Subgroups — C₂×C₅×C₁₃⋊C₃×C₃₁⋊C₃ #49136608

Order 36270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×#11925881	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#11925882	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₃₁×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₁₃×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃⋊C₃×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×#11925881	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×#11925882	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₃₁×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×C₁₃×C₃₁⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅×C₁₃×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₁₃⋊C₃×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₃₁⋊C₃	—	13	1	no	maximal, Hall
14	C₂×#11925881	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂×#11925882	C₃×C₅	1	1	yes	characteristic, complemented
16	C₂×C₃₁×C₁₃⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
17	C₂×C₁₃×C₃₁⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
18	C₅×C₁₃×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×C₃₁⋊C₃	—	13	1	no	Hall
20	#11925882	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	#11925881	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₁₃×C₃₁⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₃₁×C₁₃⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₁₃⋊C₃	—	31	1	no	maximal, Hall
25	C₂×C₃×C₅×C₃₁	—	13	1	no	—
26	C₂×C₅×C₃₁⋊C₃	—	13	1	no	—
27	C₂×C₅×C₃₁⋊C₃	—	13	1	no	—
28	C₂×C₅×C₃₁⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂×C₁₃×C₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₃⋊C₃	—	31	1	no	Hall
31	C₂×C₃×C₃₁⋊C₃	—	13	1	no	Hall
32	C₃×C₅×C₃₁	—	13	1	no	—
33	C₅×C₃₁⋊C₃	—	13	1	no	—
34	C₅×C₃₁⋊C₃	—	13	1	no	—
35	C₅×C₃₁⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
36	C₁₃×C₃₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₁₃	—	31	1	no	—
38	C₂×C₅×C₁₃⋊C₃	—	31	1	no	—
39	C₂×C₅×C₁₃⋊C₃	—	31	1	no	—
40	C₂×C₅×C₁₃⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
41	C₂×C₅×C₃₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
42	C₃×C₃₁⋊C₃	—	13	1	no	Hall
43	C₂×C₃×C₁₃⋊C₃	—	31	1	no	Hall
44	C₃×C₅×C₁₃	—	31	1	no	—
45	C₅×C₁₃⋊C₃	—	31	1	no	—
46	C₅×C₁₃⋊C₃	—	31	1	no	—
47	C₅×C₁₃⋊C₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₃₁	—	13	1	no	—
49	C₂×C₃₁⋊C₃	—	13	1	no	—
50	C₂×C₃₁⋊C₃	—	13	1	no	—
51	C₂×C₃₁⋊C₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
52	C₅×C₃₁	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₅×C₁₃	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
54	C₃×C₁₃⋊C₃	—	31	1	no	Hall
55	C₃×C₃₁	—	13	1	no	—
56	C₃₁⋊C₃	—	13	1	no	—
57	C₃₁⋊C₃	—	13	1	no	—
58	C₃₁⋊C₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×C₅	—	403	1	no	Hall
60	C₂×C₃×C₁₃	—	31	1	no	—
61	C₂×C₁₃⋊C₃	—	31	1	no	—
62	C₂×C₁₃⋊C₃	—	31	1	no	—
63	C₂×C₁₃⋊C₃	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
64	C₅×C₁₃	C₂×C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₃₁	C₃×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
66	C₃²×C₅	—	403	1	no	Hall
67	C₃×C₁₃	—	31	1	no	—
68	C₁₃⋊C₃	—	31	1	no	—
69	C₁₃⋊C₃	—	31	1	no	—
70	C₁₃⋊C₃	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
71	C₃₁	C₂×C₃×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃×C₅	—	13	1	no	—
73	C₂×C₃×C₅	—	31	1	no	—
74	C₂×C₃×C₅	—	403	1	no	—
75	C₂×C₃×C₅	—	403	1	no	—
76	C₂×C₁₃	C₃×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
77	C₂×C₃²	—	403	1	no	Hall
78	C₃×C₅	—	13	1	no	—
79	C₃×C₅	—	31	1	no	—
80	C₃×C₅	—	403	1	no	—
81	C₃×C₅	—	403	1	no	—
82	C₁₃	C₂×C₃×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₅	C₁₃⋊C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
84	C₃²	—	403	1	no	Sylow
85	C₂×C₃	—	13	1	no	—
86	C₂×C₃	—	31	1	no	—
87	C₂×C₃	—	403	1	no	—
88	C₂×C₃	—	403	1	no	—
89	C₅	C₂×C₁₃⋊C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
90	C₃	—	13	1	no	—
91	C₃	—	31	1	no	—
92	C₃	—	403	1	no	—
93	C₃	—	403	1	no	—
94	C₂	C₅×C₁₃⋊C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₃⋊C₃×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₃₁	C₃²
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂×C₅×#11925881	C₃	semidirect
3. C₂×C₅×#11925882	C₃	semidirect
4. C₂×C₅×C₃₁×C₁₃⋊C₃	C₃	semidirect
5. C₂×C₅×C₁₃×C₃₁⋊C₃	C₃	semidirect
6. C₂×C₁₃⋊C₃×C₃₁⋊C₃	C₅	direct (N × H)
7. C₅×#11925881	C₂×C₃	semidirect
8. C₅×#11925882	C₂×C₃	semidirect
9. C₅×C₃₁×C₁₃⋊C₃	C₂×C₃	semidirect
10. C₅×C₁₃×C₃₁⋊C₃	C₂×C₃	semidirect
11. C₂×C₅×C₁₃×C₃₁	C₃²	semidirect
12. C₁₃⋊C₃×C₃₁⋊C₃	C₂×C₅	direct (N × H)
14. C₂×#11925881	C₃×C₅	semidirect
15. C₂×#11925882	C₃×C₅	semidirect
16. C₂×C₃₁×C₁₃⋊C₃	C₃×C₅	semidirect
17. C₂×C₁₃×C₃₁⋊C₃	C₃×C₅	semidirect
18. C₅×C₁₃×C₃₁	C₂×C₃²	semidirect
20. #11925882	C₂×C₃×C₅	semidirect
21. #11925881	C₂×C₃×C₅	semidirect
22. C₁₃×C₃₁⋊C₃	C₂×C₃×C₅	semidirect
23. C₃₁×C₁₃⋊C₃	C₂×C₃×C₅	semidirect
28. C₂×C₅×C₃₁⋊C₃	C₁₃⋊C₃	direct (N × H)
29. C₂×C₁₃×C₃₁	C₃²×C₅	semidirect
35. C₅×C₃₁⋊C₃	C₂×C₁₃⋊C₃	direct (N × H)
36. C₁₃×C₃₁	C₂×C₃²×C₅	semidirect
40. C₂×C₅×C₁₃⋊C₃	C₃₁⋊C₃	direct (N × H)
41. C₂×C₅×C₃₁	C₃×C₁₃⋊C₃	semidirect
47. C₅×C₁₃⋊C₃	C₂×C₃₁⋊C₃	direct (N × H)
51. C₂×C₃₁⋊C₃	C₅×C₁₃⋊C₃	direct (N × H)
52. C₅×C₃₁	C₂×C₃×C₁₃⋊C₃	semidirect
53. C₂×C₅×C₁₃	C₃×C₃₁⋊C₃	semidirect
58. C₃₁⋊C₃	C₂×C₅×C₁₃⋊C₃	direct (N × H)
63. C₂×C₁₃⋊C₃	C₅×C₃₁⋊C₃	direct (N × H)
64. C₅×C₁₃	C₂×C₃×C₃₁⋊C₃	semidirect
65. C₂×C₃₁	C₃×C₅×C₁₃⋊C₃	semidirect
70. C₁₃⋊C₃	C₂×C₅×C₃₁⋊C₃	direct (N × H)
71. C₃₁	C₂×C₃×C₅×C₁₃⋊C₃	semidirect
76. C₂×C₁₃	C₃×C₅×C₃₁⋊C₃	semidirect
82. C₁₃	C₂×C₃×C₅×C₃₁⋊C₃	semidirect
83. C₂×C₅	C₁₃⋊C₃×C₃₁⋊C₃	direct (N × H)
89. C₅	C₂×C₁₃⋊C₃×C₃₁⋊C₃	direct (N × H)
94. C₂	C₅×C₁₃⋊C₃×C₃₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃⋊C₃×C₃₁⋊C₃	2
C₂×C₅×#11925881	3
C₂×C₅×#11925882	3
C₂×C₅×C₃₁×C₁₃⋊C₃	3
C₂×C₅×C₁₃×C₃₁⋊C₃	3
C₂×C₁₃⋊C₃×C₃₁⋊C₃	5
C₂×C₃×C₅×C₃₁⋊C₃	13
C₂×C₃×C₅×C₁₃⋊C₃	31

Subgroups — C2×C5×C13⋊C3×C31⋊C3 #49136608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃⋊C₃×C₃₁⋊C₃ #49136608