Subgroups — C₂×C₅₉⋊C₆₄ #21422305

Order 7552.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉⋊C₆₄	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₅₉	C₄	1	1	yes	characteristic
4	C₃₂×C₅₉	C₄	1	1	yes	characteristic
5	C₃₂×C₅₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₉	C₈	1	1	yes	characteristic
7	C₁₆×C₅₉	C₈	1	1	yes	characteristic
8	C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅₉	C₁₆	1	1	yes	characteristic
10	C₈×C₅₉	C₁₆	1	1	yes	characteristic
11	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₅₉	C₃₂	1	1	yes	characteristic
13	C₄×C₅₉	C₃₂	1	1	yes	characteristic
14	C₄×C₅₉	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₆₄	—	59	1	no	maximal, Sylow
16	C₂×C₅₉	C₆₄	1	2	yes	complemented
17	C₂×C₅₉	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₃₂	D₅₉	1	1	yes	characteristic
19	C₆₄	—	59	2	no	—
20	C₅₉	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₆	Dic₅₉	1	1	yes	characteristic
22	C₃₂	Dic₅₉	1	1	yes	characteristic
23	C₃₂	C₂×D₅₉	1	1	yes	characteristic
24	C₂×C₈	C₅₉⋊C₈	1	1	yes	characteristic
25	C₁₆	C₅₉⋊C₈	1	1	yes	characteristic
26	C₁₆	C₂×Dic₅₉	1	1	yes	characteristic
27	C₂×C₄	C₅₉⋊C₁₆	1	1	yes	characteristic
28	C₈	C₅₉⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₅₉⋊C₈	1	1	yes	characteristic
30	C₂²	C₅₉⋊C₃₂	1	1	yes	characteristic
31	C₄	C₅₉⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₅₉⋊C₁₆	1	1	yes	characteristic
33	C₂	C₅₉⋊C₆₄	1	2	yes	direct product factor
34	C₂	C₂×C₅₉⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₅₉
commutator, hypocenter	C₅₉	C₂×C₆₄
Frattini	C₃₂	C₂×D₅₉
Fitting	C₂×C₃₂×C₅₉	C₂
socle	C₂²×C₅₉	C₃₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₅₉⋊C₆₄	C₂	direct (N × H)
16. C₂×C₅₉	C₆₄	semidirect
20. C₅₉	C₂×C₆₄	semidirect
33. C₂	C₅₉⋊C₆₄	direct (N × H)

Subgroups — C2×C59⋊C64 #21422305

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅₉⋊C₆₄ #21422305