Subgroups — #23761594

Order 10112.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic
2	#19098393	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₆	—	2	1	no	—
5	Dic₆₃₂	—	2	1	no	—
6	Dic₆₃₂	C₄	1	2	yes	—
7	#14579097	—	2	1	no	—
8	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
9	C₃₂×C₇₉	—	2	1	no	—
10	C₂×Dic₁₅₈	—	4	1	no	—
11	Dic₃₁₆	—	2	2	no	—
12	Dic₃₁₆	—	4	1	no	—
13	#11929608	—	4	1	no	—
14	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
15	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
18	C₂×Dic₇₉	—	8	1	no	—
19	Dic₁₅₈	—	4	2	no	—
20	Dic₁₅₈	—	8	1	no	—
21	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
23	C₇₉⋊C₈	—	8	1	no	—
24	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
25	C₄×C₇₉	#102	1	1	yes	characteristic
26	C₄×C₇₉	D₁₆	1	1	yes	characteristic
27	Dic₇₉	—	8	2	no	—
28	C₂×C₇₉	—	2	1	no	—
29	C₂×C₇₉	#357	1	1	yes	characteristic
30	#1420	—	79	1	no	maximal, Sylow
31	C₇₉	#1420	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₃₂	—	79	1	no	—
33	M₆₄	D₇₉	1	1	yes	characteristic
34	#368	—	79	1	no	—
35	C₂×Q₁₆	—	158	1	no	—
36	Q₃₂	—	79	2	no	—
37	Q₃₂	—	158	1	no	—
38	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
39	#108	—	158	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	316	1	no	—
42	Q₁₆	—	316	1	no	—
43	Q₁₆	—	158	2	no	—
44	M₁₆	—	316	1	no	—
45	C₂×C₈	D₃₁₆	1	1	yes	characteristic
46	C₁₆	C₄×D₇₉	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
48	Q₈	—	316	2	no	—
49	Q₈	—	632	1	no	—
50	C₂×C₄	—	632	1	no	—
51	C₂×C₄	D₆₃₂	1	1	yes	characteristic
52	C₈	—	632	1	no	—
53	C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
54	C₈	#11929613	1	1	yes	characteristic
55	C₂²	#14579106	1	1	yes	characteristic
56	C₄	—	632	2	no	—
57	C₄	#14579083	1	1	yes	characteristic
58	C₄	D₁₂₆₄	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#19098365	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098365
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	M₆₄×C₇₉	C₂
socle	C₂×C₇₉	#357
prime radical	C₂²×C₇₉	SD₃₂
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	M₆₄	D₇₉
hypocenter	C₇₉	#1420
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
31. C₇₉	#1420	semidirect