Subgroups — #28318355

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#16811633	C₂	1	1	yes	maximal, characteristic
3	#20291278	C₂	1	2	yes	maximal
4	#20290521	C₂	1	4	yes	maximal, complemented
5	#20290517	C₂	1	4	yes	maximal, complemented
6	#20290396	C₂	1	2	yes	maximal
7	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×#13133296	C₂²	1	2	yes	—
10	C₂×#13133288	C₄	1	2	yes	complemented
11	D₅₃⋊#108	C₄	1	2	yes	complemented
12	D₅₃⋊#108	C₄	1	2	yes	complemented
13	D₅₃⋊#108	C₂²	1	2	yes	—
14	D₅₃⋊#108	C₂²	1	2	yes	—
15	C₂×#13133287	C₄	1	2	yes	complemented
16	#16811633	C₄	1	2	yes	complemented
17	#16811633	C₄	1	2	yes	complemented
18	#16811633	C₂²	1	2	yes	—
19	#16811633	C₂²	1	2	yes	—
20	C₂×#13133286	C₄	1	2	yes	complemented
21	C₂×#13133285	C₄	1	2	yes	complemented
22	#16811589	—	2	4	no	—
23	#16811586	C₂²	1	8	yes	—
24	M₁₆×#6157	—	2	4	no	—
25	#16811494	C₂²	1	8	yes	—
26	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	#117×D₅₃	C₂²	1	1	yes	characteristic
29	#16810581	C₄	1	1	yes	characteristic, complemented
30	#16810580	C₄	1	2	yes	complemented
31	#16810579	C₄	1	1	yes	characteristic, complemented
32	#16810578	C₄	1	1	yes	characteristic, complemented
33	#16810577	C₄	1	2	yes	complemented
34	#97×D₅₃	C₂²	1	2	yes	—
35	C₄×C₈×D₅₃	C₂²	1	2	yes	—
36	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
37	C₂×#11719936	C₂×C₄	1	4	yes	—
38	D₅₃⋊M₁₆	—	2	2	no	—
39	D₅₃⋊M₁₆	—	2	2	no	—
40	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
41	D₅₃⋊M₁₆	C₂³	1	4	yes	—
42	C₂×#11719940	—	2	2	no	—
43	C₂×D₅₃⋊C₈	—	2	2	no	—
44	#13133296	—	2	2	no	—
45	#13133296	—	2	2	no	—
46	#13133296	C₂×C₄	1	4	yes	—
47	#13133296	C₂³	1	4	yes	—
48	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊#6157	—	2	2	no	—
50	C₂×C₄×#6157	—	2	2	no	—
51	#13133288	C₂×C₄	1	4	yes	complemented
52	#13133288	C₂×C₄	1	4	yes	complemented
53	#13133287	C₂×C₄	1	4	yes	complemented
54	#13133287	C₂×C₄	1	4	yes	complemented
55	#13133286	C₂×C₄	1	4	yes	—
56	#13133286	C₂×C₄	1	4	yes	—
57	#13133285	C₂×C₄	1	4	yes	—
58	#13133285	C₂×C₄	1	4	yes	—
59	#13133271	—	2	8	no	—
60	C₈×#6157	—	2	8	no	—
61	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
62	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
63	C₂×#11719912	C₂×C₄	1	2	yes	—
64	M₁₆×D₅₃	D₄	1	2	yes	—
65	M₁₆×D₅₃	D₄	1	2	yes	—
66	M₁₆×D₅₃	Q₈	1	2	yes	—
67	M₁₆×D₅₃	Q₈	1	2	yes	—
68	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
81	C₂×C₈×D₅₃	C₂³	1	2	yes	—
82	#13133176	C₂×C₄	1	1	yes	characteristic
83	#13133175	—	2	1	no	—
84	#13133174	C₂×C₄	1	2	yes	—
85	#13133173	—	2	1	no	—
86	C₄⋊C₄×D₅₃	—	2	1	no	—
87	C₂²⋊C₄×D₅₃	—	2	1	no	—
88	C₄²×D₅₃	C₂³	1	2	yes	—
89	#13133128	C₂×C₄	1	2	yes	complemented
90	#13133127	C₂×C₄	1	2	yes	complemented
91	#13133127	C₂×C₄	1	2	yes	complemented
92	C₄×#88322	C₂×C₄	1	2	yes	complemented
93	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
94	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
95	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
97	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
98	#97×C₅₃	C₂×C₄	1	2	yes	complemented
99	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
100	C₂³×D₅₃	#41	1	1	yes	characteristic
101	C₂²×#6157	—	2	4	no	—
102	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₅₃	#41	1	1	yes	characteristic
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
117	C₂²⋊#6157	—	2	4	no	—
118	C₂²⋊#6157	—	2	4	no	—
119	#11719940	—	2	4	no	—
120	#11719940	—	2	4	no	—
121	C₂×#88324	—	2	4	no	—
122	C₄⋊#6157	—	2	4	no	—
123	C₄⋊#6157	C₂²×C₄	1	8	yes	—
124	C₄×#6157	—	2	4	no	—
125	C₄×#6157	—	2	4	no	—
126	#11719936	—	2	4	no	—
127	#11719936	C₂²×C₄	1	8	yes	—
128	D₅₃⋊C₈	—	2	4	no	—
129	D₅₃⋊C₈	—	2	4	no	—
130	M₁₆×C₅₃	C₄⋊C₄	1	2	yes	—
131	M₁₆×C₅₃	C₄⋊C₄	1	2	yes	—
132	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
134	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
135	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₅₃	—	2	1	no	—
140	C₂²⋊C₄×C₅₃	—	2	1	no	—
141	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
142	C₂²⋊Dic₅₃	—	2	1	no	—
143	#11719921	—	2	2	no	—
144	C₄⋊Dic₅₃	—	2	1	no	—
145	#11719919	—	2	2	no	—
146	C₄×Dic₅₃	—	2	2	no	—
147	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
148	#11719917	C₄⋊C₄	1	2	yes	—
149	#11719917	C₄⋊C₄	1	2	yes	—
150	C₂×#88322	C₄²	1	1	yes	characteristic
151	C₂×#88322	C₄²	1	1	yes	characteristic
152	C₂×#88322	C₄²	1	1	yes	characteristic
153	C₂×#88322	C₄²	1	1	yes	characteristic
154	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
155	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
156	C₂×#88322	C₂²×C₄	1	2	yes	—
157	#11719912	C₄⋊C₄	1	4	yes	—
158	#11719912	C₄⋊C₄	1	4	yes	—
159	C₈×D₅₃	C₄²	1	1	yes	characteristic
160	C₈×D₅₃	C₄²	1	1	yes	characteristic
161	C₈×D₅₃	C₄²	1	1	yes	characteristic
162	C₈×D₅₃	C₄²	1	1	yes	characteristic
163	C₈×D₅₃	C₄²	1	1	yes	characteristic
164	C₈×D₅₃	C₄²	1	1	yes	characteristic
165	C₈×D₅₃	C₄²	1	1	yes	characteristic
166	C₈×D₅₃	C₄²	1	1	yes	characteristic
167	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
168	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
170	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
171	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
172	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
174	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
175	C₈×D₅₃	C₂×D₄	1	4	yes	—
176	C₈×D₅₃	C₂×Q₈	1	4	yes	—
177	C₂³×C₅₃	#117	1	1	yes	characteristic
178	C₂²×D₅₃	—	4	2	no	—
179	C₂²×D₅₃	#117	1	1	yes	characteristic
180	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
181	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
182	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
183	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
184	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
185	C₂×#6157	—	2	8	no	—
186	C₂×#6157	—	8	4	no	—
187	C₂×C₄×C₅₃	—	2	2	no	—
188	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
193	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×Dic₅₃	—	2	2	no	—
195	C₂×Dic₅₃	#117	1	1	yes	characteristic
196	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
197	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
199	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
200	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
201	C₄×D₅₃	—	4	4	no	—
202	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
203	C₄×D₅₃	C₂×C₄²	1	1	yes	characteristic
204	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
207	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
208	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
209	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
210	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
211	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
212	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
213	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
214	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
215	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
216	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
217	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
218	#88324	—	2	8	no	—
219	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
220	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
221	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
222	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
223	C₈×C₅₃	C₂×C₄⋊C₄	1	4	yes	—
224	#88322	C₂×C₄²	1	1	yes	characteristic
225	#88322	C₂×C₄²	1	1	yes	characteristic
226	#88322	C₂×C₄²	1	1	yes	characteristic
227	#88322	C₂×C₄²	1	1	yes	characteristic
228	#88322	C₂×C₄⋊C₄	1	4	yes	—
229	#20446	—	53	1	no	maximal, Sylow
230	C₂²×C₅₃	—	4	1	no	—
231	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
234	C₂×D₅₃	—	2	2	no	—
235	C₂×D₅₃	—	2	2	no	—
236	C₂×D₅₃	—	2	2	no	—
237	C₂×D₅₃	—	4	1	no	—
238	C₂×D₅₃	—	4	1	no	—
239	C₂×D₅₃	—	4	1	no	—
240	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂×D₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
242	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂×D₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
244	#6157	—	4	8	no	—
245	C₄×C₅₃	—	4	2	no	—
246	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
247	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
248	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
249	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
250	Dic₅₃	—	4	2	no	—
251	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
252	Dic₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
253	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
254	Dic₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
255	C₂²×#108	—	53	1	no	—
256	C₂×#427	—	53	1	no	—
257	#2873	—	53	2	no	—
258	C₂×#405	—	53	1	no	—
259	#1773	—	53	4	no	—
260	#1772	—	53	4	no	—
261	#1733	—	53	2	no	—
262	C₂×C₅₃	—	2	1	no	—
263	C₂×C₅₃	—	2	1	no	—
264	C₂×C₅₃	—	2	1	no	—
265	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
266	D₅₃	—	2	1	no	—
267	D₅₃	—	2	1	no	—
268	D₅₃	—	2	1	no	—
269	D₅₃	#2957	1	2	yes	—
270	C₂²×M₁₆	—	53	1	no	—
271	C₂²×M₁₆	—	53	2	no	—
272	C₂³×C₈	—	53	1	no	—
273	C₂×#117	—	53	1	no	—
274	C₂×#117	—	53	2	no	—
275	C₂×#108	—	53	2	no	—
276	C₂×#108	—	53	2	no	—
277	C₂×#108	—	53	2	no	—
278	C₂×#108	—	53	2	no	—
279	C₂×#108	—	53	2	no	—
280	C₂×#108	—	53	2	no	—
281	#427	—	53	2	no	—
282	#427	—	53	2	no	—
283	#427	—	53	2	no	—
284	#427	—	53	2	no	—
285	C₂×#107	—	53	2	no	—
286	C₂×#106	—	53	2	no	—
287	#405	—	53	1	no	—
288	#405	—	53	1	no	—
289	#405	—	53	1	no	—
290	#405	—	53	2	no	—
291	#405	—	53	2	no	—
292	#405	—	53	8	no	—
293	#405	—	106	4	no	—
294	#405	#6157	1	1	yes	characteristic, complemented
295	C₄×M₁₆	—	106	4	no	—
296	C₂×#97	—	53	2	no	—
297	C₂×C₄×C₈	—	53	2	no	—
298	#339	—	53	8	no	—
299	C₅₃	#20446	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₄	—	53	1	no	—
301	C₂×M₁₆	—	53	1	no	—
302	C₂×M₁₆	—	53	2	no	—
303	C₂×M₁₆	—	53	2	no	—
304	C₂×M₁₆	—	53	2	no	—
305	C₂×M₁₆	—	53	2	no	—
306	C₂×M₁₆	—	53	2	no	—
307	C₂×M₁₆	—	53	4	no	—
308	C₂×M₁₆	—	53	4	no	—
309	C₂×M₁₆	—	53	4	no	—
310	C₂×M₁₆	—	106	2	no	—
311	C₂×M₁₆	—	106	2	no	—
312	C₂×M₁₆	—	106	2	no	—
313	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
314	C₂²×C₈	—	53	1	no	—
315	C₂²×C₈	—	53	1	no	—
316	C₂²×C₈	—	53	1	no	—
317	C₂²×C₈	—	53	1	no	—
318	C₂²×C₈	—	53	1	no	—
319	C₂²×C₈	—	53	1	no	—
320	C₂²×C₈	—	53	1	no	—
321	C₂²×C₈	—	53	1	no	—
322	C₂²×C₈	—	53	1	no	—
323	C₂²×C₈	—	53	1	no	—
324	C₂²×C₈	—	53	1	no	—
325	C₂²×C₈	—	53	1	no	—
326	C₂²×C₈	—	53	1	no	—
327	C₂²×C₈	—	53	2	no	—
328	C₂²×C₈	—	106	2	no	—
329	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
330	#117	—	53	1	no	—
331	#117	—	53	2	no	—
332	#117	—	53	4	no	—
333	#117	—	53	4	no	—
334	#117	—	106	1	no	—
335	#117	—	106	1	no	—
336	#117	—	106	2	no	—
337	#117	—	106	2	no	—
338	#117	C₂×#6157	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	53	4	no	—
340	C₂×C₄⋊C₄	—	106	1	no	—
341	C₂×C₂²⋊C₄	—	106	1	no	—
342	C₂×C₂²⋊C₄	—	106	2	no	—
343	C₂×C₄²	—	53	2	no	—
344	C₂×C₄²	—	106	2	no	—
345	#108	—	53	4	no	—
346	#108	—	53	4	no	—
347	#108	—	53	4	no	—
348	#108	—	53	4	no	—
349	#107	—	53	4	no	—
350	#107	—	53	4	no	—
351	#106	—	53	4	no	—
352	#106	—	53	4	no	—
353	#97	—	53	2	no	—
354	#97	—	53	2	no	—
355	#97	—	53	2	no	—
356	#97	—	106	8	no	—
357	#97	C₂×#6157	1	2	yes	complemented
358	C₄×C₈	—	53	2	no	—
359	C₄×C₈	—	53	2	no	—
360	C₄×C₈	—	53	2	no	—
361	C₄×C₈	—	106	8	no	—
362	C₄×C₈	C₂×#6157	1	2	yes	complemented
363	C₂⁴	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	C₂²×C₄	—	53	1	no	—
366	C₂²×C₄	—	53	1	no	—
367	C₂²×C₄	—	53	1	no	—
368	C₂²×C₄	—	53	1	no	—
369	C₂²×C₄	—	53	1	no	—
370	C₂²×C₄	—	53	1	no	—
371	C₂²×C₄	—	53	1	no	—
372	C₂²×C₄	—	53	1	no	—
373	C₂²×C₄	—	53	1	no	—
374	C₂²×C₄	—	53	1	no	—
375	C₂²×C₄	—	53	1	no	—
376	C₂²×C₄	—	53	1	no	—
377	C₂²×C₄	—	106	2	no	—
378	C₂²×C₄	—	106	4	no	—
379	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
380	M₁₆	—	53	2	no	—
381	M₁₆	—	53	2	no	—
382	M₁₆	—	53	4	no	—
383	M₁₆	—	53	4	no	—
384	M₁₆	—	53	8	no	—
385	M₁₆	—	106	4	no	—
386	M₁₆	—	106	4	no	—
387	M₁₆	—	106	4	no	—
388	M₁₆	C₄⋊#6157	1	2	yes	—
389	M₁₆	C₄⋊#6157	1	2	yes	—
390	C₂×C₈	—	53	1	no	—
391	C₂×C₈	—	53	1	no	—
392	C₂×C₈	—	53	1	no	—
393	C₂×C₈	—	53	1	no	—
394	C₂×C₈	—	53	1	no	—
395	C₂×C₈	—	53	2	no	—
396	C₂×C₈	—	53	1	no	—
397	C₂×C₈	—	53	1	no	—
398	C₂×C₈	—	53	1	no	—
399	C₂×C₈	—	53	1	no	—
400	C₂×C₈	—	53	1	no	—
401	C₂×C₈	—	53	1	no	—
402	C₂×C₈	—	53	1	no	—
403	C₂×C₈	—	53	1	no	—
404	C₂×C₈	—	53	1	no	—
405	C₂×C₈	—	53	1	no	—
406	C₂×C₈	—	53	1	no	—
407	C₂×C₈	—	53	1	no	—
408	C₂×C₈	—	53	1	no	—
409	C₂×C₈	—	53	1	no	—
410	C₂×C₈	—	53	1	no	—
411	C₂×C₈	—	53	1	no	—
412	C₂×C₈	—	53	1	no	—
413	C₂×C₈	—	53	4	no	—
414	C₂×C₈	—	53	4	no	—
415	C₂×C₈	—	106	4	no	—
416	C₂×C₈	—	106	4	no	—
417	C₂×C₈	—	106	4	no	—
418	C₂×C₈	C₄×#6157	1	1	yes	characteristic
419	C₂×C₈	C₄×#6157	1	1	yes	characteristic
420	C₂×C₈	C₄×#6157	1	1	yes	characteristic
421	C₂×C₈	C₄×#6157	1	1	yes	characteristic
422	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
423	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
424	C₂×C₈	C₂²×#6157	1	2	yes	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	53	8	no	—
427	C₄⋊C₄	—	106	2	no	—
428	C₄⋊C₄	—	106	4	no	—
429	C₄⋊C₄	—	106	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	106	2	no	—
432	C₂²⋊C₄	—	106	4	no	—
433	C₂²⋊C₄	—	106	4	no	—
434	C₂²⋊C₄	—	106	1	no	—
435	C₄²	—	53	2	no	—
436	C₄²	—	106	2	no	—
437	C₄²	—	106	4	no	—
438	C₄²	—	106	4	no	—
439	C₄²	C₂²×#6157	1	2	yes	—
440	C₂³	—	53	1	no	—
441	C₂³	—	53	1	no	—
442	C₂³	—	53	1	no	—
443	C₂³	—	53	1	no	—
444	C₂³	—	53	1	no	—
445	C₂³	—	53	1	no	—
446	C₂³	—	212	2	no	—
447	C₂³	#13133296	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	53	1	no	—
450	C₂×C₄	—	53	1	no	—
451	C₂×C₄	—	53	1	no	—
452	C₂×C₄	—	53	1	no	—
453	C₂×C₄	—	53	1	no	—
454	C₂×C₄	—	53	1	no	—
455	C₂×C₄	—	53	1	no	—
456	C₂×C₄	—	53	1	no	—
457	C₂×C₄	—	53	1	no	—
458	C₂×C₄	—	53	1	no	—
459	C₂×C₄	—	53	1	no	—
460	C₂×C₄	—	53	1	no	—
461	C₂×C₄	—	53	1	no	—
462	C₂×C₄	—	53	1	no	—
463	C₂×C₄	—	53	1	no	—
464	C₂×C₄	—	53	1	no	—
465	C₂×C₄	—	53	1	no	—
466	C₂×C₄	—	53	1	no	—
467	C₂×C₄	—	53	1	no	—
468	C₂×C₄	—	53	1	no	—
469	C₂×C₄	—	53	1	no	—
470	C₂×C₄	—	53	1	no	—
471	C₂×C₄	—	106	8	no	—
472	C₂×C₄	—	106	2	no	—
473	C₂×C₄	—	424	4	no	—
474	C₂×C₄	—	212	4	no	—
475	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
479	C₂×C₄	#13133296	1	1	yes	characteristic
480	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
481	C₈	—	53	1	no	—
482	C₈	—	53	1	no	—
483	C₈	—	53	1	no	—
484	C₈	—	53	1	no	—
485	C₈	—	53	4	no	—
486	C₈	—	106	8	no	—
487	C₈	C₂×C₄×#6157	1	1	yes	characteristic
488	C₈	C₂×C₄×#6157	1	1	yes	characteristic
489	C₈	C₂×C₄×#6157	1	1	yes	characteristic
490	C₈	C₂×C₄×#6157	1	1	yes	characteristic
491	C₈	C₂×C₄⋊#6157	1	4	yes	—
492	C₂²	—	4	1	no	—
493	C₂²	—	53	1	no	—
494	C₂²	—	53	1	no	—
495	C₂²	—	53	1	no	—
496	C₂²	—	53	1	no	—
497	C₂²	—	106	2	no	—
498	C₂²	—	106	2	no	—
499	C₂²	—	106	2	no	—
500	C₂²	—	212	1	no	—
501	C₂²	—	212	1	no	—
502	C₂²	—	212	1	no	—
503	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
504	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
505	C₂²	C₂×#13133296	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	53	1	no	—
508	C₄	—	53	1	no	—
509	C₄	—	53	1	no	—
510	C₄	—	53	1	no	—
511	C₄	—	212	2	no	—
512	C₄	—	212	8	no	—
513	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
514	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
515	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
516	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	53	2	no	—
521	C₂	—	106	1	no	—
522	C₂	—	106	1	no	—
523	C₂	—	106	1	no	—
524	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
socle	C₂×C₅₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#20446
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #20290521	C₂	semidirect
5. #20290517	C₂	semidirect
10. C₂×#13133288	C₄	semidirect
11. D₅₃⋊#108	C₄	semidirect
12. D₅₃⋊#108	C₄	semidirect
15. C₂×#13133287	C₄	semidirect
16. #16811633	C₄	semidirect
17. #16811633	C₄	semidirect
20. C₂×#13133286	C₄	semidirect
21. C₂×#13133285	C₄	semidirect
29. #16810581	C₄	semidirect
30. #16810580	C₄	semidirect
31. #16810579	C₄	semidirect
32. #16810578	C₄	semidirect
33. #16810577	C₄	semidirect
36. C₅₃×#405	C₄	semidirect
51. #13133288	C₂×C₄	semidirect
52. #13133288	C₂×C₄	semidirect
53. #13133287	C₂×C₄	semidirect
54. #13133287	C₂×C₄	semidirect
89. #13133128	C₂×C₄	semidirect
90. #13133127	C₂×C₄	semidirect
91. #13133127	C₂×C₄	semidirect
92. C₄×#88322	C₂×C₄	semidirect
93. C₈×Dic₅₃	C₂×C₄	semidirect
94. C₈×Dic₅₃	C₂×C₄	semidirect
98. #97×C₅₃	C₂×C₄	semidirect
99. C₄×C₈×C₅₃	C₂×C₄	semidirect
294. #405	#6157	semidirect
299. C₅₃	#20446	semidirect
357. #97	C₂×#6157	semidirect
362. C₄×C₈	C₂×#6157	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₃⋊#108	2
C₂×#16811633	2
#20291278	2
#20290521	2
#20290517	2
#20290396	2
#405×D₅₃	2
#20446	53