Subgroups — C₃⋊(C₃⋊#16809858) #44475674

Order 30276.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉⋊D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16809858	—	3	4	no	maximal
3	C₃²×C₂₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₉⋊D₂₉	D₃	1	4	yes	—
5	#16809858	—	9	1	no	Hall
6	C₃×C₂₉²	Dic₃	1	4	yes	complemented
7	C₂₉⋊D₂₉	C₃⋊D₃	1	1	yes	characteristic
8	C₃⋊(C₃⋊#1181)	—	29	2	no	maximal
9	C₂₉²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
10	C₃²×D₂₉	—	29	2	no	—
11	C₃²×D₂₉	—	58	14	no	—
12	C₃⋊#1181	—	87	8	no	—
13	C₃²×C₂₉	—	2	14	no	—
14	C₃²×C₂₉	#1181	1	2	yes	complemented
15	C₃×D₂₉	—	29	8	no	—
16	C₃×D₂₉	—	58	56	no	—
17	#1181	—	261	2	no	—
18	C₃×C₂₉	—	2	56	no	—
19	C₃×C₂₉	C₃⋊#1181	1	8	yes	complemented
20	D₂₉	—	29	2	no	—
21	D₂₉	—	58	14	no	—
22	C₃⋊Dic₃	—	841	1	no	Hall
23	C₂₉	—	2	14	no	—
24	C₂₉	C₃⋊(C₃⋊#1181)	1	2	yes	complemented
25	C₂×C₃²	—	841	1	no	—
26	Dic₃	—	2523	4	no	—
27	C₃²	#16809858	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	841	4	no	—
29	C₄	—	7569	1	no	Sylow
30	C₃	C₃⋊#16809858	1	4	yes	complemented
31	C₂	—	841	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₂₉²	C₄
prime radical, cosocle	C₃²×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.