Finite Group Databasebeta

← C₃₁×D₄₀₃ #38735902

Subgroups — C₃₁×D₄₀₃ #38735902

Order 24986.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₃₁	—	13	1	no	maximal, Hall
3	C₃₁²	D₁₃	1	1	yes	characteristic, complemented, Sylow
4	D₄₀₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor
5	D₁₃×C₃₁	—	31	1	no	maximal
6	C₁₃×C₃₁	—	2	15	no	—
7	C₁₃×C₃₁	D₃₁	1	1	yes	characteristic, complemented
8	C₁₃×C₃₁	C₂×C₃₁	1	1	yes	characteristic, complemented
9	C₂×C₃₁	—	403	1	no	—
10	D₃₁	—	13	1	no	—
11	C₃₁	—	2	15	no	—
12	C₃₁	D₁₃×C₃₁	1	1	yes	characteristic, complemented
13	C₃₁	D₄₀₃	1	1	yes	characteristic, direct product factor
14	D₁₃	—	31	1	no	Hall
15	C₁₃	C₃₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
16	C₂	—	403	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₄₀₃
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₁²	C₂
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁²	C₂	semidirect
3. C₃₁²	D₁₃	semidirect
4. D₄₀₃	C₃₁	direct (N × H)
7. C₁₃×C₃₁	D₃₁	semidirect
8. C₁₃×C₃₁	C₂×C₃₁	semidirect
12. C₃₁	D₁₃×C₃₁	semidirect
13. C₃₁	D₄₀₃	direct (N × H)
15. C₁₃	C₃₁×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃₁²	2
C₃₁×D₃₁	13
D₄₀₃	31
D₁₃×C₃₁	31