Subgroups — #28313924

Order 13568.

798 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291526	C₂	1	1	yes	maximal, characteristic
2	#20291526	C₂	1	1	yes	maximal, characteristic
3	#20289939	C₂	1	1	yes	maximal, characteristic, complemented
4	#20289938	C₂	1	1	yes	maximal, characteristic, complemented
5	#20289935	C₂	1	1	yes	maximal, characteristic, complemented
6	#20289934	C₂	1	1	yes	maximal, characteristic, complemented
7	#20289929	C₂	1	1	yes	maximal, characteristic, complemented
8	#20289925	C₂	1	1	yes	maximal, characteristic, complemented
9	#20289924	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11719936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11719940	C₂	1	1	yes	maximal, characteristic, complemented
12	#20289913	C₂	1	1	yes	maximal, characteristic, complemented
13	#20289913	C₂	1	1	yes	maximal, characteristic, complemented
14	#20289911	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283137	C₂	1	1	yes	maximal, characteristic
16	#16811675	C₄	1	2	yes	—
17	#16811675	C₄	1	2	yes	—
18	#16811656	C₄	1	2	yes	—
19	#16811656	C₄	1	2	yes	—
20	#16811655	C₄	1	2	yes	—
21	#16811655	C₄	1	2	yes	—
22	#16811653	C₄	1	2	yes	—
23	#16811653	C₄	1	2	yes	—
24	#16811642	C₂²	1	1	yes	characteristic
25	#16811642	C₂²	1	1	yes	characteristic
26	#16811641	C₂²	1	1	yes	characteristic
27	#16811641	C₂²	1	1	yes	characteristic
28	#16811640	C₂²	1	1	yes	characteristic
29	#16811640	C₂²	1	1	yes	characteristic
30	C₄×#11719936	C₂²	1	1	yes	characteristic
31	C₄×#11719936	C₂²	1	1	yes	characteristic
32	C₄×#11719940	C₂²	1	1	yes	characteristic
33	C₄×#11719940	C₂²	1	1	yes	characteristic
34	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
36	#88324⋊C₈	C₂²	1	1	yes	characteristic
37	#88324⋊C₈	C₂²	1	1	yes	characteristic
38	#88324⋊C₈	C₂²	1	1	yes	characteristic
39	#88324⋊C₈	C₂²	1	1	yes	characteristic
40	#88324⋊C₈	C₂²	1	1	yes	characteristic
41	#88324⋊C₈	C₂²	1	1	yes	characteristic
42	#88324⋊C₈	C₂²	1	1	yes	characteristic
43	#88324⋊C₈	C₂²	1	1	yes	characteristic
44	#16811464	C₂²	1	1	yes	characteristic
45	#16811464	C₂²	1	1	yes	characteristic
46	#16811464	C₂²	1	1	yes	characteristic
47	#16811464	C₂²	1	1	yes	characteristic
48	C₈×#88324	C₂²	1	1	yes	characteristic
49	C₈×#88324	C₂²	1	1	yes	characteristic
50	C₈×#88324	C₂²	1	1	yes	characteristic
51	C₈×#88324	C₂²	1	1	yes	characteristic
52	C₂×#13133225	C₄	1	1	yes	characteristic
53	C₂×#13133223	C₄	1	1	yes	characteristic
54	#16811091	C₂²	1	1	yes	characteristic
55	#16810580	C₄	1	1	yes	characteristic
56	#16810580	C₄	1	1	yes	characteristic
57	#16810579	C₄	1	1	yes	characteristic
58	#16810577	C₄	1	1	yes	characteristic
59	#16810577	C₄	1	1	yes	characteristic
60	#16810575	C₂²	1	1	yes	characteristic
61	#16810575	C₂²	1	1	yes	characteristic
62	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
64	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#405	C₄	1	1	yes	characteristic
67	C₂×#11719936	C₂×C₄	1	2	yes	—
68	C₂×#11719936	C₂×C₄	1	2	yes	—
69	C₂×#11719940	C₂×C₄	1	2	yes	—
70	C₂×#11719940	C₂×C₄	1	2	yes	—
71	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
72	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
73	#13133284	C₂×C₄	1	2	yes	—
74	#13133284	C₂×C₄	1	2	yes	—
75	#13133284	C₂×C₄	1	2	yes	—
76	#13133284	C₂×C₄	1	2	yes	—
77	C₄⋊#88324	C₂×C₄	1	2	yes	—
78	C₄⋊#88324	C₂×C₄	1	2	yes	—
79	#13133274	C₂×C₄	1	2	yes	—
80	#13133274	C₂×C₄	1	2	yes	—
81	#13133274	C₂×C₄	1	2	yes	—
82	#13133274	C₂×C₄	1	2	yes	—
83	C₂²⋊#88324	C₂×C₄	1	2	yes	—
84	C₂²⋊#88324	C₂×C₄	1	2	yes	—
85	#13133272	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	C₄×#88324	C₂×C₄	1	2	yes	—
90	C₄×#88324	C₂×C₄	1	2	yes	—
91	C₄×#88324	C₂³	1	1	yes	characteristic
92	C₄×#88324	C₂³	1	1	yes	characteristic
93	C₄×#88324	C₂³	1	1	yes	characteristic
94	C₄×#88324	C₂³	1	1	yes	characteristic
95	C₄×#88324	C₂³	1	1	yes	characteristic
96	C₄×#88324	C₂³	1	1	yes	characteristic
97	C₄×#88324	C₂³	1	1	yes	characteristic
98	C₄×#88324	C₂³	1	1	yes	characteristic
99	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
100	#13133225	—	2	4	no	—
101	#13133223	—	2	4	no	—
102	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
103	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
104	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
105	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
106	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
107	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
108	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
112	#13133182	C₂×C₄	1	1	yes	characteristic
113	#13133182	C₂×C₄	1	1	yes	characteristic
114	#13133179	C₂×C₄	1	1	yes	characteristic
115	#13133179	C₂×C₄	1	1	yes	characteristic
116	#13133177	C₂×C₄	1	1	yes	characteristic
117	#13133177	C₂×C₄	1	1	yes	characteristic
118	#13133177	C₂×C₄	1	1	yes	characteristic
119	#13133177	C₂×C₄	1	1	yes	characteristic
120	#13133174	C₂×C₄	1	1	yes	characteristic
121	#13133174	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
123	C₄²×D₅₃	C₂³	1	1	yes	characteristic
124	C₄²×D₅₃	C₂³	1	1	yes	characteristic
125	#13133128	C₂×C₄	1	1	yes	characteristic
126	#13133128	C₂×C₄	1	1	yes	characteristic
127	#13133127	C₂×C₄	1	1	yes	characteristic
128	#13133127	C₂×C₄	1	1	yes	characteristic
129	C₄×#88322	C₂×C₄	1	1	yes	characteristic
130	C₄×#88322	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
134	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
135	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
136	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
139	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
141	#97×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	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
147	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
149	#11719945	—	2	2	no	—
150	#11719945	—	2	2	no	—
151	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
152	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
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×Dic₁₀₆	C₄²	1	1	yes	characteristic
159	#11719940	—	2	4	no	—
160	#11719940	—	4	2	no	—
161	C₂×#88324	C₂²×C₄	1	2	yes	—
162	C₂×#88324	C₂²×C₄	1	2	yes	—
163	C₂×#88324	C₂²×C₄	1	2	yes	—
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	C₂×#88324	C₂²×C₄	1	2	yes	—
169	#11719936	—	2	4	no	—
170	#11719936	—	4	2	no	—
171	D₅₃⋊C₈	—	2	4	no	—
172	D₅₃⋊C₈	—	4	2	no	—
173	M₁₆×C₅₃	—	2	2	no	—
174	C₂×C₈×C₅₃	—	2	2	no	—
175	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
180	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
181	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
182	C₂²⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
183	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
185	#11719921	C₄²	1	1	yes	characteristic
186	#11719921	C₄²	1	1	yes	characteristic
187	#11719921	C₄²	1	1	yes	characteristic
188	#11719921	C₄²	1	1	yes	characteristic
189	#11719919	C₄²	1	1	yes	characteristic
190	#11719919	C₄²	1	1	yes	characteristic
191	#11719919	C₄²	1	1	yes	characteristic
192	#11719919	C₄²	1	1	yes	characteristic
193	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
201	#11719917	—	2	2	no	—
202	C₂×#88322	—	2	2	no	—
203	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
204	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
205	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
206	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
207	#11719912	—	2	2	no	—
208	#11719912	—	2	2	no	—
209	#11719912	M₁₆	1	4	yes	complemented
210	#11719912	M₁₆	1	4	yes	complemented
211	C₈×D₅₃	—	2	2	no	—
212	C₈×D₅₃	—	2	2	no	—
213	C₈×D₅₃	—	2	2	no	—
214	C₈×D₅₃	—	2	2	no	—
215	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
216	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
217	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₅₃	—	2	1	no	—
219	C₂×C₄×C₅₃	—	2	1	no	—
220	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
224	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
226	C₂²⋊D₅₃	—	2	2	no	—
227	C₂²⋊D₅₃	—	2	2	no	—
228	C₂×Dic₅₃	—	2	2	no	—
229	C₂×Dic₅₃	—	2	2	no	—
230	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
231	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
232	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
233	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
234	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
236	D₂₁₂	—	2	2	no	—
237	C₄×D₅₃	—	2	1	no	—
238	C₄×D₅₃	—	2	1	no	—
239	C₄×D₅₃	—	2	2	no	—
240	C₄×D₅₃	—	2	2	no	—
241	C₄×D₅₃	—	2	2	no	—
242	C₄×D₅₃	—	2	2	no	—
243	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
244	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
245	Dic₁₀₆	—	2	2	no	—
246	#88324	—	2	2	no	—
247	#88324	—	2	2	no	—
248	#88324	—	2	2	no	—
249	#88324	—	2	2	no	—
250	#88324	—	2	2	no	—
251	#88324	—	2	2	no	—
252	#88324	—	2	2	no	—
253	#88324	#131	1	4	yes	complemented
254	C₈×C₅₃	—	2	1	no	—
255	C₈×C₅₃	—	2	1	no	—
256	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
257	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
258	#88322	—	2	1	no	—
259	#88322	—	2	1	no	—
260	#88322	C₂×M₁₆	1	2	yes	—
261	#88322	C₂×M₁₆	1	2	yes	—
262	#17337	—	53	1	no	maximal, Sylow
263	C₂²×C₅₃	—	2	1	no	—
264	C₂²×C₅₃	—	2	1	no	—
265	C₂²×C₅₃	—	2	1	no	—
266	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
267	C₂×D₅₃	—	2	1	no	—
268	C₂×D₅₃	—	2	1	no	—
269	C₂×D₅₃	—	2	1	no	—
270	C₂×D₅₃	—	2	1	no	—
271	C₂×D₅₃	—	2	1	no	—
272	C₂×D₅₃	C₄×M₁₆	1	2	yes	—
273	C₄×C₅₃	—	2	1	no	—
274	C₄×C₅₃	—	2	1	no	—
275	C₄×C₅₃	—	2	1	no	—
276	C₄×C₅₃	—	2	1	no	—
277	C₄×C₅₃	—	2	1	no	—
278	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
279	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
280	Dic₅₃	—	2	1	no	—
281	Dic₅₃	—	2	1	no	—
282	Dic₅₃	—	2	1	no	—
283	Dic₅₃	C₄×M₁₆	1	2	yes	—
284	Dic₅₃	C₂×#131	1	2	yes	—
285	Dic₅₃	#568	1	2	yes	—
286	#2965	—	53	1	no	—
287	#2965	—	53	1	no	—
288	C₄×#131	—	53	1	no	—
289	#1455	—	53	1	no	—
290	#1455	—	53	1	no	—
291	#1453	—	53	1	no	—
292	#1453	—	53	1	no	—
293	#1452	—	53	1	no	—
294	#1451	—	53	1	no	—
295	#1451	—	53	1	no	—
296	C₈×M₁₆	—	53	1	no	—
297	C₈×M₁₆	—	53	1	no	—
298	C₈×M₁₆	—	53	1	no	—
299	C₈×M₁₆	—	53	1	no	—
300	C₂×#322	—	53	1	no	—
301	C₂×C₅₃	—	4	1	no	—
302	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
303	C₂×C₅₃	C₄×#131	1	1	yes	characteristic
304	C₂×C₅₃	#2875	1	1	yes	characteristic
305	D₅₃	—	2	2	no	—
306	D₅₃	—	4	1	no	—
307	C₂×#131	—	53	1	no	—
308	C₂×#131	—	53	1	no	—
309	C₄×#41	—	53	1	no	—
310	#446	—	53	2	no	—
311	#446	—	53	2	no	—
312	#436	—	53	2	no	—
313	#436	—	53	2	no	—
314	#435	—	53	2	no	—
315	#435	—	53	2	no	—
316	#435	—	53	2	no	—
317	#435	—	53	2	no	—
318	#431	—	53	1	no	—
319	#431	—	53	1	no	—
320	#431	—	53	1	no	—
321	#431	—	53	1	no	—
322	#431	—	53	1	no	—
323	#431	—	53	1	no	—
324	#405	—	53	1	no	—
325	#405	—	53	1	no	—
326	#405	—	53	1	no	—
327	#405	—	53	1	no	—
328	#405	—	53	1	no	—
329	#405	#6157	1	1	yes	characteristic
330	C₄×M₁₆	—	53	1	no	—
331	C₄×M₁₆	—	53	1	no	—
332	C₄×M₁₆	—	53	1	no	—
333	C₄×M₁₆	—	53	1	no	—
334	C₄×M₁₆	—	53	1	no	—
335	C₄×M₁₆	—	53	1	no	—
336	C₄×M₁₆	—	53	1	no	—
337	C₂×C₄×C₈	—	53	1	no	—
338	C₂×C₄×C₈	—	53	1	no	—
339	C₂×C₄×C₈	—	53	1	no	—
340	C₂×C₄×C₈	—	53	1	no	—
341	C₂×C₄×C₈	—	53	1	no	—
342	#322	—	53	1	no	—
343	#322	—	53	1	no	—
344	#322	—	53	1	no	—
345	#322	—	53	1	no	—
346	#322	—	53	1	no	—
347	#322	—	53	1	no	—
348	#322	—	53	1	no	—
349	#322	—	53	1	no	—
350	#322	—	53	1	no	—
351	#322	—	53	1	no	—
352	#322	—	53	1	no	—
353	#322	—	53	1	no	—
354	C₈²	—	53	1	no	—
355	C₈²	—	53	1	no	—
356	C₈²	—	53	1	no	—
357	C₈²	—	53	1	no	—
358	C₅₃	#17337	1	1	yes	characteristic, complemented, Sylow
359	C₂×#41	—	53	1	no	—
360	#131	—	106	4	no	—
361	#131	—	106	4	no	—
362	C₂×M₁₆	—	53	2	no	—
363	C₂×M₁₆	—	53	2	no	—
364	C₂×M₁₆	—	53	1	no	—
365	C₂×M₁₆	—	53	2	no	—
366	C₂×M₁₆	—	53	2	no	—
367	C₂×M₁₆	—	53	1	no	—
368	C₂×M₁₆	—	53	1	no	—
369	C₂×M₁₆	—	53	1	no	—
370	C₂×M₁₆	—	53	1	no	—
371	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
372	C₂²×C₈	—	53	2	no	—
373	C₂²×C₈	—	53	1	no	—
374	C₂²×C₈	—	53	2	no	—
375	C₂²×C₈	—	53	1	no	—
376	C₂²×C₈	—	53	1	no	—
377	C₂²×C₈	—	53	1	no	—
378	C₂²×C₈	—	53	1	no	—
379	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
380	C₄×Q₈	—	53	1	no	—
381	C₄×Q₈	—	53	1	no	—
382	C₄×D₄	—	53	1	no	—
383	C₄×D₄	—	53	1	no	—
384	C₄×D₄	—	53	1	no	—
385	C₄×D₄	—	53	1	no	—
386	C₄×D₄	—	53	1	no	—
387	C₄×D₄	—	53	1	no	—
388	#117	—	53	1	no	—
389	#117	—	53	1	no	—
390	#117	C₂×#6157	1	1	yes	characteristic
391	C₂×C₄²	—	53	1	no	—
392	C₂×C₄²	—	53	1	no	—
393	C₂×C₄²	—	53	1	no	—
394	C₄⋊C₈	—	53	2	no	—
395	C₄⋊C₈	—	53	2	no	—
396	C₄⋊C₈	—	53	2	no	—
397	C₄⋊C₈	—	53	2	no	—
398	C₄⋊C₈	—	53	2	no	—
399	C₄⋊C₈	—	53	2	no	—
400	C₂²⋊C₈	—	53	2	no	—
401	C₂²⋊C₈	—	53	2	no	—
402	C₂²⋊C₈	—	53	2	no	—
403	C₂²⋊C₈	—	53	2	no	—
404	C₂²⋊C₈	—	53	2	no	—
405	C₂²⋊C₈	—	53	2	no	—
406	#97	—	53	2	no	—
407	#97	—	53	2	no	—
408	#97	—	53	2	no	—
409	#97	—	53	2	no	—
410	#97	—	53	1	no	—
411	#97	—	53	1	no	—
412	#97	—	53	1	no	—
413	#97	—	53	1	no	—
414	#97	C₂×#6157	1	1	yes	characteristic
415	#97	C₂×#6157	1	1	yes	characteristic
416	C₄×C₈	—	53	1	no	—
417	C₄×C₈	—	53	1	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	2	no	—
425	C₄×C₈	—	53	2	no	—
426	C₄×C₈	—	53	1	no	—
427	C₄×C₈	—	53	1	no	—
428	C₄×C₈	—	53	1	no	—
429	C₄×C₈	—	53	1	no	—
430	C₄×C₈	—	53	1	no	—
431	C₄×C₈	—	53	1	no	—
432	C₄×C₈	—	53	1	no	—
433	C₄×C₈	—	53	1	no	—
434	C₄×C₈	C₂×#6157	1	1	yes	characteristic
435	C₄×C₈	C₂×#6157	1	1	yes	characteristic
436	#41	—	106	2	no	—
437	#41	—	106	2	no	—
438	C₂×Q₈	—	53	1	no	—
439	C₂×D₄	—	53	1	no	—
440	C₂×D₄	—	53	1	no	—
441	C₂×D₄	—	53	1	no	—
442	C₂²×C₄	—	53	1	no	—
443	C₂²×C₄	—	53	1	no	—
444	C₂²×C₄	—	53	1	no	—
445	C₂²×C₄	—	53	1	no	—
446	C₂²×C₄	—	53	1	no	—
447	C₂²×C₄	—	53	1	no	—
448	C₂²×C₄	—	53	1	no	—
449	C₂²×C₄	—	53	1	no	—
450	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
451	M₁₆	—	2	2	no	—
452	M₁₆	—	53	4	no	—
453	M₁₆	—	53	4	no	—
454	M₁₆	—	106	2	no	—
455	M₁₆	—	106	2	no	—
456	M₁₆	—	106	4	no	—
457	M₁₆	—	106	4	no	—
458	M₁₆	—	106	2	no	—
459	M₁₆	—	212	2	no	—
460	M₁₆	—	212	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	53	2	no	—
463	C₂×C₈	—	53	1	no	—
464	C₂×C₈	—	53	1	no	—
465	C₂×C₈	—	53	2	no	—
466	C₂×C₈	—	53	2	no	—
467	C₂×C₈	—	53	2	no	—
468	C₂×C₈	—	53	2	no	—
469	C₂×C₈	—	53	2	no	—
470	C₂×C₈	—	53	2	no	—
471	C₂×C₈	—	53	2	no	—
472	C₂×C₈	—	53	1	no	—
473	C₂×C₈	—	53	1	no	—
474	C₂×C₈	—	106	2	no	—
475	C₂×C₈	—	106	2	no	—
476	C₂×C₈	—	106	2	no	—
477	C₂×C₈	—	106	2	no	—
478	C₂×C₈	—	106	4	no	—
479	C₂×C₈	—	106	2	no	—
480	C₂×C₈	—	212	2	no	—
481	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
482	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
483	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
484	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
485	C₄⋊C₄	—	53	1	no	—
486	C₄⋊C₄	—	53	1	no	—
487	C₄⋊C₄	—	53	1	no	—
488	C₄⋊C₄	—	53	1	no	—
489	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
490	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
491	C₂²⋊C₄	—	53	1	no	—
492	C₂²⋊C₄	—	53	1	no	—
493	C₂²⋊C₄	—	53	1	no	—
494	C₂²⋊C₄	—	53	1	no	—
495	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
496	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
497	C₄²	—	53	1	no	—
498	C₄²	—	53	1	no	—
499	C₄²	—	53	1	no	—
500	C₄²	—	53	1	no	—
501	C₄²	—	53	1	no	—
502	C₄²	—	53	1	no	—
503	C₄²	—	53	1	no	—
504	C₄²	—	53	1	no	—
505	C₄²	C₂²×#6157	1	1	yes	characteristic
506	C₄²	C₂²×#6157	1	1	yes	characteristic
507	C₂³	—	53	1	no	—
508	C₂³	—	53	1	no	—
509	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
510	Q₈	—	106	2	no	—
511	D₄	—	106	2	no	—
512	D₄	—	106	2	no	—
513	D₄	—	106	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	53	1	no	—
517	C₂×C₄	—	53	1	no	—
518	C₂×C₄	—	53	1	no	—
519	C₂×C₄	—	53	2	no	—
520	C₂×C₄	—	53	2	no	—
521	C₂×C₄	—	53	1	no	—
522	C₂×C₄	—	53	1	no	—
523	C₂×C₄	—	53	1	no	—
524	C₂×C₄	—	106	2	no	—
525	C₂×C₄	—	106	2	no	—
526	C₂×C₄	—	106	2	no	—
527	C₂×C₄	—	106	2	no	—
528	C₂×C₄	—	106	2	no	—
529	C₂×C₄	—	106	2	no	—
530	C₂×C₄	—	106	1	no	—
531	C₂×C₄	—	106	1	no	—
532	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
535	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
536	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
537	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	53	4	no	—
541	C₈	—	53	2	no	—
542	C₈	—	53	2	no	—
543	C₈	—	106	2	no	—
544	C₈	—	106	2	no	—
545	C₈	—	106	2	no	—
546	C₈	—	106	2	no	—
547	C₈	—	106	2	no	—
548	C₈	—	106	2	no	—
549	C₈	—	106	2	no	—
550	C₈	—	106	1	no	—
551	C₈	—	106	1	no	—
552	C₈	D₅₃⋊M₁₆	1	2	yes	—
553	C₈	D₅₃⋊M₁₆	1	2	yes	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	53	2	no	—
558	C₂²	—	106	1	no	—
559	C₂²	—	106	1	no	—
560	C₂²	—	106	1	no	—
561	C₂²	—	106	1	no	—
562	C₂²	—	106	1	no	—
563	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	53	2	no	—
570	C₄	—	53	2	no	—
571	C₄	—	53	2	no	—
572	C₄	—	106	1	no	—
573	C₄	—	106	1	no	—
574	C₄	—	106	1	no	—
575	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
576	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	106	2	no	—
579	C₂	—	212	1	no	—
580	C₂	C₄×D₅₃⋊M₁₆	1	1	yes	characteristic
581	C₂	#131×#6157	1	1	yes	characteristic
582	C₂	#20291285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#405	C₄
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#17337
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #20289939	C₂	semidirect
4. #20289938	C₂	semidirect
5. #20289935	C₂	semidirect
6. #20289934	C₂	semidirect
7. #20289929	C₂	semidirect
8. #20289925	C₂	semidirect
9. #20289924	C₂	semidirect
10. C₈×#11719936	C₂	semidirect
11. C₈×#11719940	C₂	semidirect
12. #20289913	C₂	semidirect
13. #20289913	C₂	semidirect
14. #20289911	C₂	semidirect
209. #11719912	M₁₆	semidirect
210. #11719912	M₁₆	semidirect
253. #88324	#131	semidirect
358. C₅₃	#17337	semidirect

Maximal subgroups

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

subgroup	index
#20291526	2
#20289939	2
#20289938	2
#20289935	2
#20289934	2
#20289929	2
#20289925	2
#20289924	2
C₈×#11719936	2
C₈×#11719940	2
#20289913	2
#20289911	2
#20283137	2
#17337	53