Subgroups — #29502829

Order 15138.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₈₇	—	3	1	no	maximal
3	C₃×C₂₉²	D₃	1	1	yes	characteristic
4	C₂₉×D₂₉	—	9	1	no	Hall
5	C₂₉²	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₈₇	—	3	1	no	—
7	D₃×C₂₉	—	87	1	no	—
8	C₃×C₂₉	—	3	1	no	—
9	C₃×C₂₉	—	6	4	no	—
10	C₃×C₂₉	—	6	1	no	—
11	C₂×C₂₉	—	261	1	no	—
12	D₂₉	—	9	1	no	—
13	C₂₉	—	6	1	no	—
14	C₂₉	—	6	1	no	—
15	C₂₉	—	6	4	no	—
16	D₉	—	841	1	no	maximal, Hall
17	C₉	—	1682	1	no	Sylow
18	D₃	—	87	1	no	—
19	C₃	#19097943	1	1	yes	characteristic
20	C₂	—	261	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₉²⋊C₉	C₂
Frattini	C₃	#19097943
Fitting, socle	C₃×C₂₉²	D₃
LCS	G ▷ C₂₉²⋊C₉
UCS	C₁

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

N	H ≅ G/N	type
1. C₂₉²⋊C₉	C₂	semidirect
5. C₂₉²	D₉	semidirect

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