Subgroups — C₅×C₄⋊(C₃⋊D₃) #67177

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	2	yes	maximal, complemented
2	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₂	—	3	4	no	maximal
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	C₅×C₃⋊D₃	—	2	2	no	—
6	C₄⋊(C₃⋊D₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×D₃	—	3	8	no	—
8	C₃×C₄×C₅	D₃	1	4	yes	complemented
9	C₃²×C₅	D₄	1	1	yes	characteristic, complemented, Hall
10	C₅×D₄	—	9	1	no	Hall
11	C₂×C₃⋊D₃	C₂×C₅	1	2	yes	complemented
12	C₃²×C₄	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
14	C₅×D₃	—	6	8	no	—
15	D₁₂	—	3	4	no	—
16	C₂²×C₅	—	9	2	no	—
17	C₄×C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₂×C₃²	C₂²×C₅	1	1	yes	characteristic
19	C₃⋊D₃	—	2	2	no	—
20	C₃×C₅	D₁₂	1	4	yes	complemented
21	C₂×D₃	—	3	8	no	—
22	C₃×C₄	C₅×D₃	1	4	yes	complemented
23	C₂×C₅	—	18	2	no	—
24	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
25	C₃²	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
26	D₄	—	9	1	no	Sylow
27	C₂×C₃	C₂×C₅×D₃	1	4	yes	—
28	D₃	—	6	8	no	—
29	C₅	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	—	9	2	no	—
31	C₄	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
32	C₃	C₅×D₁₂	1	4	yes	complemented
33	C₂	—	18	2	no	—
34	C₂	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic

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.