Subgroups — C₂×C₅⋊D₇₆₅ #29505838

Order 15300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₇₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(C₅⋊D₈₅)	—	3	1	no	maximal
4	C₅²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇₆₅	—	5	6	no	maximal
6	C₃⋊(C₅⋊D₈₅)	—	3	2	no	—
7	C₂×C₃×C₅²×C₁₇	D₃	1	1	yes	characteristic
8	C₂×C₅⋊D₈₅	—	9	1	no	Hall
9	C₂×C₅×C₉×C₁₇	D₅	1	6	yes	complemented
10	D₇₆₅	—	5	12	no	—
11	C₃×C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic
12	C₂×D₂₅₅	—	15	6	no	—
13	C₂×C₅⋊D₄₅	—	17	1	no	maximal, Hall
14	C₂×C₅²×C₁₇	D₉	1	1	yes	characteristic, complemented
15	C₅⋊D₈₅	—	9	2	no	—
16	C₅×C₉×C₁₇	C₂×D₅	1	6	yes	complemented
17	C₂×D₁₅₃	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₇	D₁₅	1	6	yes	—
19	D₂₅₅	—	15	12	no	—
20	C₂×C₅²×C₉	D₁₇	1	1	yes	characteristic, complemented
21	C₅⋊D₄₅	—	17	2	no	—
22	C₅²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
23	C₂×D₈₅	—	45	6	no	—
24	C₂×C₉×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
25	D₁₅₃	—	25	2	no	—
26	C₂×C₃⋊(C₅⋊D₅)	—	51	1	no	—
27	C₃×C₅×C₁₇	C₂×D₁₅	1	6	yes	—
28	C₅²×C₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
29	C₂×D₅₁	—	75	1	no	—
30	C₂×D₄₅	—	85	6	no	—
31	C₂×C₅×C₁₇	D₄₅	1	6	yes	complemented
32	D₈₅	—	45	12	no	—
33	C₉×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅²	D₅₁	1	1	yes	characteristic
35	C₃⋊(C₅⋊D₅)	—	51	2	no	—
36	C₂×C₃×C₁₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
37	D₅₁	—	75	2	no	—
38	C₂×C₅⋊D₅	—	153	1	no	Hall
39	C₂×C₅×C₉	D₈₅	1	6	yes	complemented
40	D₄₅	—	85	12	no	—
41	C₅×C₁₇	C₂×D₄₅	1	6	yes	complemented
42	C₃×C₅²	C₂×D₅₁	1	1	yes	characteristic
43	C₂×D₁₇	—	225	1	no	Hall
44	C₂×D₁₅	—	255	6	no	—
45	C₃×C₁₇	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
46	C₂×C₅²	D₁₅₃	1	1	yes	characteristic, complemented
47	C₅⋊D₅	—	153	2	no	—
48	C₅×C₉	C₂×D₈₅	1	6	yes	complemented
49	C₂×D₉	—	425	1	no	Hall
50	C₂×C₁₇	C₅⋊D₄₅	1	1	yes	characteristic, complemented
51	D₁₇	—	225	2	no	—
52	C₂×C₃×C₅	D₂₅₅	1	6	yes	—
53	D₁₅	—	255	12	no	—
54	C₅²	C₂×D₁₅₃	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	765	6	no	—
56	C₂×C₉	C₅⋊D₈₅	1	1	yes	characteristic, complemented
57	D₉	—	425	2	no	—
58	C₁₇	C₂×C₅⋊D₄₅	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₅	C₂×D₂₅₅	1	6	yes	—
60	C₂×D₃	—	1275	1	no	—
61	C₂×C₅	D₇₆₅	1	6	yes	complemented
62	D₅	—	765	12	no	—
63	C₉	C₂×C₅⋊D₈₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₃⋊(C₅⋊D₈₅)	1	1	yes	characteristic
65	D₃	—	1275	2	no	—
66	C₅	C₂×D₇₆₅	1	6	yes	complemented
67	C₂²	—	3825	1	no	Sylow
68	C₃	C₂×C₃⋊(C₅⋊D₈₅)	1	1	yes	characteristic
69	C₂	—	3825	2	no	—
70	C₂	C₅⋊D₇₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₇₆₅
commutator, cosocle, hypocenter	C₅²×C₉×C₁₇	C₂²
Frattini	C₃	C₂×C₃⋊(C₅⋊D₈₅)
Fitting	C₂×C₅²×C₉×C₁₇	C₂
socle	C₂×C₃×C₅²×C₁₇	D₃
LCS	G ▷ C₅²×C₉×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₇₆₅	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₇	C₂	semidirect
4. C₅²×C₉×C₁₇	C₂²	semidirect
9. C₂×C₅×C₉×C₁₇	D₅	semidirect
14. C₂×C₅²×C₁₇	D₉	semidirect
16. C₅×C₉×C₁₇	C₂×D₅	semidirect
20. C₂×C₅²×C₉	D₁₇	semidirect
22. C₅²×C₁₇	C₂×D₉	semidirect
24. C₂×C₉×C₁₇	C₅⋊D₅	semidirect
28. C₅²×C₉	C₂×D₁₇	semidirect
31. C₂×C₅×C₁₇	D₄₅	semidirect
33. C₉×C₁₇	C₂×C₅⋊D₅	semidirect
39. C₂×C₅×C₉	D₈₅	semidirect
41. C₅×C₁₇	C₂×D₄₅	semidirect
46. C₂×C₅²	D₁₅₃	semidirect
48. C₅×C₉	C₂×D₈₅	semidirect
50. C₂×C₁₇	C₅⋊D₄₅	semidirect
54. C₅²	C₂×D₁₅₃	semidirect
56. C₂×C₉	C₅⋊D₈₅	semidirect
58. C₁₇	C₂×C₅⋊D₄₅	semidirect
61. C₂×C₅	D₇₆₅	semidirect
63. C₉	C₂×C₅⋊D₈₅	semidirect
66. C₅	C₂×D₇₆₅	semidirect
70. C₂	C₅⋊D₇₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊D₇₆₅	2
C₂×C₅²×C₉×C₁₇	2
C₂×C₃⋊(C₅⋊D₈₅)	3
C₂×D₇₆₅	5
C₂×C₅⋊D₄₅	17

Subgroups — C2×C5⋊D765 #29505838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊D₇₆₅ #29505838