Finite Group Databasebeta

← C13×#11757 #15698096

Subgroups — C13×#11757 #15698096

Order 3328.

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

normal subgroups only

This group has 700 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×#2539C211yesmaximal, characteristic
2C2×C13×#342C211yesmaximal, characteristic, complemented
3C13×#1462C211yesmaximal, characteristic, complemented
4C13×#1352C212yesmaximal, complemented
5C13×#1343C212yesmaximal, complemented
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic, complemented
8C2×C13×#120—21no—
9C22×C13×C22⋊C4—21no—
10C22×C13×C22⋊C4C2211yescharacteristic
11C13×#407—21no—
12C13×#399C411yescharacteristic, complemented
13C13×#399C2211yescharacteristic
14C13×#392C411yescharacteristic, complemented
15C13×#392C2211yescharacteristic
16C13×#390—21no—
17C13×#390—21no—
18C4×C13×C22⋊C4C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#323—21no—
22C13×#323C2212yes—
23C25×C13D411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic, complemented
28C23×C4×C13—41no—
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C2×C13×M16—41no—
32C13×#123—44no—
33C13×#121—41no—
34C13×#121—41no—
35C13×#120—44no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—24no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4—41no—
49C2×C13×C22⋊C4—41no—
50C2×C13×C22⋊C4—42no—
51C2×C13×C22⋊C4C2×C411yescharacteristic
52C2×C13×C22⋊C4D411yescharacteristic
53C2×C13×C22⋊C4D411yescharacteristic
54C2×C13×C22⋊C4C2311yescharacteristic
55C2×C42×C13—21no—
56C13×C22⋊C8—22no—
57C13×C22⋊C8—41no—
58C13×#95C2×C411yescharacteristic, complemented
59C13×#95C2×C411yescharacteristic, complemented
60#11757C1311yesmaximal, characteristic, direct product factor, Sylow
61C24×C13—21no—
62C24×C13—21no—
63C24×C13—22no—
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—21no—
67C24×C13—42no—
68C24×C13—81no—
69C24×C13C22⋊C411yescharacteristic
70C24×C13C22⋊C411yescharacteristic
71C24×C13C2×D411yescharacteristic
72C2×D4×C13—41no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—42no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—81no—
83C2×D4×C13—81no—
84C2×D4×C13—81no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—42no—
93C22×C4×C13—44no—
94C22×C4×C13—42no—
95C22×C4×C13—81no—
96C22×C4×C13—82no—
97C22×C4×C13—82no—
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C13×M16—82no—
103C2×C8×C13—42no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—42no—
106C13×C4⋊C4—42no—
107C13×C22⋊C4—24no—
108C13×C22⋊C4—24no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—44no—
119C13×C22⋊C4—42no—
120C42×C13—81no—
121#2539C2×C1311yescharacteristic
122C2×#342C2×C1311yescharacteristic, complemented
123#1462C2×C1311yescharacteristic, complemented
124#1352C2×C1312yescomplemented
125#1343C2×C1312yescomplemented
126C23×C13—22no—
127C23×C13—22no—
128C23×C13—22no—
129C23×C13—22no—
130C23×C13—22no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—41no—
138C23×C13—42no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—81no—
152C23×C13—81no—
153C23×C13—84no—
154C23×C13—82no—
155C23×C13—82no—
156C23×C13#9911yescharacteristic
157C23×C13#9911yescharacteristic
158C23×C13#10412yes—
159C23×C13C2×C22⋊C411yescharacteristic
160C23×C13AGL(1,ℤ/8)11yescharacteristic
161C23×C13#13711yescharacteristic
162D4×C13—84no—
163D4×C13—82no—
164D4×C13—82no—
165D4×C13—82no—
166D4×C13—82no—
167D4×C13—82no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—44no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—81no—
188C2×C4×C13—81no—
189C2×C4×C13—81no—
190C2×C4×C13—88no—
191C2×C4×C13—82no—
192C2×C4×C13—82no—
193C8×C13—82no—
194C2×#123—21no—
195C2×#121C4×C1311yescharacteristic, complemented
196C2×#120—21no—
197C22×C22⋊C4—21no—
198C22×C22⋊C4C22×C1311yescharacteristic
199#407—21no—
200#399C4×C1311yescharacteristic, complemented
201#399C22×C1311yescharacteristic
202#392C4×C1311yescharacteristic, complemented
203#392C22×C1311yescharacteristic
204#390—21no—
205#390—21no—
206C4×C22⋊C4C4×C1311yescharacteristic, complemented
207#342—21no—
208#342C22×C1312yes—
209#323—21no—
210#323C22×C1312yes—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—22no—
220C22×C13—21no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—42no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—44no—
227C22×C13—44no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—41no—
231C22×C13—41no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—82no—
239C22×C13—82no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13#35312yes—
244C22×C13C2×#9911yescharacteristic
245C22×C13#41711yescharacteristic
246C22×C13C2×#10411yescharacteristic
247C4×C13—42no—
248C4×C13—42no—
249C4×C13—41no—
250C4×C13—41no—
251C4×C13—41no—
252C4×C13—41no—
253C4×C13—84no—
254C4×C13—81no—
255C25D4×C1311yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4C2×C4×C1311yescharacteristic, complemented
260C23×C4—41no—
261C23×C4C2×C4×C1311yescharacteristic
262C23×C4D4×C1311yescharacteristic
263C2×M16—41no—
264#123—44no—
265#121—41no—
266#121—41no—
267#120—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
271C2×C22⋊C4—21no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—41no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4C2×C4×C1311yescharacteristic
284C2×C22⋊C4D4×C1311yescharacteristic
285C2×C22⋊C4D4×C1311yescharacteristic
286C2×C22⋊C4C23×C1311yescharacteristic
287C2×C42—21no—
288C22⋊C8—22no—
289C22⋊C8—41no—
290#95C2×C4×C1311yescharacteristic, complemented
291#95C2×C4×C1311yescharacteristic, complemented
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—22no—
295C2×C13—41no—
296C2×C13—41no—
297C2×C13—42no—
298C2×C13—41no—
299C2×C13—161no—
300C2×C13#150411yescharacteristic
301C2×C13#212111yescharacteristic
302C2×C13C2×#35311yescharacteristic
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24C13×C22⋊C411yescharacteristic
312C24C13×C22⋊C411yescharacteristic
313C24C2×D4×C1311yescharacteristic
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4—81no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—42no—
337C22×C4—81no—
338C22×C4—82no—
339C22×C4—82no—
340C22×C4C13×C22⋊C411yescharacteristic
341C22×C4C13×C22⋊C411yescharacteristic
342C22×C4C22×C4×C1311yescharacteristic
343C22×C4C2×D4×C1311yescharacteristic
344M16—82no—
345C2×C8—42no—
346C4⋊C4—41no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C42—81no—
363C13#1175711yescharacteristic, direct product factor, Sylow
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23—84no—
392C23—82no—
393C23—82no—
394C23C13×#9911yescharacteristic
395C23C13×#9911yescharacteristic
396C23C13×#10412yes—
397C23C2×C13×C22⋊C411yescharacteristic
398C23C13×AGL(1,ℤ/8)11yescharacteristic
399C23C13×#13711yescharacteristic
400D4—84no—
401D4—82no—
402D4—82no—
403D4—82no—
404D4—82no—
405D4—82no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—44no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—88no—
429C2×C4—82no—
430C2×C4—82no—
431C8—82no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—82no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22C13×#35312yes—
465C22C2×C13×#9911yescharacteristic
466C22C13×#41711yescharacteristic
467C22C2×C13×#10411yescharacteristic
468C4—42no—
469C4—42no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—84no—
475C4—81no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—161no—
484C2C13×#150411yescharacteristic
485C2C13×#212111yescharacteristic
486C2C2×C13×#35311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2539C2
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
2. C2×C13×#342C2semidirect
3. C13×#1462C2semidirect
4. C13×#1352C2semidirect
5. C13×#1343C2semidirect
7. C2×C13×#121C4semidirect
12. C13×#399C4semidirect
14. C13×#392C4semidirect
18. C4×C13×C22⋊C4C4semidirect
27. C22×D4×C13C2×C4semidirect
38. C2×C13×C4⋊C4C2×C4semidirect
58. C13×#95C2×C4semidirect
59. C13×#95C2×C4semidirect
60. #11757C13direct (N × H)
122. C2×#342C2×C13semidirect
123. #1462C2×C13semidirect
124. #1352C2×C13semidirect
125. #1343C2×C13semidirect
195. C2×#121C4×C13semidirect
200. #399C4×C13semidirect
202. #392C4×C13semidirect
206. C4×C22⋊C4C4×C13semidirect
259. C22×D4C2×C4×C13semidirect
270. C2×C4⋊C4C2×C4×C13semidirect
290. #95C2×C4×C13semidirect
291. #95C2×C4×C13semidirect
363. C13#11757direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25392
C2×C13×#3422
C13×#14622
C13×#13522
C13×#13432
#1175713