Subgroups — #67×C₂₅ #10597043

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×D₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	—	2	1	no	—
6	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
7	D₃×C₂₅	—	2	1	no	—
8	C₅×#67	C₅	1	1	yes	maximal, characteristic
9	C₂²×C₂₅	—	3	1	no	—
10	C₂²×C₂₅	D₃	1	1	yes	characteristic, complemented
11	C₄×C₂₅	—	3	1	no	—
12	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₃×C₅	C₂×C₅	1	1	yes	characteristic
14	C₂×C₅×D₃	C₂×C₅	1	1	yes	characteristic
15	C₅×Dic₃	C₂×C₅	1	1	yes	characteristic
16	C₂×C₂₅	—	2	1	no	—
17	C₂×C₂₅	—	6	1	no	—
18	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
19	C₅×D₄	—	3	1	no	—
20	C₂×C₃×C₅	—	2	1	no	—
21	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
22	C₅×D₃	—	2	1	no	—
23	C₂₅	#67	1	1	yes	characteristic, direct product factor, Sylow
24	#67	C₂₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅	—	3	1	no	—
26	C₂²×C₅	C₅×D₃	1	1	yes	characteristic
27	C₄×C₅	—	3	1	no	—
28	C₃×C₅	C₅×D₄	1	1	yes	characteristic
29	C₂²×C₃	C₂×C₂₅	1	1	yes	characteristic, complemented
30	C₂×D₃	C₂×C₂₅	1	1	yes	characteristic, complemented
31	Dic₃	C₂×C₂₅	1	1	yes	characteristic, complemented
32	C₂×C₅	—	2	1	no	—
33	C₂×C₅	—	6	1	no	—
34	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
35	D₄	—	3	1	no	Sylow
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	C₂²×C₂₅	1	1	yes	characteristic
38	D₃	—	2	1	no	—
39	C₅	C₅×#67	1	1	yes	characteristic
40	C₂²	—	3	1	no	—
41	C₂²	D₃×C₂₅	1	1	yes	characteristic, complemented
42	C₄	—	3	1	no	—
43	C₃	D₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	2	1	no	—
45	C₂	—	6	1	no	—
46	C₂	C₂×D₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	C₂×D₃
commutator	C₂×C₃	C₂²×C₂₅
Frattini	C₂×C₅	C₂×C₅×D₃
Fitting	C₂²×C₃×C₂₅	C₂
socle, cosocle	C₂×C₃×C₅	C₂²×C₅
prime radical	C₅×#67	C₅
hypercenter	C₂²×C₂₅	D₃
hypocenter	C₃	D₄×C₂₅
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₂₅ ◁ C₂²×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂₅	C₂	semidirect
2. C₂×D₃×C₂₅	C₂	semidirect
3. Dic₃×C₂₅	C₂	semidirect
10. C₂²×C₂₅	D₃	semidirect
12. C₃×C₂₅	D₄	semidirect
23. C₂₅	#67	direct (N × H)
24. #67	C₂₅	direct (N × H)
29. C₂²×C₃	C₂×C₂₅	semidirect
30. C₂×D₃	C₂×C₂₅	semidirect
31. Dic₃	C₂×C₂₅	semidirect
41. C₂²	D₃×C₂₅	semidirect
43. C₃	D₄×C₂₅	semidirect

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×D₃×C₂₅	2
Dic₃×C₂₅	2
D₄×C₂₅	3
C₅×#67	5

Subgroups — #67×C25 #10597043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #67×C₂₅ #10597043