Subgroups — C₅×C₃⋊(C₃⋊#63118) #26043782

Order 11700.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#63118	—	3	4	no	maximal
3	C₃²×C₅²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#63118)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊(C₃⋊#261)	—	5	1	no	maximal
6	C₃×C₅²×D₁₃	D₃	1	4	yes	—
7	C₅×#63118	—	9	1	no	Hall
8	C₃²×C₅×D₁₃	—	2	2	no	—
9	C₃²×C₅×D₁₃	D₅	1	1	yes	characteristic
10	C₃²×C₅×D₁₃	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²×C₁₃	Dic₃	1	4	yes	complemented
12	C₅×C₃⋊Dic₁₅	—	13	1	no	maximal, Hall
13	C₃⋊#63118	—	3	4	no	—
14	C₅×C₃⋊#261	—	15	4	no	—
15	C₅²×D₁₃	C₃⋊D₃	1	1	yes	characteristic
16	C₃²×C₅×C₁₃	—	2	2	no	—
17	C₃²×C₅×C₁₃	Dic₅	1	1	yes	characteristic, complemented
18	C₃²×C₅×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented
19	C₃⋊(C₃⋊#261)	—	5	1	no	Hall
20	C₂×C₃²×C₅²	—	13	1	no	—
21	C₃×C₅×D₁₃	—	2	8	no	—
22	C₃×C₅×D₁₃	C₅×D₃	1	4	yes	—
23	C₃×C₅×D₁₃	D₁₅	1	4	yes	—
24	C₅²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
25	C₅×Dic₁₅	—	39	4	no	—
26	#63118	—	9	1	no	—
27	C₅×#261	—	45	1	no	—
28	C₃²×D₁₃	C₅×D₅	1	1	yes	characteristic
29	C₃²×C₅²	#261	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₃	—	2	8	no	—
31	C₃×C₅×C₁₃	C₅×Dic₃	1	4	yes	complemented
32	C₃×C₅×C₁₃	Dic₁₅	1	4	yes	complemented
33	C₃⋊Dic₁₅	—	13	1	no	—
34	C₅×C₃⋊Dic₃	—	65	1	no	—
35	C₃⋊#261	—	15	4	no	—
36	C₂×C₃×C₅²	—	13	4	no	—
37	C₅×D₁₃	—	2	2	no	—
38	C₅×D₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic
39	C₅×D₁₃	C₃⋊D₁₅	1	1	yes	characteristic
40	C₃²×C₁₃	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
41	C₅×Dic₅	—	117	1	no	Hall
42	C₂×C₃²×C₅	—	13	1	no	—
43	C₂×C₃²×C₅	—	13	1	no	—
44	C₂×C₃²×C₅	—	26	2	no	—
45	C₃×D₁₃	C₅×D₁₅	1	4	yes	—
46	C₃×C₅²	C₃⋊#261	1	4	yes	complemented
47	C₅×C₁₃	—	2	2	no	—
48	C₅×C₁₃	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented
49	C₅×C₁₃	C₃⋊Dic₁₅	1	1	yes	characteristic, complemented
50	Dic₁₅	—	39	4	no	—
51	C₅×Dic₃	—	195	4	no	—
52	#261	—	45	1	no	Hall
53	C₂×C₅²	—	13	1	no	—
54	C₃²×C₅	—	2	2	no	—
55	C₃²×C₅	C₅×#261	1	1	yes	characteristic, complemented
56	C₃²×C₅	#63118	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₅×Dic₁₅	1	4	yes	complemented
58	C₃⋊Dic₃	—	65	1	no	Hall
59	C₂×C₃×C₅	—	13	4	no	—
60	C₂×C₃×C₅	—	13	4	no	—
61	C₂×C₃×C₅	—	26	8	no	—
62	D₁₃	C₅×C₃⋊D₁₅	1	1	yes	characteristic
63	C₅²	C₃⋊(C₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
64	C₄×C₅	—	585	1	no	—
65	Dic₅	—	117	1	no	—
66	C₂×C₃²	—	13	1	no	—
67	C₃×C₅	—	2	8	no	—
68	C₃×C₅	C₅×C₃⋊#261	1	4	yes	complemented
69	C₃×C₅	C₃⋊#63118	1	4	yes	complemented
70	C₁₃	C₅×C₃⋊Dic₁₅	1	1	yes	characteristic, complemented, Sylow
71	Dic₃	—	195	4	no	—
72	C₂×C₅	—	13	1	no	—
73	C₂×C₅	—	13	1	no	—
74	C₂×C₅	—	26	2	no	—
75	C₃²	C₅×#63118	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	13	4	no	—
77	C₅	—	2	2	no	—
78	C₅	C₅×C₃⋊(C₃⋊#261)	1	1	yes	characteristic, complemented
79	C₅	C₃⋊(C₃⋊#63118)	1	1	yes	characteristic, direct product factor
80	C₄	—	585	1	no	Sylow
81	C₃	C₅×C₃⋊#63118	1	4	yes	complemented
82	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₃⋊#63118)
commutator, hypocenter	C₃²×C₅×C₁₃	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₃	C₄
prime radical	C₃²×C₅²×D₁₃	C₂
cosocle	C₃²×C₅×D₁₃	C₂×C₅
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₃	C₄	semidirect
4. C₃⋊(C₃⋊#63118)	C₅	direct (N × H)
11. C₃×C₅²×C₁₃	Dic₃	semidirect
17. C₃²×C₅×C₁₃	Dic₅	semidirect
18. C₃²×C₅×C₁₃	C₄×C₅	semidirect
24. C₅²×C₁₃	C₃⋊Dic₃	semidirect
29. C₃²×C₅²	#261	semidirect
31. C₃×C₅×C₁₃	C₅×Dic₃	semidirect
32. C₃×C₅×C₁₃	Dic₁₅	semidirect
40. C₃²×C₁₃	C₅×Dic₅	semidirect
46. C₃×C₅²	C₃⋊#261	semidirect
48. C₅×C₁₃	C₅×C₃⋊Dic₃	semidirect
49. C₅×C₁₃	C₃⋊Dic₁₅	semidirect
55. C₃²×C₅	C₅×#261	semidirect
56. C₃²×C₅	#63118	semidirect
57. C₃×C₁₃	C₅×Dic₁₅	semidirect
63. C₅²	C₃⋊(C₃⋊#261)	semidirect
68. C₃×C₅	C₅×C₃⋊#261	semidirect
69. C₃×C₅	C₃⋊#63118	semidirect
70. C₁₃	C₅×C₃⋊Dic₁₅	semidirect
75. C₃²	C₅×#63118	semidirect
78. C₅	C₅×C₃⋊(C₃⋊#261)	semidirect
79. C₅	C₃⋊(C₃⋊#63118)	direct (N × H)
81. C₃	C₅×C₃⋊#63118	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×D₁₃	2
C₅×C₃⋊#63118	3
C₃⋊(C₃⋊#63118)	5
C₅×C₃⋊(C₃⋊#261)	5
C₅×C₃⋊Dic₁₅	13

Subgroups — C5×C3⋊(C3⋊#63118) #26043782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₃⋊#63118) #26043782