Finite Group Databasebeta

← C13×#11755 #15698094

Subgroups — C13×#11755 #15698094

Order 3328.

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

normal subgroups only

This group has 586 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×#2482C211yesmaximal, characteristic
2C2×C13×#342C211yesmaximal, characteristic
3C13×#1462C211yesmaximal, characteristic
4C13×#1352C212yesmaximal, complemented
5C13×#1344C212yesmaximal, complemented
6C2×C13×#117C411yescharacteristic, complemented
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#407—21no—
10C13×#399C411yescharacteristic, complemented
11C13×#399C2211yescharacteristic
12C13×#397C411yescharacteristic, complemented
13C13×#397C2211yescharacteristic
14C13×#388—21no—
15C13×#388—21no—
16C13×#385—21no—
17C13×#381C411yescharacteristic, complemented
18C13×#379—21no—
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#323—21no—
22C13×#323C2212yes—
23C25×C13D411yescharacteristic
24C23×C4×C13—41no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C2×C13×M16—41no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
33C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
34C2×C13×C22⋊C4—24no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4—42no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4D411yescharacteristic
49C2×C13×C22⋊C4C2311yescharacteristic
50C2×C42×C13—21no—
51C13×C22⋊C8—22no—
52C13×C22⋊C8—41no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic, complemented
57C13×#95C2×C411yescharacteristic, complemented
58#11755C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—21no—
63C24×C13—21no—
64C24×C13—42no—
65C24×C13—81no—
66C24×C13C22⋊C411yescharacteristic
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—42no—
78C22×C4×C13—44no—
79C22×C4×C13—42no—
80C22×C4×C13—81no—
81C22×C4×C13—82no—
82C22×C4×C13—82no—
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C13×M16—82no—
88C2×C8×C13—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—44no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—81no—
107C13×C22⋊C4—81no—
108C42×C13—42no—
109#2482C2×C1311yescharacteristic
110C2×#342C2×C1311yescharacteristic
111#1462C2×C1311yescharacteristic
112#1352C2×C1312yescomplemented
113#1344C2×C1312yescomplemented
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—41no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—42no—
132C23×C13—81no—
133C23×C13—81no—
134C23×C13—84no—
135C23×C13—82no—
136C23×C13—82no—
137C23×C13#9911yescharacteristic
138C23×C13#9911yescharacteristic
139C23×C13#10412yes—
140C23×C13C2×C22⋊C411yescharacteristic
141C23×C13AGL(1,ℤ/8)11yescharacteristic
142C23×C13#13711yescharacteristic
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—44no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
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—81no—
168C2×C4×C13—88no—
169C2×C4×C13—82no—
170C2×C4×C13—82no—
171C8×C13—82no—
172C2×#117C4×C1311yescharacteristic, complemented
173C22×C22⋊C4—21no—
174C22×C22⋊C4C22×C1311yescharacteristic
175#407—21no—
176#399C4×C1311yescharacteristic, complemented
177#399C22×C1311yescharacteristic
178#397C4×C1311yescharacteristic, complemented
179#397C22×C1311yescharacteristic
180#388—21no—
181#388—21no—
182#385—21no—
183#381C4×C1311yescharacteristic, complemented
184#379—21no—
185#342—21no—
186#342C22×C1312yes—
187#323—21no—
188#323C22×C1312yes—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—21no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—44no—
205C22×C13—44no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13#35212yes—
215C22×C13C2×#9911yescharacteristic
216C22×C13#41711yescharacteristic
217C22×C13C2×#10411yescharacteristic
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—81no—
223C4×C13—81no—
224C4×C13—84no—
225C4×C13—81no—
226C4×C13—81no—
227C25D4×C1311yescharacteristic
228C23×C4—41no—
229C23×C4C2×C4×C1311yescharacteristic
230C23×C4D4×C1311yescharacteristic
231C2×M16—41no—
232#117—41no—
233#117—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
237C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
238C2×C22⋊C4—24no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—41no—
247C2×C22⋊C4—41no—
248C2×C22⋊C4—41no—
249C2×C22⋊C4—42no—
250C2×C22⋊C4C2×C4×C1311yescharacteristic
251C2×C22⋊C4D4×C1311yescharacteristic
252C2×C22⋊C4D4×C1311yescharacteristic
253C2×C22⋊C4C23×C1311yescharacteristic
254C2×C42—21no—
255C22⋊C8—22no—
256C22⋊C8—41no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95C2×C4×C1311yescharacteristic, complemented
261#95C2×C4×C1311yescharacteristic, complemented
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—22no—
265C2×C13—41no—
266C2×C13—41no—
267C2×C13—42no—
268C2×C13—41no—
269C2×C13#150411yescharacteristic
270C2×C13C2×#35211yescharacteristic
271C2×C13#212711yescharacteristic
272C24—21no—
273C24—21no—
274C24—22no—
275C24—21no—
276C24—21no—
277C24—42no—
278C24—81no—
279C24C13×C22⋊C411yescharacteristic
280C24C13×C22⋊C411yescharacteristic
281C24C2×D4×C1311yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—44no—
292C22×C4—42no—
293C22×C4—81no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4C13×C22⋊C411yescharacteristic
297C22×C4C13×C22⋊C411yescharacteristic
298C22×C4C22×C4×C1311yescharacteristic
299C22×C4C2×D4×C1311yescharacteristic
300M16—82no—
301C2×C8—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—81no—
306C22⋊C4—24no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—44no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—81no—
320C22⋊C4—81no—
321C42—42no—
322C13#1175511yescharacteristic, direct product factor, Sylow
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—22no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—84no—
344C23—82no—
345C23—82no—
346C23C13×#9911yescharacteristic
347C23C13×#9911yescharacteristic
348C23C13×#10412yes—
349C23C2×C13×C22⋊C411yescharacteristic
350C23C13×AGL(1,ℤ/8)11yescharacteristic
351C23C13×#13711yescharacteristic
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
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—41no—
376C2×C4—81no—
377C2×C4—88no—
378C2×C4—82no—
379C2×C4—82no—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—44no—
397C22—44no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—82no—
405C22—82no—
406C22C13×#35212yes—
407C22C2×C13×#9911yescharacteristic
408C22C13×#41711yescharacteristic
409C22C2×C13×#10411yescharacteristic
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—81no—
416C4—84no—
417C4—81no—
418C4—81no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—41no—
423C2—41no—
424C2—42no—
425C2—41no—
426C2C13×#150411yescharacteristic
427C2C2×C13×#35211yescharacteristic
428C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1352C2semidirect
5. C13×#1344C2semidirect
6. C2×C13×#117C4semidirect
10. C13×#399C4semidirect
12. C13×#397C4semidirect
17. C13×#381C4semidirect
32. C2×C13×C4⋊C4C2×C4semidirect
33. C2×C13×C4⋊C4C2×C4semidirect
56. C13×#95C2×C4semidirect
57. C13×#95C2×C4semidirect
58. #11755C13direct (N × H)
112. #1352C2×C13semidirect
113. #1344C2×C13semidirect
172. C2×#117C4×C13semidirect
176. #399C4×C13semidirect
178. #397C4×C13semidirect
183. #381C4×C13semidirect
236. C2×C4⋊C4C2×C4×C13semidirect
237. C2×C4⋊C4C2×C4×C13semidirect
260. #95C2×C4×C13semidirect
261. #95C2×C4×C13semidirect
322. C13#11755direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24822
C2×C13×#3422
C13×#14622
C13×#13522
C13×#13442
#1175513