Finite Group Databasebeta

← C3×#19129729 #30655331

Subgroups — C3×#19129729 #30655331

Order 16380.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#63270C211yesmaximal, characteristic
2C3×C7⋊#63120C311yesmaximal, characteristic, complemented
3#19129729C313yesmaximal, direct product factor
4C3×C5×#63270C411yescharacteristic, complemented, Hall
5C3×#11763963—51nomaximal, Hall
6D5×#63270C2×C313yes—
7C3×C7×D5×C13C2×C311yescharacteristic
8C3×#63120⋊C3—71nomaximal, Hall
9C7⋊#63120C3211yescharacteristic, complemented, Hall
10C2×C3×#63270—51no—
11C3×C5×C7×C13C3×C411yescharacteristic, complemented
12C5×#63270C3×C413yescomplemented
13C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)—131nomaximal, Hall
14C3×D5×C13⋊C3—71no—
15C3×Dic91—51no—
16#11763963—53no—
17C7×D5×C13C2×C3211yescharacteristic
18C3×#63270AGL(1,𝔽5)11yescharacteristic, complemented, Hall
19C3×#63120—211no—
20#63120⋊C3—73no—
21C3×D5×ΓL(1,𝔽8)—131no—
22C3×C5×C13⋊C3—71noHall
23C2×C3×C7×C13—51no—
24C2×#63270—53no—
25C3×Dic13⋊C3—351noHall
26C5×C7×C13C32×C411yescharacteristic, complemented, Hall
27C3×C7⋊AGL(1,𝔽5)—391no—
28ΓL(1,𝔽8)⋊AGL(1,𝔽5)—133no—
29C3×D5×C13AGL(1,𝔽7)11yescharacteristic
30D5×C13⋊C3—73no—
31Dic91—51noHall
32C3×C5×ΓL(1,𝔽8)—131noHall
33C3×C7×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented
34#63270C3×AGL(1,𝔽5)13yescomplemented
35#63120—211noHall
36C3×ΓL(1,𝔽8)⋊C4—651noHall
37C2×C3×C13⋊C3—351no—
38C3×C7×D5D13⋊C311yescharacteristic
39D5×ΓL(1,𝔽8)—133no—
40C3×C5×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
41C5×C13⋊C3—73no—
42C2×C7×C13—51no—
43C32×AGL(1,𝔽5)—911noHall
44C3×Dic13—1051no—
45Dic13⋊C3—353no—
46C7⋊AGL(1,𝔽5)—391noHall
47D5×C13C3×AGL(1,𝔽7)11yescharacteristic
48C2×C3×ΓL(1,𝔽8)—651no—
49C3×C13⋊C3—71noHall
50C3×C5×C7Dic13⋊C311yescharacteristic, complemented
51C5×ΓL(1,𝔽8)—133no—
52C7×C13C32×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
53C32×D5—911no—
54C3×Dic7—1951no—
55ΓL(1,𝔽8)⋊C4—653no—
56C2×C3×C13—51no—
57C2×C13⋊C3—353no—
58C7×D5C3×D13⋊C311yescharacteristic
59C5×C13C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
60C3×ΓL(1,𝔽8)—131noHall
61C3×AGL(1,𝔽5)—2731no—
62C3×AGL(1,𝔽5)—913no—
63Dic13—1051noHall
64C32×C5—911noHall
65C2×C3×C7—51no—
66C2×ΓL(1,𝔽8)—653no—
67C3×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
68C13⋊C3—73no—
69C32×C4—4551noHall
70C5×C7C3×Dic13⋊C311yescharacteristic, complemented, Hall
71C3×D5—913no—
72C3×D5#1058772211yescharacteristic
73Dic7—1951noHall
74C2×C13—51no—
75C3×C7#63120⋊C311yescharacteristic, complemented
76ΓL(1,𝔽8)—133no—
77AGL(1,𝔽5)—2731noHall
78C2×C32—4551no—
79C3×C5—913no—
80C3×C5#1176396311yescharacteristic, complemented
81C2×C7—51no—
82C13C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
83C3×C4—13651no—
84C3×C4—4553no—
85D5C3×#1058772211yescharacteristic
86C32—911noSylow
87C7C3×#63120⋊C311yescharacteristic, complemented, Sylow
88C2×C3—51no—
89C2×C3—4553no—
90C5C3×#1176396311yescharacteristic, complemented, Sylow
91C4—13651noSylow
92C3—913no—
93C3#1912972911yescharacteristic, direct product factor
94C2—51no—
subgroupG/H
center, hypercenterC3#19129729
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×D5×#63270C2
cosocleC7×D5×C13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×C7⋊#63120C3semidirect
3. #19129729C3direct (N × H)
4. C3×C5×#63270C4semidirect
9. C7⋊#63120C32semidirect
11. C3×C5×C7×C13C3×C4semidirect
12. C5×#63270C3×C4semidirect
18. C3×#63270AGL(1,𝔽5)semidirect
26. C5×C7×C13C32×C4semidirect
33. C3×C7×C13C3×AGL(1,𝔽5)semidirect
34. #63270C3×AGL(1,𝔽5)semidirect
40. C3×C5×C13ΓL(1,𝔽8)⋊C4semidirect
50. C3×C5×C7Dic13⋊C3semidirect
52. C7×C13C32×AGL(1,𝔽5)semidirect
59. C5×C13C3×ΓL(1,𝔽8)⋊C4semidirect
67. C3×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
70. C5×C7C3×Dic13⋊C3semidirect
75. C3×C7#63120⋊C3semidirect
80. C3×C5#11763963semidirect
82. C13C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
87. C7C3×#63120⋊C3semidirect
90. C5C3×#11763963semidirect
93. C3#19129729direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#632702
C3×C7⋊#631203
#191297293
C3×#117639635
C3×#63120⋊C37
C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)13