Subgroups — C₃×C₄×C₁₃×C₂₉⋊C₇ #44539707

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₂₉⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₃×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₄×C₂₉⋊C₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic
9	C₄×C₁₃×C₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₂₉⋊C₇	C₂×C₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄×C₇×C₁₃	—	29	1	no	maximal, Hall
13	C₄×C₂₉⋊C₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₂₉⋊C₇	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₇×C₁₃	—	29	1	no	—
17	C₂×C₂₉⋊C₇	C₂×C₃×C₁₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₄×C₇×C₁₃	—	29	1	no	Hall
20	C₃×C₄×C₂₉	C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×C₁₃	—	29	1	no	Hall
22	C₂₉⋊C₇	C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	—	29	1	no	—
24	C₂×C₃×C₂₉	C₂×C₇×C₁₃	1	1	yes	characteristic
25	C₃×C₄×C₁₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
26	C₄×C₂₉	C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₇	—	29	1	no	Hall
30	C₂×C₃×C₁₃	C₂×C₂₉⋊C₇	1	1	yes	characteristic
31	C₂×C₂₉	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic
32	C₄×C₁₃	C₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₇	—	29	1	no	—
34	C₃×C₁₃	C₄×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂₉	C₃×C₄×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	29	1	no	Hall
37	C₂×C₁₃	C₂×C₃×C₂₉⋊C₇	1	1	yes	characteristic
38	C₃×C₇	—	29	1	no	Hall
39	C₂×C₇	—	29	1	no	—
40	C₁₃	C₃×C₄×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₄	C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	C₂×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic
44	C₄	C₃×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₄×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₃×C₁₃×C₂₉⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₃	C₂₉⋊C₇
commutator, hypocenter	C₂₉	C₃×C₄×C₇×C₁₃
Frattini	C₂	C₂×C₃×C₁₃×C₂₉⋊C₇
Fitting	C₃×C₄×C₁₃×C₂₉	C₇
socle	C₂×C₃×C₁₃×C₂₉	C₂×C₇
prime radical	C₂×C₃×C₁₃×C₂₉⋊C₇	C₂
cosocle	C₂×C₂₉	C₂×C₃×C₇×C₁₃
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₂₉⋊C₇	C₃	direct (N × H)
3. C₃×C₁₃×C₂₉⋊C₇	C₄	direct (N × H)
5. C₃×C₄×C₁₃×C₂₉	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	C₃×C₄	direct (N × H)
7. C₃×C₄×C₂₉⋊C₇	C₁₃	direct (N × H)
9. C₄×C₁₃×C₂₉	C₃×C₇	semidirect
11. C₃×C₁₃×C₂₉	C₄×C₇	semidirect
13. C₄×C₂₉⋊C₇	C₃×C₁₃	direct (N × H)
15. C₃×C₂₉⋊C₇	C₄×C₁₃	direct (N × H)
18. C₁₃×C₂₉	C₃×C₄×C₇	semidirect
20. C₃×C₄×C₂₉	C₇×C₁₃	semidirect
22. C₂₉⋊C₇	C₃×C₄×C₁₃	direct (N × H)
25. C₃×C₄×C₁₃	C₂₉⋊C₇	direct (N × H)
26. C₄×C₂₉	C₃×C₇×C₁₃	semidirect
28. C₃×C₂₉	C₄×C₇×C₁₃	semidirect
32. C₄×C₁₃	C₃×C₂₉⋊C₇	direct (N × H)
34. C₃×C₁₃	C₄×C₂₉⋊C₇	direct (N × H)
35. C₂₉	C₃×C₄×C₇×C₁₃	semidirect
40. C₁₃	C₃×C₄×C₂₉⋊C₇	direct (N × H)
41. C₃×C₄	C₁₃×C₂₉⋊C₇	direct (N × H)
44. C₄	C₃×C₁₃×C₂₉⋊C₇	direct (N × H)
45. C₃	C₄×C₁₃×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×C₃×C₁₃×C₂₉⋊C₇	2
C₄×C₁₃×C₂₉⋊C₇	3
C₃×C₄×C₁₃×C₂₉	7
C₃×C₄×C₂₉⋊C₇	13
C₃×C₄×C₇×C₁₃	29

Subgroups — C3×C4×C13×C29⋊C7 #44539707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₁₃×C₂₉⋊C₇ #44539707