²×C₅₃	1	1	yes	characteristic
602	#485	C₂²×C₅₃	1	1	yes	characteristic
603	#485	C₂²×C₅₃	1	2	yes	—
604	#485	C₂²×C₅₃	1	1	yes	characteristic
605	#485	C₂²×C₅₃	1	2	yes	—
606	#485	C₂²×C₅₃	1	2	yes	—
607	#485	C₂²×C₅₃	1	2	yes	—
608	#484	C₂²×C₅₃	1	2	yes	—
609	#484	C₂²×C₅₃	1	2	yes	—
610	#483	C₂²×C₅₃	1	2	yes	—
611	#483	C₂²×C₅₃	1	2	yes	—
612	#479	C₂²×C₅₃	1	2	yes	—
613	#479	C₂²×C₅₃	1	2	yes	—
614	#479	C₂²×C₅₃	1	2	yes	—
615	#479	C₂²×C₅₃	1	2	yes	—
616	#479	C₂²×C₅₃	1	2	yes	—
617	#479	C₂²×C₅₃	1	2	yes	—
618	#478	C₂²×C₅₃	1	2	yes	—
619	#478	C₂²×C₅₃	1	2	yes	—
620	#477	C₂²×C₅₃	1	1	yes	characteristic
621	#477	C₂²×C₅₃	1	1	yes	characteristic
622	#477	C₂²×C₅₃	1	2	yes	—
623	#477	C₂²×C₅₃	1	2	yes	—
624	#477	C₂²×C₅₃	1	1	yes	characteristic
625	#476	C₂²×C₅₃	1	1	yes	characteristic
626	#475	C₂²×C₅₃	1	1	yes	characteristic
627	#475	C₂²×C₅₃	1	1	yes	characteristic
628	#474	C₂²×C₅₃	1	1	yes	characteristic
629	#474	C₂²×C₅₃	1	1	yes	characteristic
630	#474	C₂²×C₅₃	1	2	yes	—
631	#470	C₂²×C₅₃	1	2	yes	—
632	#470	C₂²×C₅₃	1	2	yes	—
633	#467	C₂²×C₅₃	1	2	yes	—
634	#467	C₂²×C₅₃	1	2	yes	—
635	#467	C₂²×C₅₃	1	2	yes	—
636	#467	C₂²×C₅₃	1	2	yes	—
637	#462	C₂²×C₅₃	1	1	yes	characteristic
638	#462	C₂²×C₅₃	1	1	yes	characteristic
639	#462	C₂²×C₅₃	1	1	yes	characteristic
640	#462	C₂²×C₅₃	1	2	yes	—
641	#462	C₂²×C₅₃	1	2	yes	—
642	#462	C₂²×C₅₃	1	2	yes	—
643	#461	C₂²×C₅₃	1	1	yes	characteristic
644	#452	C₂²×C₅₃	1	2	yes	—
645	#452	C₂²×C₅₃	1	1	yes	characteristic
646	#452	C₂²×C₅₃	1	1	yes	characteristic
647	#452	C₂²×C₅₃	1	2	yes	—
648	#446	C₂²×C₅₃	1	1	yes	characteristic
649	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
650	#441	C₂²×C₅₃	1	2	yes	—
651	#440	C₂²×C₅₃	1	2	yes	—
652	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
653	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
654	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
655	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
656	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
657	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
658	#436	C₂²×C₅₃	1	1	yes	characteristic
659	#435	C₂²×C₅₃	1	2	yes	—
660	C₈×D₄	C₂²×C₅₃	1	2	yes	—
661	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
662	#433	C₂²×C₅₃	1	2	yes	—
663	#431	C₂²×C₅₃	1	1	yes	characteristic
664	#428	C₂²×C₅₃	1	2	yes	—
665	#427	C₂²×C₅₃	1	2	yes	—
666	C₂×#107	C₂²×C₅₃	1	2	yes	—
667	#424	C₂²×C₅₃	1	2	yes	—
668	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
669	#417	C₂²×C₅₃	1	2	yes	—
670	#416	C₂²×C₅₃	1	2	yes	—
671	#416	C₂²×C₅₃	1	2	yes	—
672	C₅₃	#62217	1	1	yes	characteristic, direct product factor, Sylow
673	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×#41	C₂³×C₅₃	1	2	yes	—
675	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
676	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
680	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
681	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
682	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
683	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
691	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	D₄×C₅₃	1	2	yes	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	1	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	1	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	D₄×C₅₃	1	1	yes	characteristic
721	#125	C₂³×C₅₃	1	2	yes	—
722	#125	C₂³×C₅₃	1	2	yes	—
723	#125	C₂³×C₅₃	1	2	yes	—
724	#124	—	2	1	no	—
725	#124	—	2	2	no	—
726	#124	D₄×C₅₃	1	1	yes	characteristic
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	D₄×C₅₃	1	2	yes	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
750	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
751	#121	—	2	1	no	—
752	#121	—	2	2	no	—
753	#121	D₄×C₅₃	1	1	yes	characteristic
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
766	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
767	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₅₃	1	2	yes	—
781	C₄×D₄	C₂³×C₅₃	1	2	yes	—
782	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	2	no	—
786	#117	—	2	2	no	—
787	#117	—	2	2	no	—
788	#117	—	2	1	no	—
789	#117	C₂³×C₅₃	1	1	yes	characteristic
790	#117	C₂³×C₅₃	1	2	yes	—
791	#117	C₂³×C₅₃	1	2	yes	—
792	#117	C₂³×C₅₃	1	2	yes	—
793	C₂×C₄⋊C₄	—	2	2	no	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
799	C₂×C₄²	—	2	1	no	—
800	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
801	#107	C₂³×C₅₃	1	1	yes	characteristic
802	#107	C₂³×C₅₃	1	2	yes	—
803	#107	C₂³×C₅₃	1	2	yes	—
804	#107	C₂³×C₅₃	1	2	yes	—
805	#107	C₂³×C₅₃	1	2	yes	—
806	#107	C₂³×C₅₃	1	1	yes	characteristic
807	#107	C₂³×C₅₃	1	2	yes	—
808	#107	C₂³×C₅₃	1	2	yes	—
809	#106	C₂³×C₅₃	1	2	yes	—
810	#106	C₂³×C₅₃	1	2	yes	—
811	#106	C₂³×C₅₃	1	2	yes	—
812	#106	C₂³×C₅₃	1	1	yes	characteristic
813	#106	C₂³×C₅₃	1	1	yes	characteristic
814	#106	C₂³×C₅₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
822	#103	C₂³×C₅₃	1	2	yes	—
823	#103	C₂³×C₅₃	1	2	yes	—
824	#103	C₂³×C₅₃	1	2	yes	—
825	#103	C₂³×C₅₃	1	2	yes	—
826	#103	C₂³×C₅₃	1	2	yes	—
827	#103	C₂³×C₅₃	1	2	yes	—
828	#103	C₂³×C₅₃	1	2	yes	—
829	#103	C₂³×C₅₃	1	1	yes	characteristic
830	#103	C₂³×C₅₃	1	1	yes	characteristic
831	#103	C₂³×C₅₃	1	1	yes	characteristic
832	#103	C₂³×C₅₃	1	1	yes	characteristic
833	#103	C₂³×C₅₃	1	1	yes	characteristic
834	#103	C₂³×C₅₃	1	1	yes	characteristic
835	#103	C₂³×C₅₃	1	2	yes	—
836	#103	C₂³×C₅₃	1	2	yes	—
837	#103	C₂³×C₅₃	1	2	yes	—
838	#102	C₂³×C₅₃	1	1	yes	characteristic
839	#102	C₂³×C₅₃	1	2	yes	—
840	#102	C₂³×C₅₃	1	2	yes	—
841	#102	C₂³×C₅₃	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
846	#97	C₂³×C₅₃	1	2	yes	—
847	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₅₃	1	2	yes	—
850	#41	—	2	2	no	—
851	#41	—	2	4	no	—
852	#41	—	4	1	no	—
853	#41	—	4	2	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
861	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
862	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
863	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
867	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
868	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
877	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
880	Q₁₆	—	4	2	no	—
881	Q₁₆	—	4	1	no	—
882	Q₁₆	—	4	2	no	—
883	Q₁₆	—	4	1	no	—
884	SD₁₆	—	2	2	no	—
885	SD₁₆	—	2	2	no	—
886	M₁₆	—	4	2	no	—
887	C₂×C₈	—	4	2	no	—
888	C₂×C₈	—	4	2	no	—
889	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
894	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
931	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
932	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
934	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
956	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
957	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
958	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
959	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
972	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
973	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
974	C₄²	C₂⁴×C₅₃	1	2	yes	—
975	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂³	—	2	1	no	—
977	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
978	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	1	no	—
992	Q₈	—	8	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	1	no	—
995	D₄	—	4	2	no	—
996	D₄	—	4	2	no	—
997	D₄	—	4	4	no	—
998	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	4	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	4	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	8	1	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1030	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1031	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	—	2	1	no	—
1035	C₈	—	2	2	no	—
1036	C₈	—	2	2	no	—
1037	C₈	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	C₅₃×#578	1	2	yes	—
1067	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1068	C₄	C₅₃×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	4	2	no	—
1072	C₂	C₅₃×#3489	1	1	yes	characteristic
1073	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1074	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3555	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3381	C₂	semidirect
5. C₅₃×#3374	C₂	semidirect
6. C₅₃×#3363	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3349	C₂	semidirect
9. C₅₃×#3338	C₂	semidirect
10. C₅₃×#3336	C₂	semidirect
11. C₅₃×#3331	C₂	semidirect
12. C₅₃×#3315	C₂	semidirect
13. C₅₃×#3302	C₂	semidirect
14. C₅₃×#3302	C₂	semidirect
15. C₅₃×#3261	C₂	semidirect
16. C₅₃×#3249	C₂	semidirect
17. C₅₃×#3242	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3120	C₂	semidirect
20. C₅₃×#3107	C₂	semidirect
21. C₅₃×#3083	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
500. #62217	C₅₃	direct (N × H)
532. #3555	C₂×C₅₃	semidirect
534. #3385	C₂×C₅₃	semidirect
535. #3381	C₂×C₅₃	semidirect
536. #3374	C₂×C₅₃	semidirect
537. #3363	C₂×C₅₃	semidirect
538. #3356	C₂×C₅₃	semidirect
539. #3349	C₂×C₅₃	semidirect
540. #3338	C₂×C₅₃	semidirect
541. #3336	C₂×C₅₃	semidirect
542. #3331	C₂×C₅₃	semidirect
543. #3315	C₂×C₅₃	semidirect
544. #3302	C₂×C₅₃	semidirect
545. #3302	C₂×C₅₃	semidirect
546. #3261	C₂×C₅₃	semidirect
547. #3249	C₂×C₅₃	semidirect
548. #3242	C₂×C₅₃	semidirect
549. #3231	C₂×C₅₃	semidirect
550. #3120	C₂×C₅₃	semidirect
551. #3107	C₂×C₅₃	semidirect
552. #3083	C₂×C₅₃	semidirect
553. #3076	C₂×C₅₃	semidirect
554. #2994	C₂×C₅₃	semidirect
672. C₅₃	#62217	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×#3555	2
C₅₃×#3515	2
C₅₃×#3385	2
C₅₃×#3381	2
C₅₃×#3374	2
C₅₃×#3363	2
C₅₃×#3356	2
C₅₃×#3349	2
C₅₃×#3338	2
C₅₃×#3336	2
C₅₃×#3331	2
C₅₃×#3315	2
C₅₃×#3302	2
C₅₃×#3261	2
C₅₃×#3249	2
C₅₃×#3242	2
C₅₃×#3231	2
C₅₃×#3120	2
C₅₃×#3107	2
C₅₃×#3083	2
C₅₃×#3076	2
C₅₃×#2994	2
#62217	53

Subgroups — C53×#62217 #27269729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62217 #27269729