Subgroups — C₃×C₂₉×#1043⋊C₃ #39908030

Order 26100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₉×#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1043⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₂₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₂₉×(C₅⋊D₅)⋊C₃	C₂×C₃	1	3	yes	—
7	C₂₉×#1043	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂₉×C₅²⋊C₃	C₃×C₄	1	3	yes	complemented
9	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×AGL(1,𝔽₅)×C₂₉	—	15	2	no	—
11	C₂₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃²×C₄×C₂₉	—	25	1	no	maximal, Hall
13	C₃×#1043⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×D₅×C₂₉	—	15	2	no	—
15	C₅²×C₂₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	AGL(1,𝔽₅)×C₂₉	—	15	2	no	—
17	C₂×C₃²×C₂₉	—	25	1	no	—
18	C₃×(C₅⋊D₅)⋊C₃	C₂×C₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	—	3	2	no	—
20	C₃×C₄×C₂₉	—	25	1	no	—
21	C₃×C₄×C₂₉	—	25	3	no	—
22	C₃×#1043	C₃×C₂₉	1	1	yes	characteristic, complemented
23	#1043⋊C₃	C₃×C₂₉	1	3	yes	direct product factor
24	D₅×C₂₉	—	15	2	no	—
25	C₃²×C₂₉	—	25	1	no	Hall
26	C₃×C₅²⋊C₃	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₉	—	25	3	no	—
28	C₂×C₃×C₂₉	—	25	1	no	—
29	C₃×C₅⋊D₅	C₂×C₃×C₂₉	1	1	yes	characteristic
30	(C₅⋊D₅)⋊C₃	C₂×C₃×C₂₉	1	3	yes	—
31	C₅×C₂₉	—	3	2	no	—
32	C₄×C₂₉	—	25	1	no	Hall
33	#1043	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
34	C₃×C₂₉	—	25	3	no	—
35	C₃×C₂₉	#1043⋊C₃	1	1	yes	characteristic, direct product factor
36	C₃×C₅²	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	C₃×C₄×C₂₉	1	3	yes	complemented
38	C₃×AGL(1,𝔽₅)	—	15	2	no	—
39	C₂×C₂₉	—	25	1	no	—
40	C₅⋊D₅	C₂×C₃²×C₂₉	1	1	yes	characteristic
41	C₃²×C₄	—	25	1	no	Hall
42	C₃×D₅	—	15	2	no	—
43	C₂₉	C₃×#1043⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₅²	C₃²×C₄×C₂₉	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	15	2	no	—
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	25	1	no	—
49	C₃×C₄	—	25	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	25	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	C₂₉×#1043⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₉	#1043⋊C₃
commutator, hypocenter	C₅²	C₃²×C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₃×C₄
prime radical	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₅⋊D₅	C₂×C₃²×C₂₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₂₉×#1043	C₃	semidirect
3. C₂₉×#1043⋊C₃	C₃	direct (N × H)
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
7. C₂₉×#1043	C₃²	semidirect
8. C₂₉×C₅²⋊C₃	C₃×C₄	semidirect
9. C₃×C₅²×C₂₉	C₃×C₄	semidirect
13. C₃×#1043⋊C₃	C₂₉	direct (N × H)
15. C₅²×C₂₉	C₃²×C₄	semidirect
22. C₃×#1043	C₃×C₂₉	semidirect
23. #1043⋊C₃	C₃×C₂₉	direct (N × H)
26. C₃×C₅²⋊C₃	C₄×C₂₉	semidirect
33. #1043	C₃²×C₂₉	semidirect
35. C₃×C₂₉	#1043⋊C₃	direct (N × H)
36. C₃×C₅²	C₃×C₄×C₂₉	semidirect
37. C₅²⋊C₃	C₃×C₄×C₂₉	semidirect
43. C₂₉	C₃×#1043⋊C₃	direct (N × H)
44. C₅²	C₃²×C₄×C₂₉	semidirect
57. C₃	C₂₉×#1043⋊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×(C₅⋊D₅)⋊C₃	2
C₃×C₂₉×#1043	3
C₂₉×#1043⋊C₃	3
C₃²×C₄×C₂₉	25
C₃×#1043⋊C₃	29

Subgroups — C3×C29×#1043⋊C3 #39908030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₉×#1043⋊C₃ #39908030