Subgroups — #67180

Order 360.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₁₅	C₂	1	2	yes	maximal
3	Dic₃₀	—	3	4	no	maximal
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	#634	—	5	1	no	maximal, Hall
6	C₃×C₄×C₅	D₃	1	4	yes	—
7	Dic₁₅	—	3	8	no	—
8	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀	—	9	1	no	Hall
10	C₃²×C₄	D₅	1	1	yes	characteristic
11	C₃⋊Dic₃	—	5	2	no	—
12	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
13	Dic₆	—	15	4	no	—
14	C₄×C₅	C₃⋊D₃	1	1	yes	characteristic
15	Dic₅	—	9	2	no	—
16	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
17	C₃×C₅	Dic₆	1	4	yes	complemented
18	C₃×C₄	D₁₅	1	4	yes	—
19	Dic₃	—	15	8	no	—
20	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
21	C₃²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	45	1	no	Sylow
23	C₂×C₃	C₂×D₁₅	1	4	yes	—
24	C₅	#634	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	45	2	no	—
26	C₄	C₃⋊D₁₅	1	1	yes	characteristic
27	C₃	Dic₃₀	1	4	yes	complemented
28	C₂	C₂×C₃⋊D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊D₁₅
commutator, socle, prime radical, cosocle	C₂×C₃²×C₅	C₂²
Fitting	C₃²×C₄×C₅	C₂
hypercenter	C₄	C₃⋊D₁₅
hypocenter	C₃²×C₅	Q₈
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₄

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.