Subgroups — #23765710

Order 10112.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098996	C₂	1	2	yes	maximal, complemented
2	#19098400	C₂	1	2	yes	maximal, complemented
3	D₂₅₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579184	—	2	2	no	—
7	#14579104	—	2	2	no	—
8	D₁₂₆₄	C₂²	1	2	yes	—
9	C₁₆×D₇₉	C₂²	1	1	yes	characteristic
10	C₇₉⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₇₉	C₂²	1	2	yes	—
12	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
13	#11929625	—	4	2	no	—
14	#11929611	—	4	2	no	—
15	D₆₃₂	—	2	2	no	—
16	C₈×D₇₉	D₄	1	1	yes	characteristic
17	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
18	Q₁₆×C₇₉	—	2	2	no	—
19	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
20	Q₈×C₇₉	—	4	2	no	—
21	D₃₁₆	—	4	2	no	—
22	D₃₁₆	—	8	2	no	—
23	C₄×D₇₉	—	8	2	no	—
24	C₄×D₇₉	D₈	1	1	yes	characteristic
25	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
26	C₇₉⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₇₉	—	8	2	no	—
28	C₂×D₇₉	D₁₆	1	1	yes	characteristic
29	C₄×C₇₉	—	8	2	no	—
30	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
31	Dic₇₉	D₁₆	1	1	yes	characteristic
32	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
33	D₇₉	—	2	1	no	—
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	D₇₉	1	1	yes	characteristic, complemented
39	SD₆₄	—	79	2	no	—
40	D₃₂	—	79	1	no	—
41	C₂×C₃₂	—	79	1	no	—
42	#135	—	158	2	no	—
43	Q₃₂	C₂×D₇₉	1	2	yes	—
44	SD₃₂	—	158	2	no	—
45	D₁₆	—	79	2	no	—
46	C₂×C₁₆	—	79	1	no	—
47	C₃₂	—	79	1	no	—
48	C₃₂	C₂×D₇₉	1	1	yes	characteristic
49	#41	—	316	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	316	2	no	—
52	D₈	—	158	2	no	—
53	C₂×C₈	—	79	1	no	—
54	C₁₆	—	79	1	no	—
55	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	316	2	no	—
58	D₄	—	632	2	no	—
59	C₂×C₄	—	79	1	no	—
60	C₂×C₄	—	632	2	no	—
61	C₈	—	79	1	no	—
62	C₈	D₄×D₇₉	1	1	yes	characteristic
63	C₂²	—	79	1	no	—
64	C₂²	—	632	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	79	1	no	—
67	C₄	D₈×D₇₉	1	1	yes	characteristic
68	C₂	—	158	1	no	—
69	C₂	—	1264	2	no	—
70	C₂	D₁₆×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₉
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	Q₆₄×C₇₉	C₂
socle	C₂×C₇₉	C₂×D₁₆
hypercenter	Q₆₄	D₇₉
hypocenter	C₇₉	#2262
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #19098996	C₂	semidirect
2. #19098400	C₂	semidirect
3. D₂₅₂₈	C₂	semidirect
4. C₃₂×D₇₉	C₂	semidirect
5. Q₆₄×C₇₉	C₂	semidirect
36. C₇₉	#2262	semidirect
38. Q₆₄	D₇₉	semidirect