Finite Group Databasebeta

← D₅×C₃₇×C₇₉ #44416175

Subgroups — D₅×C₃₇×C₇₉ #44416175

Order 29230.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₇×C₇₉	—	5	1	no	maximal, Hall
3	C₃₇×C₇₉	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₇₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
6	D₅×C₃₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₃₇	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇₉	—	5	1	no	Hall
9	C₇₉	D₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃₇	—	5	1	no	Hall
11	C₃₇	D₅×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₃₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₃₇×C₇₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇×C₇₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₅×C₃₇×C₇₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃₇×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×C₇₉	C₂	semidirect
3. C₃₇×C₇₉	D₅	direct (N × H)
4. D₅×C₇₉	C₃₇	direct (N × H)
5. C₅×C₇₉	C₂×C₃₇	semidirect
6. D₅×C₃₇	C₇₉	direct (N × H)
7. C₅×C₃₇	C₂×C₇₉	semidirect
9. C₇₉	D₅×C₃₇	direct (N × H)
11. C₃₇	D₅×C₇₉	direct (N × H)
12. D₅	C₃₇×C₇₉	direct (N × H)
13. C₅	C₂×C₃₇×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₇×C₇₉	2
C₂×C₃₇×C₇₉	5
D₅×C₇₉	37
D₅×C₃₇	79