Subgroups — C₅₃×#62237 #27269749

Order 13568.

1634 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3515	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3352	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3344	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3331	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3261	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3084	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#564	—	2	1	no	—
21	C₅₃×#563	—	2	1	no	—
22	C₅₃×#557	C₂²	1	1	yes	characteristic
23	C₅₃×#557	C₂²	1	2	yes	—
24	C₅₃×#554	C₂²	1	1	yes	characteristic
25	C₅₃×#554	C₂²	1	1	yes	characteristic
26	C₅₃×#554	C₂²	1	2	yes	—
27	C₅₃×#553	—	2	1	no	—
28	C₅₃×#552	—	2	2	no	—
29	C₅₃×#552	—	2	2	no	—
30	C₅₃×#552	—	2	1	no	—
31	C₅₃×#552	C₂²	1	2	yes	—
32	C₅₃×#552	C₂²	1	2	yes	—
33	C₅₃×#552	C₂²	1	2	yes	—
34	C₅₃×#547	C₂²	1	1	yes	characteristic
35	C₅₃×#547	C₂²	1	2	yes	—
36	C₅₃×#544	—	2	1	no	—
37	C₅₃×#544	C₂²	1	2	yes	—
38	C₅₃×#541	—	2	2	no	—
39	C₅₃×#541	C₂²	1	2	yes	—
40	C₅₃×#541	C₂²	1	2	yes	—
41	C₅₃×#539	—	2	2	no	—
42	C₅₃×#539	—	2	1	no	—
43	C₅₃×#533	C₂²	1	1	yes	characteristic
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#529	—	2	1	no	—
46	C₅₃×#529	C₂²	1	1	yes	characteristic
47	C₂×#125×C₅₃	—	2	1	no	—
48	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#520	C₂²	1	2	yes	—
50	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#501	C₂²	1	2	yes	—
52	C₅₃×#501	C₂²	1	2	yes	—
53	C₅₃×#499	C₂²	1	2	yes	—
54	C₅₃×#491	C₂²	1	2	yes	—
55	C₅₃×#491	C₂²	1	2	yes	—
56	C₅₃×#487	C₂²	1	2	yes	—
57	C₅₃×#485	C₂²	1	2	yes	—
58	C₅₃×#485	C₂²	1	2	yes	—
59	C₅₃×#485	C₂²	1	2	yes	—
60	C₅₃×#484	C₂²	1	2	yes	—
61	C₅₃×#484	C₂²	1	2	yes	—
62	C₅₃×#484	C₂²	1	2	yes	—
63	C₅₃×#483	C₂²	1	2	yes	—
64	C₅₃×#483	C₂²	1	2	yes	—
65	C₅₃×#483	C₂²	1	2	yes	—
66	C₅₃×#479	C₂²	1	2	yes	—
67	C₅₃×#479	C₂²	1	2	yes	—
68	C₅₃×#479	C₂²	1	2	yes	—
69	C₅₃×#479	C₂²	1	2	yes	—
70	C₅₃×#479	C₂²	1	2	yes	—
71	C₅₃×#479	C₂²	1	2	yes	—
72	C₅₃×#479	C₂²	1	2	yes	—
73	C₅₃×#478	C₂²	1	2	yes	—
74	C₅₃×#478	C₂²	1	2	yes	—
75	C₅₃×#478	C₂²	1	2	yes	—
76	C₅₃×#477	C₂²	1	1	yes	characteristic
77	C₅₃×#476	C₂²	1	2	yes	—
78	C₅₃×#476	C₂²	1	1	yes	characteristic
79	C₅₃×#475	C₂²	1	2	yes	—
80	C₅₃×#475	C₂²	1	2	yes	—
81	C₅₃×#475	C₂²	1	2	yes	—
82	C₅₃×#470	C₂²	1	2	yes	—
83	C₅₃×#470	C₂²	1	2	yes	—
84	C₅₃×#470	C₂²	1	2	yes	—
85	C₅₃×#470	C₂²	1	2	yes	—
86	C₅₃×#467	C₂²	1	2	yes	—
87	C₅₃×#467	C₂²	1	2	yes	—
88	C₅₃×#462	C₂²	1	2	yes	—
89	C₅₃×#462	C₂²	1	2	yes	—
90	C₅₃×#462	C₂²	1	1	yes	characteristic
91	C₅₃×#462	C₂²	1	2	yes	—
92	C₅₃×#462	C₂²	1	2	yes	—
93	C₅₃×#461	C₂²	1	1	yes	characteristic
94	C₅₃×#452	C₂²	1	2	yes	—
95	C₅₃×#452	C₂²	1	2	yes	—
96	C₅₃×#452	C₂²	1	2	yes	—
97	C₅₃×#446	C₂²	1	2	yes	—
98	C₅₃×#441	C₂²	1	2	yes	—
99	C₅₃×#441	C₂²	1	2	yes	—
100	C₅₃×#440	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	C₅₃×#433	C₂²	1	2	yes	—
108	C₅₃×#432	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	C₂×#106×C₅₃	C₂²	1	2	yes	—
113	C₅₃×#424	C₂²	1	2	yes	—
114	C₅₃×#423	C₂²	1	1	yes	characteristic
115	C₅₃×#417	C₂²	1	1	yes	characteristic
116	C₅₃×#417	C₂²	1	2	yes	—
117	C₅₃×#417	C₂²	1	1	yes	characteristic
118	C₅₃×#416	C₂²	1	2	yes	—
119	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×#41×C₅₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
125	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
128	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₅₃	—	2	2	no	—
130	C₄⋊Q₈×C₅₃	—	2	2	no	—
131	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
132	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
133	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
134	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
137	#126×C₅₃	—	2	2	no	—
138	#126×C₅₃	—	2	2	no	—
139	#126×C₅₃	—	2	2	no	—
140	#126×C₅₃	—	2	2	no	—
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#126×C₅₃	D₄	1	2	yes	—
145	#125×C₅₃	—	2	2	no	—
146	#125×C₅₃	—	2	2	no	—
147	#125×C₅₃	—	2	1	no	—
148	#125×C₅₃	—	2	1	no	—
149	#125×C₅₃	—	2	2	no	—
150	#125×C₅₃	—	2	2	no	—
151	#125×C₅₃	—	2	2	no	—
152	#125×C₅₃	—	2	2	no	—
153	#125×C₅₃	—	2	2	no	—
154	#125×C₅₃	—	2	2	no	—
155	#125×C₅₃	—	2	2	no	—
156	#125×C₅₃	—	2	2	no	—
157	#125×C₅₃	—	2	2	no	—
158	#125×C₅₃	—	2	2	no	—
159	#125×C₅₃	—	2	1	no	—
160	#125×C₅₃	—	2	1	no	—
161	#125×C₅₃	—	2	1	no	—
162	#125×C₅₃	—	2	1	no	—
163	#125×C₅₃	D₄	1	1	yes	characteristic
164	#125×C₅₃	C₂³	1	2	yes	—
165	#125×C₅₃	C₂³	1	2	yes	—
166	#125×C₅₃	C₂³	1	2	yes	—
167	#125×C₅₃	C₂³	1	2	yes	—
168	#124×C₅₃	D₄	1	1	yes	characteristic
169	#123×C₅₃	—	2	2	no	—
170	#123×C₅₃	—	2	2	no	—
171	#123×C₅₃	—	2	2	no	—
172	#123×C₅₃	—	2	2	no	—
173	#123×C₅₃	—	2	2	no	—
174	#123×C₅₃	—	2	2	no	—
175	#123×C₅₃	D₄	1	2	yes	—
176	C₂²⋊Q₈×C₅₃	—	2	2	no	—
177	C₂²⋊Q₈×C₅₃	—	2	2	no	—
178	C₂²⋊Q₈×C₅₃	—	2	2	no	—
179	C₂²⋊Q₈×C₅₃	—	2	2	no	—
180	C₂²⋊Q₈×C₅₃	—	2	2	no	—
181	C₂²⋊Q₈×C₅₃	—	2	2	no	—
182	C₂²⋊Q₈×C₅₃	—	2	1	no	—
183	C₂²⋊Q₈×C₅₃	—	2	1	no	—
184	C₂²⋊Q₈×C₅₃	—	2	1	no	—
185	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
186	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
190	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	#121×C₅₃	—	2	1	no	—
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	D₄	1	1	yes	characteristic
195	C₄×Q₈×C₅₃	—	2	2	no	—
196	C₄×Q₈×C₅₃	—	2	1	no	—
197	C₄×Q₈×C₅₃	—	2	1	no	—
198	C₄×Q₈×C₅₃	—	2	1	no	—
199	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
207	C₄×D₄×C₅₃	—	2	2	no	—
208	C₄×D₄×C₅₃	—	2	2	no	—
209	C₄×D₄×C₅₃	—	2	1	no	—
210	C₄×D₄×C₅₃	—	2	2	no	—
211	C₄×D₄×C₅₃	—	2	1	no	—
212	C₄×D₄×C₅₃	—	2	1	no	—
213	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₅₃	C₂³	1	2	yes	—
216	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₅₃	C₂³	1	2	yes	—
218	#117×C₅₃	—	2	2	no	—
219	#117×C₅₃	—	2	2	no	—
220	#117×C₅₃	—	2	2	no	—
221	#117×C₅₃	—	2	2	no	—
222	#117×C₅₃	—	2	1	no	—
223	#117×C₅₃	—	2	1	no	—
224	#117×C₅₃	—	2	1	no	—
225	#117×C₅₃	C₂³	1	1	yes	characteristic
226	#117×C₅₃	C₂³	1	2	yes	—
227	#117×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
229	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
230	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₃	—	2	1	no	—
239	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
240	#107×C₅₃	C₂³	1	2	yes	—
241	#107×C₅₃	C₂³	1	2	yes	—
242	#107×C₅₃	C₂³	1	2	yes	—
243	#107×C₅₃	C₂³	1	2	yes	—
244	#107×C₅₃	C₂³	1	2	yes	—
245	#106×C₅₃	C₂³	1	2	yes	—
246	#106×C₅₃	C₂³	1	2	yes	—
247	#106×C₅₃	C₂³	1	2	yes	—
248	#106×C₅₃	C₂³	1	2	yes	—
249	#106×C₅₃	C₂³	1	2	yes	—
250	#106×C₅₃	C₂³	1	2	yes	—
251	#106×C₅₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
258	#103×C₅₃	C₂³	1	2	yes	—
259	#103×C₅₃	C₂³	1	2	yes	—
260	#103×C₅₃	C₂³	1	2	yes	—
261	#103×C₅₃	C₂³	1	2	yes	—
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#103×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#103×C₅₃	C₂³	1	2	yes	—
269	#103×C₅₃	C₂³	1	2	yes	—
270	#103×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	#97×C₅₃	C₂³	1	2	yes	—
278	#97×C₅₃	C₂³	1	2	yes	—
279	C₄×C₈×C₅₃	C₂³	1	2	yes	—
280	#41×C₅₃	—	2	2	no	—
281	#41×C₅₃	—	2	4	no	—
282	#41×C₅₃	—	4	2	no	—
283	#41×C₅₃	—	4	1	no	—
284	C₂×Q₈×C₅₃	—	2	1	no	—
285	C₂×Q₈×C₅₃	—	2	2	no	—
286	C₂×Q₈×C₅₃	—	2	1	no	—
287	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
291	C₂×D₄×C₅₃	—	2	1	no	—
292	C₂×D₄×C₅₃	—	2	2	no	—
293	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
294	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
295	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	—	2	1	no	—
297	C₂²×C₄×C₅₃	—	2	1	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	1	no	—
301	C₂²×C₄×C₅₃	—	2	1	no	—
302	C₂²×C₄×C₅₃	—	2	2	no	—
303	C₂²×C₄×C₅₃	—	2	1	no	—
304	C₂²×C₄×C₅₃	—	2	2	no	—
305	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
309	Q₁₆×C₅₃	—	4	2	no	—
310	Q₁₆×C₅₃	—	4	2	no	—
311	Q₁₆×C₅₃	—	4	2	no	—
312	SD₁₆×C₅₃	—	2	4	no	—
313	M₁₆×C₅₃	—	4	1	no	—
314	M₁₆×C₅₃	—	4	2	no	—
315	M₁₆×C₅₃	—	4	1	no	—
316	C₂×C₈×C₅₃	—	4	2	no	—
317	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	1	no	—
323	C₄⋊C₄×C₅₃	—	2	1	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	2	no	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	2	2	no	—
329	C₄⋊C₄×C₅₃	—	2	2	no	—
330	C₄⋊C₄×C₅₃	—	2	2	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	1	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	1	no	—
338	C₄⋊C₄×C₅₃	—	2	1	no	—
339	C₄⋊C₄×C₅₃	—	2	1	no	—
340	C₄⋊C₄×C₅₃	—	2	1	no	—
341	C₄⋊C₄×C₅₃	—	2	2	no	—
342	C₄⋊C₄×C₅₃	—	2	2	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	—	2	1	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	2	no	—
348	C₄⋊C₄×C₅₃	—	2	1	no	—
349	C₄⋊C₄×C₅₃	—	2	2	no	—
350	C₄⋊C₄×C₅₃	—	2	1	no	—
351	C₄⋊C₄×C₅₃	—	2	2	no	—
352	C₄⋊C₄×C₅₃	—	2	2	no	—
353	C₄⋊C₄×C₅₃	—	2	2	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
363	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²⋊C₄×C₅₃	—	2	2	no	—
368	C₂²⋊C₄×C₅₃	—	2	2	no	—
369	C₂²⋊C₄×C₅₃	—	2	2	no	—
370	C₂²⋊C₄×C₅₃	—	2	2	no	—
371	C₂²⋊C₄×C₅₃	—	2	1	no	—
372	C₂²⋊C₄×C₅₃	—	2	2	no	—
373	C₂²⋊C₄×C₅₃	—	2	2	no	—
374	C₂²⋊C₄×C₅₃	—	2	2	no	—
375	C₂²⋊C₄×C₅₃	—	2	1	no	—
376	C₂²⋊C₄×C₅₃	—	2	2	no	—
377	C₂²⋊C₄×C₅₃	—	2	1	no	—
378	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₄²×C₅₃	—	2	1	no	—
384	C₄²×C₅₃	—	2	1	no	—
385	C₄²×C₅₃	—	2	1	no	—
386	C₄²×C₅₃	—	2	2	no	—
387	C₄²×C₅₃	—	2	2	no	—
388	C₄²×C₅₃	—	2	2	no	—
389	C₄²×C₅₃	—	2	2	no	—
390	C₄²×C₅₃	—	2	2	no	—
391	C₄²×C₅₃	—	2	2	no	—
392	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₅₃	C₂⁴	1	2	yes	—
395	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂³×C₅₃	—	2	1	no	—
398	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
400	Q₈×C₅₃	—	2	1	no	—
401	Q₈×C₅₃	—	2	2	no	—
402	Q₈×C₅₃	—	2	2	no	—
403	Q₈×C₅₃	—	2	1	no	—
404	Q₈×C₅₃	—	2	2	no	—
405	Q₈×C₅₃	—	2	2	no	—
406	Q₈×C₅₃	—	4	1	no	—
407	Q₈×C₅₃	—	8	1	no	—
408	Q₈×C₅₃	—	8	1	no	—
409	Q₈×C₅₃	—	8	2	no	—
410	D₄×C₅₃	—	2	1	no	—
411	D₄×C₅₃	—	4	1	no	—
412	D₄×C₅₃	—	4	2	no	—
413	D₄×C₅₃	—	4	4	no	—
414	D₄×C₅₃	—	4	2	no	—
415	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄×C₅₃	—	2	1	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	1	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	4	1	no	—
430	C₂×C₄×C₅₃	—	4	1	no	—
431	C₂×C₄×C₅₃	—	4	2	no	—
432	C₂×C₄×C₅₃	—	4	4	no	—
433	C₂×C₄×C₅₃	—	4	2	no	—
434	C₂×C₄×C₅₃	—	4	2	no	—
435	C₂×C₄×C₅₃	—	8	1	no	—
436	C₂×C₄×C₅₃	—	8	2	no	—
437	C₂×C₄×C₅₃	—	8	2	no	—
438	C₂×C₄×C₅₃	—	8	1	no	—
439	C₂×C₄×C₅₃	—	8	2	no	—
440	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
449	C₈×C₅₃	—	2	2	no	—
450	C₈×C₅₃	—	2	2	no	—
451	C₈×C₅₃	—	2	2	no	—
452	C₈×C₅₃	—	2	2	no	—
453	#62237	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂²×C₅₃	—	2	1	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	2	no	—
457	C₂²×C₅₃	—	2	2	no	—
458	C₂²×C₅₃	—	2	2	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	2	no	—
461	C₂²×C₅₃	—	4	1	no	—
462	C₂²×C₅₃	—	4	1	no	—
463	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₅₃	—	2	1	no	—
465	C₄×C₅₃	—	2	1	no	—
466	C₄×C₅₃	—	2	1	no	—
467	C₄×C₅₃	—	2	1	no	—
468	C₄×C₅₃	—	2	2	no	—
469	C₄×C₅₃	—	2	2	no	—
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	2	1	no	—
472	C₄×C₅₃	—	4	1	no	—
473	C₄×C₅₃	—	4	2	no	—
474	C₄×C₅₃	—	4	1	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	2	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	—	4	1	no	—
479	C₄×C₅₃	—	4	2	no	—
480	C₄×C₅₃	—	4	2	no	—
481	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
482	C₄×C₅₃	#585	1	1	yes	characteristic
483	#3563	C₂×C₅₃	1	1	yes	characteristic, complemented
484	#3515	C₂×C₅₃	1	1	yes	characteristic
485	#3388	C₂×C₅₃	1	2	yes	complemented
486	#3374	C₂×C₅₃	1	2	yes	complemented
487	#3352	C₂×C₅₃	1	2	yes	complemented
488	#3344	C₂×C₅₃	1	2	yes	complemented
489	#3344	C₂×C₅₃	1	2	yes	complemented
490	#3331	C₂×C₅₃	1	2	yes	complemented
491	#3315	C₂×C₅₃	1	2	yes	complemented
492	#3315	C₂×C₅₃	1	2	yes	complemented
493	#3261	C₂×C₅₃	1	2	yes	complemented
494	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#3242	C₂×C₅₃	1	2	yes	complemented
496	#3236	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#3120	C₂×C₅₃	1	2	yes	complemented
498	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
499	#3084	C₂×C₅₃	1	2	yes	complemented
500	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
501	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
502	C₂×C₅₃	—	4	1	no	—
503	C₂×C₅₃	—	4	2	no	—
504	C₂×C₅₃	—	4	2	no	—
505	C₂×C₅₃	#3489	1	1	yes	characteristic
506	C₂×C₅₃	#3586	1	1	yes	characteristic
507	C₂×C₅₃	#3586	1	1	yes	characteristic
508	#564	—	2	1	no	—
509	#563	—	2	1	no	—
510	#557	C₂²×C₅₃	1	1	yes	characteristic
511	#557	C₂²×C₅₃	1	2	yes	—
512	#554	C₂²×C₅₃	1	1	yes	characteristic
513	#554	C₂²×C₅₃	1	2	yes	—
514	#554	C₂²×C₅₃	1	1	yes	characteristic
515	#553	—	2	1	no	—
516	#552	—	2	2	no	—
517	#552	—	2	2	no	—
518	#552	—	2	1	no	—
519	#552	C₂²×C₅₃	1	2	yes	—
520	#552	C₂²×C₅₃	1	2	yes	—
521	#552	C₂²×C₅₃	1	2	yes	—
522	#547	C₂²×C₅₃	1	2	yes	—
523	#547	C₂²×C₅₃	1	1	yes	characteristic
524	#544	—	2	1	no	—
525	#544	C₂²×C₅₃	1	2	yes	—
526	#541	—	2	2	no	—
527	#541	C₂²×C₅₃	1	2	yes	—
528	#541	C₂²×C₅₃	1	2	yes	—
529	#539	—	2	2	no	—
530	#539	—	2	1	no	—
531	#533	C₂²×C₅₃	1	1	yes	characteristic
532	#533	C₂²×C₅₃	1	1	yes	characteristic
533	#529	—	2	1	no	—
534	#529	C₂²×C₅₃	1	1	yes	characteristic
535	C₂×#125	—	2	1	no	—
536	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
537	#520	C₂²×C₅₃	1	2	yes	—
538	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
539	#501	C₂²×C₅₃	1	2	yes	—
540	#501	C₂²×C₅₃	1	2	yes	—
541	#499	C₂²×C₅₃	1	2	yes	—
542	#491	C₂²×C₅₃	1	2	yes	—
543	#491	C₂²×C₅₃	1	2	yes	—
544	#487	C₂²×C₅₃	1	2	yes	—
545	#485	C₂²×C₅₃	1	2	yes	—
546	#485	C₂²×C₅₃	1	2	yes	—
547	#485	C₂²×C₅₃	1	2	yes	—
548	#484	C₂²×C₅₃	1	2	yes	—
549	#484	C₂²×C₅₃	1	2	yes	—
550	#484	C₂²×C₅₃	1	2	yes	—
551	#483	C₂²×C₅₃	1	2	yes	—
552	#483	C₂²×C₅₃	1	2	yes	—
553	#483	C₂²×C₅₃	1	2	yes	—
554	#479	C₂²×C₅₃	1	2	yes	—
555	#479	C₂²×C₅₃	1	2	yes	—
556	#479	C₂²×C₅₃	1	2	yes	—
557	#479	C₂²×C₅₃	1	2	yes	—
558	#479	C₂²×C₅₃	1	2	yes	—
559	#479	C₂²×C₅₃	1	2	yes	—
560	#479	C₂²×C₅₃	1	2	yes	—
561	#478	C₂²×C₅₃	1	2	yes	—
562	#478	C₂²×C₅₃	1	2	yes	—
563	#478	C₂²×C₅₃	1	2	yes	—
564	#477	C₂²×C₅₃	1	1	yes	characteristic
565	#476	C₂²×C₅₃	1	2	yes	—
566	#476	C₂²×C₅₃	1	1	yes	characteristic
567	#475	C₂²×C₅₃	1	2	yes	—
568	#475	C₂²×C₅₃	1	2	yes	—
569	#475	C₂²×C₅₃	1	2	yes	—
570	#470	C₂²×C₅₃	1	2	yes	—
571	#470	C₂²×C₅₃	1	2	yes	—
572	#470	C₂²×C₅₃	1	2	yes	—
573	#470	C₂²×C₅₃	1	2	yes	—
574	#467	C₂²×C₅₃	1	2	yes	—
575	#467	C₂²×C₅₃	1	2	yes	—
576	#462	C₂²×C₅₃	1	2	yes	—
577	#462	C₂²×C₅₃	1	1	yes	characteristic
578	#462	C₂²×C₅₃	1	2	yes	—
579	#462	C₂²×C₅₃	1	2	yes	—
580	#462	C₂²×C₅₃	1	2	yes	—
581	#461	C₂²×C₅₃	1	1	yes	characteristic
582	#452	C₂²×C₅₃	1	2	yes	—
583	#452	C₂²×C₅₃	1	2	yes	—
584	#452	C₂²×C₅₃	1	2	yes	—
585	#446	C₂²×C₅₃	1	2	yes	—
586	#441	C₂²×C₅₃	1	2	yes	—
587	#441	C₂²×C₅₃	1	2	yes	—
588	#440	C₂²×C₅₃	1	2	yes	—
589	#440	C₂²×C₅₃	1	2	yes	—
590	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
591	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
592	#436	C₂²×C₅₃	1	2	yes	—
593	#435	C₂²×C₅₃	1	2	yes	—
594	#435	C₂²×C₅₃	1	2	yes	—
595	#433	C₂²×C₅₃	1	2	yes	—
596	#432	C₂²×C₅₃	1	1	yes	characteristic
597	#428	C₂²×C₅₃	1	1	yes	characteristic
598	#428	C₂²×C₅₃	1	1	yes	characteristic
599	#428	C₂²×C₅₃	1	2	yes	—
600	C₂×#106	C₂²×C₅₃	1	2	yes	—
601	#424	C₂²×C₅₃	1	2	yes	—
602	#423	C₂²×C₅₃	1	1	yes	characteristic
603	#417	C₂²×C₅₃	1	1	yes	characteristic
604	#417	C₂²×C₅₃	1	2	yes	—
605	#417	C₂²×C₅₃	1	1	yes	characteristic
606	#416	C₂²×C₅₃	1	2	yes	—
607	C₅₃	#62237	1	1	yes	characteristic, direct product factor, Sylow
608	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
609	C₂×#41	C₂³×C₅₃	1	2	yes	—
610	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
611	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
612	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
613	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
614	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
616	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
617	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
623	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	D₄×C₅₃	1	2	yes	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	—	2	1	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	D₄×C₅₃	1	1	yes	characteristic
653	#125	C₂³×C₅₃	1	2	yes	—
654	#125	C₂³×C₅₃	1	2	yes	—
655	#125	C₂³×C₅₃	1	2	yes	—
656	#125	C₂³×C₅₃	1	2	yes	—
657	#124	D₄×C₅₃	1	1	yes	characteristic
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	D₄×C₅₃	1	2	yes	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
675	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
676	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
677	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
678	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
679	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
680	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
681	#121	—	2	1	no	—
682	#121	—	2	2	no	—
683	#121	D₄×C₅₃	1	1	yes	characteristic
684	C₄×Q₈	—	2	1	no	—
685	C₄×Q₈	—	2	2	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	1	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	2	yes	—
692	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
695	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
704	C₄×D₄	C₂³×C₅₃	1	2	yes	—
705	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
706	C₄×D₄	C₂³×C₅₃	1	2	yes	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	—	2	2	no	—
713	#117	—	2	1	no	—
714	#117	C₂³×C₅₃	1	1	yes	characteristic
715	#117	C₂³×C₅₃	1	2	yes	—
716	#117	C₂³×C₅₃	1	2	yes	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	1	no	—
719	C₂×C₄⋊C₄	—	2	2	no	—
720	C₂×C₄⋊C₄	—	2	1	no	—
721	C₂×C₄⋊C₄	—	2	2	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
727	C₂×C₄²	—	2	1	no	—
728	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
729	#107	C₂³×C₅₃	1	2	yes	—
730	#107	C₂³×C₅₃	1	2	yes	—
731	#107	C₂³×C₅₃	1	2	yes	—
732	#107	C₂³×C₅₃	1	2	yes	—
733	#107	C₂³×C₅₃	1	2	yes	—
734	#106	C₂³×C₅₃	1	2	yes	—
735	#106	C₂³×C₅₃	1	2	yes	—
736	#106	C₂³×C₅₃	1	2	yes	—
737	#106	C₂³×C₅₃	1	2	yes	—
738	#106	C₂³×C₅₃	1	2	yes	—
739	#106	C₂³×C₅₃	1	2	yes	—
740	#106	C₂³×C₅₃	1	2	yes	—
741	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
742	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
743	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
744	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
745	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
747	#103	C₂³×C₅₃	1	2	yes	—
748	#103	C₂³×C₅₃	1	2	yes	—
749	#103	C₂³×C₅₃	1	2	yes	—
750	#103	C₂³×C₅₃	1	2	yes	—
751	#103	C₂³×C₅₃	1	2	yes	—
752	#103	C₂³×C₅₃	1	2	yes	—
753	#103	C₂³×C₅₃	1	2	yes	—
754	#103	C₂³×C₅₃	1	2	yes	—
755	#103	C₂³×C₅₃	1	2	yes	—
756	#103	C₂³×C₅₃	1	2	yes	—
757	#103	C₂³×C₅₃	1	2	yes	—
758	#103	C₂³×C₅₃	1	2	yes	—
759	#103	C₂³×C₅₃	1	2	yes	—
760	#102	C₂³×C₅₃	1	2	yes	—
761	#102	C₂³×C₅₃	1	2	yes	—
762	#102	C₂³×C₅₃	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
766	#97	C₂³×C₅₃	1	2	yes	—
767	#97	C₂³×C₅₃	1	2	yes	—
768	C₄×C₈	C₂³×C₅₃	1	2	yes	—
769	#41	—	2	2	no	—
770	#41	—	2	4	no	—
771	#41	—	4	2	no	—
772	#41	—	4	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
777	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
778	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
784	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
798	Q₁₆	—	4	2	no	—
799	Q₁₆	—	4	2	no	—
800	Q₁₆	—	4	2	no	—
801	SD₁₆	—	2	4	no	—
802	M₁₆	—	4	1	no	—
803	M₁₆	—	4	2	no	—
804	M₁₆	—	4	1	no	—
805	C₂×C₈	—	4	2	no	—
806	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
807	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
808	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
809	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
845	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
846	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
849	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
868	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
869	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
870	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
871	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
872	C₄²	—	2	1	no	—
873	C₄²	—	2	1	no	—
874	C₄²	—	2	1	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
883	C₄²	C₂⁴×C₅₃	1	2	yes	—
884	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
885	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
886	C₂³	—	2	1	no	—
887	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
888	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
889	Q₈	—	2	2	no	—
890	Q₈	—	2	2	no	—
891	Q₈	—	2	1	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	1	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	8	1	no	—
897	Q₈	—	8	1	no	—
898	Q₈	—	8	2	no	—
899	D₄	—	2	1	no	—
900	D₄	—	4	1	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	4	no	—
903	D₄	—	4	2	no	—
904	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	2	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	1	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
937	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
952	C₄	—	2	2	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
970	C₄	C₅₃×#585	1	1	yes	characteristic
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	4	2	no	—
974	C₂	C₅₃×#3489	1	1	yes	characteristic
975	C₂	C₅₃×#3586	1	1	yes	characteristic
976	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×#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×#3563	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3374	C₂	semidirect
5. C₅₃×#3352	C₂	semidirect
6. C₅₃×#3344	C₂	semidirect
7. C₅₃×#3344	C₂	semidirect
8. C₅₃×#3331	C₂	semidirect
9. C₅₃×#3315	C₂	semidirect
10. C₅₃×#3315	C₂	semidirect
11. C₅₃×#3261	C₂	semidirect
12. C₅₃×#3255	C₂	semidirect
13. C₅₃×#3242	C₂	semidirect
14. C₅₃×#3236	C₂	semidirect
15. C₅₃×#3120	C₂	semidirect
16. C₅₃×#3116	C₂	semidirect
17. C₅₃×#3084	C₂	semidirect
18. C₅₃×#3080	C₂	semidirect
19. C₅₃×#2995	C₂	semidirect
453. #62237	C₅₃	direct (N × H)
483. #3563	C₂×C₅₃	semidirect
485. #3388	C₂×C₅₃	semidirect
486. #3374	C₂×C₅₃	semidirect
487. #3352	C₂×C₅₃	semidirect
488. #3344	C₂×C₅₃	semidirect
489. #3344	C₂×C₅₃	semidirect
490. #3331	C₂×C₅₃	semidirect
491. #3315	C₂×C₅₃	semidirect
492. #3315	C₂×C₅₃	semidirect
493. #3261	C₂×C₅₃	semidirect
494. #3255	C₂×C₅₃	semidirect
495. #3242	C₂×C₅₃	semidirect
496. #3236	C₂×C₅₃	semidirect
497. #3120	C₂×C₅₃	semidirect
498. #3116	C₂×C₅₃	semidirect
499. #3084	C₂×C₅₃	semidirect
500. #3080	C₂×C₅₃	semidirect
501. #2995	C₂×C₅₃	semidirect
607. C₅₃	#62237	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×#3563	2
C₅₃×#3515	2
C₅₃×#3388	2
C₅₃×#3374	2
C₅₃×#3352	2
C₅₃×#3344	2
C₅₃×#3331	2
C₅₃×#3315	2
C₅₃×#3261	2
C₅₃×#3255	2
C₅₃×#3242	2
C₅₃×#3236	2
C₅₃×#3120	2
C₅₃×#3116	2
C₅₃×#3084	2
C₅₃×#3080	2
C₅₃×#2995	2
#62237	53

Subgroups — C53×#62237 #27269749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62237 #27269749