Subgroups — #28318898

Order 13568.

798 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#446	C₂	1	1	yes	maximal, characteristic
2	#20291174	C₂	1	1	yes	maximal, characteristic
3	#20290516	C₂	1	1	yes	maximal, characteristic
4	#20290516	C₂	1	1	yes	maximal, characteristic
5	#20290513	C₂	1	1	yes	maximal, characteristic
6	#20290513	C₂	1	1	yes	maximal, characteristic
7	#20290508	C₂	1	1	yes	maximal, characteristic
8	C₈×C₄⋊#6157	C₂	1	1	yes	maximal, characteristic
9	#20290504	C₂	1	1	yes	maximal, characteristic
10	#20290504	C₂	1	1	yes	maximal, characteristic
11	C₄⋊C₈×#6157	C₂	1	1	yes	maximal, characteristic
12	#20290435	C₂	1	1	yes	maximal, characteristic
13	#20290433	C₂	1	1	yes	maximal, characteristic
14	#20290431	C₂	1	1	yes	maximal, characteristic
15	#446×D₅₃	C₂	1	1	yes	maximal, characteristic
16	#16811675	C₄	1	2	yes	complemented
17	#16811675	C₄	1	2	yes	complemented
18	#16811674	C₄	1	2	yes	complemented
19	#16811673	C₄	1	2	yes	complemented
20	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
21	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
22	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
23	#16811582	C₂²	1	1	yes	characteristic
24	#16811582	C₂²	1	1	yes	characteristic
25	C₂×#13133271	C₂²	1	1	yes	characteristic
26	C₂×#13133271	C₂²	1	1	yes	characteristic
27	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
29	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
30	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
31	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
32	(C₂×#6157)⋊Q₈	C₄	1	2	yes	—
33	#16811574	C₄	1	2	yes	—
34	#16811572	C₄	1	2	yes	—
35	#16811572	C₄	1	2	yes	—
36	C₄×C₄⋊#6157	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊#6157	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊#6157	C₂²	1	1	yes	characteristic
39	#16811559	C₂²	1	1	yes	characteristic
40	#16811559	C₂²	1	1	yes	characteristic
41	C₄²×#6157	C₂²	1	1	yes	characteristic
42	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
51	(C₂×#6157)⋊C₈	C₂²	1	1	yes	characteristic
52	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
53	#16810754	C₄	1	1	yes	characteristic, complemented
54	#16810753	C₄	1	1	yes	characteristic, complemented
55	#16810752	C₄	1	1	yes	characteristic, complemented
56	#16810752	C₄	1	1	yes	characteristic, complemented
57	#16810751	C₄	1	1	yes	characteristic, complemented
58	#16810751	C₄	1	1	yes	characteristic, complemented
59	#16810750	C₄	1	1	yes	characteristic, complemented
60	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
61	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
62	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
63	#97×D₅₃	C₂²	1	1	yes	characteristic
64	#97×D₅₃	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#446	C₄	1	1	yes	characteristic, complemented
67	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊#6157	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊#6157	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊#6157	C₂×C₄	1	2	yes	—
74	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
75	C₂×C₄×#6157	C₂×C₄	1	2	yes	—
76	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
77	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
78	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
79	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
80	#13133284	C₂×C₄	1	2	yes	—
81	#13133284	C₂×C₄	1	2	yes	—
82	#13133284	C₂×C₄	1	2	yes	—
83	C₄⋊#88324	C₂×C₄	1	2	yes	—
84	C₄⋊#88324	C₂×C₄	1	2	yes	—
85	C₄⋊#88324	C₂×C₄	1	2	yes	—
86	#13133272	C₂×C₄	1	2	yes	—
87	#13133272	C₂×C₄	1	2	yes	—
88	#13133272	C₂×C₄	1	2	yes	—
89	#13133272	C₂×C₄	1	2	yes	—
90	#13133271	—	4	1	no	—
91	#13133271	—	4	1	no	—
92	C₄×#88324	C₂×C₄	1	2	yes	—
93	C₄×#88324	C₂×C₄	1	2	yes	—
94	C₈×#6157	—	4	1	no	—
95	C₈×#6157	—	4	1	no	—
96	C₈×#6157	—	4	1	no	—
97	C₈×#6157	—	4	1	no	—
98	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
99	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
100	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
101	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×#6157)⋊C₄	C₂×C₄	1	2	yes	—
105	C₂×Q₈×D₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
107	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
108	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
109	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
110	Q₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
111	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
112	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
113	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
114	#13133182	C₂×C₄	1	1	yes	characteristic
115	#13133182	C₂×C₄	1	1	yes	characteristic
116	#13133182	C₂×C₄	1	1	yes	characteristic
117	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
118	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
119	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
120	C₄²×D₅₃	C₂³	1	1	yes	characteristic
121	C₄²×D₅₃	C₂³	1	1	yes	characteristic
122	C₄²×D₅₃	C₂³	1	1	yes	characteristic
123	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
124	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
125	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
126	#13133146	C₂×C₄	1	1	yes	characteristic
127	#13133146	C₂×C₄	1	1	yes	characteristic
128	#13133146	C₂×C₄	1	1	yes	characteristic
129	#13133146	C₂×C₄	1	1	yes	characteristic
130	#13133146	C₂×C₄	1	1	yes	characteristic
131	#13133146	C₂×C₄	1	1	yes	characteristic
132	#13133128	C₂×C₄	1	1	yes	characteristic
133	#13133128	C₂×C₄	1	1	yes	characteristic
134	#13133127	C₂×C₄	1	1	yes	characteristic
135	#13133127	C₂×C₄	1	1	yes	characteristic
136	#13133127	C₂×C₄	1	1	yes	characteristic
137	#13133127	C₂×C₄	1	1	yes	characteristic
138	C₄×#88322	C₂×C₄	1	1	yes	characteristic
139	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
140	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
142	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
143	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
144	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
145	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
146	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
147	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
148	C₂²×#6157	C₂²×C₄	1	2	yes	—
149	C₂²×#6157	C₂²×C₄	1	2	yes	—
150	C₂²×#6157	C₂²×C₄	1	2	yes	—
151	C₂²×#6157	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₅₃	C₄²	1	1	yes	characteristic
153	Q₈×D₅₃	—	4	2	no	—
154	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₁₀₆	C₄²	1	1	yes	characteristic
162	C₂×Dic₁₀₆	C₄²	1	1	yes	characteristic
163	C₂×Dic₁₀₆	C₄²	1	1	yes	characteristic
164	C₂×#88324	C₂²×C₄	1	2	yes	—
165	C₂×#88324	C₂²×C₄	1	2	yes	—
166	C₂×#88324	C₂²×C₄	1	2	yes	—
167	C₂×#88324	C₂²×C₄	1	2	yes	—
168	C₄⋊#6157	—	2	4	no	—
169	C₄⋊#6157	—	2	4	no	—
170	C₄⋊#6157	—	4	2	no	—
171	C₄×#6157	—	2	4	no	—
172	C₄×#6157	—	2	1	no	—
173	C₄×#6157	—	2	1	no	—
174	C₄×#6157	—	2	1	no	—
175	C₄×#6157	—	2	1	no	—
176	C₄×#6157	—	2	1	no	—
177	C₄×#6157	—	2	1	no	—
178	C₄×#6157	—	2	1	no	—
179	C₄×#6157	—	2	1	no	—
180	C₄×#6157	—	4	2	no	—
181	D₅₃⋊C₈	—	2	1	no	—
182	D₅₃⋊C₈	—	2	1	no	—
183	D₅₃⋊C₈	—	2	1	no	—
184	D₅₃⋊C₈	—	2	1	no	—
185	D₅₃⋊C₈	—	2	1	no	—
186	D₅₃⋊C₈	—	2	1	no	—
187	D₅₃⋊C₈	—	2	1	no	—
188	D₅₃⋊C₈	—	2	1	no	—
189	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
194	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
195	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
196	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
200	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
201	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
202	#11719919	C₄²	1	1	yes	characteristic
203	#11719919	C₄²	1	1	yes	characteristic
204	#11719919	C₄²	1	1	yes	characteristic
205	#11719919	C₄²	1	1	yes	characteristic
206	#11719919	C₄²	1	1	yes	characteristic
207	#11719919	C₄²	1	1	yes	characteristic
208	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
209	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
218	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
219	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
220	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
221	C₈×D₅₃	—	2	1	no	—
222	C₈×D₅₃	—	2	1	no	—
223	C₈×D₅₃	—	2	1	no	—
224	C₈×D₅₃	—	2	1	no	—
225	C₈×D₅₃	—	2	1	no	—
226	C₈×D₅₃	—	2	1	no	—
227	C₈×D₅₃	—	2	1	no	—
228	C₈×D₅₃	—	2	1	no	—
229	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×#6157	—	2	2	no	—
231	C₂×#6157	—	2	2	no	—
232	C₂×#6157	—	2	2	no	—
233	C₂×#6157	—	2	2	no	—
234	C₂×#6157	—	2	2	no	—
235	C₂×#6157	—	2	2	no	—
236	C₂×#6157	—	2	2	no	—
237	C₂×#6157	—	2	2	no	—
238	C₂×#6157	—	2	2	no	—
239	C₂×#6157	—	2	2	no	—
240	C₂×#6157	—	2	2	no	—
241	C₂×#6157	#131	1	4	yes	—
242	Q₈×C₅₃	—	4	1	no	—
243	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
244	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
245	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
246	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
247	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
248	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
249	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
250	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
251	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
252	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
253	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
254	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
255	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
256	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
257	C₄×D₅₃	—	2	2	no	—
258	C₄×D₅₃	—	2	2	no	—
259	C₄×D₅₃	—	2	2	no	—
260	C₄×D₅₃	—	2	2	no	—
261	C₄×D₅₃	—	2	2	no	—
262	C₄×D₅₃	—	2	2	no	—
263	C₄×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
264	C₄×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
265	C₄×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
266	C₄×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
267	Dic₁₀₆	—	4	1	no	—
268	Dic₁₀₆	—	4	1	no	—
269	Dic₁₀₆	—	4	1	no	—
270	#88324	—	2	2	no	—
271	#88324	—	2	2	no	—
272	#88324	—	2	2	no	—
273	#88324	—	2	2	no	—
274	C₈×C₅₃	—	2	1	no	—
275	C₈×C₅₃	—	2	1	no	—
276	C₈×C₅₃	—	2	1	no	—
277	C₈×C₅₃	—	2	1	no	—
278	#88322	—	2	1	no	—
279	#88322	—	2	1	no	—
280	#88322	—	2	1	no	—
281	#88322	—	2	1	no	—
282	#20575	—	53	1	no	maximal, Sylow
283	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
284	C₂×D₅₃	#519	1	1	yes	characteristic
285	C₂×D₅₃	#520	1	1	yes	characteristic
286	C₂×D₅₃	C₂×#131	1	2	yes	—
287	C₂×D₅₃	#568	1	2	yes	—
288	#6157	—	2	4	no	—
289	#6157	—	4	2	no	—
290	#6157	—	4	2	no	—
291	#6157	—	4	2	no	—
292	C₄×C₅₃	—	2	1	no	—
293	C₄×C₅₃	—	2	1	no	—
294	C₄×C₅₃	—	2	1	no	—
295	C₄×C₅₃	—	2	1	no	—
296	C₄×C₅₃	—	2	1	no	—
297	C₄×C₅₃	—	2	1	no	—
298	C₄×C₅₃	#519	1	1	yes	characteristic
299	C₄×C₅₃	#520	1	1	yes	characteristic
300	Dic₅₃	—	2	1	no	—
301	Dic₅₃	—	2	1	no	—
302	Dic₅₃	—	2	1	no	—
303	Dic₅₃	—	2	1	no	—
304	Dic₅₃	—	2	1	no	—
305	Dic₅₃	—	2	1	no	—
306	Dic₅₃	#519	1	1	yes	characteristic
307	Dic₅₃	#520	1	1	yes	characteristic
308	C₂×#446	—	53	1	no	—
309	C₂×#446	—	53	1	no	—
310	#2295	—	53	1	no	—
311	#1771	—	53	1	no	—
312	#1771	—	53	1	no	—
313	#1771	—	53	1	no	—
314	#1771	—	53	1	no	—
315	C₈×C₄⋊C₄	—	53	1	no	—
316	C₈×C₄⋊C₄	—	53	1	no	—
317	#1768	—	53	1	no	—
318	#1768	—	53	1	no	—
319	C₄×C₄⋊C₈	—	53	1	no	—
320	#1746	—	53	1	no	—
321	#1746	—	53	1	no	—
322	#1745	—	53	1	no	—
323	C₂×C₅₃	#2276	1	1	yes	characteristic
324	C₂×C₅₃	#2873	1	1	yes	characteristic
325	C₂×C₅₃	C₄×#131	1	1	yes	characteristic
326	D₅₃	#2985	1	2	yes	—
327	D₅₃	#2992	1	2	yes	—
328	C₂×C₄×Q₈	—	53	1	no	—
329	#446	—	53	2	no	—
330	#446	—	53	2	no	—
331	#446	—	53	2	no	—
332	#446	—	53	2	no	—
333	#446	—	53	1	no	—
334	#446	—	53	1	no	—
335	#446	—	53	1	no	—
336	#446	—	53	1	no	—
337	#446	—	53	1	no	—
338	#446	—	53	1	no	—
339	#446	—	53	1	no	—
340	#446	#6157	1	1	yes	characteristic, complemented
341	C₂×C₄⋊C₈	—	53	1	no	—
342	C₂×C₄⋊C₈	—	53	1	no	—
343	C₂×C₄⋊C₈	—	53	1	no	—
344	C₂×C₄⋊C₈	—	53	1	no	—
345	C₂×C₄⋊C₈	—	53	1	no	—
346	C₂×C₄⋊C₈	—	53	1	no	—
347	C₂×#97	—	53	1	no	—
348	C₂×#97	—	53	1	no	—
349	C₂×#97	—	53	1	no	—
350	C₂×#97	—	53	1	no	—
351	C₂×#97	—	53	1	no	—
352	C₂×#97	—	53	1	no	—
353	C₂×C₄×C₈	—	53	1	no	—
354	C₂×C₄×C₈	—	53	1	no	—
355	C₂×C₄×C₈	—	53	1	no	—
356	C₂×C₄×C₈	—	53	1	no	—
357	C₂×C₄×C₈	—	53	1	no	—
358	C₂×C₄×C₈	—	53	1	no	—
359	#391	—	53	2	no	—
360	#389	—	53	2	no	—
361	#387	—	53	2	no	—
362	#387	—	53	2	no	—
363	C₄×C₄⋊C₄	—	53	1	no	—
364	C₄×C₄⋊C₄	—	53	1	no	—
365	C₄×C₄⋊C₄	—	53	1	no	—
366	#376	—	53	1	no	—
367	#376	—	53	1	no	—
368	C₄³	—	53	1	no	—
369	#336	—	53	1	no	—
370	#336	—	53	1	no	—
371	#336	—	53	1	no	—
372	#336	—	53	1	no	—
373	#336	—	53	1	no	—
374	#336	—	53	1	no	—
375	#336	—	53	1	no	—
376	#336	—	53	1	no	—
377	#336	—	53	1	no	—
378	#336	—	53	1	no	—
379	C₅₃	#20575	1	1	yes	characteristic, complemented, Sylow
380	C₂²×Q₈	—	53	1	no	—
381	C₂²×C₈	—	53	1	no	—
382	C₂²×C₈	—	53	1	no	—
383	C₂²×C₈	—	53	1	no	—
384	C₂²×C₈	—	53	1	no	—
385	C₂²×C₈	—	53	1	no	—
386	C₂²×C₈	—	53	1	no	—
387	C₂²×C₈	—	53	1	no	—
388	C₂²×C₈	—	53	1	no	—
389	C₄×Q₈	—	53	1	no	—
390	C₄×Q₈	—	53	1	no	—
391	C₄×Q₈	—	53	1	no	—
392	C₄×Q₈	—	53	1	no	—
393	C₄×Q₈	—	53	1	no	—
394	C₄×Q₈	—	53	1	no	—
395	C₄×Q₈	—	53	1	no	—
396	C₄×Q₈	C₂×#6157	1	1	yes	characteristic
397	C₂×C₄⋊C₄	—	53	1	no	—
398	C₂×C₄⋊C₄	—	53	1	no	—
399	C₂×C₄⋊C₄	—	53	1	no	—
400	C₂×C₄⋊C₄	—	53	2	no	—
401	C₂×C₄⋊C₄	—	53	2	no	—
402	C₂×C₄⋊C₄	—	53	2	no	—
403	C₂×C₄²	—	53	1	no	—
404	C₂×C₄²	—	53	1	no	—
405	C₂×C₄²	—	53	1	no	—
406	C₂×C₄²	—	53	1	no	—
407	C₂×C₄²	—	53	1	no	—
408	C₂×C₄²	—	53	1	no	—
409	C₂×C₄²	—	53	1	no	—
410	C₂×C₄²	—	53	2	no	—
411	C₂×C₄²	—	53	2	no	—
412	C₄⋊C₈	—	53	2	no	—
413	C₄⋊C₈	—	53	2	no	—
414	C₄⋊C₈	—	53	2	no	—
415	C₄⋊C₈	—	53	2	no	—
416	C₄⋊C₈	—	53	2	no	—
417	C₄⋊C₈	—	53	2	no	—
418	C₄⋊C₈	—	53	1	no	—
419	C₄⋊C₈	—	53	1	no	—
420	C₄⋊C₈	—	53	1	no	—
421	C₄⋊C₈	—	53	1	no	—
422	C₄⋊C₈	—	53	1	no	—
423	C₄⋊C₈	—	53	1	no	—
424	C₄⋊C₈	—	53	1	no	—
425	C₄⋊C₈	—	53	1	no	—
426	C₄⋊C₈	—	53	1	no	—
427	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
428	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
429	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
430	#97	—	53	2	no	—
431	#97	—	53	2	no	—
432	#97	—	53	2	no	—
433	#97	—	53	2	no	—
434	#97	—	53	1	no	—
435	#97	—	53	1	no	—
436	#97	—	53	1	no	—
437	#97	—	53	1	no	—
438	#97	—	53	1	no	—
439	#97	—	53	1	no	—
440	#97	—	212	1	no	—
441	#97	—	212	1	no	—
442	#97	C₂×#6157	1	1	yes	characteristic
443	#97	C₂×#6157	1	1	yes	characteristic
444	C₄×C₈	—	53	2	no	—
445	C₄×C₈	—	53	2	no	—
446	C₄×C₈	—	53	1	no	—
447	C₄×C₈	—	53	1	no	—
448	C₄×C₈	—	53	1	no	—
449	C₄×C₈	—	212	1	no	—
450	C₄×C₈	—	212	1	no	—
451	C₄×C₈	—	212	1	no	—
452	C₄×C₈	—	212	1	no	—
453	C₄×C₈	C₂×#6157	1	1	yes	characteristic
454	#95	—	53	2	no	—
455	#95	—	53	2	no	—
456	#95	—	53	2	no	—
457	#95	—	53	2	no	—
458	#95	—	53	2	no	—
459	#95	—	53	2	no	—
460	#95	—	53	2	no	—
461	C₂×Q₈	—	53	1	no	—
462	C₂×Q₈	—	53	1	no	—
463	C₂×Q₈	—	53	1	no	—
464	C₂×Q₈	—	212	2	no	—
465	C₂×Q₈	C₄×#6157	1	1	yes	characteristic
466	C₂²×C₄	—	53	1	no	—
467	C₂²×C₄	—	53	2	no	—
468	C₂²×C₄	—	53	1	no	—
469	C₂²×C₄	—	53	1	no	—
470	C₂²×C₄	—	53	1	no	—
471	C₂²×C₄	—	53	1	no	—
472	C₂²×C₄	—	53	1	no	—
473	C₂²×C₄	—	53	1	no	—
474	C₂²×C₄	—	53	2	no	—
475	C₂²×C₄	—	53	2	no	—
476	C₂²×C₄	—	53	2	no	—
477	C₂×C₈	—	53	2	no	—
478	C₂×C₈	—	53	2	no	—
479	C₂×C₈	—	53	2	no	—
480	C₂×C₈	—	53	2	no	—
481	C₂×C₈	—	53	1	no	—
482	C₂×C₈	—	53	1	no	—
483	C₂×C₈	—	53	1	no	—
484	C₂×C₈	—	53	1	no	—
485	C₂×C₈	—	106	1	no	—
486	C₂×C₈	—	106	1	no	—
487	C₂×C₈	—	106	1	no	—
488	C₂×C₈	—	106	1	no	—
489	C₂×C₈	—	106	1	no	—
490	C₂×C₈	—	106	1	no	—
491	C₂×C₈	—	106	1	no	—
492	C₂×C₈	—	106	1	no	—
493	C₂×C₈	—	106	1	no	—
494	C₂×C₈	—	106	1	no	—
495	C₂×C₈	—	106	1	no	—
496	C₂×C₈	—	106	1	no	—
497	C₂×C₈	—	106	1	no	—
498	C₂×C₈	—	106	1	no	—
499	C₂×C₈	—	106	1	no	—
500	C₂×C₈	—	106	1	no	—
501	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
502	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
503	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
504	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
505	C₄⋊C₄	—	53	1	no	—
506	C₄⋊C₄	—	53	1	no	—
507	C₄⋊C₄	—	53	1	no	—
508	C₄⋊C₄	—	53	1	no	—
509	C₄⋊C₄	—	53	1	no	—
510	C₄⋊C₄	—	53	1	no	—
511	C₄⋊C₄	—	53	1	no	—
512	C₄⋊C₄	—	53	1	no	—
513	C₄⋊C₄	—	53	1	no	—
514	C₄⋊C₄	—	106	4	no	—
515	C₄⋊C₄	—	106	4	no	—
516	C₄⋊C₄	—	212	2	no	—
517	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
518	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
519	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
520	C₄²	—	53	1	no	—
521	C₄²	—	53	1	no	—
522	C₄²	—	53	1	no	—
523	C₄²	—	53	1	no	—
524	C₄²	—	53	1	no	—
525	C₄²	—	53	1	no	—
526	C₄²	—	53	1	no	—
527	C₄²	—	53	1	no	—
528	C₄²	—	53	1	no	—
529	C₄²	—	106	1	no	—
530	C₄²	—	106	1	no	—
531	C₄²	—	106	1	no	—
532	C₄²	—	106	1	no	—
533	C₄²	—	106	1	no	—
534	C₄²	—	106	1	no	—
535	C₄²	—	106	1	no	—
536	C₄²	—	106	1	no	—
537	C₄²	—	106	4	no	—
538	C₄²	—	212	2	no	—
539	C₄²	C₂²×#6157	1	1	yes	characteristic
540	C₄²	C₂²×#6157	1	1	yes	characteristic
541	C₄²	C₂²×#6157	1	1	yes	characteristic
542	C₂³	—	53	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	212	1	no	—
545	Q₈	—	212	1	no	—
546	Q₈	—	212	1	no	—
547	C₂×C₄	—	53	1	no	—
548	C₂×C₄	—	53	1	no	—
549	C₂×C₄	—	53	1	no	—
550	C₂×C₄	—	53	1	no	—
551	C₂×C₄	—	53	1	no	—
552	C₂×C₄	—	53	4	no	—
553	C₂×C₄	—	53	1	no	—
554	C₂×C₄	—	53	1	no	—
555	C₂×C₄	—	53	1	no	—
556	C₂×C₄	—	53	1	no	—
557	C₂×C₄	—	53	1	no	—
558	C₂×C₄	—	53	1	no	—
559	C₂×C₄	—	106	2	no	—
560	C₂×C₄	—	106	2	no	—
561	C₂×C₄	—	106	2	no	—
562	C₂×C₄	—	106	2	no	—
563	C₂×C₄	—	106	2	no	—
564	C₂×C₄	—	106	2	no	—
565	C₂×C₄	—	106	2	no	—
566	C₂×C₄	—	106	2	no	—
567	C₂×C₄	—	106	2	no	—
568	C₂×C₄	—	106	2	no	—
569	C₂×C₄	—	106	2	no	—
570	C₂×C₄	—	106	2	no	—
571	C₂×C₄	—	106	2	no	—
572	C₂×C₄	—	106	2	no	—
573	C₂×C₄	—	106	2	no	—
574	C₂×C₄	—	106	2	no	—
575	C₂×C₄	—	106	2	no	—
576	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
577	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
578	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
579	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
580	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
581	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
582	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	2	1	no	—
587	C₈	—	106	2	no	—
588	C₈	—	106	2	no	—
589	C₈	—	106	2	no	—
590	C₈	—	106	2	no	—
591	C₈	—	106	1	no	—
592	C₈	—	106	1	no	—
593	C₈	—	106	1	no	—
594	C₈	—	106	1	no	—
595	C₂²	—	53	1	no	—
596	C₂²	—	53	1	no	—
597	C₂²	—	53	2	no	—
598	C₂²	—	53	2	no	—
599	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	53	1	no	—
607	C₄	—	53	1	no	—
608	C₄	—	106	4	no	—
609	C₄	—	106	1	no	—
610	C₄	—	106	1	no	—
611	C₄	—	106	1	no	—
612	C₄	—	106	1	no	—
613	C₄	—	106	1	no	—
614	C₄	—	106	1	no	—
615	C₄	—	212	2	no	—
616	C₄	—	212	2	no	—
617	C₄	—	212	2	no	—
618	C₄	#16811691	1	1	yes	characteristic
619	C₄	#16811692	1	1	yes	characteristic
620	C₂	—	53	2	no	—
621	C₂	—	53	2	no	—
622	C₂	#20291155	1	1	yes	characteristic
623	C₂	#20291278	1	1	yes	characteristic
624	C₂	#131×#6157	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#446	C₄
prime radical	C₂²×D₅₃	C₂³×C₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#446	#6157
hypocenter	C₅₃	#20575
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
16. #16811675	C₄	semidirect
17. #16811675	C₄	semidirect
18. #16811674	C₄	semidirect
19. #16811673	C₄	semidirect
53. #16810754	C₄	semidirect
54. #16810753	C₄	semidirect
55. #16810752	C₄	semidirect
56. #16810752	C₄	semidirect
57. #16810751	C₄	semidirect
58. #16810751	C₄	semidirect
59. #16810750	C₄	semidirect
66. C₅₃×#446	C₄	semidirect
340. #446	#6157	semidirect
379. C₅₃	#20575	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#446	2
#20291174	2
#20290516	2
#20290513	2
#20290508	2
C₈×C₄⋊#6157	2
#20290504	2
C₄⋊C₈×#6157	2
#20290435	2
#20290433	2
#20290431	2
#446×D₅₃	2
#20575	53