Subgroups — C₂×C₅×D₁₅ #64504

Order 300.

48 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, complemented
2	C₅×D₁₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₅	—	3	1	no	maximal, Hall
4	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₃	—	5	1	no	maximal
7	C₂×C₅²	D₃	1	1	yes	characteristic, complemented
8	C₅×D₅	—	3	2	no	—
9	C₂×C₃×C₅	—	2	2	no	—
10	C₂×C₃×C₅	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅	C₂×C₅	1	1	yes	characteristic, complemented
12	D₁₅	C₂×C₅	1	2	yes	direct product factor
13	C₅×D₃	—	5	2	no	—
14	C₅²	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	15	1	no	—
16	C₂×D₅	—	3	1	no	—
17	C₃×C₅	—	2	2	no	—
18	C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
19	C₃×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×D₃	—	5	1	no	Hall
21	C₂×C₅	—	2	2	no	—
22	C₂×C₅	—	15	2	no	—
23	C₂×C₅	C₅×D₃	1	1	yes	characteristic, complemented
24	C₂×C₅	D₁₅	1	1	yes	characteristic, direct product factor
25	D₅	—	3	2	no	—
26	C₂×C₃	C₅×D₅	1	1	yes	characteristic, complemented
27	D₃	—	5	2	no	—
28	C₅	—	2	2	no	—
29	C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
30	C₅	C₂×D₁₅	1	1	yes	characteristic, direct product factor
31	C₂²	—	15	1	no	Sylow
32	C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	15	2	no	—
34	C₂	C₅×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅

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.