Subgroups — C₄×C₅×C₁₃×#3862 #50303672

Order 38220.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×#3862	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×#3862	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₁₃×#3862	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
6	C₄×C₅×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	maximal
7	C₂×C₁₃×#3862	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₄×C₅×#3862	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
11	C₄×C₇²×C₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₁₃×#3862	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅×C₇×C₁₃	—	3	2	no	—
14	C₄×C₅×C₇×C₁₃	ΓL(1,𝔽₈)	1	2	yes	complemented
15	C₂×C₅×#3862	C₂×C₁₃	1	1	yes	characteristic
16	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
17	C₂×C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
18	C₄×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
19	C₄×C₅×C₇²	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇×C₁₃	—	3	2	no	—
21	C₂×C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	—
22	C₃×C₄×C₅×C₁₃	—	49	1	no	Hall
23	C₅×#3862	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₇²×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
25	C₄×#3862	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
27	C₂×C₅×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic
28	C₅×C₇×C₁₃	—	3	2	no	—
29	C₅×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
30	C₄×C₅×ΓL(1,𝔽₈)	—	7	2	no	—
31	C₂×C₃×C₅×C₁₃	—	49	1	no	—
32	C₄×C₇×C₁₃	—	3	2	no	—
33	C₄×C₇×C₁₃	C₅×ΓL(1,𝔽₈)	1	2	yes	complemented
34	C₂×#3862	C₂×C₅×C₁₃	1	1	yes	characteristic
35	C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
36	C₄×C₅×C₁₃	#3862	1	1	yes	characteristic, direct product factor, Hall
37	C₅×C₇²	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅×ΓL(1,𝔽₈)	—	7	2	no	—
39	C₄×C₇²	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
40	C₃×C₅×C₁₃	—	49	1	no	Hall
41	C₂×C₇×C₁₃	—	3	2	no	—
42	C₂×C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	2	yes	—
43	C₃×C₄×C₁₃	—	49	1	no	Hall
44	#3862	C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
45	C₄×C₅×C₇	—	3	2	no	—
46	C₄×C₅×C₇	C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
47	C₂×C₅×C₁₃	C₂×#3862	1	1	yes	characteristic
48	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
49	C₂×C₇²	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
50	C₇×C₁₃	—	3	2	no	—
51	C₇×C₁₃	C₄×C₅×ΓL(1,𝔽₈)	1	2	yes	complemented
52	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
53	C₂×C₃×C₁₃	—	49	1	no	—
54	C₂×C₅×C₇	—	3	2	no	—
55	C₂×C₅×C₇	C₂×C₁₃×ΓL(1,𝔽₈)	1	2	yes	—
56	C₅×C₁₃	C₄×#3862	1	1	yes	characteristic, direct product factor, Hall
57	C₃×C₄×C₅	—	49	1	no	Hall
58	C₄×C₁₃	C₅×#3862	1	1	yes	characteristic, direct product factor, Hall
59	C₇²	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
61	C₃×C₁₃	—	49	1	no	Hall
62	C₅×C₇	—	3	2	no	—
63	C₅×C₇	C₄×C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
64	C₂×C₃×C₅	—	49	1	no	—
65	C₄×C₇	—	3	2	no	—
66	C₄×C₇	C₅×C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
67	C₂×C₁₃	C₂×C₅×#3862	1	1	yes	characteristic
68	ΓL(1,𝔽₈)	—	7	2	no	—
69	C₄×C₅	C₁₃×#3862	1	1	yes	characteristic, direct product factor, Hall
70	C₃×C₅	—	49	1	no	Hall
71	C₂×C₇	—	3	2	no	—
72	C₂×C₇	C₂×C₅×C₁₃×ΓL(1,𝔽₈)	1	2	yes	—
73	C₁₃	C₄×C₅×#3862	1	1	yes	characteristic, direct product factor, Sylow
74	C₃×C₄	—	49	1	no	Hall
75	C₂×C₅	C₂×C₁₃×#3862	1	1	yes	characteristic
76	C₇	—	3	2	no	—
77	C₇	C₄×C₅×C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
78	C₂×C₃	—	49	1	no	—
79	C₅	C₄×C₁₃×#3862	1	1	yes	characteristic, direct product factor, Sylow
80	C₄	C₅×C₁₃×#3862	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	—	49	1	no	Sylow
82	C₂	C₂×C₅×C₁₃×#3862	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅×C₁₃	#3862
commutator, hypocenter	C₇²	C₃×C₄×C₅×C₁₃
Frattini	C₂	C₂×C₅×C₁₃×#3862
Fitting	C₄×C₅×C₇²×C₁₃	C₃
socle	C₂×C₅×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₅×C₁₃×#3862	C₂
cosocle	C₂×C₇²	C₂×C₃×C₅×C₁₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₄×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₇²×C₁₃	C₃	semidirect
3. C₅×C₁₃×#3862	C₄	direct (N × H)
4. C₄×C₁₃×#3862	C₅	direct (N × H)
8. C₅×C₇²×C₁₃	C₃×C₄	semidirect
9. C₄×C₅×#3862	C₁₃	direct (N × H)
11. C₄×C₇²×C₁₃	C₃×C₅	semidirect
12. C₁₃×#3862	C₄×C₅	direct (N × H)
14. C₄×C₅×C₇×C₁₃	ΓL(1,𝔽₈)	semidirect
19. C₄×C₅×C₇²	C₃×C₁₃	semidirect
23. C₅×#3862	C₄×C₁₃	direct (N × H)
24. C₇²×C₁₃	C₃×C₄×C₅	semidirect
25. C₄×#3862	C₅×C₁₃	direct (N × H)
29. C₅×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	semidirect
33. C₄×C₇×C₁₃	C₅×ΓL(1,𝔽₈)	semidirect
36. C₄×C₅×C₁₃	#3862	direct (N × H)
37. C₅×C₇²	C₃×C₄×C₁₃	semidirect
39. C₄×C₇²	C₃×C₅×C₁₃	semidirect
44. #3862	C₄×C₅×C₁₃	direct (N × H)
46. C₄×C₅×C₇	C₁₃×ΓL(1,𝔽₈)	semidirect
51. C₇×C₁₃	C₄×C₅×ΓL(1,𝔽₈)	semidirect
56. C₅×C₁₃	C₄×#3862	direct (N × H)
58. C₄×C₁₃	C₅×#3862	direct (N × H)
59. C₇²	C₃×C₄×C₅×C₁₃	semidirect
63. C₅×C₇	C₄×C₁₃×ΓL(1,𝔽₈)	semidirect
66. C₄×C₇	C₅×C₁₃×ΓL(1,𝔽₈)	semidirect
69. C₄×C₅	C₁₃×#3862	direct (N × H)
73. C₁₃	C₄×C₅×#3862	direct (N × H)
77. C₇	C₄×C₅×C₁₃×ΓL(1,𝔽₈)	semidirect
79. C₅	C₄×C₁₃×#3862	direct (N × H)
80. C₄	C₅×C₁₃×#3862	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×C₅×C₁₃×#3862	2
C₄×C₅×C₇²×C₁₃	3
C₄×C₁₃×#3862	5
C₄×C₅×C₁₃×ΓL(1,𝔽₈)	7
C₄×C₅×#3862	13

Subgroups — C4×C5×C13×#3862 #50303672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₁₃×#3862 #50303672