Subgroups — C₂×C₃×C₂₉×C₃₁⋊C₃ #30633656

Order 16182.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₉×C₃₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂₉×C₃₁⋊C₃	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₂₉×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂₉×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₃₁⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃²×C₂₉	—	31	1	no	maximal, Hall
10	C₃×C₃₁⋊C₃	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×C₂₉	—	31	1	no	Hall
12	C₂×C₃×C₃₁	C₃×C₂₉	1	1	yes	characteristic, complemented
13	C₂×C₃₁⋊C₃	C₃×C₂₉	1	3	yes	direct product factor
14	C₂×C₃×C₂₉	—	31	3	no	—
15	C₂×C₃×C₂₉	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
16	C₃×C₃₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
17	C₃₁⋊C₃	C₂×C₃×C₂₉	1	3	yes	direct product factor
18	C₃×C₂₉	—	31	3	no	—
19	C₃×C₂₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃₁	C₂×C₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₂₉	C₂×C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃²	—	31	1	no	Hall
25	C₃²	—	31	1	no	Sylow
26	C₂×C₃	—	31	3	no	—
27	C₂×C₃	C₂₉×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃	—	31	3	no	—
29	C₃	C₂×C₂₉×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₂₉×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₂×C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₉×C₃₁	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. C₃×C₂₉×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂×C₂₉×C₃₁⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₂₉×C₃₁	C₃	semidirect
4. C₃×C₂₉×C₃₁	C₂×C₃	semidirect
5. C₂₉×C₃₁⋊C₃	C₂×C₃	direct (N × H)
6. C₂×C₂₉×C₃₁	C₃²	semidirect
7. C₂₉×C₃₁	C₂×C₃²	semidirect
8. C₂×C₃×C₃₁⋊C₃	C₂₉	direct (N × H)
10. C₃×C₃₁⋊C₃	C₂×C₂₉	direct (N × H)
12. C₂×C₃×C₃₁	C₃×C₂₉	semidirect
13. C₂×C₃₁⋊C₃	C₃×C₂₉	direct (N × H)
15. C₂×C₃×C₂₉	C₃₁⋊C₃	direct (N × H)
16. C₃×C₃₁	C₂×C₃×C₂₉	semidirect
17. C₃₁⋊C₃	C₂×C₃×C₂₉	direct (N × H)
19. C₃×C₂₉	C₂×C₃₁⋊C₃	direct (N × H)
20. C₂×C₃₁	C₃²×C₂₉	semidirect
21. C₂×C₂₉	C₃×C₃₁⋊C₃	direct (N × H)
22. C₃₁	C₂×C₃²×C₂₉	semidirect
23. C₂₉	C₂×C₃×C₃₁⋊C₃	direct (N × H)
27. C₂×C₃	C₂₉×C₃₁⋊C₃	direct (N × H)
29. C₃	C₂×C₂₉×C₃₁⋊C₃	direct (N × H)
30. C₂	C₃×C₂₉×C₃₁⋊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
C₃×C₂₉×C₃₁⋊C₃	2
C₂×C₂₉×C₃₁⋊C₃	3
C₂×C₃×C₂₉×C₃₁	3
C₂×C₃×C₃₁⋊C₃	29
C₂×C₃²×C₂₉	31

Subgroups — C2×C3×C29×C31⋊C3 #30633656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₉×C₃₁⋊C₃ #30633656