Subgroups — C₃⋊(C₃⋊#15668532) #39908197

Order 26100.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668532	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#10596817)	—	5	1	no	maximal
5	C₃⋊(C₃⋊#10596814)	—	5	1	no	maximal
6	C₃×C₅×D₁₄₅	D₃	1	4	yes	—
7	#15668532	—	9	1	no	Hall
8	C₃²×D₁₄₅	D₅	1	1	yes	characteristic
9	C₃²×C₅×D₂₉	—	5	1	no	—
10	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
11	C₃⋊#10596817	—	15	4	no	—
12	C₃⋊#10596814	—	15	4	no	—
13	C₅×D₁₄₅	C₃⋊D₃	1	1	yes	characteristic
14	C₃²×C₅×C₂₉	—	4	1	no	—
15	C₃²×C₅×C₂₉	Dic₅	1	1	yes	characteristic, complemented
16	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₃⋊(C₃⋊#1181)	—	25	1	no	Hall
18	C₃⋊(C₃⋊#1042)	—	29	1	no	maximal, Hall
19	C₃×D₁₄₅	D₁₅	1	4	yes	—
20	C₃×C₅×D₂₉	—	5	4	no	—
21	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
22	#10596817	—	45	1	no	—
23	#10596814	—	45	1	no	—
24	C₃²×D₂₉	—	5	1	no	—
25	C₃²×C₅×D₅	—	29	1	no	—
26	C₃×C₅×C₂₉	—	4	4	no	—
27	C₃×C₅×C₂₉	Dic₁₅	1	4	yes	complemented
28	C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	1	4	yes	complemented
29	C₃⋊#1181	—	75	4	no	—
30	C₃⋊#1042	—	87	4	no	—
31	D₁₄₅	C₃⋊D₁₅	1	1	yes	characteristic
32	C₅×D₂₉	—	5	1	no	—
33	C₃²×C₂₉	#1042	1	1	yes	characteristic, complemented, Hall
34	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
35	C₃⋊ΓL(1,𝔽₁₆)	—	145	1	no	—
36	C₃⋊Dic₁₅	—	145	1	no	—
37	C₃×D₂₉	—	5	4	no	—
38	C₃×C₅×D₅	—	29	4	no	—
39	C₅×C₂₉	—	4	1	no	—
40	C₅×C₂₉	C₃⋊Dic₁₅	1	1	yes	characteristic, complemented
41	C₅×C₂₉	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
42	#1181	—	225	1	no	Hall
43	#1042	—	261	1	no	Hall
44	C₂×C₃²×C₅	—	145	1	no	—
45	C₃²×D₅	—	29	1	no	—
46	C₃×C₂₉	C₃⋊#1042	1	4	yes	complemented
47	C₃×C₅²	C₃⋊#1181	1	4	yes	complemented
48	ΓL(1,𝔽₁₆)	—	435	4	no	—
49	Dic₁₅	—	435	4	no	—
50	D₂₉	—	5	1	no	—
51	C₅×D₅	—	29	1	no	—
52	C₃²×C₅	—	4	1	no	—
53	C₃²×C₅	#10596814	1	1	yes	characteristic, complemented
54	C₃²×C₅	#10596817	1	1	yes	characteristic, complemented
55	C₃⋊Dic₃	—	725	1	no	Hall
56	C₂×C₃×C₅	—	145	4	no	—
57	C₃×D₅	—	29	4	no	—
58	C₂₉	C₃⋊(C₃⋊#1042)	1	1	yes	characteristic, complemented, Sylow
59	C₅²	C₃⋊(C₃⋊#1181)	1	1	yes	characteristic, complemented, Sylow
60	AGL(1,𝔽₅)	—	1305	1	no	—
61	Dic₅	—	1305	1	no	—
62	C₂×C₃²	—	145	1	no	—
63	C₃×C₅	—	4	4	no	—
64	C₃×C₅	C₃⋊#10596814	1	4	yes	complemented
65	C₃×C₅	C₃⋊#10596817	1	4	yes	complemented
66	Dic₃	—	2175	4	no	—
67	C₂×C₅	—	145	1	no	—
68	D₅	—	29	1	no	—
69	C₃²	#15668532	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	145	4	no	—
71	C₅	—	4	1	no	—
72	C₅	C₃⋊(C₃⋊#10596814)	1	1	yes	characteristic, complemented
73	C₅	C₃⋊(C₃⋊#10596817)	1	1	yes	characteristic, complemented
74	C₄	—	6525	1	no	Sylow
75	C₃	C₃⋊#15668532	1	4	yes	complemented
76	C₂	—	145	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₂₉	C₄
prime radical, cosocle	C₃²×C₅×D₁₄₅	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
10. C₃×C₅²×C₂₉	Dic₃	semidirect
15. C₃²×C₅×C₂₉	Dic₅	semidirect
16. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₂₉	C₃⋊Dic₃	semidirect
27. C₃×C₅×C₂₉	Dic₁₅	semidirect
28. C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	semidirect
33. C₃²×C₂₉	#1042	semidirect
34. C₃²×C₅²	#1181	semidirect
40. C₅×C₂₉	C₃⋊Dic₁₅	semidirect
41. C₅×C₂₉	C₃⋊ΓL(1,𝔽₁₆)	semidirect
46. C₃×C₂₉	C₃⋊#1042	semidirect
47. C₃×C₅²	C₃⋊#1181	semidirect
53. C₃²×C₅	#10596814	semidirect
54. C₃²×C₅	#10596817	semidirect
58. C₂₉	C₃⋊(C₃⋊#1042)	semidirect
59. C₅²	C₃⋊(C₃⋊#1181)	semidirect
64. C₃×C₅	C₃⋊#10596814	semidirect
65. C₃×C₅	C₃⋊#10596817	semidirect
69. C₃²	#15668532	semidirect
72. C₅	C₃⋊(C₃⋊#10596814)	semidirect
73. C₅	C₃⋊(C₃⋊#10596817)	semidirect
75. C₃	C₃⋊#15668532	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₁₄₅	2
C₃⋊#15668532	3
C₃⋊(C₃⋊#10596817)	5
C₃⋊(C₃⋊#10596814)	5
C₃⋊(C₃⋊#1042)	29

Subgroups — C3⋊(C3⋊#15668532) #39908197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#15668532) #39908197