Subgroups — D₃²⋊D₅ #67203

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	1	yes	maximal, characteristic, complemented
2	C₅×D₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	#4379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃×D₁₅	—	2	1	no	—
6	C₃×C₅×D₃	—	2	1	no	—
7	GO⁺(4,𝔽₂)	—	5	1	no	maximal, Hall
8	C₂×C₅×D₃	—	6	1	no	—
9	D₃×D₅	—	6	1	no	—
10	C₃²×C₅	D₄	1	1	yes	characteristic, complemented, Hall
11	C₂²⋊D₅	—	9	1	no	maximal, Hall
12	D₃²	—	5	1	no	—
13	D₃²	D₅	1	1	yes	characteristic, complemented
14	#157	—	5	1	no	—
15	C₂×C₃×C₅	—	6	1	no	—
16	D₁₅	—	2	1	no	—
17	C₃×D₅	—	6	1	no	—
18	C₅×D₃	—	2	1	no	—
19	C₅×D₃	—	6	1	no	—
20	C₅×D₃	—	6	1	no	—
21	C₂²×C₅	—	9	1	no	—
22	C₂×D₅	—	9	1	no	—
23	Dic₅	—	9	1	no	—
24	C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
25	C₃×D₃	—	2	1	no	—
26	C₃×D₃	—	10	1	no	—
27	C₃×C₅	—	2	1	no	—
28	C₃×C₅	—	2	1	no	—
29	C₂×D₃	—	6	1	no	—
30	C₂×D₃	—	30	1	no	—
31	C₂×C₅	—	6	1	no	—
32	C₂×C₅	—	9	1	no	—
33	D₅	—	6	1	no	—
34	C₃²	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	45	1	no	Sylow
36	C₂×C₃	—	6	1	no	—
37	C₂×C₃	—	30	1	no	—
38	D₃	—	2	1	no	—
39	D₃	—	6	1	no	—
40	D₃	—	6	1	no	—
41	D₃	—	10	1	no	—
42	C₅	GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	9	1	no	—
44	C₂²	—	45	1	no	—
45	C₄	—	45	1	no	—
46	C₃	—	2	1	no	—
47	C₃	—	2	1	no	—
48	C₂	—	6	1	no	—
49	C₂	—	9	1	no	—
50	C₂	—	30	1	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.