Subgroups — C₂⁶×#595 #17981064

Order 4352.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×#595	C₂	1	126	yes	maximal, direct product factor
2	C₂⁶×D₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×#595	C₂²	1	2604	yes	direct product factor
4	C₂⁵×D₁₇	C₄	1	63	yes	complemented
5	C₂⁵×D₁₇	C₂²	1	63	yes	—
6	C₂⁶×C₁₇	C₄	1	1	yes	characteristic, complemented
7	C₂⁵×C₁₇	C₂×C₄	1	63	yes	complemented
8	C₂⁴×D₁₇	C₂×C₄	1	1953	yes	complemented
9	C₂⁴×D₁₇	C₂³	1	651	yes	—
10	C₂³×#595	C₂³	1	11160	yes	direct product factor
11	C₂⁴×C₁₇	C₂²×C₄	1	651	yes	complemented
12	C₂³×D₁₇	C₂²×C₄	1	9765	yes	complemented
13	C₂³×D₁₇	C₂⁴	1	1395	yes	—
14	C₂²×#595	C₂⁴	1	10416	yes	direct product factor
15	C₂⁶×C₄	—	17	1	no	maximal, Sylow
16	C₂³×C₁₇	C₂³×C₄	1	1395	yes	complemented
17	C₂²×D₁₇	C₂³×C₄	1	9765	yes	complemented
18	C₂²×D₁₇	C₂⁵	1	651	yes	—
19	C₂×#595	C₂⁵	1	2016	yes	direct product factor
20	C₂⁷	—	17	1	no	—
21	C₂⁵×C₄	—	17	126	no	—
22	C₂²×C₁₇	C₂⁴×C₄	1	651	yes	complemented
23	C₂×D₁₇	C₂⁴×C₄	1	1953	yes	complemented
24	C₂×D₁₇	C₂⁶	1	63	yes	—
25	#595	C₂⁶	1	64	yes	direct product factor
26	C₂⁶	—	17	63	no	—
27	C₂⁶	—	17	63	no	—
28	C₂⁶	#595	1	1	yes	characteristic, direct product factor
29	C₂⁴×C₄	—	17	2604	no	—
30	C₂×C₁₇	C₂⁵×C₄	1	63	yes	complemented
31	D₁₇	C₂⁵×C₄	1	63	yes	complemented
32	D₁₇	C₂⁷	1	1	yes	characteristic
33	C₂⁵	—	17	1953	no	—
34	C₂⁵	—	17	651	no	—
35	C₂⁵	C₂×#595	1	63	yes	direct product factor
36	C₂³×C₄	—	17	11160	no	—
37	C₁₇	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
38	C₂⁴	—	17	9765	no	—
39	C₂⁴	—	17	1395	no	—
40	C₂⁴	C₂²×#595	1	651	yes	direct product factor
41	C₂²×C₄	—	17	10416	no	—
42	C₂³	—	17	651	no	—
43	C₂³	—	17	9765	no	—
44	C₂³	C₂³×#595	1	1395	yes	direct product factor
45	C₂×C₄	—	17	2016	no	—
46	C₂²	—	17	63	no	—
47	C₂²	—	17	1953	no	—
48	C₂²	C₂⁴×#595	1	651	yes	direct product factor
49	C₄	—	17	64	no	—
50	C₂	—	17	1	no	—
51	C₂	—	17	63	no	—
52	C₂	C₂⁵×#595	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	#595
commutator, hypocenter	C₁₇	C₂⁶×C₄
Frattini	C₁	G
Fitting, socle	C₂⁶×C₁₇	C₄
prime radical	C₂⁶×D₁₇	C₂
cosocle	D₁₇	C₂⁷
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁵×#595	C₂	direct (N × H)
3. C₂⁴×#595	C₂²	direct (N × H)
4. C₂⁵×D₁₇	C₄	semidirect
6. C₂⁶×C₁₇	C₄	semidirect
7. C₂⁵×C₁₇	C₂×C₄	semidirect
8. C₂⁴×D₁₇	C₂×C₄	semidirect
10. C₂³×#595	C₂³	direct (N × H)
11. C₂⁴×C₁₇	C₂²×C₄	semidirect
12. C₂³×D₁₇	C₂²×C₄	semidirect
14. C₂²×#595	C₂⁴	direct (N × H)
16. C₂³×C₁₇	C₂³×C₄	semidirect
17. C₂²×D₁₇	C₂³×C₄	semidirect
19. C₂×#595	C₂⁵	direct (N × H)
22. C₂²×C₁₇	C₂⁴×C₄	semidirect
23. C₂×D₁₇	C₂⁴×C₄	semidirect
25. #595	C₂⁶	direct (N × H)
28. C₂⁶	#595	direct (N × H)
30. C₂×C₁₇	C₂⁵×C₄	semidirect
31. D₁₇	C₂⁵×C₄	semidirect
35. C₂⁵	C₂×#595	direct (N × H)
37. C₁₇	C₂⁶×C₄	semidirect
40. C₂⁴	C₂²×#595	direct (N × H)
44. C₂³	C₂³×#595	direct (N × H)
48. C₂²	C₂⁴×#595	direct (N × H)
52. C₂	C₂⁵×#595	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×#595	2
C₂⁶×D₁₇	2
C₂⁶×C₄	17

Subgroups — C26×#595 #17981064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×#595 #17981064