Finite Group Databasebeta

← C13×#12798 #15699137

Subgroups — C13×#12798 #15699137

Order 3328.

544 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C4×C13×#124C211yesmaximal, characteristic
2C2×C13×#354C212yesmaximal
3C13×#1799C212yesmaximal
4C13×#1393C212yesmaximal
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C2×C13×#99C2214yes—
9C13×#391C411yescharacteristic, complemented
10C13×#390C2211yescharacteristic
11C13×#388—22no—
12C13×#382C411yescharacteristic, complemented
13C13×#380—22no—
14C4×C13×C22⋊C4—22no—
15C43×C13C411yescharacteristic, complemented
16C13×#354—24no—
17C13×#342—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D4×C13C2311yescharacteristic
20C23×C4×C13D412yes—
21C13×#124—22no—
22C13×#124D412yes—
23C13×#124Q812yes—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—42no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—24no—
35C2×C13×C22⋊C4D412yes—
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C13×#99—24no—
43C13×#99—24no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—42no—
47#12798C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13C2×D412yes—
49C2×Q8×C13—21no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13C4⋊C412yescomplemented
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13C2×D411yescharacteristic
56C2×D4×C13C2×Q811yescharacteristic
57C2×D4×C13#4112yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—44no—
65C22×C4×C13—44no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—84no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—44no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—41no—
84C42×C13—42no—
85C42×C13—42no—
86C42×C13—41no—
87C42×C13—41no—
88C42×C13C4⋊C412yescomplemented
89C4×#124C2×C1311yescharacteristic
90C2×#354C2×C1312yes—
91#1799C2×C1312yes—
92#1393C2×C1312yes—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13#12112yes—
99C23×C13C22⋊Q812yes—
100Q8×C13—42no—
101Q8×C13—42no—
102D4×C13—41no—
103D4×C13—41no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—44no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—82no—
125C2×C4×C13—84no—
126C2×C4×C13—84no—
127C2×C4×C13—84no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13C2×C4⋊C411yescharacteristic
131C2×C4×C13#11711yescharacteristic
132C2×#124C22×C1311yescharacteristic
133C2×C4×Q8C4×C1311yescharacteristic, complemented
134C2×C4×D4C22×C1311yescharacteristic
135C2×#99C22×C1314yes—
136#391C4×C1311yescharacteristic, complemented
137#390C22×C1311yescharacteristic
138#388—22no—
139#382C4×C1311yescharacteristic, complemented
140#380—22no—
141C4×C22⋊C4—22no—
142C43C4×C1311yescharacteristic, complemented
143#354—24no—
144#342—22no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—82no—
154C22×C13#38011yescharacteristic
155C22×C13C2×#9911yescharacteristic
156C22×C13#41011yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—42no—
161C4×C13—42no—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13—164no—
167C4×C13#35412yescomplemented
168C22×Q8C2×C4×C1311yescharacteristic
169C22×D4C23×C1311yescharacteristic
170C23×C4D4×C1312yes—
171#124—22no—
172#124D4×C1312yes—
173#124Q8×C1312yes—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4C2×C4×C1311yescharacteristic
181C2×C4⋊C4C2×C4×C1311yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4D4×C1312yes—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×C4×C1311yescharacteristic
190C2×C42C2×C4×C1311yescharacteristic
191C2×C42C2×C4×C1311yescharacteristic
192#99—24no—
193#99—24no—
194#95—22no—
195#95—22no—
196#95—42no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—42no—
200C2×C13—42no—
201C2×C13#179911yescharacteristic
202C2×C13C2×#35411yescharacteristic
203C2×C13#212611yescharacteristic
204C24C2×D4×C1312yes—
205C2×Q8—21no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8C13×C4⋊C412yescomplemented
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×D4×C1311yescharacteristic
212C2×D4C2×Q8×C1311yescharacteristic
213C2×D4C13×#4112yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4C13×C22⋊C411yescharacteristic
223C22×C4C13×C22⋊C412yes—
224C22×C4C13×C22⋊C411yescharacteristic
225C22×C4C22×C4×C1311yescharacteristic
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—84no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C22⋊C4—42no—
233C22⋊C4—44no—
234C22⋊C4—44no—
235C22⋊C4—44no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—41no—
240C42—42no—
241C42—42no—
242C42—41no—
243C42—41no—
244C42C13×C4⋊C412yescomplemented
245C13#1279811yescharacteristic, direct product factor, Sylow
246C23—22no—
247C23—22no—
248C23—42no—
249C23—42no—
250C23C2×C13×C22⋊C411yescharacteristic
251C23C13×#12112yes—
252C23C13×C22⋊Q812yes—
253Q8—42no—
254Q8—42no—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—82no—
278C2×C4—84no—
279C2×C4—84no—
280C2×C4—84no—
281C2×C4C13×#9911yescharacteristic
282C2×C4C13×#9911yescharacteristic
283C2×C4C2×C13×C4⋊C411yescharacteristic
284C2×C4C13×#11711yescharacteristic
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—82no—
294C22C13×#38011yescharacteristic
295C22C2×C13×#9911yescharacteristic
296C22C13×#41011yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—42no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—81no—
306C4—164no—
307C4C13×#35412yescomplemented
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2C13×#179911yescharacteristic
313C2C2×C13×#35411yescharacteristic
314C2C13×#212611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
9. C13×#391C4semidirect
12. C13×#382C4semidirect
15. C43×C13C4semidirect
47. #12798C13direct (N × H)
52. C2×Q8×C13C4⋊C4semidirect
88. C42×C13C4⋊C4semidirect
133. C2×C4×Q8C4×C13semidirect
136. #391C4×C13semidirect
139. #382C4×C13semidirect
142. C43C4×C13semidirect
167. C4×C13#354semidirect
208. C2×Q8C13×C4⋊C4semidirect
244. C42C13×C4⋊C4semidirect
245. C13#12798direct (N × H)
307. C4C13×#354semidirect

Maximal subgroups

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

subgroupindex
C4×C13×#1242
C2×C13×#3542
C13×#17992
C13×#13932
#1279813