Subgroups — C₂×D₅×A₄ #6837

Order 240.

78 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	D₅×A₄	C₂	1	2	yes	maximal, direct product factor
3	C₂³×D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃×D₅	—	4	1	no	maximal
5	C₅×A₄	C₂²	1	1	yes	characteristic, complemented
6	C₂²×A₄	—	5	1	no	maximal, Hall
7	C₂³×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂²×D₅	—	3	1	no	—
9	C₂²×D₅	—	3	1	no	—
10	C₂²×D₅	—	3	2	no	—
11	C₂²×D₅	C₂×C₃	1	2	yes	complemented
12	C₂×C₃×C₅	—	4	1	no	—
13	C₃×D₅	—	4	2	no	—
14	C₂×A₄	—	5	2	no	—
15	C₂×A₄	D₅	1	1	yes	characteristic, direct product factor
16	C₂²×C₅	—	3	1	no	—
17	C₂²×C₅	—	3	1	no	—
18	C₂²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂×D₅	—	3	2	no	—
20	C₂×D₅	—	3	1	no	—
21	C₂×D₅	—	3	2	no	—
22	C₂×D₅	—	3	2	no	—
23	C₂×D₅	—	3	2	no	—
24	C₂×D₅	A₄	1	1	yes	characteristic, direct product factor
25	C₂⁴	—	5	1	no	Sylow
26	C₃×C₅	—	4	1	no	Hall
27	C₂²×C₃	—	20	1	no	—
28	A₄	C₂×D₅	1	1	yes	characteristic, direct product factor
29	C₂×C₅	—	3	1	no	—
30	C₂×C₅	—	3	1	no	—
31	C₂×C₅	C₂×A₄	1	1	yes	characteristic, complemented
32	D₅	—	3	2	no	—
33	D₅	C₂×A₄	1	2	yes	direct product factor
34	C₂³	—	5	2	no	—
35	C₂³	—	15	1	no	—
36	C₂³	—	15	2	no	—
37	C₂³	—	15	1	no	—
38	C₂³	C₃×D₅	1	1	yes	characteristic, complemented
39	C₂×C₃	—	4	1	no	—
40	C₂×C₃	—	20	2	no	—
41	C₅	C₂²×A₄	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	—	5	1	no	—
45	C₂²	—	15	2	no	—
46	C₂²	—	15	2	no	—
47	C₂²	—	15	2	no	—
48	C₂²	—	15	2	no	—
49	C₂²	—	15	1	no	—
50	C₂²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
51	C₃	—	4	1	no	Sylow
52	C₂	—	3	1	no	—
53	C₂	—	3	1	no	—
54	C₂	—	5	2	no	—
55	C₂	—	15	2	no	—
56	C₂	D₅×A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×A₄
commutator, cosocle, hypocenter	C₂²×C₅	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₅	C₂×C₃
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×A₄	C₂	semidirect
2. D₅×A₄	C₂	direct (N × H)
3. C₂³×D₅	C₃	semidirect
5. C₅×A₄	C₂²	semidirect
7. C₂³×C₅	C₂×C₃	semidirect
11. C₂²×D₅	C₂×C₃	semidirect
15. C₂×A₄	D₅	direct (N × H)
18. C₂²×C₅	C₂²×C₃	semidirect
24. C₂×D₅	A₄	direct (N × H)
28. A₄	C₂×D₅	direct (N × H)
31. C₂×C₅	C₂×A₄	semidirect
33. D₅	C₂×A₄	direct (N × H)
38. C₂³	C₃×D₅	semidirect
41. C₅	C₂²×A₄	semidirect
50. C₂²	C₂×C₃×D₅	semidirect
56. C₂	D₅×A₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×A₄	2
D₅×A₄	2
C₂³×D₅	3
C₂×C₃×D₅	4
C₂²×A₄	5

Subgroups — C2×D5×A4 #6837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×A₄ #6837