Subgroups — #34306059

Order 20224.

916 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23764119	C₂	1	2	yes	maximal, complemented
2	#23763959	C₂	1	4	yes	maximal, complemented
3	#23763380	C₂	1	1	yes	maximal, characteristic
4	#23763380	C₂	1	2	yes	maximal
5	C₄⋊C₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₄×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	C₄×C₂²⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
11	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇₉⋊C₈	C₂²	1	4	yes	—
16	#19098318	C₂²	1	4	yes	—
17	#19098318	C₂²	1	4	yes	—
18	#19098318	C₂²	1	2	yes	—
19	#19098318	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₇₉	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
30	C₂×#95×C₇₉	C₄	1	2	yes	—
31	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
32	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
33	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
34	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
35	C₄⋊(C₇₉⋊C₈)	—	4	4	no	—
36	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
38	C₂²⋊(C₇₉⋊C₈)	Q₈	1	4	yes	—
39	C₄×C₇₉⋊C₈	—	2	4	no	—
40	C₄×C₇₉⋊C₈	—	4	4	no	—
41	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₇₉	C₈	1	8	yes	complemented
48	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₉	—	2	4	no	—
55	C₂×C₄²×C₇₉	—	4	4	no	—
56	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
61	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
63	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
64	#95×C₇₉	C₂×C₄	1	2	yes	—
65	#95×C₇₉	C₂×C₄	1	2	yes	—
66	#95×C₇₉	C₂×C₄	1	2	yes	—
67	#95×C₇₉	C₂×C₄	1	2	yes	—
68	C₂×C₇₉⋊C₈	—	2	2	no	—
69	C₂×C₇₉⋊C₈	—	2	2	no	—
70	C₂×C₇₉⋊C₈	—	2	2	no	—
71	C₂×C₇₉⋊C₈	—	2	4	no	—
72	C₂×C₇₉⋊C₈	—	2	4	no	—
73	C₂×C₇₉⋊C₈	—	2	2	no	—
74	C₂×C₇₉⋊C₈	—	2	4	no	—
75	C₂×C₇₉⋊C₈	—	2	2	no	—
76	C₂×C₇₉⋊C₈	C₂×Q₈	1	4	yes	—
77	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₉	—	2	2	no	—
79	C₂²×C₄×C₇₉	—	2	2	no	—
80	C₂²×C₄×C₇₉	—	2	2	no	—
81	C₂²×C₄×C₇₉	—	2	2	no	—
82	C₂²×C₄×C₇₉	—	2	4	no	—
83	C₂²×C₄×C₇₉	—	2	2	no	—
84	C₂²×C₄×C₇₉	—	2	2	no	—
85	C₂²×C₄×C₇₉	—	2	4	no	—
86	C₂²×C₄×C₇₉	—	4	2	no	—
87	C₂²×C₄×C₇₉	—	4	2	no	—
88	C₂²×C₄×C₇₉	—	4	2	no	—
89	C₂²×C₄×C₇₉	—	4	1	no	—
90	C₂²×C₄×C₇₉	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₇₉	C₂×C₈	1	8	yes	—
92	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₇₉	#41	1	2	yes	—
103	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₇₉	—	2	4	no	—
105	C₄⋊C₄×C₇₉	—	2	2	no	—
106	C₄⋊C₄×C₇₉	C₂×C₈	1	8	yes	—
107	C₄⋊C₄×C₇₉	C₂×C₈	1	4	yes	—
108	C₄⋊C₄×C₇₉	C₂×C₈	1	4	yes	—
109	C₄⋊C₄×C₇₉	M₁₆	1	4	yes	—
110	C₄²×C₇₉	—	2	2	no	—
111	C₄²×C₇₉	—	2	2	no	—
112	C₄²×C₇₉	—	2	2	no	—
113	C₄²×C₇₉	—	2	4	no	—
114	C₄²×C₇₉	—	2	4	no	—
115	C₄²×C₇₉	—	4	2	no	—
116	C₄²×C₇₉	—	4	2	no	—
117	C₄²×C₇₉	#41	1	4	yes	—
118	C₂³×C₇₉	—	2	1	no	—
119	C₂³×C₇₉	—	2	1	no	—
120	C₂³×C₇₉	—	2	1	no	—
121	C₂³×C₇₉	—	2	1	no	—
122	C₂³×C₇₉	C₄×Q₈	1	2	yes	—
123	C₂³×C₇₉	C₂²×C₈	1	2	yes	—
124	C₂³×C₇₉	#131	1	2	yes	—
125	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	2	2	no	—
129	C₂×C₄×C₇₉	—	2	2	no	—
130	C₂×C₄×C₇₉	—	2	2	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	2	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	2	no	—
137	C₂×C₄×C₇₉	—	2	2	no	—
138	C₂×C₄×C₇₉	—	2	4	no	—
139	C₂×C₄×C₇₉	—	2	4	no	—
140	C₂×C₄×C₇₉	—	2	8	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	4	8	no	—
148	C₂×C₄×C₇₉	—	4	4	no	—
149	C₂×C₄×C₇₉	—	4	8	no	—
150	C₂×C₄×C₇₉	#117	1	2	yes	—
151	C₂×C₄×C₇₉	#117	1	2	yes	—
152	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
155	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
156	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
158	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
161	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
163	C₇₉⋊C₈	—	2	4	no	—
164	C₇₉⋊C₈	—	4	2	no	—
165	C₇₉⋊C₈	—	4	4	no	—
166	C₂²×C₇₉	—	2	2	no	—
167	C₂²×C₇₉	—	2	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	C₈×Q₈	1	4	yes	—
173	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
174	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
175	C₂²×C₇₉	#518	1	1	yes	characteristic
176	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
177	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
178	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
179	C₂²×C₇₉	#568	1	1	yes	characteristic
180	C₄×C₇₉	—	2	2	no	—
181	C₄×C₇₉	—	2	2	no	—
182	C₄×C₇₉	—	2	2	no	—
183	C₄×C₇₉	—	2	4	no	—
184	C₄×C₇₉	—	2	4	no	—
185	C₄×C₇₉	—	2	4	no	—
186	C₄×C₇₉	—	4	1	no	—
187	C₄×C₇₉	—	4	2	no	—
188	C₄×C₇₉	#431	1	4	yes	—
189	C₄×C₇₉	#553	1	2	yes	—
190	C₄×C₇₉	#554	1	2	yes	—
191	#22625	—	79	1	no	maximal, Sylow
192	C₂×C₇₉	—	2	4	no	—
193	C₂×C₇₉	#2345	1	1	yes	characteristic
194	C₂×C₇₉	C₂×#431	1	1	yes	characteristic
195	C₂×C₇₉	#2924	1	1	yes	characteristic
196	C₂×C₇₉	C₂×C₈×Q₈	1	1	yes	characteristic
197	C₂×C₇₉	Q₈×M₁₆	1	1	yes	characteristic
198	C₂×C₇₉	#2972	1	1	yes	characteristic
199	C₂×C₇₉	#2974	1	1	yes	characteristic
200	C₂×C₄×C₄⋊C₄	D₇₉	1	1	yes	characteristic
201	#1939	—	79	2	no	—
202	#1916	—	79	4	no	—
203	#1797	—	79	1	no	—
204	#1797	—	79	2	no	—
205	C₈×C₄⋊C₄	—	79	2	no	—
206	C₄×C₂²⋊C₈	—	79	1	no	—
207	C₄×C₂²⋊C₈	—	79	2	no	—
208	C₇₉	#22625	1	1	yes	characteristic, complemented, Sylow
209	C₂²×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
211	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
212	C₂²×C₄²	C₂×D₇₉	1	2	yes	—
213	C₂×C₄⋊C₈	—	79	4	no	—
214	C₂×C₄⋊C₈	—	79	2	no	—
215	C₂×C₂²⋊C₈	—	79	1	no	—
216	C₂×C₂²⋊C₈	—	79	1	no	—
217	C₂×C₂²⋊C₈	—	79	2	no	—
218	C₂×C₄×C₈	—	79	4	no	—
219	C₂×C₄×C₈	—	79	2	no	—
220	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
221	C₄×C₄⋊C₄	Dic₇₉	1	2	yes	—
222	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
224	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
225	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
226	C₂×#95	Dic₇₉	1	2	yes	—
227	#336	—	79	2	no	—
228	#336	—	79	4	no	—
229	#336	—	79	2	no	—
230	#336	—	79	4	no	—
231	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
232	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
233	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
234	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
235	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
236	C₂²×C₈	—	79	2	no	—
237	C₂²×C₈	—	79	2	no	—
238	C₂²×C₈	—	79	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₇₉⋊C₈	1	8	yes	complemented
241	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
244	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	—	4	4	no	—
249	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
251	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
252	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
253	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
255	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
256	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
257	C₄⋊C₈	—	316	4	no	—
258	C₄⋊C₈	—	158	4	no	—
259	C₂²⋊C₈	—	79	4	no	—
260	C₂²⋊C₈	—	158	2	no	—
261	C₂²⋊C₈	—	158	4	no	—
262	C₄×C₈	—	316	4	no	—
263	C₄×C₈	—	158	4	no	—
264	#95	C₂×Dic₇₉	1	2	yes	—
265	#95	C₂×Dic₇₉	1	2	yes	—
266	#95	C₂×Dic₇₉	1	2	yes	—
267	#95	C₂×Dic₇₉	1	2	yes	—
268	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×C₇₉⋊C₈	1	4	yes	—
282	C₂²×C₄	C₂×C₇₉⋊C₈	1	8	yes	—
283	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
288	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
289	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₇₉	1	2	yes	—
293	C₂²×C₄	#11929625	1	2	yes	—
294	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
295	C₂×C₈	—	79	4	no	—
296	C₂×C₈	—	158	2	no	—
297	C₂×C₈	—	158	4	no	—
298	C₂×C₈	—	158	2	no	—
299	C₂×C₈	—	158	4	no	—
300	C₂×C₈	—	158	4	no	—
301	C₂×C₈	—	158	2	no	—
302	C₂×C₈	—	158	2	no	—
303	C₂×C₈	—	158	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	C₂×C₇₉⋊C₈	1	8	yes	—
307	C₄⋊C₄	C₂×C₇₉⋊C₈	1	4	yes	—
308	C₄⋊C₄	C₂×C₇₉⋊C₈	1	4	yes	—
309	C₄⋊C₄	#11929608	1	4	yes	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	4	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	#11929624	1	4	yes	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	Q₈×Dic₇₉	1	2	yes	—
323	C₂³	C₂²×C₇₉⋊C₈	1	2	yes	—
324	C₂³	#14579168	1	2	yes	—
325	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	#14579120	1	2	yes	—
351	C₂×C₄	#14579120	1	2	yes	—
352	C₂×C₄	Q₈×Dic₇₉	1	2	yes	—
353	C₂×C₄	C₂²×C₇₉⋊C₈	1	4	yes	—
354	C₂×C₄	C₂²×C₇₉⋊C₈	1	4	yes	—
355	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
356	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
357	C₂×C₄	C₂×#11929608	1	4	yes	—
358	C₂×C₄	C₂×#11929608	1	2	yes	—
359	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
360	C₂×C₄	C₂×#11929624	1	2	yes	—
361	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
362	C₂×C₄	#14579206	1	2	yes	—
363	C₈	—	316	2	no	—
364	C₈	—	316	4	no	—
365	C₈	—	158	4	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	Q₈×C₇₉⋊C₈	1	4	yes	—
373	C₂²	C₂×#14579120	1	1	yes	characteristic
374	C₂²	C₂×Q₈×Dic₇₉	1	1	yes	characteristic
375	C₂²	#19099038	1	1	yes	characteristic
376	C₂²	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
377	C₂²	C₂²×#11929608	1	1	yes	characteristic
378	C₂²	C₂×#14579168	1	1	yes	characteristic
379	C₂²	#19099330	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	#19098616	1	4	yes	—
389	C₄	#19099261	1	2	yes	—
390	C₄	#19099268	1	2	yes	—
391	C₂	—	2	4	no	—
392	C₂	#23766277	1	1	yes	characteristic
393	C₂	C₂×#19098616	1	1	yes	characteristic
394	C₂	#23772058	1	1	yes	characteristic
395	C₂	C₂×Q₈×C₇₉⋊C₈	1	1	yes	characteristic
396	C₂	Q₈×#11929608	1	1	yes	characteristic
397	C₂	#23772424	1	1	yes	characteristic
398	C₂	#23772435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₈
Fitting	C₂×C₄×C₄⋊C₄×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₇₉
hypocenter	C₇₉	#22625
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #23764119	C₂	semidirect
2. #23763959	C₂	semidirect
5. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
47. C₂×C₄⋊C₄×C₇₉	C₈	semidirect
208. C₇₉	#22625	semidirect
240. C₂×C₄⋊C₄	C₇₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#23764119	2
#23763959	2
#23763380	2
C₄⋊C₄×C₇₉⋊C₈	2
C₄×C₂²⋊(C₇₉⋊C₈)	2
C₂×C₄×C₄⋊C₄×C₇₉	2
#22625	79