Finite Group Databasebeta

← C₇₉×D₂₉⋊C₇ #44545501

Subgroups — C₇₉×D₂₉⋊C₇ #44545501

Order 32074.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₉×C₇₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₇₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₇₉	—	29	1	no	maximal, Hall
5	C₇×C₇₉	—	29	1	no	Hall
6	D₂₉⋊C₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₉⋊C₇	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇₉	—	29	1	no	Hall
9	C₇₉	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
10	D₂₉	C₇×C₇₉	1	1	yes	characteristic, complemented, Hall
11	C₂₉	C₂×C₇×C₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇	—	29	1	no	Hall
13	C₇	—	29	1	no	Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₉	D₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₂×C₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₇₉	C₂×C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₇₉

Complements

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

N	H ≅ G/N	type
1. C₇₉×C₂₉⋊C₇	C₂	semidirect
2. D₂₉×C₇₉	C₇	semidirect
3. C₂₉×C₇₉	C₂×C₇	semidirect
6. D₂₉⋊C₇	C₇₉	direct (N × H)
7. C₂₉⋊C₇	C₂×C₇₉	semidirect
9. C₇₉	D₂₉⋊C₇	direct (N × H)
10. D₂₉	C₇×C₇₉	semidirect
11. C₂₉	C₂×C₇×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×C₂₉⋊C₇	2
D₂₉×C₇₉	7
C₂×C₇×C₇₉	29
D₂₉⋊C₇	79