Subgroups — C₅×A₅⋊C₄ #11925263

Order 1200.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×A₅	C₂	1	1	yes	maximal, characteristic
2	C₅×A₅	C₄	1	1	yes	characteristic, complemented
3	C₅×SL(2,ℤ/4)	—	5	1	no	maximal
4	A₅⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅×AGL(1,𝔽₅)	—	6	1	no	maximal
6	C₂×C₅×A₄	—	5	1	no	—
7	C₂×A₅	C₂×C₅	1	1	yes	characteristic
8	C₄×C₅×D₃	—	10	1	no	maximal
9	C₂×C₅×D₅	—	6	1	no	—
10	C₅×AGL(1,𝔽₅)	—	6	2	no	—
11	C₅×C₂²⋊C₄	—	15	1	no	—
12	C₂×C₅×D₃	—	10	1	no	—
13	C₅×A₄	—	5	1	no	—
14	A₅	C₄×C₅	1	1	yes	characteristic, complemented
15	C₃×C₄×C₅	—	10	1	no	—
16	C₅×Dic₃	—	10	1	no	—
17	C₂×C₅²	—	6	1	no	—
18	C₅×D₅	—	6	1	no	—
19	C₅×D₅	—	6	1	no	—
20	SL(2,ℤ/4)	—	5	1	no	Hall
21	C₂³×C₅	—	5	1	no	—
22	C₂×AGL(1,𝔽₅)	—	6	1	no	—
23	C₂×C₄×C₅	—	15	1	no	—
24	C₂×C₄×C₅	—	15	1	no	—
25	C₂×C₃×C₅	—	10	1	no	—
26	C₅×D₃	—	10	1	no	—
27	C₅×D₃	—	10	1	no	—
28	C₅²	—	6	1	no	Sylow
29	C₂×A₄	—	5	1	no	—
30	C₄×D₃	—	10	1	no	—
31	C₂²×C₅	—	5	1	no	—
32	C₂²×C₅	—	15	1	no	—
33	C₂²×C₅	—	15	1	no	—
34	C₂×D₅	—	6	1	no	—
35	AGL(1,𝔽₅)	—	6	2	no	—
36	C₄×C₅	—	10	1	no	—
37	C₄×C₅	—	30	1	no	—
38	C₂²⋊C₄	—	15	1	no	Sylow
39	C₃×C₅	—	10	1	no	—
40	C₂×D₃	—	10	1	no	—
41	A₄	—	5	1	no	—
42	C₃×C₄	—	10	1	no	—
43	Dic₃	—	10	1	no	—
44	C₂×C₅	—	6	1	no	—
45	C₂×C₅	—	15	1	no	—
46	C₂×C₅	—	15	1	no	—
47	C₂×C₅	—	24	1	no	—
48	C₂×C₅	S₅	1	1	yes	characteristic
49	D₅	—	6	1	no	—
50	D₅	—	6	1	no	—
51	C₂³	—	5	1	no	—
52	C₂×C₄	—	15	1	no	—
53	C₂×C₄	—	15	1	no	—
54	C₂×C₃	—	10	1	no	—
55	D₃	—	10	1	no	—
56	D₃	—	10	1	no	—
57	C₅	—	6	1	no	—
58	C₅	—	24	1	no	—
59	C₅	A₅⋊C₄	1	1	yes	characteristic, direct product factor
60	C₂²	—	5	1	no	—
61	C₂²	—	15	1	no	—
62	C₂²	—	15	1	no	—
63	C₄	—	10	1	no	—
64	C₄	—	30	1	no	—
65	C₃	—	10	1	no	Sylow
66	C₂	—	15	1	no	—
67	C₂	—	15	1	no	—
68	C₂	C₅×S₅	1	1	yes	characteristic

	subgroup	G/H
center, Fitting, hypercenter	C₂×C₅	S₅
commutator, hypocenter	A₅	C₄×C₅
Frattini	C₂	C₅×S₅
socle, prime radical	C₂×C₅×A₅	C₂
cosocle	C₂×A₅	C₂×C₅
LCS	G ▷ A₅
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×A₅	C₄	semidirect
4. A₅⋊C₄	C₅	direct (N × H)
14. A₅	C₄×C₅	semidirect
59. C₅	A₅⋊C₄	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×A₅	2
C₅×SL(2,ℤ/4)	5
A₅⋊C₄	5
C₂×C₅×AGL(1,𝔽₅)	6
C₄×C₅×D₃	10

Subgroups — C5×A5⋊C4 #11925263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×A₅⋊C₄ #11925263