Subgroups — C₅₃×#61859 #27269371

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1072 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×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3367	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3124	C₂	1	2	yes	maximal
20	C₅₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
26	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
27	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
28	C₅₃×#557	C₂²	1	1	yes	characteristic
29	C₅₃×#557	C₂²	1	2	yes	—
30	C₅₃×#557	C₂²	1	2	yes	—
31	C₅₃×#556	—	2	1	no	—
32	C₅₃×#556	C₂²	1	1	yes	characteristic
33	C₅₃×#556	C₂²	1	2	yes	—
34	C₅₃×#554	—	2	1	no	—
35	C₅₃×#554	—	2	1	no	—
36	C₅₃×#554	C₂²	1	1	yes	characteristic
37	C₅₃×#554	C₂²	1	1	yes	characteristic
38	C₅₃×#554	C₂²	1	1	yes	characteristic
39	C₅₃×#552	—	2	1	no	—
40	D₄×Q₈×C₅₃	—	2	2	no	—
41	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
42	C₅₃×#544	—	2	1	no	—
43	C₅₃×#544	—	2	2	no	—
44	C₅₃×#544	C₂²	1	2	yes	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#541	—	2	1	no	—
47	C₅₃×#541	—	2	2	no	—
48	C₅₃×#541	C₂²	1	2	yes	—
49	C₅₃×#533	—	2	1	no	—
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₅₃×#533	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
53	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#529	C₂²	1	1	yes	characteristic
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×#501	C₂²	1	2	yes	—
59	C₅₃×#501	C₂²	1	2	yes	—
60	C₅₃×#500	C₂²	1	1	yes	characteristic
61	C₅₃×#500	C₂²	1	1	yes	characteristic
62	C₅₃×#500	C₂²	1	2	yes	—
63	C₅₃×#499	C₂²	1	2	yes	—
64	C₅₃×#491	C₂²	1	2	yes	—
65	C₅₃×#489	C₂²	1	2	yes	—
66	C₅₃×#489	C₂²	1	2	yes	—
67	C₅₃×#488	C₂²	1	2	yes	—
68	C₅₃×#487	C₂²	1	1	yes	characteristic
69	C₅₃×#487	C₂²	1	1	yes	characteristic
70	C₅₃×#487	C₂²	1	2	yes	—
71	C₅₃×#485	C₂²	1	1	yes	characteristic
72	C₅₃×#485	C₂²	1	2	yes	—
73	C₅₃×#484	C₂²	1	2	yes	—
74	C₅₃×#484	C₂²	1	2	yes	—
75	C₅₃×#483	C₂²	1	2	yes	—
76	C₅₃×#482	C₂²	1	1	yes	characteristic
77	C₅₃×#480	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×#479	C₂²	1	1	yes	characteristic
82	C₅₃×#479	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	1	yes	characteristic
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#477	C₂²	1	2	yes	—
87	C₅₃×#477	C₂²	1	2	yes	—
88	C₅₃×#477	C₂²	1	1	yes	characteristic
89	C₅₃×#477	C₂²	1	1	yes	characteristic
90	C₅₃×#477	C₂²	1	2	yes	—
91	C₅₃×#477	C₂²	1	2	yes	—
92	C₅₃×#477	C₂²	1	1	yes	characteristic
93	C₅₃×#477	C₂²	1	2	yes	—
94	C₅₃×#476	C₂²	1	1	yes	characteristic
95	C₅₃×#476	C₂²	1	1	yes	characteristic
96	C₅₃×#476	C₂²	1	1	yes	characteristic
97	C₅₃×#475	C₂²	1	2	yes	—
98	C₅₃×#474	C₂²	1	2	yes	—
99	C₅₃×#474	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	1	yes	characteristic
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#462	C₂²	1	1	yes	characteristic
105	C₅₃×#462	C₂²	1	2	yes	—
106	C₅₃×#461	C₂²	1	1	yes	characteristic
107	C₅₃×#461	C₂²	1	2	yes	—
108	C₅₃×#452	C₂²	1	1	yes	characteristic
109	C₅₃×#452	C₂²	1	2	yes	—
110	C₅₃×#449	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	2	yes	—
112	C₅₃×#446	C₂²	1	1	yes	characteristic
113	C₅₃×#446	C₂²	1	1	yes	characteristic
114	C₅₃×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
117	C₅₃×#441	C₂²	1	2	yes	—
118	C₅₃×#441	C₂²	1	2	yes	—
119	C₅₃×#440	C₂²	1	2	yes	—
120	C₅₃×#440	C₂²	1	2	yes	—
121	C₅₃×#440	C₂²	1	2	yes	—
122	C₅₃×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
129	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₅₃	C₂²	1	2	yes	—
131	C₅₃×#433	C₂²	1	2	yes	—
132	C₅₃×#433	C₂²	1	2	yes	—
133	C₅₃×#432	C₂²	1	1	yes	characteristic
134	C₅₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₅₃	—	2	2	no	—
137	C₂²×Q₈×C₅₃	—	2	1	no	—
138	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₅₃	—	2	2	no	—
145	C₄⋊Q₈×C₅₃	—	2	1	no	—
146	C₄⋊Q₈×C₅₃	—	2	1	no	—
147	C₄⋊Q₈×C₅₃	—	2	2	no	—
148	C₄⋊Q₈×C₅₃	—	2	2	no	—
149	C₄⋊Q₈×C₅₃	—	2	2	no	—
150	C₄⋊Q₈×C₅₃	—	2	1	no	—
151	C₄⋊Q₈×C₅₃	—	2	1	no	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	2	no	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	2	no	—
172	#126×C₅₃	—	2	1	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	2	no	—
179	#125×C₅₃	—	2	1	no	—
180	#125×C₅₃	—	2	2	no	—
181	#125×C₅₃	—	2	2	no	—
182	#125×C₅₃	—	2	1	no	—
183	#125×C₅₃	D₄	1	2	yes	—
184	#125×C₅₃	C₂³	1	2	yes	—
185	#125×C₅₃	C₂³	1	2	yes	—
186	#125×C₅₃	C₂³	1	2	yes	—
187	#125×C₅₃	C₂³	1	1	yes	characteristic
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	C₂³	1	2	yes	—
190	#124×C₅₃	C₂³	1	1	yes	characteristic
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
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	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	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	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₅₃	—	2	2	no	—
215	C₄×Q₈×C₅₃	—	2	2	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	—	2	1	no	—
219	C₄×Q₈×C₅₃	—	2	1	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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×Q₈×C₅₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₄²×C₅₃	—	2	1	no	—
259	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
260	#107×C₅₃	C₂³	1	1	yes	characteristic
261	#107×C₅₃	C₂³	1	2	yes	—
262	#107×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#106×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	1	yes	characteristic
274	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
279	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	#103×C₅₃	C₂³	1	1	yes	characteristic
283	#103×C₅₃	C₂³	1	2	yes	—
284	#103×C₅₃	C₂³	1	2	yes	—
285	#103×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	1	yes	characteristic
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	#97×C₅₃	C₂³	1	2	yes	—
306	#97×C₅₃	C₂³	1	2	yes	—
307	#97×C₅₃	C₂³	1	2	yes	—
308	C₄×C₈×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	#41×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	2	no	—
314	C₂×Q₈×C₅₃	—	2	2	no	—
315	C₂×Q₈×C₅₃	—	2	1	no	—
316	C₂×Q₈×C₅₃	—	2	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	2	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	8	2	no	—
322	C₂×Q₈×C₅₃	—	8	4	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅₃	—	2	1	no	—
334	C₂²×C₄×C₅₃	—	2	2	no	—
335	C₂²×C₄×C₅₃	—	2	1	no	—
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	1	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	Q₁₆×C₅₃	—	2	2	no	—
345	Q₁₆×C₅₃	—	2	4	no	—
346	SD₁₆×C₅₃	—	2	2	no	—
347	SD₁₆×C₅₃	—	2	2	no	—
348	SD₁₆×C₅₃	—	2	4	no	—
349	D₈×C₅₃	—	2	2	no	—
350	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
353	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₅₃	—	2	1	no	—
357	C₄⋊C₄×C₅₃	—	2	1	no	—
358	C₄⋊C₄×C₅₃	—	2	2	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	1	no	—
367	C₄⋊C₄×C₅₃	—	2	1	no	—
368	C₄⋊C₄×C₅₃	—	2	1	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₃	C₂×D₄	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	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₅₃	—	2	2	no	—
404	C₂²⋊C₄×C₅₃	—	2	1	no	—
405	C₂²⋊C₄×C₅₃	—	2	1	no	—
406	C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄²×C₅₃	—	2	1	no	—
420	C₄²×C₅₃	—	2	1	no	—
421	C₄²×C₅₃	—	2	1	no	—
422	C₄²×C₅₃	—	2	2	no	—
423	C₄²×C₅₃	—	2	2	no	—
424	C₄²×C₅₃	—	2	2	no	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	2	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₄²×C₅₃	C₂⁴	1	2	yes	—
433	C₄²×C₅₃	C₂⁴	1	2	yes	—
434	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂³×C₅₃	—	2	1	no	—
436	C₂³×C₅₃	—	2	1	no	—
437	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₅₃	—	2	2	no	—
439	Q₈×C₅₃	—	2	2	no	—
440	Q₈×C₅₃	—	2	1	no	—
441	Q₈×C₅₃	—	2	1	no	—
442	Q₈×C₅₃	—	2	2	no	—
443	Q₈×C₅₃	—	2	1	no	—
444	Q₈×C₅₃	—	2	2	no	—
445	Q₈×C₅₃	—	4	2	no	—
446	Q₈×C₅₃	—	4	4	no	—
447	Q₈×C₅₃	—	8	1	no	—
448	Q₈×C₅₃	—	8	2	no	—
449	Q₈×C₅₃	—	8	1	no	—
450	Q₈×C₅₃	—	8	1	no	—
451	Q₈×C₅₃	—	8	2	no	—
452	Q₈×C₅₃	—	8	2	no	—
453	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
454	D₄×C₅₃	—	2	4	no	—
455	D₄×C₅₃	—	2	1	no	—
456	D₄×C₅₃	—	2	1	no	—
457	D₄×C₅₃	—	2	1	no	—
458	D₄×C₅₃	—	8	1	no	—
459	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
460	C₂×C₄×C₅₃	—	2	4	no	—
461	C₂×C₄×C₅₃	—	2	1	no	—
462	C₂×C₄×C₅₃	—	2	2	no	—
463	C₂×C₄×C₅₃	—	2	1	no	—
464	C₂×C₄×C₅₃	—	2	1	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	1	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	—	4	1	no	—
475	C₂×C₄×C₅₃	—	4	2	no	—
476	C₂×C₄×C₅₃	—	4	2	no	—
477	C₂×C₄×C₅₃	—	4	2	no	—
478	C₂×C₄×C₅₃	—	8	2	no	—
479	C₂×C₄×C₅₃	—	8	2	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	—	8	2	no	—
482	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
492	C₈×C₅₃	—	2	1	no	—
493	C₈×C₅₃	—	2	1	no	—
494	C₈×C₅₃	—	2	1	no	—
495	C₈×C₅₃	—	2	2	no	—
496	C₈×C₅₃	—	2	1	no	—
497	C₈×C₅₃	—	2	2	no	—
498	#61859	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂²×C₅₃	—	2	1	no	—
500	C₂²×C₅₃	—	2	1	no	—
501	C₂²×C₅₃	—	2	2	no	—
502	C₂²×C₅₃	—	2	1	no	—
503	C₂²×C₅₃	—	4	1	no	—
504	C₂²×C₅₃	—	4	1	no	—
505	C₂²×C₅₃	—	4	1	no	—
506	C₂²×C₅₃	—	4	1	no	—
507	C₂²×C₅₃	—	4	1	no	—
508	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₅₃	—	2	1	no	—
510	C₄×C₅₃	—	2	1	no	—
511	C₄×C₅₃	—	2	2	no	—
512	C₄×C₅₃	—	2	2	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	—	2	2	no	—
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	2	2	no	—
517	C₄×C₅₃	—	2	2	no	—
518	C₄×C₅₃	—	4	1	no	—
519	C₄×C₅₃	—	4	2	no	—
520	C₄×C₅₃	—	4	2	no	—
521	C₄×C₅₃	—	4	2	no	—
522	C₄×C₅₃	—	4	1	no	—
523	C₄×C₅₃	—	4	2	no	—
524	C₄×C₅₃	—	4	1	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	1	no	—
527	C₄×C₅₃	#578	1	2	yes	—
528	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	#3555	C₂×C₅₃	1	1	yes	characteristic, complemented
531	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
532	#3390	C₂×C₅₃	1	2	yes	complemented
533	#3386	C₂×C₅₃	1	2	yes	complemented
534	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
535	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
536	Q₈×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
537	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
538	#3377	C₂×C₅₃	1	2	yes	complemented
539	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#3367	C₂×C₅₃	1	2	yes	complemented
542	#3363	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
544	#3243	C₂×C₅₃	1	2	yes	complemented
545	#3242	C₂×C₅₃	1	2	yes	complemented
546	#3238	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3230	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3124	C₂×C₅₃	1	2	yes	—
549	#3120	C₂×C₅₃	1	2	yes	complemented
550	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3102	C₂×C₅₃	1	1	yes	characteristic
552	#2985	C₂×C₅₃	1	1	yes	characteristic, complemented
553	C₂×C₅₃	—	4	1	no	—
554	C₂×C₅₃	—	4	2	no	—
555	C₂×C₅₃	—	8	1	no	—
556	C₂×C₅₃	#3486	1	1	yes	characteristic
557	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
558	C₂×C₅₃	#3585	1	1	yes	characteristic
559	#563	—	2	2	no	—
560	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
561	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
562	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
563	#557	C₂²×C₅₃	1	1	yes	characteristic
564	#557	C₂²×C₅₃	1	2	yes	—
565	#557	C₂²×C₅₃	1	2	yes	—
566	#556	—	2	1	no	—
567	#556	C₂²×C₅₃	1	1	yes	characteristic
568	#556	C₂²×C₅₃	1	2	yes	—
569	#554	—	2	1	no	—
570	#554	—	2	1	no	—
571	#554	C₂²×C₅₃	1	1	yes	characteristic
572	#554	C₂²×C₅₃	1	1	yes	characteristic
573	#554	C₂²×C₅₃	1	1	yes	characteristic
574	#552	—	2	1	no	—
575	D₄×Q₈	—	2	2	no	—
576	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
577	#544	—	2	1	no	—
578	#544	—	2	2	no	—
579	#544	C₂²×C₅₃	1	2	yes	—
580	#542	C₂²×C₅₃	1	2	yes	—
581	#541	—	2	1	no	—
582	#541	—	2	2	no	—
583	#541	C₂²×C₅₃	1	2	yes	—
584	#533	—	2	1	no	—
585	#533	C₂²×C₅₃	1	1	yes	characteristic
586	#533	C₂²×C₅₃	1	1	yes	characteristic
587	C₂×C₄⋊Q₈	—	2	1	no	—
588	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
589	#529	C₂²×C₅₃	1	1	yes	characteristic
590	#520	C₂²×C₅₃	1	2	yes	—
591	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
592	#501	C₂²×C₅₃	1	2	yes	—
593	#501	C₂²×C₅₃	1	2	yes	—
594	#501	C₂²×C₅₃	1	2	yes	—
595	#500	C₂²×C₅₃	1	1	yes	characteristic
596	#500	C₂²×C₅₃	1	2	yes	—
597	#500	C₂²×C₅₃	1	1	yes	characteristic
598	#499	C₂²×C₅₃	1	2	yes	—
599	#491	C₂²×C₅₃	1	2	yes	—
600	#489	C₂²×C₅₃	1	2	yes	—
601	#489	C₂²×C₅₃	1	2	yes	—
602	#488	C₂²×C₅₃	1	2	yes	—
603	#487	C₂²×C₅₃	1	1	yes	characteristic
604	#487	C₂²×C₅₃	1	2	yes	—
605	#487	C₂²×C₅₃	1	1	yes	characteristic
606	#485	C₂²×C₅₃	1	1	yes	characteristic
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	#482	C₂²×C₅₃	1	1	yes	characteristic
612	#480	C₂²×C₅₃	1	2	yes	—
613	#479	C₂²×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
619	#478	C₂²×C₅₃	1	2	yes	—
620	#478	C₂²×C₅₃	1	2	yes	—
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	2	yes	—
625	#477	C₂²×C₅₃	1	1	yes	characteristic
626	#477	C₂²×C₅₃	1	1	yes	characteristic
627	#477	C₂²×C₅₃	1	2	yes	—
628	#477	C₂²×C₅₃	1	2	yes	—
629	#476	C₂²×C₅₃	1	1	yes	characteristic
630	#476	C₂²×C₅₃	1	1	yes	characteristic
631	#476	C₂²×C₅₃	1	1	yes	characteristic
632	#475	C₂²×C₅₃	1	2	yes	—
633	#474	C₂²×C₅₃	1	2	yes	—
634	#474	C₂²×C₅₃	1	2	yes	—
635	#464	C₂²×C₅₃	1	1	yes	characteristic
636	#464	C₂²×C₅₃	1	2	yes	—
637	#463	C₂²×C₅₃	1	1	yes	characteristic
638	#463	C₂²×C₅₃	1	2	yes	—
639	#462	C₂²×C₅₃	1	1	yes	characteristic
640	#462	C₂²×C₅₃	1	2	yes	—
641	#461	C₂²×C₅₃	1	1	yes	characteristic
642	#461	C₂²×C₅₃	1	2	yes	—
643	#452	C₂²×C₅₃	1	1	yes	characteristic
644	#452	C₂²×C₅₃	1	2	yes	—
645	#449	C₂²×C₅₃	1	1	yes	characteristic
646	#446	C₂²×C₅₃	1	2	yes	—
647	#446	C₂²×C₅₃	1	1	yes	characteristic
648	#446	C₂²×C₅₃	1	1	yes	characteristic
649	#446	C₂²×C₅₃	1	2	yes	—
650	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
651	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
652	#441	C₂²×C₅₃	1	2	yes	—
653	#441	C₂²×C₅₃	1	2	yes	—
654	#440	C₂²×C₅₃	1	2	yes	—
655	#440	C₂²×C₅₃	1	2	yes	—
656	#440	C₂²×C₅₃	1	2	yes	—
657	#440	C₂²×C₅₃	1	2	yes	—
658	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
659	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
664	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
665	C₄×D₈	C₂²×C₅₃	1	2	yes	—
666	#433	C₂²×C₅₃	1	2	yes	—
667	#433	C₂²×C₅₃	1	2	yes	—
668	#432	C₂²×C₅₃	1	1	yes	characteristic
669	#431	C₂²×C₅₃	1	1	yes	characteristic
670	C₅₃	#61859	1	1	yes	characteristic, direct product factor, Sylow
671	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
672	C₂²×Q₈	—	2	2	no	—
673	C₂²×Q₈	—	2	1	no	—
674	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
675	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
677	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
679	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	1	no	—
685	C₄⋊Q₈	—	2	2	no	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	1	no	—
689	C₄⋊Q₈	—	2	1	no	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
692	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
695	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
696	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	1	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	D₄×C₅₃	1	2	yes	—
720	#125	C₂³×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	2	no	—
725	#124	C₂³×C₅₃	1	1	yes	characteristic
726	#124	C₂³×C₅₃	1	2	yes	—
727	#123	—	2	1	no	—
728	#123	—	2	2	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
744	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
745	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
746	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
747	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
748	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
749	#121	C₂³×C₅₃	1	1	yes	characteristic
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	—	2	2	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
760	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
761	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
763	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
764	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
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×D₄	—	2	1	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
775	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₅₃	1	2	yes	—
777	C₄×D₄	C₂³×C₅₃	1	2	yes	—
778	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₅₃	1	2	yes	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	2	2	no	—
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	2	1	no	—
786	#117	C₂³×C₅₃	1	1	yes	characteristic
787	#117	C₂³×C₅₃	1	2	yes	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	2	no	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	1	no	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
794	C₂×C₄²	—	2	1	no	—
795	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
796	#107	C₂³×C₅₃	1	2	yes	—
797	#107	C₂³×C₅₃	1	1	yes	characteristic
798	#107	C₂³×C₅₃	1	2	yes	—
799	#107	C₂³×C₅₃	1	1	yes	characteristic
800	#107	C₂³×C₅₃	1	2	yes	—
801	#107	C₂³×C₅₃	1	2	yes	—
802	#107	C₂³×C₅₃	1	2	yes	—
803	#107	C₂³×C₅₃	1	2	yes	—
804	#107	C₂³×C₅₃	1	2	yes	—
805	#106	C₂³×C₅₃	1	1	yes	characteristic
806	#106	C₂³×C₅₃	1	2	yes	—
807	#106	C₂³×C₅₃	1	1	yes	characteristic
808	#106	C₂³×C₅₃	1	2	yes	—
809	#106	C₂³×C₅₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
815	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
818	#103	C₂³×C₅₃	1	1	yes	characteristic
819	#103	C₂³×C₅₃	1	2	yes	—
820	#103	C₂³×C₅₃	1	1	yes	characteristic
821	#103	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	1	yes	characteristic
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	2	yes	—
830	#103	C₂³×C₅₃	1	2	yes	—
831	#102	C₂³×C₅₃	1	1	yes	characteristic
832	#102	C₂³×C₅₃	1	2	yes	—
833	#102	C₂³×C₅₃	1	2	yes	—
834	#102	C₂³×C₅₃	1	1	yes	characteristic
835	#102	C₂³×C₅₃	1	1	yes	characteristic
836	#102	C₂³×C₅₃	1	1	yes	characteristic
837	#102	C₂³×C₅₃	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
841	#97	C₂³×C₅₃	1	2	yes	—
842	#97	C₂³×C₅₃	1	2	yes	—
843	#97	C₂³×C₅₃	1	2	yes	—
844	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
845	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₅₃	1	2	yes	—
847	C₄×C₈	C₂³×C₅₃	1	2	yes	—
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	8	2	no	—
858	C₂×Q₈	—	8	4	no	—
859	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
860	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
861	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
862	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
863	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
864	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	2	1	no	—
867	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
868	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
878	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
880	Q₁₆	—	2	2	no	—
881	Q₁₆	—	2	4	no	—
882	SD₁₆	—	2	2	no	—
883	SD₁₆	—	2	2	no	—
884	SD₁₆	—	2	4	no	—
885	D₈	—	2	2	no	—
886	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
889	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	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	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	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	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
925	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
931	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
967	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₄²	C₂⁴×C₅₃	1	2	yes	—
969	C₄²	C₂⁴×C₅₃	1	2	yes	—
970	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	4	2	no	—
982	Q₈	—	4	4	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	Q₈	—	8	1	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	2	no	—
989	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
990	D₄	—	2	4	no	—
991	D₄	—	2	1	no	—
992	D₄	—	2	1	no	—
993	D₄	—	2	1	no	—
994	D₄	—	8	1	no	—
995	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
996	C₂×C₄	—	2	4	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1021	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
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	C₂⁵×C₅₃	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	C₅₃×#578	1	2	yes	—
1063	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1064	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1065	C₂	—	4	1	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₅₃×#3486	1	1	yes	characteristic
1069	C₂	C₂×C₅₃×#578	1	1	yes	characteristic
1070	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3555	C₂	semidirect
2. C₅₃×#3503	C₂	semidirect
3. C₅₃×#3390	C₂	semidirect
4. C₅₃×#3386	C₂	semidirect
5. C₅₃×#3385	C₂	semidirect
6. C₅₃×#3385	C₂	semidirect
7. Q₈×Q₁₆×C₅₃	C₂	semidirect
8. C₅₃×#3380	C₂	semidirect
9. C₅₃×#3377	C₂	semidirect
10. C₅₃×#3372	C₂	semidirect
11. C₅₃×#3369	C₂	semidirect
12. C₅₃×#3367	C₂	semidirect
13. C₅₃×#3363	C₂	semidirect
14. C₅₃×#3360	C₂	semidirect
15. C₅₃×#3243	C₂	semidirect
16. C₅₃×#3242	C₂	semidirect
17. C₅₃×#3238	C₂	semidirect
18. C₅₃×#3230	C₂	semidirect
20. C₅₃×#3120	C₂	semidirect
21. C₅₃×#3116	C₂	semidirect
23. C₅₃×#2985	C₂	semidirect
498. #61859	C₅₃	direct (N × H)
530. #3555	C₂×C₅₃	semidirect
531. #3503	C₂×C₅₃	semidirect
532. #3390	C₂×C₅₃	semidirect
533. #3386	C₂×C₅₃	semidirect
534. #3385	C₂×C₅₃	semidirect
535. #3385	C₂×C₅₃	semidirect
536. Q₈×Q₁₆	C₂×C₅₃	semidirect
537. #3380	C₂×C₅₃	semidirect
538. #3377	C₂×C₅₃	semidirect
539. #3372	C₂×C₅₃	semidirect
540. #3369	C₂×C₅₃	semidirect
541. #3367	C₂×C₅₃	semidirect
542. #3363	C₂×C₅₃	semidirect
543. #3360	C₂×C₅₃	semidirect
544. #3243	C₂×C₅₃	semidirect
545. #3242	C₂×C₅₃	semidirect
546. #3238	C₂×C₅₃	semidirect
547. #3230	C₂×C₅₃	semidirect
549. #3120	C₂×C₅₃	semidirect
550. #3116	C₂×C₅₃	semidirect
552. #2985	C₂×C₅₃	semidirect
670. C₅₃	#61859	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×#3503	2
C₅₃×#3390	2
C₅₃×#3386	2
C₅₃×#3385	2
Q₈×Q₁₆×C₅₃	2
C₅₃×#3380	2
C₅₃×#3377	2
C₅₃×#3372	2
C₅₃×#3369	2
C₅₃×#3367	2
C₅₃×#3363	2
C₅₃×#3360	2
C₅₃×#3243	2
C₅₃×#3242	2
C₅₃×#3238	2
C₅₃×#3230	2
C₅₃×#3124	2
C₅₃×#3120	2
C₅₃×#3116	2
C₅₃×#3102	2
C₅₃×#2985	2
#61859	53

Subgroups — C53×#61859 #27269371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61859 #27269371