Subgroups — #23761601

Order 10112.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#19098389	C₂	1	1	yes	maximal, characteristic
3	#366×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579095	—	2	1	no	—
5	C₇₉⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
7	#107×C₇₉	—	2	1	no	—
8	C₄⋊Dic₇₉	—	4	1	no	—
9	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₇₉	—	4	1	no	—
11	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₉	—	8	1	no	—
14	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
15	C₂×Dic₇₉	—	8	1	no	—
16	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
19	C₄×C₇₉	—	16	1	no	—
20	C₄×C₇₉	#107	1	1	yes	characteristic
21	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
22	Dic₇₉	—	16	1	no	—
23	C₂×C₇₉	#366	1	1	yes	characteristic
24	C₂×C₇₉	SD₆₄	1	1	yes	characteristic
25	C₂×C₇₉	SD₆₄	1	1	yes	characteristic
26	#1424	—	79	1	no	maximal, Sylow
27	C₇₉	#1424	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	79	1	no	—
29	#366	—	79	1	no	—
30	#366	D₇₉	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	158	1	no	—
34	C₃₂	—	79	2	no	—
35	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	316	1	no	—
38	C₁₆	Dic₁₅₈	1	1	yes	characteristic
39	C₁₆	C₄×D₇₉	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	632	1	no	—
42	C₂×C₄	#11929609	1	1	yes	characteristic
43	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
44	C₈	#11929614	1	1	yes	characteristic
45	C₂²	#14579102	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1264	1	no	—
48	C₄	#14579094	1	1	yes	characteristic
49	C₄	#14579107	1	1	yes	characteristic
50	C₂	#19098388	1	1	yes	characteristic
51	C₂	#19098400	1	1	yes	characteristic
52	C₂	#19098401	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579102
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	#366×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	D₁₆
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	#366	D₇₉
hypocenter	C₇₉	#1424
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₇₉⋊C₃₂	C₄	semidirect
27. C₇₉	#1424	semidirect