Subgroups — C₂×C₅×C₃⋊Dic₃ #67178

Order 360.

96 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
2	C₅×C₃⋊Dic₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×Dic₃	—	3	4	no	maximal
4	C₂×C₃²×C₅	C₄	1	2	yes	complemented
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅	D₃	1	4	yes	—
8	C₅×Dic₃	—	3	8	no	—
9	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₄×C₅	—	9	1	no	Hall
11	C₂²×C₃²	C₂×C₅	1	1	yes	characteristic
12	C₃⋊Dic₃	C₂×C₅	1	2	yes	direct product factor
13	C₂×C₃×C₅	Dic₃	1	8	yes	complemented
14	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
15	C₂×Dic₃	—	3	4	no	—
16	C₂²×C₅	C₃⋊D₃	1	1	yes	characteristic
17	C₄×C₅	—	9	2	no	—
18	C₂×C₃²	C₄×C₅	1	2	yes	complemented
19	C₂×C₃²	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅	C₂×Dic₃	1	4	yes	complemented
21	C₂²×C₃	C₅×D₃	1	4	yes	—
22	Dic₃	—	3	8	no	—
23	C₂×C₅	C₃⋊Dic₃	1	2	yes	direct product factor
24	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
25	C₃²	C₂×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄	—	9	1	no	Sylow
27	C₂×C₃	C₅×Dic₃	1	8	yes	complemented
28	C₂×C₃	C₂×C₅×D₃	1	4	yes	—
29	C₅	C₂×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₅×C₃⋊D₃	1	1	yes	characteristic
31	C₄	—	9	2	no	—
32	C₃	C₂×C₅×Dic₃	1	4	yes	complemented
33	C₂	C₅×C₃⋊Dic₃	1	2	yes	direct product factor
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.