Subgroups — C₃×C₅⋊S₄ #67209

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊S₄	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂²⋊D₅	—	3	1	no	maximal
4	C₃×D₁₅	—	4	1	no	maximal
5	C₃×S₄	—	5	1	no	maximal, Hall
6	C₂²×C₃×C₅	D₃	1	1	yes	characteristic, complemented
7	C₂×C₃×D₅	—	3	1	no	—
8	C₅×A₄	—	2	1	no	—
9	C₅×A₄	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×Dic₅	—	3	1	no	—
11	C₃²×C₅	—	4	1	no	Hall
12	C₂²⋊D₅	—	3	1	no	Hall
13	C₃×A₄	D₅	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅	—	3	1	no	—
15	D₁₅	—	4	1	no	—
16	C₃×D₅	—	6	1	no	—
17	S₄	—	5	1	no	—
18	C₃×D₄	—	15	1	no	—
19	C₂²×C₅	C₃×D₃	1	1	yes	characteristic, complemented
20	C₂×D₅	—	3	1	no	—
21	Dic₅	—	3	1	no	—
22	C₃×D₃	—	20	1	no	—
23	C₃×C₅	—	4	1	no	—
24	C₃×C₅	—	8	1	no	—
25	C₃×C₅	S₄	1	1	yes	characteristic, complemented
26	C₂²×C₃	—	15	1	no	—
27	C₂²×C₃	D₁₅	1	1	yes	characteristic, complemented
28	A₄	—	2	1	no	—
29	A₄	C₃×D₅	1	1	yes	characteristic, complemented
30	C₃×C₄	—	15	1	no	—
31	C₂×C₅	—	3	1	no	—
32	D₅	—	6	1	no	—
33	C₃²	—	4	1	no	Sylow
34	D₄	—	15	1	no	Sylow
35	C₂×C₃	—	3	1	no	—
36	C₂×C₃	—	30	1	no	—
37	D₃	—	20	1	no	—
38	C₅	C₃×S₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	15	1	no	—
40	C₂²	C₃×D₁₅	1	1	yes	characteristic, complemented
41	C₄	—	15	1	no	—
42	C₃	—	4	1	no	—
43	C₃	—	8	1	no	—
44	C₃	C₅⋊S₄	1	1	yes	characteristic, direct product factor
45	C₂	—	3	1	no	—
46	C₂	—	30	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅⋊S₄
commutator, cosocle, hypocenter	C₅×A₄	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅	D₃
LCS	G ▷ C₅×A₄
UCS	C₁ ◁ C₃

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.