Subgroups — #23761606

Order 10112.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098393	C₂	1	1	yes	maximal, characteristic
2	#19098391	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579097	—	2	1	no	—
5	#14579095	—	2	1	no	—
6	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
7	C₃₂×C₇₉	C₄	1	2	yes	complemented
8	#11929608	—	4	1	no	—
9	C₄⋊Dic₇₉	—	4	1	no	—
10	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
11	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
14	C₂×Dic₇₉	—	8	1	no	—
15	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
17	C₇₉⋊C₈	—	8	1	no	—
18	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
19	C₄×C₇₉	#107	1	1	yes	characteristic
20	C₄×C₇₉	SD₃₂	1	1	yes	characteristic
21	Dic₇₉	—	16	1	no	—
22	C₂×C₇₉	—	2	1	no	—
23	C₂×C₇₉	#367	1	1	yes	characteristic
24	#1426	—	79	1	no	maximal, Sylow
25	C₇₉	#1426	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	D₇₉	1	1	yes	characteristic
27	#368	—	79	1	no	—
28	#367	—	79	1	no	—
29	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
30	#108	—	158	1	no	—
31	#107	—	158	1	no	—
32	C₃₂	Dic₇₉	1	2	yes	complemented
33	M₁₆	—	316	1	no	—
34	C₂×C₈	D₃₁₆	1	1	yes	characteristic
35	C₄⋊C₄	—	316	1	no	—
36	C₁₆	Dic₁₅₈	1	1	yes	characteristic
37	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
38	C₂×C₄	—	632	1	no	—
39	C₂×C₄	D₆₃₂	1	1	yes	characteristic
40	C₈	—	632	1	no	—
41	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
42	C₈	Dic₃₁₆	1	1	yes	characteristic
43	C₂²	#14579106	1	1	yes	characteristic
44	C₄	—	1264	1	no	—
45	C₄	#14579095	1	1	yes	characteristic
46	C₄	#14579106	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#19098391	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098391
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	M₆₄×C₇₉	C₂
socle	C₂×C₇₉	#367
prime radical	C₂²×C₇₉	SD₃₂
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	M₆₄	D₇₉
hypocenter	C₇₉	#1426
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
7. C₃₂×C₇₉	C₄	semidirect
25. C₇₉	#1426	semidirect
32. C₃₂	Dic₇₉	semidirect