Subgroups — C₂×C₃×C₁₃×#87705 #44528016

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#87705	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×#87705	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#87705	C₂×C₃	1	3	yes	direct product factor
5	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₃×C₁₃×C₁₉⋊C₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×#87705	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₃×C₁₉⋊C₃	—	7	1	no	Hall
10	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₃×ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
12	C₂×C₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₂×C₁₃×C₁₉⋊C₃	—	7	3	no	—
14	C₃×#87705	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
16	C₂×C₃×C₇×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
17	C₂×#87705	C₃×C₁₃	1	3	yes	direct product factor
18	C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₁₃×C₁₉⋊C₃	—	7	3	no	—
20	C₂×C₃×C₇×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
21	C₂×C₁₃×ΓL(1,𝔽₈)	—	19	3	no	—
22	C₂×C₁₃×C₁₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
24	#87705	C₂×C₃×C₁₃	1	3	yes	direct product factor
25	C₂×C₃×C₁₉⋊C₃	—	7	1	no	Hall
26	C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	C₁₃×ΓL(1,𝔽₈)	—	19	3	no	—
28	C₂×C₇×C₁₉	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃²×C₁₃	—	133	1	no	Hall
31	C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₉⋊C₃	—	7	1	no	Hall
33	C₇×C₁₉	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
35	C₃²×C₁₃	—	133	1	no	Hall
36	C₂×C₃×C₁₉	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
37	C₂×C₁₉⋊C₃	—	7	3	no	—
38	C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₁₃	—	133	3	no	—
40	C₂×C₃×C₁₃	#87705	1	1	yes	characteristic, direct product factor
41	C₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
42	C₃×C₁₉	C₂×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	7	3	no	—
44	C₂×C₃×C₇	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
45	C₂×ΓL(1,𝔽₈)	—	19	3	no	—
46	C₃×C₁₃	—	133	3	no	—
47	C₃×C₁₃	C₂×#87705	1	1	yes	characteristic, direct product factor
48	C₂×C₁₉	C₃×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₃	C₃×#87705	1	1	yes	characteristic, direct product factor, Hall
50	C₃×C₇	C₂×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	19	3	no	—
52	C₁₉	C₂×C₃×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃²	—	133	1	no	Hall
54	C₂×C₇	C₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
55	C₁₃	C₂×C₃×#87705	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	133	1	no	Sylow
57	C₇	C₂×C₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	133	3	no	—
59	C₂×C₃	C₁₃×#87705	1	1	yes	characteristic, direct product factor
60	C₃	—	133	3	no	—
61	C₃	C₂×C₁₃×#87705	1	1	yes	characteristic, direct product factor
62	C₂	C₃×C₁₃×#87705	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	#87705
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#87705	C₂	direct (N × H)
2. C₂×C₁₃×#87705	C₃	direct (N × H)
3. C₂×C₃×C₇×C₁₃×C₁₉	C₃	semidirect
4. C₁₃×#87705	C₂×C₃	direct (N × H)
5. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₂×C₇×C₁₃×C₁₉	C₃²	semidirect
8. C₂×C₃×#87705	C₁₃	direct (N × H)
10. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
12. C₂×C₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	semidirect
14. C₃×#87705	C₂×C₁₃	direct (N × H)
16. C₂×C₃×C₇×C₁₉	C₃×C₁₃	semidirect
17. C₂×#87705	C₃×C₁₃	direct (N × H)
18. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
20. C₂×C₃×C₇×C₁₃	C₁₉⋊C₃	semidirect
22. C₂×C₁₃×C₁₉	C₃×ΓL(1,𝔽₈)	semidirect
23. C₃×C₇×C₁₉	C₂×C₃×C₁₃	semidirect
24. #87705	C₂×C₃×C₁₃	direct (N × H)
26. C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
28. C₂×C₇×C₁₉	C₃²×C₁₃	semidirect
29. C₁₃×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
31. C₂×C₇×C₁₃	C₃×C₁₉⋊C₃	semidirect
33. C₇×C₁₉	C₂×C₃²×C₁₃	semidirect
36. C₂×C₃×C₁₉	C₁₃×ΓL(1,𝔽₈)	semidirect
38. C₇×C₁₃	C₂×C₃×C₁₉⋊C₃	semidirect
40. C₂×C₃×C₁₃	#87705	direct (N × H)
42. C₃×C₁₉	C₂×C₁₃×ΓL(1,𝔽₈)	semidirect
44. C₂×C₃×C₇	C₁₃×C₁₉⋊C₃	semidirect
47. C₃×C₁₃	C₂×#87705	direct (N × H)
48. C₂×C₁₉	C₃×C₁₃×ΓL(1,𝔽₈)	semidirect
49. C₂×C₁₃	C₃×#87705	direct (N × H)
50. C₃×C₇	C₂×C₁₃×C₁₉⋊C₃	semidirect
52. C₁₉	C₂×C₃×C₁₃×ΓL(1,𝔽₈)	semidirect
54. C₂×C₇	C₃×C₁₃×C₁₉⋊C₃	semidirect
55. C₁₃	C₂×C₃×#87705	direct (N × H)
57. C₇	C₂×C₃×C₁₃×C₁₉⋊C₃	semidirect
59. C₂×C₃	C₁₃×#87705	direct (N × H)
61. C₃	C₂×C₁₃×#87705	direct (N × H)
62. C₂	C₃×C₁₃×#87705	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₃×#87705	2
C₂×C₁₃×#87705	3
C₂×C₃×C₇×C₁₃×C₁₉	3
C₂×C₃×C₁₃×C₁₉⋊C₃	7
C₂×C₃×#87705	13
C₂×C₃×C₁₃×ΓL(1,𝔽₈)	19

Subgroups — C2×C3×C13×#87705 #44528016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃×#87705 #44528016