Subgroups — C₄×C₁₃×#10597244 #44538136

Order 31460.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#10597244	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#10597244	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁²×C₁₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₃	C₂×C₅	1	1	yes	characteristic
5	C₄×C₁₃×C₁₁⋊C₅	—	11	2	no	maximal
6	C₄×#10597244	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×#10597244	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×C₁₁⋊C₅	—	11	2	no	—
11	#10597244	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₁₁×C₁₃	—	5	2	no	—
13	C₄×C₁₁×C₁₃	C₁₁⋊C₅	1	2	yes	complemented
14	C₄×C₁₁²	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₁₃	—	5	2	no	—
16	C₂×C₁₁×C₁₃	C₂×C₁₁⋊C₅	1	2	yes	—
17	C₄×C₅×C₁₃	—	121	1	no	Hall
18	C₂×C₁₁²	C₂×C₅×C₁₃	1	1	yes	characteristic
19	C₄×C₁₁⋊C₅	—	11	2	no	—
20	C₁₁×C₁₃	—	5	2	no	—
21	C₁₁×C₁₃	C₄×C₁₁⋊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	#10597244	1	1	yes	characteristic, direct product factor, Hall
28	C₄×C₁₁	—	5	2	no	—
29	C₄×C₁₁	C₁₃×C₁₁⋊C₅	1	2	yes	complemented
30	C₂×C₁₃	C₂×#10597244	1	1	yes	characteristic
31	C₂×C₁₁	—	5	2	no	—
32	C₂×C₁₁	C₂×C₁₃×C₁₁⋊C₅	1	2	yes	—
33	C₄×C₅	—	121	1	no	Hall
34	C₁₃	C₄×#10597244	1	1	yes	characteristic, direct product factor, Sylow
35	C₁₁	—	5	2	no	—
36	C₁₁	C₄×C₁₃×C₁₁⋊C₅	1	2	yes	complemented
37	C₂×C₅	—	121	1	no	—
38	C₅	—	121	1	no	Sylow
39	C₄	C₁₃×#10597244	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	C₂×C₁₃×#10597244	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₃	#10597244
commutator, hypocenter	C₁₁²	C₄×C₅×C₁₃
Frattini	C₂	C₂×C₁₃×#10597244
Fitting	C₄×C₁₁²×C₁₃	C₅
socle	C₂×C₁₁²×C₁₃	C₂×C₅
prime radical	C₂×C₁₃×#10597244	C₂
cosocle	C₂×C₁₁²	C₂×C₅×C₁₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×#10597244	C₄	direct (N × H)
3. C₄×C₁₁²×C₁₃	C₅	semidirect
6. C₄×#10597244	C₁₃	direct (N × H)
7. C₁₁²×C₁₃	C₄×C₅	semidirect
11. #10597244	C₄×C₁₃	direct (N × H)
13. C₄×C₁₁×C₁₃	C₁₁⋊C₅	semidirect
14. C₄×C₁₁²	C₅×C₁₃	semidirect
21. C₁₁×C₁₃	C₄×C₁₁⋊C₅	semidirect
23. C₁₁²	C₄×C₅×C₁₃	semidirect
27. C₄×C₁₃	#10597244	direct (N × H)
29. C₄×C₁₁	C₁₃×C₁₁⋊C₅	semidirect
34. C₁₃	C₄×#10597244	direct (N × H)
36. C₁₁	C₄×C₁₃×C₁₁⋊C₅	semidirect
39. C₄	C₁₃×#10597244	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#10597244	2
C₄×C₁₁²×C₁₃	5
C₄×C₁₃×C₁₁⋊C₅	11
C₄×#10597244	13

Subgroups — C4×C13×#10597244 #44538136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#10597244 #44538136