Subgroups — C₂²×C₁₃×#10620252 #46799623

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#10620252	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×#10620252	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	3	yes	complemented
5	C₂²×C₁₃×C₃₁⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂²×#10620252	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₃₁⋊C₃	—	7	3	no	—
9	C₂²×C₁₃×C₃₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂×#10620252	C₂×C₁₃	1	3	yes	direct product factor
11	C₁₃×C₃₁⋊C₃	—	7	1	no	Hall
12	C₂²×C₁₃×ΓL(1,𝔽₈)	—	31	1	no	maximal, Hall
13	C₂²×C₇×C₃₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₃₁	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
15	#10620252	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃×ΓL(1,𝔽₈)	—	31	3	no	—
17	C₂×C₇×C₃₁	C₂×C₃×C₁₃	1	3	yes	complemented
18	C₁₃×C₃₁	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃₁⋊C₃	—	7	1	no	Hall
20	C₂²×C₇×C₁₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×ΓL(1,𝔽₈)	—	31	1	no	Hall
22	C₇×C₃₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃₁⋊C₃	—	7	3	no	—
24	C₂×C₇×C₁₃	C₂×C₃₁⋊C₃	1	3	yes	complemented
25	C₂²×C₃×C₁₃	—	217	1	no	Hall
26	C₂²×C₃₁	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
27	C₃₁⋊C₃	—	7	1	no	Hall
28	C₇×C₁₃	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₂²×ΓL(1,𝔽₈)	—	31	1	no	Hall
30	C₂×C₃×C₁₃	—	217	3	no	—
31	C₂×C₃₁	C₂×C₁₃×ΓL(1,𝔽₈)	1	3	yes	complemented
32	C₂²×C₁₃	#10620252	1	1	yes	characteristic, direct product factor, Hall
33	C₂×ΓL(1,𝔽₈)	—	31	3	no	—
34	C₃×C₁₃	—	217	1	no	Hall
35	C₃₁	C₂²×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₇	C₁₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₁₃	C₂×#10620252	1	3	yes	direct product factor
38	ΓL(1,𝔽₈)	—	31	1	no	Hall
39	C₂×C₇	C₂×C₁₃×C₃₁⋊C₃	1	3	yes	complemented
40	C₁₃	C₂²×#10620252	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₃	—	217	1	no	Hall
42	C₇	C₂²×C₁₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	217	3	no	—
44	C₂²	C₁₃×#10620252	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	217	1	no	Sylow
46	C₂	C₂×C₁₃×#10620252	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	#10620252
commutator, cosocle, hypocenter	C₇×C₃₁	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₃×C₃₁	C₃
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#10620252	C₂	direct (N × H)
2. C₂²×C₇×C₁₃×C₃₁	C₃	semidirect
3. C₁₃×#10620252	C₂²	direct (N × H)
4. C₂×C₇×C₁₃×C₃₁	C₂×C₃	semidirect
6. C₇×C₁₃×C₃₁	C₂²×C₃	semidirect
7. C₂²×#10620252	C₁₃	direct (N × H)
9. C₂²×C₁₃×C₃₁	ΓL(1,𝔽₈)	semidirect
10. C₂×#10620252	C₂×C₁₃	direct (N × H)
13. C₂²×C₇×C₃₁	C₃×C₁₃	semidirect
14. C₂×C₁₃×C₃₁	C₂×ΓL(1,𝔽₈)	semidirect
15. #10620252	C₂²×C₁₃	direct (N × H)
17. C₂×C₇×C₃₁	C₂×C₃×C₁₃	semidirect
18. C₁₃×C₃₁	C₂²×ΓL(1,𝔽₈)	semidirect
20. C₂²×C₇×C₁₃	C₃₁⋊C₃	semidirect
22. C₇×C₃₁	C₂²×C₃×C₁₃	semidirect
24. C₂×C₇×C₁₃	C₂×C₃₁⋊C₃	semidirect
26. C₂²×C₃₁	C₁₃×ΓL(1,𝔽₈)	semidirect
28. C₇×C₁₃	C₂²×C₃₁⋊C₃	semidirect
31. C₂×C₃₁	C₂×C₁₃×ΓL(1,𝔽₈)	semidirect
32. C₂²×C₁₃	#10620252	direct (N × H)
35. C₃₁	C₂²×C₁₃×ΓL(1,𝔽₈)	semidirect
36. C₂²×C₇	C₁₃×C₃₁⋊C₃	semidirect
37. C₂×C₁₃	C₂×#10620252	direct (N × H)
39. C₂×C₇	C₂×C₁₃×C₃₁⋊C₃	semidirect
40. C₁₃	C₂²×#10620252	direct (N × H)
42. C₇	C₂²×C₁₃×C₃₁⋊C₃	semidirect
44. C₂²	C₁₃×#10620252	direct (N × H)
46. C₂	C₂×C₁₃×#10620252	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×#10620252	2
C₂²×C₇×C₁₃×C₃₁	3
C₂²×C₁₃×C₃₁⋊C₃	7
C₂²×#10620252	13
C₂²×C₁₃×ΓL(1,𝔽₈)	31

Subgroups — C22×C13×#10620252 #46799623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#10620252 #46799623