Finite Group Databasebeta

← C13×#11762 #15698101

Subgroups — C13×#11762 #15698101

Order 3328.

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

normal subgroups only

This group has 622 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×#2406C211yesmaximal, characteristic
2C2×C13×#343C211yesmaximal, characteristic, complemented
3C13×#1463C211yesmaximal, characteristic, complemented
4C13×#1354C212yesmaximal, complemented
5C13×#1345C212yesmaximal, complemented
6C22×C13×#41C411yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#123—21no—
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#407—21no—
11C13×#395C411yescharacteristic
12C13×#395C2211yescharacteristic
13C13×#394C411yescharacteristic
14C13×#394C2211yescharacteristic
15C13×#386—21no—
16C13×#385—21no—
17C13×#385—21no—
18C13×#381C411yescharacteristic
19C13×#343—21no—
20C13×#343C2212yes—
21C13×#324—21no—
22C13×#324C2212yes—
23C2×C13×#41—41no—
24C2×C13×#41—41no—
25C2×C13×#41—44no—
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13C2×C411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C2×C13×M16—24no—
34C2×C13×M16—22no—
35C2×C13×M16—41no—
36C2×C13×M16—42no—
37C2×C13×M16—41no—
38C22×C8×C13—41no—
39C13×#123—44no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—41no—
43C2×C13×C4⋊C4—41no—
44C2×C13×C4⋊C4C2×C411yescharacteristic
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4C2311yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—41no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95C2×C411yescharacteristic
59C13×#95C2×C411yescharacteristic
60#11762C1311yesmaximal, characteristic, direct product factor, Sylow
61C24×C13—21no—
62C24×C13C22⋊C411yescharacteristic
63C13×#41—44no—
64C13×#41—44no—
65C13×#41—44no—
66C13×#41—44no—
67C2×Q8×C13—42no—
68C2×Q8×C13—41no—
69C2×D4×C13—24no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—42no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—22no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22×C411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C13×M16—24no—
99C13×M16—44no—
100C13×M16—42no—
101C13×M16—82no—
102C2×C8×C13—44no—
103C2×C8×C13—42no—
104C2×C8×C13—42no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—42no—
110C13×C4⋊C4—42no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117#2406C2×C1311yescharacteristic
118C2×#343C2×C1311yescharacteristic, complemented
119#1463C2×C1311yescharacteristic, complemented
120#1354C2×C1312yescomplemented
121#1345C2×C1312yescomplemented
122C23×C13—22no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—22no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13#9911yescharacteristic
134C23×C13#9911yescharacteristic
135C23×C13C2×C22⋊C411yescharacteristic
136Q8×C13—42no—
137Q8×C13—42no—
138D4×C13—44no—
139D4×C13—42no—
140D4×C13—44no—
141D4×C13—42no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—48no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—81no—
172C2×C4×C13#10412yes—
173C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C13#13711yescharacteristic
175C8×C13—44no—
176C8×C13—82no—
177C22×#41C4×C1311yescharacteristic
178C22×M16—21no—
179C2×#123—21no—
180C22×C4⋊C4C22×C1311yescharacteristic
181#407—21no—
182#395C4×C1311yescharacteristic
183#395C22×C1311yescharacteristic
184#394C4×C1311yescharacteristic
185#394C22×C1311yescharacteristic
186#386—21no—
187#385—21no—
188#385—21no—
189#381C4×C1311yescharacteristic
190#343—21no—
191#343C22×C1312yes—
192#324—21no—
193#324C22×C1312yes—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—42no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—81no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13AΣL(1,𝔽16)12yes—
211C22×C13C2×#9911yescharacteristic
212C22×C13#41711yescharacteristic
213C22×C13C2×#10411yescharacteristic
214C4×C13—21no—
215C4×C13—22no—
216C4×C13—21no—
217C4×C13—41no—
218C4×C13—41no—
219C4×C13—42no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—81no—
223C4×C13—81no—
224C2×#41—41no—
225C2×#41—41no—
226C2×#41—44no—
227C22×Q8C2×C4×C1311yescharacteristic
228C22×D4—21no—
229C22×D4C2×C4×C1311yescharacteristic
230C23×C4—21no—
231C23×C4C2×C4×C1311yescharacteristic
232C23×C4D4×C1311yescharacteristic
233C23×C4D4×C1311yescharacteristic
234C2×M16—24no—
235C2×M16—22no—
236C2×M16—41no—
237C2×M16—42no—
238C2×M16—41no—
239C22×C8—41no—
240#123—44no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4—41no—
245C2×C4⋊C4C2×C4×C1311yescharacteristic
246C2×C4⋊C4D4×C1311yescharacteristic
247C2×C4⋊C4D4×C1311yescharacteristic
248C2×C4⋊C4C23×C1311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C22⋊C8—22no—
255C22⋊C8—41no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95C2×C4×C1311yescharacteristic
260#95C2×C4×C1311yescharacteristic
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—22no—
264C2×C13—41no—
265C2×C13—82no—
266C2×C13#150411yescharacteristic
267C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
268C2×C13#213311yescharacteristic
269C24—21no—
270C24C13×C22⋊C411yescharacteristic
271#41—44no—
272#41—44no—
273#41—44no—
274#41—44no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×D4—24no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4C13×C22⋊C411yescharacteristic
301C22×C4C13×C22⋊C411yescharacteristic
302C22×C4C13×C22⋊C411yescharacteristic
303C22×C4C22×C4×C1311yescharacteristic
304C22×C4C2×D4×C1311yescharacteristic
305C22×C4C2×D4×C1311yescharacteristic
306M16—24no—
307M16—44no—
308M16—42no—
309M16—82no—
310C2×C8—44no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C13#1176211yescharacteristic, direct product factor, Sylow
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23C13×#9911yescharacteristic
338C23C13×#9911yescharacteristic
339C23C2×C13×C22⋊C411yescharacteristic
340Q8—42no—
341Q8—42no—
342D4—44no—
343D4—42no—
344D4—42no—
345D4—44no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—48no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4C13×#10412yes—
377C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
378C2×C4C13×#13711yescharacteristic
379C8—44no—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C13×AΣL(1,𝔽16)12yes—
398C22C2×C13×#9911yescharacteristic
399C22C13×#41711yescharacteristic
400C22C2×C13×#10411yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—41no—
405C4—41no—
406C4—42no—
407C4—41no—
408C4—41no—
409C4—81no—
410C4—81no—
411C2—21no—
412C2—21no—
413C2—22no—
414C2—41no—
415C2—82no—
416C2C13×#150411yescharacteristic
417C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
418C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC22×C13×#41C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#343C2semidirect
3. C13×#1463C2semidirect
4. C13×#1354C2semidirect
5. C13×#1345C2semidirect
60. #11762C13direct (N × H)
118. C2×#343C2×C13semidirect
119. #1463C2×C13semidirect
120. #1354C2×C13semidirect
121. #1345C2×C13semidirect
325. C13#11762direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24062
C2×C13×#3432
C13×#14632
C13×#13542
C13×#13452
#1176213