Finite Group Databasebeta

← C13×#33382 #15719721

Subgroups — C13×#33382 #15719721

Order 3328.

1124 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#578C211yesmaximal, characteristic
2C2×C13×#504C211yesmaximal, characteristic, complemented
3C13×#2913C211yesmaximal, characteristic, complemented
4C13×#2141C213yesmaximal, complemented
5C13×#2139C213yesmaximal, complemented
6C13×#2138C213yesmaximal, complemented
7C2×C13×#358C213yesmaximal, complemented
8C2×C13×2−1+4—21no—
9C13×#578—24no—
10C13×#578C418yescomplemented
11C2×C13×#137—23no—
12C2×C13×#135C2213yes—
13C22×C13×Q16C2213yes—
14C2×C13×#131C2211yescharacteristic
15C13×#520—21no—
16C13×#504—24no—
17C2×C13×M32C2213yes—
18C22×C13×C16C2213yes—
19C13×#428—23no—
20C13×#427C2213yes—
21C2×C13×#107C2213yes—
22C13×#358C2213yes—
23C13×#358C2216yes—
24C13×#358C2213yes—
25C13×#357C2211yescharacteristic
26C13×#357C2213yes—
27C13×2−1+4—28no—
28C13×2−1+4—44no—
29C2×C13×#41—23no—
30C2×C13×#41—43no—
31C2×C13×#41D411yescharacteristic
32C22×Q8×C13—23no—
33C22×Q8×C13—41no—
34C13×#137—224no—
35C13×#135—26no—
36C13×#135C2×C4112yescomplemented
37C2×C13×Q16—23no—
38C2×C13×Q16—26no—
39C2×C13×Q16C2×C4112yescomplemented
40C2×C13×Q16C2313yes—
41C2×C13×SD16—23no—
42C2×C13×D8C2311yescharacteristic
43C13×#131C2×C414yes—
44C13×#131D414yes—
45C2×C13×M16D413yes—
46C22×C8×C13C2313yes—
47C4×Q8×C13—41no—
48C4×D4×C13—43no—
49C13×#117—23no—
50C2×C13×C4⋊C4—23no—
51C13×M32—26no—
52C2×C13×C16—26no—
53C2×C13×C16C2311yescharacteristic
54C2×C13×C16C2313yes—
55C13×#107—23no—
56C13×#107C2313yes—
57C13×#107C2311yescharacteristic
58C13×#106—23no—
59#33382C1311yesmaximal, characteristic, direct product factor, Sylow
60C13×#41—212no—
61C13×#41—424no—
62C13×#41—46no—
63C13×#41C22⋊C414yes—
64C13×#41SD1614yes—
65C2×Q8×C13—212no—
66C2×Q8×C13—23no—
67C2×Q8×C13—48no—
68C2×Q8×C13—43no—
69C2×Q8×C13—46no—
70C2×Q8×C13D811yescharacteristic
71C2×D4×C13—21no—
72C2×D4×C13—43no—
73C2×D4×C13D813yes—
74C22×C4×C13—43no—
75C22×C4×C13—43no—
76C22×C4×C13—43no—
77C22×C4×C13C2×D413yes—
78C13×Q16—212no—
79C13×Q16—23no—
80C13×Q16C22×C416yes—
81C13×SD16—212no—
82C13×D8—21no—
83C13×D8C22×C412yes—
84C13×M16C22⋊C4112yes—
85C2×C8×C13C22×C416yes—
86C2×C8×C13C2×D413yes—
87C2×C8×C13C2×D416yes—
88C2×C8×C13C2411yescharacteristic
89C13×C4⋊C4—21no—
90C13×C4⋊C4—23no—
91C13×C4⋊C4—43no—
92C13×C22⋊C4—43no—
93C42×C13—43no—
94C13×C16—21no—
95C13×C16—23no—
96C2×#578C2×C1311yescharacteristic
97C2×#504C2×C1311yescharacteristic, complemented
98#2913C2×C1311yescharacteristic, complemented
99#2141C2×C1313yescomplemented
100#2139C2×C1313yescomplemented
101#2138C2×C1313yescomplemented
102C2×#358C2×C1313yescomplemented
103C23×C13—41no—
104C23×C13C2×D813yes—
105Q8×C13—26no—
106Q8×C13—43no—
107Q8×C13—412no—
108Q8×C13#10214yes—
109D4×C13—22no—
110D4×C13—412no—
111D4×C13—41no—
112D4×C13#102112yes—
113C2×C4×C13—43no—
114C2×C4×C13—412no—
115C2×C4×C13—412no—
116C2×C4×C13—41no—
117C2×C4×C13—43no—
118C2×C4×C13—163no—
119C2×C4×C13C2×C22⋊C416yes—
120C2×C4×C13C2×D813yes—
121C2×C4×C13C2×SD1616yes—
122C2×C4×C13C22×D411yescharacteristic
123C8×C13C2×C22⋊C416yes—
124C8×C13C23×C411yescharacteristic
125C8×C13C22×D411yescharacteristic
126C2×2−1+4—21no—
127#578—24no—
128#578C4×C1318yescomplemented
129C2×#137—23no—
130C2×#135C22×C1313yes—
131C22×Q16C22×C1313yes—
132C2×#131C22×C1311yescharacteristic
133#520—21no—
134#504—24no—
135C2×M32C22×C1313yes—
136C22×C16C22×C1313yes—
137#428—23no—
138#427C22×C1313yes—
139C2×#107C22×C1313yes—
140#358C22×C1313yes—
141#358C22×C1316yes—
142#358C22×C1313yes—
143#357C22×C1311yescharacteristic
144#357C22×C1313yes—
145C22×C13—23no—
146C22×C13—23no—
147C22×C13—42no—
148C22×C13—81no—
149C22×C13—81no—
150C22×C13C2×#10216yes—
151C22×C13C22×D811yescharacteristic
152C4×C13—46no—
153C4×C13—83no—
154C4×C13—81no—
155C4×C13C2×#10216yes—
156C4×C13C22×C22⋊C411yescharacteristic
157C4×C13C22×SD1611yescharacteristic
1582−1+4—28no—
1592−1+4—44no—
160C2×#41—23no—
161C2×#41—43no—
162C2×#41D4×C1311yescharacteristic
163C22×Q8—23no—
164C22×Q8—41no—
165#137—224no—
166#135—26no—
167#135C2×C4×C13112yescomplemented
168C2×Q16—23no—
169C2×Q16—26no—
170C2×Q16C2×C4×C13112yescomplemented
171C2×Q16C23×C1313yes—
172C2×SD16—23no—
173C2×D8C23×C1311yescharacteristic
174#131C2×C4×C1314yes—
175#131D4×C1314yes—
176C2×M16D4×C1313yes—
177C22×C8C23×C1313yes—
178C4×Q8—41no—
179C4×D4—43no—
180#117—23no—
181C2×C4⋊C4—23no—
182M32—26no—
183C2×C16—26no—
184C2×C16C23×C1311yescharacteristic
185C2×C16C23×C1313yes—
186#107—23no—
187#107C23×C1313yes—
188#107C23×C1311yescharacteristic
189#106—23no—
190C2×C13—26no—
191C2×C13—82no—
192C2×C13C22×#10211yescharacteristic
193C2×C13#341611yescharacteristic
194C2×C13#341711yescharacteristic
195#41—212no—
196#41—424no—
197#41—46no—
198#41C13×C22⋊C414yes—
199#41C13×SD1614yes—
200C2×Q8—212no—
201C2×Q8—23no—
202C2×Q8—48no—
203C2×Q8—43no—
204C2×Q8—46no—
205C2×Q8C13×D811yescharacteristic
206C2×D4—21no—
207C2×D4—43no—
208C2×D4C13×D813yes—
209C22×C4—43no—
210C22×C4—43no—
211C22×C4—43no—
212C22×C4C2×D4×C1313yes—
213Q16—212no—
214Q16—23no—
215Q16C22×C4×C1316yes—
216SD16—212no—
217D8—21no—
218D8C22×C4×C1312yes—
219M16C13×C22⋊C4112yes—
220C2×C8C22×C4×C1316yes—
221C2×C8C2×D4×C1313yes—
222C2×C8C2×D4×C1316yes—
223C2×C8C24×C1311yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—23no—
226C4⋊C4—43no—
227C22⋊C4—43no—
228C42—43no—
229C16—21no—
230C16—23no—
231C13#3338211yescharacteristic, direct product factor, Sylow
232C23—41no—
233C23C2×C13×D813yes—
234Q8—26no—
235Q8—412no—
236Q8—43no—
237Q8C13×#10214yes—
238D4—22no—
239D4—412no—
240D4—41no—
241D4C13×#102112yes—
242C2×C4—412no—
243C2×C4—43no—
244C2×C4—412no—
245C2×C4—41no—
246C2×C4—43no—
247C2×C4—163no—
248C2×C4C2×C13×C22⋊C416yes—
249C2×C4C2×C13×D813yes—
250C2×C4C2×C13×SD1616yes—
251C2×C4C22×D4×C1311yescharacteristic
252C8C2×C13×C22⋊C416yes—
253C8C23×C4×C1311yescharacteristic
254C8C22×D4×C1311yescharacteristic
255C22—23no—
256C22—23no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22C2×C13×#10216yes—
261C22C22×C13×D811yescharacteristic
262C4—46no—
263C4—83no—
264C4—81no—
265C4C2×C13×#10216yes—
266C4C22×C13×C22⋊C411yescharacteristic
267C4C22×C13×SD1611yescharacteristic
268C2—26no—
269C2—82no—
270C2C22×C13×#10211yescharacteristic
271C2C13×#341611yescharacteristic
272C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutatorC8C23×C4×C13
Frattini, cosocleC2×C8C24×C13
prime radicalC2×C13×#578C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#504C2semidirect
3. C13×#2913C2semidirect
4. C13×#2141C2semidirect
5. C13×#2139C2semidirect
6. C13×#2138C2semidirect
7. C2×C13×#358C2semidirect
10. C13×#578C4semidirect
36. C13×#135C2×C4semidirect
39. C2×C13×Q16C2×C4semidirect
59. #33382C13direct (N × H)
97. C2×#504C2×C13semidirect
98. #2913C2×C13semidirect
99. #2141C2×C13semidirect
100. #2139C2×C13semidirect
101. #2138C2×C13semidirect
102. C2×#358C2×C13semidirect
128. #578C4×C13semidirect
167. #135C2×C4×C13semidirect
170. C2×Q16C2×C4×C13semidirect
231. C13#33382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5782
C2×C13×#5042
C13×#29132
C13×#21412
C13×#21392
C13×#21382
C2×C13×#3582
#3338213