Subgroups — #19098965

Order 5056.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579153	C₂	1	2	yes	maximal
2	#14579095	C₂	1	2	yes	maximal
3	#14579093	C₂	1	2	yes	maximal
4	C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₇₉	C₂²	1	4	yes	—
6	Dic₇₉⋊C₄	—	2	4	no	—
7	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	C₄²×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₇₉	D₄	1	2	yes	—
11	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
12	C₂×Dic₇₉	—	2	4	no	—
13	C₈×C₇₉	Q₈	1	2	yes	—
14	C₈×C₇₉	Q₈	1	2	yes	—
15	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
16	C₄×C₇₉	—	2	2	no	—
17	C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₇₉	—	4	4	no	—
20	C₂×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₇₉	#135	1	2	yes	—
22	C₇₉	#499	1	1	yes	characteristic, complemented, Sylow
23	#499	—	79	1	no	maximal, Sylow
24	#125	—	79	2	no	—
25	#107	—	79	2	no	—
26	#106	—	79	2	no	—
27	C₄×C₈	D₇₉	1	1	yes	characteristic
28	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
29	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
30	C₄⋊C₄	—	79	4	no	—
31	C₄⋊C₄	—	158	4	no	—
32	C₄²	C₂×D₇₉	1	1	yes	characteristic
33	C₂×C₄	—	158	4	no	—
34	C₂×C₄	D₃₁₆	1	2	yes	—
35	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
36	C₈	Dic₁₅₈	1	2	yes	—
37	C₈	Dic₁₅₈	1	2	yes	—
38	C₂²	C₂×D₃₁₆	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	316	4	no	—
41	C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
42	C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
43	C₂	#14579161	1	1	yes	characteristic
44	C₂	#14579183	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	C₄×C₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	C₄×C₈	D₇₉
hypocenter	C₇₉	#499
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
22. C₇₉	#499	semidirect