Subgroups — C₃×C₃⋊#15668535 #39908147

Order 26100.

224 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	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#15668535	—	3	1	no	maximal
4	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#10596817	—	5	6	no	maximal
6	C₃×C₅²×D₂₉	—	2	1	no	—
7	C₃×C₅²×D₂₉	D₃	1	1	yes	characteristic
8	C₃×C₅²×D₂₉	C₂×C₃	1	1	yes	characteristic
9	#15668535	—	3	1	no	Hall
10	C₃²×C₅×D₂₉	D₅	1	6	yes	—
11	C₃×C₅²×C₂₉	—	2	1	no	—
12	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#10596817	—	5	6	no	—
15	C₃×#10596817	—	15	6	no	—
16	C₅²×D₂₉	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₅×C₂₉	Dic₅	1	6	yes	complemented
18	C₃×C₃⋊#1181	—	25	1	no	Hall
19	C₃×C₃⋊#1039	—	29	1	no	maximal, Hall
20	C₃×C₅×D₂₉	—	2	6	no	—
21	C₃×C₅×D₂₉	C₃×D₅	1	6	yes	—
22	C₃×C₅×D₂₉	D₁₅	1	6	yes	—
23	C₅²×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
24	#10596817	—	15	6	no	—
25	C₃²×D₂₉	C₅⋊D₅	1	1	yes	characteristic
26	C₂×C₃²×C₅²	—	29	1	no	—
27	C₃×C₅×C₂₉	—	2	6	no	—
28	C₃×C₅×C₂₉	C₃×Dic₅	1	6	yes	complemented
29	C₃×C₅×C₂₉	Dic₁₅	1	6	yes	complemented
30	C₃⋊#1181	—	25	1	no	—
31	C₃×#1181	—	75	1	no	—
32	C₃⋊#1039	—	29	1	no	—
33	C₃×#1039	—	87	1	no	—
34	C₅×D₂₉	C₃×D₁₅	1	6	yes	—
35	C₃²×C₂₉	#1039	1	1	yes	characteristic, complemented, Hall
36	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
37	C₃×Dic₁₅	—	145	6	no	—
38	C₃×D₂₉	—	2	1	no	—
39	C₃×D₂₉	C₃×C₅⋊D₅	1	1	yes	characteristic
40	C₃×D₂₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
41	C₂×C₃×C₅²	—	29	1	no	—
42	C₂×C₃×C₅²	—	29	1	no	—
43	C₂×C₃×C₅²	—	58	1	no	—
44	C₅×C₂₉	C₃×Dic₁₅	1	6	yes	complemented
45	#1181	—	75	1	no	Hall
46	#1039	—	87	1	no	Hall
47	C₂×C₃²×C₅	—	29	6	no	—
48	C₃×C₂₉	—	2	1	no	—
49	C₃×C₂₉	C₃×#1039	1	1	yes	characteristic, complemented
50	C₃×C₂₉	C₃⋊#1039	1	1	yes	characteristic, complemented
51	C₃×C₅²	—	2	1	no	—
52	C₃×C₅²	C₃×#1181	1	1	yes	characteristic, complemented
53	C₃×C₅²	C₃⋊#1181	1	1	yes	characteristic, complemented
54	Dic₁₅	—	145	6	no	—
55	C₃×Dic₅	—	435	6	no	—
56	D₂₉	C₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
57	C₂×C₅²	—	29	1	no	—
58	C₃²×C₅	#10596817	1	6	yes	complemented
59	C₃×Dic₃	—	725	1	no	Hall
60	C₂×C₃×C₅	—	29	6	no	—
61	C₂×C₃×C₅	—	29	6	no	—
62	C₂×C₃×C₅	—	58	6	no	—
63	C₂₉	C₃×C₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
64	C₅²	C₃×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
65	Dic₅	—	435	6	no	—
66	C₂×C₃²	—	29	1	no	—
67	C₃×C₅	—	2	6	no	—
68	C₃×C₅	C₃×#10596817	1	6	yes	complemented
69	C₃×C₅	C₃⋊#10596817	1	6	yes	complemented
70	C₃×C₄	—	2175	1	no	—
71	Dic₃	—	725	1	no	—
72	C₂×C₅	—	29	6	no	—
73	C₃²	#15668535	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	29	1	no	—
75	C₂×C₃	—	29	1	no	—
76	C₂×C₃	—	58	1	no	—
77	C₅	C₃×C₃⋊#10596817	1	6	yes	complemented
78	C₄	—	2175	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×#15668535	1	1	yes	characteristic, complemented
81	C₃	C₃⋊#15668535	1	1	yes	characteristic, direct product factor
82	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#15668535
commutator, hypocenter	C₃×C₅²×C₂₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₃²×C₅²×D₂₉	C₂
cosocle	C₃×C₅²×D₂₉	C₂×C₃
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#15668535	C₃	direct (N × H)
4. C₃²×C₅²×C₂₉	C₄	semidirect
12. C₃×C₅²×C₂₉	Dic₃	semidirect
13. C₃×C₅²×C₂₉	C₃×C₄	semidirect
17. C₃²×C₅×C₂₉	Dic₅	semidirect
23. C₅²×C₂₉	C₃×Dic₃	semidirect
28. C₃×C₅×C₂₉	C₃×Dic₅	semidirect
29. C₃×C₅×C₂₉	Dic₁₅	semidirect
35. C₃²×C₂₉	#1039	semidirect
36. C₃²×C₅²	#1181	semidirect
44. C₅×C₂₉	C₃×Dic₁₅	semidirect
49. C₃×C₂₉	C₃×#1039	semidirect
50. C₃×C₂₉	C₃⋊#1039	semidirect
52. C₃×C₅²	C₃×#1181	semidirect
53. C₃×C₅²	C₃⋊#1181	semidirect
58. C₃²×C₅	#10596817	semidirect
63. C₂₉	C₃×C₃⋊#1039	semidirect
64. C₅²	C₃×C₃⋊#1181	semidirect
68. C₃×C₅	C₃×#10596817	semidirect
69. C₃×C₅	C₃⋊#10596817	semidirect
73. C₃²	#15668535	semidirect
77. C₅	C₃×C₃⋊#10596817	semidirect
80. C₃	C₃×#15668535	semidirect
81. C₃	C₃⋊#15668535	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×C₅²×D₂₉	2
C₃⋊#15668535	3
C₃×#15668535	3
C₃×C₃⋊#10596817	5
C₃×C₃⋊#1039	29

Subgroups — C3×C3⋊#15668535 #39908147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#15668535 #39908147