Subgroups — C₃⋊(C₃⋊#15668535) #39908207

Order 26100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668535	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#10596817)	—	5	6	no	maximal
5	C₃×C₅²×D₂₉	D₃	1	4	yes	—
6	#15668535	—	9	1	no	Hall
7	C₃²×C₅×D₂₉	D₅	1	6	yes	—
8	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
9	C₃⋊#10596817	—	15	24	no	—
10	C₅²×D₂₉	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₂₉	Dic₅	1	6	yes	complemented
12	C₃⋊(C₃⋊#1181)	—	25	1	no	Hall
13	C₃⋊(C₃⋊#1039)	—	29	1	no	maximal, Hall
14	C₃×C₅×D₂₉	D₁₅	1	24	yes	—
15	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	#10596817	—	45	6	no	—
17	C₃²×D₂₉	C₅⋊D₅	1	1	yes	characteristic
18	C₂×C₃²×C₅²	—	29	1	no	—
19	C₃×C₅×C₂₉	Dic₁₅	1	24	yes	complemented
20	C₃⋊#1181	—	75	4	no	—
21	C₃⋊#1039	—	87	4	no	—
22	C₅×D₂₉	C₃⋊D₁₅	1	6	yes	—
23	C₃²×C₂₉	#1039	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
25	C₃⋊Dic₁₅	—	145	6	no	—
26	C₃×D₂₉	C₃⋊(C₅⋊D₅)	1	4	yes	—
27	C₂×C₃×C₅²	—	29	4	no	—
28	C₅×C₂₉	C₃⋊Dic₁₅	1	6	yes	complemented
29	#1181	—	225	1	no	Hall
30	#1039	—	261	1	no	Hall
31	C₂×C₃²×C₅	—	29	6	no	—
32	C₃×C₂₉	C₃⋊#1039	1	4	yes	complemented
33	C₃×C₅²	C₃⋊#1181	1	4	yes	complemented
34	Dic₁₅	—	435	24	no	—
35	D₂₉	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic
36	C₂×C₅²	—	29	1	no	—
37	C₃²×C₅	#10596817	1	6	yes	complemented
38	C₃⋊Dic₃	—	725	1	no	Hall
39	C₂×C₃×C₅	—	29	24	no	—
40	C₂₉	C₃⋊(C₃⋊#1039)	1	1	yes	characteristic, complemented, Sylow
41	C₅²	C₃⋊(C₃⋊#1181)	1	1	yes	characteristic, complemented, Sylow
42	Dic₅	—	1305	6	no	—
43	C₂×C₃²	—	29	1	no	—
44	C₃×C₅	C₃⋊#10596817	1	24	yes	complemented
45	Dic₃	—	2175	4	no	—
46	C₂×C₅	—	29	6	no	—
47	C₃²	#15668535	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	29	4	no	—
49	C₅	C₃⋊(C₃⋊#10596817)	1	6	yes	complemented
50	C₄	—	6525	1	no	Sylow
51	C₃	C₃⋊#15668535	1	4	yes	complemented
52	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₂₉	C₄
prime radical, cosocle	C₃²×C₅²×D₂₉	C₂
LCS	G ▷ C₃²×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₂₉	C₄	semidirect
8. C₃×C₅²×C₂₉	Dic₃	semidirect
11. C₃²×C₅×C₂₉	Dic₅	semidirect
15. C₅²×C₂₉	C₃⋊Dic₃	semidirect
19. C₃×C₅×C₂₉	Dic₁₅	semidirect
23. C₃²×C₂₉	#1039	semidirect
24. C₃²×C₅²	#1181	semidirect
28. C₅×C₂₉	C₃⋊Dic₁₅	semidirect
32. C₃×C₂₉	C₃⋊#1039	semidirect
33. C₃×C₅²	C₃⋊#1181	semidirect
37. C₃²×C₅	#10596817	semidirect
40. C₂₉	C₃⋊(C₃⋊#1039)	semidirect
41. C₅²	C₃⋊(C₃⋊#1181)	semidirect
44. C₃×C₅	C₃⋊#10596817	semidirect
47. C₃²	#15668535	semidirect
49. C₅	C₃⋊(C₃⋊#10596817)	semidirect
51. C₃	C₃⋊#15668535	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×D₂₉	2
C₃⋊#15668535	3
C₃⋊(C₃⋊#10596817)	5
C₃⋊(C₃⋊#1039)	29

Subgroups — C3⋊(C3⋊#15668535) #39908207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#15668535) #39908207