Subgroups — C₂⁶×Dic₅₃ #28297967

Order 13568.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₅₃	C₂	1	126	yes	maximal, direct product factor
2	C₂⁷×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×Dic₅₃	C₂²	1	2604	yes	direct product factor
4	C₂⁶×C₅₃	C₄	1	64	yes	complemented
5	C₂⁶×C₅₃	C₂²	1	63	yes	—
6	C₂³×Dic₅₃	C₂³	1	11160	yes	direct product factor
7	C₂⁵×C₅₃	C₂×C₄	1	2016	yes	complemented
8	C₂⁵×C₅₃	C₂³	1	651	yes	—
9	C₂⁴×C₅₃	C₂²×C₄	1	10416	yes	complemented
10	C₂⁴×C₅₃	C₂⁴	1	1395	yes	—
11	C₂²×Dic₅₃	C₂⁴	1	10416	yes	direct product factor
12	C₂³×C₅₃	C₂³×C₄	1	11160	yes	complemented
13	C₂³×C₅₃	C₂⁵	1	651	yes	—
14	C₂×Dic₅₃	C₂⁵	1	2016	yes	direct product factor
15	C₂⁶×C₄	—	53	1	no	maximal, Sylow
16	C₂²×C₅₃	C₂⁴×C₄	1	2604	yes	complemented
17	C₂²×C₅₃	C₂⁶	1	63	yes	—
18	Dic₅₃	C₂⁶	1	64	yes	direct product factor
19	C₂⁷	D₅₃	1	1	yes	characteristic
20	C₂⁵×C₄	—	53	126	no	—
21	C₂×C₅₃	C₂⁵×C₄	1	126	yes	complemented
22	C₂×C₅₃	C₂⁷	1	1	yes	characteristic
23	C₂⁶	Dic₅₃	1	64	yes	direct product factor
24	C₂⁶	C₂×D₅₃	1	63	yes	—
25	C₂⁴×C₄	—	53	2604	no	—
26	C₅₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
27	C₂⁵	C₂×Dic₅₃	1	2016	yes	direct product factor
28	C₂⁵	C₂²×D₅₃	1	651	yes	—
29	C₂³×C₄	—	53	11160	no	—
30	C₂⁴	C₂²×Dic₅₃	1	10416	yes	direct product factor
31	C₂⁴	C₂³×D₅₃	1	1395	yes	—
32	C₂²×C₄	—	53	10416	no	—
33	C₂³	C₂³×Dic₅₃	1	11160	yes	direct product factor
34	C₂³	C₂⁴×D₅₃	1	651	yes	—
35	C₂×C₄	—	53	2016	no	—
36	C₂²	C₂⁴×Dic₅₃	1	2604	yes	direct product factor
37	C₂²	C₂⁵×D₅₃	1	63	yes	—
38	C₄	—	53	64	no	—
39	C₂	C₂⁵×Dic₅₃	1	126	yes	direct product factor
40	C₂	C₂⁶×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁷	D₅₃
commutator, hypocenter	C₅₃	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₅₃
Fitting, socle, prime radical	C₂⁷×C₅₃	C₂
cosocle	C₂×C₅₃	C₂⁷
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₅₃	C₂	direct (N × H)
3. C₂⁴×Dic₅₃	C₂²	direct (N × H)
4. C₂⁶×C₅₃	C₄	semidirect
6. C₂³×Dic₅₃	C₂³	direct (N × H)
7. C₂⁵×C₅₃	C₂×C₄	semidirect
9. C₂⁴×C₅₃	C₂²×C₄	semidirect
11. C₂²×Dic₅₃	C₂⁴	direct (N × H)
12. C₂³×C₅₃	C₂³×C₄	semidirect
14. C₂×Dic₅₃	C₂⁵	direct (N × H)
16. C₂²×C₅₃	C₂⁴×C₄	semidirect
18. Dic₅₃	C₂⁶	direct (N × H)
21. C₂×C₅₃	C₂⁵×C₄	semidirect
23. C₂⁶	Dic₅₃	direct (N × H)
26. C₅₃	C₂⁶×C₄	semidirect
27. C₂⁵	C₂×Dic₅₃	direct (N × H)
30. C₂⁴	C₂²×Dic₅₃	direct (N × H)
33. C₂³	C₂³×Dic₅₃	direct (N × H)
36. C₂²	C₂⁴×Dic₅₃	direct (N × H)
39. C₂	C₂⁵×Dic₅₃	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×Dic₅₃	2
C₂⁷×C₅₃	2
C₂⁶×C₄	53

Subgroups — C26×Dic53 #28297967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×Dic₅₃ #28297967