Subgroups — C₅×C₂²⋊(C₄²⋊C₃) #11755472

Order 960.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂²⋊A₄	—	4	1	no	maximal
3	C₅×C₄²⋊C₃	—	4	4	no	maximal
4	C₂²⋊(C₄²⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₄×C₅	—	3	1	no	—
6	C₂×C₄²×C₅	—	3	4	no	—
7	C₂⁴×C₅	A₄	1	1	yes	characteristic
8	C₂²×C₄×C₅	—	3	6	no	—
9	C₂²×C₄×C₅	—	3	8	no	—
10	C₄²×C₅	—	3	4	no	—
11	C₄²×C₅	A₄	1	4	yes	complemented
12	C₂²×C₄²	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
13	C₅×A₄	—	16	4	no	—
14	C₅×A₄	—	16	1	no	—
15	C₂²⋊A₄	—	4	1	no	—
16	C₄²⋊C₃	—	4	4	no	—
17	C₂³×C₅	—	3	4	no	—
18	C₂³×C₅	—	3	1	no	—
19	C₂×C₄×C₅	—	3	24	no	—
20	C₂×C₄×C₅	—	3	4	no	—
21	C₂³×C₄	—	3	1	no	—
22	C₂×C₄²	—	3	4	no	—
23	C₂²×C₅	—	3	6	no	—
24	C₂²×C₅	—	3	4	no	—
25	C₂²×C₅	C₄²⋊C₃	1	4	yes	complemented
26	C₂²×C₅	C₂²⋊A₄	1	1	yes	characteristic
27	C₄×C₅	—	3	8	no	—
28	C₂⁴	C₅×A₄	1	1	yes	characteristic
29	C₂²×C₄	—	3	6	no	—
30	C₂²×C₄	—	3	8	no	—
31	C₄²	—	3	4	no	—
32	C₄²	C₅×A₄	1	4	yes	complemented
33	C₃×C₅	—	64	1	no	Hall
34	A₄	—	16	4	no	—
35	A₄	—	16	1	no	—
36	C₂×C₅	—	3	1	no	—
37	C₂×C₅	—	3	4	no	—
38	C₂³	—	3	4	no	—
39	C₂³	—	3	1	no	—
40	C₂×C₄	—	3	24	no	—
41	C₂×C₄	—	3	4	no	—
42	C₅	C₂²⋊(C₄²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	3	6	no	—
44	C₂²	—	3	4	no	—
45	C₂²	C₅×C₄²⋊C₃	1	4	yes	complemented
46	C₂²	C₅×C₂²⋊A₄	1	1	yes	characteristic
47	C₄	—	3	8	no	—
48	C₃	—	64	1	no	Sylow
49	C₂	—	3	1	no	—
50	C₂	—	3	4	no	—

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₄²	C₃×C₅
Frattini	C₂²	C₅×C₂²⋊A₄
Fitting	C₂²×C₄²×C₅	C₃
socle	C₂⁴×C₅	A₄
LCS	G ▷ C₂²×C₄²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄²×C₅	C₃	semidirect
4. C₂²⋊(C₄²⋊C₃)	C₅	direct (N × H)
11. C₄²×C₅	A₄	semidirect
12. C₂²×C₄²	C₃×C₅	semidirect
25. C₂²×C₅	C₄²⋊C₃	semidirect
32. C₄²	C₅×A₄	semidirect
42. C₅	C₂²⋊(C₄²⋊C₃)	direct (N × H)
45. C₂²	C₅×C₄²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₅	3
C₅×C₂²⋊A₄	4
C₅×C₄²⋊C₃	4
C₂²⋊(C₄²⋊C₃)	5

Subgroups — C5×C22⋊(C42⋊C3) #11755472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊(C₄²⋊C₃) #11755472