Subgroups — C₂²×C₁₃⋊C₃×C₂₉⋊C₇ #44539798

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₂₉⋊C₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₂₉⋊C₇	C₂×C₃	1	3	yes	complemented
5	C₂²×C₂₉×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂²×C₃×C₂₉⋊C₇	—	13	1	no	maximal, Hall
8	C₂×C₂₉×C₁₃⋊C₃	C₂×C₇	1	3	yes	complemented
9	C₂²×C₁₃×C₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₂₉⋊C₇	—	13	3	no	—
11	C₂₉×C₁₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₇×C₁₃⋊C₃	—	29	1	no	maximal, Hall
13	C₂²×C₂₉⋊C₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₂₉	C₂×C₃×C₇	1	3	yes	complemented
15	C₃×C₂₉⋊C₇	—	13	1	no	Hall
16	C₂×C₇×C₁₃⋊C₃	—	29	3	no	—
17	C₂×C₂₉⋊C₇	C₂×C₁₃⋊C₃	1	3	yes	direct product factor
18	C₁₃×C₂₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₇×C₁₃	—	29	1	no	Hall
20	C₂²×C₃×C₂₉	—	13	1	no	Hall
21	C₇×C₁₃⋊C₃	—	29	1	no	Hall
22	C₂₉⋊C₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	—	29	3	no	—
24	C₂×C₃×C₂₉	—	13	3	no	—
25	C₂²×C₁₃⋊C₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₂₉	C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	—	13	1	no	Hall
29	C₂²×C₃×C₇	—	377	1	no	Hall
30	C₂×C₁₃⋊C₃	C₂×C₂₉⋊C₇	1	3	yes	direct product factor
31	C₂×C₂₉	C₂×C₇×C₁₃⋊C₃	1	3	yes	complemented
32	C₂²×C₁₃	C₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	377	3	no	—
34	C₁₃⋊C₃	C₂²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂₉	C₂²×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₇	—	29	1	no	Hall
37	C₂×C₁₃	C₂×C₃×C₂₉⋊C₇	1	3	yes	complemented
38	C₃×C₇	—	377	1	no	Hall
39	C₂×C₇	—	29	3	no	—
40	C₁₃	C₂²×C₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₃	—	13	1	no	Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	—	13	3	no	—
44	C₂²	C₁₃⋊C₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	C₂×C₁₃⋊C₃×C₂₉⋊C₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₁₃⋊C₃×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₁₃×C₂₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₂₉	C₃×C₇
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊C₃×C₂₉⋊C₇	C₂	direct (N × H)
2. C₂²×C₁₃×C₂₉⋊C₇	C₃	semidirect
3. C₁₃⋊C₃×C₂₉⋊C₇	C₂²	direct (N × H)
4. C₂×C₁₃×C₂₉⋊C₇	C₂×C₃	semidirect
5. C₂²×C₂₉×C₁₃⋊C₃	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	C₂²×C₃	semidirect
8. C₂×C₂₉×C₁₃⋊C₃	C₂×C₇	semidirect
9. C₂²×C₁₃×C₂₉	C₃×C₇	semidirect
11. C₂₉×C₁₃⋊C₃	C₂²×C₇	semidirect
13. C₂²×C₂₉⋊C₇	C₁₃⋊C₃	direct (N × H)
14. C₂×C₁₃×C₂₉	C₂×C₃×C₇	semidirect
17. C₂×C₂₉⋊C₇	C₂×C₁₃⋊C₃	direct (N × H)
18. C₁₃×C₂₉	C₂²×C₃×C₇	semidirect
22. C₂₉⋊C₇	C₂²×C₁₃⋊C₃	direct (N × H)
25. C₂²×C₁₃⋊C₃	C₂₉⋊C₇	direct (N × H)
26. C₂²×C₂₉	C₇×C₁₃⋊C₃	semidirect
30. C₂×C₁₃⋊C₃	C₂×C₂₉⋊C₇	direct (N × H)
31. C₂×C₂₉	C₂×C₇×C₁₃⋊C₃	semidirect
32. C₂²×C₁₃	C₃×C₂₉⋊C₇	semidirect
34. C₁₃⋊C₃	C₂²×C₂₉⋊C₇	direct (N × H)
35. C₂₉	C₂²×C₇×C₁₃⋊C₃	semidirect
37. C₂×C₁₃	C₂×C₃×C₂₉⋊C₇	semidirect
40. C₁₃	C₂²×C₃×C₂₉⋊C₇	semidirect
44. C₂²	C₁₃⋊C₃×C₂₉⋊C₇	direct (N × H)
46. C₂	C₂×C₁₃⋊C₃×C₂₉⋊C₇	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×C₁₃⋊C₃×C₂₉⋊C₇	2
C₂²×C₁₃×C₂₉⋊C₇	3
C₂²×C₂₉×C₁₃⋊C₃	7
C₂²×C₃×C₂₉⋊C₇	13
C₂²×C₇×C₁₃⋊C₃	29

Subgroups — C22×C13⋊C3×C29⋊C7 #44539798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃⋊C₃×C₂₉⋊C₇ #44539798