Finite Group Databasebeta

← C13×#32881 #15719220

Subgroups — C13×#32881 #15719220

Order 3328.

5942 conjugacy classes of subgroups; only the 438 normal subgroups are shown.

normal subgroups only

This group has 5942 conjugacy classes of subgroups — too many to draw. Only its 438 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
1C24×D4×C13C211yesmaximal, characteristic
2C2×C13×#450C216yesmaximal, complemented
3C13×#2848C211yesmaximal, characteristic, complemented
4C13×#1786C216yesmaximal, complemented
5C13×#1779C211yesmaximal, characteristic, complemented
6C26×C13—21no—
7C23×D4×C13—224no—
8C23×D4×C13—23no—
9C23×D4×C13C2216yes—
10C24×C4×C13C2211yescharacteristic
11C22×C13×SD16C2214yescomplemented
12C2×C13×C22⋊Q8C2213yescomplemented
13C13×#450—224no—
14C2×C13×#102C22112yescomplemented
15C2×C13×C22⋊C8C2216yescomplemented
16C13×#385—23no—
17C13×#380C2213yescomplemented
18C13×#379—21no—
19C25×C13—224no—
20C25×C13—26no—
21C25×C13—412no—
22C25×C13—44no—
23C25×C13D411yescharacteristic
24C22×Q8×C13C2311yescharacteristic, complemented
25C22×D4×C13—2128no—
26C22×D4×C13—224no—
27C22×D4×C13—248no—
28C22×D4×C13—248no—
29C22×D4×C13—26no—
30C22×D4×C13—212no—
31C22×D4×C13D4124yes—
32C22×D4×C13C2314yes—
33C23×C4×C13—212no—
34C23×C4×C13D413yes—
35C23×C4×C13C2313yes—
36C2×C13×SD16—224no—
37C22×C8×C13C2314yescomplemented
38C13×C22⋊Q8—212no—
39C2×C13×C4⋊C4—23no—
40C2×C13×C4⋊C4C2313yescomplemented
41C2×C13×C22⋊C4—23no—
42C2×C13×C22⋊C4—23no—
43C13×#102—224no—
44C13×C22⋊C8—212no—
45C13×#95—23no—
46#32881C1311yesmaximal, characteristic, direct product factor, Sylow
47C24×C13—26no—
48C24×C13—26no—
49C24×C13—264no—
50C24×C13—248no—
51C24×C13—224no—
52C24×C13—24no—
53C24×C13—496no—
54C24×C13—424no—
55C24×C13—496no—
56C24×C13—412no—
57C24×C13—412no—
58C24×C13SD1614yescomplemented
59C24×C13C2×D413yes—
60C2×Q8×C13—26no—
61C2×D4×C13—2192no—
62C2×D4×C13—248no—
63C2×D4×C13—296no—
64C2×D4×C13—296no—
65C2×D4×C13—224no—
66C2×D4×C13—212no—
67C2×D4×C13C2×D4124yes—
68C22×C4×C13—232no—
69C22×C4×C13—26no—
70C22×C4×C13—212no—
71C22×C4×C13—212no—
72C22×C4×C13—23no—
73C22×C4×C13—21no—
74C22×C4×C13C2×D413yes—
75C22×C4×C13C2×D4112yes—
76C22×C4×C13C2411yescharacteristic
77C13×SD16—416no—
78C2×C8×C13—212no—
79C13×C4⋊C4—26no—
80C13×C4⋊C4—46no—
81C13×C22⋊C4—46no—
82C13×C22⋊C4—46no—
83C24×D4C2×C1311yescharacteristic
84C2×#450C2×C1316yescomplemented
85#2848C2×C1311yescharacteristic, complemented
86#1786C2×C1316yescomplemented
87#1779C2×C1311yescharacteristic, complemented
88C23×C13—28no—
89C23×C13—224no—
90C23×C13—26no—
91C23×C13—26no—
92C23×C13—224no—
93C23×C13—296no—
94C23×C13—224no—
95C23×C13—4256no—
96C23×C13—496no—
97C23×C13—448no—
98C23×C13—496no—
99C23×C13—44no—
100C23×C13—412no—
101C23×C13—448no—
102C23×C13#12016yes—
103C23×C13C2×SD1616yes—
104C23×C13AGL(1,ℤ/8)16yes—
105C23×C13C22×D411yescharacteristic
106Q8×C13—44no—
107D4×C13—296no—
108D4×C13—224no—
109D4×C13#120116yes—
110C2×C4×C13—224no—
111C2×C4×C13—26no—
112C2×C4×C13—224no—
113C2×C4×C13—43no—
114C2×C4×C13—43no—
115C2×C4×C13—46no—
116C2×C4×C13#12016yes—
117C2×C4×C13C22×D416yes—
118C8×C13—44no—
119C26—21no—
120C23×D4—224no—
121C23×D4—23no—
122C23×D4C22×C1316yes—
123C24×C4C22×C1311yescharacteristic
124C22×SD16C22×C1314yescomplemented
125C2×C22⋊Q8C22×C1313yescomplemented
126#450—224no—
127C2×#102C22×C13112yescomplemented
128C2×C22⋊C8C22×C1316yescomplemented
129#385—23no—
130#380C22×C1313yescomplemented
131#379—21no—
132C22×C13—232no—
133C22×C13—26no—
134C22×C13—212no—
135C22×C13—26no—
136C22×C13—212no—
137C22×C13—216no—
138C22×C13—4192no—
139C22×C13—424no—
140C22×C13—424no—
141C22×C13#450112yescomplemented
142C22×C13C2×#12013yes—
143C22×C13C22×SD1611yescharacteristic
144C22×C13C2×AGL(1,ℤ/8)13yes—
145C4×C13—26no—
146C4×C13—81no—
147C4×C13—83no—
148C4×C13C2×#12014yes—
149C25—224no—
150C25—26no—
151C25—412no—
152C25—44no—
153C25D4×C1311yescharacteristic
154C22×Q8C23×C1311yescharacteristic, complemented
155C22×D4—2128no—
156C22×D4—224no—
157C22×D4—248no—
158C22×D4—248no—
159C22×D4—26no—
160C22×D4—212no—
161C22×D4D4×C13124yes—
162C22×D4C23×C1314yes—
163C23×C4—212no—
164C23×C4D4×C1313yes—
165C23×C4C23×C1313yes—
166C2×SD16—224no—
167C22×C8C23×C1314yescomplemented
168C22⋊Q8—212no—
169C2×C4⋊C4—23no—
170C2×C4⋊C4C23×C1313yescomplemented
171C2×C22⋊C4—23no—
172C2×C22⋊C4—23no—
173#102—224no—
174C22⋊C8—212no—
175#95—23no—
176C2×C13—212no—
177C2×C13—416no—
178C2×C13#284611yescharacteristic
179C2×C13C2×#45013yes—
180C2×C13#300313yes—
181C24—26no—
182C24—26no—
183C24—264no—
184C24—248no—
185C24—224no—
186C24—24no—
187C24—496no—
188C24—496no—
189C24—424no—
190C24—412no—
191C24—412no—
192C24C13×SD1614yescomplemented
193C24C2×D4×C1313yes—
194C2×Q8—26no—
195C2×D4—2192no—
196C2×D4—248no—
197C2×D4—296no—
198C2×D4—296no—
199C2×D4—224no—
200C2×D4—212no—
201C2×D4C2×D4×C13124yes—
202C22×C4—232no—
203C22×C4—26no—
204C22×C4—212no—
205C22×C4—212no—
206C22×C4—23no—
207C22×C4—21no—
208C22×C4C2×D4×C1313yes—
209C22×C4C2×D4×C13112yes—
210C22×C4C24×C1311yescharacteristic
211SD16—416no—
212C2×C8—212no—
213C4⋊C4—26no—
214C4⋊C4—46no—
215C22⋊C4—46no—
216C22⋊C4—46no—
217C13#3288111yescharacteristic, direct product factor, Sylow
218C23—28no—
219C23—224no—
220C23—224no—
221C23—26no—
222C23—26no—
223C23—296no—
224C23—224no—
225C23—4256no—
226C23—496no—
227C23—448no—
228C23—496no—
229C23—448no—
230C23—44no—
231C23—412no—
232C23C13×#12016yes—
233C23C2×C13×SD1616yes—
234C23C13×AGL(1,ℤ/8)16yes—
235C23C22×D4×C1311yescharacteristic
236Q8—44no—
237D4—296no—
238D4—224no—
239D4C13×#120116yes—
240C2×C4—224no—
241C2×C4—26no—
242C2×C4—224no—
243C2×C4—43no—
244C2×C4—43no—
245C2×C4—46no—
246C2×C4C13×#12016yes—
247C2×C4C22×D4×C1316yes—
248C8—44no—
249C22—232no—
250C22—26no—
251C22—212no—
252C22—26no—
253C22—212no—
254C22—216no—
255C22—4192no—
256C22—424no—
257C22—424no—
258C22C13×#450112yescomplemented
259C22C2×C13×#12013yes—
260C22C22×C13×SD1611yescharacteristic
261C22C2×C13×AGL(1,ℤ/8)13yes—
262C4—26no—
263C4—81no—
264C4—83no—
265C4C2×C13×#12014yes—
266C2—212no—
267C2—416no—
268C2C13×#284611yescharacteristic
269C2C2×C13×#45013yes—
270C2C13×#300313yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC24×D4×C13C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#450C2semidirect
3. C13×#2848C2semidirect
4. C13×#1786C2semidirect
5. C13×#1779C2semidirect
11. C22×C13×SD16C22semidirect
12. C2×C13×C22⋊Q8C22semidirect
14. C2×C13×#102C22semidirect
15. C2×C13×C22⋊C8C22semidirect
17. C13×#380C22semidirect
24. C22×Q8×C13C23semidirect
37. C22×C8×C13C23semidirect
40. C2×C13×C4⋊C4C23semidirect
46. #32881C13direct (N × H)
58. C24×C13SD16semidirect
84. C2×#450C2×C13semidirect
85. #2848C2×C13semidirect
86. #1786C2×C13semidirect
87. #1779C2×C13semidirect
124. C22×SD16C22×C13semidirect
125. C2×C22⋊Q8C22×C13semidirect
127. C2×#102C22×C13semidirect
128. C2×C22⋊C8C22×C13semidirect
130. #380C22×C13semidirect
141. C22×C13#450semidirect
154. C22×Q8C23×C13semidirect
167. C22×C8C23×C13semidirect
170. C2×C4⋊C4C23×C13semidirect
192. C24C13×SD16semidirect
217. C13#32881direct (N × H)
258. C22C13×#450semidirect

Maximal subgroups

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

subgroupindex
C24×D4×C132
C2×C13×#4502
C13×#28482
C13×#17862
C13×#17792
#3288113