Finite Group Databasebeta

← C13×#13217 #15699556

Subgroups — C13×#13217 #15699556

Order 3328.

536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2486C211yesmaximal, characteristic
2C2×C13×#352C214yesmaximal
3C13×#1799C211yesmaximal, characteristic
4C4×C13×#100C211yesmaximal, characteristic
5C2×C13×#123C2212yes—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C2×C13×#100C2212yes—
9C2×C13×#99C2212yes—
10C4×C13×M16—21no—
11C13×#398—21no—
12C13×#397—21no—
13C13×#389—21no—
14C13×#381C412yescomplemented
15C13×#380—21no—
16C13×#380—21no—
17C13×#380C411yescharacteristic, complemented
18C13×#352—28no—
19C13×#343—21no—
20C13×#342—21no—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C2×C13×M16—22no—
26C13×#123—24no—
27C13×#123—24no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4C2×C412yes—
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C13×#100—22no—
45C13×#100D414yes—
46C13×#99—24no—
47C13×#97—41no—
48C4×C8×C13—41no—
49C13×#95—22no—
50C13×#95—21no—
51C13×#95—22no—
52C13×#95—41no—
53#13217C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13C22×C411yescharacteristic
55C24×C13C2×D411yescharacteristic
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13C2×D412yes—
59C2×D4×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—24no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×M16—24no—
78C13×M16—42no—
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—44no—
86C13×C4⋊C4—82no—
87C13×C22⋊C4—24no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C42×C13—21no—
95C42×C13—21no—
96#2486C2×C1311yescharacteristic
97C2×#352C2×C1314yes—
98#1799C2×C1311yescharacteristic
99C4×#100C2×C1311yescharacteristic
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×D412yes—
110C23×C13#12411yescharacteristic
111C23×C13#12711yescharacteristic
112D4×C13—42no—
113D4×C13—42no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—81no—
133C2×C4×C13—84no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#12112yes—
140C8×C13—44no—
141C2×#123C22×C1312yes—
142C2×C4×D4C22×C1311yescharacteristic
143C22×C4⋊C4C4×C1311yescharacteristic, complemented
144C2×#100C22×C1312yes—
145C2×#99C22×C1312yes—
146C4×M16—21no—
147#398—21no—
148#397—21no—
149#389—21no—
150#381C4×C1312yescomplemented
151#380—21no—
152#380—21no—
153#380C4×C1311yescharacteristic, complemented
154#352—28no—
155#343—21no—
156#342—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—42no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—42no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13#39011yescharacteristic
172C22×C13C2×#9911yescharacteristic
173C22×C13#41011yescharacteristic
174C4×C13—21no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—82no—
180C4×C13—82no—
181C4×C13—162no—
182C4×C13#35212yescomplemented
183C22×D4C23×C1311yescharacteristic
184C23×C4C2×C4×C1312yes—
185C23×C4C2×C4×C1311yescharacteristic
186C23×C4D4×C1311yescharacteristic
187C2×M16—22no—
188#123—24no—
189#123—24no—
190C4×D4—41no—
191C4×D4—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4D4×C1311yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4C2×C4×C1312yes—
203C2×C22⋊C4C2×C4×C1311yescharacteristic
204C2×C22⋊C4D4×C1311yescharacteristic
205C2×C42D4×C1311yescharacteristic
206#100—22no—
207#100D4×C1314yes—
208#99—24no—
209#97—41no—
210C4×C8—41no—
211#95—22no—
212#95—21no—
213#95—22no—
214#95—41no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—41no—
218C2×C13—42no—
219C2×C13—41no—
220C2×C13#196411yescharacteristic
221C2×C13C2×#35211yescharacteristic
222C2×C13#212311yescharacteristic
223C24C22×C4×C1311yescharacteristic
224C24C2×D4×C1311yescharacteristic
225C2×D4—41no—
226C2×D4—41no—
227C2×D4C2×D4×C1312yes—
228C2×D4C13×#4112yes—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C13×C22⋊C411yescharacteristic
242C22×C4C13×C22⋊C411yescharacteristic
243C22×C4C13×C22⋊C411yescharacteristic
244C22×C4C13×C22⋊C411yescharacteristic
245C22×C4C2×D4×C1311yescharacteristic
246M16—24no—
247M16—42no—
248C2×C8—42no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—44no—
255C4⋊C4—82no—
256C22⋊C4—24no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—21no—
264C42—21no—
265C13#1321711yescharacteristic, direct product factor, Sylow
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C13×C22⋊C411yescharacteristic
275C23C4×D4×C1312yes—
276C23C13×#12411yescharacteristic
277C23C13×#12711yescharacteristic
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—84no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4C13×#9911yescharacteristic
304C2×C4C13×#9911yescharacteristic
305C2×C4C13×#12112yes—
306C8—44no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C13×#39011yescharacteristic
322C22C2×C13×#9911yescharacteristic
323C22C13×#41011yescharacteristic
324C4—21no—
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—82no—
330C4—82no—
331C4—162no—
332C4C13×#35212yescomplemented
333C2—21no—
334C2—21no—
335C2—41no—
336C2—42no—
337C2—41no—
338C2C13×#196411yescharacteristic
339C2C2×C13×#35211yescharacteristic
340C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C24 ▷ 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
7. C22×C13×C4⋊C4C4semidirect
14. C13×#381C4semidirect
17. C13×#380C4semidirect
53. #13217C13direct (N × H)
143. C22×C4⋊C4C4×C13semidirect
150. #381C4×C13semidirect
153. #380C4×C13semidirect
182. C4×C13#352semidirect
265. C13#13217direct (N × H)
332. C4C13×#352semidirect

Maximal subgroups

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

subgroupindex
C13×#24862
C2×C13×#3522
C13×#17992
C4×C13×#1002
#1321713