Subgroups — #67139

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#1202	—	3	4	no	maximal
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	C₃⋊D₁₅	—	2	1	no	—
7	C₃²×D₅	—	2	1	no	—
8	#638	—	5	1	no	maximal, Hall
9	C₂×D₁₅	—	3	4	no	—
10	C₂×C₃×D₅	D₃	1	4	yes	complemented
11	C₅×Dic₃	—	3	4	no	—
12	C₃²×C₅	D₄	1	1	yes	characteristic, complemented, Hall
13	D₂₀	—	9	1	no	Hall
14	C₂²×C₃²	—	5	1	no	—
15	C₂×C₃⋊D₃	—	5	1	no	—
16	C₃⋊Dic₃	D₅	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
18	D₁₅	—	6	4	no	—
19	C₃×D₅	—	2	4	no	—
20	#67	—	15	4	no	—
21	C₂×D₅	—	9	1	no	—
22	C₂×D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
23	C₄×C₅	—	9	1	no	—
24	C₂×C₃²	—	10	1	no	—
25	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
26	C₃⋊D₃	—	10	1	no	—
27	C₃×C₅	#67	1	4	yes	complemented
28	C₂²×C₃	—	5	4	no	—
29	C₂×D₃	—	15	4	no	—
30	Dic₃	—	3	4	no	—
31	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
32	D₅	—	2	1	no	—
33	D₅	—	18	1	no	—
34	C₃²	D₂₀	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	45	1	no	Sylow
36	C₂×C₃	—	10	4	no	—
37	C₂×C₃	D₃×D₅	1	4	yes	—
38	D₃	—	30	4	no	—
39	C₅	#638	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	5	1	no	—
41	C₂²	—	45	1	no	—
42	C₄	—	9	1	no	—
43	C₃	#1202	1	4	yes	complemented
44	C₂	—	10	1	no	—
45	C₂	—	90	1	no	—
46	C₂	D₅×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₃⋊D₃
commutator, Fitting, socle, cosocle	C₂×C₃²×C₅	C₂²
hypocenter	C₃²×C₅	D₄
LCS	G ▷ C₂×C₃²×C₅ ▷ 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.