Finite Group Databasebeta

← C13×#33983 #15720322

Subgroups — C13×#33983 #15720322

Order 3328.

462 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 202 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×#3417C211yesmaximal, characteristic, complemented
2C13×#3415C211yesmaximal, characteristic, complemented
3C13×#2264C213yesmaximal, complemented
4C13×#2263C213yesmaximal, complemented
5C13×#2262C213yesmaximal, complemented
6C2×C13×SD64C213yesmaximal, complemented
7C13×#2258C211yesmaximal, characteristic, complemented
8C13×#578—21no—
9C13×#576—21no—
10C13×#510—23no—
11C13×#509—23no—
12C13×#508C2213yes—
13C13×#508C2213yescomplemented
14C2×C13×Q32C2213yescomplemented
15C2×C13×D16C2213yes—
16C13×#504C2211yescharacteristic
17C13×Q64C2213yescomplemented
18C13×SD64C2213yescomplemented
19C13×SD64C2216yescomplemented
20C13×SD64C2211yescharacteristic, complemented
21C13×D32C2213yescomplemented
22C13×M64C2213yescomplemented
23C2×C13×C32C2213yescomplemented
24C13×2−1+4—41no—
25C13×H(5,𝔽2)—41no—
26C13×#137—43no—
27C13×AGL(1,ℤ/8)—43no—
28C13×#135—23no—
29C13×#135—23no—
30C2×C13×Q16—23no—
31C2×C13×D8—23no—
32C13×#131D411yescharacteristic
33C13×Q32—23no—
34C13×Q32C2313yes—
35C13×Q32C2311yescharacteristic
36C13×SD32—23no—
37C13×SD32—23no—
38C13×D16—23no—
39C13×D16C2311yescharacteristic
40C13×D16C2313yes—
41C13×M32D413yes—
42C2×C13×C16C2313yes—
43C13×C32C2311yescharacteristic
44C13×C32C2313yes—
45#33983C1311yesmaximal, characteristic, direct product factor, Sylow
46C13×#41—43no—
47C13×#41—43no—
48C13×#41—81no—
49C13×#41—83no—
50C13×#41D811yescharacteristic
51C2×Q8×C13—43no—
52C2×Q8×C13—81no—
53C2×D4×C13—43no—
54C2×D4×C13—83no—
55C13×Q16—21no—
56C13×Q16—23no—
57C13×Q16—43no—
58C13×SD16—43no—
59C13×SD16—43no—
60C13×D8—23no—
61C13×D8—21no—
62C13×D8—43no—
63C13×M16D813yes—
64C2×C8×C13C2×D413yes—
65C13×C16C2×D413yes—
66C13×C16C2411yescharacteristic
67#3417C2×C1311yescharacteristic, complemented
68#3415C2×C1311yescharacteristic, complemented
69#2264C2×C1313yescomplemented
70#2263C2×C1313yescomplemented
71#2262C2×C1313yescomplemented
72C2×SD64C2×C1313yescomplemented
73#2258C2×C1311yescharacteristic, complemented
74C23×C13—83no—
75Q8×C13—41no—
76Q8×C13—43no—
77Q8×C13—83no—
78Q8×C13D1611yescharacteristic
79D4×C13—43no—
80D4×C13—41no—
81D4×C13—83no—
82D4×C13—83no—
83D4×C13—83no—
84D4×C13D1613yes—
85C2×C4×C13—83no—
86C2×C4×C13—83no—
87C2×C4×C13—83no—
88C2×C4×C13C2×D813yes—
89C8×C13C2×D813yes—
90C8×C13C22×D411yescharacteristic
91#578—21no—
92#576—21no—
93#510—23no—
94#509—23no—
95#508C22×C1313yes—
96#508C22×C1313yescomplemented
97C2×Q32C22×C1313yescomplemented
98C2×D16C22×C1313yes—
99#504C22×C1311yescharacteristic
100Q64C22×C1313yescomplemented
101SD64C22×C1313yescomplemented
102SD64C22×C1316yescomplemented
103SD64C22×C1311yescharacteristic, complemented
104D32C22×C1313yescomplemented
105M64C22×C1313yescomplemented
106C2×C32C22×C1313yescomplemented
107C22×C13—81no—
108C22×C13—83no—
109C22×C13—323no—
110C22×C13C2×D1613yes—
111C4×C13—81no—
112C4×C13—83no—
113C4×C13C2×D1613yes—
114C4×C13C22×D811yescharacteristic
1152−1+4—41no—
116H(5,𝔽2)—41no—
117#137—43no—
118AGL(1,ℤ/8)—43no—
119#135—23no—
120#135—23no—
121C2×Q16—23no—
122C2×D8—23no—
123#131D4×C1311yescharacteristic
124Q32—23no—
125Q32C23×C1313yes—
126Q32C23×C1311yescharacteristic
127SD32—23no—
128SD32—23no—
129D16—23no—
130D16C23×C1311yescharacteristic
131D16C23×C1313yes—
132M32D4×C1313yes—
133C2×C16C23×C1313yes—
134C32C23×C1311yescharacteristic
135C32C23×C1313yes—
136C2×C13—23no—
137C2×C13—161no—
138C2×C13—163no—
139C2×C13C22×D1611yescharacteristic
140#41—43no—
141#41—43no—
142#41—81no—
143#41—83no—
144#41C13×D811yescharacteristic
145C2×Q8—43no—
146C2×Q8—81no—
147C2×D4—43no—
148C2×D4—83no—
149Q16—21no—
150Q16—23no—
151Q16—43no—
152SD16—43no—
153SD16—43no—
154D8—23no—
155D8—21no—
156D8—43no—
157M16C13×D813yes—
158C2×C8C2×D4×C1313yes—
159C16C2×D4×C1313yes—
160C16C24×C1311yescharacteristic
161C13#3398311yescharacteristic, direct product factor, Sylow
162C23—83no—
163Q8—41no—
164Q8—43no—
165Q8—83no—
166Q8C13×D1611yescharacteristic
167D4—43no—
168D4—41no—
169D4—83no—
170D4—83no—
171D4—83no—
172D4C13×D1613yes—
173C2×C4—83no—
174C2×C4—83no—
175C2×C4—83no—
176C2×C4C2×C13×D813yes—
177C8C2×C13×D813yes—
178C8C22×D4×C1311yescharacteristic
179C22—81no—
180C22—83no—
181C22—323no—
182C22C2×C13×D1613yes—
183C4—81no—
184C4—83no—
185C4C2×C13×D1613yes—
186C4C22×C13×D811yescharacteristic
187C2—23no—
188C2—163no—
189C2—161no—
190C2C22×C13×D1611yescharacteristic
subgroupG/H
center, socleC2×C13C22×D16
commutator, Frattini, cosocleC16C24×C13
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C13×#41 ◁ C13×#131 ◁ C13×#504 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3417C2semidirect
2. C13×#3415C2semidirect
3. C13×#2264C2semidirect
4. C13×#2263C2semidirect
5. C13×#2262C2semidirect
6. C2×C13×SD64C2semidirect
7. C13×#2258C2semidirect
13. C13×#508C22semidirect
14. C2×C13×Q32C22semidirect
17. C13×Q64C22semidirect
18. C13×SD64C22semidirect
19. C13×SD64C22semidirect
20. C13×SD64C22semidirect
21. C13×D32C22semidirect
22. C13×M64C22semidirect
23. C2×C13×C32C22semidirect
45. #33983C13direct (N × H)
67. #3417C2×C13semidirect
68. #3415C2×C13semidirect
69. #2264C2×C13semidirect
70. #2263C2×C13semidirect
71. #2262C2×C13semidirect
72. C2×SD64C2×C13semidirect
73. #2258C2×C13semidirect
96. #508C22×C13semidirect
97. C2×Q32C22×C13semidirect
100. Q64C22×C13semidirect
101. SD64C22×C13semidirect
102. SD64C22×C13semidirect
103. SD64C22×C13semidirect
104. D32C22×C13semidirect
105. M64C22×C13semidirect
106. C2×C32C22×C13semidirect
161. C13#33983direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34172
C13×#34152
C13×#22642
C13×#22632
C13×#22622
C2×C13×SD642
C13×#22582
#3398313