Subgroups — C₂³×D₁₅ #6846

Order 240.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₂²	1	7	yes	complemented
5	C₂×D₁₅	C₂²	1	28	yes	direct product factor
6	C₂³×D₃	—	5	1	no	maximal, Hall
7	C₂³×C₅	D₃	1	1	yes	characteristic, complemented
8	C₂²×D₅	—	3	14	no	—
9	C₂×C₃×C₅	C₂³	1	7	yes	complemented
10	D₁₅	C₂³	1	8	yes	direct product factor
11	C₂³×C₃	D₅	1	1	yes	characteristic, complemented
12	C₂²×D₃	—	5	14	no	—
13	C₂²×C₅	C₂×D₃	1	7	yes	complemented
14	C₂×D₅	—	3	28	no	—
15	C₂⁴	—	15	1	no	Sylow
16	C₃×C₅	C₂⁴	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃	C₂×D₅	1	7	yes	complemented
18	C₂×D₃	—	5	28	no	—
19	C₂×C₅	C₂²×D₃	1	7	yes	complemented
20	D₅	—	3	8	no	—
21	C₂³	—	15	14	no	—
22	C₂³	D₁₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃	C₂²×D₅	1	7	yes	complemented
24	D₃	—	5	8	no	—
25	C₅	C₂³×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	15	28	no	—
27	C₂²	C₂×D₁₅	1	7	yes	direct product factor
28	C₃	C₂³×D₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	15	8	no	—
30	C₂	C₂²×D₁₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

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.