Subgroups — C₂⁵×#261 #13131833

Order 1664.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×#261	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₁₃	C₄	1	1	yes	characteristic, complemented
4	C₂⁴×D₁₃	C₄	1	31	yes	complemented
5	C₂⁴×D₁₃	C₂²	1	31	yes	—
6	C₂³×#261	C₂²	1	620	yes	direct product factor
7	C₂⁴×C₁₃	C₂×C₄	1	31	yes	complemented
8	C₂³×D₁₃	C₂×C₄	1	465	yes	complemented
9	C₂³×D₁₃	C₂³	1	155	yes	—
10	C₂²×#261	C₂³	1	1240	yes	direct product factor
11	C₂⁵×C₄	—	13	1	no	maximal, Sylow
12	C₂³×C₁₃	C₂²×C₄	1	155	yes	complemented
13	C₂²×D₁₃	C₂²×C₄	1	1085	yes	complemented
14	C₂²×D₁₃	C₂⁴	1	155	yes	—
15	C₂×#261	C₂⁴	1	496	yes	direct product factor
16	C₂⁶	—	13	1	no	—
17	C₂⁴×C₄	—	13	62	no	—
18	C₂²×C₁₃	C₂³×C₄	1	155	yes	complemented
19	C₂×D₁₃	C₂³×C₄	1	465	yes	complemented
20	C₂×D₁₃	C₂⁵	1	31	yes	—
21	#261	C₂⁵	1	32	yes	direct product factor
22	C₂⁵	—	13	31	no	—
23	C₂⁵	—	13	31	no	—
24	C₂⁵	#261	1	1	yes	characteristic, direct product factor
25	C₂³×C₄	—	13	620	no	—
26	C₂×C₁₃	C₂⁴×C₄	1	31	yes	complemented
27	D₁₃	C₂⁴×C₄	1	31	yes	complemented
28	D₁₃	C₂⁶	1	1	yes	characteristic
29	C₂⁴	—	13	155	no	—
30	C₂⁴	—	13	465	no	—
31	C₂⁴	C₂×#261	1	31	yes	direct product factor
32	C₂²×C₄	—	13	1240	no	—
33	C₁₃	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
34	C₂³	—	13	155	no	—
35	C₂³	—	13	1085	no	—
36	C₂³	C₂²×#261	1	155	yes	direct product factor
37	C₂×C₄	—	13	496	no	—
38	C₂²	—	13	465	no	—
39	C₂²	—	13	31	no	—
40	C₂²	C₂³×#261	1	155	yes	direct product factor
41	C₄	—	13	32	no	—
42	C₂	—	13	1	no	—
43	C₂	—	13	31	no	—
44	C₂	C₂⁴×#261	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	#261
commutator, hypocenter	C₁₃	C₂⁵×C₄
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₄
prime radical	C₂⁵×D₁₃	C₂
cosocle	D₁₃	C₂⁶
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂⁴×#261	C₂	direct (N × H)
3. C₂⁵×C₁₃	C₄	semidirect
4. C₂⁴×D₁₃	C₄	semidirect
6. C₂³×#261	C₂²	direct (N × H)
7. C₂⁴×C₁₃	C₂×C₄	semidirect
8. C₂³×D₁₃	C₂×C₄	semidirect
10. C₂²×#261	C₂³	direct (N × H)
12. C₂³×C₁₃	C₂²×C₄	semidirect
13. C₂²×D₁₃	C₂²×C₄	semidirect
15. C₂×#261	C₂⁴	direct (N × H)
18. C₂²×C₁₃	C₂³×C₄	semidirect
19. C₂×D₁₃	C₂³×C₄	semidirect
21. #261	C₂⁵	direct (N × H)
24. C₂⁵	#261	direct (N × H)
26. C₂×C₁₃	C₂⁴×C₄	semidirect
27. D₁₃	C₂⁴×C₄	semidirect
31. C₂⁴	C₂×#261	direct (N × H)
33. C₁₃	C₂⁵×C₄	semidirect
36. C₂³	C₂²×#261	direct (N × H)
40. C₂²	C₂³×#261	direct (N × H)
44. C₂	C₂⁴×#261	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×D₁₃	2
C₂⁴×#261	2
C₂⁵×C₄	13

Subgroups — C25×#261 #13131833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#261 #13131833