Subgroups — C₅₃×#62204 #27269716

Order 13568.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3544	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3312	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3298	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3082	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#557	—	2	1	no	—
27	C₅₃×#557	C₂²	1	1	yes	characteristic
28	C₅₃×#557	C₂²	1	1	yes	characteristic
29	C₅₃×#556	—	2	1	no	—
30	C₅₃×#556	C₂²	1	1	yes	characteristic
31	C₅₃×#555	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#554	C₂²	1	1	yes	characteristic
34	C₅₃×#552	—	2	2	no	—
35	C₅₃×#552	—	2	1	no	—
36	C₅₃×#552	C₂²	1	2	yes	—
37	C₅₃×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
39	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#547	—	2	1	no	—
41	C₅₃×#547	C₂²	1	2	yes	—
42	C₅₃×#544	—	2	1	no	—
43	C₅₃×#544	C₂²	1	2	yes	—
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	C₂²	1	2	yes	—
46	C₅₃×#541	—	2	2	no	—
47	C₅₃×#541	C₂²	1	2	yes	—
48	C₅₃×#536	—	2	2	no	—
49	C₅₃×#533	—	2	1	no	—
50	C₅₃×#533	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#529	—	2	1	no	—
53	C₅₃×#529	C₂²	1	1	yes	characteristic
54	C₅₃×#529	C₂²	1	1	yes	characteristic
55	C₅₃×#519	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	—
58	C₅₃×#499	C₂²	1	2	yes	—
59	C₅₃×#498	C₂²	1	1	yes	characteristic
60	C₅₃×#498	C₂²	1	1	yes	characteristic
61	C₅₃×#491	C₂²	1	2	yes	—
62	C₅₃×#487	C₂²	1	1	yes	characteristic
63	C₅₃×#487	C₂²	1	1	yes	characteristic
64	C₅₃×#487	C₂²	1	2	yes	—
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#485	C₂²	1	2	yes	—
67	C₅₃×#485	C₂²	1	2	yes	—
68	C₅₃×#484	C₂²	1	2	yes	—
69	C₅₃×#483	C₂²	1	2	yes	—
70	C₅₃×#483	C₂²	1	2	yes	—
71	C₅₃×#483	C₂²	1	2	yes	—
72	C₅₃×#483	C₂²	1	1	yes	characteristic
73	C₅₃×#482	C₂²	1	2	yes	—
74	C₅₃×#480	C₂²	1	1	yes	characteristic
75	C₅₃×#479	C₂²	1	1	yes	characteristic
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	2	yes	—
82	C₅₃×#477	C₂²	1	2	yes	—
83	C₅₃×#477	C₂²	1	1	yes	characteristic
84	C₅₃×#477	C₂²	1	1	yes	characteristic
85	C₅₃×#477	C₂²	1	2	yes	—
86	C₅₃×#477	C₂²	1	1	yes	characteristic
87	C₅₃×#477	C₂²	1	1	yes	characteristic
88	C₅₃×#477	C₂²	1	2	yes	—
89	C₅₃×#475	C₂²	1	2	yes	—
90	C₅₃×#475	C₂²	1	2	yes	—
91	C₅₃×#475	C₂²	1	1	yes	characteristic
92	C₅₃×#475	C₂²	1	2	yes	—
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	—
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#467	C₂²	1	2	yes	—
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	2	yes	—
101	C₅₃×#464	C₂²	1	1	yes	characteristic
102	C₅₃×#464	C₂²	1	1	yes	characteristic
103	C₅₃×#462	C₂²	1	1	yes	characteristic
104	C₅₃×#462	C₂²	1	2	yes	—
105	C₅₃×#461	C₂²	1	1	yes	characteristic
106	C₅₃×#461	C₂²	1	2	yes	—
107	C₅₃×#451	C₂²	1	2	yes	—
108	C₅₃×#451	C₂²	1	1	yes	characteristic
109	C₅₃×#448	C₂²	1	1	yes	characteristic
110	C₅₃×#448	C₂²	1	2	yes	—
111	C₅₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₅₃×#441	C₂²	1	2	yes	—
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#436	C₂²	1	1	yes	characteristic
122	C₅₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₅₃	C₂²	1	2	yes	—
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#433	C₂²	1	2	yes	—
126	C₅₃×#431	C₂²	1	1	yes	characteristic
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#427	C₂²	1	2	yes	—
129	C₂×#107×C₅₃	C₂²	1	2	yes	—
130	C₅₃×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#419	C₂²	1	2	yes	—
133	C₂×#103×C₅₃	C₂²	1	2	yes	—
134	C₂×#103×C₅₃	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂²×Q₈×C₅₃	—	2	1	no	—
137	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×M₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₅₃	—	2	1	no	—
149	C₄⋊Q₈×C₅₃	—	2	2	no	—
150	C₄⋊Q₈×C₅₃	—	2	2	no	—
151	C₄⋊Q₈×C₅₃	—	2	2	no	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	1	no	—
170	#126×C₅₃	D₄	1	2	yes	—
171	#125×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	—	2	2	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	1	no	—
178	#125×C₅₃	—	2	2	no	—
179	#125×C₅₃	—	2	2	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	D₄	1	1	yes	characteristic
182	#125×C₅₃	C₂³	1	2	yes	—
183	#125×C₅₃	C₂³	1	2	yes	—
184	#125×C₅₃	C₂³	1	1	yes	characteristic
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	—	2	2	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	D₄	1	1	yes	characteristic
189	#124×C₅₃	C₂³	1	1	yes	characteristic
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	D₄	1	2	yes	—
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	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	D₄	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₅₃	—	2	2	no	—
219	C₄×Q₈×C₅₃	—	2	2	no	—
220	C₄×Q₈×C₅₃	—	2	1	no	—
221	C₄×Q₈×C₅₃	—	2	1	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	—	2	1	no	—
226	C₄×Q₈×C₅₃	—	2	1	no	—
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
237	C₄×D₄×C₅₃	—	2	2	no	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	1	no	—
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
245	#117×C₅₃	—	2	1	no	—
246	#117×C₅₃	—	2	2	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	—	2	2	no	—
249	#117×C₅₃	—	2	2	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	—	2	1	no	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄²×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	1	yes	characteristic
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	1	yes	characteristic
300	#103×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	#97×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	—	8	4	no	—
313	C₂×Q₈×C₅₃	—	2	1	no	—
314	C₂×Q₈×C₅₃	—	2	2	no	—
315	C₂×Q₈×C₅₃	—	2	1	no	—
316	C₂×Q₈×C₅₃	—	2	1	no	—
317	C₂×Q₈×C₅₃	—	2	2	no	—
318	C₂×Q₈×C₅₃	—	2	2	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	4	no	—
322	C₂×Q₈×C₅₃	—	4	1	no	—
323	C₂×Q₈×C₅₃	—	4	2	no	—
324	C₂×Q₈×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
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×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅₃	—	2	1	no	—
336	C₂²×C₄×C₅₃	—	2	1	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	2	no	—
342	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
346	Q₁₆×C₅₃	—	2	2	no	—
347	Q₁₆×C₅₃	—	4	2	no	—
348	Q₁₆×C₅₃	—	4	1	no	—
349	SD₁₆×C₅₃	—	2	2	no	—
350	SD₁₆×C₅₃	—	4	1	no	—
351	SD₁₆×C₅₃	—	4	2	no	—
352	M₁₆×C₅₃	—	4	2	no	—
353	C₂×C₈×C₅₃	—	4	2	no	—
354	C₂×C₈×C₅₃	—	4	2	no	—
355	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₅₃	—	2	1	no	—
362	C₄⋊C₄×C₅₃	—	2	1	no	—
363	C₄⋊C₄×C₅₃	—	2	1	no	—
364	C₄⋊C₄×C₅₃	—	2	1	no	—
365	C₄⋊C₄×C₅₃	—	2	1	no	—
366	C₄⋊C₄×C₅₃	—	2	1	no	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	2	no	—
377	C₄⋊C₄×C₅₃	—	2	1	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	1	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₄²×C₅₃	—	2	1	no	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	1	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	1	no	—
433	C₄²×C₅₃	—	2	2	no	—
434	C₄²×C₅₃	—	2	2	no	—
435	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₄²×C₅₃	C₂⁴	1	2	yes	—
439	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₂³×C₅₃	—	2	1	no	—
441	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
442	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₅₃	—	2	2	no	—
444	Q₈×C₅₃	—	2	1	no	—
445	Q₈×C₅₃	—	2	1	no	—
446	Q₈×C₅₃	—	2	2	no	—
447	Q₈×C₅₃	—	2	1	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	2	2	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	4	2	no	—
452	Q₈×C₅₃	—	4	4	no	—
453	Q₈×C₅₃	—	4	2	no	—
454	Q₈×C₅₃	—	8	1	no	—
455	Q₈×C₅₃	—	8	2	no	—
456	Q₈×C₅₃	—	8	1	no	—
457	Q₈×C₅₃	—	8	2	no	—
458	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₅₃	—	2	4	no	—
460	D₄×C₅₃	—	2	2	no	—
461	D₄×C₅₃	—	2	1	no	—
462	D₄×C₅₃	—	2	1	no	—
463	D₄×C₅₃	—	4	2	no	—
464	D₄×C₅₃	—	8	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	1	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	1	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	1	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	1	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	—	4	2	no	—
483	C₂×C₄×C₅₃	—	4	4	no	—
484	C₂×C₄×C₅₃	—	4	2	no	—
485	C₂×C₄×C₅₃	—	4	4	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	8	2	no	—
488	C₂×C₄×C₅₃	—	8	2	no	—
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
498	C₈×C₅₃	—	2	1	no	—
499	C₈×C₅₃	—	2	1	no	—
500	C₈×C₅₃	—	2	1	no	—
501	C₈×C₅₃	—	2	2	no	—
502	C₈×C₅₃	—	2	2	no	—
503	C₈×C₅₃	—	2	1	no	—
504	#62204	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₅₃	—	2	1	no	—
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	2	no	—
508	C₂²×C₅₃	—	2	2	no	—
509	C₂²×C₅₃	—	2	2	no	—
510	C₂²×C₅₃	—	4	1	no	—
511	C₂²×C₅₃	—	4	1	no	—
512	C₂²×C₅₃	—	4	1	no	—
513	C₂²×C₅₃	#577	1	2	yes	—
514	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	2	2	no	—
517	C₄×C₅₃	—	2	2	no	—
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	1	no	—
520	C₄×C₅₃	—	2	2	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	2	2	no	—
523	C₄×C₅₃	—	4	1	no	—
524	C₄×C₅₃	—	4	2	no	—
525	C₄×C₅₃	—	4	1	no	—
526	C₄×C₅₃	—	4	1	no	—
527	C₄×C₅₃	—	4	1	no	—
528	C₄×C₅₃	—	4	2	no	—
529	C₄×C₅₃	—	4	2	no	—
530	C₄×C₅₃	—	4	1	no	—
531	C₄×C₅₃	—	4	1	no	—
532	C₄×C₅₃	—	4	2	no	—
533	C₄×C₅₃	#578	1	2	yes	—
534	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₄×C₅₃	#585	1	1	yes	characteristic
536	#3544	C₂×C₅₃	1	1	yes	characteristic
537	#3523	C₂×C₅₃	1	1	yes	characteristic, complemented
538	#3387	C₂×C₅₃	1	1	yes	characteristic, complemented
539	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
540	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
541	#3363	C₂×C₅₃	1	1	yes	characteristic, complemented
542	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
543	#3343	C₂×C₅₃	1	2	yes	complemented
544	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
545	#3336	C₂×C₅₃	1	2	yes	complemented
546	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3312	C₂×C₅₃	1	2	yes	complemented
548	#3299	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3298	C₂×C₅₃	1	2	yes	complemented
550	#3258	C₂×C₅₃	1	2	yes	complemented
551	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3242	C₂×C₅₃	1	2	yes	complemented
553	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3121	C₂×C₅₃	1	2	yes	complemented
555	#3108	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3082	C₂×C₅₃	1	2	yes	complemented
557	C₂×#477	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
559	C₂×C₅₃	—	2	2	no	—
560	C₂×C₅₃	—	4	2	no	—
561	C₂×C₅₃	—	8	1	no	—
562	C₂×C₅₃	#3489	1	1	yes	characteristic
563	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
564	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
565	#563	—	2	2	no	—
566	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
567	#557	—	2	1	no	—
568	#557	C₂²×C₅₃	1	1	yes	characteristic
569	#557	C₂²×C₅₃	1	1	yes	characteristic
570	#556	—	2	1	no	—
571	#556	C₂²×C₅₃	1	1	yes	characteristic
572	#555	C₂²×C₅₃	1	1	yes	characteristic
573	#554	C₂²×C₅₃	1	1	yes	characteristic
574	#554	C₂²×C₅₃	1	1	yes	characteristic
575	#552	—	2	2	no	—
576	#552	—	2	1	no	—
577	#552	C₂²×C₅₃	1	2	yes	—
578	#552	C₂²×C₅₃	1	2	yes	—
579	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
580	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
581	#547	—	2	1	no	—
582	#547	C₂²×C₅₃	1	2	yes	—
583	#544	—	2	1	no	—
584	#544	C₂²×C₅₃	1	2	yes	—
585	#542	—	2	1	no	—
586	#542	C₂²×C₅₃	1	2	yes	—
587	#541	—	2	2	no	—
588	#541	C₂²×C₅₃	1	2	yes	—
589	#536	—	2	2	no	—
590	#533	—	2	1	no	—
591	#533	C₂²×C₅₃	1	1	yes	characteristic
592	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
593	#529	—	2	1	no	—
594	#529	C₂²×C₅₃	1	1	yes	characteristic
595	#529	C₂²×C₅₃	1	1	yes	characteristic
596	#519	C₂²×C₅₃	1	2	yes	—
597	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
598	#501	C₂²×C₅₃	1	2	yes	—
599	#499	C₂²×C₅₃	1	2	yes	—
600	#498	C₂²×C₅₃	1	1	yes	characteristic
601	#498	C₂²×C₅₃	1	1	yes	characteristic
602	#491	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	2	yes	—
607	#485	C₂²×C₅₃	1	2	yes	—
608	#485	C₂²×C₅₃	1	2	yes	—
609	#484	C₂²×C₅₃	1	2	yes	—
610	#483	C₂²×C₅₃	1	1	yes	characteristic
611	#483	C₂²×C₅₃	1	2	yes	—
612	#483	C₂²×C₅₃	1	2	yes	—
613	#483	C₂²×C₅₃	1	2	yes	—
614	#482	C₂²×C₅₃	1	2	yes	—
615	#480	C₂²×C₅₃	1	1	yes	characteristic
616	#479	C₂²×C₅₃	1	2	yes	—
617	#479	C₂²×C₅₃	1	2	yes	—
618	#479	C₂²×C₅₃	1	1	yes	characteristic
619	#479	C₂²×C₅₃	1	2	yes	—
620	#479	C₂²×C₅₃	1	2	yes	—
621	#479	C₂²×C₅₃	1	1	yes	characteristic
622	#478	C₂²×C₅₃	1	2	yes	—
623	#477	C₂²×C₅₃	1	1	yes	characteristic
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	1	yes	characteristic
628	#477	C₂²×C₅₃	1	2	yes	—
629	#477	C₂²×C₅₃	1	2	yes	—
630	#475	C₂²×C₅₃	1	2	yes	—
631	#475	C₂²×C₅₃	1	2	yes	—
632	#475	C₂²×C₅₃	1	1	yes	characteristic
633	#475	C₂²×C₅₃	1	2	yes	—
634	#474	C₂²×C₅₃	1	1	yes	characteristic
635	#470	C₂²×C₅₃	1	2	yes	—
636	#468	C₂²×C₅₃	1	2	yes	—
637	#467	C₂²×C₅₃	1	2	yes	—
638	#467	C₂²×C₅₃	1	2	yes	—
639	#465	C₂²×C₅₃	1	2	yes	—
640	#465	C₂²×C₅₃	1	2	yes	—
641	#464	C₂²×C₅₃	1	1	yes	characteristic
642	#464	C₂²×C₅₃	1	1	yes	characteristic
643	#464	C₂²×C₅₃	1	2	yes	—
644	#462	C₂²×C₅₃	1	1	yes	characteristic
645	#462	C₂²×C₅₃	1	2	yes	—
646	#461	C₂²×C₅₃	1	1	yes	characteristic
647	#461	C₂²×C₅₃	1	2	yes	—
648	#451	C₂²×C₅₃	1	1	yes	characteristic
649	#451	C₂²×C₅₃	1	2	yes	—
650	#448	C₂²×C₅₃	1	2	yes	—
651	#448	C₂²×C₅₃	1	1	yes	characteristic
652	#446	C₂²×C₅₃	1	1	yes	characteristic
653	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
654	#441	C₂²×C₅₃	1	2	yes	—
655	#440	C₂²×C₅₃	1	2	yes	—
656	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
657	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
658	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
659	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
660	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
661	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
662	#436	C₂²×C₅₃	1	1	yes	characteristic
663	#435	C₂²×C₅₃	1	2	yes	—
664	C₈×D₄	C₂²×C₅₃	1	2	yes	—
665	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
666	#433	C₂²×C₅₃	1	2	yes	—
667	#431	C₂²×C₅₃	1	1	yes	characteristic
668	#428	C₂²×C₅₃	1	2	yes	—
669	#427	C₂²×C₅₃	1	2	yes	—
670	C₂×#107	C₂²×C₅₃	1	2	yes	—
671	#424	C₂²×C₅₃	1	2	yes	—
672	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
673	#419	C₂²×C₅₃	1	2	yes	—
674	C₂×#103	C₂²×C₅₃	1	2	yes	—
675	C₂×#103	C₂²×C₅₃	1	2	yes	—
676	C₅₃	#62204	1	1	yes	characteristic, direct product factor, Sylow
677	C₂×#41	—	2	2	no	—
678	C₂²×Q₈	—	2	1	no	—
679	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
680	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
684	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
685	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
687	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
688	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
689	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	1	no	—
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	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	1	no	—
712	#126	D₄×C₅₃	1	2	yes	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	D₄×C₅₃	1	1	yes	characteristic
724	#125	C₂³×C₅₃	1	1	yes	characteristic
725	#125	C₂³×C₅₃	1	2	yes	—
726	#125	C₂³×C₅₃	1	2	yes	—
727	#124	—	2	1	no	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	D₄×C₅₃	1	1	yes	characteristic
731	#124	C₂³×C₅₃	1	1	yes	characteristic
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	1	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	D₄×C₅₃	1	2	yes	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
756	#121	—	2	1	no	—
757	#121	D₄×C₅₃	1	1	yes	characteristic
758	#121	C₂³×C₅₃	1	1	yes	characteristic
759	#121	C₂³×C₅₃	1	2	yes	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
774	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₅₃	1	2	yes	—
785	C₄×D₄	C₂³×C₅₃	1	2	yes	—
786	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
787	#117	—	2	1	no	—
788	#117	—	2	1	no	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	—	2	1	no	—
794	#117	C₂³×C₅₃	1	2	yes	—
795	#117	C₂³×C₅₃	1	2	yes	—
796	#117	C₂³×C₅₃	1	2	yes	—
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
805	#107	C₂³×C₅₃	1	2	yes	—
806	#107	C₂³×C₅₃	1	2	yes	—
807	#107	C₂³×C₅₃	1	2	yes	—
808	#107	C₂³×C₅₃	1	2	yes	—
809	#107	C₂³×C₅₃	1	2	yes	—
810	#107	C₂³×C₅₃	1	1	yes	characteristic
811	#107	C₂³×C₅₃	1	1	yes	characteristic
812	#106	C₂³×C₅₃	1	1	yes	characteristic
813	#106	C₂³×C₅₃	1	2	yes	—
814	#106	C₂³×C₅₃	1	2	yes	—
815	#106	C₂³×C₅₃	1	2	yes	—
816	#106	C₂³×C₅₃	1	2	yes	—
817	#106	C₂³×C₅₃	1	1	yes	characteristic
818	#106	C₂³×C₅₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
824	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
825	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
826	#103	C₂³×C₅₃	1	2	yes	—
827	#103	C₂³×C₅₃	1	1	yes	characteristic
828	#103	C₂³×C₅₃	1	2	yes	—
829	#103	C₂³×C₅₃	1	2	yes	—
830	#103	C₂³×C₅₃	1	2	yes	—
831	#103	C₂³×C₅₃	1	2	yes	—
832	#103	C₂³×C₅₃	1	2	yes	—
833	#103	C₂³×C₅₃	1	1	yes	characteristic
834	#103	C₂³×C₅₃	1	2	yes	—
835	#103	C₂³×C₅₃	1	2	yes	—
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	1	yes	characteristic
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	1	yes	characteristic
840	#103	C₂³×C₅₃	1	1	yes	characteristic
841	#103	C₂³×C₅₃	1	2	yes	—
842	#103	C₂³×C₅₃	1	2	yes	—
843	#102	C₂³×C₅₃	1	1	yes	characteristic
844	#102	C₂³×C₅₃	1	2	yes	—
845	#102	C₂³×C₅₃	1	1	yes	characteristic
846	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
850	#97	C₂³×C₅₃	1	2	yes	—
851	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₅₃	1	2	yes	—
854	#41	—	8	4	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	4	no	—
864	C₂×Q₈	—	4	1	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
869	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
875	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
876	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
888	Q₁₆	—	2	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	1	no	—
891	SD₁₆	—	2	2	no	—
892	SD₁₆	—	4	1	no	—
893	SD₁₆	—	4	2	no	—
894	M₁₆	—	4	2	no	—
895	C₂×C₈	—	4	2	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
901	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	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	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	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	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
941	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
942	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
944	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
962	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
963	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
978	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
979	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₄²	C₂⁴×C₅₃	1	2	yes	—
981	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₂³	—	2	1	no	—
983	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
984	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	1	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	4	2	no	—
994	Q₈	—	4	4	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	8	1	no	—
997	Q₈	—	8	2	no	—
998	Q₈	—	8	1	no	—
999	Q₈	—	8	2	no	—
1000	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1001	D₄	—	2	4	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	4	2	no	—
1006	D₄	—	8	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1032	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1034	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1035	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1036	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1039	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	C₅₃×#577	1	2	yes	—
1055	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	C₅₃×#578	1	2	yes	—
1075	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1076	C₄	C₅₃×#585	1	1	yes	characteristic
1077	C₂	—	2	2	no	—
1078	C₂	—	4	2	no	—
1079	C₂	—	8	1	no	—
1080	C₂	C₅₃×#3489	1	1	yes	characteristic
1081	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1082	C₂	C₂×C₅₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3544	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
2. C₅₃×#3523	C₂	semidirect
3. C₅₃×#3387	C₂	semidirect
4. C₅₃×#3381	C₂	semidirect
5. C₅₃×#3372	C₂	semidirect
6. C₅₃×#3363	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3343	C₂	semidirect
9. C₅₃×#3340	C₂	semidirect
10. C₅₃×#3336	C₂	semidirect
11. C₅₃×#3329	C₂	semidirect
12. C₅₃×#3312	C₂	semidirect
13. C₅₃×#3299	C₂	semidirect
14. C₅₃×#3298	C₂	semidirect
15. C₅₃×#3258	C₂	semidirect
16. C₅₃×#3248	C₂	semidirect
17. C₅₃×#3242	C₂	semidirect
18. C₅₃×#3229	C₂	semidirect
19. C₅₃×#3121	C₂	semidirect
20. C₅₃×#3108	C₂	semidirect
21. C₅₃×#3082	C₂	semidirect
22. C₂×C₅₃×#477	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
504. #62204	C₅₃	direct (N × H)
537. #3523	C₂×C₅₃	semidirect
538. #3387	C₂×C₅₃	semidirect
539. #3381	C₂×C₅₃	semidirect
540. #3372	C₂×C₅₃	semidirect
541. #3363	C₂×C₅₃	semidirect
542. #3356	C₂×C₅₃	semidirect
543. #3343	C₂×C₅₃	semidirect
544. #3340	C₂×C₅₃	semidirect
545. #3336	C₂×C₅₃	semidirect
546. #3329	C₂×C₅₃	semidirect
547. #3312	C₂×C₅₃	semidirect
548. #3299	C₂×C₅₃	semidirect
549. #3298	C₂×C₅₃	semidirect
550. #3258	C₂×C₅₃	semidirect
551. #3248	C₂×C₅₃	semidirect
552. #3242	C₂×C₅₃	semidirect
553. #3229	C₂×C₅₃	semidirect
554. #3121	C₂×C₅₃	semidirect
555. #3108	C₂×C₅₃	semidirect
556. #3082	C₂×C₅₃	semidirect
557. C₂×#477	C₂×C₅₃	semidirect
558. #2994	C₂×C₅₃	semidirect
676. C₅₃	#62204	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×#3544	2
C₅₃×#3523	2
C₅₃×#3387	2
C₅₃×#3381	2
C₅₃×#3372	2
C₅₃×#3363	2
C₅₃×#3356	2
C₅₃×#3343	2
C₅₃×#3340	2
C₅₃×#3336	2
C₅₃×#3329	2
C₅₃×#3312	2
C₅₃×#3299	2
C₅₃×#3298	2
C₅₃×#3258	2
C₅₃×#3248	2
C₅₃×#3242	2
C₅₃×#3229	2
C₅₃×#3121	2
C₅₃×#3108	2
C₅₃×#3082	2
C₂×C₅₃×#477	2
C₅₃×#2994	2
#62204	53

Subgroups — C53×#62204 #27269716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62204 #27269716