Subgroups — C₃×C₅×Dic₃ #4369

Order 180.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅	—	3	1	no	maximal
3	C₅×Dic₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅	—	2	1	no	—
7	C₂×C₃×C₅	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅	C₂×C₃	1	1	yes	characteristic
9	C₄×C₅	—	3	1	no	Hall
10	C₂×C₃²	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅	—	2	1	no	—
12	C₃×C₅	Dic₃	1	1	yes	characteristic, direct product factor
13	C₃×C₅	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃×C₄	—	3	1	no	—
15	Dic₃	C₃×C₅	1	1	yes	characteristic, direct product factor
16	C₂×C₅	C₃×D₃	1	1	yes	characteristic
17	C₃²	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	2	1	no	—
19	C₂×C₃	C₅×D₃	1	1	yes	characteristic
20	C₂×C₃	C₂×C₃×C₅	1	1	yes	characteristic
21	C₅	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₄	—	3	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	C₅×Dic₃	1	1	yes	characteristic, direct product factor
25	C₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented
26	C₂	C₃×C₅×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.