Subgroups — C₂²×C₂₃×#4294 #30628563

Order 15732.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#4294	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₂₃	C₃	1	1	yes	maximal, characteristic
3	C₂₃×#4294	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉×C₂₃	C₂×C₃	1	3	yes	—
5	C₂²×C₁₉×C₂₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic
7	C₂×C₁₉×C₂₃	C₂×C₉	1	3	yes	complemented
8	C₂²×C₉×C₂₃	—	19	1	no	maximal, Hall
9	C₂²×#4294	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×C₂₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₉×C₂₃	—	19	3	no	—
12	C₂×#4294	C₂×C₂₃	1	3	yes	direct product factor
13	C₂²×C₃×C₂₃	C₁₉⋊C₃	1	1	yes	characteristic
14	C₂²×C₃×C₁₉	C₃×C₂₃	1	1	yes	characteristic
15	C₉×C₂₃	—	19	1	no	Hall
16	#4294	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₂₃	C₂×C₁₉⋊C₃	1	3	yes	—
18	C₂×C₃×C₁₉	C₂×C₃×C₂₃	1	3	yes	—
19	C₂²×C₂₃	#4294	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₁₉	C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₂₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
22	C₃×C₁₉	C₂²×C₃×C₂₃	1	1	yes	characteristic
23	C₂×C₂₃	C₂×#4294	1	3	yes	direct product factor
24	C₂×C₁₉	C₂×C₉×C₂₃	1	3	yes	complemented
25	C₂²×C₉	—	19	1	no	Hall
26	C₂₃	C₂²×#4294	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₉	C₂²×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	19	3	no	—
29	C₂²×C₃	C₂₃×C₁₉⋊C₃	1	1	yes	characteristic
30	C₉	—	19	1	no	Sylow
31	C₂×C₃	C₂×C₂₃×C₁₉⋊C₃	1	3	yes	—
32	C₂²	C₂₃×#4294	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₂₃×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂	C₂×C₂₃×#4294	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₂₃	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₉×C₂₃
Frattini	C₃	C₂²×C₂₃×C₁₉⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₂₃	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₂₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#4294	C₂	direct (N × H)
3. C₂₃×#4294	C₂²	direct (N × H)
5. C₂²×C₁₉×C₂₃	C₉	semidirect
7. C₂×C₁₉×C₂₃	C₂×C₉	semidirect
9. C₂²×#4294	C₂₃	direct (N × H)
10. C₁₉×C₂₃	C₂²×C₉	semidirect
12. C₂×#4294	C₂×C₂₃	direct (N × H)
16. #4294	C₂²×C₂₃	direct (N × H)
19. C₂²×C₂₃	#4294	direct (N × H)
20. C₂²×C₁₉	C₉×C₂₃	semidirect
23. C₂×C₂₃	C₂×#4294	direct (N × H)
24. C₂×C₁₉	C₂×C₉×C₂₃	semidirect
26. C₂₃	C₂²×#4294	direct (N × H)
27. C₁₉	C₂²×C₉×C₂₃	semidirect
32. C₂²	C₂₃×#4294	direct (N × H)
34. C₂	C₂×C₂₃×#4294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#4294	2
C₂²×C₃×C₁₉×C₂₃	3
C₂²×C₉×C₂₃	19
C₂²×#4294	23

Subgroups — C22×C23×#4294 #30628563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#4294 #30628563