Subgroups — C₅₃×#62124 #27269636

Order 13568.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3313	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3256	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3240	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3117	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3078	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
25	C₅₃×#557	C₂²	1	1	yes	characteristic
26	C₅₃×#556	—	2	1	no	—
27	C₅₃×#556	—	2	2	no	—
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#556	C₂²	1	2	yes	—
31	C₅₃×#556	C₂²	1	1	yes	characteristic
32	C₅₃×#555	C₂²	1	2	yes	—
33	C₅₃×#555	C₂²	1	1	yes	characteristic
34	C₅₃×#552	—	2	2	no	—
35	C₅₃×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#548	C₂²	1	2	yes	—
40	C₅₃×#547	—	2	1	no	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#542	—	2	1	no	—
43	C₅₃×#542	—	2	2	no	—
44	C₅₃×#533	—	2	1	no	—
45	C₅₃×#533	C₂²	1	1	yes	characteristic
46	C₅₃×#533	C₂²	1	1	yes	characteristic
47	C₅₃×#533	C₂²	1	2	yes	—
48	C₅₃×#529	—	2	2	no	—
49	C₅₃×#529	C₂²	1	2	yes	—
50	C₅₃×#529	C₂²	1	1	yes	characteristic
51	C₅₃×#529	C₂²	1	2	yes	—
52	C₅₃×#519	—	2	1	no	—
53	C₄×#41×C₅₃	—	2	1	no	—
54	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#501	C₂²	1	2	yes	—
59	C₅₃×#500	C₂²	1	1	yes	characteristic
60	C₅₃×#498	C₂²	1	1	yes	characteristic
61	C₅₃×#489	C₂²	1	2	yes	—
62	C₅₃×#489	C₂²	1	2	yes	—
63	C₅₃×#487	C₂²	1	1	yes	characteristic
64	C₅₃×#487	C₂²	1	1	yes	characteristic
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×#484	C₂²	1	2	yes	—
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#482	C₂²	1	2	yes	—
73	C₅₃×#482	C₂²	1	1	yes	characteristic
74	C₅₃×#481	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	1	yes	characteristic
81	C₅₃×#478	C₂²	1	1	yes	characteristic
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#477	C₂²	1	2	yes	—
85	C₅₃×#477	C₂²	1	1	yes	characteristic
86	C₅₃×#477	C₂²	1	2	yes	—
87	C₅₃×#476	C₂²	1	1	yes	characteristic
88	C₅₃×#475	C₂²	1	1	yes	characteristic
89	C₅₃×#475	C₂²	1	2	yes	—
90	C₅₃×#475	C₂²	1	1	yes	characteristic
91	C₅₃×#475	C₂²	1	2	yes	—
92	C₅₃×#474	C₂²	1	1	yes	characteristic
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#469	C₂²	1	2	yes	—
96	C₅₃×#468	C₂²	1	2	yes	—
97	C₅₃×#468	C₂²	1	2	yes	—
98	C₅₃×#467	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	2	yes	—
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#464	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	1	yes	characteristic
104	C₅₃×#463	C₂²	1	2	yes	—
105	C₅₃×#462	C₂²	1	1	yes	characteristic
106	C₅₃×#461	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	1	yes	characteristic
108	C₅₃×#451	C₂²	1	2	yes	—
109	C₅₃×#449	C₂²	1	1	yes	characteristic
110	C₅₃×#448	C₂²	1	2	yes	—
111	C₅₃×#446	C₂²	1	1	yes	characteristic
112	C₅₃×#446	C₂²	1	1	yes	characteristic
113	C₅₃×#441	C₂²	1	2	yes	—
114	C₅₃×#441	C₂²	1	2	yes	—
115	C₅₃×#440	C₂²	1	2	yes	—
116	C₅₃×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#436	C₂²	1	1	yes	characteristic
123	C₅₃×#435	C₂²	1	2	yes	—
124	C₅₃×#435	C₂²	1	2	yes	—
125	C₅₃×#432	C₂²	1	2	yes	—
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#428	C₂²	1	2	yes	—
129	C₅₃×#427	C₂²	1	2	yes	—
130	C₅₃×#423	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#419	C₂²	1	2	yes	—
133	C₅₃×#419	C₂²	1	2	yes	—
134	C₅₃×#416	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	—	2	1	no	—
139	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	—	2	1	no	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
166	#126×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	1	no	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	1	yes	characteristic
172	#125×C₅₃	C₂³	1	2	yes	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	2	no	—
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	C₂³	1	2	yes	—
180	#124×C₅₃	C₂³	1	1	yes	characteristic
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	1	no	—
185	#123×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	1	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	1	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	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	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₅₃	—	2	1	no	—
208	C₄×Q₈×C₅₃	—	2	2	no	—
209	C₄×Q₈×C₅₃	—	2	1	no	—
210	C₄×Q₈×C₅₃	—	2	2	no	—
211	C₄×Q₈×C₅₃	—	2	2	no	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	2	no	—
215	C₄×Q₈×C₅₃	—	2	1	no	—
216	C₄×Q₈×C₅₃	—	2	2	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
235	C₄×D₄×C₅₃	D₄	1	2	yes	—
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	#117×C₅₃	—	2	1	no	—
243	#117×C₅₃	—	2	2	no	—
244	#117×C₅₃	—	2	1	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	—	2	2	no	—
249	#117×C₅₃	—	2	2	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	D₄	1	2	yes	—
252	#117×C₅₃	D₄	1	1	yes	characteristic
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	1	yes	characteristic
255	#117×C₅₃	C₂³	1	2	yes	—
256	#117×C₅₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄²×C₅₃	—	2	1	no	—
260	C₂×C₄²×C₅₃	—	2	2	no	—
261	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
269	#107×C₅₃	C₂³	1	2	yes	—
270	#106×C₅₃	C₂³	1	1	yes	characteristic
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
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	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	4	2	no	—
314	#41×C₅₃	—	4	1	no	—
315	#41×C₅₃	—	4	4	no	—
316	C₂×Q₈×C₅₃	—	2	2	no	—
317	C₂×Q₈×C₅₃	—	2	2	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	—	2	1	no	—
322	C₂×Q₈×C₅₃	—	2	4	no	—
323	C₂×Q₈×C₅₃	—	4	2	no	—
324	C₂×Q₈×C₅₃	—	4	4	no	—
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₅₃	—	2	2	no	—
351	Q₁₆×C₅₃	—	4	2	no	—
352	SD₁₆×C₅₃	—	2	2	no	—
353	SD₁₆×C₅₃	—	4	2	no	—
354	SD₁₆×C₅₃	—	4	1	no	—
355	D₈×C₅₃	—	4	1	no	—
356	M₁₆×C₅₃	—	4	2	no	—
357	M₁₆×C₅₃	—	4	2	no	—
358	C₂×C₈×C₅₃	—	4	2	no	—
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₅₃	—	2	1	no	—
366	C₄⋊C₄×C₅₃	—	2	2	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	2	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	1	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	2	no	—
384	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₅₃	—	2	2	no	—
402	C₂²⋊C₄×C₅₃	—	2	2	no	—
403	C₂²⋊C₄×C₅₃	—	2	1	no	—
404	C₂²⋊C₄×C₅₃	—	2	2	no	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	1	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	2	no	—
430	C₄²×C₅₃	—	2	2	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₅₃	C₂×D₄	1	2	yes	—
436	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₃	C₂×D₄	1	2	yes	—
438	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₅₃	C₂⁴	1	2	yes	—
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₃	—	2	1	no	—
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
444	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₅₃	—	2	2	no	—
446	Q₈×C₅₃	—	2	1	no	—
447	Q₈×C₅₃	—	2	2	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	2	2	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	4	4	no	—
452	Q₈×C₅₃	—	4	4	no	—
453	Q₈×C₅₃	—	4	2	no	—
454	Q₈×C₅₃	—	4	2	no	—
455	Q₈×C₅₃	—	8	2	no	—
456	Q₈×C₅₃	—	8	1	no	—
457	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
458	D₄×C₅₃	—	2	2	no	—
459	D₄×C₅₃	—	2	1	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	2	1	no	—
462	D₄×C₅₃	—	2	1	no	—
463	D₄×C₅₃	—	4	2	no	—
464	D₄×C₅₃	—	4	2	no	—
465	D₄×C₅₃	—	4	4	no	—
466	D₄×C₅₃	—	8	2	no	—
467	D₄×C₅₃	—	8	1	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	1	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	1	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	4	2	no	—
484	C₂×C₄×C₅₃	—	4	1	no	—
485	C₂×C₄×C₅₃	—	4	2	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	4	4	no	—
488	C₂×C₄×C₅₃	—	4	2	no	—
489	C₂×C₄×C₅₃	—	4	4	no	—
490	C₂×C₄×C₅₃	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	4	2	no	—
493	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
502	C₈×C₅₃	—	2	1	no	—
503	C₈×C₅₃	—	2	1	no	—
504	C₈×C₅₃	—	2	2	no	—
505	C₈×C₅₃	—	2	2	no	—
506	C₈×C₅₃	—	2	1	no	—
507	C₈×C₅₃	—	2	1	no	—
508	#62124	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
509	C₂²×C₅₃	—	2	2	no	—
510	C₂²×C₅₃	—	2	1	no	—
511	C₂²×C₅₃	—	2	2	no	—
512	C₂²×C₅₃	—	2	1	no	—
513	C₂²×C₅₃	—	2	1	no	—
514	C₂²×C₅₃	—	2	2	no	—
515	C₂²×C₅₃	—	4	1	no	—
516	C₂²×C₅₃	—	4	1	no	—
517	C₂²×C₅₃	—	4	1	no	—
518	C₂²×C₅₃	—	4	1	no	—
519	C₂²×C₅₃	—	4	1	no	—
520	C₂²×C₅₃	—	4	1	no	—
521	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
522	C₄×C₅₃	—	2	1	no	—
523	C₄×C₅₃	—	2	2	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	1	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	2	no	—
528	C₄×C₅₃	—	2	1	no	—
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	4	1	no	—
531	C₄×C₅₃	—	4	2	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	2	no	—
534	C₄×C₅₃	—	4	1	no	—
535	C₄×C₅₃	—	4	1	no	—
536	C₄×C₅₃	—	4	2	no	—
537	C₄×C₅₃	—	4	2	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	#575	1	2	yes	—
540	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₄×C₅₃	#585	1	1	yes	characteristic
542	#3518	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3387	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3354	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3349	C₂×C₅₃	1	2	yes	complemented
551	#3348	C₂×C₅₃	1	2	yes	complemented
552	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
553	#3328	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3321	C₂×C₅₃	1	2	yes	complemented
555	#3313	C₂×C₅₃	1	2	yes	complemented
556	#3256	C₂×C₅₃	1	2	yes	complemented
557	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3240	C₂×C₅₃	1	2	yes	complemented
559	#3231	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3117	C₂×C₅₃	1	2	yes	complemented
561	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3078	C₂×C₅₃	1	2	yes	complemented
563	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
565	C₂×C₅₃	—	4	2	no	—
566	C₂×C₅₃	—	4	1	no	—
567	C₂×C₅₃	—	8	1	no	—
568	C₂×C₅₃	—	8	1	no	—
569	C₂×C₅₃	#3489	1	1	yes	characteristic
570	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
571	C₂×C₅₃	#3586	1	1	yes	characteristic
572	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
573	#557	C₂²×C₅₃	1	1	yes	characteristic
574	#556	—	2	1	no	—
575	#556	—	2	2	no	—
576	#556	—	2	1	no	—
577	#556	C₂²×C₅₃	1	1	yes	characteristic
578	#556	C₂²×C₅₃	1	1	yes	characteristic
579	#556	C₂²×C₅₃	1	2	yes	—
580	#555	C₂²×C₅₃	1	1	yes	characteristic
581	#555	C₂²×C₅₃	1	2	yes	—
582	#552	—	2	2	no	—
583	#552	C₂²×C₅₃	1	2	yes	—
584	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
585	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
586	#548	—	2	1	no	—
587	#548	C₂²×C₅₃	1	2	yes	—
588	#547	—	2	1	no	—
589	#547	C₂²×C₅₃	1	1	yes	characteristic
590	#542	—	2	1	no	—
591	#542	—	2	2	no	—
592	#533	—	2	1	no	—
593	#533	C₂²×C₅₃	1	1	yes	characteristic
594	#533	C₂²×C₅₃	1	1	yes	characteristic
595	#533	C₂²×C₅₃	1	2	yes	—
596	#529	—	2	2	no	—
597	#529	C₂²×C₅₃	1	1	yes	characteristic
598	#529	C₂²×C₅₃	1	2	yes	—
599	#529	C₂²×C₅₃	1	2	yes	—
600	#519	—	2	1	no	—
601	C₄×#41	—	2	1	no	—
602	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
603	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
604	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
605	#501	C₂²×C₅₃	1	2	yes	—
606	#501	C₂²×C₅₃	1	2	yes	—
607	#500	C₂²×C₅₃	1	1	yes	characteristic
608	#498	C₂²×C₅₃	1	1	yes	characteristic
609	#489	C₂²×C₅₃	1	2	yes	—
610	#489	C₂²×C₅₃	1	2	yes	—
611	#487	C₂²×C₅₃	1	1	yes	characteristic
612	#487	C₂²×C₅₃	1	1	yes	characteristic
613	#485	C₂²×C₅₃	1	2	yes	—
614	#485	C₂²×C₅₃	1	2	yes	—
615	#485	C₂²×C₅₃	1	2	yes	—
616	#485	C₂²×C₅₃	1	1	yes	characteristic
617	#485	C₂²×C₅₃	1	2	yes	—
618	#484	C₂²×C₅₃	1	2	yes	—
619	#482	C₂²×C₅₃	1	1	yes	characteristic
620	#482	C₂²×C₅₃	1	2	yes	—
621	#482	C₂²×C₅₃	1	2	yes	—
622	#481	C₂²×C₅₃	1	2	yes	—
623	#479	C₂²×C₅₃	1	2	yes	—
624	#479	C₂²×C₅₃	1	1	yes	characteristic
625	#479	C₂²×C₅₃	1	2	yes	—
626	#479	C₂²×C₅₃	1	2	yes	—
627	#479	C₂²×C₅₃	1	2	yes	—
628	#479	C₂²×C₅₃	1	2	yes	—
629	#478	C₂²×C₅₃	1	2	yes	—
630	#478	C₂²×C₅₃	1	2	yes	—
631	#478	C₂²×C₅₃	1	1	yes	characteristic
632	#477	C₂²×C₅₃	1	1	yes	characteristic
633	#477	C₂²×C₅₃	1	2	yes	—
634	#477	C₂²×C₅₃	1	2	yes	—
635	#476	C₂²×C₅₃	1	1	yes	characteristic
636	#475	C₂²×C₅₃	1	1	yes	characteristic
637	#475	C₂²×C₅₃	1	2	yes	—
638	#475	C₂²×C₅₃	1	2	yes	—
639	#475	C₂²×C₅₃	1	1	yes	characteristic
640	#474	C₂²×C₅₃	1	1	yes	characteristic
641	#474	C₂²×C₅₃	1	1	yes	characteristic
642	#470	C₂²×C₅₃	1	2	yes	—
643	#469	C₂²×C₅₃	1	2	yes	—
644	#468	C₂²×C₅₃	1	2	yes	—
645	#468	C₂²×C₅₃	1	2	yes	—
646	#467	C₂²×C₅₃	1	2	yes	—
647	#465	C₂²×C₅₃	1	2	yes	—
648	#464	C₂²×C₅₃	1	1	yes	characteristic
649	#464	C₂²×C₅₃	1	2	yes	—
650	#464	C₂²×C₅₃	1	2	yes	—
651	#463	C₂²×C₅₃	1	1	yes	characteristic
652	#463	C₂²×C₅₃	1	2	yes	—
653	#462	C₂²×C₅₃	1	1	yes	characteristic
654	#461	C₂²×C₅₃	1	1	yes	characteristic
655	#452	C₂²×C₅₃	1	1	yes	characteristic
656	#451	C₂²×C₅₃	1	2	yes	—
657	#449	C₂²×C₅₃	1	1	yes	characteristic
658	#448	C₂²×C₅₃	1	2	yes	—
659	#446	C₂²×C₅₃	1	1	yes	characteristic
660	#446	C₂²×C₅₃	1	1	yes	characteristic
661	#441	C₂²×C₅₃	1	2	yes	—
662	#441	C₂²×C₅₃	1	2	yes	—
663	#440	C₂²×C₅₃	1	2	yes	—
664	#440	C₂²×C₅₃	1	2	yes	—
665	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
666	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
668	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
669	#436	C₂²×C₅₃	1	1	yes	characteristic
670	#436	C₂²×C₅₃	1	1	yes	characteristic
671	#435	C₂²×C₅₃	1	2	yes	—
672	#435	C₂²×C₅₃	1	2	yes	—
673	#432	C₂²×C₅₃	1	2	yes	—
674	#431	C₂²×C₅₃	1	1	yes	characteristic
675	#428	C₂²×C₅₃	1	2	yes	—
676	#428	C₂²×C₅₃	1	2	yes	—
677	#427	C₂²×C₅₃	1	2	yes	—
678	#423	C₂²×C₅₃	1	2	yes	—
679	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
680	#419	C₂²×C₅₃	1	2	yes	—
681	#419	C₂²×C₅₃	1	2	yes	—
682	#416	C₂²×C₅₃	1	2	yes	—
683	C₅₃	#62124	1	1	yes	characteristic, direct product factor, Sylow
684	C₂×#41	—	2	1	no	—
685	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
686	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
687	C₂²×Q₈	—	2	1	no	—
688	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
689	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
694	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
696	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
697	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	1	no	—
715	#126	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	C₂³×C₅₃	1	1	yes	characteristic
720	#125	C₂³×C₅₃	1	2	yes	—
721	#125	C₂³×C₅₃	1	2	yes	—
722	#124	—	2	1	no	—
723	#124	—	2	2	no	—
724	#124	—	2	2	no	—
725	#124	—	2	2	no	—
726	#124	—	2	2	no	—
727	#124	—	2	2	no	—
728	#124	C₂³×C₅₃	1	1	yes	characteristic
729	#124	C₂³×C₅₃	1	2	yes	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	1	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
750	#121	—	2	2	no	—
751	#121	—	2	1	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₅₃	1	2	yes	—
754	#121	C₂³×C₅₃	1	2	yes	—
755	#121	C₂³×C₅₃	1	1	yes	characteristic
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	2	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	D₄×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	2	yes	—
772	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
784	C₄×D₄	D₄×C₅₃	1	2	yes	—
785	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₅₃	1	2	yes	—
789	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₅₃	1	2	yes	—
791	#117	—	2	1	no	—
792	#117	—	2	1	no	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	—	2	2	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	D₄×C₅₃	1	2	yes	—
801	#117	D₄×C₅₃	1	1	yes	characteristic
802	#117	C₂³×C₅₃	1	1	yes	characteristic
803	#117	C₂³×C₅₃	1	2	yes	—
804	#117	C₂³×C₅₃	1	2	yes	—
805	#117	C₂³×C₅₃	1	2	yes	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
808	C₂×C₄²	—	2	2	no	—
809	C₂×C₄²	—	2	1	no	—
810	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
811	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
812	#107	C₂³×C₅₃	1	2	yes	—
813	#107	C₂³×C₅₃	1	2	yes	—
814	#107	C₂³×C₅₃	1	1	yes	characteristic
815	#107	C₂³×C₅₃	1	2	yes	—
816	#107	C₂³×C₅₃	1	2	yes	—
817	#107	C₂³×C₅₃	1	1	yes	characteristic
818	#107	C₂³×C₅₃	1	2	yes	—
819	#106	C₂³×C₅₃	1	2	yes	—
820	#106	C₂³×C₅₃	1	2	yes	—
821	#106	C₂³×C₅₃	1	1	yes	characteristic
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	2	yes	—
824	#106	C₂³×C₅₃	1	1	yes	characteristic
825	#106	C₂³×C₅₃	1	2	yes	—
826	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
827	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
833	#103	C₂³×C₅₃	1	2	yes	—
834	#103	C₂³×C₅₃	1	2	yes	—
835	#103	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	2	yes	—
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#103	C₂³×C₅₃	1	2	yes	—
841	#103	C₂³×C₅₃	1	1	yes	characteristic
842	#103	C₂³×C₅₃	1	1	yes	characteristic
843	#103	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	2	yes	—
845	#103	C₂³×C₅₃	1	2	yes	—
846	#102	C₂³×C₅₃	1	2	yes	—
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	1	yes	characteristic
849	#102	C₂³×C₅₃	1	1	yes	characteristic
850	#102	C₂³×C₅₃	1	1	yes	characteristic
851	#102	C₂³×C₅₃	1	1	yes	characteristic
852	#102	C₂³×C₅₃	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
857	#97	C₂³×C₅₃	1	2	yes	—
858	#97	C₂³×C₅₃	1	2	yes	—
859	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
861	#41	—	2	2	no	—
862	#41	—	4	2	no	—
863	#41	—	4	1	no	—
864	#41	—	4	4	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	4	no	—
872	C₂×Q₈	—	4	2	no	—
873	C₂×Q₈	—	4	4	no	—
874	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
875	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
876	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
883	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
884	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
885	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
895	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
896	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
899	Q₁₆	—	2	2	no	—
900	Q₁₆	—	4	2	no	—
901	SD₁₆	—	2	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	1	no	—
904	D₈	—	4	1	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
913	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
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	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
984	C₄²	C₂×D₄×C₅₃	1	2	yes	—
985	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
986	C₄²	C₂×D₄×C₅₃	1	2	yes	—
987	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₄²	C₂⁴×C₅₃	1	2	yes	—
989	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
993	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	4	4	no	—
1001	Q₈	—	4	4	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	4	no	—
1015	D₄	—	8	1	no	—
1016	D₄	—	8	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1050	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	2	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	C₅₃×#575	1	2	yes	—
1088	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1089	C₄	C₅₃×#585	1	1	yes	characteristic
1090	C₂	—	4	2	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	8	1	no	—
1093	C₂	—	8	1	no	—
1094	C₂	C₅₃×#3489	1	1	yes	characteristic
1095	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1096	C₂	C₅₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3518	C₂	semidirect
2. C₅₃×#3482	C₂	semidirect
3. C₅₃×#3387	C₂	semidirect
4. C₅₃×#3386	C₂	semidirect
5. C₅₃×#3369	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3354	C₂	semidirect
8. C₅₃×#3353	C₂	semidirect
9. C₅₃×#3349	C₂	semidirect
10. C₅₃×#3348	C₂	semidirect
11. C₅₃×#3329	C₂	semidirect
12. C₅₃×#3328	C₂	semidirect
13. C₅₃×#3321	C₂	semidirect
14. C₅₃×#3313	C₂	semidirect
15. C₅₃×#3256	C₂	semidirect
16. C₅₃×#3248	C₂	semidirect
17. C₅₃×#3240	C₂	semidirect
18. C₅₃×#3231	C₂	semidirect
19. C₅₃×#3117	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3078	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2989	C₂	semidirect
508. #62124	C₅₃	direct (N × H)
542. #3518	C₂×C₅₃	semidirect
543. #3482	C₂×C₅₃	semidirect
544. #3387	C₂×C₅₃	semidirect
545. #3386	C₂×C₅₃	semidirect
546. #3369	C₂×C₅₃	semidirect
547. #3367	C₂×C₅₃	semidirect
548. #3354	C₂×C₅₃	semidirect
549. #3353	C₂×C₅₃	semidirect
550. #3349	C₂×C₅₃	semidirect
551. #3348	C₂×C₅₃	semidirect
552. #3329	C₂×C₅₃	semidirect
553. #3328	C₂×C₅₃	semidirect
554. #3321	C₂×C₅₃	semidirect
555. #3313	C₂×C₅₃	semidirect
556. #3256	C₂×C₅₃	semidirect
557. #3248	C₂×C₅₃	semidirect
558. #3240	C₂×C₅₃	semidirect
559. #3231	C₂×C₅₃	semidirect
560. #3117	C₂×C₅₃	semidirect
561. #3102	C₂×C₅₃	semidirect
562. #3078	C₂×C₅₃	semidirect
563. #3076	C₂×C₅₃	semidirect
564. #2989	C₂×C₅₃	semidirect
683. C₅₃	#62124	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×#3518	2
C₅₃×#3482	2
C₅₃×#3387	2
C₅₃×#3386	2
C₅₃×#3369	2
C₅₃×#3367	2
C₅₃×#3354	2
C₅₃×#3353	2
C₅₃×#3349	2
C₅₃×#3348	2
C₅₃×#3329	2
C₅₃×#3328	2
C₅₃×#3321	2
C₅₃×#3313	2
C₅₃×#3256	2
C₅₃×#3248	2
C₅₃×#3240	2
C₅₃×#3231	2
C₅₃×#3117	2
C₅₃×#3102	2
C₅₃×#3078	2
C₅₃×#3076	2
C₅₃×#2989	2
#62124	53

Subgroups — C53×#62124 #27269636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62124 #27269636