Subgroups — C₂₅×C₂²⋊AGL(1,𝔽₅) #14522331

Order 2000.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₅)×C₂₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₂₅	C₄	1	1	yes	characteristic, complemented
4	C₂×D₅×C₂₅	—	2	2	no	—
5	C₂×D₅×C₂₅	C₄	1	1	yes	characteristic, complemented
6	C₂×D₅×C₂₅	C₂²	1	1	yes	characteristic
7	AGL(1,𝔽₅)×C₂₅	—	2	2	no	—
8	C₅×C₂²⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic
9	C₂²⋊C₄×C₂₅	—	5	1	no	maximal
10	C₂×C₅×C₂₅	—	2	1	no	—
11	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
12	D₅×C₂₅	—	2	1	no	—
13	D₅×C₂₅	D₄	1	2	yes	—
14	C₂²×C₅×D₅	C₂×C₅	1	1	yes	characteristic
15	C₂×C₅×AGL(1,𝔽₅)	C₂×C₅	1	2	yes	—
16	C₂³×C₂₅	—	5	1	no	—
17	C₂×C₄×C₂₅	—	5	2	no	—
18	C₅×C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅²	C₄×C₅	1	1	yes	characteristic
20	C₂×C₅×D₅	—	2	2	no	—
21	C₂×C₅×D₅	C₄×C₅	1	1	yes	characteristic
22	C₂×C₅×D₅	C₂²×C₅	1	1	yes	characteristic
23	C₅×AGL(1,𝔽₅)	—	2	2	no	—
24	C₂²×C₂₅	—	4	1	no	—
25	C₂²×C₂₅	—	5	1	no	—
26	C₂²×C₂₅	—	5	1	no	—
27	C₂²×C₂₅	—	10	2	no	—
28	C₂²×C₂₅	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
29	C₄×C₂₅	—	10	2	no	—
30	C₂²⋊AGL(1,𝔽₅)	C₂₅	1	1	yes	characteristic, direct product factor
31	C₅×C₂²⋊C₄	—	5	1	no	—
32	C₂×C₅²	—	2	1	no	—
33	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
34	C₅×D₅	—	2	1	no	—
35	C₅×D₅	C₅×D₄	1	2	yes	—
36	C₂×C₂₅	—	2	1	no	—
37	C₂×C₂₅	—	4	2	no	—
38	C₂×C₂₅	—	4	1	no	—
39	C₂×C₂₅	—	5	2	no	—
40	C₂×C₂₅	—	10	1	no	—
41	C₂×C₂₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₂³×C₅	—	5	1	no	—
43	C₂²×D₅	C₂×C₂₅	1	1	yes	characteristic
44	C₂×AGL(1,𝔽₅)	C₂×C₂₅	1	2	yes	complemented
45	C₂×C₄×C₅	—	5	2	no	—
46	C₅²	C₅×C₂²⋊C₄	1	1	yes	characteristic
47	C₂₅	—	4	1	no	—
48	C₂₅	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
49	C₂²×C₅	—	4	1	no	—
50	C₂²×C₅	—	5	1	no	—
51	C₂²×C₅	—	5	1	no	—
52	C₂²×C₅	—	10	2	no	—
53	C₂²×C₅	C₄×C₂₅	1	1	yes	characteristic, complemented
54	C₂²×C₅	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂×D₅	—	2	2	no	—
56	C₂×D₅	C₄×C₂₅	1	1	yes	characteristic, complemented
57	C₂×D₅	C₂²×C₂₅	1	1	yes	characteristic
58	AGL(1,𝔽₅)	—	2	2	no	—
59	C₄×C₅	—	10	2	no	—
60	C₂²⋊C₄	—	5	1	no	Sylow
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	—	2	1	no	—
63	C₂×C₅	—	4	2	no	—
64	C₂×C₅	—	4	1	no	—
65	C₂×C₅	—	5	2	no	—
66	C₂×C₅	—	10	1	no	—
67	C₂×C₅	C₂×C₄×C₂₅	1	1	yes	characteristic
68	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
69	D₅	—	2	1	no	—
70	D₅	D₄×C₂₅	1	2	yes	—
71	C₂³	—	5	1	no	—
72	C₂×C₄	—	5	2	no	—
73	C₅	—	4	1	no	—
74	C₅	C₂²⋊C₄×C₂₅	1	1	yes	characteristic, complemented
75	C₅	C₅×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
76	C₂²	—	5	1	no	—
77	C₂²	—	5	1	no	—
78	C₂²	—	10	2	no	—
79	C₂²	AGL(1,𝔽₅)×C₂₅	1	1	yes	characteristic, complemented
80	C₄	—	10	2	no	—
81	C₂	—	2	1	no	—
82	C₂	—	5	2	no	—
83	C₂	—	10	1	no	—
84	C₂	C₂×AGL(1,𝔽₅)×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₄×C₂₅
Frattini	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₂²×C₅×C₂₅	C₄
socle	C₂×C₅²	C₂×C₄×C₅
prime radical	C₂²×C₅×D₅	C₂×C₅
cosocle	C₂×C₅×D₅	C₂²×C₅
hypercenter	C₂²×C₂₅	AGL(1,𝔽₅)
hypocenter	C₅	C₂²⋊C₄×C₂₅
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₂₅ ◁ C₂²×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₂×AGL(1,𝔽₅)×C₂₅	C₂	semidirect
3. C₂²×C₅×C₂₅	C₄	semidirect
5. C₂×D₅×C₂₅	C₄	semidirect
18. C₅×C₂₅	C₂²⋊C₄	semidirect
28. C₂²×C₂₅	AGL(1,𝔽₅)	semidirect
30. C₂²⋊AGL(1,𝔽₅)	C₂₅	direct (N × H)
44. C₂×AGL(1,𝔽₅)	C₂×C₂₅	semidirect
48. C₂₅	C₂²⋊AGL(1,𝔽₅)	direct (N × H)
53. C₂²×C₅	C₄×C₂₅	semidirect
56. C₂×D₅	C₄×C₂₅	semidirect
74. C₅	C₂²⋊C₄×C₂₅	semidirect
79. C₂²	AGL(1,𝔽₅)×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₂₅	2
C₂×AGL(1,𝔽₅)×C₂₅	2
C₅×C₂²⋊AGL(1,𝔽₅)	5
C₂²⋊C₄×C₂₅	5

Subgroups — C25×C22⋊AGL(1,𝔽5) #14522331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₂²⋊AGL(1,𝔽₅) #14522331