Subgroups — C₃²×C₂₉×#1181 #44475648

Order 30276.

114 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
2	C₃×C₂₉×#1181	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₉×D₂₉	C₂×C₃	1	4	yes	—
5	C₂₉×#1181	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉²	C₃×C₄	1	4	yes	complemented
7	C₂₉×D₂₉	C₂×C₃²	1	1	yes	characteristic
8	C₃²×#1181	C₂₉	1	1	yes	maximal, characteristic, direct product factor
9	C₃²×C₄×C₂₉	—	29	1	no	maximal
10	C₂₉²	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃²×C₂₉	—	29	1	no	—
12	C₃²×D₂₉	C₂×C₂₉	1	1	yes	characteristic
13	C₃×#1181	C₃×C₂₉	1	4	yes	direct product factor
14	C₃×C₄×C₂₉	—	29	4	no	—
15	C₃²×C₂₉	—	4	7	no	—
16	C₃²×C₂₉	C₄×C₂₉	1	1	yes	characteristic, complemented
17	C₃²×C₂₉	#1181	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₂₉	—	29	4	no	—
19	C₃×D₂₉	C₂×C₃×C₂₉	1	4	yes	—
20	#1181	C₃²×C₂₉	1	1	yes	characteristic, direct product factor
21	C₄×C₂₉	—	29	1	no	—
22	C₃×C₂₉	—	4	28	no	—
23	C₃×C₂₉	C₃×C₄×C₂₉	1	4	yes	complemented
24	C₃×C₂₉	C₃×#1181	1	4	yes	direct product factor
25	C₂×C₂₉	—	29	1	no	—
26	D₂₉	C₂×C₃²×C₂₉	1	1	yes	characteristic
27	C₃²×C₄	—	29	1	no	Hall
28	C₂₉	—	4	7	no	—
29	C₂₉	C₃²×C₄×C₂₉	1	1	yes	characteristic, complemented
30	C₂₉	C₃²×#1181	1	1	yes	characteristic, direct product factor
31	C₂×C₃²	—	29	1	no	—
32	C₃×C₄	—	29	4	no	—
33	C₃²	C₂₉×#1181	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃	—	29	4	no	—
35	C₄	—	29	1	no	Sylow
36	C₃	C₃×C₂₉×#1181	1	4	yes	direct product factor
37	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₂₉	#1181
commutator, hypocenter	C₂₉	C₃²×C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉²	C₄
prime radical	C₃²×C₂₉×D₂₉	C₂
cosocle	D₂₉	C₂×C₃²×C₂₉
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃²×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₂₉×#1181	C₃	direct (N × H)
3. C₃²×C₂₉²	C₄	semidirect
5. C₂₉×#1181	C₃²	direct (N × H)
6. C₃×C₂₉²	C₃×C₄	semidirect
8. C₃²×#1181	C₂₉	direct (N × H)
10. C₂₉²	C₃²×C₄	semidirect
13. C₃×#1181	C₃×C₂₉	direct (N × H)
16. C₃²×C₂₉	C₄×C₂₉	semidirect
17. C₃²×C₂₉	#1181	direct (N × H)
20. #1181	C₃²×C₂₉	direct (N × H)
23. C₃×C₂₉	C₃×C₄×C₂₉	semidirect
24. C₃×C₂₉	C₃×#1181	direct (N × H)
29. C₂₉	C₃²×C₄×C₂₉	semidirect
30. C₂₉	C₃²×#1181	direct (N × H)
33. C₃²	C₂₉×#1181	direct (N × H)
36. C₃	C₃×C₂₉×#1181	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×C₂₉×D₂₉	2
C₃×C₂₉×#1181	3
C₃²×#1181	29
C₃²×C₄×C₂₉	29

Subgroups — C32×C29×#1181 #44475648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₂₉×#1181 #44475648