Finite Group Databasebeta

← #50303644

Subgroups — #50303644

Order 38220.

104 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×C5×C13×#3862C211yesmaximal, characteristic
2C7×Dic455C311yesmaximal, characteristic, complemented, Hall
3C5×C13×#3862C411yescharacteristic, complemented, Hall
4#21439542—51nomaximal, Hall
5C2×C5×C72×C13C2×C311yescharacteristic
6ΓL(1,𝔽8)⋊Dic65—71nomaximal
7ΓL(1,𝔽8)×Dic65—71nomaximal
8C2×C13×#3862D511yescharacteristic
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10#15668737—131nomaximal, Hall
11C2×C5×C13×ΓL(1,𝔽8)—71no—
12C2×C5×C13×ΓL(1,𝔽8)—71no—
13C7×Dic91—51noHall
14C13×#3862Dic511yescharacteristic, complemented, Hall
15Dic455ΓL(1,𝔽8)11yescharacteristic, complemented
16C7×Dic65—71no—
17C2×C5×#3862D1311yescharacteristic
18C5×C13×ΓL(1,𝔽8)—71no—
19C5×C13×ΓL(1,𝔽8)—71no—
20C2×C72×C13C3×D511yescharacteristic
21ΓL(1,𝔽8)⋊Dic13—351no—
22ΓL(1,𝔽8)×Dic13—351no—
23C7×Dic35—131noHall
24C2×C5×C7×C13—61no—
25C2×C5×C7×C13AGL(1,𝔽7)11yescharacteristic
26C2×C5×C7×C13C2×ΓL(1,𝔽8)11yescharacteristic
27C3×Dic65—491noHall
28C5×#3862Dic1311yescharacteristic, complemented, Hall
29C72×C13C3×Dic511yescharacteristic, complemented, Hall
30#10596872—651noHall
31C2×C13×ΓL(1,𝔽8)—71no—
32C2×C13×ΓL(1,𝔽8)—71no—
33C2×C5×C72C3×D1311yescharacteristic
34C5×C7×C13—61no—
35C5×C7×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
36C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
37ΓL(1,𝔽8)⋊Dic5—911no—
38Dic5×ΓL(1,𝔽8)—911no—
39C2×C3×C5×C13—491no—
40Dic91—51no—
41C7×Dic13—351no—
42C2×#3862D6511yescharacteristic
43C13×ΓL(1,𝔽8)—71no—
44C13×ΓL(1,𝔽8)—71no—
45Dic65—71noHall
46C5×C72C3×Dic1311yescharacteristic, complemented, Hall
47C2×C5×ΓL(1,𝔽8)—71no—
48C2×C5×ΓL(1,𝔽8)—71no—
49C7×Dic7—651noHall
50C3×C5×C13—491noHall
51C2×C7×C13—61no—
52C2×C7×C13D5×ΓL(1,𝔽8)11yescharacteristic
53C2×C7×C13C5⋊AGL(1,𝔽7)11yescharacteristic
54C3×Dic13—2451noHall
55#3862Dic6511yescharacteristic, complemented, Hall
56Dic35—131no—
57C7×Dic5—911no—
58C2×C5×C13#6442211yescharacteristic
59C5×ΓL(1,𝔽8)—71no—
60C5×ΓL(1,𝔽8)—71no—
61C2×C72C3×D6511yescharacteristic
62C7×C13—61no—
63C7×C13Dic5×ΓL(1,𝔽8)11yescharacteristic, complemented
64C7×C13ΓL(1,𝔽8)⋊Dic511yescharacteristic, complemented
65C4×ΓL(1,𝔽8)—4551no—
66ΓL(1,𝔽8)⋊C4—4551no—
67C2×C3×C13—491no—
68C2×C5×C7—61no—
69C2×C5×C7ΓL(1,𝔽8)×D1311yescharacteristic
70C2×C5×C7ΓL(1,𝔽8)⋊D1311yescharacteristic
71C5×C13#1059687211yescharacteristic, complemented, Hall
72C3×Dic5—6371noHall
73Dic13—351noHall
74C72C3×Dic6511yescharacteristic, complemented, Sylow
75C2×ΓL(1,𝔽8)—71no—
76C2×ΓL(1,𝔽8)—71no—
77C3×C13—491noHall
78C5×C7—61no—
79C5×C7ΓL(1,𝔽8)×Dic1311yescharacteristic, complemented
80C5×C7ΓL(1,𝔽8)⋊Dic1311yescharacteristic, complemented
81C2×C3×C5—491no—
82C4×C7—4551no—
83Dic7—651no—
84C2×C13C5⋊#6442211yescharacteristic
85ΓL(1,𝔽8)—71no—
86ΓL(1,𝔽8)—71no—
87Dic5—911noHall
88C3×C5—491noHall
89C2×C7—61no—
90C2×C7ΓL(1,𝔽8)×D6511yescharacteristic
91C2×C7C5⋊(ΓL(1,𝔽8)⋊D13)11yescharacteristic
92C13#1566873711yescharacteristic, complemented, Sylow
93C3×C4—31851noHall
94C2×C5#1683846611yescharacteristic
95C7—61no—
96C7ΓL(1,𝔽8)×Dic6511yescharacteristic, complemented
97C7ΓL(1,𝔽8)⋊Dic6511yescharacteristic, complemented
98C2×C3—491no—
99C5#2143954211yescharacteristic, complemented, Sylow
100C4—4551noSylow
101C3—491noSylow
102C2C5⋊#1683846611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C5⋊#16838466
commutator, hypocenterC5×C72×C13C3×C4
Fitting, socle, cosocleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C13×#3862C2
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C7×Dic455C3semidirect
3. C5×C13×#3862C4semidirect
9. C5×C72×C13C3×C4semidirect
14. C13×#3862Dic5semidirect
15. Dic455ΓL(1,𝔽8)semidirect
28. C5×#3862Dic13semidirect
29. C72×C13C3×Dic5semidirect
35. C5×C7×C13ΓL(1,𝔽8)⋊C4semidirect
36. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
46. C5×C72C3×Dic13semidirect
55. #3862Dic65semidirect
63. C7×C13Dic5×ΓL(1,𝔽8)semidirect
64. C7×C13ΓL(1,𝔽8)⋊Dic5semidirect
71. C5×C13#10596872semidirect
74. C72C3×Dic65semidirect
79. C5×C7ΓL(1,𝔽8)×Dic13semidirect
80. C5×C7ΓL(1,𝔽8)⋊Dic13semidirect
92. C13#15668737semidirect
96. C7ΓL(1,𝔽8)×Dic65semidirect
97. C7ΓL(1,𝔽8)⋊Dic65semidirect
99. C5#21439542semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C13×#38622
C7×Dic4553
#214395425
ΓL(1,𝔽8)⋊Dic657
ΓL(1,𝔽8)×Dic657
#1566873713