Subgroups — D₅×D₁₅ #64496

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	C₅×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅²	—	3	1	no	maximal, Hall
5	C₃×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₅	—	5	1	no	maximal
7	D₃×D₅	—	5	1	no	maximal
8	C₅⋊D₅	—	3	1	no	—
9	C₅×D₅	—	3	1	no	—
10	C₅×D₅	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅	—	5	1	no	—
12	D₁₅	—	5	1	no	—
13	D₁₅	—	5	1	no	—
14	D₁₅	—	10	2	no	—
15	D₁₅	D₅	1	1	yes	characteristic, direct product factor
16	C₃×D₅	D₅	1	1	yes	characteristic, complemented
17	C₅×D₃	—	5	1	no	—
18	C₅²	C₂×D₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₅	—	15	1	no	—
20	C₂×D₅	—	15	1	no	—
21	C₃×C₅	—	2	2	no	—
22	C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
24	C₂×D₃	—	25	1	no	Hall
25	C₂×C₅	—	5	1	no	—
26	C₂×C₅	—	15	1	no	—
27	D₅	—	3	1	no	—
28	D₅	—	15	1	no	—
29	D₅	—	15	1	no	—
30	D₅	—	30	2	no	—
31	D₅	D₁₅	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	5	1	no	—
33	D₃	—	5	1	no	—
34	D₃	—	25	1	no	—
35	C₅	—	2	2	no	—
36	C₅	D₃×D₅	1	1	yes	characteristic, complemented
37	C₅	C₂×D₁₅	1	1	yes	characteristic, complemented
38	C₂²	—	75	1	no	Sylow
39	C₃	D₅²	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	5	1	no	—
41	C₂	—	15	1	no	—
42	C₂	—	75	1	no	—

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

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.