Subgroups — #67155

Order 360.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₅	C₂	1	2	yes	maximal, complemented
3	D₃×Dic₅	—	3	2	no	maximal
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	C₅×C₃⋊D₃	C₄	1	2	yes	complemented
6	#624	—	5	1	no	maximal, Hall
7	C₂×C₅×D₃	—	3	2	no	—
8	C₂×C₅×D₃	—	6	1	no	—
9	Dic₁₅	D₃	1	2	yes	complemented
10	C₃×Dic₅	—	3	2	no	—
11	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×Dic₅	—	9	1	no	Hall
13	C₂×C₃⋊D₃	D₅	1	1	yes	characteristic
14	C₃×Dic₃	—	5	2	no	—
15	C₂×C₃×C₅	—	2	1	no	—
16	C₂×C₃×C₅	C₂×D₃	1	2	yes	—
17	C₅×D₃	—	3	4	no	—
18	C₅×D₃	—	6	2	no	—
19	C₄×D₃	—	15	2	no	—
20	C₂²×C₅	—	9	1	no	—
21	Dic₅	—	3	2	no	—
22	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
23	C₃⋊D₃	Dic₅	1	2	yes	complemented
24	C₃×C₅	—	2	1	no	—
25	C₃×C₅	C₄×D₃	1	2	yes	complemented
26	C₂×D₃	—	3	2	no	—
27	C₂×D₃	—	6	1	no	—
28	C₃×C₄	—	15	2	no	—
29	Dic₃	—	5	2	no	—
30	C₂×C₅	—	9	2	no	—
31	C₂×C₅	D₃²	1	1	yes	characteristic
32	C₃²	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	—	45	1	no	Sylow
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	D₃×D₅	1	2	yes	—
36	D₃	—	3	4	no	—
37	D₃	—	6	2	no	—
38	C₅	#624	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	9	1	no	—
40	C₄	—	15	2	no	—
41	C₃	—	2	1	no	—
42	C₃	D₃×Dic₅	1	2	yes	complemented
43	C₂	—	9	2	no	—
44	C₂	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic

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

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.