Subgroups — #23765709

Order 10112.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098995	C₂	1	2	yes	maximal, complemented
2	Dic₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098402	C₂	1	2	yes	maximal, complemented
4	D₂₅₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579183	—	2	2	no	—
7	Dic₆₃₂	C₂²	1	2	yes	—
8	#14579106	—	2	2	no	—
9	D₁₂₆₄	C₂²	1	2	yes	—
10	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
11	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
12	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
13	#11929624	—	4	2	no	—
14	Dic₃₁₆	—	2	2	no	—
15	#11929613	—	4	2	no	—
16	D₆₃₂	—	2	2	no	—
17	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
18	C₁₆×C₇₉	D₄	1	1	yes	characteristic
19	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
21	C₂²⋊D₇₉	—	8	2	no	—
22	D₃₁₆	—	4	2	no	—
23	C₄×D₇₉	—	8	2	no	—
24	Dic₁₅₈	—	4	2	no	—
25	C₈×C₇₉	D₈	1	1	yes	characteristic
26	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
28	C₂×D₇₉	—	8	2	no	—
29	C₄×C₇₉	D₁₆	1	1	yes	characteristic
30	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
31	Dic₇₉	—	8	2	no	—
32	C₂×C₇₉	—	2	1	no	—
33	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
34	D₇₉	—	16	2	no	—
35	#2262	—	79	1	no	maximal, Sylow
36	C₇₉	#2262	1	1	yes	characteristic, complemented, Sylow
37	#508	—	79	2	no	—
38	Q₆₄	—	79	1	no	—
39	SD₆₄	—	79	2	no	—
40	D₃₂	—	79	1	no	—
41	C₂×C₃₂	D₇₉	1	1	yes	characteristic, complemented
42	#135	—	158	2	no	—
43	Q₃₂	—	79	2	no	—
44	SD₃₂	—	158	2	no	—
45	D₁₆	—	79	2	no	—
46	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
47	C₃₂	C₂×D₇₉	1	1	yes	characteristic
48	C₃₂	C₂×D₇₉	1	1	yes	characteristic
49	#41	—	316	2	no	—
50	Q₁₆	—	158	2	no	—
51	SD₁₆	—	316	2	no	—
52	D₈	—	158	2	no	—
53	C₂×C₈	D₃₁₆	1	1	yes	characteristic
54	C₁₆	D₃₁₆	1	1	yes	characteristic
55	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
56	Q₈	—	316	2	no	—
57	D₄	—	316	2	no	—
58	D₄	—	632	2	no	—
59	C₂×C₄	—	632	2	no	—
60	C₂×C₄	D₆₃₂	1	1	yes	characteristic
61	C₈	D₆₃₂	1	1	yes	characteristic
62	C₈	C₂×D₃₁₆	1	1	yes	characteristic
63	C₂²	—	632	2	no	—
64	C₂²	D₁₂₆₄	1	1	yes	characteristic
65	C₄	—	632	2	no	—
66	C₄	D₁₂₆₄	1	1	yes	characteristic
67	C₄	C₂×D₆₃₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	1264	2	no	—
70	C₂	C₂×D₁₂₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₂₆₄
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	C₂×C₃₂×C₇₉	C₂
socle	C₂×C₇₉	C₂×D₁₆
hypercenter	C₂×C₃₂	D₇₉
hypocenter	C₇₉	#2262
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #19098995	C₂	semidirect
2. Dic₁₂₆₄	C₂	semidirect
3. #19098402	C₂	semidirect
4. D₂₅₂₈	C₂	semidirect
5. C₂×C₃₂×C₇₉	C₂	semidirect
36. C₇₉	#2262	semidirect
41. C₂×C₃₂	D₇₉	semidirect