Subgroups — C₂⁵×Dic₁₁₃ #28405364

Order 14464.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₁₁₃	C₂	1	62	yes	maximal, direct product factor
2	C₂⁶×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₁₁₃	C₂²	1	620	yes	direct product factor
4	C₂⁵×C₁₁₃	C₄	1	32	yes	complemented
5	C₂⁵×C₁₁₃	C₂²	1	31	yes	—
6	C₂²×Dic₁₁₃	C₂³	1	1240	yes	direct product factor
7	C₂⁴×C₁₁₃	C₂×C₄	1	496	yes	complemented
8	C₂⁴×C₁₁₃	C₂³	1	155	yes	—
9	C₂³×C₁₁₃	C₂²×C₄	1	1240	yes	complemented
10	C₂³×C₁₁₃	C₂⁴	1	155	yes	—
11	C₂×Dic₁₁₃	C₂⁴	1	496	yes	direct product factor
12	C₂²×C₁₁₃	C₂³×C₄	1	620	yes	complemented
13	C₂²×C₁₁₃	C₂⁵	1	31	yes	—
14	Dic₁₁₃	C₂⁵	1	32	yes	direct product factor
15	C₂×C₁₁₃	C₂⁴×C₄	1	62	yes	complemented
16	C₂×C₁₁₃	C₂⁶	1	1	yes	characteristic
17	C₂⁵×C₄	—	113	1	no	maximal, Sylow
18	C₁₁₃	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂⁶	D₁₁₃	1	1	yes	characteristic
20	C₂⁴×C₄	—	113	62	no	—
21	C₂⁵	Dic₁₁₃	1	32	yes	direct product factor
22	C₂⁵	C₂×D₁₁₃	1	31	yes	—
23	C₂³×C₄	—	113	620	no	—
24	C₂⁴	C₂×Dic₁₁₃	1	496	yes	direct product factor
25	C₂⁴	C₂²×D₁₁₃	1	155	yes	—
26	C₂²×C₄	—	113	1240	no	—
27	C₂³	C₂²×Dic₁₁₃	1	1240	yes	direct product factor
28	C₂³	C₂³×D₁₁₃	1	155	yes	—
29	C₂×C₄	—	113	496	no	—
30	C₂²	C₂³×Dic₁₁₃	1	620	yes	direct product factor
31	C₂²	C₂⁴×D₁₁₃	1	31	yes	—
32	C₄	—	113	32	no	—
33	C₂	C₂⁴×Dic₁₁₃	1	62	yes	direct product factor
34	C₂	C₂⁵×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	D₁₁₃
commutator, hypocenter	C₁₁₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×D₁₁₃
Fitting, socle, prime radical	C₂⁶×C₁₁₃	C₂
cosocle	C₂×C₁₁₃	C₂⁶
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Dic₁₁₃	C₂	direct (N × H)
3. C₂³×Dic₁₁₃	C₂²	direct (N × H)
4. C₂⁵×C₁₁₃	C₄	semidirect
6. C₂²×Dic₁₁₃	C₂³	direct (N × H)
7. C₂⁴×C₁₁₃	C₂×C₄	semidirect
9. C₂³×C₁₁₃	C₂²×C₄	semidirect
11. C₂×Dic₁₁₃	C₂⁴	direct (N × H)
12. C₂²×C₁₁₃	C₂³×C₄	semidirect
14. Dic₁₁₃	C₂⁵	direct (N × H)
15. C₂×C₁₁₃	C₂⁴×C₄	semidirect
18. C₁₁₃	C₂⁵×C₄	semidirect
21. C₂⁵	Dic₁₁₃	direct (N × H)
24. C₂⁴	C₂×Dic₁₁₃	direct (N × H)
27. C₂³	C₂²×Dic₁₁₃	direct (N × H)
30. C₂²	C₂³×Dic₁₁₃	direct (N × H)
33. C₂	C₂⁴×Dic₁₁₃	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×Dic₁₁₃	2
C₂⁶×C₁₁₃	2
C₂⁵×C₄	113

Subgroups — C25×Dic113 #28405364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×Dic₁₁₃ #28405364