Subgroups — C₂×C₁₃²×D₂₅ #30683407

Order 16900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×D₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₁₃²	—	5	1	no	maximal
5	C₂×C₅×C₁₃²	D₅	1	1	yes	characteristic
6	D₅×C₁₃²	—	5	2	no	—
7	C₂×C₁₃×D₂₅	C₁₃	1	14	yes	maximal, direct product factor
8	C₅×C₁₃²	C₂×D₅	1	1	yes	characteristic
9	C₂²×C₁₃²	—	25	1	no	Hall
10	C₂×C₁₃×C₂₅	C₂×C₁₃	1	14	yes	complemented
11	C₁₃×D₂₅	C₂×C₁₃	1	28	yes	direct product factor
12	C₂×C₁₃²	—	25	2	no	—
13	C₂×C₁₃²	D₂₅	1	1	yes	characteristic, direct product factor
14	C₁₃×C₂₅	C₂²×C₁₃	1	14	yes	complemented
15	C₂×D₅×C₁₃	—	5	14	no	—
16	C₁₃²	C₂×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₅×C₁₃	D₅×C₁₃	1	14	yes	—
18	D₅×C₁₃	—	5	28	no	—
19	C₂×D₂₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	C₂×D₅×C₁₃	1	14	yes	—
21	C₂²×C₁₃	—	25	14	no	—
22	C₂×C₂₅	C₂×C₁₃²	1	1	yes	characteristic, complemented
23	D₂₅	C₂×C₁₃²	1	2	yes	direct product factor
24	C₂×C₁₃	—	25	28	no	—
25	C₂×C₁₃	C₁₃×D₂₅	1	14	yes	direct product factor
26	C₂₅	C₂²×C₁₃²	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	5	1	no	—
28	C₁₃	C₂×C₁₃×D₂₅	1	14	yes	direct product factor
29	C₂×C₅	D₅×C₁₃²	1	1	yes	characteristic
30	D₅	—	5	2	no	—
31	C₅	C₂×D₅×C₁₃²	1	1	yes	characteristic
32	C₂²	—	25	1	no	Sylow
33	C₂	—	25	2	no	—
34	C₂	C₁₃²×D₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃²	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₁₃²
Frattini	C₅	C₂×D₅×C₁₃²
Fitting	C₂×C₁₃²×C₂₅	C₂
socle	C₂×C₅×C₁₃²	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₁₃²

Complements

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

N	H ≅ G/N	type
1. C₁₃²×D₂₅	C₂	direct (N × H)
2. C₂×C₁₃²×C₂₅	C₂	semidirect
3. C₁₃²×C₂₅	C₂²	semidirect
7. C₂×C₁₃×D₂₅	C₁₃	direct (N × H)
10. C₂×C₁₃×C₂₅	C₂×C₁₃	semidirect
11. C₁₃×D₂₅	C₂×C₁₃	direct (N × H)
13. C₂×C₁₃²	D₂₅	direct (N × H)
14. C₁₃×C₂₅	C₂²×C₁₃	semidirect
16. C₁₃²	C₂×D₂₅	direct (N × H)
19. C₂×D₂₅	C₁₃²	direct (N × H)
22. C₂×C₂₅	C₂×C₁₃²	semidirect
23. D₂₅	C₂×C₁₃²	direct (N × H)
25. C₂×C₁₃	C₁₃×D₂₅	direct (N × H)
26. C₂₅	C₂²×C₁₃²	semidirect
28. C₁₃	C₂×C₁₃×D₂₅	direct (N × H)
34. C₂	C₁₃²×D₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃²×D₂₅	2
C₂×C₁₃²×C₂₅	2
C₂×D₅×C₁₃²	5
C₂×C₁₃×D₂₅	13

Subgroups — C2×C132×D25 #30683407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃²×D₂₅ #30683407