Subgroups — C₅×Dic₁₅ #64476

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	—	3	1	no	maximal, Hall
3	C₃×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₃	—	5	1	no	maximal
6	C₂×C₅²	D₃	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	Dic₃	1	1	yes	characteristic, complemented, Sylow
11	C₄×C₅	—	15	1	no	—
12	Dic₅	—	3	1	no	—
13	C₃×C₅	—	2	2	no	—
14	C₃×C₅	Dic₅	1	1	yes	characteristic, complemented
15	C₃×C₅	C₄×C₅	1	1	yes	characteristic, complemented
16	Dic₃	—	5	1	no	Hall
17	C₂×C₅	—	2	2	no	—
18	C₂×C₅	C₅×D₃	1	1	yes	characteristic
19	C₂×C₅	D₁₅	1	1	yes	characteristic
20	C₂×C₃	C₅×D₅	1	1	yes	characteristic
21	C₅	—	2	2	no	—
22	C₅	C₅×Dic₃	1	1	yes	characteristic, complemented
23	C₅	Dic₁₅	1	1	yes	characteristic, direct product factor
24	C₄	—	15	1	no	Sylow
25	C₃	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
26	C₂	C₅×D₁₅	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.