Subgroups — #34176180

Order 20224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉⋊C₁₂₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₇₉	C₄	1	1	yes	characteristic
4	C₆₄×C₇₉	C₄	1	1	yes	characteristic
5	C₆₄×C₇₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₇₉	C₈	1	1	yes	characteristic
7	C₃₂×C₇₉	C₈	1	1	yes	characteristic
8	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₉	C₁₆	1	1	yes	characteristic
10	C₁₆×C₇₉	C₁₆	1	1	yes	characteristic
11	C₁₆×C₇₉	C₂×C₈	1	1	yes	characteristic
12	C₂×C₄×C₇₉	C₃₂	1	1	yes	characteristic
13	C₈×C₇₉	C₃₂	1	1	yes	characteristic
14	C₈×C₇₉	C₂×C₁₆	1	1	yes	characteristic
15	C₂²×C₇₉	C₆₄	1	1	yes	characteristic
16	C₄×C₇₉	C₆₄	1	1	yes	characteristic
17	C₄×C₇₉	C₂×C₃₂	1	1	yes	characteristic
18	M₂₅₆	—	79	1	no	maximal, Sylow
19	C₂×C₇₉	—	2	1	no	—
20	C₂×C₇₉	C₂×C₆₄	1	1	yes	characteristic
21	C₂×C₆₄	D₇₉	1	1	yes	characteristic
22	C₁₂₈	—	79	2	no	—
23	C₇₉	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	Dic₇₉	1	1	yes	characteristic
25	C₆₄	Dic₇₉	1	1	yes	characteristic
26	C₆₄	C₂×D₇₉	1	1	yes	characteristic
27	C₂×C₁₆	C₇₉⋊C₈	1	1	yes	characteristic
28	C₃₂	C₇₉⋊C₈	1	1	yes	characteristic
29	C₃₂	C₂×Dic₇₉	1	1	yes	characteristic
30	C₂×C₈	C₇₉⋊C₁₆	1	1	yes	characteristic
31	C₁₆	C₇₉⋊C₁₆	1	1	yes	characteristic
32	C₁₆	C₂×C₇₉⋊C₈	1	1	yes	characteristic
33	C₂×C₄	C₇₉⋊C₃₂	1	1	yes	characteristic
34	C₈	C₇₉⋊C₃₂	1	1	yes	characteristic
35	C₈	C₂×C₇₉⋊C₁₆	1	1	yes	characteristic
36	C₂²	C₇₉⋊C₆₄	1	1	yes	characteristic
37	C₄	C₇₉⋊C₆₄	1	1	yes	characteristic
38	C₄	C₂×C₇₉⋊C₃₂	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×C₇₉⋊C₆₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₆₄	C₂×D₇₉
commutator, socle	C₂×C₇₉	C₂×C₆₄
Fitting	C₂×C₆₄×C₇₉	C₂
prime radical	C₂²×C₇₉	C₆₄
cosocle	C₆₄×C₇₉	C₂²
hypercenter	C₂×C₆₄	D₇₉
hypocenter	C₇₉	M₂₅₆
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₆₄ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₇₉⋊C₁₂₈	C₂	semidirect
23. C₇₉	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
C₇₉⋊C₁₂₈	2
C₂×C₆₄×C₇₉	2
M₂₅₆	79