Subgroups — C₂²×C₃⋊D₁₅ #67231

Order 360.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊D₁₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₁₅	—	3	4	no	maximal
4	C₂×C₃²×C₅	C₂²	1	3	yes	complemented
5	C₃⋊D₁₅	C₂²	1	4	yes	direct product factor
6	C₂²×C₃⋊D₃	—	5	1	no	maximal, Hall
7	C₂²×C₃×C₅	D₃	1	4	yes	complemented
8	C₂×D₁₅	—	3	24	no	—
9	C₃²×C₅	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×D₅	—	9	1	no	Hall
11	C₂²×C₃²	D₅	1	1	yes	characteristic, complemented
12	C₂×C₃⋊D₃	—	5	6	no	—
13	C₂×C₃×C₅	C₂×D₃	1	12	yes	complemented
14	D₁₅	—	3	16	no	—
15	C₂²×D₃	—	15	4	no	—
16	C₂²×C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₂×D₅	—	9	6	no	—
18	C₂×C₃²	C₂×D₅	1	3	yes	complemented
19	C₃⋊D₃	—	5	4	no	—
20	C₃×C₅	C₂²×D₃	1	4	yes	complemented
21	C₂²×C₃	D₁₅	1	4	yes	complemented
22	C₂×D₃	—	15	24	no	—
23	C₂×C₅	C₂×C₃⋊D₃	1	3	yes	complemented
24	D₅	—	9	4	no	—
25	C₃²	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	45	1	no	Sylow
27	C₂×C₃	C₂×D₁₅	1	12	yes	complemented
28	D₃	—	15	16	no	—
29	C₅	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	45	6	no	—
31	C₂²	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×D₁₅	1	4	yes	complemented
33	C₂	—	45	4	no	—
34	C₂	C₂×C₃⋊D₁₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂²

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.