Subgroups — #10597032

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₂₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	D₇₅	—	2	1	no	—
7	D₃×C₂₅	—	2	1	no	—
8	#1203	—	5	1	no	maximal
9	C₂²×C₂₅	—	3	1	no	—
10	C₂×D₂₅	—	3	1	no	—
11	Dic₂₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₂₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₁₅	—	5	1	no	—
14	C₂×C₅×D₃	D₅	1	1	yes	characteristic
15	C₃×Dic₅	—	5	1	no	—
16	C₂×C₂₅	—	6	1	no	—
17	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
18	D₂₅	—	6	1	no	—
19	C₂²⋊D₅	—	15	1	no	—
20	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
21	D₁₅	—	10	1	no	—
22	C₅×D₃	—	2	1	no	—
23	C₂₅	D₁₂	1	1	yes	characteristic, complemented, Sylow
24	D₁₂	—	25	1	no	Hall
25	C₂²×C₅	—	3	1	no	—
26	C₂×D₅	—	15	1	no	—
27	Dic₅	—	5	1	no	—
28	C₃×C₅	C₂²⋊D₅	1	1	yes	characteristic
29	C₂×D₃	—	25	1	no	—
30	C₂×D₃	D₂₅	1	1	yes	characteristic, complemented
31	C₃×C₄	—	25	1	no	—
32	C₂×C₅	—	6	1	no	—
33	C₂×C₅	D₃×D₅	1	1	yes	characteristic
34	D₅	—	30	1	no	—
35	D₄	—	75	1	no	Sylow
36	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
37	D₃	—	2	1	no	—
38	D₃	—	50	1	no	—
39	C₅	#1203	1	1	yes	characteristic
40	C₂²	—	3	1	no	—
41	C₂²	—	75	1	no	—
42	C₄	—	25	1	no	—
43	C₃	C₂²⋊D₂₅	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	6	1	no	—
45	C₂	—	150	1	no	—
46	C₂	D₃×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₃×D₂₅
commutator, Fitting, cosocle	C₂×C₃×C₂₅	C₂²
Frattini	C₂×C₅	D₃×D₅
socle	C₂×C₃×C₅	C₂×D₅
hypocenter	C₃×C₂₅	D₄
LCS	G ▷ C₂×C₃×C₂₅ ▷ C₃×C₂₅
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₇₅	C₂	semidirect
2. C₂×D₃×C₂₅	C₂	semidirect
3. C₃×Dic₂₅	C₂	semidirect
11. Dic₂₅	D₃	semidirect
12. C₃×C₂₅	D₄	semidirect
23. C₂₅	D₁₂	semidirect
30. C₂×D₃	D₂₅	semidirect
43. C₃	C₂²⋊D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₇₅	2
C₂×D₃×C₂₅	2
C₃×Dic₂₅	2
C₂²⋊D₂₅	3
#1203	5