Finite Group Databasebeta

← C23×C13×#131 #15749412

Subgroups — C23×C13×#131 #15749412

Order 3328.

11422 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×#41C211yesmaximal, characteristic
2C22×C13×#131C2156yesmaximal, direct product factor
3C23×C13×M16C213yesmaximal, complemented
4C24×C8×C13C213yesmaximal, complemented
5C22×C13×#41C4128yes—
6C22×C13×#41C22128yes—
7C23×Q8×C13C411yescharacteristic
8C23×D4×C13C413yes—
9C24×C4×C13C2213yes—
10C2×C13×#131C221448yesdirect product factor
11C22×C13×M16C22184yescomplemented
12C23×C8×C13C2213yes—
13C23×C8×C13C2211yescharacteristic
14C23×C8×C13C22184yescomplemented
15C25×C13C2×C413yes—
16C2×C13×#41C2×C41336yes—
17C2×C13×#41C231112yes—
18C22×Q8×C13C2×C4128yes—
19C22×D4×C13C2×C4184yes—
20C23×C4×C13C2×C413yes—
21C23×C4×C13C2×C4142yes—
22C23×C4×C13C2311yescharacteristic
23C23×C4×C13C23142yes—
24C13×#131C231512yesdirect product factor
25C2×C13×M16C231336yescomplemented
26C22×C8×C13C23142yes—
27C22×C8×C13C23114yes—
28C22×C8×C13C231336yescomplemented
29C23×#131C1311yesmaximal, characteristic, direct product factor, Sylow
30C24×C13—224no—
31C24×C13C22×C4142yes—
32C24×C13C22×C411yescharacteristic
33C13×#41C22×C41448yes—
34C13×#41C24164yes—
35C2×Q8×C13C22×C41112yes—
36C2×D4×C13C22×C41336yes—
37C22×C4×C13C22×C417yes—
38C22×C4×C13C22×C4142yes—
39C22×C4×C13C22×C41252yes—
40C22×C4×C13C2417yes—
41C22×C4×C13C24184yes—
42C13×M16C241192yescomplemented
43C2×C8×C13C24128yes—
44C2×C8×C13C24184yes—
45C2×C8×C13C241192yescomplemented
46C23×#41C2×C1311yescharacteristic
47C22×#131C2×C13156yesdirect product factor
48C23×M16C2×C1313yescomplemented
49C24×C8C2×C1313yescomplemented
50C23×C13—2168no—
51C23×C13#13118yesdirect product factor
52C23×C13C23×C4184yes—
53C23×C13C23×C417yes—
54Q8×C13C23×C4164yes—
55D4×C13C23×C41192yes—
56C2×C4×C13C23×C4121yes—
57C2×C4×C13C23×C4184yes—
58C2×C4×C13C23×C41168yes—
59C2×C4×C13C2517yes—
60C2×C4×C13C25124yes—
61C8×C13C2518yes—
62C8×C13C25124yes—
63C22×#41C4×C13128yes—
64C22×#41C22×C13128yes—
65C23×Q8C4×C1311yescharacteristic
66C23×D4C4×C1313yes—
67C24×C4C22×C1313yes—
68C2×#131C22×C131448yesdirect product factor
69C22×M16C22×C13184yescomplemented
70C23×C8C22×C1313yes—
71C23×C8C22×C1311yescharacteristic
72C23×C8C22×C13184yescomplemented
73C22×C13—2168no—
74C22×C13C2×#131128yesdirect product factor
75C22×C13C24×C4124yes—
76C22×C13C24×C417yes—
77C4×C13C24×C417yes—
78C4×C13C24×C4124yes—
79C4×C13C2611yescharacteristic
80C25C2×C4×C1313yes—
81C2×#41C2×C4×C131336yes—
82C2×#41C23×C131112yes—
83C22×Q8C2×C4×C13128yes—
84C22×D4C2×C4×C13184yes—
85C23×C4C2×C4×C1313yes—
86C23×C4C2×C4×C13142yes—
87C23×C4C23×C1311yescharacteristic
88C23×C4C23×C13142yes—
89#131C23×C131512yesdirect product factor
90C2×M16C23×C131336yescomplemented
91C22×C8C23×C13114yes—
92C22×C8C23×C13142yes—
93C22×C8C23×C131336yescomplemented
94C2×C13—224no—
95C2×C13C22×#131114yesdirect product factor
96C2×C13C25×C411yescharacteristic
97C24—224no—
98C24C22×C4×C13142yes—
99C24C22×C4×C1311yescharacteristic
100#41C22×C4×C131448yes—
101#41C24×C13164yes—
102C2×Q8C22×C4×C131112yes—
103C2×D4C22×C4×C131336yes—
104C22×C4C22×C4×C1317yes—
105C22×C4C22×C4×C13142yes—
106C22×C4C22×C4×C131252yes—
107C22×C4C24×C1317yes—
108C22×C4C24×C13184yes—
109M16C24×C131192yescomplemented
110C2×C8C24×C13128yes—
111C2×C8C24×C13184yes—
112C2×C8C24×C131192yescomplemented
113C13C23×#13111yescharacteristic, direct product factor, Sylow
114C23—2168no—
115C23C13×#13118yesdirect product factor
116C23C23×C4×C13184yes—
117C23C23×C4×C1317yes—
118Q8C23×C4×C13164yes—
119D4C23×C4×C131192yes—
120C2×C4C23×C4×C13121yes—
121C2×C4C23×C4×C13184yes—
122C2×C4C23×C4×C131168yes—
123C2×C4C25×C1317yes—
124C2×C4C25×C13124yes—
125C8C25×C1318yes—
126C8C25×C13124yes—
127C22—2168no—
128C22C2×C13×#131128yesdirect product factor
129C22C24×C4×C13124yes—
130C22C24×C4×C1317yes—
131C4C24×C4×C1317yes—
132C4C24×C4×C13124yes—
133C4C26×C1311yescharacteristic
134C2—224no—
135C2C22×C13×#131114yesdirect product factor
136C2C25×C4×C1311yescharacteristic
subgroupG/H
centerC23×C8×C13C22
commutatorC2C25×C4×C13
Frattini, cosocleC4C26×C13
socleC24×C13C22×C4
prime radicalC23×C13×#41C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C13×#131C2direct (N × H)
3. C23×C13×M16C2semidirect
4. C24×C8×C13C2semidirect
10. C2×C13×#131C22direct (N × H)
11. C22×C13×M16C22semidirect
14. C23×C8×C13C22semidirect
24. C13×#131C23direct (N × H)
25. C2×C13×M16C23semidirect
28. C22×C8×C13C23semidirect
29. C23×#131C13direct (N × H)
42. C13×M16C24semidirect
45. C2×C8×C13C24semidirect
47. C22×#131C2×C13direct (N × H)
48. C23×M16C2×C13semidirect
49. C24×C8C2×C13semidirect
51. C23×C13#131direct (N × H)
68. C2×#131C22×C13direct (N × H)
69. C22×M16C22×C13semidirect
72. C23×C8C22×C13semidirect
74. C22×C13C2×#131direct (N × H)
89. #131C23×C13direct (N × H)
90. C2×M16C23×C13semidirect
93. C22×C8C23×C13semidirect
95. C2×C13C22×#131direct (N × H)
109. M16C24×C13semidirect
112. C2×C8C24×C13semidirect
113. C13C23×#131direct (N × H)
115. C23C13×#131direct (N × H)
128. C22C2×C13×#131direct (N × H)
135. C2C22×C13×#131direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C13×#412
C22×C13×#1312
C23×C13×M162
C24×C8×C132
C23×#13113