Subgroups — C₂³×C₃×D₅ #6844

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×C₃×D₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₂²	1	7	yes	complemented
5	C₂×C₃×D₅	C₂²	1	28	yes	direct product factor
6	C₂⁴×C₃	—	5	1	no	maximal, Hall
7	C₂³×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂²×D₅	C₂×C₃	1	14	yes	direct product factor
9	C₂×C₃×C₅	C₂³	1	7	yes	complemented
10	C₃×D₅	C₂³	1	8	yes	direct product factor
11	C₂³×C₃	—	5	14	no	—
12	C₂³×C₃	D₅	1	1	yes	characteristic, direct product factor
13	C₂²×C₅	C₂²×C₃	1	7	yes	complemented
14	C₂×D₅	C₂²×C₃	1	28	yes	direct product factor
15	C₂⁴	—	5	1	no	Sylow
16	C₃×C₅	C₂⁴	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃	—	5	28	no	—
18	C₂²×C₃	C₂×D₅	1	7	yes	direct product factor
19	C₂×C₅	C₂³×C₃	1	7	yes	complemented
20	D₅	C₂³×C₃	1	8	yes	direct product factor
21	C₂³	—	5	14	no	—
22	C₂³	C₃×D₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃	—	5	8	no	—
24	C₂×C₃	C₂²×D₅	1	7	yes	direct product factor
25	C₅	C₂⁴×C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	5	28	no	—
27	C₂²	C₂×C₃×D₅	1	7	yes	direct product factor
28	C₃	C₂³×D₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	5	8	no	—
30	C₂	C₂²×C₃×D₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₅
commutator, cosocle, hypocenter	C₅	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₅	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂³×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.