Subgroups — #28313920

Order 13568.

782 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291525	C₂	1	1	yes	maximal, characteristic
2	C₄×#13133304	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	#20289933	C₂	1	1	yes	maximal, characteristic, complemented
6	#20289932	C₂	1	1	yes	maximal, characteristic, complemented
7	#20289927	C₂	1	1	yes	maximal, characteristic, complemented
8	#20289926	C₂	1	1	yes	maximal, characteristic, complemented
9	#20289926	C₂	1	1	yes	maximal, characteristic, complemented
10	#20289924	C₂	1	1	yes	maximal, characteristic, complemented
11	#20289923	C₂	1	1	yes	maximal, characteristic, complemented
12	#20289922	C₂	1	1	yes	maximal, characteristic, complemented
13	#20289920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#88324⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283675	C₂	1	1	yes	maximal, characteristic
16	C₂×#13133304	C₄	1	2	yes	—
17	#16811675	C₄	1	2	yes	—
18	#16811656	C₄	1	2	yes	—
19	#16811654	C₄	1	2	yes	—
20	#16811652	C₄	1	2	yes	—
21	#16811641	C₂²	1	1	yes	characteristic
22	#16811640	C₂²	1	1	yes	characteristic
23	#16811639	C₂²	1	1	yes	characteristic
24	#16811588	C₄	1	2	yes	—
25	#16811587	C₄	1	2	yes	—
26	#16811587	C₄	1	2	yes	—
27	C₄×#11719936	C₂²	1	1	yes	characteristic
28	C₄×#11719936	C₂²	1	1	yes	characteristic
29	C₄×#11719940	C₂²	1	1	yes	characteristic
30	C₄×#11719940	C₂²	1	1	yes	characteristic
31	C₄×#11719940	C₂²	1	1	yes	characteristic
32	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×#88324	C₂²	1	1	yes	characteristic
34	C₂×C₄×#88324	C₂²	1	1	yes	characteristic
35	C₂×C₄×#88324	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	#88324⋊C₈	C₂²	1	1	yes	characteristic
45	#88324⋊C₈	C₂²	1	1	yes	characteristic
46	#16811464	C₂²	1	1	yes	characteristic
47	#16811464	C₂²	1	1	yes	characteristic
48	#16811464	C₂²	1	1	yes	characteristic
49	#16811464	C₂²	1	1	yes	characteristic
50	C₈×#88324	C₂²	1	1	yes	characteristic
51	C₈×#88324	C₂²	1	1	yes	characteristic
52	C₄×#11719947	C₂²	1	1	yes	characteristic
53	#16810752	C₄	1	1	yes	characteristic
54	#16810751	C₄	1	1	yes	characteristic
55	#16810699	C₄	1	1	yes	characteristic
56	#16810698	C₄	1	1	yes	characteristic
57	#16810695	C₄	1	1	yes	characteristic
58	#16810694	C₄	1	1	yes	characteristic
59	#16810691	C₄	1	1	yes	characteristic
60	#16810675	C₂²	1	1	yes	characteristic
61	#16810673	C₂²	1	1	yes	characteristic
62	#16810673	C₂²	1	1	yes	characteristic
63	#16810575	C₂²	1	1	yes	characteristic
64	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#435	C₄	1	1	yes	characteristic
67	#13133304	—	2	8	no	—
68	C₂×#11719936	C₂×C₄	1	2	yes	—
69	C₂×#11719936	C₂×C₄	1	2	yes	—
70	C₂×#11719940	C₂×C₄	1	2	yes	—
71	C₂×#11719940	C₂×C₄	1	2	yes	—
72	C₂×#11719940	C₂×C₄	1	2	yes	—
73	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×#88324	C₂×C₄	1	2	yes	—
75	C₂²×#88324	C₂×C₄	1	2	yes	—
76	C₂²×#88324	C₂×C₄	1	2	yes	—
77	#13133284	C₂×C₄	1	2	yes	—
78	#13133284	C₂×C₄	1	2	yes	—
79	C₄⋊#88324	C₂×C₄	1	2	yes	—
80	#13133274	C₂×C₄	1	2	yes	—
81	C₂²⋊#88324	C₂×C₄	1	2	yes	—
82	C₂²⋊#88324	C₂×C₄	1	2	yes	—
83	#13133272	C₂×C₄	1	2	yes	—
84	#13133272	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	C₄×#88324	C₂×C₄	1	2	yes	—
89	C₄×#88324	C₂×C₄	1	2	yes	—
90	C₄×#88324	C₂×C₄	1	2	yes	—
91	C₄×#88324	C₂×C₄	1	2	yes	—
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	C₄×#88324	C₂³	1	1	yes	characteristic
100	C₂×#11719947	C₂×C₄	1	1	yes	characteristic
101	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
102	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
103	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
104	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
106	#13133182	C₂×C₄	1	1	yes	characteristic
107	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
109	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
110	#13133177	C₂×C₄	1	1	yes	characteristic
111	#13133177	C₂×C₄	1	1	yes	characteristic
112	#13133175	C₂×C₄	1	1	yes	characteristic
113	#13133173	C₂×C₄	1	1	yes	characteristic
114	#13133173	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
117	C₄²×D₅₃	C₂³	1	1	yes	characteristic
118	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
119	#13133146	C₂×C₄	1	1	yes	characteristic
120	#13133146	C₂×C₄	1	1	yes	characteristic
121	#13133146	C₂×C₄	1	1	yes	characteristic
122	#13133146	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊#88322	C₂×C₄	1	1	yes	characteristic
125	#13133129	C₂×C₄	1	1	yes	characteristic
126	#13133129	C₂×C₄	1	1	yes	characteristic
127	#13133128	C₂×C₄	1	1	yes	characteristic
128	#13133127	C₂×C₄	1	1	yes	characteristic
129	#13133127	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅₃	C₂³	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	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
137	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
139	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
142	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
143	C₂×D₄×C₅₃	C₄²	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₃	C₄²	1	1	yes	characteristic
148	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
152	#11719947	—	2	4	no	—
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×Dic₁₀₆	C₄²	1	1	yes	characteristic
157	#11719940	—	2	4	no	—
158	#11719940	—	2	4	no	—
159	#11719940	—	4	2	no	—
160	C₂×#88324	—	2	4	no	—
161	C₂×#88324	—	4	2	no	—
162	C₂×#88324	M₁₆	1	8	yes	complemented
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	C₂×#88324	C₂²×C₄	1	2	yes	—
170	C₂×#88324	C₂²×C₄	1	2	yes	—
171	#11719936	—	2	4	no	—
172	#11719936	—	4	2	no	—
173	D₅₃⋊C₈	—	2	4	no	—
174	M₁₆×C₅₃	—	4	1	no	—
175	C₂×C₈×C₅₃	—	4	1	no	—
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	C₂×C₈×C₅₃	C₂²×C₄	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	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
185	C₂²⋊Dic₅₃	C₄²	1	1	yes	characteristic
186	#11719921	C₄²	1	1	yes	characteristic
187	#11719921	C₄²	1	1	yes	characteristic
188	C₄⋊Dic₅₃	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	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
202	#11719917	—	4	1	no	—
203	C₂×#88322	—	4	1	no	—
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	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
208	#11719912	—	4	1	no	—
209	#11719912	—	4	1	no	—
210	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
211	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
212	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
213	D₄×C₅₃	—	2	2	no	—
214	C₂×C₄×C₅₃	—	2	1	no	—
215	C₂×C₄×C₅₃	—	2	1	no	—
216	C₂×C₄×C₅₃	—	2	1	no	—
217	C₂×C₄×C₅₃	—	2	1	no	—
218	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
223	C₂²⋊D₅₃	—	2	2	no	—
224	C₂²⋊D₅₃	—	2	2	no	—
225	C₂×Dic₅₃	—	2	2	no	—
226	C₂×Dic₅₃	—	2	2	no	—
227	C₂×Dic₅₃	—	2	2	no	—
228	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
229	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
234	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
236	C₄×D₅₃	—	2	1	no	—
237	C₄×D₅₃	—	2	1	no	—
238	C₄×D₅₃	—	2	2	no	—
239	C₄×D₅₃	—	2	2	no	—
240	Dic₁₀₆	—	2	2	no	—
241	#88324	—	2	2	no	—
242	#88324	—	2	2	no	—
243	#88324	—	2	2	no	—
244	#88324	—	2	2	no	—
245	#88324	—	2	2	no	—
246	#88324	—	2	2	no	—
247	#88324	C₂×M₁₆	1	4	yes	—
248	#88324	C₂×M₁₆	1	4	yes	—
249	C₈×C₅₃	—	2	1	no	—
250	C₈×C₅₃	—	2	1	no	—
251	C₈×C₅₃	—	2	1	no	—
252	C₈×C₅₃	—	2	1	no	—
253	#88322	—	2	1	no	—
254	#88322	—	2	1	no	—
255	#88322	—	2	1	no	—
256	#88322	—	2	1	no	—
257	#17336	—	53	1	no	maximal, Sylow
258	C₂²×C₅₃	—	2	1	no	—
259	C₂²×C₅₃	—	2	1	no	—
260	C₂²×C₅₃	—	2	1	no	—
261	C₂²×C₅₃	—	2	1	no	—
262	C₂²×C₅₃	—	2	1	no	—
263	C₂²×C₅₃	C₄×M₁₆	1	2	yes	—
264	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
265	C₂×D₅₃	—	2	1	no	—
266	C₂×D₅₃	—	2	1	no	—
267	C₂×D₅₃	—	2	1	no	—
268	C₄×C₅₃	—	2	1	no	—
269	C₄×C₅₃	—	2	1	no	—
270	C₄×C₅₃	—	2	1	no	—
271	C₄×C₅₃	—	2	1	no	—
272	C₄×C₅₃	#568	1	1	yes	characteristic
273	C₄×C₅₃	#568	1	1	yes	characteristic
274	Dic₅₃	—	2	1	no	—
275	Dic₅₃	—	2	1	no	—
276	Dic₅₃	—	2	1	no	—
277	Dic₅₃	—	2	1	no	—
278	Dic₅₃	C₄×M₁₆	1	2	yes	—
279	Dic₅₃	C₂²×M₁₆	1	2	yes	—
280	Dic₅₃	#568	1	2	yes	—
281	#2965	—	53	1	no	—
282	#2965	—	53	1	no	—
283	C₄×#131	—	53	1	no	—
284	#1455	—	53	1	no	—
285	#1455	—	53	1	no	—
286	#1453	—	53	1	no	—
287	#1453	—	53	1	no	—
288	#1451	—	53	1	no	—
289	#1451	—	53	1	no	—
290	#1451	—	53	1	no	—
291	#1451	—	53	1	no	—
292	#1451	—	53	1	no	—
293	#1451	—	53	1	no	—
294	#1450	—	53	1	no	—
295	C₂×#322	—	53	1	no	—
296	C₂×C₅₃	—	2	2	no	—
297	C₂×C₅₃	—	4	1	no	—
298	C₂×C₅₃	C₂×C₄×M₁₆	1	1	yes	characteristic
299	C₂×C₅₃	#2875	1	1	yes	characteristic
300	C₂×C₅₃	#2875	1	1	yes	characteristic
301	D₅₃	—	4	1	no	—
302	C₂×#131	—	53	2	no	—
303	C₄×#41	—	53	1	no	—
304	#446	—	53	2	no	—
305	#446	—	53	1	no	—
306	#446	—	53	1	no	—
307	#436	—	53	2	no	—
308	#436	—	53	1	no	—
309	#436	—	53	1	no	—
310	#435	—	53	2	no	—
311	#435	—	53	2	no	—
312	#435	—	53	1	no	—
313	#435	—	53	1	no	—
314	#435	—	53	1	no	—
315	#435	#6157	1	1	yes	characteristic
316	#431	—	53	1	no	—
317	#431	—	53	1	no	—
318	#431	—	53	1	no	—
319	#431	—	53	1	no	—
320	#431	—	53	1	no	—
321	#431	—	53	1	no	—
322	#405	—	53	2	no	—
323	#405	—	53	2	no	—
324	#405	—	53	2	no	—
325	C₄×M₁₆	—	53	1	no	—
326	C₄×M₁₆	—	53	1	no	—
327	C₄×M₁₆	—	53	1	no	—
328	C₄×M₁₆	—	53	1	no	—
329	C₄×M₁₆	—	53	1	no	—
330	C₄×M₁₆	—	53	1	no	—
331	C₄×M₁₆	—	53	1	no	—
332	C₂×C₄×C₈	—	53	1	no	—
333	C₂×C₄×C₈	—	53	1	no	—
334	C₂×C₄×C₈	—	53	1	no	—
335	C₂×C₄×C₈	—	53	1	no	—
336	C₂×C₄×C₈	—	53	1	no	—
337	#322	—	53	1	no	—
338	#322	—	53	1	no	—
339	#322	—	53	1	no	—
340	#322	—	53	1	no	—
341	#322	—	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	C₈²	—	53	1	no	—
352	C₈²	—	53	1	no	—
353	C₅₃	#17336	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	—	53	1	no	—
355	#131	—	106	8	no	—
356	C₂×M₁₆	—	53	2	no	—
357	C₂×M₁₆	—	53	2	no	—
358	C₂×M₁₆	—	53	2	no	—
359	C₂×M₁₆	—	53	2	no	—
360	C₂×M₁₆	—	53	2	no	—
361	C₂×M₁₆	—	53	1	no	—
362	C₂×M₁₆	—	53	1	no	—
363	C₂×M₁₆	—	53	1	no	—
364	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
365	C₂²×C₈	—	53	2	no	—
366	C₂²×C₈	—	53	2	no	—
367	C₂²×C₈	—	53	2	no	—
368	C₂²×C₈	—	53	2	no	—
369	C₂²×C₈	—	53	1	no	—
370	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
371	C₄×Q₈	—	53	1	no	—
372	C₄×Q₈	—	53	1	no	—
373	C₄×D₄	—	53	1	no	—
374	C₄×D₄	—	53	1	no	—
375	C₄×D₄	—	53	1	no	—
376	C₄×D₄	—	53	1	no	—
377	C₄×D₄	—	53	1	no	—
378	C₄×D₄	C₂×#6157	1	1	yes	characteristic
379	#117	—	53	1	no	—
380	#117	—	53	1	no	—
381	#117	—	53	1	no	—
382	C₂×C₄²	—	53	1	no	—
383	C₂×C₄²	—	53	1	no	—
384	C₂×C₄²	—	53	1	no	—
385	C₄⋊C₈	—	53	2	no	—
386	C₄⋊C₈	—	53	2	no	—
387	C₄⋊C₈	—	53	2	no	—
388	C₄⋊C₈	—	53	1	no	—
389	C₄⋊C₈	—	53	1	no	—
390	C₄⋊C₈	—	53	1	no	—
391	C₄⋊C₈	—	53	1	no	—
392	C₄⋊C₈	—	53	1	no	—
393	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
394	C₂²⋊C₈	—	53	2	no	—
395	C₂²⋊C₈	—	53	2	no	—
396	C₂²⋊C₈	—	53	2	no	—
397	C₂²⋊C₈	—	53	1	no	—
398	C₂²⋊C₈	—	53	1	no	—
399	C₂²⋊C₈	—	53	1	no	—
400	C₂²⋊C₈	—	53	1	no	—
401	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
402	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
403	#97	—	53	2	no	—
404	#97	—	53	2	no	—
405	#97	—	53	2	no	—
406	#97	—	53	2	no	—
407	#97	—	53	2	no	—
408	#97	—	53	1	no	—
409	#97	—	53	1	no	—
410	#97	—	53	1	no	—
411	#97	C₂×#6157	1	1	yes	characteristic
412	C₄×C₈	—	53	1	no	—
413	C₄×C₈	—	53	1	no	—
414	C₄×C₈	—	53	1	no	—
415	C₄×C₈	—	53	1	no	—
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	2	no	—
421	C₄×C₈	—	53	2	no	—
422	C₄×C₈	—	53	2	no	—
423	C₄×C₈	—	53	2	no	—
424	C₄×C₈	—	53	1	no	—
425	C₄×C₈	—	53	1	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	#41	—	106	4	no	—
431	C₂×Q₈	—	53	1	no	—
432	C₂×D₄	—	53	1	no	—
433	C₂×D₄	—	53	1	no	—
434	C₂×D₄	C₄×#6157	1	1	yes	characteristic
435	C₂²×C₄	—	53	1	no	—
436	C₂²×C₄	—	53	1	no	—
437	C₂²×C₄	—	53	1	no	—
438	C₂²×C₄	—	53	1	no	—
439	C₂²×C₄	—	53	1	no	—
440	C₂²×C₄	—	53	1	no	—
441	C₂²×C₄	—	53	1	no	—
442	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
443	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
444	M₁₆	—	4	1	no	—
445	M₁₆	—	106	4	no	—
446	M₁₆	—	106	4	no	—
447	M₁₆	—	106	4	no	—
448	M₁₆	—	212	1	no	—
449	M₁₆	—	212	1	no	—
450	M₁₆	—	212	1	no	—
451	M₁₆	—	212	2	no	—
452	M₁₆	—	212	2	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	—	53	8	no	—
455	C₂×C₈	—	53	2	no	—
456	C₂×C₈	—	53	2	no	—
457	C₂×C₈	—	53	2	no	—
458	C₂×C₈	—	53	2	no	—
459	C₂×C₈	—	53	2	no	—
460	C₂×C₈	—	53	2	no	—
461	C₂×C₈	—	53	2	no	—
462	C₂×C₈	—	53	2	no	—
463	C₂×C₈	—	53	1	no	—
464	C₂×C₈	—	53	1	no	—
465	C₂×C₈	—	53	1	no	—
466	C₂×C₈	—	53	1	no	—
467	C₂×C₈	—	106	4	no	—
468	C₂×C₈	—	106	4	no	—
469	C₂×C₈	—	212	1	no	—
470	C₂×C₈	—	212	2	no	—
471	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
472	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
473	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
474	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
475	C₄⋊C₄	—	53	1	no	—
476	C₄⋊C₄	—	53	1	no	—
477	C₄⋊C₄	—	53	1	no	—
478	C₄⋊C₄	—	53	1	no	—
479	C₄⋊C₄	—	53	1	no	—
480	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
481	C₂²⋊C₄	—	53	1	no	—
482	C₂²⋊C₄	—	53	1	no	—
483	C₂²⋊C₄	—	53	1	no	—
484	C₂²⋊C₄	—	53	1	no	—
485	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
486	C₂²⋊C₄	C₄×#6157	1	1	yes	characteristic
487	C₄²	—	53	1	no	—
488	C₄²	—	53	1	no	—
489	C₄²	—	53	1	no	—
490	C₄²	—	53	1	no	—
491	C₄²	—	53	1	no	—
492	C₄²	—	53	1	no	—
493	C₄²	—	53	1	no	—
494	C₄²	—	53	1	no	—
495	C₄²	—	53	1	no	—
496	C₄²	C₂²×#6157	1	1	yes	characteristic
497	C₂³	—	53	1	no	—
498	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
499	C₂³	C₂×C₄×#6157	1	1	yes	characteristic
500	Q₈	—	106	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	106	2	no	—
503	D₄	—	106	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	53	4	no	—
509	C₂×C₄	—	53	1	no	—
510	C₂×C₄	—	53	1	no	—
511	C₂×C₄	—	53	1	no	—
512	C₂×C₄	—	53	1	no	—
513	C₂×C₄	—	53	1	no	—
514	C₂×C₄	—	53	1	no	—
515	C₂×C₄	—	53	1	no	—
516	C₂×C₄	—	106	2	no	—
517	C₂×C₄	—	106	2	no	—
518	C₂×C₄	—	106	2	no	—
519	C₂×C₄	—	106	2	no	—
520	C₂×C₄	—	106	2	no	—
521	C₂×C₄	—	106	1	no	—
522	C₂×C₄	—	106	1	no	—
523	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
526	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
527	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	53	4	no	—
533	C₈	—	53	4	no	—
534	C₈	—	106	2	no	—
535	C₈	—	106	2	no	—
536	C₈	—	106	2	no	—
537	C₈	—	106	2	no	—
538	C₈	—	106	2	no	—
539	C₈	—	106	2	no	—
540	C₈	—	106	1	no	—
541	C₈	—	106	1	no	—
542	C₈	—	106	1	no	—
543	C₈	—	106	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	106	1	no	—
550	C₂²	—	106	1	no	—
551	C₂²	—	106	1	no	—
552	C₂²	M₁₆×#6157	1	2	yes	—
553	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	53	2	no	—
559	C₄	—	53	2	no	—
560	C₄	—	53	2	no	—
561	C₄	—	106	1	no	—
562	C₄	—	106	1	no	—
563	C₄	—	106	1	no	—
564	C₄	—	106	1	no	—
565	C₄	#16811701	1	1	yes	characteristic
566	C₄	#16811702	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	212	1	no	—
570	C₂	C₂×M₁₆×#6157	1	1	yes	characteristic
571	C₂	#20291285	1	1	yes	characteristic
572	C₂	#20291286	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#435	C₄
prime radical	C₂×#11719947	C₂×C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	#435	#6157
hypocenter	C₅₃	#17336
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

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. #20289933	C₂	semidirect
6. #20289932	C₂	semidirect
7. #20289927	C₂	semidirect
8. #20289926	C₂	semidirect
9. #20289926	C₂	semidirect
10. #20289924	C₂	semidirect
11. #20289923	C₂	semidirect
12. #20289922	C₂	semidirect
13. #20289920	C₂	semidirect
14. C₂×#88324⋊C₈	C₂	semidirect
162. C₂×#88324	M₁₆	semidirect
353. C₅₃	#17336	semidirect

Maximal subgroups

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

subgroup	index
#20291525	2
C₄×#13133304	2
#20289939	2
#20289938	2
#20289933	2
#20289932	2
#20289927	2
#20289926	2
#20289924	2
#20289923	2
#20289922	2
#20289920	2
C₂×#88324⋊C₈	2
#20283675	2
#17336	53