Subgroups — D₅⋊#157 #67201

Order 360.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#4380	C₂	1	2	yes	maximal, complemented
3	C₃⋊D₁₅	C₂²	1	1	yes	characteristic
4	C₅×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
5	C₃²×D₅	C₄	1	1	yes	characteristic, complemented
6	C₂×#157	—	5	1	no	maximal, Hall
7	D₃×D₅	—	6	2	no	—
8	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
10	C₂×C₃⋊D₃	—	5	1	no	—
11	#157	—	5	2	no	—
12	D₁₅	—	6	2	no	—
13	C₃×D₅	—	2	2	no	—
14	C₅×D₃	—	6	2	no	—
15	C₂×D₅	—	9	1	no	—
16	AGL(1,𝔽₅)	—	9	2	no	—
17	C₂×C₃²	—	5	1	no	—
18	C₃⋊D₃	—	5	1	no	—
19	C₃⋊D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
20	C₃×C₅	—	2	2	no	—
21	C₂×D₃	—	30	2	no	—
22	C₂×C₅	—	9	1	no	—
23	D₅	—	9	1	no	—
24	D₅	#157	1	1	yes	characteristic, complemented
25	C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	45	1	no	Sylow
27	C₂×C₃	—	10	2	no	—
28	D₃	—	6	2	no	—
29	D₃	—	30	2	no	—
30	C₅	C₂×#157	1	1	yes	characteristic, complemented, Sylow
31	C₂²	—	45	1	no	—
32	C₄	—	45	2	no	—
33	C₃	—	2	2	no	—
34	C₂	—	5	1	no	—
35	C₂	—	9	1	no	—
36	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₂×C₄
prime radical	D₅×C₃⋊D₃	C₂
cosocle	C₃⋊D₁₅	C₂²
LCS	G ▷ 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.