Finite Group Databasebeta

← D₅×C₁₇×C₁₆₇ #43249149

Subgroups — D₅×C₁₇×C₁₆₇ #43249149

Order 28390.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₇×C₁₆₇	—	5	1	no	maximal, Hall
3	C₁₇×C₁₆₇	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₆₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₆₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₆₇	—	5	1	no	Hall
7	D₅×C₁₇	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₆₇	D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₇	C₂×C₁₆₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇	—	5	1	no	Hall
11	C₁₇	D₅×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₁₇×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₇×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₁₆₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₇×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₁₆₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₇×C₁₆₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₁₆₇	C₂	semidirect
3. C₁₇×C₁₆₇	D₅	direct (N × H)
4. D₅×C₁₆₇	C₁₇	direct (N × H)
5. C₅×C₁₆₇	C₂×C₁₇	semidirect
7. D₅×C₁₇	C₁₆₇	direct (N × H)
8. C₁₆₇	D₅×C₁₇	direct (N × H)
9. C₅×C₁₇	C₂×C₁₆₇	semidirect
11. C₁₇	D₅×C₁₆₇	direct (N × H)
12. D₅	C₁₇×C₁₆₇	direct (N × H)
13. C₅	C₂×C₁₇×C₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₇×C₁₆₇	2
C₂×C₁₇×C₁₆₇	5
D₅×C₁₆₇	17
D₅×C₁₇	167