Subgroups — C₄×C₂²⋊(C₅²⋊C₃) #11925672

Order 1200.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²⋊(C₅²⋊C₃)	C₄	1	1	yes	characteristic, direct product factor
4	C₄×C₅²⋊C₃	—	4	1	no	maximal
5	C₂³×C₅²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄×C₅²	—	3	1	no	—
7	C₂×C₄×C₅²	—	3	1	no	—
8	C₂×C₅²⋊C₃	—	4	1	no	—
9	C₂²×C₅²	—	3	1	no	—
10	C₂²×C₅²	—	3	1	no	—
11	C₂²×C₅²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₄×C₅²	—	3	1	no	—
13	C₄×C₅²	A₄	1	1	yes	characteristic, complemented
14	C₂²×C₄×C₅	—	3	2	no	—
15	C₅²⋊C₃	—	4	1	no	Hall
16	C₂×C₅²	—	3	1	no	—
17	C₂×C₅²	—	3	1	no	—
18	C₂×C₅²	C₂×A₄	1	1	yes	characteristic
19	C₄×A₄	—	25	1	no	maximal, Hall
20	C₂³×C₅	—	3	2	no	—
21	C₂×C₄×C₅	—	3	6	no	—
22	C₂×C₄×C₅	—	3	6	no	—
23	C₅²	C₄×A₄	1	1	yes	characteristic, complemented, Sylow
24	C₂×A₄	—	25	1	no	—
25	C₂²×C₅	—	3	6	no	—
26	C₂²×C₅	—	3	6	no	—
27	C₂²×C₅	—	3	2	no	—
28	C₄×C₅	—	3	6	no	—
29	C₄×C₅	—	3	2	no	—
30	C₂²×C₄	C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	A₄	—	25	1	no	—
32	C₃×C₄	—	100	1	no	—
33	C₂×C₅	—	3	6	no	—
34	C₂×C₅	—	3	6	no	—
35	C₂×C₅	—	3	2	no	—
36	C₂³	C₂×C₅²⋊C₃	1	1	yes	characteristic
37	C₂×C₄	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₃	—	100	1	no	—
40	C₅	—	3	2	no	—
41	C₂²	—	3	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented
44	C₄	—	3	1	no	—
45	C₄	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
46	C₃	—	100	1	no	Sylow
47	C₂	—	3	1	no	—
48	C₂	—	3	1	no	—
49	C₂	C₂×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₂²⋊(C₅²⋊C₃)
commutator, hypocenter	C₂²×C₅²	C₃×C₄
Frattini	C₂	C₂×C₂²⋊(C₅²⋊C₃)
Fitting	C₂²×C₄×C₅²	C₃
socle, cosocle	C₂³×C₅²	C₂×C₃
prime radical	C₂×C₂²⋊(C₅²⋊C₃)	C₂
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₅²	C₃	semidirect
3. C₂²⋊(C₅²⋊C₃)	C₄	direct (N × H)
11. C₂²×C₅²	C₃×C₄	semidirect
13. C₄×C₅²	A₄	semidirect
23. C₅²	C₄×A₄	semidirect
30. C₂²×C₄	C₅²⋊C₃	semidirect
43. C₂²	C₄×C₅²⋊C₃	semidirect
45. C₄	C₂²⋊(C₅²⋊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
C₂×C₂²⋊(C₅²⋊C₃)	2
C₂²×C₄×C₅²	3
C₄×C₅²⋊C₃	4
C₄×A₄	25

Subgroups — C4×C22⋊(C52⋊C3) #11925672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊(C₅²⋊C₃) #11925672