Subgroups — C₄×C₇×C₁₉×C₇⋊C₉ #45691519

Order 33516.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₉×C₇⋊C₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₉×C₇⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₄×C₇×C₉×C₁₉	—	7	1	no	maximal
7	C₄×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₇⋊C₉	C₂×C₇	1	1	yes	characteristic
10	C₂×C₇×C₉×C₁₉	—	7	1	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
12	C₄×C₇×C₇⋊C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₇×C₁₉	—	3	2	no	—
14	C₃×C₄×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₄×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic
16	C₇×C₉×C₁₉	—	7	1	no	—
17	C₁₉×C₇⋊C₉	C₄×C₇	1	1	yes	characteristic, direct product factor
18	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₇⋊C₉	C₂×C₁₉	1	1	yes	characteristic
20	C₂×C₃×C₇×C₁₉	—	3	2	no	—
21	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic
23	C₄×C₉×C₁₉	—	7	1	no	Hall
24	C₃×C₄×C₇²	C₃×C₁₉	1	1	yes	characteristic
25	C₄×C₇×C₁₉	—	3	2	no	—
26	C₄×C₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor
27	C₄×C₇×C₁₉	C₇×C₉	1	1	yes	characteristic, complemented
28	C₇×C₇⋊C₉	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₇×C₁₉	—	3	2	no	—
30	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃×C₇×C₁₉	C₃×C₄×C₇	1	1	yes	characteristic
32	C₂×C₉×C₁₉	—	7	1	no	—
33	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
34	C₂×C₇×C₁₉	—	3	2	no	—
35	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic
36	C₂×C₇×C₁₉	C₂×C₇×C₉	1	1	yes	characteristic
37	C₄×C₇×C₉	—	7	1	no	—
38	C₄×C₇⋊C₉	C₇×C₁₉	1	1	yes	characteristic, direct product factor
39	C₃×C₄×C₁₉	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₄×C₇²	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
41	C₉×C₁₉	—	7	1	no	Hall
42	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic
43	C₇×C₁₉	—	3	2	no	—
44	C₇×C₁₉	C₄×C₇⋊C₉	1	1	yes	characteristic, direct product factor
45	C₇×C₁₉	C₄×C₇×C₉	1	1	yes	characteristic, complemented
46	C₂×C₇×C₉	—	7	1	no	—
47	C₂×C₇⋊C₉	C₂×C₇×C₁₉	1	1	yes	characteristic
48	C₂×C₃×C₁₉	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₂×C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic
50	C₃×C₄×C₇	—	3	2	no	—
51	C₃×C₄×C₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
52	C₃×C₄×C₇	C₃×C₇×C₁₉	1	1	yes	characteristic
53	C₄×C₁₉	C₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
54	C₇×C₉	—	7	1	no	—
55	C₇⋊C₉	C₄×C₇×C₁₉	1	1	yes	characteristic, direct product factor
56	C₃×C₁₉	C₄×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
57	C₇²	C₄×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	3	2	no	—
59	C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
60	C₂×C₃×C₇	C₂×C₃×C₇×C₁₉	1	1	yes	characteristic
61	C₂×C₁₉	C₂×C₇×C₇⋊C₉	1	1	yes	characteristic
62	C₄×C₉	—	7	1	no	Hall
63	C₄×C₇	—	3	2	no	—
64	C₄×C₇	C₁₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor
65	C₄×C₇	C₇×C₉×C₁₉	1	1	yes	characteristic, complemented
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	C₄×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
68	C₃×C₇	C₃×C₄×C₇×C₁₉	1	1	yes	characteristic
69	C₁₉	C₄×C₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₉	—	7	1	no	—
71	C₂×C₇	—	3	2	no	—
72	C₂×C₇	C₂×C₇×C₉×C₁₉	1	1	yes	characteristic
73	C₂×C₇	C₂×C₁₉×C₇⋊C₉	1	1	yes	characteristic
74	C₃×C₄	C₇×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
75	C₉	—	7	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	C₄×C₇×C₉×C₁₉	1	1	yes	characteristic, complemented
78	C₇	C₄×C₁₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃	C₂×C₇×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
80	C₄	C₇×C₁₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	C₄×C₇×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
82	C₂	C₂×C₇×C₁₉×C₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₇×C₁₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₄×C₇×C₉×C₁₉
Frattini	C₂×C₃	C₂×C₇×C₁₉×ΓL(1,𝔽₈)
Fitting	C₃×C₄×C₇²×C₁₉	C₃
socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₇×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄×C₇×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₉×C₇⋊C₉	C₄	direct (N × H)
5. C₄×C₁₉×C₇⋊C₉	C₇	direct (N × H)
7. C₄×C₇²×C₁₉	C₉	semidirect
12. C₄×C₇×C₇⋊C₉	C₁₉	direct (N × H)
17. C₁₉×C₇⋊C₉	C₄×C₇	direct (N × H)
18. C₇²×C₁₉	C₄×C₉	semidirect
26. C₄×C₇×C₁₉	C₇⋊C₉	direct (N × H)
27. C₄×C₇×C₁₉	C₇×C₉	semidirect
28. C₇×C₇⋊C₉	C₄×C₁₉	direct (N × H)
38. C₄×C₇⋊C₉	C₇×C₁₉	direct (N × H)
40. C₄×C₇²	C₉×C₁₉	semidirect
44. C₇×C₁₉	C₄×C₇⋊C₉	direct (N × H)
45. C₇×C₁₉	C₄×C₇×C₉	semidirect
53. C₄×C₁₉	C₇×C₇⋊C₉	direct (N × H)
55. C₇⋊C₉	C₄×C₇×C₁₉	direct (N × H)
57. C₇²	C₄×C₉×C₁₉	semidirect
64. C₄×C₇	C₁₉×C₇⋊C₉	direct (N × H)
65. C₄×C₇	C₇×C₉×C₁₉	semidirect
69. C₁₉	C₄×C₇×C₇⋊C₉	direct (N × H)
77. C₇	C₄×C₇×C₉×C₁₉	semidirect
78. C₇	C₄×C₁₉×C₇⋊C₉	direct (N × H)
80. C₄	C₇×C₁₉×C₇⋊C₉	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×C₇×C₁₉×C₇⋊C₉	2
C₃×C₄×C₇²×C₁₉	3
C₄×C₁₉×C₇⋊C₉	7
C₄×C₇×C₉×C₁₉	7
C₄×C₇×C₇⋊C₉	19

Subgroups — C4×C7×C19×C7⋊C9 #45691519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₁₉×C₇⋊C₉ #45691519