Subgroups — #23761472

Order 10112.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098316	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
4	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	C₂×C₇₉⋊C₈	—	4	2	no	—
8	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
10	C₄²×C₇₉	D₄	1	1	yes	characteristic
11	C₁₆×C₇₉	—	2	1	no	—
12	C₁₆×C₇₉	C₈	1	2	yes	complemented
13	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
15	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
16	C₈×C₇₉	—	2	1	no	—
17	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
18	C₈×C₇₉	M₁₆	1	1	yes	characteristic
19	C₇₉⋊C₈	—	8	2	no	—
20	C₂²×C₇₉	#107	1	1	yes	characteristic
21	C₄×C₇₉	—	2	1	no	—
22	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₇₉	#108	1	1	yes	characteristic
24	C₄×C₇₉	D₁₆	1	1	yes	characteristic
25	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
26	C₂×C₇₉	#335	1	1	yes	characteristic
27	C₂×C₇₉	#366	1	1	yes	characteristic
28	C₂×C₇₉	#368	1	1	yes	characteristic
29	#1371	—	79	1	no	maximal, Sylow
30	C₇₉	#1371	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₆	D₇₉	1	1	yes	characteristic
32	#335	—	79	2	no	—
33	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
34	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
35	C₄⋊C₈	—	158	2	no	—
36	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
37	C₂×C₈	—	316	2	no	—
38	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
39	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
40	C₄²	D₃₁₆	1	1	yes	characteristic
41	C₁₆	—	2	1	no	—
42	C₁₆	C₇₉⋊C₈	1	2	yes	complemented
43	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
44	C₂×C₄	D₆₃₂	1	1	yes	characteristic
45	C₂×C₄	Dic₃₁₆	1	1	yes	characteristic
46	C₈	—	2	1	no	—
47	C₈	—	632	2	no	—
48	C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
49	C₈	#11929608	1	1	yes	characteristic
50	C₂²	#14579095	1	1	yes	characteristic
51	C₄	—	2	1	no	—
52	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
53	C₄	#14579097	1	1	yes	characteristic
54	C₄	D₁₂₆₄	1	1	yes	characteristic
55	C₄	Dic₆₃₂	1	1	yes	characteristic
56	C₂	#19098316	1	1	yes	characteristic
57	C₂	#19098389	1	1	yes	characteristic
58	C₂	#19098393	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₆₃₂
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	C₄×C₁₆×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#107
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#1371
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₇₉	C₈	semidirect
30. C₇₉	#1371	semidirect
42. C₁₆	C₇₉⋊C₈	semidirect