Subgroups — #34183601

Order 20224.

726 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#23763380	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#23761241	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₇₉⋊C₈	—	2	1	no	—
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
9	C₂×C₄×C₇₉⋊C₈	—	2	4	no	—
10	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
11	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
12	#19098318	—	2	1	no	—
13	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
17	#391×C₇₉	C₄	1	1	yes	characteristic
18	#389×C₇₉	C₄	1	1	yes	characteristic
19	#387×C₇₉	—	2	1	no	—
20	#385×C₇₉	—	2	1	no	—
21	#380×C₇₉	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
25	C₂²×C₇₉⋊C₈	—	2	4	no	—
26	C₂²×C₇₉⋊C₈	—	2	4	no	—
27	C₂²×C₇₉⋊C₈	—	2	4	no	—
28	C₂²×C₇₉⋊C₈	—	2	2	no	—
29	C₂²×C₇₉⋊C₈	—	2	2	no	—
30	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₂²⋊(C₇₉⋊C₈)	—	4	2	no	—
33	C₄×C₇₉⋊C₈	—	2	4	no	—
34	C₄×C₇₉⋊C₈	—	2	2	no	—
35	C₄×C₇₉⋊C₈	D₄	1	4	yes	—
36	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
40	C₂²⋊Q₈×C₇₉	—	2	2	no	—
41	C₂²⋊Q₈×C₇₉	C₈	1	4	yes	complemented
42	C₄×Q₈×C₇₉	—	2	2	no	—
43	C₄×Q₈×C₇₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
52	C₂×C₄²×C₇₉	—	2	2	no	—
53	C₂×C₄²×C₇₉	—	2	2	no	—
54	C₂×C₄²×C₇₉	—	2	1	no	—
55	C₂×C₄²×C₇₉	—	2	1	no	—
56	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
60	#95×C₇₉	—	2	1	no	—
61	#95×C₇₉	—	2	1	no	—
62	#95×C₇₉	—	2	1	no	—
63	#95×C₇₉	—	2	1	no	—
64	#95×C₇₉	—	2	1	no	—
65	C₂×C₇₉⋊C₈	—	2	16	no	—
66	C₂×C₇₉⋊C₈	—	2	4	no	—
67	C₂×C₇₉⋊C₈	—	2	4	no	—
68	C₂×C₇₉⋊C₈	—	2	4	no	—
69	C₂×C₇₉⋊C₈	—	4	2	no	—
70	C₂×C₇₉⋊C₈	—	4	2	no	—
71	C₂×C₇₉⋊C₈	—	4	2	no	—
72	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×Q₈×C₇₉	—	2	1	no	—
74	C₂×Q₈×C₇₉	—	2	2	no	—
75	C₂×Q₈×C₇₉	—	2	2	no	—
76	C₂×Q₈×C₇₉	C₂×C₈	1	2	yes	complemented
77	C₂²×C₄×C₇₉	—	2	2	no	—
78	C₂²×C₄×C₇₉	—	2	2	no	—
79	C₂²×C₄×C₇₉	—	2	2	no	—
80	C₂²×C₄×C₇₉	—	2	1	no	—
81	C₂²×C₄×C₇₉	—	2	2	no	—
82	C₂²×C₄×C₇₉	—	2	1	no	—
83	C₂²×C₄×C₇₉	—	2	2	no	—
84	C₂²×C₄×C₇₉	—	2	2	no	—
85	C₂²×C₄×C₇₉	—	2	1	no	—
86	C₂²×C₄×C₇₉	—	2	1	no	—
87	C₂²×C₄×C₇₉	—	2	1	no	—
88	C₂²×C₄×C₇₉	—	2	1	no	—
89	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂×C₈	1	2	yes	—
93	C₂²×C₄×C₇₉	M₁₆	1	2	yes	—
94	C₂²×C₄×C₇₉	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₇₉	Q₁₆	1	2	yes	—
96	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
99	C₄⋊C₄×C₇₉	—	2	4	no	—
100	C₄⋊C₄×C₇₉	—	2	1	no	—
101	C₄⋊C₄×C₇₉	—	2	2	no	—
102	C₄⋊C₄×C₇₉	—	2	2	no	—
103	C₄⋊C₄×C₇₉	—	4	2	no	—
104	C₄⋊C₄×C₇₉	—	4	1	no	—
105	C₄⋊C₄×C₇₉	—	4	1	no	—
106	C₄⋊C₄×C₇₉	C₂×C₈	1	2	yes	complemented
107	C₂²⋊C₄×C₇₉	—	2	4	no	—
108	C₂²⋊C₄×C₇₉	—	4	2	no	—
109	C₄²×C₇₉	—	2	2	no	—
110	C₄²×C₇₉	—	2	1	no	—
111	C₄²×C₇₉	—	2	2	no	—
112	C₄²×C₇₉	—	2	1	no	—
113	C₄²×C₇₉	—	4	2	no	—
114	C₄²×C₇₉	—	4	2	no	—
115	C₄²×C₇₉	C₂×D₄	1	2	yes	—
116	C₄²×C₇₉	#41	1	2	yes	—
117	C₂³×C₇₉	—	2	1	no	—
118	C₂³×C₇₉	—	2	1	no	—
119	C₂³×C₇₉	—	2	1	no	—
120	C₂³×C₇₉	—	2	1	no	—
121	C₂³×C₇₉	C₂²⋊C₈	1	2	yes	—
122	C₂³×C₇₉	#103	1	2	yes	—
123	C₂³×C₇₉	#104	1	2	yes	—
124	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	Q₈×C₇₉	—	2	4	no	—
126	Q₈×C₇₉	—	4	2	no	—
127	C₂×C₄×C₇₉	—	2	4	no	—
128	C₂×C₄×C₇₉	—	2	4	no	—
129	C₂×C₄×C₇₉	—	2	1	no	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	—	2	1	no	—
132	C₂×C₄×C₇₉	—	2	1	no	—
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	4	no	—
138	C₂×C₄×C₇₉	—	2	4	no	—
139	C₂×C₄×C₇₉	—	2	4	no	—
140	C₂×C₄×C₇₉	—	2	4	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	4	1	no	—
144	C₂×C₄×C₇₉	—	4	1	no	—
145	C₂×C₄×C₇₉	—	4	1	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	—	4	1	no	—
148	C₂×C₄×C₇₉	—	4	1	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	4	1	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
154	C₂×C₄×C₇₉	#103	1	2	yes	—
155	C₂×C₄×C₇₉	#104	1	2	yes	—
156	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#121	1	2	yes	—
159	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#131	1	2	yes	—
163	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#135	1	2	yes	—
166	C₇₉⋊C₈	—	2	8	no	—
167	C₇₉⋊C₈	—	8	2	no	—
168	C₂²×C₇₉	—	2	2	no	—
169	C₂²×C₇₉	—	2	2	no	—
170	C₂²×C₇₉	—	2	2	no	—
171	C₂²×C₇₉	—	2	2	no	—
172	C₂²×C₇₉	—	2	2	no	—
173	C₂²×C₇₉	—	2	2	no	—
174	C₂²×C₇₉	Q₈⋊C₈	1	4	yes	complemented
175	C₂²×C₇₉	#386	1	1	yes	characteristic
176	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
177	C₂²×C₇₉	#408	1	1	yes	characteristic
178	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
179	C₂²×C₇₉	#416	1	1	yes	characteristic
180	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
181	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
182	C₄×C₇₉	—	2	2	no	—
183	C₄×C₇₉	—	2	2	no	—
184	C₄×C₇₉	—	2	2	no	—
185	C₄×C₇₉	—	2	1	no	—
186	C₄×C₇₉	—	2	1	no	—
187	C₄×C₇₉	—	4	2	no	—
188	C₄×C₇₉	—	4	2	no	—
189	C₄×C₇₉	—	8	1	no	—
190	C₄×C₇₉	—	8	1	no	—
191	C₄×C₇₉	C₈×D₄	1	2	yes	—
192	C₄×C₇₉	#435	1	2	yes	—
193	C₄×C₇₉	#465	1	2	yes	—
194	C₄×C₇₉	#467	1	2	yes	—
195	#9071	—	79	1	no	maximal, Sylow
196	C₂×C₇₉	—	2	4	no	—
197	C₂×C₇₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
198	C₂×C₇₉	#1476	1	1	yes	characteristic
199	C₂×C₇₉	#1493	1	1	yes	characteristic
200	C₂×C₇₉	#1494	1	1	yes	characteristic
201	C₂×C₇₉	#1869	1	1	yes	characteristic
202	C₂×C₇₉	#1892	1	1	yes	characteristic
203	C₂×C₇₉	#1896	1	1	yes	characteristic
204	C₂²×C₄×C₈	—	79	1	no	—
205	C₄×C₂²⋊Q₈	D₇₉	1	1	yes	characteristic
206	#1797	—	79	1	no	—
207	C₂×Q₈⋊C₈	—	79	2	no	—
208	#1279	—	79	2	no	—
209	C₇₉	#9071	1	1	yes	characteristic, complemented, Sylow
210	C₂³×C₈	—	158	1	no	—
211	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
213	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	79	2	no	—
215	C₂×C₂²⋊C₈	—	158	1	no	—
216	C₂×C₄×C₈	—	79	2	no	—
217	C₂×C₄×C₈	—	158	4	no	—
218	C₂×C₄×C₈	—	158	1	no	—
219	#391	Dic₇₉	1	1	yes	characteristic
220	#389	Dic₇₉	1	1	yes	characteristic
221	#387	—	2	1	no	—
222	#385	—	2	1	no	—
223	#380	Dic₇₉	1	1	yes	characteristic
224	C₄×C₄⋊C₄	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	#336	—	158	1	no	—
228	Q₈⋊C₈	—	158	4	no	—
229	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
233	C₂²×C₈	—	158	2	no	—
234	C₂²×C₈	—	158	4	no	—
235	C₂²×C₈	—	158	4	no	—
236	C₂²×C₈	—	158	4	no	—
237	C₂²×C₈	—	158	2	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	C₇₉⋊C₈	1	4	yes	complemented
240	C₄×Q₈	—	2	2	no	—
241	C₄×Q₈	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
258	C₄⋊C₈	—	158	2	no	—
259	C₄⋊C₈	—	158	2	no	—
260	C₂²⋊C₈	—	316	2	no	—
261	C₄×C₈	—	79	4	no	—
262	C₄×C₈	—	158	4	no	—
263	C₄×C₈	—	158	2	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	—	2	1	no	—
269	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₂×C₇₉⋊C₈	1	2	yes	complemented
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₇₉⋊C₈	1	2	yes	—
290	C₂²×C₄	#11929608	1	2	yes	—
291	C₂²×C₄	#11929611	1	2	yes	—
292	C₂²×C₄	#11929614	1	2	yes	—
293	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
296	C₂×C₈	—	316	2	no	—
297	C₂×C₈	—	316	2	no	—
298	C₂×C₈	—	316	2	no	—
299	C₂×C₈	—	158	16	no	—
300	C₂×C₈	—	158	4	no	—
301	C₂×C₈	—	158	4	no	—
302	C₂×C₈	—	158	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	C₂×C₇₉⋊C₈	1	2	yes	complemented
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	4	2	no	—
318	C₄²	—	4	2	no	—
319	C₄²	D₄×D₇₉	1	2	yes	—
320	C₄²	#11929623	1	2	yes	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
326	C₂³	#14579085	1	2	yes	—
327	C₂³	#14579088	1	2	yes	—
328	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
358	C₂×C₄	#14579085	1	2	yes	—
359	C₂×C₄	#14579088	1	2	yes	—
360	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
361	C₂×C₄	#14579129	1	1	yes	characteristic
362	C₂×C₄	#14579133	1	2	yes	—
363	C₂×C₄	#14579142	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
365	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
366	C₂×C₄	#14579168	1	2	yes	—
367	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
368	C₂×C₄	C₂×#11929614	1	1	yes	characteristic
369	C₂×C₄	#14579181	1	2	yes	—
370	C₈	—	632	2	no	—
371	C₈	—	158	8	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	Q₈⋊(C₇₉⋊C₈)	1	4	yes	complemented
379	C₂²	#19098443	1	1	yes	characteristic
380	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
381	C₂²	#19098530	1	1	yes	characteristic
382	C₂²	C₂×#14579085	1	1	yes	characteristic
383	C₂²	#19098559	1	1	yes	characteristic
384	C₂²	C₂×#14579088	1	1	yes	characteristic
385	C₂²	C₂×#14579088	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	D₄×C₇₉⋊C₈	1	2	yes	—
396	C₄	#19098635	1	2	yes	—
397	C₄	#19098794	1	2	yes	—
398	C₄	#19098802	1	2	yes	—
399	C₂	—	2	4	no	—
400	C₂	C₂×Q₈⋊(C₇₉⋊C₈)	1	1	yes	characteristic
401	C₂	#23761782	1	1	yes	characteristic
402	C₂	#23761855	1	1	yes	characteristic
403	C₂	#23761860	1	1	yes	characteristic
404	C₂	#23763693	1	1	yes	characteristic
405	C₂	#23763824	1	1	yes	characteristic
406	C₂	#23763844	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₄×C₂²⋊Q₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₇₉
hypocenter	C₇₉	#9071
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₇₉⋊C₈)	C₂	semidirect
4. #23761241	C₂	semidirect
41. C₂²⋊Q₈×C₇₉	C₈	semidirect
76. C₂×Q₈×C₇₉	C₂×C₈	semidirect
106. C₄⋊C₄×C₇₉	C₂×C₈	semidirect
174. C₂²×C₇₉	Q₈⋊C₈	semidirect
209. C₇₉	#9071	semidirect
239. C₂²⋊Q₈	C₇₉⋊C₈	semidirect
273. C₂×Q₈	C₂×C₇₉⋊C₈	semidirect
310. C₄⋊C₄	C₂×C₇₉⋊C₈	semidirect
378. C₂²	Q₈⋊(C₇₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₇₉⋊C₈	2
#23763380	2
C₂×Q₈⋊(C₇₉⋊C₈)	2
#23761241	2
C₄×C₂²⋊Q₈×C₇₉	2
#9071	79