Subgroups — C₂×C₃×C₁₃×D₁₁₃ #31798721

Order 17628.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₁₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃×C₁₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₃×D₁₁₃	C₂×C₃	1	2	yes	direct product factor
7	C₁₃×C₁₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
10	C₃×D₁₁₃	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×D₁₁₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₁₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
14	D₁₁₃	C₂×C₃×C₁₃	1	2	yes	direct product factor
15	C₂²×C₃×C₁₃	—	113	1	no	maximal, Hall
16	C₁₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₃	—	113	2	no	—
18	C₂×C₃×C₁₃	D₁₁₃	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₃	—	113	1	no	Hall
20	C₃×C₁₃	C₂×D₁₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₃	—	113	2	no	—
22	C₂×C₁₃	C₃×D₁₁₃	1	1	yes	characteristic, direct product factor
23	C₁₃	C₂×C₃×D₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	113	1	no	Hall
25	C₂×C₃	—	113	2	no	—
26	C₂×C₃	C₁₃×D₁₁₃	1	1	yes	characteristic, direct product factor
27	C₂²	—	113	1	no	Sylow
28	C₃	C₂×C₁₃×D₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	113	2	no	—
30	C₂	C₃×C₁₃×D₁₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₁₃
commutator, cosocle, hypocenter	C₁₁₃	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₁₃	C₂
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₁₁₃	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₁₃	C₂	semidirect
3. C₂×C₁₃×D₁₁₃	C₃	direct (N × H)
4. C₃×C₁₃×C₁₁₃	C₂²	semidirect
5. C₂×C₁₃×C₁₁₃	C₂×C₃	semidirect
6. C₁₃×D₁₁₃	C₂×C₃	direct (N × H)
7. C₁₃×C₁₁₃	C₂²×C₃	semidirect
8. C₂×C₃×D₁₁₃	C₁₃	direct (N × H)
9. C₂×C₃×C₁₁₃	C₂×C₁₃	semidirect
10. C₃×D₁₁₃	C₂×C₁₃	direct (N × H)
11. C₂×D₁₁₃	C₃×C₁₃	direct (N × H)
12. C₃×C₁₁₃	C₂²×C₁₃	semidirect
13. C₂×C₁₁₃	C₂×C₃×C₁₃	semidirect
14. D₁₁₃	C₂×C₃×C₁₃	direct (N × H)
16. C₁₁₃	C₂²×C₃×C₁₃	semidirect
18. C₂×C₃×C₁₃	D₁₁₃	direct (N × H)
20. C₃×C₁₃	C₂×D₁₁₃	direct (N × H)
22. C₂×C₁₃	C₃×D₁₁₃	direct (N × H)
23. C₁₃	C₂×C₃×D₁₁₃	direct (N × H)
26. C₂×C₃	C₁₃×D₁₁₃	direct (N × H)
28. C₃	C₂×C₁₃×D₁₁₃	direct (N × H)
30. C₂	C₃×C₁₃×D₁₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×D₁₁₃	2
C₂×C₃×C₁₃×C₁₁₃	2
C₂×C₁₃×D₁₁₃	3
C₂×C₃×D₁₁₃	13
C₂²×C₃×C₁₃	113

Subgroups — C2×C3×C13×D113 #31798721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×D₁₁₃ #31798721