Subgroups — #157⋊D₅ #67204

Order 360.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃⋊D₃)⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₅×#157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	C₃×D₁₅	—	2	2	no	—
5	GO⁺(4,𝔽₂)	—	5	1	no	maximal, Hall
6	D₃×D₅	—	6	2	no	—
7	C₃²×C₅	D₄	1	1	yes	characteristic, complemented, Hall
8	D₂₀	—	9	1	no	maximal, Hall
9	D₃²	—	5	2	no	—
10	#157	D₅	1	1	yes	characteristic, complemented
11	D₁₅	—	2	2	no	—
12	C₃×D₅	—	6	2	no	—
13	C₅×D₃	—	6	2	no	—
14	C₂×D₅	—	9	2	no	—
15	C₄×C₅	—	9	1	no	—
16	C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
17	C₃×D₃	—	10	2	no	—
18	C₃×C₅	—	2	2	no	—
19	C₂×D₃	—	30	2	no	—
20	C₂×C₅	—	9	1	no	—
21	D₅	—	6	2	no	—
22	C₃²	D₂₀	1	1	yes	characteristic, complemented, Sylow
23	D₄	—	45	1	no	Sylow
24	C₂×C₃	—	30	2	no	—
25	D₃	—	6	2	no	—
26	D₃	—	10	2	no	—
27	C₅	GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	45	2	no	—
29	C₄	—	9	1	no	—
30	C₃	—	2	2	no	—
31	C₂	—	9	1	no	—
32	C₂	—	30	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₅×C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃²×C₅	D₄
LCS	G ▷ C₅×C₃⋊D₃ ▷ C₃²×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.