Subgroups — #67141

Order 360.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#1204	—	3	4	no	maximal
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	#634	—	5	1	no	maximal, Hall
7	Dic₁₅	—	3	4	no	—
8	C₃×Dic₅	D₃	1	4	yes	—
9	C₅×Dic₃	—	3	4	no	—
10	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₀	—	9	1	no	Hall
12	C₃²×C₄	—	5	1	no	—
13	C₃⋊Dic₃	—	5	1	no	—
14	C₃⋊Dic₃	D₅	1	1	yes	characteristic
15	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
16	Dic₆	—	15	4	no	—
17	C₄×C₅	—	9	1	no	—
18	Dic₅	—	9	1	no	—
19	Dic₅	C₃⋊D₃	1	1	yes	characteristic
20	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
21	C₃×C₅	Dic₆	1	4	yes	complemented
22	C₃×C₄	—	5	4	no	—
23	Dic₃	—	3	4	no	—
24	Dic₃	—	15	4	no	—
25	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₃²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	45	1	no	Sylow
28	C₂×C₃	D₃×D₅	1	4	yes	—
29	C₅	#634	1	1	yes	characteristic, complemented, Sylow
30	C₄	—	5	1	no	—
31	C₄	—	9	1	no	—
32	C₄	—	45	1	no	—
33	C₃	#1204	1	4	yes	complemented
34	C₂	D₅×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₃⋊D₃
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃²×C₅	C₂²
hypocenter	C₃²×C₅	Q₈
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.