Subgroups — #44475647

Order 30276.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₉²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃⋊(C₂₉⋊D₂₉)	—	6	2	no	—
4	#16809857	—	9	1	no	maximal, Hall
5	C₃×C₂₉²	—	2	2	no	—
6	C₂₉⋊D₂₉	—	9	1	no	—
7	#11760329	—	29	30	no	maximal
8	C₂₉²	#157	1	1	yes	characteristic, complemented, Sylow
9	C₃⋊D₈₇	—	29	30	no	—
10	C₃²×C₂₉	#1181	1	30	yes	complemented
11	D₈₇	—	174	60	no	—
12	#1181	—	261	30	no	—
13	C₃×C₂₉	—	2	60	no	—
14	D₂₉	—	261	30	no	—
15	#157	—	841	1	no	Hall
16	C₂₉	#11760329	1	30	yes	complemented
17	C₃⋊D₃	—	841	1	no	—
18	C₃²	#16809857	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	5046	2	no	—
20	C₄	—	7569	1	no	Sylow
21	C₃	—	2	2	no	—
22	C₂	—	7569	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₂₉²	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂
LCS	G ▷ C₃²×C₂₉²
UCS	C₁

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

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