Subgroups — C₂⁵×Dic₂₆ #16776799

Order 3328.

63326 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₂₆	C₂	1	124	yes	maximal, direct product factor
2	C₂⁵×Dic₁₃	C₂	1	2	yes	maximal
3	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₃	C₂²	1	62	yes	—
6	C₂⁴×Dic₁₃	C₂²	1	124	yes	—
7	C₂³×Dic₂₆	C₂²	1	2480	yes	direct product factor
8	C₂⁵×C₁₃	Q₈	1	32	yes	complemented
9	C₂⁵×C₁₃	C₂³	1	31	yes	—
10	C₂³×C₄×C₁₃	C₂³	1	620	yes	—
11	C₂³×Dic₁₃	C₂³	1	1240	yes	—
12	C₂²×Dic₂₆	C₂³	1	9920	yes	direct product factor
13	C₂⁵×Q₈	—	13	1	no	maximal, Sylow
14	C₂⁴×C₁₃	C₂×Q₈	1	496	yes	complemented
15	C₂⁴×C₁₃	C₂⁴	1	155	yes	—
16	C₂²×C₄×C₁₃	C₂⁴	1	1240	yes	—
17	C₂²×Dic₁₃	C₂⁴	1	2480	yes	—
18	C₂×Dic₂₆	C₂⁴	1	7936	yes	direct product factor
19	C₂⁴×Q₈	—	13	124	no	—
20	C₂⁵×C₄	—	13	2	no	—
21	C₂⁵×C₄	D₁₃	1	1	yes	characteristic
22	C₂³×C₁₃	C₂²×Q₈	1	1240	yes	complemented
23	C₂³×C₁₃	C₂⁵	1	155	yes	—
24	C₂×C₄×C₁₃	C₂⁵	1	496	yes	—
25	C₂×Dic₁₃	C₂⁵	1	992	yes	—
26	Dic₂₆	C₂⁵	1	1024	yes	direct product factor
27	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
28	C₂³×Q₈	—	13	2480	no	—
29	C₂⁴×C₄	—	13	124	no	—
30	C₂⁴×C₄	C₂×D₁₃	1	62	yes	—
31	C₂²×C₁₃	C₂³×Q₈	1	620	yes	complemented
32	C₂²×C₁₃	C₂⁶	1	31	yes	—
33	C₄×C₁₃	C₂⁶	1	32	yes	—
34	Dic₁₃	C₂⁶	1	64	yes	—
35	C₂⁵	Dic₂₆	1	32	yes	direct product factor
36	C₂⁵	C₂²×D₁₃	1	31	yes	—
37	C₂²×Q₈	—	13	9920	no	—
38	C₂³×C₄	—	13	1240	no	—
39	C₂³×C₄	C₂²×D₁₃	1	620	yes	—
40	C₂×C₁₃	C₂⁴×Q₈	1	62	yes	complemented
41	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
42	C₂⁴	C₂×Dic₂₆	1	496	yes	direct product factor
43	C₂⁴	C₂³×D₁₃	1	155	yes	—
44	C₂×Q₈	—	13	7936	no	—
45	C₂²×C₄	—	13	2480	no	—
46	C₂²×C₄	C₂³×D₁₃	1	1240	yes	—
47	C₁₃	C₂⁵×Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₂³	C₂²×Dic₂₆	1	1240	yes	direct product factor
49	C₂³	C₂⁴×D₁₃	1	155	yes	—
50	Q₈	—	13	1024	no	—
51	C₂×C₄	—	13	992	no	—
52	C₂×C₄	C₂⁴×D₁₃	1	496	yes	—
53	C₂²	C₂³×Dic₂₆	1	620	yes	direct product factor
54	C₂²	C₂⁵×D₁₃	1	31	yes	—
55	C₄	—	13	64	no	—
56	C₄	C₂⁵×D₁₃	1	32	yes	—
57	C₂	C₂⁴×Dic₂₆	1	62	yes	direct product factor
58	C₂	C₂⁶×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁶	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂⁷
Frattini	C₂	C₂⁶×D₁₃
Fitting	C₂⁵×C₄×C₁₃	C₂
socle, prime radical	C₂⁶×C₁₃	C₂²
hypercenter	C₂⁵×C₄	D₁₃
hypocenter	C₁₃	C₂⁵×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Dic₂₆	C₂	direct (N × H)
7. C₂³×Dic₂₆	C₂²	direct (N × H)
8. C₂⁵×C₁₃	Q₈	semidirect
12. C₂²×Dic₂₆	C₂³	direct (N × H)
14. C₂⁴×C₁₃	C₂×Q₈	semidirect
18. C₂×Dic₂₆	C₂⁴	direct (N × H)
22. C₂³×C₁₃	C₂²×Q₈	semidirect
26. Dic₂₆	C₂⁵	direct (N × H)
31. C₂²×C₁₃	C₂³×Q₈	semidirect
35. C₂⁵	Dic₂₆	direct (N × H)
40. C₂×C₁₃	C₂⁴×Q₈	semidirect
42. C₂⁴	C₂×Dic₂₆	direct (N × H)
47. C₁₃	C₂⁵×Q₈	semidirect
48. C₂³	C₂²×Dic₂₆	direct (N × H)
53. C₂²	C₂³×Dic₂₆	direct (N × H)
57. C₂	C₂⁴×Dic₂₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₂₆	2
C₂⁵×Dic₁₃	2
C₂⁵×C₄×C₁₃	2
C₂⁵×Q₈	13

Subgroups — C25×Dic26 #16776799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×Dic₂₆ #16776799