Finite Group Databasebeta

← C3×C13⋊C3×#63118 #44477977

Subgroups — C3×C13⋊C3×#63118 #44477977

Order 30420.

148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 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×D13×C13⋊C3C211yesmaximal, characteristic
2C3×C13×#63118C311yesmaximal, characteristic, complemented
3C13⋊C3×#63118C313yesmaximal, direct product factor
4C3×C5×C13×C13⋊C3C411yescharacteristic, complemented, Hall
5C3×C13⋊C3×#261—51nomaximal, Hall
6C3×C5×C13×D13C2×C311yescharacteristic
7C5×D13×C13⋊C3C2×C313yes—
8C13×#63118C3211yescharacteristic, complemented, Hall
9C3×D13×C13⋊C3D511yescharacteristic
10C5×C13×C13⋊C3C3×C413yescomplemented
11C3×C5×C132C3×C411yescharacteristic, complemented
12C32×#63118—131nomaximal
13C3×Dic5×C13⋊C3—131nomaximal
14C3×C13×#261—51no—
15C13⋊C3×#261—53no—
16C5×C13×D13C2×C3211yescharacteristic
17C3×C13×C13⋊C3Dic511yescharacteristic, complemented, Hall
18C32×C5×D13—131no—
19C2×C3×C5×C13⋊C3—131no—
20C3×C13×D13C3×D511yescharacteristic
21D13×C13⋊C3C3×D513yes—
22C5×C132C32×C411yescharacteristic, complemented, Hall
23C3×#63118—133no—
24C3×#63118C13⋊C311yescharacteristic, direct product factor
25C3×C13×Dic5—131no—
26Dic5×C13⋊C3—133no—
27C13×#261—51noHall
28C32×C5×C13—131no—
29C3×C5×C13⋊C3#26111yescharacteristic, complemented
30C3×C132C3×Dic511yescharacteristic, complemented
31C13×C13⋊C3C3×Dic513yescomplemented
32C32×#261—651no—
33C3×C4×C13⋊C3—651no—
34C2×C3×C5×C13—131no—
35C3×C5×D13—133no—
36C3×C5×D13C2×C13⋊C311yescharacteristic
37C2×C5×C13⋊C3—133no—
38C13×D13C32×D511yescharacteristic
39#63118C3×C13⋊C311yescharacteristic, direct product factor
40C13×Dic5—131no—
41C32×D13—131no—
42C2×C3×C13⋊C3—131no—
43C3×C5×C13—121no—
44C3×C5×C13—133no—
45C3×C5×C13C4×C13⋊C311yescharacteristic, complemented
46C3×C5×C13C3×#26111yescharacteristic, complemented
47C5×C13⋊C3C3×#26113yescomplemented
48C32×Dic5—1691noHall
49C132C32×Dic511yescharacteristic, complemented, Sylow
50C3×#261—51no—
51C3×#261—653no—
52C3×C4×C13—651no—
53C4×C13⋊C3—653no—
54C2×C5×C13—131no—
55C5×D13C2×C3×C13⋊C311yescharacteristic
56C32×C13—131no—
57C3×C13⋊C3#6311811yescharacteristic, direct product factor
58C2×C32×C5—1691no—
59C2×C3×C13—131no—
60C3×D13—133no—
61C3×D13D5×C13⋊C311yescharacteristic
62C2×C13⋊C3—133no—
63C5×C13—121no—
64C5×C13C3×C4×C13⋊C311yescharacteristic, complemented
65C5×C13C32×#26111yescharacteristic, complemented
66C3×Dic5—131no—
67C3×Dic5—1693no—
68#261—51no—
69C4×C13—651no—
70C32×C5—131noHall
71C3×C13—121no—
72C3×C13—133no—
73C3×C13Dic5×C13⋊C311yescharacteristic, complemented
74C3×C13C3×#6311811yescharacteristic, complemented
75C13⋊C3C3×#6311813yesdirect product factor
76C32×C4—8451noHall
77C2×C3×C5—131no—
78C2×C3×C5—1693no—
79C2×C13—131no—
80D13C3×D5×C13⋊C311yescharacteristic
81Dic5—131noHall
82C2×C32—1691no—
83C3×C5—133no—
84C3×C5C13⋊C3×#26111yescharacteristic, complemented
85C13—121no—
86C13C3×Dic5×C13⋊C311yescharacteristic, complemented
87C13C32×#6311811yescharacteristic, complemented
88C3×C4—651no—
89C3×C4—8453no—
90C2×C5—131no—
91C32—131noSylow
92C2×C3—131no—
93C2×C3—1693no—
94C5C3×C13⋊C3×#26111yescharacteristic, complemented, Sylow
95C4—651noSylow
96C3—133no—
97C3C13⋊C3×#6311811yescharacteristic, direct product factor
98C2—131no—
subgroupG/H
center, hypercenterC3C13⋊C3×#63118
commutator, hypocenterC5×C132C32×C4
FrattiniC1G
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C5×D13×C13⋊C3C2
cosocleC5×C13×D13C2×C32
LCSG ▷ C5×C132
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×C13×#63118C3semidirect
3. C13⋊C3×#63118C3direct (N × H)
4. C3×C5×C13×C13⋊C3C4semidirect
8. C13×#63118C32semidirect
10. C5×C13×C13⋊C3C3×C4semidirect
11. C3×C5×C132C3×C4semidirect
17. C3×C13×C13⋊C3Dic5semidirect
22. C5×C132C32×C4semidirect
24. C3×#63118C13⋊C3direct (N × H)
29. C3×C5×C13⋊C3#261semidirect
30. C3×C132C3×Dic5semidirect
31. C13×C13⋊C3C3×Dic5semidirect
39. #63118C3×C13⋊C3direct (N × H)
45. C3×C5×C13C4×C13⋊C3semidirect
46. C3×C5×C13C3×#261semidirect
47. C5×C13⋊C3C3×#261semidirect
49. C132C32×Dic5semidirect
57. C3×C13⋊C3#63118direct (N × H)
64. C5×C13C3×C4×C13⋊C3semidirect
65. C5×C13C32×#261semidirect
73. C3×C13Dic5×C13⋊C3semidirect
74. C3×C13C3×#63118semidirect
75. C13⋊C3C3×#63118direct (N × H)
84. C3×C5C13⋊C3×#261semidirect
86. C13C3×Dic5×C13⋊C3semidirect
87. C13C32×#63118semidirect
94. C5C3×C13⋊C3×#261semidirect
97. C3C13⋊C3×#63118direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D13×C13⋊C32
C3×C13×#631183
C13⋊C3×#631183
C3×C13⋊C3×#2615
C32×#6311813
C3×Dic5×C13⋊C313