Finite Group Databasebeta

← C13×#32878 #15719217

Subgroups — C13×#32878 #15719217

Order 3328.

6020 conjugacy classes of subgroups; only the 438 normal subgroups are shown.

normal subgroups only

This group has 6020 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, complemented
2C2×C13×#447C216yesmaximal, complemented
3C13×#2847C211yesmaximal, 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×D8C2214yescomplemented
12C2×C13×#121C2213yescomplemented
13C2×C13×#120—21no—
14C13×#447—224no—
15C2×C13×#102C22112yescomplemented
16C2×C13×C22⋊C8C2216yescomplemented
17C13×#386—23no—
18C13×#380C2213yescomplemented
19C25×C13—224no—
20C25×C13—26no—
21C25×C13—412no—
22C25×C13—44no—
23C25×C13D411yescharacteristic
24C22×D4×C13—2128no—
25C22×D4×C13—224no—
26C22×D4×C13—248no—
27C22×D4×C13—248no—
28C22×D4×C13—23no—
29C22×D4×C13—26no—
30C22×D4×C13—212no—
31C22×D4×C13D4124yescomplemented
32C22×D4×C13C2314yes—
33C22×D4×C13C2311yescharacteristic, complemented
34C23×C4×C13—212no—
35C23×C4×C13D413yes—
36C23×C4×C13C2313yes—
37C2×C13×D8—224no—
38C22×C8×C13C2314yescomplemented
39C13×#121—212no—
40C13×#120—44no—
41C2×C13×C4⋊C4C2313yescomplemented
42C2×C13×C22⋊C4—23no—
43C2×C13×C22⋊C4—23no—
44C13×#102—224no—
45C13×C22⋊C8—212no—
46C13×#95—23no—
47#32878C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13—26no—
49C24×C13—26no—
50C24×C13—264no—
51C24×C13—248no—
52C24×C13—224no—
53C24×C13—24no—
54C24×C13—21no—
55C24×C13—496no—
56C24×C13—424no—
57C24×C13—496no—
58C24×C13—412no—
59C24×C13—412no—
60C24×C13D814yescomplemented
61C24×C13C2×D413yes—
62C2×D4×C13—2192no—
63C2×D4×C13—248no—
64C2×D4×C13—296no—
65C2×D4×C13—296no—
66C2×D4×C13—224no—
67C2×D4×C13—212no—
68C2×D4×C13—26no—
69C2×D4×C13—46no—
70C2×D4×C13—46no—
71C2×D4×C13—46no—
72C2×D4×C13C2×D4124yes—
73C22×C4×C13—232no—
74C22×C4×C13—26no—
75C22×C4×C13—212no—
76C22×C4×C13—212no—
77C22×C4×C13—23no—
78C22×C4×C13C2×D413yes—
79C22×C4×C13C2×D4112yes—
80C22×C4×C13C2411yescharacteristic
81C13×D8—416no—
82C2×C8×C13—212no—
83C13×C4⋊C4—26no—
84C13×C22⋊C4—46no—
85C13×C22⋊C4—46no—
86C24×D4C2×C1311yescharacteristic, complemented
87C2×#447C2×C1316yescomplemented
88#2847C2×C1311yescharacteristic, complemented
89#1786C2×C1316yescomplemented
90#1779C2×C1311yescharacteristic, complemented
91C23×C13—28no—
92C23×C13—224no—
93C23×C13—26no—
94C23×C13—26no—
95C23×C13—224no—
96C23×C13—296no—
97C23×C13—224no—
98C23×C13—4256no—
99C23×C13—496no—
100C23×C13—448no—
101C23×C13—496no—
102C23×C13—44no—
103C23×C13—412no—
104C23×C13—448no—
105C23×C13—43no—
106C23×C13—41no—
107C23×C13—43no—
108C23×C13#12016yes—
109C23×C13C2×D816yes—
110C23×C13AGL(1,ℤ/8)16yes—
111C23×C13C22×D411yescharacteristic
112D4×C13—296no—
113D4×C13—224no—
114D4×C13—44no—
115D4×C13—812no—
116D4×C13#120116yescomplemented
117C2×C4×C13—224no—
118C2×C4×C13—26no—
119C2×C4×C13—224no—
120C2×C4×C13—43no—
121C2×C4×C13—43no—
122C2×C4×C13—43no—
123C2×C4×C13#12016yes—
124C2×C4×C13C22×D416yes—
125C8×C13—44no—
126C26—21no—
127C23×D4—224no—
128C23×D4—23no—
129C23×D4C22×C1316yes—
130C24×C4C22×C1311yescharacteristic
131C22×D8C22×C1314yescomplemented
132C2×#121C22×C1313yescomplemented
133C2×#120—21no—
134#447—224no—
135C2×#102C22×C13112yescomplemented
136C2×C22⋊C8C22×C1316yescomplemented
137#386—23no—
138#380C22×C1313yescomplemented
139C22×C13—232no—
140C22×C13—26no—
141C22×C13—212no—
142C22×C13—26no—
143C22×C13—212no—
144C22×C13—216no—
145C22×C13—4192no—
146C22×C13—424no—
147C22×C13—424no—
148C22×C13—81no—
149C22×C13—83no—
150C22×C13—83no—
151C22×C13#447112yescomplemented
152C22×C13C2×#12013yes—
153C22×C13C22×D811yescharacteristic
154C22×C13C2×AGL(1,ℤ/8)13yes—
155C4×C13—26no—
156C4×C13—83no—
157C4×C13C2×#12014yes—
158C25—224no—
159C25—26no—
160C25—412no—
161C25—44no—
162C25D4×C1311yescharacteristic
163C22×D4—2128no—
164C22×D4—224no—
165C22×D4—248no—
166C22×D4—248no—
167C22×D4—23no—
168C22×D4—26no—
169C22×D4—212no—
170C22×D4D4×C13124yescomplemented
171C22×D4C23×C1314yes—
172C22×D4C23×C1311yescharacteristic, complemented
173C23×C4—212no—
174C23×C4D4×C1313yes—
175C23×C4C23×C1313yes—
176C2×D8—224no—
177C22×C8C23×C1314yescomplemented
178#121—212no—
179#120—44no—
180C2×C4⋊C4C23×C1313yescomplemented
181C2×C22⋊C4—23no—
182C2×C22⋊C4—23no—
183#102—224no—
184C22⋊C8—212no—
185#95—23no—
186C2×C13—212no—
187C2×C13—416no—
188C2×C13—161no—
189C2×C13#284611yescharacteristic
190C2×C13C2×#44713yes—
191C2×C13#300313yes—
192C24—26no—
193C24—26no—
194C24—264no—
195C24—248no—
196C24—224no—
197C24—24no—
198C24—21no—
199C24—496no—
200C24—496no—
201C24—424no—
202C24—412no—
203C24—412no—
204C24C13×D814yescomplemented
205C24C2×D4×C1313yes—
206C2×D4—2192no—
207C2×D4—248no—
208C2×D4—296no—
209C2×D4—296no—
210C2×D4—224no—
211C2×D4—212no—
212C2×D4—26no—
213C2×D4—46no—
214C2×D4—46no—
215C2×D4—46no—
216C2×D4C2×D4×C13124yes—
217C22×C4—232no—
218C22×C4—26no—
219C22×C4—212no—
220C22×C4—212no—
221C22×C4—23no—
222C22×C4C2×D4×C1313yes—
223C22×C4C2×D4×C13112yes—
224C22×C4C24×C1311yescharacteristic
225D8—416no—
226C2×C8—212no—
227C4⋊C4—26no—
228C22⋊C4—46no—
229C22⋊C4—46no—
230C13#3287811yescharacteristic, direct product factor, Sylow
231C23—28no—
232C23—224no—
233C23—224no—
234C23—26no—
235C23—26no—
236C23—296no—
237C23—224no—
238C23—4256no—
239C23—496no—
240C23—448no—
241C23—496no—
242C23—448no—
243C23—44no—
244C23—412no—
245C23—43no—
246C23—41no—
247C23—43no—
248C23C13×#12016yes—
249C23C2×C13×D816yes—
250C23C13×AGL(1,ℤ/8)16yes—
251C23C22×D4×C1311yescharacteristic
252D4—296no—
253D4—224no—
254D4—44no—
255D4—812no—
256D4C13×#120116yescomplemented
257C2×C4—224no—
258C2×C4—26no—
259C2×C4—224no—
260C2×C4—43no—
261C2×C4—43no—
262C2×C4—43no—
263C2×C4C13×#12016yes—
264C2×C4C22×D4×C1316yes—
265C8—44no—
266C22—232no—
267C22—26no—
268C22—212no—
269C22—26no—
270C22—212no—
271C22—216no—
272C22—4192no—
273C22—424no—
274C22—424no—
275C22—81no—
276C22—83no—
277C22—83no—
278C22C13×#447112yescomplemented
279C22C2×C13×#12013yes—
280C22C22×C13×D811yescharacteristic
281C22C2×C13×AGL(1,ℤ/8)13yes—
282C4—26no—
283C4—83no—
284C4C2×C13×#12014yes—
285C2—212no—
286C2—416no—
287C2—161no—
288C2C13×#284611yescharacteristic
289C2C2×C13×#44713yes—
290C2C13×#300313yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
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
1. C24×D4×C13C2semidirect
2. C2×C13×#447C2semidirect
3. C13×#2847C2semidirect
4. C13×#1786C2semidirect
5. C13×#1779C2semidirect
11. C22×C13×D8C22semidirect
12. C2×C13×#121C22semidirect
15. C2×C13×#102C22semidirect
16. C2×C13×C22⋊C8C22semidirect
18. C13×#380C22semidirect
31. C22×D4×C13D4semidirect
33. C22×D4×C13C23semidirect
38. C22×C8×C13C23semidirect
41. C2×C13×C4⋊C4C23semidirect
47. #32878C13direct (N × H)
60. C24×C13D8semidirect
86. C24×D4C2×C13semidirect
87. C2×#447C2×C13semidirect
88. #2847C2×C13semidirect
89. #1786C2×C13semidirect
90. #1779C2×C13semidirect
116. D4×C13#120semidirect
131. C22×D8C22×C13semidirect
132. C2×#121C22×C13semidirect
135. C2×#102C22×C13semidirect
136. C2×C22⋊C8C22×C13semidirect
138. #380C22×C13semidirect
151. C22×C13#447semidirect
170. C22×D4D4×C13semidirect
172. C22×D4C23×C13semidirect
177. C22×C8C23×C13semidirect
180. C2×C4⋊C4C23×C13semidirect
204. C24C13×D8semidirect
230. C13#32878direct (N × H)
256. D4C13×#120semidirect
278. C22C13×#447semidirect

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×#4472
C13×#28472
C13×#17862
C13×#17792
#3287813