Subgroups — C₁₃×#14559052 #44538113

Order 31460.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#10597245	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×C₁₁⋊Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₃	C₂×C₅	1	1	yes	characteristic
5	C₁₃×Dic₁₁⋊C₅	—	11	2	no	maximal
6	#14559052	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁²×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×C₁₁⋊C₅	—	11	2	no	—
9	C₂×#10597245	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×C₁₁⋊C₅	—	11	2	no	—
11	#10597245	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×Dic₁₁	—	11	2	no	—
13	C₁₃×Dic₁₁	—	55	2	no	—
14	C₁₁⋊Dic₁₁	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₁₃	—	5	2	no	—
16	C₂×C₁₁×C₁₃	AGL(1,𝔽₁₁)	1	2	yes	—
17	C₄×C₅×C₁₃	—	121	1	no	Hall
18	C₂×C₁₁²	C₂×C₅×C₁₃	1	1	yes	characteristic
19	Dic₁₁⋊C₅	—	11	2	no	—
20	C₁₁×C₁₃	—	5	2	no	—
21	C₁₁×C₁₃	Dic₁₁⋊C₅	1	2	yes	complemented
22	C₂×C₅×C₁₃	—	121	1	no	—
23	C₁₁²	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₁⋊C₅	—	11	2	no	—
25	C₅×C₁₃	—	121	1	no	Hall
26	C₁₁⋊C₅	—	11	2	no	—
27	C₄×C₁₃	—	121	1	no	Hall
28	Dic₁₁	—	11	2	no	—
29	Dic₁₁	—	55	2	no	—
30	C₂×C₁₃	#11925893	1	1	yes	characteristic
31	C₂×C₁₁	—	5	2	no	—
32	C₂×C₁₁	C₁₃×AGL(1,𝔽₁₁)	1	2	yes	—
33	C₄×C₅	—	121	1	no	Hall
34	C₁₃	#14559052	1	1	yes	characteristic, direct product factor, Sylow
35	C₁₁	—	5	2	no	—
36	C₁₁	C₁₃×Dic₁₁⋊C₅	1	2	yes	complemented
37	C₂×C₅	—	121	1	no	—
38	C₅	—	121	1	no	Sylow
39	C₄	—	121	1	no	Sylow
40	C₂	C₁₃×#11925893	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	#11925893
commutator, hypocenter	C₁₁²	C₄×C₅×C₁₃
Frattini	C₂	C₁₃×#11925893
Fitting, socle	C₂×C₁₁²×C₁₃	C₂×C₅
prime radical	C₂×C₁₃×#10597245	C₂
cosocle	C₂×C₁₁²	C₂×C₅×C₁₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#10597245	C₄	semidirect
3. C₁₃×C₁₁⋊Dic₁₁	C₅	semidirect
6. #14559052	C₁₃	direct (N × H)
7. C₁₁²×C₁₃	C₄×C₅	semidirect
11. #10597245	C₄×C₁₃	semidirect
14. C₁₁⋊Dic₁₁	C₅×C₁₃	semidirect
21. C₁₁×C₁₃	Dic₁₁⋊C₅	semidirect
23. C₁₁²	C₄×C₅×C₁₃	semidirect
34. C₁₃	#14559052	direct (N × H)
36. C₁₁	C₁₃×Dic₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#10597245	2
C₁₃×C₁₁⋊Dic₁₁	5
C₁₃×Dic₁₁⋊C₅	11
#14559052	13

Subgroups — C13×#14559052 #44538113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14559052 #44538113