Subgroups — C₃×#15668527⋊C₃ #39908033

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×#15668527	C₃	1	1	yes	maximal, characteristic, complemented
3	#15668527⋊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	#15668527	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×#10596816	—	15	2	no	—
11	C₂₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃²×Dic₂₉	—	25	1	no	maximal, Hall
13	C₃×#1043⋊C₃	—	29	1	no	maximal, Hall
14	C₃×D₅×C₂₉	—	15	2	no	—
15	C₅²×C₂₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	#10596816	—	15	2	no	—
17	C₂×C₃²×C₂₉	—	25	1	no	—
18	C₃×(C₅⋊D₅)⋊C₃	D₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	—	3	2	no	—
20	C₃×Dic₂₉	—	25	3	no	—
21	C₃×Dic₂₉	—	75	1	no	—
22	C₃×#1043	—	29	1	no	—
23	#1043⋊C₃	—	29	3	no	—
24	D₅×C₂₉	—	15	2	no	—
25	C₃²×C₂₉	—	25	1	no	Hall
26	C₃×C₅²⋊C₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₉	—	25	3	no	—
28	C₂×C₃×C₂₉	—	75	1	no	—
29	C₃×C₅⋊D₅	C₃×D₂₉	1	1	yes	characteristic
30	(C₅⋊D₅)⋊C₃	C₃×D₂₉	1	3	yes	—
31	C₅×C₂₉	—	3	2	no	—
32	Dic₂₉	—	75	1	no	Hall
33	#1043	—	29	1	no	Hall
34	C₃×C₂₉	—	25	3	no	—
35	C₃×C₂₉	#1043⋊C₃	1	1	yes	characteristic, complemented
36	C₃×C₅²	C₃×Dic₂₉	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	C₃×Dic₂₉	1	3	yes	complemented
38	C₃×AGL(1,𝔽₅)	—	435	2	no	—
39	C₂×C₂₉	—	75	1	no	—
40	C₅⋊D₅	C₃²×D₂₉	1	1	yes	characteristic
41	C₃²×C₄	—	725	1	no	Hall
42	C₃×D₅	—	15	2	no	—
43	C₂₉	C₃×#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₅²	C₃²×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	435	2	no	—
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	2175	1	no	—
49	C₃×C₄	—	725	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	75	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	2175	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	#15668527⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#15668527⋊C₃
commutator, hypocenter	C₅²×C₂₉	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₃×C₄
prime radical	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₂₉×C₅⋊D₅	C₂×C₃²
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#15668527	C₃	semidirect
3. #15668527⋊C₃	C₃	direct (N × H)
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
7. #15668527	C₃²	semidirect
8. C₂₉×C₅²⋊C₃	C₃×C₄	semidirect
9. C₃×C₅²×C₂₉	C₃×C₄	semidirect
15. C₅²×C₂₉	C₃²×C₄	semidirect
26. C₃×C₅²⋊C₃	Dic₂₉	semidirect
35. C₃×C₂₉	#1043⋊C₃	semidirect
36. C₃×C₅²	C₃×Dic₂₉	semidirect
37. C₅²⋊C₃	C₃×Dic₂₉	semidirect
43. C₂₉	C₃×#1043⋊C₃	semidirect
44. C₅²	C₃²×Dic₂₉	semidirect
57. C₃	#15668527⋊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×#15668527	3
#15668527⋊C₃	3
C₃²×Dic₂₉	25
C₃×#1043⋊C₃	29

Subgroups — C3×#15668527⋊C3 #39908033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#15668527⋊C₃ #39908033