Finite Group Databasebeta

← C₂₃×C₂₉×D₂₃ #44501601

Subgroups — C₂₃×C₂₉×D₂₃ #44501601

Order 30682.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₃×C₂₉	—	23	1	no	maximal
3	C₂₉×D₂₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂₃×D₂₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₃×C₂₉	—	2	11	no	—
6	C₂₃×C₂₉	D₂₃	1	1	yes	characteristic, direct product factor
7	C₂₃×C₂₉	C₂×C₂₃	1	1	yes	characteristic, complemented
8	C₂₃²	C₂×C₂₉	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₂₉	—	23	1	no	Hall
10	C₂×C₂₃	—	23	1	no	—
11	D₂₃	C₂₃×C₂₉	1	1	yes	characteristic, direct product factor
12	C₂₉	C₂₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂₃	—	2	11	no	—
14	C₂₃	C₂₉×D₂₃	1	1	yes	characteristic, direct product factor
15	C₂₃	C₂×C₂₃×C₂₉	1	1	yes	characteristic, complemented
16	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃×C₂₉	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₂₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₃²×C₂₉	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₃²×C₂₉	C₂	semidirect
3. C₂₉×D₂₃	C₂₃	direct (N × H)
4. C₂₃×D₂₃	C₂₉	direct (N × H)
6. C₂₃×C₂₉	D₂₃	direct (N × H)
7. C₂₃×C₂₉	C₂×C₂₃	semidirect
8. C₂₃²	C₂×C₂₉	semidirect
11. D₂₃	C₂₃×C₂₉	direct (N × H)
12. C₂₉	C₂₃×D₂₃	direct (N × H)
14. C₂₃	C₂₉×D₂₃	direct (N × H)
15. C₂₃	C₂×C₂₃×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₃²×C₂₉	2
C₂×C₂₃×C₂₉	23
C₂₉×D₂₃	23
C₂₃×D₂₃	29