Subgroups — C₂×C₅⋊S₄ #6836

Order 240.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊S₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂²⋊D₅	—	3	1	no	maximal, Hall
4	C₂×D₁₅	—	4	1	no	maximal
5	C₅×A₄	C₂²	1	1	yes	characteristic, complemented
6	C₂×S₄	—	5	1	no	maximal, Hall
7	C₂³×C₅	D₃	1	1	yes	characteristic, complemented
8	C₂²×D₅	—	3	1	no	—
9	C₂²⋊D₅	—	3	2	no	—
10	C₂²⋊D₅	—	3	2	no	—
11	C₂×Dic₅	—	3	1	no	—
12	C₂×C₃×C₅	—	4	1	no	—
13	D₁₅	—	4	2	no	—
14	C₂×A₄	D₅	1	1	yes	characteristic, complemented
15	S₄	—	5	2	no	—
16	C₂²×C₅	—	3	1	no	—
17	C₂²×C₅	—	3	1	no	—
18	C₂²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
19	C₂×D₅	—	3	2	no	—
20	C₂×D₅	—	6	1	no	—
21	C₂×D₅	—	6	1	no	—
22	Dic₅	—	3	2	no	—
23	C₂×D₄	—	15	1	no	Sylow
24	C₃×C₅	—	4	1	no	Hall
25	C₂×D₃	—	20	1	no	—
26	A₄	C₂×D₅	1	1	yes	characteristic, complemented
27	C₂×C₅	—	3	1	no	—
28	C₂×C₅	—	3	1	no	—
29	C₂×C₅	S₄	1	1	yes	characteristic, complemented
30	D₅	—	6	2	no	—
31	C₂³	—	15	1	no	—
32	C₂³	D₁₅	1	1	yes	characteristic, complemented
33	D₄	—	15	2	no	—
34	D₄	—	15	2	no	—
35	C₂×C₄	—	15	1	no	—
36	C₂×C₃	—	4	1	no	—
37	D₃	—	20	2	no	—
38	C₅	C₂×S₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	3	1	no	—
40	C₂²	—	3	1	no	—
41	C₂²	—	15	2	no	—
42	C₂²	—	30	1	no	—
43	C₂²	—	30	1	no	—
44	C₂²	C₂×D₁₅	1	1	yes	characteristic, complemented
45	C₄	—	15	2	no	—
46	C₃	—	4	1	no	Sylow
47	C₂	—	3	1	no	—
48	C₂	—	3	1	no	—
49	C₂	—	30	2	no	—
50	C₂	C₅⋊S₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊S₄
commutator, cosocle, hypocenter	C₅×A₄	C₂²
Frattini	C₁	G
Fitting, socle	C₂³×C₅	D₃
LCS	G ▷ C₅×A₄
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.