Subgroups — C₂×C₅⋊D₈₅₅ #30685628

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₈₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(C₅⋊D₉₅)	—	3	1	no	maximal
4	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₈₅₅	—	5	6	no	maximal
6	C₃⋊(C₅⋊D₉₅)	—	3	2	no	—
7	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic
8	C₂×C₅⋊D₉₅	—	9	1	no	Hall
9	C₂×C₅×C₉×C₁₉	D₅	1	6	yes	complemented
10	D₈₅₅	—	5	12	no	—
11	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
12	C₂×D₂₈₅	—	15	6	no	—
13	C₂×C₅²×C₁₉	D₉	1	1	yes	characteristic, complemented
14	C₅⋊D₉₅	—	9	2	no	—
15	C₂×C₅⋊D₄₅	—	19	1	no	maximal, Hall
16	C₅×C₉×C₁₉	C₂×D₅	1	6	yes	complemented
17	C₂×D₁₇₁	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₉	D₁₅	1	6	yes	—
19	D₂₈₅	—	15	12	no	—
20	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²×C₉	D₁₉	1	1	yes	characteristic, complemented
22	C₅⋊D₄₅	—	19	2	no	—
23	C₂×D₉₅	—	45	6	no	—
24	C₂×C₉×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented
25	D₁₇₁	—	25	2	no	—
26	C₂×C₃⋊(C₅⋊D₅)	—	57	1	no	—
27	C₃×C₅×C₁₉	C₂×D₁₅	1	6	yes	—
28	C₂×D₅₇	—	75	1	no	—
29	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	D₄₅	1	6	yes	complemented
31	D₉₅	—	45	12	no	—
32	C₂×D₄₅	—	95	6	no	—
33	C₉×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅²	D₅₇	1	1	yes	characteristic
35	C₃⋊(C₅⋊D₅)	—	57	2	no	—
36	C₂×C₃×C₁₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
37	D₅₇	—	75	2	no	—
38	C₂×C₅⋊D₅	—	171	1	no	Hall
39	C₅×C₁₉	C₂×D₄₅	1	6	yes	complemented
40	C₂×C₅×C₉	D₉₅	1	6	yes	complemented
41	D₄₅	—	95	12	no	—
42	C₂×D₁₉	—	225	1	no	Hall
43	C₃×C₅²	C₂×D₅₇	1	1	yes	characteristic
44	C₂×D₁₅	—	285	6	no	—
45	C₃×C₁₉	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
46	C₂×C₅²	D₁₇₁	1	1	yes	characteristic, complemented
47	C₅⋊D₅	—	171	2	no	—
48	C₅×C₉	C₂×D₉₅	1	6	yes	complemented
49	C₂×C₁₉	C₅⋊D₄₅	1	1	yes	characteristic, complemented
50	D₁₉	—	225	2	no	—
51	C₂×D₉	—	475	1	no	Hall
52	C₂×C₃×C₅	D₂₈₅	1	6	yes	—
53	D₁₅	—	285	12	no	—
54	C₅²	C₂×D₁₇₁	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	855	6	no	—
56	C₁₉	C₂×C₅⋊D₄₅	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₉	C₅⋊D₉₅	1	1	yes	characteristic, complemented
58	D₉	—	475	2	no	—
59	C₃×C₅	C₂×D₂₈₅	1	6	yes	—
60	C₂×D₃	—	1425	1	no	—
61	C₂×C₅	D₈₅₅	1	6	yes	complemented
62	D₅	—	855	12	no	—
63	C₉	C₂×C₅⋊D₉₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₃⋊(C₅⋊D₉₅)	1	1	yes	characteristic
65	D₃	—	1425	2	no	—
66	C₅	C₂×D₈₅₅	1	6	yes	complemented
67	C₂²	—	4275	1	no	Sylow
68	C₃	C₂×C₃⋊(C₅⋊D₉₅)	1	1	yes	characteristic
69	C₂	—	4275	2	no	—
70	C₂	C₅⋊D₈₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₈₅₅
commutator, cosocle, hypocenter	C₅²×C₉×C₁₉	C₂²
Frattini	C₃	C₂×C₃⋊(C₅⋊D₉₅)
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₅²×C₉×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₈₅₅	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₉	C₂	semidirect
4. C₅²×C₉×C₁₉	C₂²	semidirect
9. C₂×C₅×C₉×C₁₉	D₅	semidirect
13. C₂×C₅²×C₁₉	D₉	semidirect
16. C₅×C₉×C₁₉	C₂×D₅	semidirect
20. C₅²×C₁₉	C₂×D₉	semidirect
21. C₂×C₅²×C₉	D₁₉	semidirect
24. C₂×C₉×C₁₉	C₅⋊D₅	semidirect
29. C₅²×C₉	C₂×D₁₉	semidirect
30. C₂×C₅×C₁₉	D₄₅	semidirect
33. C₉×C₁₉	C₂×C₅⋊D₅	semidirect
39. C₅×C₁₉	C₂×D₄₅	semidirect
40. C₂×C₅×C₉	D₉₅	semidirect
46. C₂×C₅²	D₁₇₁	semidirect
48. C₅×C₉	C₂×D₉₅	semidirect
49. C₂×C₁₉	C₅⋊D₄₅	semidirect
54. C₅²	C₂×D₁₇₁	semidirect
56. C₁₉	C₂×C₅⋊D₄₅	semidirect
57. C₂×C₉	C₅⋊D₉₅	semidirect
61. C₂×C₅	D₈₅₅	semidirect
63. C₉	C₂×C₅⋊D₉₅	semidirect
66. C₅	C₂×D₈₅₅	semidirect
70. C₂	C₅⋊D₈₅₅	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⋊D₈₅₅	2
C₂×C₅²×C₉×C₁₉	2
C₂×C₃⋊(C₅⋊D₉₅)	3
C₂×D₈₅₅	5
C₂×C₅⋊D₄₅	19

Subgroups — C2×C5⋊D855 #30685628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊D₈₅₅ #30685628