Finite Group Databasebeta

← C13×#11777 #15698116

Subgroups — C13×#11777 #15698116

Order 3328.

480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2547C211yesmaximal, characteristic
2C4×C13×#99C211yesmaximal, characteristic
3C13×#1465C211yesmaximal, characteristic
4C13×#1344C214yesmaximal, complemented
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×#124—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C2×C13×#99—21no—
9C13×#407—21no—
10C13×#397C412yescomplemented
11C13×#397C2212yes—
12C13×#391—21no—
13C13×#380—21no—
14C13×#380—21no—
15C4×C13×C4⋊C4C411yescharacteristic, complemented
16C4×C13×C22⋊C4—21no—
17C13×#342C2212yes—
18C13×#324—21no—
19C13×#323C2212yes—
20C22×Q8×C13—21no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C2×C13×M16—41no—
25C13×C4⋊Q8—41no—
26C13×C4⋊Q8—41no—
27C13×#124—44no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4C2311yescharacteristic
39C2×C42×C13—21no—
40C2×C42×C13—41no—
41C2×C42×C13C2×C411yescharacteristic
42C13×#99—24no—
43C13×C22⋊C8—22no—
44C13×C22⋊C8—41no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—41no—
48C13×#95C2×C412yes—
49#11777C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C2×D411yescharacteristic
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C13×M16—82no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—44no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—44no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—42no—
88C42×C13—82no—
89#2547C2×C1311yescharacteristic
90C4×#99C2×C1311yescharacteristic
91#1465C2×C1311yescharacteristic
92#1344C2×C1314yescomplemented
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13AGL(1,ℤ/8)12yes—
104Q8×C13—84no—
105D4×C13—44no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—82no—
127C2×C4×C13—82no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#10412yes—
131C8×C13—82no—
132C2×C4⋊Q8C4×C1311yescharacteristic, complemented
133C2×#124—21no—
134C2×C4×D4C22×C1311yescharacteristic
135C2×#99—21no—
136#407—21no—
137#397C4×C1312yescomplemented
138#397C22×C1312yes—
139#391—21no—
140#380—21no—
141#380—21no—
142C4×C4⋊C4C4×C1311yescharacteristic, complemented
143C4×C22⋊C4—21no—
144#342C22×C1312yes—
145#324—21no—
146#323C22×C1312yes—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13C2×#9911yescharacteristic
160C22×C13#41811yescharacteristic
161C22×C13C2×#10411yescharacteristic
162C4×C13—21no—
163C4×C13—22no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—82no—
168C4×C13—84no—
169C4×C13—82no—
170C4×C13#35412yes—
171C22×Q8—21no—
172C22×D4D4×C1311yescharacteristic
173C23×C4D4×C1311yescharacteristic
174C23×C4D4×C1311yescharacteristic
175C2×M16—41no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178#124—44no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C1312yes—
184C2×C4⋊C4D4×C1311yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4C2×C4×C1311yescharacteristic
189C2×C22⋊C4C23×C1311yescharacteristic
190C2×C42—21no—
191C2×C42—41no—
192C2×C42C2×C4×C1311yescharacteristic
193#99—24no—
194C22⋊C8—22no—
195C22⋊C8—41no—
196#95—22no—
197#95—22no—
198#95—41no—
199#95C2×C4×C1312yes—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—42no—
203C2×C13—81no—
204C2×C13#150711yescharacteristic
205C2×C13#212311yescharacteristic
206C2×C13C2×#35411yescharacteristic
207C24C13×C22⋊C411yescharacteristic
208C24C2×D4×C1311yescharacteristic
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C13×C22⋊C411yescharacteristic
225C22×C4C13×C22⋊C411yescharacteristic
226C22×C4C13×C22⋊C411yescharacteristic
227C22×C4C22×C4×C1311yescharacteristic
228C22×C4C2×D4×C1311yescharacteristic
229M16—82no—
230C2×C8—42no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C22⋊C4—24no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C22⋊C4—42no—
242C42—21no—
243C42—21no—
244C42—42no—
245C42—82no—
246C13#1177711yescharacteristic, direct product factor, Sylow
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C2×C13×C22⋊C411yescharacteristic
257C23C13×AGL(1,ℤ/8)12yes—
258Q8—84no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4C13×#9911yescharacteristic
283C2×C4C13×#9911yescharacteristic
284C2×C4C13×#10412yes—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22C2×C13×#9911yescharacteristic
299C22C13×#41811yescharacteristic
300C22C2×C13×#10411yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—82no—
307C4—84no—
308C4—82no—
309C4C13×#35412yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2C13×#150711yescharacteristic
315C2C13×#212311yescharacteristic
316C2C2×C13×#35411yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C13×#1344C2semidirect
5. C2×C13×C4⋊Q8C4semidirect
10. C13×#397C4semidirect
15. C4×C13×C4⋊C4C4semidirect
49. #11777C13direct (N × H)
92. #1344C2×C13semidirect
132. C2×C4⋊Q8C4×C13semidirect
137. #397C4×C13semidirect
142. C4×C4⋊C4C4×C13semidirect
246. C13#11777direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25472
C4×C13×#992
C13×#14652
C13×#13442
#1177713