Finite Group Databasebeta

← C13×#11753 #15698092

Subgroups — C13×#11753 #15698092

Order 3328.

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

normal subgroups only

This group has 778 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×#2404C211yesmaximal, characteristic
2C2×C13×#342C211yesmaximal, characteristic, complemented
3C13×#1462C211yesmaximal, characteristic, complemented
4C13×#1351C212yesmaximal, complemented
5C13×#1343C212yesmaximal, complemented
6C22×C13×#41C411yescharacteristic, complemented
7C2×C13×#120—21no—
8C22×C13×C22⋊C4—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C13×#407—21no—
11C13×#393C411yescharacteristic, complemented
12C13×#393C2211yescharacteristic
13C13×#392C411yescharacteristic, complemented
14C13×#392C2211yescharacteristic
15C13×#386—21no—
16C13×#386—21no—
17C13×#386—21no—
18C13×#381C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#323—21no—
22C13×#323C2212yes—
23C25×C13D411yescharacteristic
24C2×C13×#41—41no—
25C2×C13×#41—41no—
26C2×C13×#41—44no—
27C22×Q8×C13C2×C411yescharacteristic, complemented
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13—21no—
31C22×D4×C13C2×C411yescharacteristic, complemented
32C23×C4×C13—21no—
33C23×C4×C13—41no—
34C23×C4×C13C2×C411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C2×C13×M16—41no—
37C13×#120—44no—
38C2×C13×C22⋊C4—24no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—41no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4—42no—
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4D411yescharacteristic
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C13×C22⋊C4C2311yescharacteristic
53C13×C22⋊C8—22no—
54C13×C22⋊C8—41no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95C2×C411yescharacteristic, complemented
59C13×#95C2×C411yescharacteristic, complemented
60#11753C1311yesmaximal, 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
72C13×#41—44no—
73C13×#41—44no—
74C13×#41—44no—
75C13×#41—44no—
76C2×Q8×C13—42no—
77C2×Q8×C13—41no—
78C2×D4×C13—24no—
79C2×D4×C13—41no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—42no—
84C2×D4×C13—42no—
85C2×D4×C13—42no—
86C2×D4×C13—42no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—81no—
90C2×D4×C13—81no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—42no—
102C22×C4×C13—44no—
103C22×C4×C13—42no—
104C22×C4×C13—81no—
105C22×C4×C13—82no—
106C22×C4×C13—82no—
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22⋊C411yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C13×M16—82no—
112C2×C8×C13—42no—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—42no—
120C13×C22⋊C4—44no—
121C13×C22⋊C4—42no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—81no—
124C13×C22⋊C4—81no—
125#2404C2×C1311yescharacteristic
126C2×#342C2×C1311yescharacteristic, complemented
127#1462C2×C1311yescharacteristic, complemented
128#1351C2×C1312yescomplemented
129#1343C2×C1312yescomplemented
130C23×C13—22no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13—22no—
134C23×C13—22no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—22no—
142C23×C13—41no—
143C23×C13—42no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—42no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—81no—
156C23×C13—81no—
157C23×C13—84no—
158C23×C13—82no—
159C23×C13—82no—
160C23×C13#9911yescharacteristic
161C23×C13#9911yescharacteristic
162C23×C13#10412yes—
163C23×C13C2×C22⋊C411yescharacteristic
164C23×C13AGL(1,ℤ/8)11yescharacteristic
165C23×C13#13711yescharacteristic
166Q8×C13—42no—
167Q8×C13—42no—
168D4×C13—44no—
169D4×C13—42no—
170D4×C13—44no—
171D4×C13—42no—
172D4×C13—84no—
173D4×C13—82no—
174D4×C13—82no—
175C2×C4×C13—22no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—48no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—44no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—81no—
198C2×C4×C13—88no—
199C2×C4×C13—82no—
200C2×C4×C13—82no—
201C8×C13—82no—
202C22×#41C4×C1311yescharacteristic, complemented
203C2×#120—21no—
204C22×C22⋊C4—21no—
205C22×C22⋊C4C22×C1311yescharacteristic
206#407—21no—
207#393C4×C1311yescharacteristic, complemented
208#393C22×C1311yescharacteristic
209#392C4×C1311yescharacteristic, complemented
210#392C22×C1311yescharacteristic
211#386—21no—
212#386—21no—
213#386—21no—
214#381C4×C1311yescharacteristic, complemented
215#342—21no—
216#342C22×C1312yes—
217#323—21no—
218#323C22×C1312yes—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—22no—
228C22×C13—21no—
229C22×C13—42no—
230C22×C13—42no—
231C22×C13—42no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—44no—
235C22×C13—44no—
236C22×C13—42no—
237C22×C13—42no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—41no—
241C22×C13—41no—
242C22×C13—42no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13—81no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13—81no—
250C22×C13—81no—
251C22×C13AΣL(1,𝔽16)12yes—
252C22×C13C2×#9911yescharacteristic
253C22×C13#41711yescharacteristic
254C22×C13C2×#10411yescharacteristic
255C4×C13—41no—
256C4×C13—42no—
257C4×C13—41no—
258C4×C13—41no—
259C4×C13—41no—
260C4×C13—81no—
261C4×C13—81no—
262C4×C13—84no—
263C25D4×C1311yescharacteristic
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—44no—
267C22×Q8C2×C4×C1311yescharacteristic, complemented
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2×C4×C1311yescharacteristic, complemented
272C23×C4—21no—
273C23×C4—41no—
274C23×C4C2×C4×C1311yescharacteristic
275C23×C4D4×C1311yescharacteristic
276C2×M16—41no—
277#120—44no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4C2×C4×C1311yescharacteristic
290C2×C22⋊C4D4×C1311yescharacteristic
291C2×C22⋊C4D4×C1311yescharacteristic
292C2×C22⋊C4C23×C1311yescharacteristic
293C22⋊C8—22no—
294C22⋊C8—41no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95C2×C4×C1311yescharacteristic, complemented
299#95C2×C4×C1311yescharacteristic, complemented
300C2×C13—21no—
301C2×C13—21no—
302C2×C13—22no—
303C2×C13—41no—
304C2×C13—41no—
305C2×C13—42no—
306C2×C13—41no—
307C2×C13—82no—
308C2×C13#150411yescharacteristic
309C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
310C2×C13#212711yescharacteristic
311C24—21no—
312C24—21no—
313C24—22no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—42no—
318C24—81no—
319C24C13×C22⋊C411yescharacteristic
320C24C13×C22⋊C411yescharacteristic
321C24C2×D4×C1311yescharacteristic
322#41—44no—
323#41—44no—
324#41—44no—
325#41—44no—
326C2×Q8—42no—
327C2×Q8—41no—
328C2×D4—24no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—81no—
340C2×D4—81no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—81no—
355C22×C4—82no—
356C22×C4—82no—
357C22×C4C13×C22⋊C411yescharacteristic
358C22×C4C13×C22⋊C411yescharacteristic
359C22×C4C22×C4×C1311yescharacteristic
360C22×C4C2×D4×C1311yescharacteristic
361M16—82no—
362C2×C8—42no—
363C22⋊C4—24no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—44no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—81no—
374C22⋊C4—81no—
375C13#1175311yescharacteristic, direct product factor, Sylow
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—84no—
404C23—82no—
405C23—82no—
406C23C13×#9911yescharacteristic
407C23C13×#9911yescharacteristic
408C23C13×#10412yes—
409C23C2×C13×C22⋊C411yescharacteristic
410C23C13×AGL(1,ℤ/8)11yescharacteristic
411C23C13×#13711yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—44no—
415D4—42no—
416D4—42no—
417D4—44no—
418D4—84no—
419D4—82no—
420D4—82no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—44no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—88no—
445C2×C4—82no—
446C2×C4—82no—
447C8—82no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—44no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22C13×AΣL(1,𝔽16)12yes—
481C22C2×C13×#9911yescharacteristic
482C22C13×#41711yescharacteristic
483C22C2×C13×#10411yescharacteristic
484C4—41no—
485C4—42no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—81no—
490C4—81no—
491C4—84no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—41no—
496C2—41no—
497C2—42no—
498C2—41no—
499C2—82no—
500C2C13×#150411yescharacteristic
501C2C2×C13×AΣL(1,𝔽16)11yescharacteristic
502C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC13×#2404C2
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×#1351C2semidirect
5. C13×#1343C2semidirect
6. C22×C13×#41C4semidirect
11. C13×#393C4semidirect
13. C13×#392C4semidirect
18. C13×#381C4semidirect
27. C22×Q8×C13C2×C4semidirect
31. C22×D4×C13C2×C4semidirect
58. C13×#95C2×C4semidirect
59. C13×#95C2×C4semidirect
60. #11753C13direct (N × H)
126. C2×#342C2×C13semidirect
127. #1462C2×C13semidirect
128. #1351C2×C13semidirect
129. #1343C2×C13semidirect
202. C22×#41C4×C13semidirect
207. #393C4×C13semidirect
209. #392C4×C13semidirect
214. #381C4×C13semidirect
267. C22×Q8C2×C4×C13semidirect
271. C22×D4C2×C4×C13semidirect
298. #95C2×C4×C13semidirect
299. #95C2×C4×C13semidirect
375. C13#11753direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24042
C2×C13×#3422
C13×#14622
C13×#13512
C13×#13432
#1175313