Subgroups — C₃×D₅×D₂₅₉ #29509669

Order 15540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₂₅₉	—	5	1	no	maximal, Hall
7	D₁₂₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₂₅₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅×D₃₇	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇×C₃₇	—	5	1	no	—
12	C₃×D₂₅₉	—	5	1	no	—
13	C₃×D₂₅₉	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₁₈₅	—	7	1	no	—
16	C₃×D₅×C₃₇	D₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₃₇	—	7	1	no	—
18	C₂×D₂₅₉	—	5	1	no	Hall
19	C₃×C₇×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₃₇	—	7	1	no	Hall
21	C₃×C₅×C₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₃₇	—	5	1	no	—
23	D₂₅₉	—	5	1	no	—
24	D₂₅₉	C₃×D₅	1	1	yes	characteristic, direct product factor
25	C₂×C₃×D₃₇	—	35	1	no	Hall
26	C₃×D₅×D₇	—	37	1	no	maximal, Hall
27	D₁₈₅	—	7	1	no	—
28	C₅×D₃₇	—	7	1	no	—
29	D₅×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented
30	C₇×C₃₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₃₇	—	5	1	no	—
32	C₃×D₃₇	—	7	1	no	—
33	C₃×D₃₇	—	35	1	no	—
34	C₃×D₃₅	—	37	1	no	—
35	C₃×C₇×D₅	D₃₇	1	1	yes	characteristic, complemented
36	C₃×C₅×D₇	—	37	1	no	—
37	C₅×C₃₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃₇	—	35	1	no	Hall
39	D₅×D₇	—	37	1	no	Hall
40	C₃×C₃₇	D₅×D₇	1	1	yes	characteristic, complemented, Hall
41	C₃×C₅×C₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₇	—	185	1	no	Hall
43	C₂×C₃₇	—	5	1	no	—
44	D₃₇	—	7	1	no	—
45	D₃₇	—	35	1	no	—
46	D₃₅	—	37	1	no	—
47	C₅×D₇	—	37	1	no	—
48	C₇×D₅	C₃×D₃₇	1	1	yes	characteristic, complemented
49	C₂×C₃×D₅	—	259	1	no	Hall
50	C₂×C₃×C₇	—	5	1	no	—
51	C₃×D₇	—	37	1	no	—
52	C₃×D₇	—	185	1	no	—
53	C₃₇	C₃×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
54	C₅×C₇	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	259	1	no	—
56	C₃×D₅	—	259	1	no	—
57	C₃×D₅	D₂₅₉	1	1	yes	characteristic, direct product factor
58	C₂×D₇	—	185	1	no	Hall
59	C₃×C₇	D₅×D₃₇	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	259	1	no	Hall
61	C₃×C₅	C₂×D₂₅₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	5	1	no	—
63	D₇	—	37	1	no	—
64	D₇	—	185	1	no	—
65	C₂²×C₃	—	1295	1	no	Hall
66	C₂×C₅	—	259	1	no	—
67	D₅	—	259	1	no	—
68	D₅	C₃×D₂₅₉	1	1	yes	characteristic, direct product factor
69	C₇	C₃×D₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	259	1	no	—
71	C₂×C₃	—	5	1	no	—
72	C₂×C₃	—	1295	1	no	—
73	C₅	C₂×C₃×D₂₅₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1295	1	no	Sylow
75	C₃	D₅×D₂₅₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	259	1	no	—
77	C₂	—	5	1	no	—
78	C₂	—	1295	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₂₅₉
commutator, cosocle, hypocenter	C₅×C₇×C₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₃₇	C₂²
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₂₉₅	C₂	semidirect
2. C₃×C₇×D₅×C₃₇	C₂	semidirect
3. C₃×C₅×D₂₅₉	C₂	semidirect
4. D₅×D₂₅₉	C₃	direct (N × H)
5. C₃×C₅×C₇×C₃₇	C₂²	semidirect
7. D₁₂₉₅	C₂×C₃	semidirect
8. C₇×D₅×C₃₇	C₂×C₃	semidirect
9. C₅×D₂₅₉	C₂×C₃	semidirect
13. C₃×D₂₅₉	D₅	direct (N × H)
14. C₅×C₇×C₃₇	C₂²×C₃	semidirect
16. C₃×D₅×C₃₇	D₇	semidirect
19. C₃×C₇×C₃₇	C₂×D₅	semidirect
21. C₃×C₅×C₃₇	C₂×D₇	semidirect
24. D₂₅₉	C₃×D₅	direct (N × H)
29. D₅×C₃₇	C₃×D₇	semidirect
30. C₇×C₃₇	C₂×C₃×D₅	semidirect
35. C₃×C₇×D₅	D₃₇	semidirect
37. C₅×C₃₇	C₂×C₃×D₇	semidirect
40. C₃×C₃₇	D₅×D₇	semidirect
41. C₃×C₅×C₇	C₂×D₃₇	semidirect
48. C₇×D₅	C₃×D₃₇	semidirect
53. C₃₇	C₃×D₅×D₇	semidirect
54. C₅×C₇	C₂×C₃×D₃₇	semidirect
57. C₃×D₅	D₂₅₉	direct (N × H)
59. C₃×C₇	D₅×D₃₇	semidirect
61. C₃×C₅	C₂×D₂₅₉	semidirect
68. D₅	C₃×D₂₅₉	direct (N × H)
69. C₇	C₃×D₅×D₃₇	semidirect
73. C₅	C₂×C₃×D₂₅₉	semidirect
75. C₃	D₅×D₂₅₉	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×D₁₂₉₅	2
C₃×C₇×D₅×C₃₇	2
C₃×C₅×D₂₅₉	2
D₅×D₂₅₉	3
C₂×C₃×D₂₅₉	5
C₃×D₅×D₃₇	7
C₃×D₅×D₇	37

Subgroups — C3×D5×D259 #29509669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₂₅₉ #29509669