Subgroups — AGL(1,𝔽₇)×D₂₅ #14523536

Order 2100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)⋊D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	ΓL(1,𝔽₈)×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	ΓL(1,𝔽₈)×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×AGL(1,𝔽₇)	—	5	1	no	maximal
7	D₁₇₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×D₂₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×D₂₅	—	7	1	no	maximal, Hall
11	C₅⋊AGL(1,𝔽₇)	—	5	1	no	—
12	D₅×ΓL(1,𝔽₈)	—	5	1	no	—
13	C₅×AGL(1,𝔽₇)	D₅	1	1	yes	characteristic
14	C₇×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₂₅	—	7	1	no	—
16	C₃×D₂₅	—	7	1	no	—
17	C₃×D₂₅	—	7	1	no	—
18	D₅×D₇	—	5	1	no	—
19	C₅×ΓL(1,𝔽₈)	C₂×D₅	1	1	yes	characteristic
20	C₂×D₂₅	—	7	1	no	Hall
21	C₂×AGL(1,𝔽₇)	—	25	1	no	Hall
22	C₃×C₂₅	—	7	1	no	Hall
23	D₃₅	—	5	1	no	—
24	C₅×D₇	C₃×D₅	1	1	yes	characteristic
25	C₇×D₅	—	5	1	no	—
26	C₂×C₃×D₅	—	35	1	no	—
27	C₂×C₂₅	—	7	1	no	—
28	D₂₅	—	7	1	no	—
29	D₂₅	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
30	C₂×ΓL(1,𝔽₈)	—	25	1	no	—
31	AGL(1,𝔽₇)	—	25	1	no	—
32	AGL(1,𝔽₇)	D₂₅	1	1	yes	characteristic, direct product factor
33	C₅×C₇	C₂×C₃×D₅	1	1	yes	characteristic
34	C₂×C₃×C₅	—	7	1	no	—
35	C₃×D₅	—	35	1	no	—
36	C₃×D₅	—	35	1	no	—
37	C₂×D₇	—	25	1	no	Hall
38	C₂₅	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
39	ΓL(1,𝔽₈)	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
40	C₂×D₅	—	35	1	no	—
41	C₃×C₅	—	7	1	no	—
42	C₂×C₇	—	25	1	no	—
43	D₇	—	25	1	no	—
44	D₇	C₃×D₂₅	1	1	yes	characteristic, complemented
45	C₂²×C₃	—	175	1	no	Hall
46	C₂×C₅	—	7	1	no	—
47	D₅	—	5	1	no	—
48	D₅	—	35	1	no	—
49	C₇	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	7	1	no	—
51	C₂×C₃	—	175	1	no	—
52	C₂×C₃	—	175	1	no	—
53	C₅	D₅×AGL(1,𝔽₇)	1	1	yes	characteristic
54	C₂²	—	175	1	no	Sylow
55	C₃	—	7	1	no	Sylow
56	C₂	—	7	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	175	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₂₅	C₂²×C₃
Frattini	C₅	D₅×AGL(1,𝔽₇)
socle	C₅×C₇	C₂×C₃×D₅
LCS	G ▷ C₇×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)⋊D₂₅	C₂	semidirect
2. ΓL(1,𝔽₈)×D₂₅	C₂	semidirect
3. C₂₅×AGL(1,𝔽₇)	C₂	semidirect
4. D₇×D₂₅	C₃	semidirect
5. ΓL(1,𝔽₈)×C₂₅	C₂²	semidirect
7. D₁₇₅	C₂×C₃	semidirect
8. D₇×C₂₅	C₂×C₃	semidirect
9. C₇×D₂₅	C₂×C₃	semidirect
14. C₇×C₂₅	C₂²×C₃	semidirect
29. D₂₅	AGL(1,𝔽₇)	direct (N × H)
32. AGL(1,𝔽₇)	D₂₅	direct (N × H)
38. C₂₅	C₂×AGL(1,𝔽₇)	semidirect
39. ΓL(1,𝔽₈)	C₂×D₂₅	semidirect
44. D₇	C₃×D₂₅	semidirect
49. C₇	C₂×C₃×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
ΓL(1,𝔽₈)⋊D₂₅	2
ΓL(1,𝔽₈)×D₂₅	2
C₂₅×AGL(1,𝔽₇)	2
D₇×D₂₅	3
D₅×AGL(1,𝔽₇)	5
C₂×C₃×D₂₅	7

Subgroups — AGL(1,𝔽7)×D25 #14523536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₇)×D₂₅ #14523536