Subgroups — C₂₃×#11763979 #38737367

Order 25116.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₇⋊#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃×AGL(1,𝔽₁₃)	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₂₃×Dic₇	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃⋊C₃	D₇	1	1	yes	characteristic
9	C₂₃×#261	—	7	1	no	Hall
10	#11763979	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₂₃	—	13	1	no	—
12	C₂₃×C₁₃⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
13	C₂₃×Dic₇	—	13	1	no	Hall
14	C₂₃×D₁₃	C₃×D₇	1	1	yes	characteristic
15	C₇×D₁₃⋊C₃	C₂×C₂₃	1	1	yes	characteristic
16	C₃×C₇×C₂₃	—	13	1	no	Hall
17	C₇⋊#261	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₂₃	—	13	1	no	—
19	C₁₃×C₂₃	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₂₃	—	91	1	no	Hall
21	C₇×C₁₃⋊C₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₇×D₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
23	C₇×C₂₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
24	AGL(1,𝔽₁₃)	—	7	1	no	Hall
25	C₂×C₃×C₂₃	—	13	1	no	—
26	C₄×C₂₃	—	91	1	no	Hall
27	C₇×C₁₃	C₃×C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
28	C₃×Dic₇	—	13	1	no	Hall
29	D₁₃⋊C₃	D₇×C₂₃	1	1	yes	characteristic
30	C₃×C₂₃	—	13	1	no	Hall
31	#261	—	7	1	no	Hall
32	C₂×C₂₃	—	13	1	no	—
33	C₂×C₃×C₇	—	13	1	no	—
34	C₁₃⋊C₃	C₂₃×Dic₇	1	1	yes	characteristic, complemented, Hall
35	Dic₇	—	13	1	no	Hall
36	D₁₃	C₃×D₇×C₂₃	1	1	yes	characteristic
37	C₂₃	#11763979	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₇	—	13	1	no	Hall
39	C₂×C₇	—	13	1	no	—
40	C₁₃	C₃×C₂₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	91	1	no	Hall
42	C₇	C₂₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	91	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	#11763979
commutator, hypocenter	C₇×C₁₃	C₃×C₄×C₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₃	C₃×C₄
prime radical	C₇×C₂₃×D₁₃⋊C₃	C₂
cosocle	C₇×D₁₃	C₂×C₃×C₂₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
2. C₂₃×C₇⋊#261	C₃	semidirect
3. C₇×C₂₃×C₁₃⋊C₃	C₄	semidirect
6. C₇×C₁₃×C₂₃	C₃×C₄	semidirect
10. #11763979	C₂₃	direct (N × H)
12. C₂₃×C₁₃⋊C₃	Dic₇	semidirect
17. C₇⋊#261	C₃×C₂₃	semidirect
19. C₁₃×C₂₃	C₃×Dic₇	semidirect
21. C₇×C₁₃⋊C₃	C₄×C₂₃	semidirect
23. C₇×C₂₃	AGL(1,𝔽₁₃)	semidirect
27. C₇×C₁₃	C₃×C₄×C₂₃	semidirect
34. C₁₃⋊C₃	C₂₃×Dic₇	semidirect
37. C₂₃	#11763979	direct (N × H)
40. C₁₃	C₃×C₂₃×Dic₇	semidirect
42. C₇	C₂₃×AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₂₃×D₁₃⋊C₃	2
C₂₃×C₇⋊#261	3
C₂₃×AGL(1,𝔽₁₃)	7
C₃×C₂₃×Dic₇	13
#11763979	23

Subgroups — C23×#11763979 #38737367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#11763979 #38737367