Finite Group Databasebeta

← C7⋊AGL(1,𝔽5)×#63271 #50303882

Subgroups — C7⋊AGL(1,𝔽5)×#63271 #50303882

Order 38220.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C7×D5×#63271C211yesmaximal, characteristic
2C7×C13×C7⋊AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
3C5×C7×#63271C411yescharacteristic, complemented, Hall
4Dic7×#63271—51nomaximal, Hall
5C72×D5×C13C2×C311yescharacteristic
6C13⋊C3×C7⋊AGL(1,𝔽5)—71nomaximal
7AGL(1,𝔽5)×#63271—71nomaximal
8C2×C7×#63271—51no—
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5)—131nomaximal, Hall
11D5×#63271D711yescharacteristic
12C7×D5×C13⋊C3—71no—
13C7×C13×Dic7—51noHall
14C7×#63271AGL(1,𝔽5)11yescharacteristic, complemented, Hall
15C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)11yescharacteristic, complemented
16C7×C13×AGL(1,𝔽5)—71no—
17C7×D5×ΓL(1,𝔽8)—131no—
18C5×#63271Dic711yescharacteristic, complemented
19C5×C7×C13⋊C3—71no—
20C2×C72×C13—51no—
21C4×#63271—351no—
22Dic7×C13⋊C3—351no—
23C7×C7⋊AGL(1,𝔽5)C13⋊C311yescharacteristic, complemented, Hall
24C7×D5×C13—61no—
25C7×D5×C13C2×ΓL(1,𝔽8)11yescharacteristic
26C7×D5×C13C3×D711yescharacteristic
27AGL(1,𝔽5)×C13⋊C3—491noHall
28C5×C7×ΓL(1,𝔽8)—131noHall
29C72×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
30ΓL(1,𝔽8)×Dic7—651noHall
31C2×#63271—51no—
32C2×C7×C13⋊C3—351no—
33C72×D5C2×C13⋊C311yescharacteristic
34C5×C7×C13—61no—
35C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
36C5×C7×C13C3×Dic711yescharacteristic, complemented
37C3×C7⋊AGL(1,𝔽5)—911no—
38AGL(1,𝔽5)×ΓL(1,𝔽8)—911no—
39D5×C13⋊C3—71no—
40C4×C7×C13—351no—
41C13×Dic7—51no—
42C2×C7×ΓL(1,𝔽8)—651no—
43#63271C7⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
44C7×C13⋊C3—71no—
45C13×AGL(1,𝔽5)—71noHall
46C5×C72C4×C13⋊C311yescharacteristic, complemented, Hall
47C3×C7×D5—911no—
48D5×ΓL(1,𝔽8)—131no—
49C7×Dic7—51noHall
50C5×C13⋊C3—71noHall
51C2×C7×C13—51no—
52C2×C7×C13—51no—
53C2×C7×C13—301no—
54C4×C13⋊C3—2451noHall
55C7×ΓL(1,𝔽8)—131noHall
56C7⋊AGL(1,𝔽5)#6327111yescharacteristic, direct product factor
57C7×AGL(1,𝔽5)—71no—
58D5×C13D7×ΓL(1,𝔽8)11yescharacteristic
59C3×C5×C7—911no—
60C5×ΓL(1,𝔽8)—131no—
61C2×C72—51no—
62C7×C13—61no—
63C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
64C7×C13C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
65C3×Dic7—4551no—
66C4×ΓL(1,𝔽8)—4551no—
67C2×C13⋊C3—351no—
68C7×D5—61no—
69C7×D5D7×C13⋊C311yescharacteristic
70C7×D5C2×#6327111yescharacteristic
71C5×C13ΓL(1,𝔽8)×Dic711yescharacteristic, complemented, Hall
72C3×AGL(1,𝔽5)—6371noHall
73C4×C13—351noHall
74C72AGL(1,𝔽5)×C13⋊C311yescharacteristic, complemented, Sylow
75C2×C3×C7—4551no—
76C2×ΓL(1,𝔽8)—651no—
77C13⋊C3—71noHall
78C5×C7—61no—
79C5×C7Dic7×C13⋊C311yescharacteristic, complemented
80C5×C7C4×#6327111yescharacteristic, complemented
81C3×D5—911no—
82C4×C7—351no—
83Dic7—51no—
84C2×C13—51no—
85C3×C7—911no—
86ΓL(1,𝔽8)—131no—
87AGL(1,𝔽5)—71noHall
88C3×C5—911noHall
89C2×C7—51no—
90C2×C7—51no—
91C2×C7—301no—
92C13ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
93C3×C4—31851noHall
94D5D7×#6327111yescharacteristic
95C7—61no—
96C7AGL(1,𝔽5)×#6327111yescharacteristic, complemented
97C7C13⋊C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
98C2×C3—4551no—
99C5Dic7×#6327111yescharacteristic, complemented, Sylow
100C4—351noSylow
101C3—911noSylow
102C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C72×C13C3×C4
prime radicalC7×D5×#63271C2
cosocleC72×D5×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. C7×C13×C7⋊AGL(1,𝔽5)C3semidirect
3. C5×C7×#63271C4semidirect
9. C5×C72×C13C3×C4semidirect
14. C7×#63271AGL(1,𝔽5)semidirect
15. C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
18. C5×#63271Dic7semidirect
23. C7×C7⋊AGL(1,𝔽5)C13⋊C3semidirect
29. C72×C13C3×AGL(1,𝔽5)semidirect
35. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
36. C5×C7×C13C3×Dic7semidirect
43. #63271C7⋊AGL(1,𝔽5)direct (N × H)
46. C5×C72C4×C13⋊C3semidirect
56. C7⋊AGL(1,𝔽5)#63271direct (N × H)
63. C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
64. C7×C13C3×C7⋊AGL(1,𝔽5)semidirect
71. C5×C13ΓL(1,𝔽8)×Dic7semidirect
74. C72AGL(1,𝔽5)×C13⋊C3semidirect
79. C5×C7Dic7×C13⋊C3semidirect
80. C5×C7C4×#63271semidirect
92. C13ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5)semidirect
96. C7AGL(1,𝔽5)×#63271semidirect
97. C7C13⋊C3×C7⋊AGL(1,𝔽5)semidirect
99. C5Dic7×#63271semidirect

Maximal subgroups

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

subgroupindex
C7×D5×#632712
C7×C13×C7⋊AGL(1,𝔽5)3
Dic7×#632715
C13⋊C3×C7⋊AGL(1,𝔽5)7
AGL(1,𝔽5)×#632717
ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5)13