Subgroups — (C₃⋊D₃)⋊D₅ #4385

Order 180.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅	C₂	1	2	yes	maximal, complemented
3	D₃×D₅	—	3	2	no	maximal
4	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃²	—	5	1	no	maximal, Hall
6	D₁₅	D₃	1	2	yes	complemented
7	C₃×D₅	—	3	2	no	—
8	C₅×D₃	—	3	2	no	—
9	C₅×D₃	—	6	1	no	—
10	C₂×D₅	—	9	1	no	Hall
11	C₃⋊D₃	D₅	1	1	yes	characteristic, complemented
12	C₃×D₃	—	5	2	no	—
13	C₃×C₅	—	2	1	no	—
14	C₃×C₅	C₂×D₃	1	2	yes	complemented
15	C₂×D₃	—	15	2	no	—
16	C₂×C₅	—	9	1	no	—
17	D₅	—	3	2	no	—
18	C₃²	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	15	2	no	—
20	D₃	—	3	2	no	—
21	D₃	—	5	2	no	—
22	D₃	—	6	1	no	—
23	C₅	D₃²	1	1	yes	characteristic, complemented, Sylow
24	C₂²	—	45	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	D₃×D₅	1	2	yes	complemented
27	C₂	—	9	1	no	—
28	C₂	—	15	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁

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.