Subgroups — C₁₃×#11744719 #26043809

Order 11700.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₃⋊D₁₅	C₂	1	2	yes	maximal, complemented
2	C₃²×C₁₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₁₅⋊D₅	—	3	4	no	maximal
4	C₃²×C₅²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₃×C₃⋊D₃	—	5	2	no	maximal
6	C₅×C₁₃×D₁₅	—	3	8	no	—
7	C₃×C₁₃×C₅⋊D₅	D₃	1	4	yes	complemented
8	D₅²×C₁₃	—	9	1	no	Hall
9	C₁₃×C₃⋊D₁₅	D₅	1	2	yes	complemented
10	C₅×C₁₃×C₃⋊D₃	—	5	2	no	—
11	C₃²×D₅×C₁₃	—	5	2	no	—
12	C₃²×D₅×C₁₃	—	10	2	no	—
13	C₃×C₅²×C₁₃	C₂×D₃	1	4	yes	complemented
14	#11744719	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	D₃×D₅×C₁₃	—	15	8	no	—
16	C₁₃×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₅×D₅×C₁₃	—	9	2	no	—
18	C₃²×C₅×C₁₃	—	2	2	no	—
19	C₃²×C₅×C₁₃	C₂×D₅	1	2	yes	complemented
20	C₂×C₁₃×C₃⋊D₃	—	25	1	no	Hall
21	C₅×C₃⋊D₁₅	C₂×C₁₃	1	2	yes	complemented
22	C₃²×C₅⋊D₅	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₁₃×D₁₅	—	3	8	no	—
24	C₅×D₃×C₁₃	—	15	8	no	—
25	C₃×D₅×C₁₃	—	5	8	no	—
26	C₃×D₅×C₁₃	—	10	8	no	—
27	C₅²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	D₁₅⋊D₅	—	3	4	no	—
29	C₂×D₅×C₁₃	—	45	2	no	—
30	C₂×C₃²×C₁₃	—	25	1	no	—
31	C₁₃×C₃⋊D₃	—	5	2	no	—
32	C₃²×C₅²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₁₃	—	2	8	no	—
34	C₃×C₅×C₁₃	D₃×D₅	1	8	yes	complemented
35	D₅×C₃⋊D₃	—	5	2	no	—
36	C₂×D₃×C₁₃	—	75	4	no	—
37	C₅×D₁₅	—	3	8	no	—
38	C₃×C₅⋊D₅	D₃×C₁₃	1	4	yes	complemented
39	C₂×C₅×C₁₃	—	45	2	no	—
40	D₅×C₁₃	—	5	2	no	—
41	D₅×C₁₃	—	9	2	no	—
42	D₅×C₁₃	—	10	2	no	—
43	C₃²×C₁₃	D₅²	1	1	yes	characteristic, complemented, Hall
44	D₅²	—	9	1	no	Hall
45	C₃⋊D₁₅	D₅×C₁₃	1	2	yes	complemented
46	C₅×C₃⋊D₃	—	5	2	no	—
47	C₃²×D₅	—	5	2	no	—
48	C₃²×D₅	—	10	2	no	—
49	C₂×C₃×C₁₃	—	25	4	no	—
50	D₃×C₁₃	—	15	8	no	—
51	C₃×C₅²	C₂×D₃×C₁₃	1	4	yes	complemented
52	C₅×C₁₃	—	2	2	no	—
53	C₅×C₁₃	D₅×C₃⋊D₃	1	2	yes	complemented
54	D₃×D₅	—	15	8	no	—
55	C₂²×C₁₃	—	225	1	no	Hall
56	C₅⋊D₅	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
57	C₅×D₅	—	9	2	no	—
58	C₃²×C₅	—	2	2	no	—
59	C₃²×C₅	C₂×D₅×C₁₃	1	2	yes	complemented
60	C₃×C₁₃	D₁₅⋊D₅	1	4	yes	complemented
61	C₂×C₃⋊D₃	—	25	1	no	Hall
62	D₁₅	—	3	8	no	—
63	C₃×D₅	—	5	8	no	—
64	C₃×D₅	—	10	8	no	—
65	C₅×D₃	—	15	8	no	—
66	C₂×C₁₃	—	25	1	no	—
67	C₂×C₁₃	—	45	2	no	—
68	C₅²	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	45	2	no	—
70	C₂×C₃²	—	25	1	no	—
71	C₃⋊D₃	—	5	2	no	—
72	C₃×C₅	—	2	8	no	—
73	C₃×C₅	D₃×D₅×C₁₃	1	8	yes	complemented
74	C₁₃	#11744719	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×D₃	—	75	4	no	—
76	C₂×C₅	—	45	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	9	2	no	—
79	D₅	—	10	2	no	—
80	C₃²	D₅²×C₁₃	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	4	no	—
82	D₃	—	15	8	no	—
83	C₅	—	2	2	no	—
84	C₅	D₅×C₁₃×C₃⋊D₃	1	2	yes	complemented
85	C₂²	—	225	1	no	Sylow
86	C₃	C₁₃×D₁₅⋊D₅	1	4	yes	complemented
87	C₂	—	25	1	no	—
88	C₂	—	45	2	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#11744719
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. C₅×C₁₃×C₃⋊D₁₅	C₂	semidirect
2. C₃²×C₁₃×C₅⋊D₅	C₂	semidirect
4. C₃²×C₅²×C₁₃	C₂²	semidirect
7. C₃×C₁₃×C₅⋊D₅	D₃	semidirect
9. C₁₃×C₃⋊D₁₅	D₅	semidirect
13. C₃×C₅²×C₁₃	C₂×D₃	semidirect
14. #11744719	C₁₃	direct (N × H)
16. C₁₃×C₅⋊D₅	C₃⋊D₃	semidirect
19. C₃²×C₅×C₁₃	C₂×D₅	semidirect
21. C₅×C₃⋊D₁₅	C₂×C₁₃	semidirect
22. C₃²×C₅⋊D₅	C₂×C₁₃	semidirect
27. C₅²×C₁₃	C₂×C₃⋊D₃	semidirect
32. C₃²×C₅²	C₂²×C₁₃	semidirect
34. C₃×C₅×C₁₃	D₃×D₅	semidirect
38. C₃×C₅⋊D₅	D₃×C₁₃	semidirect
43. C₃²×C₁₃	D₅²	semidirect
45. C₃⋊D₁₅	D₅×C₁₃	semidirect
51. C₃×C₅²	C₂×D₃×C₁₃	semidirect
53. C₅×C₁₃	D₅×C₃⋊D₃	semidirect
56. C₅⋊D₅	C₁₃×C₃⋊D₃	semidirect
59. C₃²×C₅	C₂×D₅×C₁₃	semidirect
60. C₃×C₁₃	D₁₅⋊D₅	semidirect
68. C₅²	C₂×C₁₃×C₃⋊D₃	semidirect
73. C₃×C₅	D₃×D₅×C₁₃	semidirect
74. C₁₃	#11744719	direct (N × H)
80. C₃²	D₅²×C₁₃	semidirect
84. C₅	D₅×C₁₃×C₃⋊D₃	semidirect
86. C₃	C₁₃×D₁₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₃⋊D₁₅	2
C₃²×C₁₃×C₅⋊D₅	2
C₁₃×D₁₅⋊D₅	3
D₅×C₁₃×C₃⋊D₃	5
#11744719	13

Subgroups — C13×#11744719 #26043809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#11744719 #26043809