Subgroups — D₃×D₁₃×C₁₁₃ #31798708

Order 17628.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₃×C₁₁₃	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₁₃	—	3	1	no	—
7	D₁₃×C₁₁₃	—	3	1	no	—
8	D₁₃×C₁₁₃	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₁₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₃×C₁₁₃	—	13	1	no	maximal, Hall
11	C₂×C₃×C₁₁₃	—	13	1	no	—
12	D₃×C₁₁₃	—	13	1	no	—
13	D₃×C₁₁₃	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂²×C₁₁₃	—	39	1	no	Hall
15	C₃×C₁₁₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁₃	—	3	1	no	—
17	C₂×C₁₁₃	—	13	1	no	—
18	C₂×C₁₁₃	—	39	1	no	—
19	D₃×D₁₃	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₁₁₃	D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	D₃₉	C₂×C₁₁₃	1	1	yes	characteristic, complemented
22	C₃×D₁₃	C₂×C₁₁₃	1	1	yes	characteristic, complemented
23	D₃×C₁₃	C₂×C₁₁₃	1	1	yes	characteristic, complemented
24	C₂×D₁₃	—	3	1	no	Hall
25	C₃×C₁₃	C₂²×C₁₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	D₁₃	—	3	1	no	—
28	D₁₃	D₃×C₁₁₃	1	1	yes	characteristic, direct product factor
29	C₁₃	C₂×D₃×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	13	1	no	Hall
31	C₂×C₃	—	13	1	no	—
32	D₃	—	13	1	no	—
33	D₃	D₁₃×C₁₁₃	1	1	yes	characteristic, direct product factor
34	C₂²	—	39	1	no	Sylow
35	C₃	C₂×D₁₃×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	13	1	no	—
38	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁₃	D₃×D₁₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₁₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₁₃

Complements

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

N	H ≅ G/N	type
1. D₃₉×C₁₁₃	C₂	semidirect
2. D₃×C₁₃×C₁₁₃	C₂	semidirect
3. C₃×D₁₃×C₁₁₃	C₂	semidirect
5. C₃×C₁₃×C₁₁₃	C₂²	semidirect
8. D₁₃×C₁₁₃	D₃	direct (N × H)
9. C₁₃×C₁₁₃	C₂×D₃	semidirect
13. D₃×C₁₁₃	D₁₃	direct (N × H)
15. C₃×C₁₁₃	C₂×D₁₃	semidirect
19. D₃×D₁₃	C₁₁₃	direct (N × H)
20. C₁₁₃	D₃×D₁₃	direct (N × H)
21. D₃₉	C₂×C₁₁₃	semidirect
22. C₃×D₁₃	C₂×C₁₁₃	semidirect
23. D₃×C₁₃	C₂×C₁₁₃	semidirect
25. C₃×C₁₃	C₂²×C₁₁₃	semidirect
28. D₁₃	D₃×C₁₁₃	direct (N × H)
29. C₁₃	C₂×D₃×C₁₁₃	semidirect
33. D₃	D₁₃×C₁₁₃	direct (N × H)
35. C₃	C₂×D₁₃×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₃₉×C₁₁₃	2
D₃×C₁₃×C₁₁₃	2
C₃×D₁₃×C₁₁₃	2
C₂×D₁₃×C₁₁₃	3
C₂×D₃×C₁₁₃	13
D₃×D₁₃	113

Subgroups — D3×D13×C113 #31798708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₃×C₁₁₃ #31798708