Subgroups — C₃×D₅×C₁₇×D₁₃ #27210549

Order 13260.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇×D₁₃	—	5	1	no	maximal, Hall
7	C₁₇×D₆₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₃×C₁₇	—	5	1	no	—
11	C₃×C₁₇×D₁₃	—	5	1	no	—
12	C₃×C₁₇×D₁₃	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₁₃×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×D₅×C₁₇	—	13	1	no	maximal, Hall
15	C₂×C₁₇×D₁₃	—	5	1	no	Hall
16	C₃×D₅×D₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₇	—	13	1	no	—
19	C₃×D₅×C₁₇	—	13	1	no	—
20	C₃×D₅×C₁₇	D₁₃	1	1	yes	characteristic, direct product factor
21	C₂×C₁₃×C₁₇	—	5	1	no	—
22	C₁₇×D₁₃	—	5	1	no	—
23	C₁₇×D₁₃	C₃×D₅	1	1	yes	characteristic, direct product factor
24	C₃×D₆₅	C₂×C₁₇	1	1	yes	characteristic, complemented
25	C₃×D₅×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented
26	C₃×C₅×D₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented
27	C₂×D₅×C₁₇	—	13	1	no	Hall
28	D₅×D₁₃	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₅×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₁₃×C₁₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₃×C₁₇	—	65	1	no	Hall
32	C₃×C₅×C₁₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₁₇	—	13	1	no	—
34	D₅×C₁₇	—	13	1	no	—
35	D₅×C₁₇	C₃×D₁₃	1	1	yes	characteristic, direct product factor
36	C₂×C₃×D₁₃	—	5	1	no	Hall
37	D₆₅	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
38	C₅×D₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
39	D₅×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
40	C₂×C₃×C₁₇	—	5	1	no	—
41	C₂×C₃×C₁₇	—	13	1	no	—
42	C₂×C₃×C₁₇	—	65	1	no	—
43	C₅×C₁₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₃	—	5	1	no	—
45	C₃×D₁₃	—	5	1	no	—
46	C₃×D₁₃	D₅×C₁₇	1	1	yes	characteristic, direct product factor
47	C₂²×C₁₇	—	65	1	no	Hall
48	C₅×C₁₃	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×D₅	—	13	1	no	Hall
50	C₂×D₁₃	—	5	1	no	Hall
51	C₃×C₁₇	D₅×D₁₃	1	1	yes	characteristic, direct product factor, Hall
52	C₃×C₁₃	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₇	—	5	1	no	—
54	C₂×C₁₇	—	13	1	no	—
55	C₂×C₁₇	—	65	1	no	—
56	C₂×C₃×C₅	—	13	1	no	—
57	C₃×D₅	—	13	1	no	—
58	C₃×D₅	C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
59	C₂×C₁₃	—	5	1	no	—
60	D₁₃	—	5	1	no	—
61	D₁₃	C₃×D₅×C₁₇	1	1	yes	characteristic, direct product factor
62	C₂×D₅	—	13	1	no	Hall
63	C₁₇	C₃×D₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₅	C₂×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
65	C₁₃	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	65	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	D₅	—	13	1	no	—
69	D₅	C₃×C₁₇×D₁₃	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	65	1	no	—
73	C₅	C₂×C₃×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	65	1	no	Sylow
75	C₃	D₅×C₁₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	13	1	no	—
78	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₅×D₁₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₆₅	C₂	semidirect
2. C₃×D₅×C₁₃×C₁₇	C₂	semidirect
3. C₃×C₅×C₁₇×D₁₃	C₂	semidirect
4. D₅×C₁₇×D₁₃	C₃	direct (N × H)
5. C₃×C₅×C₁₃×C₁₇	C₂²	semidirect
7. C₁₇×D₆₅	C₂×C₃	semidirect
8. D₅×C₁₃×C₁₇	C₂×C₃	semidirect
9. C₅×C₁₇×D₁₃	C₂×C₃	semidirect
12. C₃×C₁₇×D₁₃	D₅	direct (N × H)
13. C₅×C₁₃×C₁₇	C₂²×C₃	semidirect
16. C₃×D₅×D₁₃	C₁₇	direct (N × H)
17. C₃×C₁₃×C₁₇	C₂×D₅	semidirect
20. C₃×D₅×C₁₇	D₁₃	direct (N × H)
23. C₁₇×D₁₃	C₃×D₅	direct (N × H)
24. C₃×D₆₅	C₂×C₁₇	semidirect
25. C₃×D₅×C₁₃	C₂×C₁₇	semidirect
26. C₃×C₅×D₁₃	C₂×C₁₇	semidirect
28. D₅×D₁₃	C₃×C₁₇	direct (N × H)
29. C₃×C₅×C₁₇	C₂×D₁₃	semidirect
30. C₁₃×C₁₇	C₂×C₃×D₅	semidirect
32. C₃×C₅×C₁₃	C₂²×C₁₇	semidirect
35. D₅×C₁₇	C₃×D₁₃	direct (N × H)
37. D₆₅	C₂×C₃×C₁₇	semidirect
38. C₅×D₁₃	C₂×C₃×C₁₇	semidirect
39. D₅×C₁₃	C₂×C₃×C₁₇	semidirect
43. C₅×C₁₇	C₂×C₃×D₁₃	semidirect
46. C₃×D₁₃	D₅×C₁₇	direct (N × H)
48. C₅×C₁₃	C₂²×C₃×C₁₇	semidirect
51. C₃×C₁₇	D₅×D₁₃	direct (N × H)
52. C₃×C₁₃	C₂×D₅×C₁₇	semidirect
58. C₃×D₅	C₁₇×D₁₃	direct (N × H)
61. D₁₃	C₃×D₅×C₁₇	direct (N × H)
63. C₁₇	C₃×D₅×D₁₃	direct (N × H)
64. C₃×C₅	C₂×C₁₇×D₁₃	semidirect
65. C₁₃	C₂×C₃×D₅×C₁₇	semidirect
69. D₅	C₃×C₁₇×D₁₃	direct (N × H)
73. C₅	C₂×C₃×C₁₇×D₁₃	semidirect
75. C₃	D₅×C₁₇×D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₆₅	2
C₃×D₅×C₁₃×C₁₇	2
C₃×C₅×C₁₇×D₁₃	2
D₅×C₁₇×D₁₃	3
C₂×C₃×C₁₇×D₁₃	5
C₂×C₃×D₅×C₁₇	13
C₃×D₅×D₁₃	17

Subgroups — C3×D5×C17×D13 #27210549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₇×D₁₃ #27210549