Subgroups — C₂⁵×D₁₃⋊C₃ #72276164

Order 2496.

11300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₁₃⋊C₃	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂⁴×C₁₃⋊C₃	C₂²	1	31	yes	complemented
5	C₂³×D₁₃⋊C₃	C₂²	1	620	yes	direct product factor
6	C₂⁵×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂⁴×D₁₃	C₂×C₃	1	62	yes	complemented
8	C₂³×C₁₃⋊C₃	C₂³	1	155	yes	complemented
9	C₂²×D₁₃⋊C₃	C₂³	1	1240	yes	direct product factor
10	C₂⁴×C₁₃	C₂²×C₃	1	31	yes	complemented
11	C₂³×D₁₃	C₂²×C₃	1	620	yes	complemented
12	C₂⁶×C₃	—	13	1	no	maximal, Hall
13	C₂²×C₁₃⋊C₃	C₂⁴	1	155	yes	complemented
14	C₂×D₁₃⋊C₃	C₂⁴	1	496	yes	direct product factor
15	C₂³×C₁₃	C₂³×C₃	1	155	yes	complemented
16	C₂²×D₁₃	C₂³×C₃	1	1240	yes	complemented
17	C₂⁵×C₃	—	13	62	no	—
18	C₂⁵×C₃	—	13	1	no	—
19	C₂×C₁₃⋊C₃	C₂⁵	1	31	yes	complemented
20	D₁₃⋊C₃	C₂⁵	1	32	yes	direct product factor
21	C₂⁶	—	13	1	no	Sylow
22	C₂²×C₁₃	C₂⁴×C₃	1	155	yes	complemented
23	C₂×D₁₃	C₂⁴×C₃	1	496	yes	complemented
24	C₂⁴×C₃	—	13	620	no	—
25	C₂⁴×C₃	—	13	31	no	—
26	C₁₃⋊C₃	C₂⁶	1	1	yes	characteristic, complemented, Hall
27	C₂⁵	—	13	62	no	—
28	C₂⁵	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂×C₁₃	C₂⁵×C₃	1	31	yes	complemented
30	D₁₃	C₂⁵×C₃	1	32	yes	complemented
31	C₂³×C₃	—	13	1240	no	—
32	C₂³×C₃	—	13	155	no	—
33	C₂⁴	—	13	620	no	—
34	C₂⁴	C₂×D₁₃⋊C₃	1	31	yes	direct product factor
35	C₁₃	C₂⁶×C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	—	13	496	no	—
37	C₂²×C₃	—	13	155	no	—
38	C₂³	—	13	1240	no	—
39	C₂³	C₂²×D₁₃⋊C₃	1	155	yes	direct product factor
40	C₂×C₃	—	13	32	no	—
41	C₂×C₃	—	13	31	no	—
42	C₂²	—	13	496	no	—
43	C₂²	C₂³×D₁₃⋊C₃	1	155	yes	direct product factor
44	C₃	—	13	1	no	Sylow
45	C₂	—	13	32	no	—
46	C₂	C₂⁴×D₁₃⋊C₃	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂⁶×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₁₃⋊C₃	C₂	semidirect
2. C₂⁴×D₁₃⋊C₃	C₂	direct (N × H)
3. C₂⁵×D₁₃	C₃	semidirect
4. C₂⁴×C₁₃⋊C₃	C₂²	semidirect
5. C₂³×D₁₃⋊C₃	C₂²	direct (N × H)
6. C₂⁵×C₁₃	C₂×C₃	semidirect
7. C₂⁴×D₁₃	C₂×C₃	semidirect
8. C₂³×C₁₃⋊C₃	C₂³	semidirect
9. C₂²×D₁₃⋊C₃	C₂³	direct (N × H)
10. C₂⁴×C₁₃	C₂²×C₃	semidirect
11. C₂³×D₁₃	C₂²×C₃	semidirect
13. C₂²×C₁₃⋊C₃	C₂⁴	semidirect
14. C₂×D₁₃⋊C₃	C₂⁴	direct (N × H)
15. C₂³×C₁₃	C₂³×C₃	semidirect
16. C₂²×D₁₃	C₂³×C₃	semidirect
19. C₂×C₁₃⋊C₃	C₂⁵	semidirect
20. D₁₃⋊C₃	C₂⁵	direct (N × H)
22. C₂²×C₁₃	C₂⁴×C₃	semidirect
23. C₂×D₁₃	C₂⁴×C₃	semidirect
26. C₁₃⋊C₃	C₂⁶	semidirect
28. C₂⁵	D₁₃⋊C₃	direct (N × H)
29. C₂×C₁₃	C₂⁵×C₃	semidirect
30. D₁₃	C₂⁵×C₃	semidirect
34. C₂⁴	C₂×D₁₃⋊C₃	direct (N × H)
35. C₁₃	C₂⁶×C₃	semidirect
39. C₂³	C₂²×D₁₃⋊C₃	direct (N × H)
43. C₂²	C₂³×D₁₃⋊C₃	direct (N × H)
46. C₂	C₂⁴×D₁₃⋊C₃	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×C₁₃⋊C₃	2
C₂⁴×D₁₃⋊C₃	2
C₂⁵×D₁₃	3
C₂⁶×C₃	13

Subgroups — C25×D13⋊C3 #72276164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₁₃⋊C₃ #72276164