Subgroups — C₅×D₅×D₂₆₉ #41001969

Order 26900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×C₂₆₉	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×C₅×D₂₆₉	—	5	1	no	maximal
6	D₅×D₂₆₉	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅×C₂₆₉	—	5	1	no	—
8	D₁₃₄₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₆₉	—	2	2	no	—
10	C₅×D₂₆₉	—	5	1	no	—
11	C₅×D₂₆₉	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₂₆₉	C₂×C₅	1	1	yes	characteristic, complemented
13	D₅×C₂₆₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₂₆₉	—	2	2	no	—
15	C₅×C₂₆₉	C₂×D₅	1	1	yes	characteristic, complemented
16	C₅×C₂₆₉	C₂²×C₅	1	1	yes	characteristic, complemented
17	C₂×D₂₆₉	—	5	1	no	Hall
18	C₂×C₂₆₉	—	5	1	no	—
19	D₂₆₉	—	5	1	no	—
20	D₂₆₉	C₅×D₅	1	1	yes	characteristic, direct product factor
21	C₂₆₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₅×D₅	—	269	1	no	maximal, Hall
23	C₂×C₅²	—	269	1	no	—
24	C₅×D₅	—	269	1	no	—
25	C₅×D₅	D₂₆₉	1	1	yes	characteristic, direct product factor
26	C₅²	C₂×D₂₆₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₅	—	1345	1	no	—
28	C₂×D₅	—	269	1	no	—
29	C₂×C₅	—	5	1	no	—
30	C₂×C₅	—	269	1	no	—
31	C₂×C₅	—	269	1	no	—
32	C₂×C₅	—	538	2	no	—
33	C₂×C₅	—	1345	1	no	—
34	D₅	—	269	1	no	—
35	D₅	C₅×D₂₆₉	1	1	yes	characteristic, direct product factor
36	C₅	—	2	2	no	—
37	C₅	D₅×D₂₆₉	1	1	yes	characteristic, direct product factor
38	C₅	C₂×C₅×D₂₆₉	1	1	yes	characteristic, complemented
39	C₂²	—	1345	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	269	1	no	—
42	C₂	—	1345	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅×D₂₆₉
commutator, cosocle, hypocenter	C₅×C₂₆₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₂₆₉	C₂²
LCS	G ▷ C₅×C₂₆₉
UCS	C₁ ◁ C₅

Complements

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

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

Maximal subgroups

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

subgroup	index
C₅²×D₂₆₉	2
C₅×D₅×C₂₆₉	2
C₅×D₁₃₄₅	2
C₂×C₅×D₂₆₉	5
D₅×D₂₆₉	5
C₂×C₅×D₅	269

Subgroups — C5×D5×D269 #41001969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×D₂₆₉ #41001969