Subgroups — #34295758

Order 20224.

862 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098519	C₂	1	1	yes	maximal, characteristic
3	#23764341	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764124	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763966	C₂	1	2	yes	maximal, complemented
6	#23763585	C₂	1	2	yes	maximal
7	#23763384	C₂	1	1	yes	maximal, characteristic
8	C₄⋊C₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₄×C₇₉⋊C₈	C₂	1	2	yes	maximal
11	C₇₉×#2396	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	C₂²	1	1	yes	characteristic
13	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	Q₈×C₇₉⋊C₈	—	2	4	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
20	#19098519	—	2	4	no	—
21	C₂×#14579072	C₂²	1	1	yes	characteristic
22	C₂×#14579072	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
27	#19098318	C₂²	1	2	yes	—
28	#19098318	C₂²	1	2	yes	—
29	#19098318	C₂²	1	2	yes	—
30	#19098318	C₂²	1	2	yes	—
31	#19098318	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
34	#400×C₇₉	C₄	1	1	yes	characteristic
35	#399×C₇₉	C₄	1	1	yes	characteristic
36	#398×C₇₉	C₄	1	2	yes	—
37	#396×C₇₉	C₄	1	2	yes	—
38	#395×C₇₉	C₄	1	1	yes	characteristic
39	#393×C₇₉	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
42	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
43	C₂×#11929608	—	2	2	no	—
44	C₂×#11929608	—	2	2	no	—
45	C₂×#11929608	—	2	2	no	—
46	C₂²×C₇₉⋊C₈	—	2	2	no	—
47	C₂²×C₇₉⋊C₈	—	2	2	no	—
48	C₂²×C₇₉⋊C₈	Q₈	1	4	yes	complemented
49	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
55	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
59	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
60	#14579072	—	2	2	no	—
61	#14579072	—	2	2	no	—
62	C₄×C₇₉⋊C₈	—	2	4	no	—
63	C₄×C₇₉⋊C₈	—	2	2	no	—
64	C₄×C₇₉⋊C₈	—	2	4	no	—
65	C₄×C₇₉⋊C₈	D₄	1	4	yes	—
66	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₄×Q₈×C₇₉	—	2	2	no	—
69	C₄×Q₈×C₇₉	—	2	2	no	—
70	#117×C₇₉	—	2	2	no	—
71	#117×C₇₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
87	#95×C₇₉	C₂×C₄	1	2	yes	—
88	#95×C₇₉	C₂×C₄	1	2	yes	—
89	#95×C₇₉	C₂×C₄	1	2	yes	—
90	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
91	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
92	#95×C₇₉	C₂×C₄	1	2	yes	—
93	#11929608	—	2	8	no	—
94	C₂×C₇₉⋊C₈	—	2	8	no	—
95	C₂×C₇₉⋊C₈	—	2	1	no	—
96	C₂×C₇₉⋊C₈	—	2	1	no	—
97	C₂×C₇₉⋊C₈	—	2	2	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	—	2	1	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	2	no	—
106	C₂×C₇₉⋊C₈	—	2	2	no	—
107	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
108	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
109	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
110	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
111	C₂×C₇₉⋊C₈	#41	1	2	yes	—
112	C₂×C₇₉⋊C₈	#41	1	2	yes	—
113	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×Q₈×C₇₉	—	2	2	no	—
115	C₂×Q₈×C₇₉	—	2	4	no	—
116	C₂²×C₄×C₇₉	—	2	1	no	—
117	C₂²×C₄×C₇₉	—	2	1	no	—
118	C₂²×C₄×C₇₉	—	2	1	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₇₉	#41	1	2	yes	—
131	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₇₉	—	2	2	no	—
133	C₄⋊C₄×C₇₉	—	2	2	no	—
134	C₄⋊C₄×C₇₉	—	2	4	no	—
135	C₄⋊C₄×C₇₉	—	2	2	no	—
136	C₄⋊C₄×C₇₉	—	2	4	no	—
137	C₄⋊C₄×C₇₉	—	2	4	no	—
138	C₄⋊C₄×C₇₉	—	2	4	no	—
139	C₂²⋊C₄×C₇₉	—	2	2	no	—
140	C₂²⋊C₄×C₇₉	—	2	2	no	—
141	C₂²⋊C₄×C₇₉	—	2	4	no	—
142	C₂²⋊C₄×C₇₉	—	2	4	no	—
143	C₄²×C₇₉	—	2	1	no	—
144	C₄²×C₇₉	—	2	2	no	—
145	C₄²×C₇₉	—	2	1	no	—
146	C₄²×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	—	2	2	no	—
149	C₄²×C₇₉	C₂×D₄	1	2	yes	—
150	C₄²×C₇₉	#41	1	2	yes	—
151	C₂³×C₇₉	—	2	1	no	—
152	C₂³×C₇₉	—	2	1	no	—
153	C₂³×C₇₉	—	2	2	no	—
154	C₂³×C₇₉	—	2	2	no	—
155	C₂³×C₇₉	C₄×Q₈	1	2	yes	—
156	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
157	Q₈×C₇₉	—	2	8	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
183	C₂×C₄×C₇₉	#131	1	4	yes	—
184	C₂×C₄×C₇₉	#131	1	4	yes	—
185	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
191	C₇₉⋊C₈	—	2	2	no	—
192	C₇₉⋊C₈	—	2	2	no	—
193	C₇₉⋊C₈	—	2	2	no	—
194	C₇₉⋊C₈	—	4	2	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₇₉⋊C₈	C₂²⋊Q₈	1	4	yes	—
197	C₂²×C₇₉	—	2	4	no	—
198	C₂²×C₇₉	—	2	2	no	—
199	C₂²×C₇₉	—	4	1	no	—
200	C₂²×C₇₉	—	4	1	no	—
201	C₂²×C₇₉	—	4	2	no	—
202	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
204	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
205	C₂²×C₇₉	C₂×#131	1	2	yes	—
206	C₂²×C₇₉	C₂×#131	1	2	yes	—
207	C₄×C₇₉	—	2	2	no	—
208	C₄×C₇₉	—	2	4	no	—
209	C₄×C₇₉	—	2	2	no	—
210	C₄×C₇₉	—	2	4	no	—
211	C₄×C₇₉	—	2	2	no	—
212	C₄×C₇₉	—	4	1	no	—
213	C₄×C₇₉	—	4	1	no	—
214	C₄×C₇₉	—	4	2	no	—
215	C₄×C₇₉	—	4	2	no	—
216	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₄×C₇₉	#525	1	1	yes	characteristic
218	C₄×C₇₉	#529	1	1	yes	characteristic
219	C₄×C₇₉	#533	1	1	yes	characteristic
220	#21601	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	4	2	no	—
222	C₂×C₇₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₇₉	#2929	1	1	yes	characteristic
224	C₂×C₇₉	#2931	1	1	yes	characteristic
225	C₂×C₇₉	#2960	1	2	yes	—
226	C₂×C₇₉	#2966	1	2	yes	—
227	C₂×C₈×Q₈	—	79	1	no	—
228	C₂×#405	—	79	1	no	—
229	#2396	D₇₉	1	1	yes	characteristic
230	#1985	—	79	1	no	—
231	#1940	—	79	1	no	—
232	#1917	—	79	2	no	—
233	#1851	—	79	2	no	—
234	#1798	—	79	1	no	—
235	C₈×C₄⋊C₄	—	79	2	no	—
236	C₈×C₄⋊C₄	—	79	1	no	—
237	C₈×C₂²⋊C₄	—	79	2	no	—
238	C₇₉	#21601	1	1	yes	characteristic, complemented, Sylow
239	C₂²×M₁₆	—	79	1	no	—
240	C₂³×C₈	—	79	1	no	—
241	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
242	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
243	C₈×Q₈	—	158	4	no	—
244	C₂×C₄⋊C₈	—	79	1	no	—
245	C₂×C₄⋊C₈	—	79	1	no	—
246	C₂×C₄⋊C₈	—	79	2	no	—
247	C₂×C₄⋊C₈	—	79	2	no	—
248	C₂×C₂²⋊C₈	—	79	2	no	—
249	#405	—	158	4	no	—
250	C₂×#97	—	79	1	no	—
251	C₂×#97	—	79	1	no	—
252	C₂×C₄×C₈	—	79	1	no	—
253	C₂×C₄×C₈	—	79	1	no	—
254	C₂×C₄×C₈	—	79	2	no	—
255	C₂×C₄×C₈	—	79	2	no	—
256	#400	Dic₇₉	1	1	yes	characteristic
257	#399	Dic₇₉	1	1	yes	characteristic
258	#398	Dic₇₉	1	2	yes	—
259	#396	Dic₇₉	1	2	yes	—
260	#395	Dic₇₉	1	1	yes	characteristic
261	#393	Dic₇₉	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
263	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
265	#336	—	79	2	no	—
266	#336	—	79	2	no	—
267	#336	—	79	2	no	—
268	#336	—	79	2	no	—
269	#336	—	79	2	no	—
270	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
271	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
272	C₂×M₁₆	—	158	2	no	—
273	C₂×M₁₆	—	158	2	no	—
274	C₂×M₁₆	—	158	2	no	—
275	C₂²×C₈	—	79	1	no	—
276	C₂²×C₈	—	79	4	no	—
277	C₂²×C₈	—	79	1	no	—
278	C₂²×C₈	—	79	1	no	—
279	C₂²×C₈	—	79	1	no	—
280	C₂²×C₈	—	79	2	no	—
281	C₂²×C₈	—	79	2	no	—
282	C₂²×C₈	—	158	2	no	—
283	C₂²×C₈	—	158	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
299	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
300	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
301	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
302	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
303	C₄⋊C₈	—	158	4	no	—
304	C₄⋊C₈	—	158	4	no	—
305	C₄⋊C₈	—	158	2	no	—
306	C₄⋊C₈	—	158	2	no	—
307	C₂²⋊C₈	—	158	4	no	—
308	#97	—	158	2	no	—
309	#97	—	158	2	no	—
310	C₄×C₈	—	79	4	no	—
311	C₄×C₈	—	158	4	no	—
312	C₄×C₈	—	158	2	no	—
313	C₄×C₈	—	158	4	no	—
314	#95	C₂×Dic₇₉	1	2	yes	—
315	#95	C₂×Dic₇₉	1	2	yes	—
316	#95	C₂×Dic₇₉	1	2	yes	—
317	#95	C₂×Dic₇₉	1	1	yes	characteristic
318	#95	C₂×Dic₇₉	1	1	yes	characteristic
319	#95	C₂×Dic₇₉	1	2	yes	—
320	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
328	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
335	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
336	C₂²×C₄	Q₈×D₇₉	1	2	yes	—
337	C₂²×C₄	#11929625	1	2	yes	—
338	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
339	M₁₆	—	158	8	no	—
340	C₂×C₈	—	79	2	no	—
341	C₂×C₈	—	79	2	no	—
342	C₂×C₈	—	79	2	no	—
343	C₂×C₈	—	79	2	no	—
344	C₂×C₈	—	79	2	no	—
345	C₂×C₈	—	79	2	no	—
346	C₂×C₈	—	158	2	no	—
347	C₂×C₈	—	158	2	no	—
348	C₂×C₈	—	158	2	no	—
349	C₂×C₈	—	158	2	no	—
350	C₂×C₈	—	158	2	no	—
351	C₂×C₈	—	158	2	no	—
352	C₂×C₈	—	158	8	no	—
353	C₂×C₈	—	158	1	no	—
354	C₂×C₈	—	158	1	no	—
355	C₂×C₈	—	158	1	no	—
356	C₂×C₈	—	158	1	no	—
357	C₂×C₈	—	158	1	no	—
358	C₂×C₈	—	158	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	D₄×D₇₉	1	2	yes	—
377	C₄²	#11929623	1	2	yes	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	Q₈×Dic₇₉	1	2	yes	—
383	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
384	Q₈	—	2	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
408	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
409	C₂×C₄	Q₈×Dic₇₉	1	2	yes	—
410	C₂×C₄	#14579168	1	4	yes	—
411	C₂×C₄	#14579168	1	4	yes	—
412	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
414	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
415	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
417	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
418	C₈	—	316	2	no	—
419	C₈	—	316	2	no	—
420	C₈	—	79	4	no	—
421	C₈	—	158	2	no	—
422	C₈	—	158	2	no	—
423	C₈	—	158	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
430	C₂²	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
431	C₂²	#41×Dic₇₉	1	1	yes	characteristic
432	C₂²	C₂×#14579168	1	2	yes	—
433	C₂²	C₂×#14579168	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	C₂²⋊Q₈×D₇₉	1	1	yes	characteristic
444	C₄	#19099076	1	1	yes	characteristic
445	C₄	#19099099	1	1	yes	characteristic
446	C₄	#19099115	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₂²⋊Q₈×Dic₇₉	1	1	yes	characteristic
449	C₂	#23772095	1	1	yes	characteristic
450	C₂	#23772112	1	1	yes	characteristic
451	C₂	#23772335	1	2	yes	—
452	C₂	#23772376	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2396	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2396	D₇₉
hypocenter	C₇₉	#21601
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
3. #23764341	C₂	semidirect
4. #23764124	C₂	semidirect
5. #23763966	C₂	semidirect
8. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
9. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
48. C₂²×C₇₉⋊C₈	Q₈	semidirect
238. C₇₉	#21601	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₇₉⋊C₈	2
C₂×#19098519	2
#23764341	2
#23764124	2
#23763966	2
#23763585	2
#23763384	2
C₄⋊C₄×C₇₉⋊C₈	2
C₂²⋊C₄×C₇₉⋊C₈	2
C₇₉×#2396	2
#21601	79