Finite Group Databasebeta

← C₅×D₁₁×C₁₇₉ #34089003

Subgroups — C₅×D₁₁×C₁₇₉ #34089003

Order 19690.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁×C₁₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₇₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₇₉	—	11	1	no	maximal, Hall
5	C₅×C₁₇₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₇₉	—	11	1	no	Hall
7	C₁₇₉	C₅×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×D₁₁	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁	C₂×C₁₇₉	1	1	yes	characteristic, complemented, Hall
10	D₁₁	C₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁	C₂×C₅×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	11	1	no	Hall
13	C₅	D₁₁×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₁₇₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇₉	C₂	semidirect
2. D₁₁×C₁₇₉	C₅	direct (N × H)
3. C₁₁×C₁₇₉	C₂×C₅	semidirect
5. C₅×C₁₇₉	D₁₁	direct (N × H)
7. C₁₇₉	C₅×D₁₁	direct (N × H)
8. C₅×D₁₁	C₁₇₉	direct (N × H)
9. C₅×C₁₁	C₂×C₁₇₉	semidirect
10. D₁₁	C₅×C₁₇₉	direct (N × H)
11. C₁₁	C₂×C₅×C₁₇₉	semidirect
13. C₅	D₁₁×C₁₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×C₁₇₉	2
D₁₁×C₁₇₉	5
C₂×C₅×C₁₇₉	11
C₅×D₁₁	179