Subgroups — #19098960

Order 5056.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579160	C₂	1	2	yes	maximal
2	#14579093	C₂	1	1	yes	maximal, characteristic
3	#14579092	C₂	1	2	yes	maximal
4	C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic
5	#106×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₅₈	—	2	2	no	—
7	C₂×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	Dic₇₉⋊C₄	—	2	2	no	—
10	C₄×Dic₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
13	C₂×C₄×C₇₉	—	2	2	no	—
14	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₇₉	—	2	2	no	—
16	C₂×Dic₇₉	D₄	1	2	yes	—
17	Dic₁₅₈	—	4	4	no	—
18	C₈×C₇₉	Q₈	1	2	yes	complemented
19	C₇₉⋊C₈	Q₈	1	2	yes	complemented
20	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₇₉	—	4	2	no	—
22	C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₇₉	—	4	2	no	—
25	Dic₇₉	SD₁₆	1	4	yes	—
26	C₂×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₇₉	C₂×SD₁₆	1	2	yes	—
28	C₇₉	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	79	1	no	maximal, Sylow
30	C₄⋊Q₈	—	79	2	no	—
31	#106	—	79	1	no	—
32	#106	—	79	2	no	—
33	#106	D₇₉	1	1	yes	characteristic
34	C₄×C₈	—	79	1	no	—
35	C₂×Q₈	—	158	2	no	—
36	C₂×C₈	—	79	1	no	—
37	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
38	C₄⋊C₄	—	79	2	no	—
39	C₄⋊C₄	—	158	2	no	—
40	C₄⋊C₄	C₂×D₇₉	1	2	yes	—
41	C₄²	—	79	1	no	—
42	Q₈	—	316	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	79	2	no	—
45	C₂×C₄	—	158	2	no	—
46	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
47	C₈	—	79	2	no	—
48	C₈	Dic₁₅₈	1	2	yes	complemented
49	C₂²	D₄×D₇₉	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	316	2	no	—
52	C₄	—	79	4	no	—
53	C₄	Q₈×D₇₉	1	1	yes	characteristic
54	C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
55	C₂	#14579160	1	1	yes	characteristic
56	C₂	SD₁₆×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	#106×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	#106	D₇₉
hypocenter	C₇₉	#498
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₇₉	Q₈	semidirect
19. C₇₉⋊C₈	Q₈	semidirect
28. C₇₉	#498	semidirect
48. C₈	Dic₁₅₈	semidirect