Subgroups — C₂²×#19098635 #35152108

Order 20224.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098635	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14579072	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929608	—	2	8	no	—
10	C₂²×#11929608	C₂²	1	12	yes	complemented
11	C₂³×C₇₉⋊C₈	—	2	8	no	—
12	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₇₉⋊C₈	C₂²	1	12	yes	complemented
17	#19098635	C₂²	1	64	yes	direct product factor
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	12	yes	complemented
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	12	yes	complemented
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	12	yes	complemented
21	C₂×#14579072	C₂²	1	12	yes	complemented
22	C₂³×D₄×C₇₉	C₄	1	1	yes	characteristic
23	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₉	C₄	1	12	yes	—
26	C₂×C₄×D₄×C₇₉	C₂²	1	12	yes	—
27	C₂²×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₇₉	C₄	1	1	yes	characteristic
30	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#11929608	—	2	48	no	—
32	C₂×#11929608	C₂³	1	16	yes	complemented
33	C₂²×C₇₉⋊C₈	—	2	4	no	—
34	C₂²×C₇₉⋊C₈	—	2	4	no	—
35	C₂²×C₇₉⋊C₈	—	2	4	no	—
36	C₂²×C₇₉⋊C₈	—	2	48	no	—
37	C₂²×C₇₉⋊C₈	D₄	1	8	yes	complemented
38	C₂²×C₇₉⋊C₈	C₂³	1	6	yes	—
39	C₂²×C₇₉⋊C₈	C₂³	1	6	yes	—
40	C₂²×C₇₉⋊C₈	C₂³	1	6	yes	—
41	C₂²×C₇₉⋊C₈	C₂³	1	6	yes	—
42	C₂²×C₇₉⋊C₈	C₂³	1	16	yes	complemented
43	C₄⋊(C₇₉⋊C₈)	C₂³	1	16	yes	complemented
44	C₂²⋊(C₇₉⋊C₈)	C₂³	1	16	yes	complemented
45	C₂²⋊(C₇₉⋊C₈)	C₂³	1	16	yes	complemented
46	#14579072	C₂³	1	16	yes	complemented
47	C₂⁵×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂⁵×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₇₉	—	2	8	no	—
50	C₂²×D₄×C₇₉	C₂×C₄	1	12	yes	—
51	C₂³×C₄×C₇₉	—	2	4	no	—
52	C₂³×C₄×C₇₉	—	2	4	no	—
53	C₂³×C₄×C₇₉	—	2	4	no	—
54	C₂³×C₄×C₇₉	—	2	4	no	—
55	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	C₂×C₄	1	6	yes	—
60	C₂³×C₄×C₇₉	C₂×C₄	1	6	yes	—
61	C₂³×C₄×C₇₉	C₂³	1	6	yes	—
62	C₂³×C₄×C₇₉	C₂³	1	6	yes	—
63	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₇₉	C₂×C₄	1	48	yes	—
65	C₄×D₄×C₇₉	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	12	yes	—
67	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	12	yes	—
68	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	12	yes	—
69	C₂×C₄²×C₇₉	C₂×C₄	1	6	yes	—
70	C₂×C₄²×C₇₉	C₂³	1	6	yes	—
71	#11929608	—	2	32	no	—
72	C₂×C₇₉⋊C₈	—	2	32	no	—
73	C₂×C₇₉⋊C₈	—	2	12	no	—
74	C₂×C₇₉⋊C₈	—	2	12	no	—
75	C₂×C₇₉⋊C₈	—	2	12	no	—
76	C₂×C₇₉⋊C₈	C₂×D₄	1	24	yes	complemented
77	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
78	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
79	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
80	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
81	C₂⁴×C₇₉	—	2	4	no	—
82	C₂⁴×C₇₉	—	2	4	no	—
83	C₂⁴×C₇₉	—	2	4	no	—
84	C₂⁴×C₇₉	—	2	4	no	—
85	C₂⁴×C₇₉	—	2	4	no	—
86	C₂⁴×C₇₉	M₁₆	1	8	yes	complemented
87	C₂⁴×C₇₉	C₂²×C₄	1	6	yes	—
88	C₂⁴×C₇₉	C₂²×C₄	1	6	yes	—
89	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×D₄×C₇₉	—	2	48	no	—
91	C₂×D₄×C₇₉	C₂²×C₄	1	16	yes	—
92	C₂²×C₄×C₇₉	—	2	4	no	—
93	C₂²×C₄×C₇₉	—	2	4	no	—
94	C₂²×C₄×C₇₉	—	2	4	no	—
95	C₂²×C₄×C₇₉	—	2	4	no	—
96	C₂²×C₄×C₇₉	—	2	24	no	—
97	C₂²×C₄×C₇₉	—	2	24	no	—
98	C₂²×C₄×C₇₉	—	2	12	no	—
99	C₂²×C₄×C₇₉	—	2	12	no	—
100	C₂²×C₄×C₇₉	—	2	12	no	—
101	C₂²×C₄×C₇₉	—	2	12	no	—
102	C₂²×C₄×C₇₉	C₂²×C₄	1	6	yes	—
103	C₂²×C₄×C₇₉	C₂²×C₄	1	6	yes	—
104	C₂²×C₄×C₇₉	C₂²×C₄	1	6	yes	—
105	C₂²×C₄×C₇₉	C₂²×C₄	1	6	yes	—
106	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
107	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
108	C₂²×C₄×C₇₉	C₂²×C₄	1	3	yes	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₇₉	#41	1	4	yes	—
111	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
114	C₄⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
115	C₂²⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
116	C₂²⋊C₄×C₇₉	C₂²×C₄	1	16	yes	—
117	C₄²×C₇₉	C₂²×C₄	1	12	yes	—
118	C₄²×C₇₉	C₂⁴	1	4	yes	—
119	C₂³×C₇₉	—	2	12	no	—
120	C₂³×C₇₉	—	2	12	no	—
121	C₂³×C₇₉	—	2	32	no	—
122	C₂³×C₇₉	—	2	12	no	—
123	C₂³×C₇₉	—	2	12	no	—
124	C₂³×C₇₉	—	2	12	no	—
125	C₂³×C₇₉	—	4	16	no	—
126	C₂³×C₇₉	C₄×D₄	1	4	yes	—
127	C₂³×C₇₉	C₂×M₁₆	1	4	yes	—
128	C₂³×C₇₉	C₂×M₁₆	1	24	yes	complemented
129	C₂³×C₇₉	#131	1	4	yes	—
130	C₂³×C₇₉	C₂³×C₄	1	4	yes	—
131	C₂³×C₇₉	C₂³×C₄	1	4	yes	—
132	C₂³×C₇₉	C₂³×C₄	1	3	yes	—
133	D₄×C₇₉	—	2	32	no	—
134	C₂×C₄×C₇₉	—	2	12	no	—
135	C₂×C₄×C₇₉	—	2	12	no	—
136	C₂×C₄×C₇₉	—	2	12	no	—
137	C₂×C₄×C₇₉	—	2	12	no	—
138	C₂×C₄×C₇₉	—	2	24	no	—
139	C₂×C₄×C₇₉	—	2	24	no	—
140	C₂×C₄×C₇₉	—	2	4	no	—
141	C₂×C₄×C₇₉	—	2	4	no	—
142	C₂×C₄×C₇₉	—	2	4	no	—
143	C₂×C₄×C₇₉	—	2	4	no	—
144	C₂×C₄×C₇₉	C₄×D₄	1	12	yes	—
145	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₇₉	C₂³×C₄	1	3	yes	—
150	C₂×C₄×C₇₉	C₂²×D₄	1	6	yes	—
151	C₂×C₄×C₇₉	C₂×#41	1	6	yes	—
152	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
153	C₇₉⋊C₈	—	2	4	no	—
154	C₇₉⋊C₈	—	2	4	no	—
155	C₇₉⋊C₈	—	2	4	no	—
156	C₇₉⋊C₈	C₂²×D₄	1	8	yes	complemented
157	C₂²×C₇₉	—	2	4	no	—
158	C₂²×C₇₉	—	2	48	no	—
159	C₂²×C₇₉	—	2	4	no	—
160	C₂²×C₇₉	—	2	4	no	—
161	C₂²×C₇₉	—	2	4	no	—
162	C₂²×C₇₉	—	2	4	no	—
163	C₂²×C₇₉	—	4	24	no	—
164	C₂²×C₇₉	#435	1	16	yes	complemented
165	C₂²×C₇₉	C₂×C₄×D₄	1	6	yes	—
166	C₂²×C₇₉	C₂²×M₁₆	1	6	yes	—
167	C₂²×C₇₉	C₂²×M₁₆	1	8	yes	complemented
168	C₂²×C₇₉	C₂×#131	1	6	yes	—
169	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
170	C₄×C₇₉	—	2	4	no	—
171	C₄×C₇₉	—	2	4	no	—
172	C₄×C₇₉	—	2	4	no	—
173	C₄×C₇₉	—	2	4	no	—
174	C₄×C₇₉	C₂×C₄×D₄	1	6	yes	—
175	C₄×C₇₉	C₂³×D₄	1	1	yes	characteristic
176	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
177	C₂²×#435	—	79	1	no	maximal, Sylow
178	C₂×C₇₉	—	2	8	no	—
179	C₂×C₇₉	—	4	4	no	—
180	C₂×C₇₉	C₂×#435	1	12	yes	complemented
181	C₂×C₇₉	C₂²×C₄×D₄	1	1	yes	characteristic
182	C₂×C₇₉	C₂³×M₁₆	1	1	yes	characteristic
183	C₂×C₇₉	C₂²×#131	1	1	yes	characteristic
184	C₂³×M₁₆	—	79	1	no	—
185	C₂⁴×C₈	—	79	1	no	—
186	C₂²×C₄×D₄	D₇₉	1	1	yes	characteristic
187	C₂×#435	—	79	24	no	—
188	C₂²×C₄⋊C₈	—	79	1	no	—
189	C₂²×C₂²⋊C₈	—	79	1	no	—
190	C₂²×C₂²⋊C₈	—	79	1	no	—
191	C₂²×#97	—	79	1	no	—
192	C₇₉	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
193	C₂³×D₄	Dic₇₉	1	1	yes	characteristic
194	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
195	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
196	C₂²×M₁₆	—	79	12	no	—
197	C₂²×M₁₆	—	158	8	no	—
198	C₂³×C₈	—	79	1	no	—
199	C₂³×C₈	—	79	12	no	—
200	C₂³×C₈	—	79	1	no	—
201	C₂³×C₈	—	79	1	no	—
202	C₂³×C₈	—	79	1	no	—
203	C₂³×C₈	—	158	8	no	—
204	C₂×C₄×D₄	Dic₇₉	1	12	yes	—
205	C₂×C₄×D₄	C₂×D₇₉	1	12	yes	—
206	C₂²×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
208	C₂²×C₂²⋊C₄	Dic₇₉	1	1	yes	characteristic
209	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
210	#435	—	79	64	no	—
211	C₂×C₄⋊C₈	—	79	12	no	—
212	C₂×C₂²⋊C₈	—	79	12	no	—
213	C₂×C₂²⋊C₈	—	79	12	no	—
214	C₂×#97	—	79	12	no	—
215	C₂⁵	C₂×Dic₇₉	1	1	yes	characteristic
216	C₂⁵	C₂×Dic₇₉	1	1	yes	characteristic
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	C₂×Dic₇₉	1	12	yes	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
225	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
226	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
227	C₂³×C₄	C₂×Dic₇₉	1	6	yes	—
228	C₂³×C₄	C₂×Dic₇₉	1	6	yes	—
229	C₂³×C₄	C₂²×D₇₉	1	6	yes	—
230	C₂³×C₄	C₂²×D₇₉	1	6	yes	—
231	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
232	C₂×M₁₆	—	79	16	no	—
233	C₂×M₁₆	—	158	48	no	—
234	C₂²×C₈	—	79	8	no	—
235	C₂²×C₈	—	79	6	no	—
236	C₂²×C₈	—	79	6	no	—
237	C₂²×C₈	—	79	16	no	—
238	C₂²×C₈	—	79	6	no	—
239	C₂²×C₈	—	79	6	no	—
240	C₂²×C₈	—	158	48	no	—
241	C₂²×C₈	—	158	4	no	—
242	C₂²×C₈	—	158	4	no	—
243	C₂²×C₈	—	158	4	no	—
244	C₄×D₄	C₂×Dic₇₉	1	48	yes	—
245	C₄×D₄	C₂²×D₇₉	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×Dic₇₉	1	12	yes	—
247	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	12	yes	—
248	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	12	yes	—
249	C₂×C₄²	C₂×Dic₇₉	1	6	yes	—
250	C₂×C₄²	C₂²×D₇₉	1	6	yes	—
251	C₄⋊C₈	—	79	16	no	—
252	C₂²⋊C₈	—	79	16	no	—
253	C₂²⋊C₈	—	79	16	no	—
254	#97	—	79	16	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	#11929608	1	8	yes	complemented
261	C₂⁴	C₂²×Dic₇₉	1	6	yes	—
262	C₂⁴	C₂²×Dic₇₉	1	6	yes	—
263	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	C₂²×Dic₇₉	1	16	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	12	no	—
271	C₂²×C₄	—	2	12	no	—
272	C₂²×C₄	—	2	24	no	—
273	C₂²×C₄	—	2	24	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	—	2	12	no	—
276	C₂²×C₄	C₂²×Dic₇₉	1	6	yes	—
277	C₂²×C₄	C₂²×Dic₇₉	1	6	yes	—
278	C₂²×C₄	C₂²×Dic₇₉	1	6	yes	—
279	C₂²×C₄	C₂²×Dic₇₉	1	6	yes	—
280	C₂²×C₄	C₂²×Dic₇₉	1	12	yes	—
281	C₂²×C₄	C₂²×Dic₇₉	1	12	yes	—
282	C₂²×C₄	C₂²×Dic₇₉	1	3	yes	—
283	C₂²×C₄	D₄×D₇₉	1	4	yes	—
284	C₂²×C₄	#11929623	1	4	yes	—
285	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
286	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
287	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
288	M₁₆	—	158	32	no	—
289	C₂×C₈	—	79	4	no	—
290	C₂×C₈	—	79	24	no	—
291	C₂×C₈	—	79	4	no	—
292	C₂×C₈	—	79	4	no	—
293	C₂×C₈	—	79	4	no	—
294	C₂×C₈	—	158	32	no	—
295	C₂×C₈	—	158	12	no	—
296	C₂×C₈	—	158	12	no	—
297	C₂×C₈	—	158	12	no	—
298	C₄⋊C₄	C₂²×Dic₇₉	1	16	yes	—
299	C₂²⋊C₄	C₂²×Dic₇₉	1	16	yes	—
300	C₂²⋊C₄	C₂²×Dic₇₉	1	16	yes	—
301	C₄²	C₂²×Dic₇₉	1	12	yes	—
302	C₄²	C₂³×D₇₉	1	4	yes	—
303	C₂³	—	2	32	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	D₄×Dic₇₉	1	4	yes	—
311	C₂³	C₂×#11929608	1	4	yes	—
312	C₂³	C₂×#11929608	1	24	yes	complemented
313	C₂³	#14579168	1	4	yes	—
314	C₂³	C₂³×Dic₇₉	1	4	yes	—
315	C₂³	C₂³×Dic₇₉	1	4	yes	—
316	C₂³	C₂³×Dic₇₉	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	D₄×Dic₇₉	1	12	yes	—
329	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
330	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
331	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
332	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
333	C₂×C₄	C₂³×Dic₇₉	1	3	yes	—
334	C₂×C₄	C₂×D₄×D₇₉	1	6	yes	—
335	C₂×C₄	C₂×#11929623	1	6	yes	—
336	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
337	C₈	—	79	8	no	—
338	C₈	—	158	4	no	—
339	C₈	—	158	4	no	—
340	C₈	—	158	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#19098635	1	16	yes	direct product factor
349	C₂²	C₂×D₄×Dic₇₉	1	6	yes	—
350	C₂²	C₂²×#11929608	1	6	yes	—
351	C₂²	C₂²×#11929608	1	8	yes	complemented
352	C₂²	C₂×#14579168	1	6	yes	—
353	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×D₄×Dic₇₉	1	6	yes	—
359	C₄	C₂²×D₄×D₇₉	1	1	yes	characteristic
360	C₄	C₂²×#11929623	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#19098635	1	12	yes	direct product factor
364	C₂	C₂²×D₄×Dic₇₉	1	1	yes	characteristic
365	C₂	C₂³×#11929608	1	1	yes	characteristic
366	C₂	C₂²×#14579168	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂²×C₄×D₄×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂²×C₄
prime radical	C₂³×D₄×C₇₉	C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂²×C₄×D₄	D₇₉
hypocenter	C₇₉	C₂²×#435
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929608	C₂	semidirect
2. C₂⁴×C₇₉⋊C₈	C₂	semidirect
3. C₂×#19098635	C₂	direct (N × H)
4. C₂²×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
5. C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	semidirect
6. C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	semidirect
7. C₂²×#14579072	C₂	semidirect
10. C₂²×#11929608	C₂²	semidirect
16. C₂³×C₇₉⋊C₈	C₂²	semidirect
17. #19098635	C₂²	direct (N × H)
18. C₂×C₄⋊(C₇₉⋊C₈)	C₂²	semidirect
19. C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	semidirect
20. C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	semidirect
21. C₂×#14579072	C₂²	semidirect
32. C₂×#11929608	C₂³	semidirect
37. C₂²×C₇₉⋊C₈	D₄	semidirect
42. C₂²×C₇₉⋊C₈	C₂³	semidirect
43. C₄⋊(C₇₉⋊C₈)	C₂³	semidirect
44. C₂²⋊(C₇₉⋊C₈)	C₂³	semidirect
45. C₂²⋊(C₇₉⋊C₈)	C₂³	semidirect
46. #14579072	C₂³	semidirect
76. C₂×C₇₉⋊C₈	C₂×D₄	semidirect
86. C₂⁴×C₇₉	M₁₆	semidirect
128. C₂³×C₇₉	C₂×M₁₆	semidirect
156. C₇₉⋊C₈	C₂²×D₄	semidirect
164. C₂²×C₇₉	#435	semidirect
167. C₂²×C₇₉	C₂²×M₁₆	semidirect
180. C₂×C₇₉	C₂×#435	semidirect
192. C₇₉	C₂²×#435	semidirect
260. C₂⁴	#11929608	semidirect
312. C₂³	C₂×#11929608	semidirect
348. C₂²	#19098635	direct (N × H)
351. C₂²	C₂²×#11929608	semidirect
363. C₂	C₂×#19098635	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11929608	2
C₂⁴×C₇₉⋊C₈	2
C₂×#19098635	2
C₂²×C₄⋊(C₇₉⋊C₈)	2
C₂²×C₂²⋊(C₇₉⋊C₈)	2
C₂²×#14579072	2
C₂²×C₄×D₄×C₇₉	2
C₂²×#435	79

Subgroups — C22×#19098635 #35152108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19098635 #35152108