Subgroups — C₁₉×Dic₇×C₇⋊C₉ #45691508

Order 33516.

80 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×C₇×C₁₉×Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₉×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₉×C₁₉×Dic₇	—	7	1	no	maximal
6	C₄×C₁₉×C₇⋊C₉	—	7	1	no	maximal
7	C₇×C₁₉×Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₇⋊C₉	D₇	1	1	yes	characteristic
10	C₂×C₇×C₉×C₁₉	—	7	1	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
12	Dic₇×C₇⋊C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₇×C₁₉	—	7	1	no	—
14	C₃×C₁₉×Dic₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₇×C₉×C₁₉	—	7	1	no	—
16	C₁₉×C₇⋊C₉	Dic₇	1	1	yes	characteristic, direct product factor
17	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇⋊C₉	C₂×C₁₉	1	1	yes	characteristic
19	C₂×C₃×C₇×C₁₉	—	6	1	no	—
20	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
22	C₄×C₉×C₁₉	—	49	1	no	Hall
23	C₃×C₇×Dic₇	C₃×C₁₉	1	1	yes	characteristic
24	C₄×C₇×C₁₉	—	7	1	no	—
25	C₁₉×Dic₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor
26	C₇×C₇⋊C₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇×C₁₉	—	6	1	no	—
28	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic
30	C₂×C₉×C₁₉	—	7	1	no	—
31	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
32	C₂×C₇×C₁₉	—	6	1	no	—
33	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic
34	C₂×C₇×C₁₉	C₉×D₇	1	1	yes	characteristic
35	C₉×Dic₇	—	7	1	no	—
36	C₄×C₇⋊C₉	—	7	1	no	—
37	C₃×C₄×C₁₉	—	7	1	no	—
38	C₇×Dic₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
39	C₉×C₁₉	—	7	1	no	Hall
40	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic
41	C₇×C₁₉	—	6	1	no	—
42	C₇×C₁₉	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
43	C₇×C₁₉	C₉×Dic₇	1	1	yes	characteristic, complemented
44	C₂×C₇×C₉	—	7	1	no	—
45	C₂×C₇⋊C₉	D₇×C₁₉	1	1	yes	characteristic
46	C₂×C₃×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
47	C₂×C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic
48	C₃×C₄×C₇	—	7	1	no	—
49	C₃×Dic₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
50	C₄×C₁₉	—	7	1	no	Hall
51	C₇×C₉	—	7	1	no	—
52	C₇⋊C₉	C₁₉×Dic₇	1	1	yes	characteristic, direct product factor
53	C₃×C₁₉	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic
54	C₇²	C₄×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	6	1	no	—
56	C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
57	C₂×C₃×C₇	C₃×D₇×C₁₉	1	1	yes	characteristic
58	C₂×C₁₉	D₇×C₇⋊C₉	1	1	yes	characteristic
59	C₄×C₉	—	49	1	no	Hall
60	C₄×C₇	—	7	1	no	—
61	Dic₇	C₁₉×C₇⋊C₉	1	1	yes	characteristic, direct product factor
62	C₃×C₇	—	6	1	no	—
63	C₃×C₇	C₄×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
64	C₃×C₇	C₃×C₁₉×Dic₇	1	1	yes	characteristic
65	C₁₉	Dic₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₉	—	7	1	no	—
67	C₂×C₇	—	6	1	no	—
68	C₂×C₇	C₂×C₁₉×C₇⋊C₉	1	1	yes	characteristic
69	C₂×C₇	C₉×D₇×C₁₉	1	1	yes	characteristic
70	C₃×C₄	—	7	1	no	—
71	C₉	—	7	1	no	Sylow
72	C₇	—	6	1	no	—
73	C₇	C₄×C₁₉×C₇⋊C₉	1	1	yes	characteristic, complemented
74	C₇	C₉×C₁₉×Dic₇	1	1	yes	characteristic, complemented
75	C₂×C₃	D₇×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
76	C₄	—	7	1	no	Sylow
77	C₃	C₁₉×ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic
78	C₂	D₇×C₁₉×C₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₂×C₃	D₇×C₁₉×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₉×C₇⋊C₉	C₄	semidirect
7. C₇×C₁₉×Dic₇	C₉	semidirect
12. Dic₇×C₇⋊C₉	C₁₉	direct (N × H)
16. C₁₉×C₇⋊C₉	Dic₇	direct (N × H)
17. C₇²×C₁₉	C₄×C₉	semidirect
25. C₁₉×Dic₇	C₇⋊C₉	direct (N × H)
26. C₇×C₇⋊C₉	C₄×C₁₉	semidirect
38. C₇×Dic₇	C₉×C₁₉	semidirect
42. C₇×C₁₉	C₄×C₇⋊C₉	semidirect
43. C₇×C₁₉	C₉×Dic₇	semidirect
52. C₇⋊C₉	C₁₉×Dic₇	direct (N × H)
54. C₇²	C₄×C₉×C₁₉	semidirect
61. Dic₇	C₁₉×C₇⋊C₉	direct (N × H)
65. C₁₉	Dic₇×C₇⋊C₉	direct (N × H)
73. C₇	C₄×C₁₉×C₇⋊C₉	semidirect
74. C₇	C₉×C₁₉×Dic₇	semidirect

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×C₇×C₁₉×Dic₇	3
C₉×C₁₉×Dic₇	7
C₄×C₁₉×C₇⋊C₉	7
Dic₇×C₇⋊C₉	19

Subgroups — C19×Dic7×C7⋊C9 #45691508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×Dic₇×C₇⋊C₉ #45691508