Subgroups — C₃⋊D₃×C₂₉⋊D₂₉ #44475673

Order 30276.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉⋊D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₂₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₂₉⋊D₂₉	—	3	4	no	maximal
5	C₃²×C₂₉²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₂₉⋊D₂₉)	—	3	4	no	—
7	D₃×C₂₉²	—	3	4	no	—
8	C₃×C₂₉⋊D₂₉	D₃	1	4	yes	complemented
9	C₂×C₂₉⋊D₂₉	—	9	1	no	Hall
10	C₃×C₂₉²	C₂×D₃	1	4	yes	complemented
11	C₂×C₂₉²	—	9	1	no	—
12	C₂₉⋊D₂₉	—	9	1	no	—
13	C₂₉⋊D₂₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₃⋊D₃×D₂₉	—	29	30	no	maximal
15	C₂₉²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
16	C₃⋊D₈₇	—	29	30	no	—
17	C₃⋊D₃×C₂₉	D₂₉	1	30	yes	complemented
18	C₃²×D₂₉	—	29	30	no	—
19	D₃×D₂₉	—	87	120	no	—
20	C₃²×C₂₉	C₂×D₂₉	1	30	yes	complemented
21	D₈₇	—	87	120	no	—
22	C₃×D₂₉	—	29	120	no	—
23	D₃×C₂₉	—	3	120	no	—
24	C₂×D₂₉	—	261	30	no	—
25	C₃×C₂₉	D₃×D₂₉	1	120	yes	complemented
26	C₂×C₂₉	—	9	30	no	—
27	D₂₉	—	261	30	no	—
28	D₂₉	—	29	30	no	—
29	C₂×C₃⋊D₃	—	841	1	no	Hall
30	C₂₉	C₃⋊D₃×D₂₉	1	30	yes	complemented
31	C₂×C₃²	—	841	1	no	—
32	C₃⋊D₃	—	841	1	no	—
33	C₃⋊D₃	C₂₉⋊D₂₉	1	1	yes	characteristic, direct product factor
34	C₂×D₃	—	2523	4	no	—
35	C₃²	C₂×C₂₉⋊D₂₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	841	4	no	—
37	D₃	—	3	4	no	—
38	D₃	—	2523	4	no	—
39	C₂²	—	7569	1	no	Sylow
40	C₃	D₃×C₂₉⋊D₂₉	1	4	yes	complemented
41	C₂	—	9	1	no	—
42	C₂	—	841	1	no	—
43	C₂	—	7569	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉²	C₂²
LCS	G ▷ C₃²×C₂₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₉⋊D₂₉	C₂	semidirect
2. C₃⋊D₃×C₂₉²	C₂	semidirect
3. C₃⋊(C₃⋊(C₂₉⋊D₂₉))	C₂	semidirect
5. C₃²×C₂₉²	C₂²	semidirect
8. C₃×C₂₉⋊D₂₉	D₃	semidirect
10. C₃×C₂₉²	C₂×D₃	semidirect
13. C₂₉⋊D₂₉	C₃⋊D₃	direct (N × H)
15. C₂₉²	C₂×C₃⋊D₃	semidirect
17. C₃⋊D₃×C₂₉	D₂₉	semidirect
20. C₃²×C₂₉	C₂×D₂₉	semidirect
25. C₃×C₂₉	D₃×D₂₉	semidirect
30. C₂₉	C₃⋊D₃×D₂₉	semidirect
33. C₃⋊D₃	C₂₉⋊D₂₉	direct (N × H)
35. C₃²	C₂×C₂₉⋊D₂₉	semidirect
40. C₃	D₃×C₂₉⋊D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₉⋊D₂₉	2
C₃⋊D₃×C₂₉²	2
C₃⋊(C₃⋊(C₂₉⋊D₂₉))	2
D₃×C₂₉⋊D₂₉	3
C₃⋊D₃×D₂₉	29

Subgroups — C3⋊D3×C29⋊D29 #44475673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₂₉⋊D₂₉ #44475673