Subgroups — C₂²×C₇²×C₁₃⋊C₉ #37524612

Order 22932.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₁₃⋊C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	3	yes	—
5	C₂²×C₇×C₁₃⋊C₉	C₇	1	8	yes	maximal, direct product factor
6	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
8	C₂²×C₇²×C₉	—	13	1	no	maximal, Hall
9	C₂×C₇×C₁₃⋊C₉	C₂×C₇	1	24	yes	direct product factor
10	C₂×C₇²×C₁₃	C₂×C₉	1	3	yes	complemented
11	C₂²×C₃×C₇×C₁₃	C₃×C₇	1	8	yes	—
12	C₂×C₇²×C₉	—	13	3	no	—
13	C₇×C₁₃⋊C₉	C₂²×C₇	1	8	yes	direct product factor
14	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₇²	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	24	yes	—
17	C₂²×C₁₃⋊C₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₇²×C₉	—	13	1	no	Hall
19	C₂²×C₇×C₁₃	C₇×C₉	1	8	yes	complemented
20	C₂×C₃×C₇²	C₂×C₁₃⋊C₃	1	3	yes	—
21	C₃×C₇×C₁₃	C₂²×C₃×C₇	1	8	yes	—
22	C₂²×C₇×C₉	—	13	8	no	—
23	C₂×C₁₃⋊C₉	C₂×C₇²	1	3	yes	direct product factor
24	C₂²×C₇²	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×C₁₃	C₂×C₇×C₉	1	24	yes	complemented
26	C₂²×C₃×C₁₃	C₃×C₇²	1	1	yes	characteristic
27	C₃×C₇²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
28	C₂×C₇×C₉	—	13	24	no	—
29	C₁₃⋊C₉	C₂²×C₇²	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₇²	C₂×C₁₃⋊C₉	1	3	yes	direct product factor
31	C₇×C₁₃	C₂²×C₇×C₉	1	8	yes	complemented
32	C₂²×C₃×C₇	C₇×C₁₃⋊C₃	1	8	yes	—
33	C₂×C₃×C₁₃	C₂×C₃×C₇²	1	3	yes	—
34	C₇×C₉	—	13	8	no	—
35	C₂²×C₁₃	C₇²×C₉	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₇	C₂×C₇×C₁₃⋊C₃	1	24	yes	—
38	C₃×C₁₃	C₂²×C₃×C₇²	1	1	yes	characteristic
39	C₂²×C₉	—	13	1	no	Hall
40	C₂²×C₇	C₇×C₁₃⋊C₉	1	8	yes	direct product factor
41	C₂×C₁₃	C₂×C₇²×C₉	1	3	yes	complemented
42	C₃×C₇	C₂²×C₇×C₁₃⋊C₃	1	8	yes	—
43	C₂×C₉	—	13	3	no	—
44	C₂×C₇	C₂×C₇×C₁₃⋊C₉	1	24	yes	direct product factor
45	C₁₃	C₂²×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₃	C₇²×C₁₃⋊C₃	1	1	yes	characteristic
47	C₉	—	13	1	no	Sylow
48	C₇	C₂²×C₇×C₁₃⋊C₉	1	8	yes	direct product factor
49	C₂×C₃	C₂×C₇²×C₁₃⋊C₃	1	3	yes	—
50	C₂²	C₇²×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×C₇²×C₁₃⋊C₃	1	1	yes	characteristic
52	C₂	C₂×C₇²×C₁₃⋊C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₇²	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₇²×C₉
Frattini	C₃	C₂²×C₇²×C₁₃⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₇²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃×C₇²

Complements

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

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

Subgroups — C22×C72×C13⋊C9 #37524612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇²×C₁₃⋊C₉ #37524612