Subgroups — D₂₃×#10625202 #46801774

Order 34086.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10625202	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₁₉×D₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₃×C₁₉⋊C₃	—	13	1	no	maximal, Hall
5	C₁₃⋊C₃×D₂₃	—	19	1	no	maximal, Hall
6	C₂×#10625202	—	23	1	no	maximal, Hall
7	C₂₃×C₁₉⋊C₃	—	13	1	no	Hall
8	C₂₃×C₁₃⋊C₃	—	19	1	no	Hall
9	C₁₉×D₂₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
10	#10625202	D₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃×D₂₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₃×C₁₉	—	23	1	no	Hall
13	C₁₉×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×C₂₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₁₉	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃×D₂₃	—	247	1	no	Hall
17	C₂×C₁₉⋊C₃	—	299	1	no	Hall
18	C₂×C₁₃⋊C₃	—	437	1	no	Hall
19	C₃×C₂₃	—	247	1	no	Hall
20	C₁₉⋊C₃	—	13	1	no	Hall
21	D₂₃	#10625202	1	1	yes	characteristic, direct product factor, Hall
22	C₁₃⋊C₃	—	19	1	no	Hall
23	C₂×C₁₉	—	23	1	no	Hall
24	C₂×C₁₃	—	23	1	no	Hall
25	C₂₃	C₂×#10625202	1	1	yes	characteristic, complemented, Sylow
26	C₁₉	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₃	D₂₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5681	1	no	Hall
29	C₃	—	247	1	no	Sylow
30	C₂	—	23	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₁₃×C₁₉×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₃×#10625202	C₂	semidirect
2. C₁₃×C₁₉×D₂₃	C₃	semidirect
3. C₁₃×C₁₉×C₂₃	C₂×C₃	semidirect
9. C₁₉×D₂₃	C₁₃⋊C₃	semidirect
10. #10625202	D₂₃	direct (N × H)
11. C₁₃×D₂₃	C₁₉⋊C₃	semidirect
13. C₁₉×C₂₃	C₂×C₁₃⋊C₃	semidirect
14. C₁₃×C₂₃	C₂×C₁₉⋊C₃	semidirect
15. C₁₃×C₁₉	C₃×D₂₃	semidirect
21. D₂₃	#10625202	direct (N × H)
25. C₂₃	C₂×#10625202	semidirect
26. C₁₉	C₁₃⋊C₃×D₂₃	semidirect
27. C₁₃	D₂₃×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#10625202	2
C₁₃×C₁₉×D₂₃	3
D₂₃×C₁₉⋊C₃	13
C₁₃⋊C₃×D₂₃	19
C₂×#10625202	23

Subgroups — D23×#10625202 #46801774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#10625202 #46801774