Subgroups — C₂×C₇×D₁₁₀₅ #44525969

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₂₂₁	—	5	1	no	maximal, Hall
5	C₂×D₁₁₀₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₂₁	—	5	2	no	—
7	C₂×C₇×C₁₃×C₁₇	D₅	1	1	yes	characteristic, complemented
8	C₂×C₇×D₈₅	—	13	1	no	maximal, Hall
9	D₁₁₀₅	C₂×C₇	1	2	yes	direct product factor
10	C₂×C₅×C₁₃×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
11	C₂×C₇×D₆₅	—	17	1	no	maximal, Hall
12	C₇×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₇×C₁₇	D₁₃	1	1	yes	characteristic, complemented
14	C₇×D₈₅	—	13	2	no	—
15	C₅×C₁₃×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇×C₁₃	D₁₇	1	1	yes	characteristic, complemented
17	C₇×D₆₅	—	17	2	no	—
18	C₂×D₂₂₁	—	5	1	no	Hall
19	C₅×C₇×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×D₁₇	—	65	1	no	Hall
21	C₅×C₇×C₁₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃×C₁₇	C₇×D₅	1	1	yes	characteristic, complemented
23	D₂₂₁	—	5	2	no	—
24	C₂×C₇×D₁₃	—	85	1	no	Hall
25	C₂×D₈₅	—	13	1	no	Hall
26	C₂×D₆₅	—	17	1	no	Hall
27	C₂×C₇×C₁₇	D₆₅	1	1	yes	characteristic, complemented
28	C₇×D₁₇	—	65	2	no	—
29	C₁₃×C₁₇	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	D₈₅	1	1	yes	characteristic, complemented
31	C₇×D₁₃	—	85	2	no	—
32	C₂×C₅×C₁₇	C₇×D₁₃	1	1	yes	characteristic, complemented
33	D₈₅	—	13	2	no	—
34	C₂×C₇×D₅	—	221	1	no	Hall
35	C₂×C₅×C₁₃	C₇×D₁₇	1	1	yes	characteristic, complemented
36	D₆₅	—	17	2	no	—
37	C₇×C₁₇	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₃	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅×C₇	D₂₂₁	1	1	yes	characteristic, complemented
41	C₇×D₅	—	221	2	no	—
42	C₂×D₁₇	—	65	1	no	Hall
43	C₅×C₁₃	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₁₃	—	85	1	no	Hall
45	C₅×C₇	C₂×D₂₂₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₁₇	C₇×D₆₅	1	1	yes	characteristic, complemented
47	D₁₇	—	65	2	no	—
48	C₂²×C₇	—	1105	1	no	Hall
49	C₂×C₁₃	C₇×D₈₅	1	1	yes	characteristic, complemented
50	D₁₃	—	85	2	no	—
51	C₂×D₅	—	221	1	no	Hall
52	C₁₇	C₂×C₇×D₆₅	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₇	—	1105	2	no	—
54	C₂×C₇	D₁₁₀₅	1	1	yes	characteristic, direct product factor
55	C₁₃	C₂×C₇×D₈₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	C₇×D₂₂₁	1	1	yes	characteristic, complemented
57	D₅	—	221	2	no	—
58	C₇	C₂×D₁₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₅	C₂×C₇×D₂₂₁	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	1105	1	no	Sylow
61	C₂	—	1105	2	no	—
62	C₂	C₇×D₁₁₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₀₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃×C₁₇	C₂
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₀₅	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₃×C₁₇	C₂	semidirect
3. C₅×C₇×C₁₃×C₁₇	C₂²	semidirect
5. C₂×D₁₁₀₅	C₇	direct (N × H)
7. C₂×C₇×C₁₃×C₁₇	D₅	semidirect
9. D₁₁₀₅	C₂×C₇	direct (N × H)
10. C₂×C₅×C₁₃×C₁₇	C₂×C₇	semidirect
12. C₇×C₁₃×C₁₇	C₂×D₅	semidirect
13. C₂×C₅×C₇×C₁₇	D₁₃	semidirect
15. C₅×C₁₃×C₁₇	C₂²×C₇	semidirect
16. C₂×C₅×C₇×C₁₃	D₁₇	semidirect
19. C₅×C₇×C₁₇	C₂×D₁₃	semidirect
21. C₅×C₇×C₁₃	C₂×D₁₇	semidirect
22. C₂×C₁₃×C₁₇	C₇×D₅	semidirect
27. C₂×C₇×C₁₇	D₆₅	semidirect
29. C₁₃×C₁₇	C₂×C₇×D₅	semidirect
30. C₂×C₇×C₁₃	D₈₅	semidirect
32. C₂×C₅×C₁₇	C₇×D₁₃	semidirect
35. C₂×C₅×C₁₃	C₇×D₁₇	semidirect
37. C₇×C₁₇	C₂×D₆₅	semidirect
38. C₇×C₁₃	C₂×D₈₅	semidirect
39. C₅×C₁₇	C₂×C₇×D₁₃	semidirect
40. C₂×C₅×C₇	D₂₂₁	semidirect
43. C₅×C₁₃	C₂×C₇×D₁₇	semidirect
45. C₅×C₇	C₂×D₂₂₁	semidirect
46. C₂×C₁₇	C₇×D₆₅	semidirect
49. C₂×C₁₃	C₇×D₈₅	semidirect
52. C₁₇	C₂×C₇×D₆₅	semidirect
54. C₂×C₇	D₁₁₀₅	direct (N × H)
55. C₁₃	C₂×C₇×D₈₅	semidirect
56. C₂×C₅	C₇×D₂₂₁	semidirect
58. C₇	C₂×D₁₁₀₅	direct (N × H)
59. C₅	C₂×C₇×D₂₂₁	semidirect
62. C₂	C₇×D₁₁₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₁₀₅	2
C₂×C₅×C₇×C₁₃×C₁₇	2
C₂×C₇×D₂₂₁	5
C₂×D₁₁₀₅	7
C₂×C₇×D₈₅	13
C₂×C₇×D₆₅	17

Subgroups — C2×C7×D1105 #44525969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₁₀₅ #44525969