Subgroups — C₂×D₃×D₅ #1232

Order 120.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂

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.