Finite Group Databasebeta

← C₇×D₂₉×C₅₉ #37561713

Subgroups — C₇×D₂₉×C₅₉ #37561713

Order 23954.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₉×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₅₉	—	29	1	no	maximal, Hall
5	C₇×C₅₉	D₂₉	1	1	yes	characteristic, direct product factor, Hall
6	C₇×D₂₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₂₉	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅₉	—	29	1	no	Hall
9	C₅₉	C₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
10	D₂₉	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂₉	C₂×C₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇	—	29	1	no	Hall
13	C₇	D₂₉×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₅₉	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₇×C₂₉×C₅₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₇×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×C₅₉	C₂	semidirect
2. D₂₉×C₅₉	C₇	direct (N × H)
3. C₂₉×C₅₉	C₂×C₇	semidirect
5. C₇×C₅₉	D₂₉	direct (N × H)
6. C₇×D₂₉	C₅₉	direct (N × H)
7. C₇×C₂₉	C₂×C₅₉	semidirect
9. C₅₉	C₇×D₂₉	direct (N × H)
10. D₂₉	C₇×C₅₉	direct (N × H)
11. C₂₉	C₂×C₇×C₅₉	semidirect
13. C₇	D₂₉×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₉×C₅₉	2
D₂₉×C₅₉	7
C₂×C₇×C₅₉	29
C₇×D₂₉	59