Subgroups — C₂²×C₇²×C₉×C₁₃ #37524399

Order 22932.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₉×C₁₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	3	yes	—
5	C₂²×C₇×C₉×C₁₃	C₇	1	8	yes	maximal, direct product factor
6	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
8	C₂²×C₇²×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₉×C₁₃	C₂×C₇	1	24	yes	direct product factor
10	C₂×C₇²×C₁₃	C₂×C₉	1	3	yes	direct product factor
11	C₂²×C₃×C₇×C₁₃	C₃×C₇	1	8	yes	—
12	C₂×C₇²×C₉	C₂×C₁₃	1	3	yes	direct product factor
13	C₇×C₉×C₁₃	C₂²×C₇	1	8	yes	direct product factor
14	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₃×C₇²	C₃×C₁₃	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	24	yes	—
17	C₂²×C₉×C₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₇²×C₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₇×C₁₃	C₇×C₉	1	8	yes	direct product factor
20	C₂×C₃×C₇²	C₂×C₃×C₁₃	1	3	yes	—
21	C₃×C₇×C₁₃	C₂²×C₃×C₇	1	8	yes	—
22	C₂²×C₇×C₉	C₇×C₁₃	1	8	yes	direct product factor
23	C₂×C₉×C₁₃	C₂×C₇²	1	3	yes	direct product factor
24	C₂²×C₇²	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×C₁₃	C₂×C₇×C₉	1	24	yes	direct product factor
26	C₂²×C₃×C₁₃	C₃×C₇²	1	1	yes	characteristic
27	C₃×C₇²	C₂²×C₃×C₁₃	1	1	yes	characteristic
28	C₂×C₇×C₉	C₂×C₇×C₁₃	1	24	yes	direct product factor
29	C₉×C₁₃	C₂²×C₇²	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₇²	C₂×C₉×C₁₃	1	3	yes	direct product factor
31	C₇×C₁₃	C₂²×C₇×C₉	1	8	yes	direct product factor
32	C₂²×C₃×C₇	C₃×C₇×C₁₃	1	8	yes	—
33	C₂×C₃×C₁₃	C₂×C₃×C₇²	1	3	yes	—
34	C₇×C₉	C₂²×C₇×C₁₃	1	8	yes	direct product factor
35	C₂²×C₁₃	C₇²×C₉	1	1	yes	characteristic, direct product factor, Hall
36	C₇²	C₂²×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₇	C₂×C₃×C₇×C₁₃	1	24	yes	—
38	C₃×C₁₃	C₂²×C₃×C₇²	1	1	yes	characteristic
39	C₂²×C₉	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₇	C₇×C₉×C₁₃	1	8	yes	direct product factor
41	C₂×C₁₃	C₂×C₇²×C₉	1	3	yes	direct product factor
42	C₃×C₇	C₂²×C₃×C₇×C₁₃	1	8	yes	—
43	C₂×C₉	C₂×C₇²×C₁₃	1	3	yes	direct product factor
44	C₂×C₇	C₂×C₇×C₉×C₁₃	1	24	yes	direct product factor
45	C₁₃	C₂²×C₇²×C₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₃	C₃×C₇²×C₁₃	1	1	yes	characteristic
47	C₉	C₂²×C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₂²×C₇×C₉×C₁₃	1	8	yes	direct product factor
49	C₂×C₃	C₂×C₃×C₇²×C₁₃	1	3	yes	—
50	C₂²	C₇²×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×C₃×C₇²×C₁₃	1	1	yes	characteristic
52	C₂	C₂×C₇²×C₉×C₁₃	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₇²×C₁₃
socle, prime radical	C₂²×C₃×C₇²×C₁₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₉×C₁₃	C₂	direct (N × H)
3. C₇²×C₉×C₁₃	C₂²	direct (N × H)
5. C₂²×C₇×C₉×C₁₃	C₇	direct (N × H)
6. C₂²×C₇²×C₁₃	C₉	direct (N × H)
8. C₂²×C₇²×C₉	C₁₃	direct (N × H)
9. C₂×C₇×C₉×C₁₃	C₂×C₇	direct (N × H)
10. C₂×C₇²×C₁₃	C₂×C₉	direct (N × H)
12. C₂×C₇²×C₉	C₂×C₁₃	direct (N × H)
13. C₇×C₉×C₁₃	C₂²×C₇	direct (N × H)
14. C₇²×C₁₃	C₂²×C₉	direct (N × H)
17. C₂²×C₉×C₁₃	C₇²	direct (N × H)
18. C₇²×C₉	C₂²×C₁₃	direct (N × H)
19. C₂²×C₇×C₁₃	C₇×C₉	direct (N × H)
22. C₂²×C₇×C₉	C₇×C₁₃	direct (N × H)
23. C₂×C₉×C₁₃	C₂×C₇²	direct (N × H)
24. C₂²×C₇²	C₉×C₁₃	direct (N × H)
25. C₂×C₇×C₁₃	C₂×C₇×C₉	direct (N × H)
28. C₂×C₇×C₉	C₂×C₇×C₁₃	direct (N × H)
29. C₉×C₁₃	C₂²×C₇²	direct (N × H)
30. C₂×C₇²	C₂×C₉×C₁₃	direct (N × H)
31. C₇×C₁₃	C₂²×C₇×C₉	direct (N × H)
34. C₇×C₉	C₂²×C₇×C₁₃	direct (N × H)
35. C₂²×C₁₃	C₇²×C₉	direct (N × H)
36. C₇²	C₂²×C₉×C₁₃	direct (N × H)
39. C₂²×C₉	C₇²×C₁₃	direct (N × H)
40. C₂²×C₇	C₇×C₉×C₁₃	direct (N × H)
41. C₂×C₁₃	C₂×C₇²×C₉	direct (N × H)
43. C₂×C₉	C₂×C₇²×C₁₃	direct (N × H)
44. C₂×C₇	C₂×C₇×C₉×C₁₃	direct (N × H)
45. C₁₃	C₂²×C₇²×C₉	direct (N × H)
47. C₉	C₂²×C₇²×C₁₃	direct (N × H)
48. C₇	C₂²×C₇×C₉×C₁₃	direct (N × H)
50. C₂²	C₇²×C₉×C₁₃	direct (N × H)
52. C₂	C₂×C₇²×C₉×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
C₂×C₇²×C₉×C₁₃	2
C₂²×C₃×C₇²×C₁₃	3
C₂²×C₇×C₉×C₁₃	7
C₂²×C₇²×C₉	13

Subgroups — C22×C72×C9×C13 #37524399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇²×C₉×C₁₃ #37524399