Subgroups — C₂×S₅ #6828

Order 240.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	S₅	C₂	1	2	yes	maximal, direct product factor
3	A₅	C₂²	1	1	yes	characteristic, complemented
4	C₂×S₄	—	5	1	no	maximal, Hall
5	C₂×AGL(1,𝔽₅)	—	6	1	no	maximal
6	C₂²×D₃	—	10	1	no	maximal
7	C₂×A₄	—	5	1	no	—
8	S₄	—	5	2	no	—
9	C₂×D₅	—	6	1	no	—
10	AGL(1,𝔽₅)	—	6	2	no	—
11	C₂×D₄	—	15	1	no	Sylow
12	C₂²×C₃	—	10	1	no	—
13	C₂×D₃	—	10	1	no	—
14	C₂×D₃	—	10	2	no	—
15	C₂×D₃	—	10	1	no	—
16	C₂×D₃	—	10	2	no	—
17	A₄	—	5	1	no	—
18	C₂×C₅	—	6	1	no	—
19	D₅	—	6	1	no	—
20	D₅	—	6	1	no	—
21	C₂³	—	5	1	no	—
22	C₂³	—	15	1	no	—
23	D₄	—	15	2	no	—
24	D₄	—	15	2	no	—
25	C₂×C₄	—	15	1	no	—
26	C₂×C₃	—	10	2	no	—
27	C₂×C₃	—	10	1	no	—
28	D₃	—	10	2	no	—
29	D₃	—	10	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	Sylow
32	C₂²	—	5	1	no	—
33	C₂²	—	10	1	no	—
34	C₂²	—	15	2	no	—
35	C₂²	—	15	1	no	—
36	C₂²	—	15	1	no	—
37	C₂²	—	30	1	no	—
38	C₄	—	15	2	no	—
39	C₃	—	10	1	no	Sylow
40	C₂	—	10	2	no	—
41	C₂	—	15	1	no	—
42	C₂	—	15	1	no	—
43	C₂	S₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, Fitting, hypercenter	C₂	S₅
commutator, cosocle, hypocenter	A₅	C₂²
Frattini	C₁	G
socle	C₂×A₅	C₂
LCS	G ▷ A₅
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.