Subgroups — C₂×C₃×C₂₉×D₃₁⋊C₃ #44569088

Order 32364.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₉×D₃₁⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₂₉×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×D₃₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₂₉×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₃₁⋊C₃	C₂×C₃	1	6	yes	direct product factor
7	C₃×C₂₉×D₃₁	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₉×C₃₁⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₂×C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₂₉×D₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₂₉×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₂₉×C₃₁⋊C₃	C₂²×C₃	1	3	yes	complemented
13	C₂×C₂₉×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₂₉×D₃₁	C₂×C₃²	1	2	yes	complemented
15	C₂×C₃×D₃₁⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃²×C₂₉	—	31	1	no	maximal, Hall
17	C₂₉×C₃₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₃₁⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented
19	C₃×D₃₁⋊C₃	C₂×C₂₉	1	2	yes	direct product factor
20	C₂×C₃²×C₂₉	—	31	2	no	—
21	C₂×C₃²×C₂₉	—	31	1	no	—
22	C₂×C₃×D₃₁	C₃×C₂₉	1	1	yes	characteristic, complemented
23	C₂×D₃₁⋊C₃	C₃×C₂₉	1	3	yes	direct product factor
24	C₂²×C₃×C₂₉	—	31	3	no	—
25	C₂²×C₃×C₂₉	—	31	1	no	—
26	C₃×C₃₁⋊C₃	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
27	C₃²×C₂₉	—	31	1	no	Hall
28	C₂×C₃×C₃₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
29	C₃×D₃₁	C₂×C₃×C₂₉	1	2	yes	complemented
30	C₂×C₃₁⋊C₃	C₂×C₃×C₂₉	1	3	yes	complemented
31	D₃₁⋊C₃	C₂×C₃×C₂₉	1	6	yes	direct product factor
32	C₂×C₃×C₂₉	—	31	6	no	—
33	C₂×C₃×C₂₉	—	31	2	no	—
34	C₂×C₃×C₂₉	—	31	3	no	—
35	C₂×C₃×C₂₉	D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
36	C₂×D₃₁	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₂₉	—	31	1	no	Hall
38	C₃×C₃₁	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
39	C₃₁⋊C₃	C₂²×C₃×C₂₉	1	3	yes	complemented
40	C₃×C₂₉	—	31	3	no	—
41	C₃×C₂₉	C₂×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
42	C₂×C₃₁	C₂×C₃²×C₂₉	1	1	yes	characteristic, complemented
43	D₃₁	C₂×C₃²×C₂₉	1	2	yes	complemented
44	C₂×C₂₉	—	31	2	no	—
45	C₂×C₂₉	C₃×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂²×C₃²	—	31	1	no	Hall
47	C₃₁	C₂²×C₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
48	C₂₉	C₂×C₃×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃²	—	31	2	no	—
50	C₂×C₃²	—	31	1	no	—
51	C₂²×C₃	—	31	3	no	—
52	C₂²×C₃	—	31	1	no	—
53	C₃²	—	31	1	no	Sylow
54	C₂×C₃	—	31	6	no	—
55	C₂×C₃	—	31	2	no	—
56	C₂×C₃	—	31	3	no	—
57	C₂×C₃	C₂₉×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂²	—	31	1	no	Sylow
59	C₃	—	31	3	no	—
60	C₃	C₂×C₂₉×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
61	C₂	—	31	2	no	—
62	C₂	C₃×C₂₉×D₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₂²×C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₉×C₃₁⋊C₃	C₂	semidirect
2. C₃×C₂₉×D₃₁⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₂₉×D₃₁	C₃	semidirect
4. C₂×C₂₉×D₃₁⋊C₃	C₃	direct (N × H)
5. C₃×C₂₉×C₃₁⋊C₃	C₂²	semidirect
6. C₂₉×D₃₁⋊C₃	C₂×C₃	direct (N × H)
7. C₃×C₂₉×D₃₁	C₂×C₃	semidirect
8. C₂×C₂₉×C₃₁⋊C₃	C₂×C₃	semidirect
9. C₂×C₃×C₂₉×C₃₁	C₂×C₃	semidirect
10. C₂×C₂₉×D₃₁	C₃²	semidirect
11. C₃×C₂₉×C₃₁	C₂²×C₃	semidirect
12. C₂₉×C₃₁⋊C₃	C₂²×C₃	semidirect
13. C₂×C₂₉×C₃₁	C₂×C₃²	semidirect
14. C₂₉×D₃₁	C₂×C₃²	semidirect
15. C₂×C₃×D₃₁⋊C₃	C₂₉	direct (N × H)
17. C₂₉×C₃₁	C₂²×C₃²	semidirect
18. C₂×C₃×C₃₁⋊C₃	C₂×C₂₉	semidirect
19. C₃×D₃₁⋊C₃	C₂×C₂₉	direct (N × H)
22. C₂×C₃×D₃₁	C₃×C₂₉	semidirect
23. C₂×D₃₁⋊C₃	C₃×C₂₉	direct (N × H)
26. C₃×C₃₁⋊C₃	C₂²×C₂₉	semidirect
28. C₂×C₃×C₃₁	C₂×C₃×C₂₉	semidirect
29. C₃×D₃₁	C₂×C₃×C₂₉	semidirect
30. C₂×C₃₁⋊C₃	C₂×C₃×C₂₉	semidirect
31. D₃₁⋊C₃	C₂×C₃×C₂₉	direct (N × H)
35. C₂×C₃×C₂₉	D₃₁⋊C₃	direct (N × H)
36. C₂×D₃₁	C₃²×C₂₉	semidirect
38. C₃×C₃₁	C₂²×C₃×C₂₉	semidirect
39. C₃₁⋊C₃	C₂²×C₃×C₂₉	semidirect
41. C₃×C₂₉	C₂×D₃₁⋊C₃	direct (N × H)
42. C₂×C₃₁	C₂×C₃²×C₂₉	semidirect
43. D₃₁	C₂×C₃²×C₂₉	semidirect
45. C₂×C₂₉	C₃×D₃₁⋊C₃	direct (N × H)
47. C₃₁	C₂²×C₃²×C₂₉	semidirect
48. C₂₉	C₂×C₃×D₃₁⋊C₃	direct (N × H)
57. C₂×C₃	C₂₉×D₃₁⋊C₃	direct (N × H)
60. C₃	C₂×C₂₉×D₃₁⋊C₃	direct (N × H)
62. C₂	C₃×C₂₉×D₃₁⋊C₃	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×C₃×C₂₉×C₃₁⋊C₃	2
C₃×C₂₉×D₃₁⋊C₃	2
C₂×C₃×C₂₉×D₃₁	3
C₂×C₂₉×D₃₁⋊C₃	3
C₂×C₃×D₃₁⋊C₃	29
C₂²×C₃²×C₂₉	31

Subgroups — C2×C3×C29×D31⋊C3 #44569088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₉×D₃₁⋊C₃ #44569088