Subgroups — C₂×C₅⋊D₁₅₉₅ #44542129

Order 31900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₁₅₉₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₅₉₅	—	5	6	no	maximal
5	D₁₅₉₅	—	5	12	no	—
6	C₂×C₅×C₁₁×C₂₉	D₅	1	6	yes	complemented
7	C₂×C₅⋊D₁₄₅	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₂₉	C₂×D₅	1	6	yes	complemented
9	C₂×C₅²×C₂₉	D₁₁	1	1	yes	characteristic, complemented
10	C₅⋊D₁₄₅	—	11	2	no	—
11	C₂×D₃₁₉	—	25	1	no	Hall
12	C₂×C₅⋊D₅₅	—	29	1	no	maximal, Hall
13	C₅²×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₂₉	C₅⋊D₅	1	1	yes	characteristic, complemented
15	D₃₁₉	—	25	2	no	—
16	C₂×D₁₄₅	—	55	6	no	—
17	C₂×C₅²×C₁₁	D₂₉	1	1	yes	characteristic, complemented
18	C₅⋊D₅₅	—	29	2	no	—
19	C₁₁×C₂₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₂₉	D₅₅	1	6	yes	complemented
21	D₁₄₅	—	55	12	no	—
22	C₅²×C₁₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅₅	—	145	6	no	—
24	C₅×C₂₉	C₂×D₅₅	1	6	yes	complemented
25	C₂×D₂₉	—	275	1	no	Hall
26	C₂×C₅×C₁₁	D₁₄₅	1	6	yes	complemented
27	D₅₅	—	145	12	no	—
28	C₂×C₅⋊D₅	—	319	1	no	Hall
29	C₂×C₂₉	C₅⋊D₅₅	1	1	yes	characteristic, complemented
30	D₂₉	—	275	2	no	—
31	C₅×C₁₁	C₂×D₁₄₅	1	6	yes	complemented
32	C₂×C₅²	D₃₁₉	1	1	yes	characteristic, complemented
33	C₅⋊D₅	—	319	2	no	—
34	C₂×D₁₁	—	725	1	no	Hall
35	C₂₉	C₂×C₅⋊D₅₅	1	1	yes	characteristic, complemented, Sylow
36	C₅²	C₂×D₃₁₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	C₅⋊D₁₄₅	1	1	yes	characteristic, complemented
38	D₁₁	—	725	2	no	—
39	C₂×D₅	—	1595	6	no	—
40	C₁₁	C₂×C₅⋊D₁₄₅	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	D₁₅₉₅	1	6	yes	complemented
42	D₅	—	1595	12	no	—
43	C₅	C₂×D₁₅₉₅	1	6	yes	complemented
44	C₂²	—	7975	1	no	Sylow
45	C₂	—	7975	2	no	—
46	C₂	C₅⋊D₁₅₉₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₁₅₉₅
commutator, cosocle, hypocenter	C₅²×C₁₁×C₂₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₂₉	C₂
LCS	G ▷ C₅²×C₁₁×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₁₅₉₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₂₉	C₂	semidirect
3. C₅²×C₁₁×C₂₉	C₂²	semidirect
6. C₂×C₅×C₁₁×C₂₉	D₅	semidirect
8. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
9. C₂×C₅²×C₂₉	D₁₁	semidirect
13. C₅²×C₂₉	C₂×D₁₁	semidirect
14. C₂×C₁₁×C₂₉	C₅⋊D₅	semidirect
17. C₂×C₅²×C₁₁	D₂₉	semidirect
19. C₁₁×C₂₉	C₂×C₅⋊D₅	semidirect
20. C₂×C₅×C₂₉	D₅₅	semidirect
22. C₅²×C₁₁	C₂×D₂₉	semidirect
24. C₅×C₂₉	C₂×D₅₅	semidirect
26. C₂×C₅×C₁₁	D₁₄₅	semidirect
29. C₂×C₂₉	C₅⋊D₅₅	semidirect
31. C₅×C₁₁	C₂×D₁₄₅	semidirect
32. C₂×C₅²	D₃₁₉	semidirect
35. C₂₉	C₂×C₅⋊D₅₅	semidirect
36. C₅²	C₂×D₃₁₉	semidirect
37. C₂×C₁₁	C₅⋊D₁₄₅	semidirect
40. C₁₁	C₂×C₅⋊D₁₄₅	semidirect
41. C₂×C₅	D₁₅₉₅	semidirect
43. C₅	C₂×D₁₅₉₅	semidirect
46. C₂	C₅⋊D₁₅₉₅	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⋊D₁₅₉₅	2
C₂×C₅²×C₁₁×C₂₉	2
C₂×D₁₅₉₅	5
C₂×C₅⋊D₁₄₅	11
C₂×C₅⋊D₅₅	29

Subgroups — C2×C5⋊D1595 #44542129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊D₁₅₉₅ #44542129