Subgroups — C₂₅×AGL(1,ℤ/8) #11716538

Order 800.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	SD₁₆×C₂₅	C₂	1	2	yes	maximal, complemented
4	D₈×C₂₅	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₂₅	—	2	1	no	—
7	Q₈×C₂₅	C₂²	1	1	yes	characteristic, complemented
8	D₄×C₂₅	—	2	1	no	—
9	D₄×C₂₅	—	2	1	no	—
10	D₄×C₂₅	C₂²	1	2	yes	—
11	D₄×C₂₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₄×C₂₅	—	2	1	no	—
13	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
14	C₈×C₂₅	C₂²	1	2	yes	complemented
15	C₅×AGL(1,ℤ/8)	C₅	1	1	yes	maximal, characteristic
16	C₂²×C₂₅	—	2	1	no	—
17	C₂²×C₂₅	—	2	2	no	—
18	C₂²×C₂₅	—	4	2	no	—
19	C₂²×C₂₅	D₄	1	1	yes	characteristic
20	C₄×C₂₅	—	2	1	no	—
21	C₄×C₂₅	D₄	1	1	yes	characteristic
22	C₄×C₂₅	C₂³	1	1	yes	characteristic
23	C₅×#41	C₂×C₅	1	1	yes	characteristic
24	C₂×C₅×D₄	C₂×C₅	1	1	yes	characteristic
25	C₅×SD₁₆	C₂×C₅	1	2	yes	—
26	C₅×D₈	C₂×C₅	1	2	yes	—
27	C₅×M₁₆	C₂×C₅	1	1	yes	characteristic
28	C₂×C₂₅	—	2	1	no	—
29	C₂×C₂₅	—	4	1	no	—
30	C₂×C₂₅	—	4	2	no	—
31	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
32	C₂³×C₅	—	2	1	no	—
33	C₅×Q₈	C₂²×C₅	1	1	yes	characteristic
34	C₅×D₄	—	2	1	no	—
35	C₅×D₄	—	2	1	no	—
36	C₅×D₄	C₂²×C₅	1	2	yes	—
37	C₅×D₄	C₂²×C₅	1	1	yes	characteristic
38	C₂×C₄×C₅	—	2	1	no	—
39	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
40	C₅×C₈	C₂²×C₅	1	2	yes	—
41	AGL(1,ℤ/8)	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂₅	AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	—	2	1	no	—
44	C₂²×C₅	—	2	2	no	—
45	C₂²×C₅	—	4	2	no	—
46	C₂²×C₅	C₅×D₄	1	1	yes	characteristic
47	C₄×C₅	—	2	1	no	—
48	C₄×C₅	C₅×D₄	1	1	yes	characteristic
49	C₄×C₅	C₂³×C₅	1	1	yes	characteristic
50	#41	C₂×C₂₅	1	1	yes	characteristic, complemented
51	C₂×D₄	C₂×C₂₅	1	1	yes	characteristic, complemented
52	SD₁₆	C₂×C₂₅	1	2	yes	complemented
53	D₈	C₂×C₂₅	1	2	yes	complemented
54	M₁₆	C₂×C₂₅	1	1	yes	characteristic, complemented
55	C₂×C₅	—	2	1	no	—
56	C₂×C₅	—	4	2	no	—
57	C₂×C₅	—	4	1	no	—
58	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
59	C₂³	—	2	1	no	—
60	Q₈	C₂²×C₂₅	1	1	yes	characteristic, complemented
61	D₄	—	2	1	no	—
62	D₄	—	2	1	no	—
63	D₄	C₂²×C₂₅	1	2	yes	—
64	D₄	C₂²×C₂₅	1	1	yes	characteristic, complemented
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂²×C₂₅	1	1	yes	characteristic
67	C₈	C₂²×C₂₅	1	2	yes	complemented
68	C₅	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₂²	—	2	1	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	4	2	no	—
72	C₂²	D₄×C₂₅	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	D₄×C₂₅	1	1	yes	characteristic
75	C₄	C₂³×C₂₅	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	2	no	—
78	C₂	—	4	1	no	—
79	C₂	C₂×D₄×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	C₂×D₄
commutator	C₄	C₂³×C₂₅
Frattini, cosocle	C₄×C₅	C₂³×C₅
socle	C₂×C₅	C₂×C₅×D₄
prime radical	C₅×AGL(1,ℤ/8)	C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₅ ◁ C₂×C₄×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. #41×C₂₅	C₂	semidirect
2. C₂×D₄×C₂₅	C₂	semidirect
3. SD₁₆×C₂₅	C₂	semidirect
4. D₈×C₂₅	C₂	semidirect
5. M₁₆×C₂₅	C₂	semidirect
7. Q₈×C₂₅	C₂²	semidirect
11. D₄×C₂₅	C₂²	semidirect
14. C₈×C₂₅	C₂²	semidirect
41. AGL(1,ℤ/8)	C₂₅	direct (N × H)
42. C₂₅	AGL(1,ℤ/8)	direct (N × H)
50. #41	C₂×C₂₅	semidirect
51. C₂×D₄	C₂×C₂₅	semidirect
52. SD₁₆	C₂×C₂₅	semidirect
53. D₈	C₂×C₂₅	semidirect
54. M₁₆	C₂×C₂₅	semidirect
60. Q₈	C₂²×C₂₅	semidirect
64. D₄	C₂²×C₂₅	semidirect
67. C₈	C₂²×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
#41×C₂₅	2
C₂×D₄×C₂₅	2
SD₁₆×C₂₅	2
D₈×C₂₅	2
M₁₆×C₂₅	2
C₅×AGL(1,ℤ/8)	5

Subgroups — C25×AGL(1,ℤ/8) #11716538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×AGL(1,ℤ/8) #11716538