Subgroups — C₃×C₂²⋊D₂₅ #10597038

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₂₅	—	2	1	no	—
6	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
7	C₃×D₂₅	—	2	1	no	—
8	C₃×C₂²⋊D₅	—	5	1	no	maximal
9	C₂²×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×D₂₅	C₂×C₃	1	1	yes	characteristic, complemented
11	Dic₂₅	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₃×C₅	D₅	1	1	yes	characteristic
14	C₂×C₃×D₅	—	5	1	no	—
15	C₃×Dic₅	—	5	1	no	—
16	C₂×C₂₅	—	2	1	no	—
17	C₂×C₂₅	C₂²×C₃	1	1	yes	characteristic
18	D₂₅	—	2	1	no	—
19	C₂²⋊D₅	—	5	1	no	—
20	C₂×C₃×C₅	—	2	1	no	—
21	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
22	C₃×D₅	—	10	1	no	—
23	C₂₅	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₄	—	25	1	no	Hall
25	C₂²×C₅	C₃×D₅	1	1	yes	characteristic
26	C₂×D₅	—	5	1	no	—
27	Dic₅	—	5	1	no	—
28	C₃×C₅	C₂²⋊D₅	1	1	yes	characteristic
29	C₂²×C₃	—	25	1	no	—
30	C₂²×C₃	D₂₅	1	1	yes	characteristic, complemented
31	C₃×C₄	—	25	1	no	—
32	C₂×C₅	—	2	1	no	—
33	C₂×C₅	C₂×C₃×D₅	1	1	yes	characteristic
34	D₅	—	10	1	no	—
35	D₄	—	25	1	no	Sylow
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	—	50	1	no	—
38	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
39	C₅	C₃×C₂²⋊D₅	1	1	yes	characteristic
40	C₂²	—	25	1	no	—
41	C₂²	C₃×D₂₅	1	1	yes	characteristic, complemented
42	C₄	—	25	1	no	—
43	C₃	C₂²⋊D₂₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	2	1	no	—
45	C₂	—	50	1	no	—
46	C₂	C₂×C₃×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₂₅
commutator, cosocle	C₂×C₂₅	C₂²×C₃
Frattini	C₂×C₅	C₂×C₃×D₅
Fitting	C₂²×C₃×C₂₅	C₂
socle	C₂×C₃×C₅	C₂×D₅
hypercenter	C₂²×C₃	D₂₅
hypocenter	C₂₅	C₃×D₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂₅	C₂	semidirect
2. C₂×C₃×D₂₅	C₂	semidirect
3. C₃×Dic₂₅	C₂	semidirect
4. C₂²⋊D₂₅	C₃	direct (N × H)
9. C₂²×C₂₅	C₂×C₃	semidirect
10. C₂×D₂₅	C₂×C₃	semidirect
11. Dic₂₅	C₂×C₃	semidirect
12. C₃×C₂₅	D₄	semidirect
23. C₂₅	C₃×D₄	semidirect
30. C₂²×C₃	D₂₅	semidirect
41. C₂²	C₃×D₂₅	semidirect
43. C₃	C₂²⋊D₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₂₅	2
C₂×C₃×D₂₅	2
C₃×Dic₂₅	2
C₂²⋊D₂₅	3
C₃×C₂²⋊D₅	5

Subgroups — C3×C22⋊D25 #10597038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊D₂₅ #10597038