Subgroups — C₅×C₂₃×#64425 #46798939

Order 33810.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₂₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×#64425	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₃×AGL(1,𝔽₇)	—	7	2	no	maximal
6	C₂₃×#3862	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×ΓL(1,𝔽₈)×C₂₃	—	7	2	no	—
8	C₂₃×C₇⋊D₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₅×D₇×C₂₃	—	7	2	no	—
10	C₅×D₇×C₂₃	—	21	2	no	—
11	C₅×#64425	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇²×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂₃×AGL(1,𝔽₇)	—	7	2	no	—
14	C₅×C₇×C₂₃	—	3	2	no	—
15	C₅×C₇×C₂₃	AGL(1,𝔽₇)	1	2	yes	complemented
16	C₅×#3862	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₂₃	—	49	1	no	Hall
18	C₅×C₇⋊D₇	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
19	ΓL(1,𝔽₈)×C₂₃	—	7	2	no	—
20	C₃×C₅×C₂₃	—	49	1	no	Hall
21	D₇×C₂₃	—	7	2	no	—
22	D₇×C₂₃	—	21	2	no	—
23	#64425	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇²	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₂₃	—	49	1	no	Hall
26	C₅×AGL(1,𝔽₇)	—	7	2	no	—
27	C₇×C₂₃	—	3	2	no	—
28	C₇×C₂₃	C₅×AGL(1,𝔽₇)	1	2	yes	complemented
29	#3862	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₃	—	49	1	no	Hall
31	C₅×C₂₃	#64425	1	1	yes	characteristic, direct product factor, Hall
32	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
33	C₇⋊D₇	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
34	C₅×D₇	—	7	2	no	—
35	C₅×D₇	—	21	2	no	—
36	C₃×C₂₃	—	49	1	no	Hall
37	C₇²	C₂×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₂₃	—	49	1	no	Hall
39	AGL(1,𝔽₇)	—	7	2	no	—
40	C₅×C₇	—	3	2	no	—
41	C₅×C₇	C₂₃×AGL(1,𝔽₇)	1	2	yes	complemented
42	C₂×C₃×C₅	—	49	1	no	Hall
43	C₂₃	C₅×#64425	1	1	yes	characteristic, direct product factor, Sylow
44	ΓL(1,𝔽₈)	—	7	2	no	—
45	C₃×C₅	—	49	1	no	Hall
46	D₇	—	7	2	no	—
47	D₇	—	21	2	no	—
48	C₂×C₅	—	49	1	no	Hall
49	C₇	—	3	2	no	—
50	C₇	C₅×C₂₃×AGL(1,𝔽₇)	1	2	yes	complemented
51	C₂×C₃	—	49	1	no	Hall
52	C₅	C₂₃×#64425	1	1	yes	characteristic, direct product factor, Sylow
53	C₃	—	49	1	no	Sylow
54	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	#64425
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₃	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×#3862	C₂	semidirect
2. C₅×C₂₃×C₇⋊D₇	C₃	semidirect
3. C₂₃×#64425	C₅	direct (N × H)
4. C₅×C₇²×C₂₃	C₂×C₃	semidirect
6. C₂₃×#3862	C₂×C₅	semidirect
8. C₂₃×C₇⋊D₇	C₃×C₅	semidirect
11. C₅×#64425	C₂₃	direct (N × H)
12. C₇²×C₂₃	C₂×C₃×C₅	semidirect
15. C₅×C₇×C₂₃	AGL(1,𝔽₇)	semidirect
16. C₅×#3862	C₂×C₂₃	semidirect
18. C₅×C₇⋊D₇	C₃×C₂₃	semidirect
23. #64425	C₅×C₂₃	direct (N × H)
24. C₅×C₇²	C₂×C₃×C₂₃	semidirect
28. C₇×C₂₃	C₅×AGL(1,𝔽₇)	semidirect
29. #3862	C₂×C₅×C₂₃	semidirect
31. C₅×C₂₃	#64425	direct (N × H)
33. C₇⋊D₇	C₃×C₅×C₂₃	semidirect
37. C₇²	C₂×C₃×C₅×C₂₃	semidirect
41. C₅×C₇	C₂₃×AGL(1,𝔽₇)	semidirect
43. C₂₃	C₅×#64425	direct (N × H)
50. C₇	C₅×C₂₃×AGL(1,𝔽₇)	semidirect
52. C₅	C₂₃×#64425	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×#3862	2
C₅×C₂₃×C₇⋊D₇	3
C₂₃×#64425	5
C₅×C₂₃×AGL(1,𝔽₇)	7
C₅×#64425	23

Subgroups — C5×C23×#64425 #46798939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×#64425 #46798939