Subgroups — C₁₃×C₃⋊D₃×C₅⋊D₅ #26043801

Order 11700.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×C₅⋊D₅	—	3	4	no	maximal
5	C₃²×C₅²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×C₁₃×C₃⋊D₃	—	5	6	no	maximal
7	C₁₃×C₃⋊(C₅⋊D₅)	—	3	4	no	—
8	C₅²×D₃×C₁₃	—	3	4	no	—
9	C₃×C₁₃×C₅⋊D₅	D₃	1	4	yes	complemented
10	C₂×C₁₃×C₅⋊D₅	—	9	1	no	Hall
11	C₁₃×C₃⋊D₁₅	—	5	6	no	—
12	C₅×C₁₃×C₃⋊D₃	D₅	1	6	yes	complemented
13	C₃²×D₅×C₁₃	—	5	6	no	—
14	C₃×C₅²×C₁₃	C₂×D₃	1	4	yes	complemented
15	C₃⋊D₃×C₅⋊D₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	D₃×D₅×C₁₃	—	15	24	no	—
17	C₂×C₅²×C₁₃	—	9	1	no	—
18	C₁₃×C₅⋊D₅	—	9	1	no	—
19	C₁₃×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
20	C₃²×C₅×C₁₃	C₂×D₅	1	6	yes	complemented
21	C₂×C₁₃×C₃⋊D₃	—	25	1	no	Hall
22	C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₅²×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₃²×C₅⋊D₅	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₁₃×D₁₅	—	15	24	no	—
26	C₅×D₃×C₁₃	—	3	24	no	—
27	C₃×D₅×C₁₃	—	5	24	no	—
28	C₅²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
29	D₃×C₅⋊D₅	—	3	4	no	—
30	C₂×D₅×C₁₃	—	45	6	no	—
31	C₂×C₃²×C₁₃	—	25	1	no	—
32	C₁₃×C₃⋊D₃	—	25	1	no	—
33	C₁₃×C₃⋊D₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
34	C₃²×C₅²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
35	C₃×C₅×C₁₃	D₃×D₅	1	24	yes	complemented
36	D₅×C₃⋊D₃	—	5	6	no	—
37	C₂×D₃×C₁₃	—	75	4	no	—
38	C₃⋊(C₅⋊D₅)	—	3	4	no	—
39	C₅²×D₃	—	3	4	no	—
40	C₃×C₅⋊D₅	D₃×C₁₃	1	4	yes	complemented
41	C₂×C₅×C₁₃	—	9	6	no	—
42	D₅×C₁₃	—	5	6	no	—
43	D₅×C₁₃	—	45	6	no	—
44	C₃²×C₁₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅⋊D₅	—	9	1	no	Hall
46	C₃⋊D₁₅	—	5	6	no	—
47	C₅×C₃⋊D₃	D₅×C₁₃	1	6	yes	complemented
48	C₃²×D₅	—	5	6	no	—
49	C₂×C₃×C₁₃	—	25	4	no	—
50	D₃×C₁₃	—	3	4	no	—
51	D₃×C₁₃	—	75	4	no	—
52	C₃×C₅²	C₂×D₃×C₁₃	1	4	yes	complemented
53	C₅×C₁₃	D₅×C₃⋊D₃	1	6	yes	complemented
54	D₃×D₅	—	15	24	no	—
55	C₂²×C₁₃	—	225	1	no	Hall
56	C₂×C₅²	—	9	1	no	—
57	C₅⋊D₅	—	9	1	no	—
58	C₅⋊D₅	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
59	C₃²×C₅	C₂×D₅×C₁₃	1	6	yes	complemented
60	C₃×C₁₃	D₃×C₅⋊D₅	1	4	yes	complemented
61	C₂×C₃⋊D₃	—	25	1	no	Hall
62	D₁₅	—	15	24	no	—
63	C₃×D₅	—	5	24	no	—
64	C₅×D₃	—	3	24	no	—
65	C₂×C₁₃	—	9	1	no	—
66	C₂×C₁₃	—	25	1	no	—
67	C₂×C₁₃	—	225	1	no	—
68	C₅²	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	45	6	no	—
70	C₂×C₃²	—	25	1	no	—
71	C₃⋊D₃	—	25	1	no	—
72	C₃⋊D₃	C₁₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
73	C₃×C₅	D₃×D₅×C₁₃	1	24	yes	complemented
74	C₁₃	C₃⋊D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×D₃	—	75	4	no	—
76	C₂×C₅	—	9	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	45	6	no	—
79	C₃²	C₂×C₁₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	25	4	no	—
81	D₃	—	3	4	no	—
82	D₃	—	75	4	no	—
83	C₅	D₅×C₁₃×C₃⋊D₃	1	6	yes	complemented
84	C₂²	—	225	1	no	Sylow
85	C₃	D₃×C₁₃×C₅⋊D₅	1	4	yes	complemented
86	C₂	—	9	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊D₃×C₅⋊D₅
commutator, cosocle, hypocenter	C₃²×C₅²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₃	C₂²
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	semidirect
2. C₅²×C₁₃×C₃⋊D₃	C₂	semidirect
3. C₃²×C₁₃×C₅⋊D₅	C₂	semidirect
5. C₃²×C₅²×C₁₃	C₂²	semidirect
9. C₃×C₁₃×C₅⋊D₅	D₃	semidirect
12. C₅×C₁₃×C₃⋊D₃	D₅	semidirect
14. C₃×C₅²×C₁₃	C₂×D₃	semidirect
15. C₃⋊D₃×C₅⋊D₅	C₁₃	direct (N × H)
19. C₁₃×C₅⋊D₅	C₃⋊D₃	direct (N × H)
20. C₃²×C₅×C₁₃	C₂×D₅	semidirect
22. C₃⋊(C₃⋊(C₅⋊D₅))	C₂×C₁₃	semidirect
23. C₅²×C₃⋊D₃	C₂×C₁₃	semidirect
24. C₃²×C₅⋊D₅	C₂×C₁₃	semidirect
28. C₅²×C₁₃	C₂×C₃⋊D₃	semidirect
33. C₁₃×C₃⋊D₃	C₅⋊D₅	direct (N × H)
34. C₃²×C₅²	C₂²×C₁₃	semidirect
35. C₃×C₅×C₁₃	D₃×D₅	semidirect
40. C₃×C₅⋊D₅	D₃×C₁₃	semidirect
44. C₃²×C₁₃	C₂×C₅⋊D₅	semidirect
47. C₅×C₃⋊D₃	D₅×C₁₃	semidirect
52. C₃×C₅²	C₂×D₃×C₁₃	semidirect
53. C₅×C₁₃	D₅×C₃⋊D₃	semidirect
58. C₅⋊D₅	C₁₃×C₃⋊D₃	direct (N × H)
59. C₃²×C₅	C₂×D₅×C₁₃	semidirect
60. C₃×C₁₃	D₃×C₅⋊D₅	semidirect
68. C₅²	C₂×C₁₃×C₃⋊D₃	semidirect
72. C₃⋊D₃	C₁₃×C₅⋊D₅	direct (N × H)
73. C₃×C₅	D₃×D₅×C₁₃	semidirect
74. C₁₃	C₃⋊D₃×C₅⋊D₅	direct (N × H)
79. C₃²	C₂×C₁₃×C₅⋊D₅	semidirect
83. C₅	D₅×C₁₃×C₃⋊D₃	semidirect
85. C₃	D₃×C₁₃×C₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊(C₃⋊(C₅⋊D₅))	2
C₅²×C₁₃×C₃⋊D₃	2
C₃²×C₁₃×C₅⋊D₅	2
D₃×C₁₃×C₅⋊D₅	3
D₅×C₁₃×C₃⋊D₃	5
C₃⋊D₃×C₅⋊D₅	13

Subgroups — C13×C3⋊D3×C5⋊D5 #26043801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊D₃×C₅⋊D₅ #26043801