Subgroups — C₂×C₃×#1035 #10597056

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#1035	C₂	1	2	yes	maximal, direct product factor
3	C₂×#1035	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₂₅	C₄	1	1	yes	characteristic, complemented
5	C₃×D₂₅	C₄	1	1	yes	characteristic, complemented
6	C₃×D₂₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×AGL(1,𝔽₅)	—	5	1	no	maximal
8	C₂×D₂₅	C₂×C₃	1	1	yes	characteristic
9	#1035	C₂×C₃	1	2	yes	direct product factor
10	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₅	—	5	1	no	—
12	C₃×AGL(1,𝔽₅)	—	5	2	no	—
13	C₂×C₂₅	C₃×C₄	1	1	yes	characteristic, complemented
14	D₂₅	C₃×C₄	1	1	yes	characteristic, complemented
15	D₂₅	C₂²×C₃	1	1	yes	characteristic
16	C₂×AGL(1,𝔽₅)	—	5	1	no	—
17	C₂×C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
18	C₃×D₅	—	5	1	no	—
19	C₃×D₅	—	5	1	no	—
20	C₂₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₄	—	25	1	no	Hall
22	C₂×D₅	—	5	1	no	—
23	AGL(1,𝔽₅)	—	5	2	no	—
24	C₃×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₂²×C₃	—	25	1	no	—
26	C₃×C₄	—	25	2	no	—
27	C₂×C₅	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
28	D₅	—	5	1	no	—
29	D₅	—	5	1	no	—
30	C₂×C₄	—	25	1	no	Sylow
31	C₂×C₃	—	25	1	no	—
32	C₂×C₃	—	25	1	no	—
33	C₂×C₃	#1035	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
35	C₂²	—	25	1	no	—
36	C₄	—	25	2	no	—
37	C₃	C₂×#1035	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	—	25	1	no	—
39	C₂	—	25	1	no	—
40	C₂	C₃×#1035	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#1035
commutator, hypocenter	C₂₅	C₂×C₃×C₄
Frattini	C₅	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₂₅	C₄
socle	C₂×C₃×C₅	AGL(1,𝔽₅)
prime radical	C₂×C₃×D₂₅	C₂
cosocle	D₂₅	C₂²×C₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#1035	C₂	direct (N × H)
3. C₂×#1035	C₃	direct (N × H)
4. C₂×C₃×C₂₅	C₄	semidirect
5. C₃×D₂₅	C₄	semidirect
9. #1035	C₂×C₃	direct (N × H)
10. C₃×C₂₅	C₂×C₄	semidirect
13. C₂×C₂₅	C₃×C₄	semidirect
14. D₂₅	C₃×C₄	semidirect
20. C₂₅	C₂×C₃×C₄	semidirect
33. C₂×C₃	#1035	direct (N × H)
37. C₃	C₂×#1035	direct (N × H)
40. C₂	C₃×#1035	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×C₃×D₂₅	2
C₃×#1035	2
C₂×#1035	3
C₂×C₃×AGL(1,𝔽₅)	5

Subgroups — C2×C3×#1035 #10597056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#1035 #10597056