Subgroups — D₅×C₇⋊AGL(1,𝔽₂₃) #47978408

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₇⋊AGL(1,𝔽₂₃))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇⋊AGL(1,𝔽₂₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇⋊AGL(1,𝔽₂₃)	—	5	1	no	maximal, Hall
6	D₅×AGL(1,𝔽₂₃)	—	7	1	no	maximal, Hall
7	C₇⋊AGL(1,𝔽₂₃)	—	5	1	no	—
8	C₇⋊AGL(1,𝔽₂₃)	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₂₃⋊C₁₁	—	5	1	no	—
10	D₅×D₁₆₁	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
11	C₅⋊AGL(1,𝔽₂₃)	—	7	1	no	—
12	D₅×C₂₃⋊C₁₁	D₇	1	1	yes	characteristic, complemented
13	C₅×AGL(1,𝔽₂₃)	—	7	1	no	—
14	C₇×C₂₃⋊C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	D₈₀₅	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₇×D₅×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
17	C₅×D₁₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₅×C₁₁×D₇	—	23	1	no	maximal, Hall
19	C₅×C₂₃⋊C₁₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₂×AGL(1,𝔽₂₃)	—	35	1	no	Hall
21	C₅×C₇×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×D₃₅	—	23	1	no	—
23	C₇×D₅×C₁₁	—	23	1	no	—
24	C₅×C₁₁×D₇	—	23	1	no	—
25	C₂×D₁₆₁	—	5	1	no	Hall
26	C₂×C₂₃⋊C₁₁	—	5	1	no	—
27	AGL(1,𝔽₂₃)	—	7	1	no	—
28	AGL(1,𝔽₂₃)	—	35	1	no	—
29	D₅×D₂₃	—	7	1	no	Hall
30	C₅×C₇×C₁₁	—	23	1	no	Hall
31	C₂×C₇×C₂₃	—	5	1	no	—
32	D₁₆₁	—	5	1	no	—
33	D₁₆₁	D₅×C₁₁	1	1	yes	characteristic, complemented
34	C₂×C₁₁×D₇	—	115	1	no	Hall
35	C₂₃⋊C₁₁	D₅×D₇	1	1	yes	characteristic, complemented, Hall
36	D₁₁₅	—	7	1	no	—
37	C₅×D₂₃	—	7	1	no	—
38	D₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic, complemented
39	C₂×D₅×C₁₁	—	161	1	no	Hall
40	C₇×C₂₃	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂×C₇×C₁₁	—	115	1	no	—
42	C₁₁×D₇	—	23	1	no	—
43	C₁₁×D₇	—	115	1	no	—
44	D₅×D₇	—	23	1	no	Hall
45	C₅×C₂₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₅×C₁₁	—	161	1	no	—
47	D₅×C₁₁	—	23	1	no	—
48	D₅×C₁₁	—	161	1	no	—
49	C₂×D₂₃	—	35	1	no	Hall
50	C₇×C₁₁	—	23	1	no	Hall
51	D₃₅	—	23	1	no	—
52	C₅×D₇	—	23	1	no	—
53	C₇×D₅	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
54	C₅×C₁₁	—	23	1	no	Hall
55	C₂×C₂₃	—	5	1	no	—
56	D₂₃	—	7	1	no	—
57	D₂₃	—	35	1	no	—
58	C₂²×C₁₁	—	805	1	no	Hall
59	C₅×C₇	C₂×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Hall
60	C₂×D₇	—	115	1	no	Hall
61	C₂₃	D₅×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₁	—	805	1	no	—
63	C₂×C₁₁	—	115	1	no	—
64	C₂×C₁₁	—	161	1	no	—
65	C₂×D₅	—	161	1	no	Hall
66	C₂×C₇	—	5	1	no	—
67	D₇	—	23	1	no	—
68	D₇	—	115	1	no	—
69	C₁₁	—	23	1	no	Sylow
70	C₂×C₅	—	161	1	no	—
71	D₅	—	161	1	no	—
72	D₅	C₇⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor
73	C₇	D₅×AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
74	C₅	C₂×C₇⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	805	1	no	Sylow
76	C₂	—	5	1	no	—
77	C₂	—	805	1	no	—
78	C₂	—	161	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₂₃	C₂²×C₁₁
LCS	G ▷ C₅×C₇×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₇⋊AGL(1,𝔽₂₃))	C₂	semidirect
2. C₇×D₅×C₂₃⋊C₁₁	C₂	semidirect
3. C₅×C₇⋊AGL(1,𝔽₂₃)	C₂	semidirect
4. C₅×C₇×C₂₃⋊C₁₁	C₂²	semidirect
8. C₇⋊AGL(1,𝔽₂₃)	D₅	direct (N × H)
10. D₅×D₁₆₁	C₁₁	semidirect
12. D₅×C₂₃⋊C₁₁	D₇	semidirect
14. C₇×C₂₃⋊C₁₁	C₂×D₅	semidirect
15. D₈₀₅	C₂×C₁₁	semidirect
16. C₇×D₅×C₂₃	C₂×C₁₁	semidirect
17. C₅×D₁₆₁	C₂×C₁₁	semidirect
19. C₅×C₂₃⋊C₁₁	C₂×D₇	semidirect
21. C₅×C₇×C₂₃	C₂²×C₁₁	semidirect
33. D₁₆₁	D₅×C₁₁	semidirect
35. C₂₃⋊C₁₁	D₅×D₇	semidirect
38. D₅×C₂₃	C₁₁×D₇	semidirect
40. C₇×C₂₃	C₂×D₅×C₁₁	semidirect
45. C₅×C₂₃	C₂×C₁₁×D₇	semidirect
53. C₇×D₅	AGL(1,𝔽₂₃)	semidirect
59. C₅×C₇	C₂×AGL(1,𝔽₂₃)	semidirect
61. C₂₃	D₅×C₁₁×D₇	semidirect
72. D₅	C₇⋊AGL(1,𝔽₂₃)	direct (N × H)
73. C₇	D₅×AGL(1,𝔽₂₃)	semidirect
74. C₅	C₂×C₇⋊AGL(1,𝔽₂₃)	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊(C₇⋊AGL(1,𝔽₂₃))	2
C₇×D₅×C₂₃⋊C₁₁	2
C₅×C₇⋊AGL(1,𝔽₂₃)	2
C₂×C₇⋊AGL(1,𝔽₂₃)	5
D₅×AGL(1,𝔽₂₃)	7
D₅×D₁₆₁	11
D₅×C₁₁×D₇	23

Subgroups — D5×C7⋊AGL(1,𝔽23) #47978408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₇⋊AGL(1,𝔽₂₃) #47978408