Subgroups — C₂×C₇²×D₅×C₁₃ #27164975

Order 12740.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅×C₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₇²×C₁₃	—	5	1	no	maximal, Hall
5	C₂×C₇×D₅×C₁₃	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₇²×C₁₃	—	5	2	no	—
7	C₂×C₇²×C₁₃	D₅	1	1	yes	characteristic, direct product factor
8	C₂×C₇²×D₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇×C₁₃	C₂×C₇	1	8	yes	complemented
10	C₇×D₅×C₁₃	C₂×C₇	1	16	yes	direct product factor
11	C₇²×C₁₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₇²	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₇²×D₅	C₂×C₁₃	1	2	yes	direct product factor
14	C₅×C₇×C₁₃	C₂²×C₇	1	8	yes	complemented
15	C₂²×C₇×C₁₃	—	5	8	no	—
16	C₂×D₅×C₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₇²	—	5	1	no	Hall
19	C₂×C₇×C₁₃	—	5	16	no	—
20	C₂×C₇×C₁₃	C₇×D₅	1	8	yes	direct product factor
21	C₂×C₇×D₅	C₇×C₁₃	1	8	yes	direct product factor
22	C₂×C₅×C₁₃	C₂×C₇²	1	1	yes	characteristic, complemented
23	D₅×C₁₃	C₂×C₇²	1	2	yes	direct product factor
24	C₂×C₇²	—	5	2	no	—
25	C₂×C₇²	D₅×C₁₃	1	1	yes	characteristic, direct product factor
26	C₇×C₁₃	C₂×C₇×D₅	1	8	yes	direct product factor
27	C₂×C₅×C₇	C₂×C₇×C₁₃	1	8	yes	complemented
28	C₇×D₅	C₂×C₇×C₁₃	1	16	yes	direct product factor
29	C₅×C₁₃	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₁₃	—	5	1	no	Hall
31	C₇²	C₂×D₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₅×C₇	C₂²×C₇×C₁₃	1	8	yes	complemented
33	C₂²×C₇	—	5	8	no	—
34	C₂×C₁₃	—	5	2	no	—
35	C₂×C₁₃	C₇²×D₅	1	1	yes	characteristic, direct product factor
36	C₂×D₅	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₇	—	5	16	no	—
38	C₂×C₇	C₇×D₅×C₁₃	1	8	yes	direct product factor
39	C₁₃	C₂×C₇²×D₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₅	C₂×C₇²×C₁₃	1	1	yes	characteristic, complemented
41	D₅	C₂×C₇²×C₁₃	1	2	yes	direct product factor
42	C₇	C₂×C₇×D₅×C₁₃	1	8	yes	direct product factor
43	C₅	C₂²×C₇²×C₁₃	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	5	1	no	Sylow
45	C₂	—	5	2	no	—
46	C₂	C₇²×D₅×C₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₃	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₇²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₇²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇²×D₅×C₁₃	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₃	C₂	semidirect
3. C₅×C₇²×C₁₃	C₂²	semidirect
5. C₂×C₇×D₅×C₁₃	C₇	direct (N × H)
7. C₂×C₇²×C₁₃	D₅	direct (N × H)
8. C₂×C₇²×D₅	C₁₃	direct (N × H)
9. C₂×C₅×C₇×C₁₃	C₂×C₇	semidirect
10. C₇×D₅×C₁₃	C₂×C₇	direct (N × H)
11. C₇²×C₁₃	C₂×D₅	direct (N × H)
12. C₂×C₅×C₇²	C₂×C₁₃	semidirect
13. C₇²×D₅	C₂×C₁₃	direct (N × H)
14. C₅×C₇×C₁₃	C₂²×C₇	semidirect
16. C₂×D₅×C₁₃	C₇²	direct (N × H)
17. C₅×C₇²	C₂²×C₁₃	semidirect
20. C₂×C₇×C₁₃	C₇×D₅	direct (N × H)
21. C₂×C₇×D₅	C₇×C₁₃	direct (N × H)
22. C₂×C₅×C₁₃	C₂×C₇²	semidirect
23. D₅×C₁₃	C₂×C₇²	direct (N × H)
25. C₂×C₇²	D₅×C₁₃	direct (N × H)
26. C₇×C₁₃	C₂×C₇×D₅	direct (N × H)
27. C₂×C₅×C₇	C₂×C₇×C₁₃	semidirect
28. C₇×D₅	C₂×C₇×C₁₃	direct (N × H)
29. C₅×C₁₃	C₂²×C₇²	semidirect
31. C₇²	C₂×D₅×C₁₃	direct (N × H)
32. C₅×C₇	C₂²×C₇×C₁₃	semidirect
35. C₂×C₁₃	C₇²×D₅	direct (N × H)
36. C₂×D₅	C₇²×C₁₃	direct (N × H)
38. C₂×C₇	C₇×D₅×C₁₃	direct (N × H)
39. C₁₃	C₂×C₇²×D₅	direct (N × H)
40. C₂×C₅	C₂×C₇²×C₁₃	semidirect
41. D₅	C₂×C₇²×C₁₃	direct (N × H)
42. C₇	C₂×C₇×D₅×C₁₃	direct (N × H)
43. C₅	C₂²×C₇²×C₁₃	semidirect
46. C₂	C₇²×D₅×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×D₅×C₁₃	2
C₂×C₅×C₇²×C₁₃	2
C₂²×C₇²×C₁₃	5
C₂×C₇×D₅×C₁₃	7
C₂×C₇²×D₅	13

Subgroups — C2×C72×D5×C13 #27164975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₅×C₁₃ #27164975