Subgroups — C₂³×C₅×D₃ #6845

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×C₅×D₃	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₂²	1	7	yes	complemented
5	C₂×C₅×D₃	C₂²	1	28	yes	direct product factor
6	C₂³×D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₅	—	3	14	no	—
8	C₂³×C₅	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₅	C₂³	1	7	yes	complemented
10	C₅×D₃	C₂³	1	8	yes	direct product factor
11	C₂³×C₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₂²×D₃	C₂×C₅	1	14	yes	direct product factor
13	C₂²×C₅	—	3	28	no	—
14	C₂²×C₅	C₂×D₃	1	7	yes	direct product factor
15	C₂⁴	—	3	1	no	Sylow
16	C₃×C₅	C₂⁴	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃	C₂²×C₅	1	7	yes	complemented
18	C₂×D₃	C₂²×C₅	1	28	yes	direct product factor
19	C₂×C₅	—	3	8	no	—
20	C₂×C₅	C₂²×D₃	1	7	yes	direct product factor
21	C₂³	—	3	14	no	—
22	C₂³	C₅×D₃	1	1	yes	characteristic, direct product factor
23	C₂×C₃	C₂³×C₅	1	7	yes	complemented
24	D₃	C₂³×C₅	1	8	yes	direct product factor
25	C₅	C₂³×D₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	—	3	28	no	—
27	C₂²	C₂×C₅×D₃	1	7	yes	direct product factor
28	C₃	C₂⁴×C₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	8	no	—
30	C₂	C₂²×C₅×D₃	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₅	D₃
commutator, cosocle, hypocenter	C₃	C₂⁴×C₅
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₅	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×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.