Subgroups — #67158

Order 360.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₅	C₂	1	2	yes	maximal
3	#1204	—	3	2	no	maximal
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	#627	—	5	1	no	maximal, Hall
6	Dic₁₅	D₃	1	2	yes	—
7	C₃×Dic₅	—	3	2	no	—
8	C₅×Dic₃	—	3	2	no	—
9	C₅×Dic₃	—	6	1	no	—
10	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₀	—	9	1	no	Hall
12	C₃⋊Dic₃	D₅	1	1	yes	characteristic
13	C₃×Dic₃	—	5	2	no	—
14	C₂×C₃×C₅	—	2	1	no	—
15	C₂×C₃×C₅	C₂×D₃	1	2	yes	—
16	Dic₆	—	15	2	no	—
17	C₄×C₅	—	9	1	no	—
18	Dic₅	—	3	2	no	—
19	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	—	2	1	no	—
21	C₃×C₅	Dic₆	1	2	yes	complemented
22	C₃×C₄	—	15	2	no	—
23	Dic₃	—	3	2	no	—
24	Dic₃	—	5	2	no	—
25	Dic₃	—	6	1	no	—
26	C₂×C₅	D₃²	1	1	yes	characteristic
27	C₃²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	45	1	no	Sylow
29	C₂×C₃	—	2	1	no	—
30	C₂×C₃	D₃×D₅	1	2	yes	—
31	C₅	#627	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	9	1	no	—
33	C₄	—	15	2	no	—
34	C₃	—	2	1	no	—
35	C₃	#1204	1	2	yes	complemented
36	C₂	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₃⋊D₃)⋊D₅
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.