Subgroups — C₂×C₇₉⋊C₆₄ #23761609

Order 10112.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₇₉
commutator, hypocenter	C₇₉	C₂×C₆₄
Frattini	C₃₂	C₂×D₇₉
Fitting	C₂×C₃₂×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₃₂
cosocle	C₃₂×C₇₉	C₂²
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₇₉⋊C₆₄	C₂	direct (N × H)
15. C₂×C₇₉	C₆₄	semidirect
18. C₇₉	C₂×C₆₄	semidirect
33. C₂	C₇₉⋊C₆₄	direct (N × H)

Subgroups — C2×C79⋊C64 #23761609

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇₉⋊C₆₄ #23761609