Subgroups — C₃×D₅² #64493

Order 300.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅	C₂	1	2	yes	maximal, complemented
3	D₅²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅	—	5	2	no	maximal
6	C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×C₅	—	5	2	no	—
9	C₃×D₅	—	5	2	no	—
10	C₃×D₅	—	10	2	no	—
11	C₃×D₅	D₅	1	2	yes	direct product factor
12	C₅²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×D₅	—	5	2	no	—
14	C₃×C₅	—	2	2	no	—
15	C₃×C₅	C₂×D₅	1	2	yes	complemented
16	C₂²×C₃	—	25	1	no	Hall
17	C₂×C₅	—	5	2	no	—
18	D₅	—	5	2	no	—
19	D₅	—	10	2	no	—
20	D₅	C₃×D₅	1	2	yes	direct product factor
21	C₂×C₃	—	5	2	no	—
22	C₂×C₃	—	25	1	no	—
23	C₅	—	2	2	no	—
24	C₅	C₂×C₃×D₅	1	2	yes	complemented
25	C₂²	—	25	1	no	Sylow
26	C₃	D₅²	1	1	yes	characteristic, direct product factor, Sylow
27	C₂	—	5	2	no	—
28	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃

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.