Subgroups — #13108537

Order 1620.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic
2	C₃⁴×C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	#66472	—	5	1	no	maximal, Hall
4	C₅×C₃⋊(C₃⋊D₃)	—	6	20	no	—
5	#4379	—	9	10	no	maximal
6	C₃⋊(C₃⋊(C₃⋊D₃))	D₅	1	1	yes	characteristic
7	C₃³×C₅	—	2	20	no	—
8	C₅×C₃⋊D₃	—	9	10	no	—
9	C₅×C₃⋊D₃	—	18	60	no	—
10	C₃⁴	Dic₅	1	1	yes	characteristic, complemented, Sylow
11	C₃⋊(C₃⋊D₃)	—	6	20	no	—
12	C₃²×C₅	—	2	60	no	—
13	C₃²×C₅	#157	1	10	yes	complemented
14	#157	—	45	10	no	—
15	C₅×D₃	—	54	20	no	—
16	C₃³	—	2	20	no	—
17	Dic₅	—	81	1	no	Hall
18	C₃⋊D₃	—	9	10	no	—
19	C₃⋊D₃	—	18	60	no	—
20	C₃×C₅	—	2	20	no	—
21	C₂×C₅	—	81	1	no	—
22	C₃²	—	2	60	no	—
23	C₃²	#4379	1	10	yes	complemented
24	D₃	—	54	20	no	—
25	C₅	#66472	1	1	yes	characteristic, complemented, Sylow
26	C₄	—	405	1	no	Sylow
27	C₃	—	2	20	no	—
28	C₂	—	81	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃⁴×C₅	C₄
prime radical, cosocle	C₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂
LCS	G ▷ C₃⁴×C₅
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.