Subgroups — #23764802

Order 10112.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098611	C₂	1	3	yes	maximal
2	C₂×#14579079	C₂	1	3	yes	maximal
3	#338×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
5	C₂×#11929608	C₂²	1	3	yes	—
6	#14579096	—	2	6	no	—
7	#14579079	—	2	6	no	—
8	C₂×M₁₆×C₇₉	C₂²	1	3	yes	—
9	C₂×Dic₁₅₈	—	2	3	no	—
10	C₂×Dic₁₅₈	—	2	3	no	—
11	C₂²×Dic₇₉	Q₈	1	2	yes	—
12	#11929608	—	2	3	no	—
13	#11929608	D₄	1	6	yes	—
14	C₂×C₇₉⋊C₈	—	2	3	no	—
15	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
16	M₁₆×C₇₉	—	2	3	no	—
17	M₁₆×C₇₉	—	2	3	no	—
18	C₂×C₈×C₇₉	—	2	3	no	—
19	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₇₉	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₇₉	#41	1	3	yes	—
22	C₂×Dic₇₉	—	2	6	no	—
23	Dic₁₅₈	—	4	3	no	—
24	Dic₁₅₈	—	4	1	no	—
25	C₈×C₇₉	—	4	3	no	—
26	C₇₉⋊C₈	—	2	6	no	—
27	C₂²×C₇₉	—	4	1	no	—
28	C₂²×C₇₉	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₇₉	#121	1	3	yes	—
30	C₄×C₇₉	#126	1	1	yes	characteristic
31	Dic₇₉	—	4	2	no	—
32	C₂×C₇₉	—	2	3	no	—
33	C₂×C₇₉	#396	1	1	yes	characteristic
34	#2070	—	79	1	no	maximal, Sylow
35	C₇₉	#2070	1	1	yes	characteristic, complemented, Sylow
36	#430	—	79	3	no	—
37	C₂×#101	—	79	3	no	—
38	#338	D₇₉	1	1	yes	characteristic
39	C₂²×Q₈	—	79	1	no	—
40	C₂×M₁₆	—	79	3	no	—
41	C₂×M₁₆	C₂×D₇₉	1	3	yes	—
42	#108	—	158	6	no	—
43	#101	—	158	6	no	—
44	C₂×Q₈	—	158	3	no	—
45	C₂×Q₈	—	158	3	no	—
46	C₂²×C₄	—	79	2	no	—
47	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	79	6	no	—
51	M₁₆	—	158	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	158	3	no	—
54	C₂³	Q₈×D₇₉	1	1	yes	characteristic
55	Q₈	—	316	3	no	—
56	Q₈	—	316	1	no	—
57	C₂×C₄	—	158	6	no	—
58	C₂×C₄	D₄×D₇₉	1	3	yes	—
59	C₂×C₄	#11929624	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	158	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14579139	1	3	yes	—
64	C₄	—	316	2	no	—
65	C₄	#14579134	1	3	yes	—
66	C₄	#14579155	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#19098487	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098487
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#338×C₇₉	C₂
socle	C₂×C₇₉	#396
prime radical	C₂³×C₇₉	C₂×Q₈
hypercenter	#338	D₇₉
hypocenter	C₇₉	#2070
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
35. C₇₉	#2070	semidirect