Finite Group Databasebeta

← C₄₁×D₃₇₇ #44525645

Subgroups — C₄₁×D₃₇₇ #44525645

Order 30914.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₂₉	—	13	1	no	maximal, Hall
3	C₂₉×C₄₁	D₁₃	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₄₁	—	29	1	no	maximal, Hall
5	D₃₇₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₁	D₂₉	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₂₉	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₁	—	377	1	no	Hall
9	D₂₉	—	13	1	no	Hall
10	C₄₁	D₃₇₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	D₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
12	D₁₃	—	29	1	no	Hall
13	C₁₃	C₄₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	377	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	D₃₇₇
commutator, cosocle, hypocenter	C₁₃×C₂₉	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₂₉×C₄₁	C₂
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₉×C₄₁	C₂	semidirect
3. C₂₉×C₄₁	D₁₃	semidirect
5. D₃₇₇	C₄₁	direct (N × H)
6. C₁₃×C₄₁	D₂₉	semidirect
7. C₁₃×C₂₉	C₂×C₄₁	semidirect
10. C₄₁	D₃₇₇	direct (N × H)
11. C₂₉	D₁₃×C₄₁	semidirect
13. C₁₃	C₄₁×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₂₉×C₄₁	2
C₄₁×D₂₉	13
D₁₃×C₄₁	29
D₃₇₇	41