Finite Group Databasebeta

← C5×#63271⋊A4 #30655554

Subgroups — C5×#63271⋊A4 #30655554

Order 16380.

112 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C5×C22⋊#63270C311yesmaximal, characteristic, complemented
2C5×C13×C22⋊ΓL(1,𝔽8)C311yesmaximal, characteristic, complemented
3C5×C7×C22⋊(C13⋊C3)C311yesmaximal, characteristic, complemented
4C22×C5×#63271C311yesmaximal, characteristic, complemented
5C5×ΓL(1,𝔽8)×C13⋊C3—41nomaximal, Hall
6#63271⋊A4C511yesmaximal, characteristic, direct product factor, Hall
7C2×C5×#63271—31no—
8C5×A4×C13⋊C3—71nomaximal, Hall
9C22×C5×C7×C13C3211yescharacteristic, complemented, Hall
10C5×#63270—41no—
11C5×#63271A411yescharacteristic, complemented
12C5×C13×ΓL(1,𝔽8)—41no—
13C5×C7×C13⋊C3—41no—
14C5×A4×ΓL(1,𝔽8)—131nomaximal, Hall
15C22⋊#63270C3×C511yescharacteristic, complemented
16C13×C22⋊ΓL(1,𝔽8)C3×C511yescharacteristic, complemented
17C7×C22⋊(C13⋊C3)C3×C511yescharacteristic, complemented
18C22×#63271C3×C511yescharacteristic, complemented
19C2×C5×C7×C13—31no—
20ΓL(1,𝔽8)×C13⋊C3—41noHall
21C5×C22⋊(C13⋊C3)—71no—
22C5×C22⋊(C13⋊C3)ΓL(1,𝔽8)11yescharacteristic, complemented
23C5×A4×C13—71no—
24C22×C5×C13⋊C3—71no—
25C3×C5×C13⋊C3—281noHall
26C2×#63271—31no—
27A4×C13⋊C3—71noHall
28C5×C7×C13C3×A411yescharacteristic, complemented, Hall
29C5×C22⋊ΓL(1,𝔽8)—131no—
30C5×C22⋊ΓL(1,𝔽8)C13⋊C311yescharacteristic, complemented
31C5×C7×A4—131no—
32C22×C5×ΓL(1,𝔽8)—131no—
33C2×C5×C13⋊C3—211no—
34C22×C7×C13C32×C511yescharacteristic, complemented, Hall
35C3×C5×ΓL(1,𝔽8)—521noHall
36#63271C5×A411yescharacteristic, complemented
37#63270—41no—
38C7×C13⋊C3—41no—
39C13×ΓL(1,𝔽8)—41no—
40C22×C5×C13C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
41A4×ΓL(1,𝔽8)—131noHall
42C2×C5×ΓL(1,𝔽8)—391no—
43C3×C5×C13—281no—
44C5×C13⋊C3—41no—
45C5×C13⋊C3—71no—
46C5×C13⋊C3—281no—
47C2×C7×C13—31no—
48C3×C5×A4—911noHall
49C22⋊(C13⋊C3)—71no—
50C22⋊(C13⋊C3)C5×ΓL(1,𝔽8)11yescharacteristic, complemented
51A4×C13—71no—
52C22×C13⋊C3—71no—
53C22×C5×C7C3×C13⋊C311yescharacteristic, complemented, Hall
54C2×C5×C13—31no—
55C3×C13⋊C3—281noHall
56C3×C5×C7—521no—
57C5×ΓL(1,𝔽8)—41no—
58C5×ΓL(1,𝔽8)—131no—
59C5×ΓL(1,𝔽8)—521no—
60C7×C13C3×C5×A411yescharacteristic, complemented, Hall
61C22⋊ΓL(1,𝔽8)—131no—
62C22⋊ΓL(1,𝔽8)C5×C13⋊C311yescharacteristic, complemented
63C7×A4—131no—
64C22×ΓL(1,𝔽8)—131no—
65C2×C13⋊C3—211no—
66C2×C5×C7—31no—
67C5×C13A4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
68C3×ΓL(1,𝔽8)—521noHall
69C22×C3×C5—911no—
70C5×A4—71no—
71C5×A4—131no—
72C5×A4—911no—
73C22×C13C3×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
74C32×C5—3641noHall
75C2×ΓL(1,𝔽8)—391no—
76C3×C13—281no—
77C13⋊C3—41no—
78C13⋊C3—71no—
79C13⋊C3—281no—
80C3×A4—911noHall
81C5×C7A4×C13⋊C311yescharacteristic, complemented, Hall
82C2×C3×C5—2731no—
83C22×C7C3×C5×C13⋊C311yescharacteristic, complemented, Hall
84C2×C13—31no—
85C3×C7—521no—
86ΓL(1,𝔽8)—41no—
87ΓL(1,𝔽8)—131no—
88ΓL(1,𝔽8)—521no—
89C22×C5ΓL(1,𝔽8)×C13⋊C311yescharacteristic, complemented, Hall
90C3×C5—281no—
91C3×C5—521no—
92C3×C5—911no—
93C3×C5—3641no—
94C2×C7—31no—
95C13C5×A4×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
96C22×C3—911no—
97A4—71no—
98A4—131no—
99A4—911no—
100C2×C5—31no—
101C32—3641noSylow
102C7C5×A4×C13⋊C311yescharacteristic, complemented, Sylow
103C2×C3—2731no—
104C5#63271⋊A411yescharacteristic, direct product factor, Sylow
105C22C5×ΓL(1,𝔽8)×C13⋊C311yescharacteristic, complemented, Sylow
106C3—281no—
107C3—521no—
108C3—911no—
109C3—3641no—
110C2—31no—
subgroupG/H
center, hypercenterC5#63271⋊A4
commutator, cosocle, hypocenterC22×C7×C13C32×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C13C32
LCSG ▷ C22×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C22⋊#63270C3semidirect
2. C5×C13×C22⋊ΓL(1,𝔽8)C3semidirect
3. C5×C7×C22⋊(C13⋊C3)C3semidirect
4. C22×C5×#63271C3semidirect
6. #63271⋊A4C5direct (N × H)
9. C22×C5×C7×C13C32semidirect
11. C5×#63271A4semidirect
15. C22⋊#63270C3×C5semidirect
16. C13×C22⋊ΓL(1,𝔽8)C3×C5semidirect
17. C7×C22⋊(C13⋊C3)C3×C5semidirect
18. C22×#63271C3×C5semidirect
22. C5×C22⋊(C13⋊C3)ΓL(1,𝔽8)semidirect
28. C5×C7×C13C3×A4semidirect
30. C5×C22⋊ΓL(1,𝔽8)C13⋊C3semidirect
34. C22×C7×C13C32×C5semidirect
36. #63271C5×A4semidirect
40. C22×C5×C13C3×ΓL(1,𝔽8)semidirect
50. C22⋊(C13⋊C3)C5×ΓL(1,𝔽8)semidirect
53. C22×C5×C7C3×C13⋊C3semidirect
60. C7×C13C3×C5×A4semidirect
62. C22⋊ΓL(1,𝔽8)C5×C13⋊C3semidirect
67. C5×C13A4×ΓL(1,𝔽8)semidirect
73. C22×C13C3×C5×ΓL(1,𝔽8)semidirect
81. C5×C7A4×C13⋊C3semidirect
83. C22×C7C3×C5×C13⋊C3semidirect
89. C22×C5ΓL(1,𝔽8)×C13⋊C3semidirect
95. C13C5×A4×ΓL(1,𝔽8)semidirect
102. C7C5×A4×C13⋊C3semidirect
104. C5#63271⋊A4direct (N × H)
105. C22C5×ΓL(1,𝔽8)×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×C22⋊#632703
C5×C13×C22⋊ΓL(1,𝔽8)3
C5×C7×C22⋊(C13⋊C3)3
C22×C5×#632713
C5×ΓL(1,𝔽8)×C13⋊C34
#63271⋊A45
C5×A4×C13⋊C37
C5×A4×ΓL(1,𝔽8)13