Subgroups — #34286190

Order 20224.

1146 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098587	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098519	C₂	1	2	yes	maximal
4	#23763257	C₂	1	4	yes	maximal, complemented
5	#23763253	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#23763097	C₂	1	2	yes	maximal
8	C₄×#117×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929608	C₂²	1	2	yes	—
10	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
11	#19098587	C₄	1	8	yes	complemented
12	C₂×C₄⋊(C₇₉⋊C₈)	C₄	1	8	yes	complemented
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	#19098519	—	2	8	no	—
19	C₂×#14579072	C₂²	1	4	yes	—
20	C₂×C₄×C₇₉⋊C₈	C₂²	1	4	yes	—
21	#19098318	C₂²	1	4	yes	—
22	#19098318	C₂²	1	4	yes	—
23	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₇₉	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₇₉	C₄	1	2	yes	—
28	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	—
29	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	—
30	#376×C₇₉	C₂²	1	2	yes	—
31	C₄³×C₇₉	C₂²	1	2	yes	—
32	C₂×#11929608	—	2	4	no	—
33	C₂×#11929608	—	2	4	no	—
34	C₂×#11929608	C₂×C₄	1	8	yes	—
35	C₂²×C₇₉⋊C₈	—	2	4	no	—
36	C₂²×C₇₉⋊C₈	—	2	4	no	—
37	C₂²×C₇₉⋊C₈	C₂×C₄	1	8	yes	—
38	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
39	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
40	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
41	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
42	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
43	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	8	yes	—
44	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	8	yes	—
45	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	8	yes	—
46	#14579072	—	2	8	no	—
47	C₄×C₇₉⋊C₈	—	2	8	no	—
48	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
51	#117×C₇₉	—	2	2	no	—
52	#117×C₇₉	—	2	2	no	—
53	#117×C₇₉	D₄	1	4	yes	—
54	#117×C₇₉	Q₈	1	4	yes	—
55	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
69	#95×C₇₉	C₂×C₄	1	4	yes	—
70	#95×C₇₉	C₂×C₄	1	4	yes	—
71	#11929608	—	2	16	no	—
72	C₂×C₇₉⋊C₈	—	2	16	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	—	2	2	no	—
77	C₂×C₇₉⋊C₈	—	2	2	no	—
78	C₂×C₇₉⋊C₈	—	2	4	no	—
79	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
80	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
81	C₂×C₇₉⋊C₈	C₂²×C₄	1	8	yes	—
82	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	—	2	4	no	—
84	C₂²×C₄×C₇₉	—	4	2	no	—
85	C₂²×C₄×C₇₉	C₄²	1	4	yes	—
86	C₂²×C₄×C₇₉	C₄²	1	4	yes	—
87	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
92	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₇₉	#41	1	2	yes	—
99	C₂²×C₄×C₇₉	#41	1	2	yes	—
100	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
101	C₄⋊C₄×C₇₉	—	2	4	no	—
102	C₄⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
103	C₂²⋊C₄×C₇₉	—	2	4	no	—
104	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
105	C₄²×C₇₉	—	2	8	no	—
106	C₄²×C₇₉	—	2	2	no	—
107	C₄²×C₇₉	—	2	2	no	—
108	C₄²×C₇₉	—	4	4	no	—
109	C₄²×C₇₉	C₄²	1	4	yes	—
110	C₄²×C₇₉	C₄²	1	4	yes	—
111	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
112	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
113	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
114	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
115	C₄²×C₇₉	C₂×D₄	1	4	yes	—
116	C₄²×C₇₉	C₂×Q₈	1	4	yes	—
117	C₂³×C₇₉	—	2	2	no	—
118	C₂³×C₇₉	—	2	2	no	—
119	C₂³×C₇₉	C₂×C₄²	1	2	yes	—
120	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₇₉	#117	1	2	yes	—
122	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₇₉	—	2	4	no	—
124	C₂×C₄×C₇₉	—	2	2	no	—
125	C₂×C₄×C₇₉	—	2	2	no	—
126	C₂×C₄×C₇₉	—	2	4	no	—
127	C₂×C₄×C₇₉	—	2	2	no	—
128	C₂×C₄×C₇₉	—	2	8	no	—
129	C₂×C₄×C₇₉	—	2	4	no	—
130	C₂×C₄×C₇₉	—	2	4	no	—
131	C₂×C₄×C₇₉	—	2	4	no	—
132	C₂×C₄×C₇₉	—	4	4	no	—
133	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
137	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	8	yes	—
139	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₇₉	#117	1	2	yes	—
141	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
144	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
145	C₂×C₄×C₇₉	#131	1	4	yes	—
146	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
152	C₇₉⋊C₈	—	2	4	no	—
153	C₇₉⋊C₈	—	2	4	no	—
154	C₇₉⋊C₈	—	2	8	no	—
155	C₂²×C₇₉	—	2	2	no	—
156	C₂²×C₇₉	—	2	2	no	—
157	C₂²×C₇₉	—	2	4	no	—
158	C₂²×C₇₉	—	2	4	no	—
159	C₂²×C₇₉	C₄×C₄⋊C₄	1	4	yes	—
160	C₂²×C₇₉	C₂²×C₄²	1	1	yes	characteristic
161	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
163	C₂²×C₇₉	C₂×#131	1	2	yes	—
164	C₂²×C₇₉	#568	1	2	yes	—
165	C₄×C₇₉	—	2	2	no	—
166	C₄×C₇₉	—	2	2	no	—
167	C₄×C₇₉	—	2	2	no	—
168	C₄×C₇₉	—	2	8	no	—
169	C₄×C₇₉	—	4	4	no	—
170	C₄×C₇₉	C₄×C₄⋊C₄	1	4	yes	—
171	C₄×C₇₉	#405	1	4	yes	complemented
172	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
174	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
175	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
176	#20431	—	79	1	no	maximal, Sylow
177	C₂×C₇₉	—	2	4	no	—
178	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₇₉	C₂×#405	1	1	yes	characteristic
180	C₂×C₇₉	#2873	1	1	yes	characteristic
181	C₂×C₇₉	#2906	1	2	yes	—
182	C₂×C₇₉	#2925	1	2	yes	—
183	C₂×#423	—	79	1	no	—
184	C₂²×C₄⋊C₈	—	79	1	no	—
185	C₂×#405	—	79	2	no	—
186	C₄×#117	D₇₉	1	1	yes	characteristic
187	#1768	—	79	4	no	—
188	#1767	—	79	2	no	—
189	C₄×C₄⋊C₈	—	79	2	no	—
190	#1729	—	79	2	no	—
191	C₇₉	#20431	1	1	yes	characteristic, complemented, Sylow
192	C₂²×M₁₆	—	79	2	no	—
193	C₂³×C₈	—	79	2	no	—
194	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
195	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
196	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
197	#423	—	79	8	no	—
198	C₂×C₄⋊C₈	—	79	1	no	—
199	C₂×C₄⋊C₈	—	79	1	no	—
200	C₂×C₄⋊C₈	—	79	2	no	—
201	C₂×C₄⋊C₈	—	79	2	no	—
202	C₂×C₄⋊C₈	—	79	2	no	—
203	C₂×C₄⋊C₈	—	79	8	no	—
204	#405	—	158	8	no	—
205	C₂×#97	—	79	4	no	—
206	C₂×C₄×C₈	—	79	4	no	—
207	C₄×C₄⋊C₄	Dic₇₉	1	2	yes	—
208	C₄×C₄⋊C₄	Dic₇₉	1	2	yes	—
209	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	—
210	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	—
211	#376	C₂×D₇₉	1	2	yes	—
212	C₄³	C₂×D₇₉	1	2	yes	—
213	#336	—	79	4	no	—
214	#336	—	79	4	no	—
215	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
218	C₂×M₁₆	—	79	8	no	—
219	C₂×M₁₆	—	158	4	no	—
220	C₂×M₁₆	—	158	4	no	—
221	C₂²×C₈	—	79	8	no	—
222	C₂²×C₈	—	79	2	no	—
223	C₂²×C₈	—	79	2	no	—
224	C₂²×C₈	—	79	4	no	—
225	C₂²×C₈	—	158	4	no	—
226	C₂²×C₈	—	158	4	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	Dic₁₅₈	1	4	yes	—
230	#117	D₃₁₆	1	4	yes	—
231	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
235	C₂×C₄²	C₄×D₇₉	1	4	yes	—
236	C₂×C₄²	C₄×D₇₉	1	4	yes	—
237	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
238	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
239	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
242	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
245	C₄⋊C₈	—	79	4	no	—
246	C₄⋊C₈	—	79	4	no	—
247	C₄⋊C₈	—	79	8	no	—
248	C₄⋊C₈	—	79	8	no	—
249	C₄⋊C₈	—	79	8	no	—
250	#97	—	158	8	no	—
251	C₄×C₈	—	158	8	no	—
252	#95	C₂×Dic₇₉	1	4	yes	—
253	#95	C₂×Dic₇₉	1	4	yes	—
254	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₄×Dic₇₉	1	4	yes	—
258	C₂²×C₄	C₄×Dic₇₉	1	4	yes	—
259	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
260	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
261	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
262	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
266	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
269	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
270	C₂²×C₄	#11929624	1	2	yes	—
271	C₂²×C₄	#11929624	1	2	yes	—
272	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
273	M₁₆	—	158	16	no	—
274	C₂×C₈	—	79	4	no	—
275	C₂×C₈	—	79	4	no	—
276	C₂×C₈	—	79	8	no	—
277	C₂×C₈	—	158	2	no	—
278	C₂×C₈	—	158	2	no	—
279	C₂×C₈	—	158	4	no	—
280	C₂×C₈	—	158	16	no	—
281	C₂×C₈	—	158	2	no	—
282	C₂×C₈	—	158	4	no	—
283	C₂×C₈	—	158	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₂²⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	C₄×Dic₇₉	1	4	yes	—
293	C₄²	C₄×Dic₇₉	1	4	yes	—
294	C₄²	C₂×C₄×D₇₉	1	2	yes	—
295	C₄²	C₂×C₄×D₇₉	1	2	yes	—
296	C₄²	C₂×C₄×D₇₉	1	2	yes	—
297	C₄²	C₂×C₄×D₇₉	1	2	yes	—
298	C₄²	C₂×D₃₁₆	1	4	yes	—
299	C₄²	C₂×Dic₁₅₈	1	4	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₄×Dic₇₉	1	2	yes	—
303	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
304	C₂³	#14579120	1	2	yes	—
305	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
317	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
318	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
319	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
320	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊Dic₇₉	1	8	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
323	C₂×C₄	#14579120	1	2	yes	—
324	C₂×C₄	C₄×D₃₁₆	1	4	yes	—
325	C₂×C₄	C₄×D₃₁₆	1	4	yes	—
326	C₂×C₄	C₄×Dic₁₅₈	1	4	yes	—
327	C₂×C₄	C₄×Dic₁₅₈	1	4	yes	—
328	C₂×C₄	#14579168	1	4	yes	—
329	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
332	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
333	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
334	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
335	C₈	—	158	4	no	—
336	C₈	—	158	4	no	—
337	C₈	—	158	8	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	C₄×C₄⋊Dic₇₉	1	4	yes	—
343	C₂²	C₂²×C₄×Dic₇₉	1	1	yes	characteristic
344	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
345	C₂²	C₂×#14579120	1	1	yes	characteristic
346	C₂²	C₂×#14579168	1	2	yes	—
347	C₂²	#19099330	1	2	yes	—
348	C₄	—	2	8	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	4	no	—
353	C₄	C₄×C₄⋊Dic₇₉	1	4	yes	—
354	C₄	#19098519	1	4	yes	complemented
355	C₄	C₂×C₄×D₃₁₆	1	1	yes	characteristic
356	C₄	C₂×C₄×D₃₁₆	1	1	yes	characteristic
357	C₄	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
358	C₄	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
359	C₂	—	2	4	no	—
360	C₂	C₂×C₄×C₄⋊Dic₇₉	1	1	yes	characteristic
361	C₂	C₂×#19098519	1	1	yes	characteristic
362	C₂	#23771819	1	1	yes	characteristic
363	C₂	#23771968	1	2	yes	—
364	C₂	#23772066	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂²×C₄²
Fitting	C₄×#117×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#117	D₇₉
hypocenter	C₇₉	#20431
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
4. #23763257	C₂	semidirect
5. #23763253	C₂	semidirect
6. C₄×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
11. #19098587	C₄	semidirect
12. C₂×C₄⋊(C₇₉⋊C₈)	C₄	semidirect
171. C₄×C₇₉	#405	semidirect
191. C₇₉	#20431	semidirect
354. C₄	#19098519	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098587	2
C₂²×C₄⋊(C₇₉⋊C₈)	2
C₂×#19098519	2
#23763257	2
#23763253	2
C₄×C₄⋊(C₇₉⋊C₈)	2
#23763097	2
C₄×#117×C₇₉	2
#20431	79