Subgroups — D₅×D₁₃₄₅ #41001979

Order 26900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₃₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊D₁₃₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₂₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₃₄₅	—	5	1	no	maximal
6	D₅×D₂₆₉	—	5	1	no	maximal
7	C₂×C₅×C₂₆₉	—	5	1	no	—
8	D₁₃₄₅	—	5	1	no	—
9	D₁₃₄₅	—	5	1	no	—
10	D₁₃₄₅	—	10	2	no	—
11	D₁₃₄₅	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₂₆₉	—	5	1	no	—
13	D₅×C₂₆₉	D₅	1	1	yes	characteristic, complemented
14	C₅×C₂₆₉	—	2	2	no	—
15	C₅×C₂₆₉	C₂×D₅	1	1	yes	characteristic, complemented
16	C₅×C₂₆₉	C₂×D₅	1	1	yes	characteristic, complemented
17	C₂×D₂₆₉	—	25	1	no	Hall
18	C₂×C₂₆₉	—	5	1	no	—
19	D₂₆₉	—	5	1	no	—
20	D₂₆₉	—	25	1	no	—
21	C₂₆₉	D₅²	1	1	yes	characteristic, complemented, Sylow
22	D₅²	—	269	1	no	maximal, Hall
23	C₅⋊D₅	—	269	1	no	—
24	C₅×D₅	—	269	1	no	—
25	C₅×D₅	D₂₆₉	1	1	yes	characteristic, complemented
26	C₅²	C₂×D₂₆₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	1345	1	no	—
28	C₂×D₅	—	1345	1	no	—
29	C₂×C₅	—	5	1	no	—
30	C₂×C₅	—	1345	1	no	—
31	D₅	—	269	1	no	—
32	D₅	—	1345	1	no	—
33	D₅	—	1345	1	no	—
34	D₅	—	2690	2	no	—
35	D₅	D₁₃₄₅	1	1	yes	characteristic, direct product factor
36	C₅	—	2	2	no	—
37	C₅	D₅×D₂₆₉	1	1	yes	characteristic, complemented
38	C₅	C₂×D₁₃₄₅	1	1	yes	characteristic, complemented
39	C₂²	—	6725	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	1345	1	no	—
42	C₂	—	6725	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₂₆₉	C₂²
LCS	G ▷ C₅²×C₂₆₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₂₆₉	C₂	semidirect
2. C₅×D₁₃₄₅	C₂	semidirect
3. C₅⋊D₁₃₄₅	C₂	semidirect
4. C₅²×C₂₆₉	C₂²	semidirect
11. D₁₃₄₅	D₅	direct (N × H)
13. D₅×C₂₆₉	D₅	semidirect
15. C₅×C₂₆₉	C₂×D₅	semidirect
16. C₅×C₂₆₉	C₂×D₅	semidirect
21. C₂₆₉	D₅²	semidirect
25. C₅×D₅	D₂₆₉	semidirect
26. C₅²	C₂×D₂₆₉	semidirect
35. D₅	D₁₃₄₅	direct (N × H)
37. C₅	D₅×D₂₆₉	semidirect
38. C₅	C₂×D₁₃₄₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₂₆₉	2
C₅×D₁₃₄₅	2
C₅⋊D₁₃₄₅	2
C₂×D₁₃₄₅	5
D₅×D₂₆₉	5
D₅²	269

Subgroups — D5×D1345 #41001979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₃₄₅ #41001979