Subgroups — C₁₃⋊C₃×#11717964 #44544375

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#11717964	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃⋊C₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊C₃×#4223	—	5	1	no	maximal, Hall
5	C₅×C₁₃×D₄₁	C₂×C₃	1	1	yes	characteristic
6	C₁₃⋊C₃×D₄₁	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#11717964	—	13	1	no	maximal, Hall
9	C₁₃×#4223	—	5	1	no	Hall
10	C₁₃⋊C₃×C₄₁	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×D₄₁	—	13	1	no	—
12	C₁₃×D₄₁	C₃×D₅	1	1	yes	characteristic
13	#11717964	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	Dic₅×C₁₃⋊C₃	—	41	1	no	maximal, Hall
15	C₃×C₅×C₄₁	—	13	1	no	Hall
16	C₁₃×C₄₁	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
17	C₃×#4223	—	65	1	no	Hall
18	C₅×D₄₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₂×C₅×C₁₃⋊C₃	—	41	1	no	—
20	C₁₃×Dic₅	—	41	1	no	Hall
21	C₃×D₄₁	—	13	1	no	—
22	C₅×C₄₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₃⋊C₃	#4223	1	1	yes	characteristic, complemented, Hall
24	#4223	—	5	1	no	Hall
25	C₄×C₁₃⋊C₃	—	205	1	no	Hall
26	C₂×C₅×C₁₃	—	41	1	no	—
27	C₃×C₄₁	—	13	1	no	Hall
28	D₄₁	D₅×C₁₃⋊C₃	1	1	yes	characteristic
29	C₂×C₁₃⋊C₃	—	41	1	no	—
30	C₅×C₁₃	C₃×#4223	1	1	yes	characteristic, complemented, Hall
31	C₃×Dic₅	—	533	1	no	Hall
32	C₄×C₁₃	—	205	1	no	Hall
33	C₄₁	Dic₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₁₃⋊C₃	#11717964	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₃×C₅	—	533	1	no	—
36	C₂×C₁₃	—	41	1	no	—
37	Dic₅	—	41	1	no	Hall
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×#11717964	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2665	1	no	Hall
41	C₂×C₅	—	41	1	no	—
42	C₂×C₃	—	533	1	no	—
43	C₅	C₁₃⋊C₃×#4223	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	205	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	41	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₄₁	C₃×C₄
prime radical	C₅×C₁₃⋊C₃×D₄₁	C₂
cosocle	C₅×C₁₃×D₄₁	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₃×#11717964	C₃	semidirect
3. C₅×C₁₃⋊C₃×C₄₁	C₄	semidirect
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
10. C₁₃⋊C₃×C₄₁	Dic₅	semidirect
13. #11717964	C₁₃⋊C₃	direct (N × H)
16. C₁₃×C₄₁	C₃×Dic₅	semidirect
22. C₅×C₄₁	C₄×C₁₃⋊C₃	semidirect
23. C₅×C₁₃⋊C₃	#4223	semidirect
30. C₅×C₁₃	C₃×#4223	semidirect
33. C₄₁	Dic₅×C₁₃⋊C₃	semidirect
34. C₁₃⋊C₃	#11717964	direct (N × H)
39. C₁₃	C₃×#11717964	semidirect
43. C₅	C₁₃⋊C₃×#4223	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃⋊C₃×D₄₁	2
C₁₃×#11717964	3
C₁₃⋊C₃×#4223	5
C₃×#11717964	13
Dic₅×C₁₃⋊C₃	41

Subgroups — C13⋊C3×#11717964 #44544375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×#11717964 #44544375