Subgroups — C₇×C₁₃×Dic₈₇ #44539721

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×Dic₂₉	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₂₉	D₃	1	1	yes	characteristic
5	C₁₃×Dic₈₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₇×Dic₈₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic
9	C₁₃×Dic₂₉	—	3	1	no	Hall
10	C₂×C₃×C₇×C₂₉	C₂×C₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×Dic₃×C₁₃	—	29	1	no	maximal, Hall
13	C₇×Dic₂₉	—	3	1	no	Hall
14	C₂×C₁₃×C₂₉	D₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₂₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₃	D₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	D₃×C₁₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₄×C₇×C₁₃	—	87	1	no	Hall
20	Dic₈₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₇×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	Dic₃×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	D₈₇	1	1	yes	characteristic
24	C₂×C₃×C₂₉	C₂×C₇×C₁₃	1	1	yes	characteristic
25	Dic₃×C₁₃	—	29	1	no	Hall
26	Dic₂₉	—	3	1	no	Hall
27	C₇×C₁₃	Dic₈₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₂₉	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₇×Dic₃	—	29	1	no	Hall
30	C₂×C₃×C₁₃	C₇×D₂₉	1	1	yes	characteristic
31	C₂×C₂₉	D₃×C₇×C₁₃	1	1	yes	characteristic
32	C₄×C₁₃	—	87	1	no	Hall
33	C₂×C₃×C₇	C₁₃×D₂₉	1	1	yes	characteristic
34	C₃×C₁₃	C₇×Dic₂₉	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₇×Dic₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	87	1	no	Hall
37	C₂×C₁₃	C₇×D₈₇	1	1	yes	characteristic
38	C₃×C₇	C₁₃×Dic₂₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	C₁₃×D₈₇	1	1	yes	characteristic
40	C₁₃	C₇×Dic₈₇	1	1	yes	characteristic, direct product factor, Sylow
41	Dic₃	—	29	1	no	Hall
42	C₇	C₁₃×Dic₈₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₇×C₁₃×D₂₉	1	1	yes	characteristic
44	C₄	—	87	1	no	Sylow
45	C₃	C₇×C₁₃×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₇×C₁₃×D₈₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃	D₈₇
commutator, hypocenter	C₃×C₂₉	C₄×C₇×C₁₃
Frattini	C₂	C₇×C₁₃×D₈₇
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₂₉	C₂
cosocle	C₂×C₃×C₂₉	C₂×C₇×C₁₃
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₂×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₃×C₂₉	C₄	semidirect
5. C₁₃×Dic₈₇	C₇	direct (N × H)
6. C₇×C₁₃×C₂₉	Dic₃	semidirect
7. C₇×Dic₈₇	C₁₃	direct (N × H)
11. C₃×C₁₃×C₂₉	C₄×C₇	semidirect
15. C₃×C₇×C₂₉	C₄×C₁₃	semidirect
18. C₁₃×C₂₉	C₇×Dic₃	semidirect
20. Dic₈₇	C₇×C₁₃	direct (N × H)
21. C₃×C₇×C₁₃	Dic₂₉	semidirect
22. C₇×C₂₉	Dic₃×C₁₃	semidirect
27. C₇×C₁₃	Dic₈₇	direct (N × H)
28. C₃×C₂₉	C₄×C₇×C₁₃	semidirect
34. C₃×C₁₃	C₇×Dic₂₉	semidirect
35. C₂₉	C₇×Dic₃×C₁₃	semidirect
38. C₃×C₇	C₁₃×Dic₂₉	semidirect
40. C₁₃	C₇×Dic₈₇	direct (N × H)
42. C₇	C₁₃×Dic₈₇	direct (N × H)
45. C₃	C₇×C₁₃×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₃×C₂₉	2
C₇×C₁₃×Dic₂₉	3
C₁₃×Dic₈₇	7
C₇×Dic₈₇	13
C₇×Dic₃×C₁₃	29

Subgroups — C7×C13×Dic87 #44539721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×Dic₈₇ #44539721