Subgroups — C₂×C₅²×C₇×D₁₃ #22603333

Order 9100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇×D₁₃	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₃	C₂×C₅	1	6	yes	complemented
7	C₅×C₇×D₁₃	C₂×C₅	1	12	yes	direct product factor
8	C₂²×C₅²×C₇	—	13	1	no	maximal, Hall
9	C₂×C₅²×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
10	C₅²×D₁₃	C₂×C₇	1	2	yes	direct product factor
11	C₅×C₇×C₁₃	C₂²×C₅	1	6	yes	complemented
12	C₂×C₇×D₁₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅²×C₇	—	13	2	no	—
14	C₂×C₅²×C₇	D₁₃	1	1	yes	characteristic, direct product factor
15	C₅²×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₁₃	C₅×C₇	1	6	yes	direct product factor
17	C₂×C₇×C₁₃	C₂×C₅²	1	1	yes	characteristic, complemented
18	C₇×D₁₃	C₂×C₅²	1	2	yes	direct product factor
19	C₅²×C₇	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₅×C₇	—	13	6	no	—
21	C₂×C₅×C₁₃	C₂×C₅×C₇	1	6	yes	complemented
22	C₅×D₁₃	C₂×C₅×C₇	1	12	yes	direct product factor
23	C₂²×C₅²	—	13	1	no	Hall
24	C₇×C₁₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₇	—	13	12	no	—
26	C₂×C₅×C₇	C₅×D₁₃	1	6	yes	direct product factor
27	C₅×C₁₃	C₂²×C₅×C₇	1	6	yes	complemented
28	C₂×D₁₃	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅²	—	13	2	no	—
30	C₂×C₅²	C₇×D₁₃	1	1	yes	characteristic, direct product factor
31	C₅×C₇	C₂×C₅×D₁₃	1	6	yes	direct product factor
32	C₂²×C₇	—	13	1	no	Hall
33	C₂×C₁₃	C₂×C₅²×C₇	1	1	yes	characteristic, complemented
34	D₁₃	C₂×C₅²×C₇	1	2	yes	direct product factor
35	C₅²	C₂×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	—	13	6	no	—
37	C₂×C₇	—	13	2	no	—
38	C₂×C₇	C₅²×D₁₃	1	1	yes	characteristic, direct product factor
39	C₁₃	C₂²×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	13	12	no	—
41	C₂×C₅	C₅×C₇×D₁₃	1	6	yes	direct product factor
42	C₇	C₂×C₅²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₂×C₅×C₇×D₁₃	1	6	yes	direct product factor
44	C₂²	—	13	1	no	Sylow
45	C₂	—	13	2	no	—
46	C₂	C₅²×C₇×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₇	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₅²×C₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×D₁₃	C₂	direct (N × H)
2. C₂×C₅²×C₇×C₁₃	C₂	semidirect
3. C₅²×C₇×C₁₃	C₂²	semidirect
4. C₂×C₅×C₇×D₁₃	C₅	direct (N × H)
5. C₂×C₅²×D₁₃	C₇	direct (N × H)
6. C₂×C₅×C₇×C₁₃	C₂×C₅	semidirect
7. C₅×C₇×D₁₃	C₂×C₅	direct (N × H)
9. C₂×C₅²×C₁₃	C₂×C₇	semidirect
10. C₅²×D₁₃	C₂×C₇	direct (N × H)
11. C₅×C₇×C₁₃	C₂²×C₅	semidirect
12. C₂×C₇×D₁₃	C₅²	direct (N × H)
14. C₂×C₅²×C₇	D₁₃	direct (N × H)
15. C₅²×C₁₃	C₂²×C₇	semidirect
16. C₂×C₅×D₁₃	C₅×C₇	direct (N × H)
17. C₂×C₇×C₁₃	C₂×C₅²	semidirect
18. C₇×D₁₃	C₂×C₅²	direct (N × H)
19. C₅²×C₇	C₂×D₁₃	direct (N × H)
21. C₂×C₅×C₁₃	C₂×C₅×C₇	semidirect
22. C₅×D₁₃	C₂×C₅×C₇	direct (N × H)
24. C₇×C₁₃	C₂²×C₅²	semidirect
26. C₂×C₅×C₇	C₅×D₁₃	direct (N × H)
27. C₅×C₁₃	C₂²×C₅×C₇	semidirect
28. C₂×D₁₃	C₅²×C₇	direct (N × H)
30. C₂×C₅²	C₇×D₁₃	direct (N × H)
31. C₅×C₇	C₂×C₅×D₁₃	direct (N × H)
33. C₂×C₁₃	C₂×C₅²×C₇	semidirect
34. D₁₃	C₂×C₅²×C₇	direct (N × H)
35. C₅²	C₂×C₇×D₁₃	direct (N × H)
38. C₂×C₇	C₅²×D₁₃	direct (N × H)
39. C₁₃	C₂²×C₅²×C₇	semidirect
41. C₂×C₅	C₅×C₇×D₁₃	direct (N × H)
42. C₇	C₂×C₅²×D₁₃	direct (N × H)
43. C₅	C₂×C₅×C₇×D₁₃	direct (N × H)
46. C₂	C₅²×C₇×D₁₃	direct (N × H)

Subgroups — C2×C52×C7×D13 #22603333

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×C₇×D₁₃ #22603333