Subgroups — C₂₃×D₁₃×D₃₁ #49150511

Order 37076.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₄₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂₃×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₂₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×D₃₁	—	13	1	no	maximal, Hall
6	D₁₃×D₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₂₃×C₃₁	—	13	1	no	—
8	C₂₃×D₃₁	—	13	1	no	—
9	C₂₃×D₃₁	D₁₃	1	1	yes	characteristic, direct product factor
10	C₂×C₂₃×D₁₃	—	31	1	no	maximal, Hall
11	D₄₀₃	C₂×C₂₃	1	1	yes	characteristic, complemented
12	C₁₃×D₃₁	C₂×C₂₃	1	1	yes	characteristic, complemented
13	D₁₃×C₃₁	C₂×C₂₃	1	1	yes	characteristic, complemented
14	C₂₃×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₃×C₂₃	—	31	1	no	—
16	C₂₃×D₁₃	—	31	1	no	—
17	C₂₃×D₁₃	D₃₁	1	1	yes	characteristic, direct product factor
18	C₁₃×C₃₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₂₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	—	13	1	no	Hall
21	C₂²×C₂₃	—	403	1	no	Hall
22	C₂×C₃₁	—	13	1	no	—
23	D₃₁	—	13	1	no	—
24	D₃₁	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
25	C₂×D₁₃	—	31	1	no	Hall
26	C₂×C₂₃	—	13	1	no	—
27	C₂×C₂₃	—	31	1	no	—
28	C₂×C₂₃	—	403	1	no	—
29	C₃₁	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₃	—	31	1	no	—
31	D₁₃	—	31	1	no	—
32	D₁₃	C₂₃×D₃₁	1	1	yes	characteristic, direct product factor
33	C₂₃	D₁₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₃	C₂×C₂₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	403	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	31	1	no	—
38	C₂	—	403	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₁₃×D₃₁
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₂₃×C₃₁	C₂²
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₄₀₃	C₂	semidirect
2. C₂₃×D₁₃×C₃₁	C₂	semidirect
3. C₁₃×C₂₃×D₃₁	C₂	semidirect
4. C₁₃×C₂₃×C₃₁	C₂²	semidirect
6. D₁₃×D₃₁	C₂₃	direct (N × H)
9. C₂₃×D₃₁	D₁₃	direct (N × H)
11. D₄₀₃	C₂×C₂₃	semidirect
12. C₁₃×D₃₁	C₂×C₂₃	semidirect
13. D₁₃×C₃₁	C₂×C₂₃	semidirect
14. C₂₃×C₃₁	C₂×D₁₃	semidirect
17. C₂₃×D₁₃	D₃₁	direct (N × H)
18. C₁₃×C₃₁	C₂²×C₂₃	semidirect
19. C₁₃×C₂₃	C₂×D₃₁	semidirect
24. D₃₁	C₂₃×D₁₃	direct (N × H)
29. C₃₁	C₂×C₂₃×D₁₃	semidirect
32. D₁₃	C₂₃×D₃₁	direct (N × H)
33. C₂₃	D₁₃×D₃₁	direct (N × H)
34. C₁₃	C₂×C₂₃×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×D₄₀₃	2
C₂₃×D₁₃×C₃₁	2
C₁₃×C₂₃×D₃₁	2
C₂×C₂₃×D₃₁	13
D₁₃×D₃₁	23
C₂×C₂₃×D₁₃	31

Subgroups — C23×D13×D31 #49150511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×D₁₃×D₃₁ #49150511