Subgroups — C₃×C₇×C₃₁×Dic₁₃ #46799221

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃₁×Dic₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₃₁×Dic₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₇×C₃₁	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₃₁	C₂×C₇	1	1	yes	characteristic
9	C₃₁×Dic₁₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₃₁	D₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₃₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×Dic₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₇×C₃₁	—	13	1	no	Hall
14	C₂×C₁₃×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₃₁	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₇×C₁₃	C₂×C₃₁	1	1	yes	characteristic
17	C₂×C₇×C₃₁	C₃×D₁₃	1	1	yes	characteristic
18	C₁₃×C₃₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄×C₃₁	—	13	1	no	Hall
20	C₇×Dic₁₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₇×C₁₃	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₇×C₃₁	C₃×Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₃₁	C₇×D₁₃	1	1	yes	characteristic
24	C₂×C₇×C₁₃	C₂×C₃×C₃₁	1	1	yes	characteristic
25	C₃×Dic₁₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₄×C₃₁	—	13	1	no	Hall
27	C₃×C₃₁	C₇×Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₇	—	13	1	no	Hall
30	C₂×C₃×C₁₃	C₂×C₇×C₃₁	1	1	yes	characteristic
31	C₂×C₃₁	C₃×C₇×D₁₃	1	1	yes	characteristic
32	Dic₁₃	C₃×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₇	D₁₃×C₃₁	1	1	yes	characteristic
34	C₃×C₁₃	C₄×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
35	C₃₁	C₃×C₇×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₇	—	13	1	no	Hall
37	C₂×C₁₃	C₂×C₃×C₇×C₃₁	1	1	yes	characteristic
38	C₃×C₇	C₃₁×Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	C₃×D₁₃×C₃₁	1	1	yes	characteristic
40	C₁₃	C₃×C₄×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	13	1	no	Hall
42	C₇	C₃×C₃₁×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₇×D₁₃×C₃₁	1	1	yes	characteristic
44	C₄	—	13	1	no	Sylow
45	C₃	C₇×C₃₁×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₇×D₁₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₃₁	D₁₃
commutator, hypocenter	C₁₃	C₃×C₄×C₇×C₃₁
Frattini	C₂	C₃×C₇×D₁₃×C₃₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₃₁	C₂
cosocle	C₂×C₁₃	C₂×C₃×C₇×C₃₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₇×C₃₁×Dic₁₃	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₃₁	C₄	semidirect
5. C₃×C₃₁×Dic₁₃	C₇	direct (N × H)
6. C₇×C₁₃×C₃₁	C₃×C₄	semidirect
9. C₃₁×Dic₁₃	C₃×C₇	direct (N × H)
11. C₃×C₁₃×C₃₁	C₄×C₇	semidirect
12. C₃×C₇×Dic₁₃	C₃₁	direct (N × H)
15. C₃×C₇×C₃₁	Dic₁₃	direct (N × H)
18. C₁₃×C₃₁	C₃×C₄×C₇	semidirect
20. C₇×Dic₁₃	C₃×C₃₁	direct (N × H)
21. C₃×C₇×C₁₃	C₄×C₃₁	semidirect
22. C₇×C₃₁	C₃×Dic₁₃	direct (N × H)
25. C₃×Dic₁₃	C₇×C₃₁	direct (N × H)
27. C₃×C₃₁	C₇×Dic₁₃	direct (N × H)
28. C₇×C₁₃	C₃×C₄×C₃₁	semidirect
32. Dic₁₃	C₃×C₇×C₃₁	direct (N × H)
34. C₃×C₁₃	C₄×C₇×C₃₁	semidirect
35. C₃₁	C₃×C₇×Dic₁₃	direct (N × H)
38. C₃×C₇	C₃₁×Dic₁₃	direct (N × H)
40. C₁₃	C₃×C₄×C₇×C₃₁	semidirect
42. C₇	C₃×C₃₁×Dic₁₃	direct (N × H)
45. C₃	C₇×C₃₁×Dic₁₃	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×C₇×C₁₃×C₃₁	2
C₇×C₃₁×Dic₁₃	3
C₃×C₃₁×Dic₁₃	7
C₃×C₄×C₇×C₃₁	13
C₃×C₇×Dic₁₃	31

Subgroups — C3×C7×C31×Dic13 #46799221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₃₁×Dic₁₃ #46799221