Subgroups — C₂⁶×C₁₇×C₂₅ #72204271

Order 27200.

16950 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₁₇×C₂₅	C₂	1	63	yes	maximal, direct product factor
2	C₂⁴×C₁₇×C₂₅	C₂²	1	651	yes	direct product factor
3	C₂⁶×C₅×C₁₇	C₅	1	1	yes	maximal, characteristic
4	C₂³×C₁₇×C₂₅	C₂³	1	1395	yes	direct product factor
5	C₂⁵×C₅×C₁₇	C₂×C₅	1	63	yes	—
6	C₂²×C₁₇×C₂₅	C₂⁴	1	651	yes	direct product factor
7	C₂⁶×C₂₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₅×C₁₇	C₂²×C₅	1	651	yes	—
9	C₂⁶×C₁₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₇×C₂₅	C₂⁵	1	63	yes	direct product factor
11	C₂⁵×C₂₅	C₂×C₁₇	1	63	yes	direct product factor
12	C₂³×C₅×C₁₇	C₂³×C₅	1	1395	yes	—
13	C₂⁵×C₁₇	C₂×C₂₅	1	63	yes	direct product factor
14	C₁₇×C₂₅	C₂⁶	1	1	yes	characteristic, direct product factor, Hall
15	C₂⁴×C₂₅	C₂²×C₁₇	1	651	yes	direct product factor
16	C₂²×C₅×C₁₇	C₂⁴×C₅	1	651	yes	—
17	C₂⁶×C₅	C₅×C₁₇	1	1	yes	characteristic
18	C₂⁴×C₁₇	C₂²×C₂₅	1	651	yes	direct product factor
19	C₂³×C₂₅	C₂³×C₁₇	1	1395	yes	direct product factor
20	C₂×C₅×C₁₇	C₂⁵×C₅	1	63	yes	—
21	C₂⁵×C₅	C₂×C₅×C₁₇	1	63	yes	—
22	C₂³×C₁₇	C₂³×C₂₅	1	1395	yes	direct product factor
23	C₂²×C₂₅	C₂⁴×C₁₇	1	651	yes	direct product factor
24	C₅×C₁₇	C₂⁶×C₅	1	1	yes	characteristic
25	C₂⁴×C₅	C₂²×C₅×C₁₇	1	651	yes	—
26	C₂²×C₁₇	C₂⁴×C₂₅	1	651	yes	direct product factor
27	C₂⁶	C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₂₅	C₂⁵×C₁₇	1	63	yes	direct product factor
29	C₂³×C₅	C₂³×C₅×C₁₇	1	1395	yes	—
30	C₂×C₁₇	C₂⁵×C₂₅	1	63	yes	direct product factor
31	C₂⁵	C₂×C₁₇×C₂₅	1	63	yes	direct product factor
32	C₂₅	C₂⁶×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²×C₅	C₂⁴×C₅×C₁₇	1	651	yes	—
34	C₁₇	C₂⁶×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
35	C₂⁴	C₂²×C₁₇×C₂₅	1	651	yes	direct product factor
36	C₂×C₅	C₂⁵×C₅×C₁₇	1	63	yes	—
37	C₂³	C₂³×C₁₇×C₂₅	1	1395	yes	direct product factor
38	C₅	C₂⁶×C₅×C₁₇	1	1	yes	characteristic
39	C₂²	C₂⁴×C₁₇×C₂₅	1	651	yes	direct product factor
40	C₂	C₂⁵×C₁₇×C₂₅	1	63	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂⁶×C₅×C₁₇
socle, prime radical	C₂⁶×C₅×C₁₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₁₇×C₂₅	C₂	direct (N × H)
2. C₂⁴×C₁₇×C₂₅	C₂²	direct (N × H)
4. C₂³×C₁₇×C₂₅	C₂³	direct (N × H)
6. C₂²×C₁₇×C₂₅	C₂⁴	direct (N × H)
7. C₂⁶×C₂₅	C₁₇	direct (N × H)
9. C₂⁶×C₁₇	C₂₅	direct (N × H)
10. C₂×C₁₇×C₂₅	C₂⁵	direct (N × H)
11. C₂⁵×C₂₅	C₂×C₁₇	direct (N × H)
13. C₂⁵×C₁₇	C₂×C₂₅	direct (N × H)
14. C₁₇×C₂₅	C₂⁶	direct (N × H)
15. C₂⁴×C₂₅	C₂²×C₁₇	direct (N × H)
18. C₂⁴×C₁₇	C₂²×C₂₅	direct (N × H)
19. C₂³×C₂₅	C₂³×C₁₇	direct (N × H)
22. C₂³×C₁₇	C₂³×C₂₅	direct (N × H)
23. C₂²×C₂₅	C₂⁴×C₁₇	direct (N × H)
26. C₂²×C₁₇	C₂⁴×C₂₅	direct (N × H)
27. C₂⁶	C₁₇×C₂₅	direct (N × H)
28. C₂×C₂₅	C₂⁵×C₁₇	direct (N × H)
30. C₂×C₁₇	C₂⁵×C₂₅	direct (N × H)
31. C₂⁵	C₂×C₁₇×C₂₅	direct (N × H)
32. C₂₅	C₂⁶×C₁₇	direct (N × H)
34. C₁₇	C₂⁶×C₂₅	direct (N × H)
35. C₂⁴	C₂²×C₁₇×C₂₅	direct (N × H)
37. C₂³	C₂³×C₁₇×C₂₅	direct (N × H)
39. C₂²	C₂⁴×C₁₇×C₂₅	direct (N × H)
40. C₂	C₂⁵×C₁₇×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₁₇×C₂₅	2
C₂⁶×C₅×C₁₇	5
C₂⁶×C₂₅	17

Subgroups — C26×C17×C25 #72204271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₁₇×C₂₅ #72204271