Subgroups — C₂×C₃²×C₁₃×D₂₉ #28331007

Order 13572.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₃×D₂₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₂₉	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₁₃×C₂₉	C₂×C₃	1	4	yes	complemented
7	C₂×C₁₃×D₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₂₉	C₂²×C₃	1	4	yes	complemented
9	C₂×C₃²×D₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₁₃×D₂₉	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×C₂₉	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₃²×D₂₉	C₂×C₁₃	1	2	yes	direct product factor
14	C₂²×C₃²×C₁₃	—	29	1	no	maximal, Hall
15	C₁₃×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×D₂₉	C₃×C₁₃	1	4	yes	direct product factor
17	C₃²×C₂₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₁₃	—	29	2	no	—
19	C₂×C₃²×C₁₃	D₂₉	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₂₉	C₂×C₃×C₁₃	1	4	yes	complemented
21	C₃×D₂₉	C₂×C₃×C₁₃	1	8	yes	direct product factor
22	C₂²×C₃×C₁₃	—	29	4	no	—
23	C₃²×C₁₃	C₂×D₂₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×D₂₉	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₂₉	C₂²×C₃×C₁₃	1	4	yes	complemented
26	C₂×C₃×C₁₃	—	29	8	no	—
27	C₂×C₃×C₁₃	C₃×D₂₉	1	4	yes	direct product factor
28	C₂×C₂₉	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
29	D₂₉	C₂×C₃²×C₁₃	1	2	yes	direct product factor
30	C₂²×C₁₃	—	29	1	no	Hall
31	C₃×C₁₃	C₂×C₃×D₂₉	1	4	yes	direct product factor
32	C₂²×C₃²	—	29	1	no	Hall
33	C₂₉	C₂²×C₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₃	—	29	2	no	—
35	C₂×C₁₃	C₃²×D₂₉	1	1	yes	characteristic, direct product factor
36	C₂×C₃²	—	29	2	no	—
37	C₂×C₃²	C₁₃×D₂₉	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂×C₃²×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	—	29	4	no	—
40	C₃²	C₂×C₁₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	29	8	no	—
42	C₂×C₃	C₃×C₁₃×D₂₉	1	4	yes	direct product factor
43	C₂²	—	29	1	no	Sylow
44	C₃	C₂×C₃×C₁₃×D₂₉	1	4	yes	direct product factor
45	C₂	—	29	2	no	—
46	C₂	C₃²×C₁₃×D₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₃	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×D₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₉	C₂	semidirect
3. C₂×C₃×C₁₃×D₂₉	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₉	C₂²	semidirect
5. C₃×C₁₃×D₂₉	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₃×C₂₉	C₂×C₃	semidirect
7. C₂×C₁₃×D₂₉	C₃²	direct (N × H)
8. C₃×C₁₃×C₂₉	C₂²×C₃	semidirect
9. C₂×C₃²×D₂₉	C₁₃	direct (N × H)
10. C₂×C₁₃×C₂₉	C₂×C₃²	semidirect
11. C₁₃×D₂₉	C₂×C₃²	direct (N × H)
12. C₂×C₃²×C₂₉	C₂×C₁₃	semidirect
13. C₃²×D₂₉	C₂×C₁₃	direct (N × H)
15. C₁₃×C₂₉	C₂²×C₃²	semidirect
16. C₂×C₃×D₂₉	C₃×C₁₃	direct (N × H)
17. C₃²×C₂₉	C₂²×C₁₃	semidirect
19. C₂×C₃²×C₁₃	D₂₉	direct (N × H)
20. C₂×C₃×C₂₉	C₂×C₃×C₁₃	semidirect
21. C₃×D₂₉	C₂×C₃×C₁₃	direct (N × H)
23. C₃²×C₁₃	C₂×D₂₉	direct (N × H)
24. C₂×D₂₉	C₃²×C₁₃	direct (N × H)
25. C₃×C₂₉	C₂²×C₃×C₁₃	semidirect
27. C₂×C₃×C₁₃	C₃×D₂₉	direct (N × H)
28. C₂×C₂₉	C₂×C₃²×C₁₃	semidirect
29. D₂₉	C₂×C₃²×C₁₃	direct (N × H)
31. C₃×C₁₃	C₂×C₃×D₂₉	direct (N × H)
33. C₂₉	C₂²×C₃²×C₁₃	semidirect
35. C₂×C₁₃	C₃²×D₂₉	direct (N × H)
37. C₂×C₃²	C₁₃×D₂₉	direct (N × H)
38. C₁₃	C₂×C₃²×D₂₉	direct (N × H)
40. C₃²	C₂×C₁₃×D₂₉	direct (N × H)
42. C₂×C₃	C₃×C₁₃×D₂₉	direct (N × H)
44. C₃	C₂×C₃×C₁₃×D₂₉	direct (N × H)
46. C₂	C₃²×C₁₃×D₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×D₂₉	2
C₂×C₃²×C₁₃×C₂₉	2
C₂×C₃×C₁₃×D₂₉	3
C₂×C₃²×D₂₉	13
C₂²×C₃²×C₁₃	29

Subgroups — C2×C32×C13×D29 #28331007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₃×D₂₉ #28331007