Subgroups — #34176170

Order 20224.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#23761600	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1423	C₂	1	1	yes	maximal, characteristic
4	#19098389	—	2	1	no	—
5	C₇₉⋊C₆₄	C₄	1	2	yes	complemented
6	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	#366×C₇₉	—	2	1	no	—
8	#14579095	—	4	1	no	—
9	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
10	#107×C₇₉	—	4	1	no	—
11	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₉	Q₈	1	1	yes	characteristic
13	C₄⋊Dic₇₉	—	8	1	no	—
14	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₇₉	—	8	1	no	—
16	C₁₆×C₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₉	—	16	1	no	—
19	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
20	C₂×Dic₇₉	—	16	1	no	—
21	C₈×C₇₉	#107	1	1	yes	characteristic
22	C₈×C₇₉	Q₃₂	1	1	yes	characteristic
23	C₂²×C₇₉	D₃₂	1	1	yes	characteristic
24	C₄×C₇₉	—	32	1	no	—
25	C₄×C₇₉	#366	1	1	yes	characteristic
26	C₄×C₇₉	Q₆₄	1	1	yes	characteristic
27	Dic₇₉	—	32	1	no	—
28	#7546	—	79	1	no	maximal, Sylow
29	C₂×C₇₉	#1423	1	1	yes	characteristic
30	C₂×C₇₉	SD₁₂₈	1	1	yes	characteristic
31	C₂×C₇₉	SD₁₂₈	1	1	yes	characteristic
32	C₂×C₆₄	—	79	1	no	—
33	#1423	—	79	1	no	—
34	#1423	D₇₉	1	1	yes	characteristic
35	C₇₉	#7546	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
37	#366	—	2	1	no	—
38	#366	—	158	1	no	—
39	C₆₄	—	79	2	no	—
40	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
41	#107	—	4	1	no	—
42	#107	—	316	1	no	—
43	C₃₂	Dic₁₅₈	1	1	yes	characteristic
44	C₃₂	C₄×D₇₉	1	1	yes	characteristic
45	C₂×C₈	#11929609	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	632	1	no	—
48	C₁₆	Dic₇₉⋊C₄	1	1	yes	characteristic
49	C₁₆	#11929614	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	1264	1	no	—
52	C₂×C₄	#14579102	1	1	yes	characteristic
53	C₈	#14579094	1	1	yes	characteristic
54	C₈	#14579107	1	1	yes	characteristic
55	C₂²	#19098398	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	2528	1	no	—
58	C₄	#19098388	1	1	yes	characteristic
59	C₄	#19098403	1	1	yes	characteristic
60	C₂	#23761599	1	1	yes	characteristic
61	C₂	#23761614	1	1	yes	characteristic
62	C₂	#23761615	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19098398
commutator	C₃₂×C₇₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₇₉×#1423	C₂
socle, prime radical	C₂²×C₇₉	D₃₂
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	#1423	D₇₉
hypocenter	C₇₉	#7546
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. C₇₉⋊C₆₄	C₄	semidirect
35. C₇₉	#7546	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇₉⋊C₆₄	2
#23761600	2
C₇₉×#1423	2
#7546	79