Finite Group Databasebeta

← C5×C13×C3⋊(C7⋊AGL(1,𝔽5)) #41031997

Subgroups — C5×C13×C3⋊(C7⋊AGL(1,𝔽5)) #41031997

Order 27300.

104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C7×D5×C13C211yesmaximal, characteristic
2C5×C13×C7⋊AGL(1,𝔽5)—31nomaximal, Hall
3C3×C52×C7×C13C411yescharacteristic, complemented, Hall
4C13×C3⋊(C7⋊AGL(1,𝔽5))C511yesmaximal, characteristic, direct product factor
5C5×C13×Dic21—51nomaximal
6C5×C7×D5×C13D311yescharacteristic
7C5×C13×ΓL(1,𝔽16)—71nomaximal, Hall
8C3×C7×D5×C13C2×C511yescharacteristic
9C2×C3×C5×C7×C13—51no—
10C52×C7×C13Dic311yescharacteristic, complemented, Hall
11C5×C3⋊(C7⋊AGL(1,𝔽5))C1311yesmaximal, characteristic, direct product factor, Hall
12C3×C5×D5×C13D711yescharacteristic
13C13×C7⋊AGL(1,𝔽5)—31no—
14C5×C13×Dic7—151no—
15C3×C5×C7×C13—41no—
16C3×C5×C7×C13C4×C511yescharacteristic, complemented
17C3×C5×C7×C13AGL(1,𝔽5)11yescharacteristic, complemented
18C5×C13×AGL(1,𝔽5)—211noHall
19C13×Dic21—51noHall
20C3×C5×C7×D5C2×C1311yescharacteristic
21C3×C52×C13Dic711yescharacteristic, complemented, Hall
22C2×C5×C7×C13—51no—
23C7×D5×C13C5×D311yescharacteristic
24C13×ΓL(1,𝔽16)—71no—
25C5×Dic3×C13—351no—
26C5×C7⋊AGL(1,𝔽5)—31noHall
27C5×D5×C13D2111yescharacteristic
28C2×C3×C7×C13—51no—
29C3×C52×C7C4×C1311yescharacteristic, complemented, Hall
30C5×C7×C13—41no—
31C5×C7×C13C5×Dic311yescharacteristic, complemented
32C5×C7×C13ΓL(1,𝔽16)11yescharacteristic, complemented
33C3⋊(C7⋊AGL(1,𝔽5))C5×C1311yescharacteristic, direct product factor
34C5×Dic21—51no—
35C2×C3×C5×C13—51no—
36C3×D5×C13C5×D711yescharacteristic
37C13×Dic7—151noHall
38C5×C7×D5D3×C1311yescharacteristic
39C52×C13Dic2111yescharacteristic, complemented, Hall
40C5×ΓL(1,𝔽16)—71noHall
41C3×C7×C13C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
42C13×AGL(1,𝔽5)—211no—
43C4×C5×C13—1051no—
44C2×C3×C5×C7—51no—
45C3×C7×D5C2×C5×C1311yescharacteristic
46C3×C5×C13—41no—
47C3×C5×C13C5×Dic711yescharacteristic, complemented
48C3×C5×C13C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
49C2×C7×C13—51no—
50C52×C7Dic3×C1311yescharacteristic, complemented, Hall
51Dic3×C13—351noHall
52C3×C5×D5C13×D711yescharacteristic
53C7⋊AGL(1,𝔽5)—31no—
54C5×Dic7—151no—
55C2×C5×C13—51no—
56D5×C13C5×D2111yescharacteristic
57C3×C5×C7—41no—
58C3×C5×C7C4×C5×C1311yescharacteristic, complemented
59C3×C5×C7C13×AGL(1,𝔽5)11yescharacteristic, complemented
60C5×AGL(1,𝔽5)—211noHall
61C7×C13C5×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
62Dic21—51noHall
63C2×C3×C13—51no—
64C3×C52C13×Dic711yescharacteristic, complemented, Hall
65C2×C5×C7—51no—
66C7×D5C5×D3×C1311yescharacteristic
67C5×C13—41no—
68C5×C13C5×Dic2111yescharacteristic, complemented
69C5×C13C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, direct product factor
70ΓL(1,𝔽16)—71no—
71C5×Dic3—351no—
72C4×C13—1051noHall
73C5×D5C13×D2111yescharacteristic
74C2×C3×C7—51no—
75C3×C13C5×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
76C5×C7—41no—
77C5×C7C5×Dic3×C1311yescharacteristic, complemented
78C5×C7C13×ΓL(1,𝔽16)11yescharacteristic, complemented
79C2×C3×C5—51no—
80C3×D5C5×C13×D711yescharacteristic
81Dic7—151noHall
82C2×C13—51no—
83C52C13×Dic2111yescharacteristic, complemented, Sylow
84C3×C7C5×C13×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
85AGL(1,𝔽5)—211no—
86C4×C5—1051no—
87C3×C5—41no—
88C3×C5C5×C13×Dic711yescharacteristic, complemented
89C3×C5C13×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
90C2×C7—51no—
91C13C5×C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, direct product factor, Sylow
92Dic3—351noHall
93C2×C5—51no—
94D5C5×C13×D2111yescharacteristic
95C7C5×C13×ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
96C2×C3—51no—
97C5—41no—
98C5C5×C13×Dic2111yescharacteristic, complemented
99C5C13×C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, direct product factor
100C4—1051noSylow
101C3C5×C13×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
102C2—51no—
subgroupG/H
center, hypercenterC5×C13C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C4×C5×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C5×C7×D5×C13C2
cosocleC3×C7×D5C2×C5×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C13

Complements

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

NH ≅ G/Ntype
3. C3×C52×C7×C13C4semidirect
4. C13×C3⋊(C7⋊AGL(1,𝔽5))C5direct (N × H)
10. C52×C7×C13Dic3semidirect
11. C5×C3⋊(C7⋊AGL(1,𝔽5))C13direct (N × H)
16. C3×C5×C7×C13C4×C5semidirect
17. C3×C5×C7×C13AGL(1,𝔽5)semidirect
21. C3×C52×C13Dic7semidirect
29. C3×C52×C7C4×C13semidirect
31. C5×C7×C13C5×Dic3semidirect
32. C5×C7×C13ΓL(1,𝔽16)semidirect
33. C3⋊(C7⋊AGL(1,𝔽5))C5×C13direct (N × H)
39. C52×C13Dic21semidirect
41. C3×C7×C13C5×AGL(1,𝔽5)semidirect
47. C3×C5×C13C5×Dic7semidirect
48. C3×C5×C13C7⋊AGL(1,𝔽5)semidirect
50. C52×C7Dic3×C13semidirect
58. C3×C5×C7C4×C5×C13semidirect
59. C3×C5×C7C13×AGL(1,𝔽5)semidirect
61. C7×C13C5×ΓL(1,𝔽16)semidirect
64. C3×C52C13×Dic7semidirect
68. C5×C13C5×Dic21semidirect
69. C5×C13C3⋊(C7⋊AGL(1,𝔽5))direct (N × H)
75. C3×C13C5×C7⋊AGL(1,𝔽5)semidirect
77. C5×C7C5×Dic3×C13semidirect
78. C5×C7C13×ΓL(1,𝔽16)semidirect
83. C52C13×Dic21semidirect
84. C3×C7C5×C13×AGL(1,𝔽5)semidirect
88. C3×C5C5×C13×Dic7semidirect
89. C3×C5C13×C7⋊AGL(1,𝔽5)semidirect
91. C13C5×C3⋊(C7⋊AGL(1,𝔽5))direct (N × H)
95. C7C5×C13×ΓL(1,𝔽16)semidirect
98. C5C5×C13×Dic21semidirect
99. C5C13×C3⋊(C7⋊AGL(1,𝔽5))direct (N × H)
101. C3C5×C13×C7⋊AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C132
C5×C13×C7⋊AGL(1,𝔽5)3
C13×C3⋊(C7⋊AGL(1,𝔽5))5
C5×C13×Dic215
C5×C13×ΓL(1,𝔽16)7
C5×C3⋊(C7⋊AGL(1,𝔽5))13