Subgroups — D₅×C₁₃×D₁₁₉ #44525945

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₅₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×D₁₁₉	—	5	1	no	maximal, Hall
6	D₅×C₁₃×D₁₇	—	7	1	no	maximal, Hall
7	C₁₃×D₁₁₉	—	5	1	no	—
8	C₁₃×D₁₁₉	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₁₃×C₁₇	—	5	1	no	—
10	D₅×D₁₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×D₈₅	—	7	1	no	—
12	D₅×C₁₃×C₁₇	D₇	1	1	yes	characteristic, complemented
13	C₅×C₁₃×D₁₇	—	7	1	no	—
14	D₅×C₁₃×D₇	—	17	1	no	maximal, Hall
15	C₇×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	D₅₉₅	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₇×D₅×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₅×D₁₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₅×C₁₃×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₁₃×D₃₅	—	17	1	no	—
21	C₇×D₅×C₁₃	D₁₇	1	1	yes	characteristic, complemented
22	C₅×C₁₃×D₇	—	17	1	no	—
23	C₂×C₁₃×D₁₇	—	35	1	no	Hall
24	C₅×C₇×C₁₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁₉	—	5	1	no	Hall
26	C₅×C₇×C₁₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₃×C₁₇	—	5	1	no	—
28	C₁₃×D₁₇	—	7	1	no	—
29	C₁₃×D₁₇	—	35	1	no	—
30	C₂×C₁₃×D₇	—	85	1	no	Hall
31	D₅×D₁₇	—	7	1	no	Hall
32	C₂×D₅×C₁₃	—	119	1	no	Hall
33	C₂×C₇×C₁₇	—	5	1	no	—
34	D₁₁₉	—	5	1	no	—
35	D₁₁₉	D₅×C₁₃	1	1	yes	characteristic, direct product factor
36	C₁₃×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	5	1	no	—
38	C₁₃×D₇	—	17	1	no	—
39	C₁₃×D₇	—	85	1	no	—
40	D₈₅	—	7	1	no	—
41	C₅×D₁₇	—	7	1	no	—
42	D₅×C₁₇	C₁₃×D₇	1	1	yes	characteristic, complemented
43	D₅×D₇	—	17	1	no	Hall
44	C₂×C₅×C₁₃	—	119	1	no	—
45	D₅×C₁₃	—	119	1	no	—
46	D₅×C₁₃	D₁₁₉	1	1	yes	characteristic, direct product factor
47	C₇×C₁₇	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
48	C₇×C₁₃	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
50	D₃₅	—	17	1	no	—
51	C₅×D₇	—	17	1	no	—
52	C₇×D₅	C₁₃×D₁₇	1	1	yes	characteristic, complemented
53	C₂×D₁₇	—	35	1	no	Hall
54	C₅×C₁₃	C₂×D₁₁₉	1	1	yes	characteristic, complemented, Hall
55	C₂²×C₁₃	—	595	1	no	Hall
56	C₅×C₇	C₂×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₇	—	5	1	no	—
58	D₁₇	—	7	1	no	—
59	D₁₇	—	35	1	no	—
60	C₂×D₇	—	85	1	no	Hall
61	C₂×C₁₃	—	5	1	no	—
62	C₂×C₁₃	—	595	1	no	—
63	C₂×C₁₃	—	119	1	no	—
64	C₂×D₅	—	119	1	no	Hall
65	C₁₇	D₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₇	—	5	1	no	—
67	D₇	—	17	1	no	—
68	D₇	—	85	1	no	—
69	C₁₃	D₅×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₅	—	119	1	no	—
71	D₅	—	119	1	no	—
72	D₅	C₁₃×D₁₁₉	1	1	yes	characteristic, direct product factor
73	C₇	D₅×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
74	C₅	C₂×C₁₃×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	595	1	no	Sylow
76	C₂	—	5	1	no	—
77	C₂	—	595	1	no	—
78	C₂	—	119	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₅×D₁₁₉
commutator, cosocle, hypocenter	C₅×C₇×C₁₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₅₉₅	C₂	semidirect
2. C₇×D₅×C₁₃×C₁₇	C₂	semidirect
3. C₅×C₁₃×D₁₁₉	C₂	semidirect
4. C₅×C₇×C₁₃×C₁₇	C₂²	semidirect
8. C₁₃×D₁₁₉	D₅	direct (N × H)
10. D₅×D₁₁₉	C₁₃	direct (N × H)
12. D₅×C₁₃×C₁₇	D₇	semidirect
15. C₇×C₁₃×C₁₇	C₂×D₅	semidirect
16. D₅₉₅	C₂×C₁₃	semidirect
17. C₇×D₅×C₁₇	C₂×C₁₃	semidirect
18. C₅×D₁₁₉	C₂×C₁₃	semidirect
19. C₅×C₁₃×C₁₇	C₂×D₇	semidirect
21. C₇×D₅×C₁₃	D₁₇	semidirect
24. C₅×C₇×C₁₇	C₂²×C₁₃	semidirect
26. C₅×C₇×C₁₃	C₂×D₁₇	semidirect
35. D₁₁₉	D₅×C₁₃	direct (N × H)
36. C₁₃×C₁₇	D₅×D₇	semidirect
42. D₅×C₁₇	C₁₃×D₇	semidirect
46. D₅×C₁₃	D₁₁₉	direct (N × H)
47. C₇×C₁₇	C₂×D₅×C₁₃	semidirect
48. C₇×C₁₃	D₅×D₁₇	semidirect
49. C₅×C₁₇	C₂×C₁₃×D₇	semidirect
52. C₇×D₅	C₁₃×D₁₇	semidirect
54. C₅×C₁₃	C₂×D₁₁₉	semidirect
56. C₅×C₇	C₂×C₁₃×D₁₇	semidirect
65. C₁₇	D₅×C₁₃×D₇	semidirect
69. C₁₃	D₅×D₁₁₉	direct (N × H)
72. D₅	C₁₃×D₁₁₉	direct (N × H)
73. C₇	D₅×C₁₃×D₁₇	semidirect
74. C₅	C₂×C₁₃×D₁₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₅₉₅	2
C₇×D₅×C₁₃×C₁₇	2
C₅×C₁₃×D₁₁₉	2
C₂×C₁₃×D₁₁₉	5
D₅×C₁₃×D₁₇	7
D₅×D₁₁₉	13
D₅×C₁₃×D₇	17

Subgroups — D5×C13×D119 #44525945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃×D₁₁₉ #44525945