Subgroups — C₃×D₁₃×D₈₅ #27210550

Order 13260.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₇×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₃×D₁₇	—	5	1	no	maximal, Hall
7	D₁₁₀₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₈₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₂₂₁	—	5	1	no	—
11	C₃×C₁₇×D₁₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₁₇	—	5	1	no	—
13	C₅×C₁₃×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×D₈₅	—	13	1	no	maximal, Hall
15	D₁₃×D₁₇	—	5	1	no	Hall
16	C₃×D₅×D₁₃	—	17	1	no	maximal, Hall
17	C₃×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₇	—	13	1	no	—
19	C₃×D₈₅	—	13	1	no	—
20	C₃×D₈₅	D₁₃	1	1	yes	characteristic, direct product factor
21	D₂₂₁	—	5	1	no	—
22	C₁₃×D₁₇	—	5	1	no	—
23	C₁₇×D₁₃	C₃×D₅	1	1	yes	characteristic, complemented
24	C₃×D₆₅	—	17	1	no	—
25	C₃×D₅×C₁₃	—	17	1	no	—
26	C₃×C₅×D₁₃	D₁₇	1	1	yes	characteristic, complemented
27	C₂×D₈₅	—	13	1	no	Hall
28	D₅×D₁₃	—	17	1	no	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	C₂×C₃×D₁₇	—	65	1	no	Hall
32	C₃×C₅×C₁₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₁₇	—	13	1	no	—
34	D₈₅	—	13	1	no	—
35	D₈₅	C₃×D₁₃	1	1	yes	characteristic, direct product factor
36	C₂×C₃×D₁₃	—	85	1	no	Hall
37	D₆₅	—	17	1	no	—
38	C₅×D₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
39	D₅×C₁₃	—	17	1	no	—
40	C₂×C₃×C₁₇	—	13	1	no	—
41	C₃×D₁₇	—	5	1	no	—
42	C₃×D₁₇	—	65	1	no	—
43	C₅×C₁₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₁₃	—	85	1	no	—
45	C₃×D₁₃	—	85	1	no	—
46	C₃×D₁₃	D₈₅	1	1	yes	characteristic, direct product factor
47	C₂×D₁₇	—	65	1	no	Hall
48	C₅×C₁₃	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×D₅	—	221	1	no	Hall
50	C₂×D₁₃	—	85	1	no	Hall
51	C₃×C₁₇	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
52	C₃×C₁₃	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
53	C₂×C₁₇	—	13	1	no	—
54	D₁₇	—	5	1	no	—
55	D₁₇	—	65	1	no	—
56	C₂×C₃×C₅	—	13	1	no	—
57	C₃×D₅	—	17	1	no	—
58	C₃×D₅	—	221	1	no	—
59	C₂×C₁₃	—	85	1	no	—
60	D₁₃	—	85	1	no	—
61	D₁₃	C₃×D₈₅	1	1	yes	characteristic, direct product factor
62	C₂×D₅	—	221	1	no	Hall
63	C₁₇	C₃×D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₅	D₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
65	C₁₃	C₂×C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	1105	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	D₅	—	17	1	no	—
69	D₅	—	221	1	no	—
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	1105	1	no	—
72	C₂×C₃	—	85	1	no	—
73	C₅	C₃×D₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1105	1	no	Sylow
75	C₃	D₁₃×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	1105	1	no	—
78	C₂	—	85	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₈₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₁₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₁₀₅	C₂	semidirect
2. C₃×C₁₃×D₈₅	C₂	semidirect
3. C₃×C₅×C₁₇×D₁₃	C₂	semidirect
4. D₁₃×D₈₅	C₃	direct (N × H)
5. C₃×C₅×C₁₃×C₁₇	C₂²	semidirect
7. D₁₁₀₅	C₂×C₃	semidirect
8. C₁₃×D₈₅	C₂×C₃	semidirect
9. C₅×C₁₇×D₁₃	C₂×C₃	semidirect
11. C₃×C₁₇×D₁₃	D₅	semidirect
13. C₅×C₁₃×C₁₇	C₂²×C₃	semidirect
17. C₃×C₁₃×C₁₇	C₂×D₅	semidirect
20. C₃×D₈₅	D₁₃	direct (N × H)
23. C₁₇×D₁₃	C₃×D₅	semidirect
26. C₃×C₅×D₁₃	D₁₇	semidirect
29. C₃×C₅×C₁₇	C₂×D₁₃	semidirect
30. C₁₃×C₁₇	C₂×C₃×D₅	semidirect
32. C₃×C₅×C₁₃	C₂×D₁₇	semidirect
35. D₈₅	C₃×D₁₃	direct (N × H)
38. C₅×D₁₃	C₃×D₁₇	semidirect
43. C₅×C₁₇	C₂×C₃×D₁₃	semidirect
46. C₃×D₁₃	D₈₅	direct (N × H)
48. C₅×C₁₃	C₂×C₃×D₁₇	semidirect
51. C₃×C₁₇	D₅×D₁₃	semidirect
52. C₃×C₁₃	C₂×D₈₅	semidirect
61. D₁₃	C₃×D₈₅	direct (N × H)
63. C₁₇	C₃×D₅×D₁₃	semidirect
64. C₃×C₅	D₁₃×D₁₇	semidirect
65. C₁₃	C₂×C₃×D₈₅	semidirect
73. C₅	C₃×D₁₃×D₁₇	semidirect
75. C₃	D₁₃×D₈₅	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×D₁₁₀₅	2
C₃×C₁₃×D₈₅	2
C₃×C₅×C₁₇×D₁₃	2
D₁₃×D₈₅	3
C₃×D₁₃×D₁₇	5
C₂×C₃×D₈₅	13
C₃×D₅×D₁₃	17

Subgroups — C3×D13×D85 #27210550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₈₅ #27210550