Subgroups — C₇×C₁₃×#63118 #37556880

Order 23660.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₃×#261	—	5	1	no	maximal, Hall
4	C₁₃×#63118	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃×D₁₃	D₅	1	1	yes	characteristic
6	C₇×#63118	C₁₃	1	1	yes	maximal, characteristic, direct product factor
7	C₇×C₁₃×Dic₅	—	13	1	no	maximal
8	C₅×C₁₃×D₁₃	C₂×C₇	1	1	yes	characteristic
9	C₇×C₁₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₃	—	13	1	no	—
11	C₅×C₇×D₁₃	C₂×C₁₃	1	1	yes	characteristic
12	C₅×C₁₃²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₁₃×#261	—	5	1	no	Hall
14	C₅×C₇×C₁₃	—	4	3	no	—
15	C₅×C₇×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
16	C₅×C₇×C₁₃	#261	1	1	yes	characteristic, complemented
17	C₇×#261	—	5	1	no	—
18	C₄×C₇×C₁₃	—	65	1	no	—
19	C₁₃×D₁₃	C₇×D₅	1	1	yes	characteristic
20	#63118	C₇×C₁₃	1	1	yes	characteristic, direct product factor
21	C₁₃×Dic₅	—	13	1	no	—
22	C₂×C₇×C₁₃	—	13	1	no	—
23	C₇×D₁₃	D₅×C₁₃	1	1	yes	characteristic
24	C₁₃²	C₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
25	C₇×Dic₅	—	13	1	no	Hall
26	C₂×C₅×C₁₃	—	13	1	no	—
27	C₅×D₁₃	C₂×C₇×C₁₃	1	1	yes	characteristic
28	C₇×C₁₃	—	4	3	no	—
29	C₇×C₁₃	C₁₃×Dic₅	1	1	yes	characteristic, complemented
30	C₇×C₁₃	#63118	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₇	—	13	1	no	—
32	C₅×C₁₃	—	4	3	no	—
33	C₅×C₁₃	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented
34	C₅×C₁₃	C₇×#261	1	1	yes	characteristic, complemented
35	#261	—	5	1	no	—
36	C₄×C₁₃	—	65	1	no	—
37	C₅×C₇	C₁₃×#261	1	1	yes	characteristic, complemented, Hall
38	C₄×C₇	—	65	1	no	Hall
39	C₂×C₁₃	—	13	1	no	—
40	D₁₃	C₇×D₅×C₁₃	1	1	yes	characteristic
41	Dic₅	—	13	1	no	Hall
42	C₂×C₇	—	13	1	no	—
43	C₁₃	—	4	3	no	—
44	C₁₃	C₇×C₁₃×Dic₅	1	1	yes	characteristic, complemented
45	C₁₃	C₇×#63118	1	1	yes	characteristic, direct product factor
46	C₂×C₅	—	13	1	no	—
47	C₇	C₁₃×#63118	1	1	yes	characteristic, direct product factor, Sylow
48	C₅	C₇×C₁₃×#261	1	1	yes	characteristic, complemented, Sylow
49	C₄	—	65	1	no	Sylow
50	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₃	#63118
commutator, hypocenter	C₅×C₁₃	C₄×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃²	C₄
prime radical	C₅×C₇×C₁₃×D₁₃	C₂
cosocle	C₅×D₁₃	C₂×C₇×C₁₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃²	C₄	semidirect
4. C₁₃×#63118	C₇	direct (N × H)
6. C₇×#63118	C₁₃	direct (N × H)
9. C₇×C₁₃²	Dic₅	semidirect
12. C₅×C₁₃²	C₄×C₇	semidirect
15. C₅×C₇×C₁₃	C₄×C₁₃	semidirect
16. C₅×C₇×C₁₃	#261	semidirect
20. #63118	C₇×C₁₃	direct (N × H)
24. C₁₃²	C₇×Dic₅	semidirect
29. C₇×C₁₃	C₁₃×Dic₅	semidirect
30. C₇×C₁₃	#63118	direct (N × H)
33. C₅×C₁₃	C₄×C₇×C₁₃	semidirect
34. C₅×C₁₃	C₇×#261	semidirect
37. C₅×C₇	C₁₃×#261	semidirect
44. C₁₃	C₇×C₁₃×Dic₅	semidirect
45. C₁₃	C₇×#63118	direct (N × H)
47. C₇	C₁₃×#63118	direct (N × H)
48. C₅	C₇×C₁₃×#261	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃×D₁₃	2
C₇×C₁₃×#261	5
C₁₃×#63118	7
C₇×#63118	13
C₇×C₁₃×Dic₅	13

Subgroups — C7×C13×#63118 #37556880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×#63118 #37556880