Subgroups — C₂×C₅×C₄²⋊C₃ #91578

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₄²×C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×A₄	—	4	1	no	maximal
4	C₂×C₄²⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₄×C₅	—	3	1	no	—
6	C₄²×C₅	—	3	1	no	—
7	C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×A₄	—	4	1	no	—
9	C₄²⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor
10	C₂³×C₅	A₄	1	1	yes	characteristic
11	C₂×C₄×C₅	—	3	2	no	—
12	C₂×C₄×C₅	—	3	2	no	—
13	C₂×C₄×C₅	—	3	1	no	—
14	C₂×C₄×C₅	—	3	1	no	—
15	C₂×C₄²	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₅	—	16	1	no	—
17	C₂×A₄	—	4	1	no	—
18	C₂²×C₅	—	3	1	no	—
19	C₂²×C₅	—	3	1	no	—
20	C₂²×C₅	C₂×A₄	1	1	yes	characteristic
21	C₄×C₅	—	3	2	no	—
22	C₄×C₅	—	3	2	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₄²	—	3	1	no	—
25	C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	C₃×C₅	—	16	1	no	Hall
27	A₄	—	4	1	no	—
28	C₂×C₅	—	3	1	no	—
29	C₂×C₅	—	3	1	no	—
30	C₂×C₅	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
31	C₂³	C₅×A₄	1	1	yes	characteristic
32	C₂×C₄	—	3	2	no	—
33	C₂×C₄	—	3	2	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₃	—	16	1	no	—
37	C₅	C₂×C₄²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	—	3	1	no	—
39	C₂²	—	3	1	no	—
40	C₂²	C₂×C₅×A₄	1	1	yes	characteristic
41	C₄	—	3	2	no	—
42	C₄	—	3	2	no	—
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	1	no	—
45	C₂	—	3	1	no	—
46	C₂	C₅×C₄²⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₂×C₄²×C₅	C₃
socle	C₂³×C₅	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₄²⋊C₃	C₂	direct (N × H)
2. C₂×C₄²×C₅	C₃	semidirect
4. C₂×C₄²⋊C₃	C₅	direct (N × H)
7. C₄²×C₅	C₂×C₃	semidirect
9. C₄²⋊C₃	C₂×C₅	direct (N × H)
15. C₂×C₄²	C₃×C₅	semidirect
25. C₄²	C₂×C₃×C₅	semidirect
30. C₂×C₅	C₄²⋊C₃	direct (N × H)
37. C₅	C₂×C₄²⋊C₃	direct (N × H)
46. C₂	C₅×C₄²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄²⋊C₃	2
C₂×C₄²×C₅	3
C₂×C₅×A₄	4
C₂×C₄²⋊C₃	5

Subgroups — C2×C5×C42⋊C3 #91578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₄²⋊C₃ #91578