Subgroups — C₃⋊D₃×Dic₅ #67136

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₃⋊D₃
commutator, hypocenter	C₃²×C₅	C₂×C₄
Fitting, socle, cosocle	C₂×C₃²×C₅	C₂²
prime radical	C₂×C₅×C₃⋊D₃	C₂
LCS	G ▷ 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.