Subgroups — C₃×C₅×Dic₅ #64473

Order 300.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄×C₅	—	5	1	no	maximal
5	C₃×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅²	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅	—	2	2	no	—
8	C₂×C₃×C₅	D₅	1	1	yes	characteristic
9	C₂×C₃×C₅	C₂×C₅	1	1	yes	characteristic
10	C₅²	C₃×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₄×C₅	—	5	1	no	—
12	Dic₅	C₃×C₅	1	1	yes	characteristic, direct product factor
13	C₃×C₅	—	2	2	no	—
14	C₃×C₅	Dic₅	1	1	yes	characteristic, direct product factor
15	C₃×C₅	C₄×C₅	1	1	yes	characteristic, complemented
16	C₃×C₄	—	5	1	no	Hall
17	C₂×C₅	—	2	2	no	—
18	C₂×C₅	C₃×D₅	1	1	yes	characteristic
19	C₂×C₅	C₂×C₃×C₅	1	1	yes	characteristic
20	C₂×C₃	C₅×D₅	1	1	yes	characteristic
21	C₅	—	2	2	no	—
22	C₅	C₃×Dic₅	1	1	yes	characteristic, direct product factor
23	C₅	C₃×C₄×C₅	1	1	yes	characteristic, complemented
24	C₄	—	5	1	no	Sylow
25	C₃	C₅×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×C₅×D₅	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.