Finite Group Databasebeta

← C2×C13×#560 #13112583

Subgroups — C2×C13×#560 #13112583

Order 1664.

1344 conjugacy classes of subgroups; only the 776 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 776 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
1C13×#560C2116yesmaximal, direct product factor
2C2×C13×#127C211yesmaximal, characteristic, complemented
3C2×C13×#126C212yesmaximal, complemented
4C2×C13×#123C213yesmaximal, complemented
5C2×C13×#121C216yesmaximal, complemented
6C2×C13×#120C213yesmaximal, complemented
7C25×C13C2211yescharacteristic
8C22×D4×C13C2216yes—
9C22×D4×C13C2213yes—
10C22×D4×C13C2213yescomplemented
11C23×C4×C13C2213yescomplemented
12C13×#127C2218yescomplemented
13C13×#126C22116yescomplemented
14C13×#123C22124yescomplemented
15C13×#121C22148yescomplemented
16C13×#120C22124yescomplemented
17C2×C13×C4⋊C4C2216yescomplemented
18C2×C13×C22⋊C4C2216yes—
19C2×C13×C22⋊C4C2213yes—
20C2×C13×C22⋊C4C2213yescomplemented
21C2×C42×C13C2211yescharacteristic, complemented
22C24×C13—46no—
23C24×C13C2312yes—
24C24×C13C2311yescharacteristic
25C24×C13C2313yes—
26C24×C13C2314yes—
27C2×D4×C13—412no—
28C2×D4×C13—46no—
29C2×D4×C13—46no—
30C2×D4×C13C23124yes—
31C2×D4×C13C23112yes—
32C2×D4×C13C23112yescomplemented
33C22×C4×C13—46no—
34C22×C4×C13C2313yes—
35C22×C4×C13C2316yes—
36C22×C4×C13C23112yescomplemented
37C13×C4⋊C4C23124yescomplemented
38C13×C22⋊C4C23124yes—
39C13×C22⋊C4C23112yes—
40C13×C22⋊C4C23112yescomplemented
41C42×C13C2314yescomplemented
42C2×#560C1311yesmaximal, characteristic, direct product factor, Sylow
43C23×C13—26no—
44C23×C13—212no—
45C23×C13—212no—
46C23×C13—26no—
47C23×C13—412no—
48C23×C13—416no—
49C23×C13C2414yes—
50C23×C13C2412yes—
51C23×C13C2416yes—
52C23×C13C2411yescharacteristic
53D4×C13—424no—
54D4×C13—412no—
55D4×C13—412no—
56C2×C4×C13—212no—
57C2×C4×C13—26no—
58C2×C4×C13—412no—
59C2×C4×C13C2416yes—
60C2×C4×C13C24112yes—
61#560C2×C13116yesdirect product factor
62C2×#127C2×C1311yescharacteristic, complemented
63C2×#126C2×C1312yescomplemented
64C2×#123C2×C1313yescomplemented
65C2×#121C2×C1316yescomplemented
66C2×#120C2×C1313yescomplemented
67C22×C13—26no—
68C22×C13—212no—
69C22×C13—212no—
70C22×C13—26no—
71C22×C13—416no—
72C22×C13—412no—
73C22×C13—48no—
74C22×C13—44no—
75C22×C13H(5,𝔽2)16yes—
76C22×C13C2511yescharacteristic
77C4×C13—212no—
78C4×C13—26no—
79C25C22×C1311yescharacteristic
80C22×D4C22×C1316yes—
81C22×D4C22×C1313yes—
82C22×D4C22×C1313yescomplemented
83C23×C4C22×C1313yescomplemented
84#127C22×C1318yescomplemented
85#126C22×C13116yescomplemented
86#123C22×C13124yescomplemented
87#121C22×C13148yescomplemented
88#120C22×C13124yescomplemented
89C2×C4⋊C4C22×C1316yescomplemented
90C2×C22⋊C4C22×C1316yes—
91C2×C22⋊C4C22×C1313yes—
92C2×C22⋊C4C22×C1313yescomplemented
93C2×C42C22×C1311yescharacteristic, complemented
94C2×C13—46no—
95C2×C13—44no—
96C2×C13—42no—
97C2×C13#56014yesdirect product factor
98C2×C13C2×H(5,𝔽2)13yes—
99C24—46no—
100C24C23×C1312yes—
101C24C23×C1311yescharacteristic
102C24C23×C1313yes—
103C24C23×C1314yes—
104C2×D4—412no—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4C23×C13124yes—
108C2×D4C23×C13112yes—
109C2×D4C23×C13112yescomplemented
110C22×C4—46no—
111C22×C4C23×C1313yes—
112C22×C4C23×C1316yes—
113C22×C4C23×C13112yescomplemented
114C4⋊C4C23×C13124yescomplemented
115C22⋊C4C23×C13124yes—
116C22⋊C4C23×C13112yes—
117C22⋊C4C23×C13112yescomplemented
118C42C23×C1314yescomplemented
119C13C2×#56011yescharacteristic, direct product factor, Sylow
120C23—26no—
121C23—212no—
122C23—212no—
123C23—26no—
124C23—412no—
125C23—416no—
126C23C24×C1314yes—
127C23C24×C1312yes—
128C23C24×C1316yes—
129C23C24×C1311yescharacteristic
130D4—424no—
131D4—412no—
132D4—412no—
133C2×C4—212no—
134C2×C4—26no—
135C2×C4—412no—
136C2×C4C24×C1316yes—
137C2×C4C24×C13112yes—
138C22—26no—
139C22—212no—
140C22—212no—
141C22—26no—
142C22—416no—
143C22—412no—
144C22—48no—
145C22—44no—
146C22C13×H(5,𝔽2)16yes—
147C22C25×C1311yescharacteristic
148C4—212no—
149C4—26no—
150C2—44no—
151C2—42no—
152C2—46no—
153C2C13×#56014yesdirect product factor
154C2C2×C13×H(5,𝔽2)13yes—
subgroupG/H
center, socleC23×C13C24
commutator, Frattini, cosocleC22C25×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#560C2direct (N × H)
2. C2×C13×#127C2semidirect
3. C2×C13×#126C2semidirect
4. C2×C13×#123C2semidirect
5. C2×C13×#121C2semidirect
6. C2×C13×#120C2semidirect
10. C22×D4×C13C22semidirect
11. C23×C4×C13C22semidirect
12. C13×#127C22semidirect
13. C13×#126C22semidirect
14. C13×#123C22semidirect
15. C13×#121C22semidirect
16. C13×#120C22semidirect
17. C2×C13×C4⋊C4C22semidirect
20. C2×C13×C22⋊C4C22semidirect
21. C2×C42×C13C22semidirect
32. C2×D4×C13C23semidirect
36. C22×C4×C13C23semidirect
37. C13×C4⋊C4C23semidirect
40. C13×C22⋊C4C23semidirect
41. C42×C13C23semidirect
42. C2×#560C13direct (N × H)
61. #560C2×C13direct (N × H)
62. C2×#127C2×C13semidirect
63. C2×#126C2×C13semidirect
64. C2×#123C2×C13semidirect
65. C2×#121C2×C13semidirect
66. C2×#120C2×C13semidirect
82. C22×D4C22×C13semidirect
83. C23×C4C22×C13semidirect
84. #127C22×C13semidirect
85. #126C22×C13semidirect
86. #123C22×C13semidirect
87. #121C22×C13semidirect
88. #120C22×C13semidirect
89. C2×C4⋊C4C22×C13semidirect
92. C2×C22⋊C4C22×C13semidirect
93. C2×C42C22×C13semidirect
97. C2×C13#560direct (N × H)
109. C2×D4C23×C13semidirect
113. C22×C4C23×C13semidirect
114. C4⋊C4C23×C13semidirect
117. C22⋊C4C23×C13semidirect
118. C42C23×C13semidirect
119. C13C2×#560direct (N × H)
153. C2C13×#560direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5602
C2×C13×#1272
C2×C13×#1262
C2×C13×#1232
C2×C13×#1212
C2×C13×#1202
C2×#56013