Subgroups — #27401100

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810684	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810587	C₂	1	1	yes	maximal, characteristic
3	#20275330	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275330	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275323	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275323	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274900	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274900	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274786	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274699	C₂	1	1	yes	maximal, characteristic, complemented
11	#20274625	C₂	1	1	yes	maximal, characteristic
12	#20274499	C₂	1	1	yes	maximal, characteristic, complemented
13	#20274499	C₂	1	1	yes	maximal, characteristic, complemented
14	#20274481	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11719917	C₂²	1	1	yes	characteristic
17	C₂²×#11719917	C₂²	1	1	yes	characteristic
18	#16810684	—	2	4	no	—
19	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
23	#16810587	—	2	4	no	—
24	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
34	C₂×#13133128	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133128	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
38	#16810378	C₂²	1	1	yes	characteristic, complemented
39	#16810378	C₂²	1	1	yes	characteristic, complemented
40	#16810378	C₂²	1	1	yes	characteristic, complemented
41	#16810378	C₂²	1	1	yes	characteristic, complemented
42	#16810378	C₂²	1	1	yes	characteristic, complemented
43	#16810378	C₂²	1	1	yes	characteristic, complemented
44	#16810378	C₂²	1	1	yes	characteristic, complemented
45	#16810378	C₂²	1	1	yes	characteristic, complemented
46	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#381	C₄	1	1	yes	characteristic
50	C₅₃×#381	C₄	1	1	yes	characteristic
51	C₅₃×#380	C₄	1	1	yes	characteristic
52	C₅₃×#380	C₄	1	1	yes	characteristic
53	C₅₃×#380	C₄	1	1	yes	characteristic
54	C₅₃×#380	C₄	1	1	yes	characteristic
55	C₅₃×#379	C₄	1	1	yes	characteristic
56	C₅₃×#379	C₄	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#11719917	—	2	2	no	—
62	C₂×#11719917	—	2	2	no	—
63	C₂×#11719917	—	2	2	no	—
64	C₂×#11719917	—	2	2	no	—
65	C₂×#11719917	—	4	1	no	—
66	C₂×#11719917	—	4	1	no	—
67	C₂²×#88322	C₂³	1	1	yes	characteristic
68	C₂²×#88322	C₂³	1	1	yes	characteristic
69	C₂²×#88322	C₂³	1	1	yes	characteristic
70	C₂²×#88322	C₂³	1	1	yes	characteristic
71	C₂²×#88322	C₂³	1	1	yes	characteristic
72	C₂²×#88322	C₂³	1	1	yes	characteristic
73	C₂²×#88322	C₂³	1	1	yes	characteristic
74	C₂²×#88322	C₂³	1	1	yes	characteristic
75	C₄⋊#88322	—	2	2	no	—
76	C₄⋊#88322	—	2	2	no	—
77	C₄⋊#88322	—	4	1	no	—
78	C₄⋊#88322	—	4	1	no	—
79	C₂²⋊#88322	—	2	2	no	—
80	C₂²⋊#88322	—	2	2	no	—
81	C₂²⋊#88322	—	2	2	no	—
82	C₂²⋊#88322	—	2	2	no	—
83	C₂²⋊#88322	—	2	2	no	—
84	C₂²⋊#88322	—	2	2	no	—
85	C₂²⋊#88322	—	2	2	no	—
86	C₂²⋊#88322	—	4	1	no	—
87	C₂²⋊#88322	—	4	1	no	—
88	C₂²⋊#88322	D₄	1	4	yes	—
89	#13133128	—	2	2	no	—
90	#13133128	—	4	1	no	—
91	C₄×#88322	—	2	2	no	—
92	C₄×#88322	—	4	1	no	—
93	C₂⁵×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₅₃	—	2	2	no	—
95	C₂³×C₄×C₅₃	—	2	2	no	—
96	C₂³×C₄×C₅₃	—	2	2	no	—
97	C₂³×C₄×C₅₃	—	2	2	no	—
98	C₂³×C₄×C₅₃	—	4	1	no	—
99	C₂³×C₄×C₅₃	—	4	1	no	—
100	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
106	#117×C₅₃	—	2	2	no	—
107	#117×C₅₃	—	2	2	no	—
108	#117×C₅₃	—	4	1	no	—
109	#117×C₅₃	—	4	1	no	—
110	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
130	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
131	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
132	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
133	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
134	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
135	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
136	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
137	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₅₃	—	2	2	no	—
139	C₂⁴×C₅₃	—	2	2	no	—
140	C₂⁴×C₅₃	—	2	2	no	—
141	C₂⁴×C₅₃	—	4	1	no	—
142	C₂⁴×C₅₃	—	4	1	no	—
143	C₂⁴×C₅₃	—	4	1	no	—
144	C₂⁴×C₅₃	—	4	1	no	—
145	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅₃	—	2	1	no	—
149	C₂²×C₄×C₅₃	—	2	1	no	—
150	C₂²×C₄×C₅₃	—	2	1	no	—
151	C₂²×C₄×C₅₃	—	2	1	no	—
152	C₂²×C₄×C₅₃	—	2	1	no	—
153	C₂²×C₄×C₅₃	—	2	1	no	—
154	C₂²×C₄×C₅₃	—	2	1	no	—
155	C₂²×C₄×C₅₃	—	2	1	no	—
156	C₂²×C₄×C₅₃	—	2	2	no	—
157	C₂²×C₄×C₅₃	—	2	2	no	—
158	C₂²×C₄×C₅₃	—	2	2	no	—
159	C₂²×C₄×C₅₃	—	2	2	no	—
160	C₂²×C₄×C₅₃	—	2	2	no	—
161	C₂²×C₄×C₅₃	—	2	2	no	—
162	C₂²×C₄×C₅₃	—	2	1	no	—
163	C₂²×C₄×C₅₃	—	2	1	no	—
164	C₂²×C₄×C₅₃	—	2	1	no	—
165	C₂²×C₄×C₅₃	—	2	1	no	—
166	C₂²×C₄×C₅₃	—	2	1	no	—
167	C₂²×C₄×C₅₃	—	2	1	no	—
168	C₂²×C₄×C₅₃	—	4	1	no	—
169	C₂²×C₄×C₅₃	—	4	1	no	—
170	C₂²×C₄×C₅₃	—	4	1	no	—
171	C₂²×C₄×C₅₃	—	4	4	no	—
172	C₂²×C₄×C₅₃	—	4	4	no	—
173	C₂²×C₄×C₅₃	—	4	4	no	—
174	C₂²×C₄×C₅₃	—	4	4	no	—
175	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₅₃	#41	1	2	yes	—
188	C₂²×C₄×C₅₃	#41	1	2	yes	—
189	C₂²×C₄×C₅₃	#41	1	2	yes	—
190	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₅₃	—	2	2	no	—
192	C₄⋊C₄×C₅₃	—	2	2	no	—
193	C₄⋊C₄×C₅₃	—	4	1	no	—
194	C₄⋊C₄×C₅₃	—	4	1	no	—
195	C₂²⋊C₄×C₅₃	—	2	2	no	—
196	C₂²⋊C₄×C₅₃	—	2	2	no	—
197	C₂²⋊C₄×C₅₃	—	2	2	no	—
198	C₂²⋊C₄×C₅₃	—	2	2	no	—
199	C₂²⋊C₄×C₅₃	—	4	1	no	—
200	C₂²⋊C₄×C₅₃	—	4	1	no	—
201	C₂²⋊C₄×C₅₃	—	4	1	no	—
202	C₂²⋊C₄×C₅₃	—	4	1	no	—
203	C₂²⋊C₄×C₅₃	—	4	1	no	—
204	C₂²⋊C₄×C₅₃	—	4	1	no	—
205	C₂²⋊C₄×C₅₃	—	4	1	no	—
206	C₂²⋊C₄×C₅₃	—	4	1	no	—
207	C₄²×C₅₃	—	2	1	no	—
208	C₄²×C₅₃	—	2	1	no	—
209	C₄²×C₅₃	—	2	1	no	—
210	C₄²×C₅₃	—	2	1	no	—
211	C₄²×C₅₃	—	2	1	no	—
212	C₄²×C₅₃	—	2	1	no	—
213	C₄²×C₅₃	—	2	1	no	—
214	C₄²×C₅₃	—	2	1	no	—
215	#11719917	—	4	4	no	—
216	#11719917	—	4	4	no	—
217	C₂×#88322	—	2	1	no	—
218	C₂×#88322	—	2	1	no	—
219	C₂×#88322	—	2	1	no	—
220	C₂×#88322	—	2	1	no	—
221	C₂×#88322	—	2	1	no	—
222	C₂×#88322	—	2	1	no	—
223	C₂×#88322	—	2	1	no	—
224	C₂×#88322	—	2	1	no	—
225	C₂×#88322	—	2	1	no	—
226	C₂×#88322	—	2	1	no	—
227	C₂×#88322	—	2	1	no	—
228	C₂×#88322	—	2	1	no	—
229	C₂×#88322	—	2	1	no	—
230	C₂×#88322	—	2	1	no	—
231	C₂×#88322	—	2	1	no	—
232	C₂×#88322	—	2	1	no	—
233	C₂×#88322	—	2	1	no	—
234	C₂×#88322	—	2	1	no	—
235	C₂×#88322	—	2	1	no	—
236	C₂×#88322	—	2	1	no	—
237	C₂×#88322	—	2	1	no	—
238	C₂×#88322	—	2	1	no	—
239	C₂×#88322	C₂×D₄	1	2	yes	—
240	C₂×#88322	C₂×D₄	1	2	yes	—
241	C₂³×C₅₃	—	2	1	no	—
242	C₂³×C₅₃	—	2	1	no	—
243	C₂³×C₅₃	—	2	1	no	—
244	C₂³×C₅₃	—	2	1	no	—
245	C₂³×C₅₃	—	2	1	no	—
246	C₂³×C₅₃	—	2	1	no	—
247	C₂³×C₅₃	—	2	1	no	—
248	C₂³×C₅₃	—	2	1	no	—
249	C₂³×C₅₃	—	2	1	no	—
250	C₂³×C₅₃	—	2	1	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	1	no	—
253	C₂³×C₅₃	—	2	1	no	—
254	C₂³×C₅₃	—	2	1	no	—
255	C₂³×C₅₃	—	2	1	no	—
256	C₂³×C₅₃	—	2	1	no	—
257	C₂³×C₅₃	—	2	1	no	—
258	C₂³×C₅₃	—	2	1	no	—
259	C₂³×C₅₃	—	4	4	no	—
260	C₂³×C₅₃	—	4	4	no	—
261	C₂³×C₅₃	—	4	4	no	—
262	C₂³×C₅₃	—	4	4	no	—
263	C₂³×C₅₃	—	4	4	no	—
264	C₂³×C₅₃	—	4	4	no	—
265	C₂³×C₅₃	—	4	4	no	—
266	C₂³×C₅₃	#117	1	2	yes	—
267	C₂³×C₅₃	C₄×D₄	1	2	yes	—
268	C₂³×C₅₃	#131	1	2	yes	—
269	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₅₃	—	2	1	no	—
271	C₂×C₄×C₅₃	—	2	1	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	1	no	—
274	C₂×C₄×C₅₃	—	2	2	no	—
275	C₂×C₄×C₅₃	—	2	2	no	—
276	C₂×C₄×C₅₃	—	2	2	no	—
277	C₂×C₄×C₅₃	—	2	2	no	—
278	C₂×C₄×C₅₃	—	2	2	no	—
279	C₂×C₄×C₅₃	—	2	2	no	—
280	C₂×C₄×C₅₃	—	2	2	no	—
281	C₂×C₄×C₅₃	—	2	2	no	—
282	C₂×C₄×C₅₃	—	2	1	no	—
283	C₂×C₄×C₅₃	—	2	1	no	—
284	C₂×C₄×C₅₃	—	2	1	no	—
285	C₂×C₄×C₅₃	—	2	1	no	—
286	C₂×C₄×C₅₃	—	2	1	no	—
287	C₂×C₄×C₅₃	—	2	1	no	—
288	C₂×C₄×C₅₃	—	2	1	no	—
289	C₂×C₄×C₅₃	—	2	1	no	—
290	C₂×C₄×C₅₃	—	2	1	no	—
291	C₂×C₄×C₅₃	—	2	1	no	—
292	C₂×C₄×C₅₃	—	2	1	no	—
293	C₂×C₄×C₅₃	—	2	1	no	—
294	C₂×C₄×C₅₃	—	2	1	no	—
295	C₂×C₄×C₅₃	—	2	1	no	—
296	C₂×C₄×C₅₃	—	2	1	no	—
297	C₂×C₄×C₅₃	—	2	1	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	1	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	—	2	1	no	—
303	C₂×C₄×C₅₃	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	4	4	no	—
310	C₂×C₄×C₅₃	—	4	4	no	—
311	C₂×C₄×C₅₃	—	4	4	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	1	no	—
314	C₂×C₄×C₅₃	—	4	1	no	—
315	C₂×C₄×C₅₃	—	4	1	no	—
316	C₂×C₄×C₅₃	#117	1	2	yes	—
317	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
318	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
324	#88322	—	2	2	no	—
325	#88322	—	2	2	no	—
326	#88322	—	4	1	no	—
327	#88322	—	4	1	no	—
328	#88322	—	4	1	no	—
329	#88322	—	4	1	no	—
330	#88322	—	4	1	no	—
331	#88322	—	4	1	no	—
332	#22559	—	53	1	no	maximal, Sylow
333	C₂²×C₅₃	—	2	2	no	—
334	C₂²×C₅₃	—	2	2	no	—
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	2	no	—
339	C₂²×C₅₃	—	2	2	no	—
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	4	16	no	—
343	C₂²×C₅₃	—	4	1	no	—
344	C₂²×C₅₃	—	4	1	no	—
345	C₂²×C₅₃	—	4	1	no	—
346	C₂²×C₅₃	—	4	1	no	—
347	C₂²×C₅₃	—	4	1	no	—
348	C₂²×C₅₃	—	4	1	no	—
349	C₂²×C₅₃	—	4	1	no	—
350	C₂²×C₅₃	—	4	1	no	—
351	C₂²×C₅₃	—	4	1	no	—
352	C₂²×C₅₃	—	4	1	no	—
353	C₂²×C₅₃	—	4	1	no	—
354	C₂²×C₅₃	—	4	1	no	—
355	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
356	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂²×C₅₃	#518	1	1	yes	characteristic
358	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
359	C₂²×C₅₃	#568	1	1	yes	characteristic
360	C₂²×C₅₃	#568	1	1	yes	characteristic
361	C₂²×C₅₃	#568	1	1	yes	characteristic
362	C₄×C₅₃	—	2	2	no	—
363	C₄×C₅₃	—	2	2	no	—
364	C₄×C₅₃	—	4	1	no	—
365	C₄×C₅₃	—	4	1	no	—
366	C₄×C₅₃	—	4	1	no	—
367	C₄×C₅₃	—	4	1	no	—
368	C₄×C₅₃	—	4	1	no	—
369	C₄×C₅₃	—	4	1	no	—
370	C₄×C₅₃	—	4	1	no	—
371	C₄×C₅₃	—	4	1	no	—
372	C₄×C₅₃	—	4	1	no	—
373	C₄×C₅₃	#546	1	1	yes	characteristic
374	C₄×C₅₃	#546	1	1	yes	characteristic
375	C₄×C₅₃	#551	1	1	yes	characteristic
376	C₄×C₅₃	#551	1	1	yes	characteristic
377	C₂×#433	—	53	1	no	—
378	C₂×#407	—	53	1	no	—
379	#2280	D₅₃	1	1	yes	characteristic
380	#1924	—	53	1	no	—
381	#1924	—	53	1	no	—
382	#1923	—	53	1	no	—
383	#1923	—	53	1	no	—
384	#1851	—	53	1	no	—
385	#1851	—	53	1	no	—
386	#1818	—	53	1	no	—
387	#1798	—	53	1	no	—
388	#1779	—	53	1	no	—
389	#1753	—	53	1	no	—
390	#1753	—	53	1	no	—
391	#1750	—	53	1	no	—
392	C₂×C₅₃	—	4	2	no	—
393	C₂×C₅₃	—	4	2	no	—
394	C₂×C₅₃	—	4	2	no	—
395	C₂×C₅₃	#2342	1	1	yes	characteristic
396	C₂×C₅₃	#2921	1	1	yes	characteristic
397	C₂×C₅₃	#2924	1	1	yes	characteristic
398	C₂×C₅₃	#2930	1	1	yes	characteristic
399	C₂×C₅₃	#2933	1	1	yes	characteristic
400	C₂×C₅₃	#2976	1	1	yes	characteristic
401	C₂×C₅₃	#2978	1	1	yes	characteristic
402	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic
403	C₂²×M₁₆	—	53	1	no	—
404	C₂²×M₁₆	—	53	1	no	—
405	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
406	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
407	#433	—	106	4	no	—
408	C₂×C₄⋊C₈	—	53	1	no	—
409	C₂×C₄⋊C₈	—	53	1	no	—
410	C₂×C₄⋊C₈	—	53	1	no	—
411	C₂×C₄⋊C₈	—	53	1	no	—
412	#407	—	106	4	no	—
413	C₂×C₂²⋊C₈	—	53	1	no	—
414	C₂×C₂²⋊C₈	—	53	1	no	—
415	C₂×C₂²⋊C₈	—	53	1	no	—
416	C₂×C₂²⋊C₈	—	53	1	no	—
417	C₂×C₂²⋊C₈	—	53	1	no	—
418	C₂×C₂²⋊C₈	—	53	1	no	—
419	C₂×C₂²⋊C₈	—	53	1	no	—
420	C₂×C₂²⋊C₈	—	53	1	no	—
421	C₂×C₂²⋊C₈	—	53	1	no	—
422	C₂×C₂²⋊C₈	—	53	1	no	—
423	C₂×#97	—	53	1	no	—
424	C₂×#97	—	53	1	no	—
425	C₂×C₄×C₈	—	53	1	no	—
426	C₂×C₄×C₈	—	53	1	no	—
427	#381	Dic₅₃	1	1	yes	characteristic
428	#381	Dic₅₃	1	1	yes	characteristic
429	#380	Dic₅₃	1	1	yes	characteristic
430	#380	Dic₅₃	1	1	yes	characteristic
431	#380	Dic₅₃	1	1	yes	characteristic
432	#380	Dic₅₃	1	1	yes	characteristic
433	#379	Dic₅₃	1	1	yes	characteristic
434	#379	Dic₅₃	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
439	#336	—	53	1	no	—
440	#336	—	53	1	no	—
441	#336	—	53	1	no	—
442	#336	—	53	1	no	—
443	#336	—	53	1	no	—
444	#336	—	53	1	no	—
445	#336	—	53	1	no	—
446	#336	—	53	1	no	—
447	C₅₃	#22559	1	1	yes	characteristic, complemented, Sylow
448	C₂⁵	C₂×Dic₅₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	—	2	2	no	—
451	C₂³×C₄	—	2	2	no	—
452	C₂³×C₄	—	2	2	no	—
453	C₂³×C₄	—	4	1	no	—
454	C₂³×C₄	—	4	1	no	—
455	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
456	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
457	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
458	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
459	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
460	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
461	C₂×M₁₆	—	106	2	no	—
462	C₂×M₁₆	—	106	2	no	—
463	C₂×M₁₆	—	106	2	no	—
464	C₂×M₁₆	—	106	2	no	—
465	C₂×M₁₆	—	212	1	no	—
466	C₂×M₁₆	—	212	1	no	—
467	C₂²×C₈	—	53	1	no	—
468	C₂²×C₈	—	53	1	no	—
469	C₂²×C₈	—	53	1	no	—
470	C₂²×C₈	—	53	1	no	—
471	C₂²×C₈	—	53	1	no	—
472	C₂²×C₈	—	53	1	no	—
473	C₂²×C₈	—	53	1	no	—
474	C₂²×C₈	—	53	1	no	—
475	#117	—	2	2	no	—
476	#117	—	2	2	no	—
477	#117	—	4	1	no	—
478	#117	—	4	1	no	—
479	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
495	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
496	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
497	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
499	C₄⋊C₈	—	106	2	no	—
500	C₄⋊C₈	—	106	2	no	—
501	C₄⋊C₈	—	212	1	no	—
502	C₄⋊C₈	—	212	1	no	—
503	C₂²⋊C₈	—	53	4	no	—
504	C₂²⋊C₈	—	106	2	no	—
505	C₂²⋊C₈	—	106	2	no	—
506	C₂²⋊C₈	—	106	2	no	—
507	C₂²⋊C₈	—	106	2	no	—
508	C₂²⋊C₈	—	106	2	no	—
509	C₂²⋊C₈	—	106	2	no	—
510	C₂²⋊C₈	—	106	2	no	—
511	C₂²⋊C₈	—	212	1	no	—
512	C₂²⋊C₈	—	212	1	no	—
513	#97	—	106	2	no	—
514	#97	—	212	1	no	—
515	C₄×C₈	—	106	2	no	—
516	C₄×C₈	—	212	1	no	—
517	#95	C₂×Dic₅₃	1	1	yes	characteristic
518	#95	C₂×Dic₅₃	1	1	yes	characteristic
519	#95	C₂×Dic₅₃	1	1	yes	characteristic
520	#95	C₂×Dic₅₃	1	1	yes	characteristic
521	#95	C₂×Dic₅₃	1	1	yes	characteristic
522	#95	C₂×Dic₅₃	1	1	yes	characteristic
523	#95	C₂×Dic₅₃	1	1	yes	characteristic
524	#95	C₂×Dic₅₃	1	1	yes	characteristic
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	4	1	no	—
529	C₂⁴	—	4	1	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	C₂²×Dic₅₃	1	1	yes	characteristic
533	C₂⁴	C₂²×Dic₅₃	1	1	yes	characteristic
534	C₂⁴	C₂²×Dic₅₃	1	1	yes	characteristic
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	#11719945	1	2	yes	—
563	C₂²×C₄	#11719945	1	2	yes	—
564	C₂²×C₄	D₄×D₅₃	1	2	yes	—
565	C₂²×C₄	#11719947	1	2	yes	—
566	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
569	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
570	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
571	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
572	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
573	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
574	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
575	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
576	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
577	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
578	M₁₆	—	212	4	no	—
579	M₁₆	—	212	4	no	—
580	C₂×C₈	—	53	2	no	—
581	C₂×C₈	—	53	2	no	—
582	C₂×C₈	—	106	1	no	—
583	C₂×C₈	—	106	1	no	—
584	C₂×C₈	—	106	1	no	—
585	C₂×C₈	—	106	1	no	—
586	C₂×C₈	—	106	1	no	—
587	C₂×C₈	—	106	1	no	—
588	C₂×C₈	—	106	1	no	—
589	C₂×C₈	—	106	1	no	—
590	C₂×C₈	—	106	1	no	—
591	C₂×C₈	—	106	1	no	—
592	C₂×C₈	—	106	1	no	—
593	C₂×C₈	—	106	1	no	—
594	C₂×C₈	—	106	1	no	—
595	C₂×C₈	—	106	1	no	—
596	C₂×C₈	—	106	1	no	—
597	C₂×C₈	—	106	1	no	—
598	C₂×C₈	—	106	1	no	—
599	C₂×C₈	—	106	1	no	—
600	C₂×C₈	—	106	1	no	—
601	C₂×C₈	—	106	1	no	—
602	C₂×C₈	—	106	1	no	—
603	C₂×C₈	—	106	1	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	#13133176	1	2	yes	—
654	C₂³	D₄×Dic₅₃	1	2	yes	—
655	C₂³	#13133224	1	2	yes	—
656	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	#13133176	1	2	yes	—
704	C₂×C₄	D₄×Dic₅₃	1	2	yes	—
705	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
706	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
707	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
708	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
709	C₂×C₄	#13133262	1	1	yes	characteristic
710	C₂×C₄	#13133262	1	1	yes	characteristic
711	C₈	—	106	2	no	—
712	C₈	—	106	2	no	—
713	C₈	—	212	1	no	—
714	C₈	—	212	1	no	—
715	C₈	—	212	1	no	—
716	C₈	—	212	1	no	—
717	C₈	—	212	1	no	—
718	C₈	—	212	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	4	16	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	C₂×#13133176	1	1	yes	characteristic
742	C₂²	C₂×D₄×Dic₅₃	1	1	yes	characteristic
743	C₂²	#16811098	1	1	yes	characteristic
744	C₂²	C₂×#13133224	1	1	yes	characteristic
745	C₂²	#16811390	1	1	yes	characteristic
746	C₂²	#16811390	1	1	yes	characteristic
747	C₂²	#16811390	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	#16811263	1	1	yes	characteristic
760	C₄	#16811263	1	1	yes	characteristic
761	C₄	#16811299	1	1	yes	characteristic
762	C₄	#16811299	1	1	yes	characteristic
763	C₂	—	4	2	no	—
764	C₂	—	4	2	no	—
765	C₂	—	4	2	no	—
766	C₂	#20277564	1	1	yes	characteristic
767	C₂	#20283353	1	1	yes	characteristic
768	C₂	#20283373	1	1	yes	characteristic
769	C₂	#20283419	1	1	yes	characteristic
770	C₂	#20283442	1	1	yes	characteristic
771	C₂	#20283763	1	1	yes	characteristic
772	C₂	#20283777	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₃
commutator, socle	C₂³×C₅₃	C₂³×C₄
Fitting	C₅₃×#2280	C₂
prime radical	C₂⁵×C₅₃	C₂×C₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#2280	D₅₃
hypocenter	C₅₃	#22559
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2280

Complements

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

N	H ≅ G/N	type
1. C₂×#16810684	C₂	semidirect
3. #20275330	C₂	semidirect
4. #20275330	C₂	semidirect
5. #20275323	C₂	semidirect
6. #20275323	C₂	semidirect
7. #20274900	C₂	semidirect
8. #20274900	C₂	semidirect
9. #20274786	C₂	semidirect
10. #20274699	C₂	semidirect
12. #20274499	C₂	semidirect
13. #20274499	C₂	semidirect
14. #20274481	C₂	semidirect
19. C₂×C₄⋊#88322	C₂²	semidirect
20. C₂×C₄⋊#88322	C₂²	semidirect
21. C₂×C₄⋊#88322	C₂²	semidirect
22. C₂×C₄⋊#88322	C₂²	semidirect
34. C₂×#13133128	C₂²	semidirect
35. C₂×#13133128	C₂²	semidirect
36. C₂×C₄×#88322	C₂²	semidirect
37. C₂×C₄×#88322	C₂²	semidirect
38. #16810378	C₂²	semidirect
39. #16810378	C₂²	semidirect
40. #16810378	C₂²	semidirect
41. #16810378	C₂²	semidirect
42. #16810378	C₂²	semidirect
43. #16810378	C₂²	semidirect
44. #16810378	C₂²	semidirect
45. #16810378	C₂²	semidirect
447. C₅₃	#22559	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#16810684	2
C₂×#16810587	2
#20275330	2
#20275323	2
#20274900	2
#20274786	2
#20274699	2
#20274625	2
#20274499	2
#20274481	2
C₅₃×#2280	2
#22559	53