Finite Group Databasebeta

← C13×#10329 #15696668

Subgroups — C13×#10329 #15696668

Order 3328.

1044 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1044 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×#3193C211yesmaximal, characteristic, complemented
2C13×#2435C211yesmaximal, characteristic, complemented
3C13×#2433C211yesmaximal, characteristic
4C13×#1783C211yesmaximal, characteristic, complemented
5C13×#1508C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic, complemented
7C13×#1297C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C2×C13×#127—21no—
10C2×C13×#124—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×#121C2211yescharacteristic
13C2×C13×#120—22no—
14C13×#484—21no—
15C13×#480—21no—
16C13×#468—22no—
17C13×#450—21no—
18C13×#448—21no—
19C2×C13×#100—22no—
20C13×#407C2211yescharacteristic
21C13×#407C2211yescharacteristic
22C13×#394—22no—
23C13×#392—22no—
24C13×#390—21no—
25C13×#390—21no—
26C13×#379—22no—
27C4×C13×C22⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4C2211yescharacteristic
29C13×#328—22no—
30C13×#327—22no—
31C25×C13D412yes—
32C22×Q8×C13D411yescharacteristic, complemented
33C22×D4×C13—21no—
34C22×D4×C13—24no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13—44no—
42C22×D4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C2×C13×SD16—22no—
45C2×C13×M16—21no—
46C2×C13×M16D412yescomplemented
47C13×#127—44no—
48C13×#124—44no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×#121—21no—
54C13×#121—21no—
55C13×#121—21no—
56C13×#121—21no—
57C13×#120—48no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic, complemented
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—24no—
68C2×C42×C13—21no—
69C2×C42×C13—21no—
70C13×#107—22no—
71C13×#103—22no—
72C13×#102—22no—
73C13×#100—44no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×#95D412yes—
79C13×#95D412yescomplemented
80#10329C1311yesmaximal, characteristic, direct product factor, Sylow
81C24×C13—22no—
82C24×C13—22no—
83C24×C13—22no—
84C24×C13—21no—
85C24×C13—44no—
86C24×C13—44no—
87C24×C13—44no—
88C24×C13C2×D411yescharacteristic
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—42no—
92C2×D4×C13—24no—
93C2×D4×C13—24no—
94C2×D4×C13—24no—
95C2×D4×C13—21no—
96C2×D4×C13—21no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—48no—
102C2×D4×C13—44no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13—48no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—84no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—42no—
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C13×SD16—82no—
127C13×M16—42no—
128C13×M16—42no—
129C2×C8×C13—22no—
130C2×C8×C13—41no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C22⋊C4—24no—
138C13×C22⋊C4—48no—
139C13×C22⋊C4—42no—
140C13×C22⋊C4—48no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—84no—
146C42×C13—42no—
147C42×C13—42no—
148#3193C2×C1311yescharacteristic, complemented
149#2435C2×C1311yescharacteristic, complemented
150#2433C2×C1311yescharacteristic
151#1783C2×C1311yescharacteristic, complemented
152#1508C2×C1311yescharacteristic, complemented
153#1507C2×C1311yescharacteristic, complemented
154#1297C2×C1311yescharacteristic, complemented
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—24no—
158C23×C13—24no—
159C23×C13—24no—
160C23×C13—41no—
161C23×C13—44no—
162C23×C13—42no—
163C23×C13—42no—
164C23×C13—42no—
165C23×C13—44no—
166C23×C13—42no—
167C23×C13—42no—
168C23×C13—42no—
169C23×C13—44no—
170C23×C13—44no—
171C23×C13—41no—
172C23×C13—42no—
173C23×C13—82no—
174C23×C13—82no—
175C23×C13—816no—
176C23×C13#12011yescharacteristic
177C23×C13#12011yescharacteristic
178C23×C13#12111yescharacteristic
179Q8×C13—42no—
180Q8×C13—81no—
181D4×C13—44no—
182D4×C13—44no—
183D4×C13—44no—
184D4×C13—44no—
185D4×C13—42no—
186D4×C13—81no—
187D4×C13—816no—
188D4×C13—82no—
189D4×C13—82no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—24no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12111yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12711yescharacteristic
212C8×C13—42no—
213C8×C13—81no—
214C23×D4C22×C1311yescharacteristic
215C2×#127—21no—
216C2×#124—21no—
217C2×C22⋊Q8C22×C1311yescharacteristic
218C2×#121C22×C1311yescharacteristic
219C2×#120—22no—
220#484—21no—
221#480—21no—
222#468—22no—
223#450—21no—
224#448—21no—
225C2×#100—22no—
226#407C22×C1311yescharacteristic
227#407C22×C1311yescharacteristic
228#394—22no—
229#392—22no—
230#390—21no—
231#390—21no—
232#379—22no—
233C4×C22⋊C4C22×C1311yescharacteristic
234C4×C22⋊C4C22×C1311yescharacteristic
235#328—22no—
236#327—22no—
237C22×C13—21no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—44no—
245C22×C13—48no—
246C22×C13—48no—
247C22×C13—44no—
248C22×C13—84no—
249C22×C13—84no—
250C22×C13—84no—
251C22×C13—84no—
252C22×C13—84no—
253C22×C13—82no—
254C22×C13—82no—
255C22×C13—81no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13#39211yescharacteristic
259C22×C13#45312yes—
260C22×C13#45512yes—
261C4×C13—21no—
262C4×C13—21no—
263C4×C13—21no—
264C4×C13—44no—
265C4×C13—82no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13—81no—
269C4×C13B(4,𝔽2)12yes—
270C25D4×C1312yes—
271C22×Q8D4×C1311yescharacteristic, complemented
272C22×D4—21no—
273C22×D4—24no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—44no—
281C22×D4D4×C1311yescharacteristic
282C23×C4C23×C1311yescharacteristic
283C2×SD16—22no—
284C2×M16—21no—
285C2×M16D4×C1312yescomplemented
286#127—44no—
287#124—44no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#120—48no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C1311yescharacteristic
299C2×C4⋊C4D4×C1311yescharacteristic, complemented
300C2×C22⋊C4—21no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C42—21no—
308C2×C42—21no—
309#107—22no—
310#103—22no—
311#102—22no—
312#100—44no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317#95D4×C1312yes—
318#95D4×C1312yescomplemented
319C2×C13—22no—
320C2×C13—22no—
321C2×C13—41no—
322C2×C13—84no—
323C2×C13—161no—
324C2×C13#200211yescharacteristic
325C2×C13#200411yescharacteristic
326C2×C13#202111yescharacteristic
327C24—22no—
328C24—22no—
329C24—22no—
330C24—21no—
331C24—44no—
332C24—44no—
333C24—44no—
334C24C2×D4×C1311yescharacteristic
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C2×D4—24no—
339C2×D4—24no—
340C2×D4—24no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—48no—
348C2×D4—44no—
349C2×D4—44no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—48no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—84no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—42no—
366C22×C4C2×D4×C1311yescharacteristic
367C22×C4C2×D4×C1311yescharacteristic
368C22×C4C2×D4×C1311yescharacteristic
369C22×C4C2×D4×C1311yescharacteristic
370C22×C4C2×D4×C1311yescharacteristic
371C22×C4C13×#4111yescharacteristic
372SD16—82no—
373M16—42no—
374M16—42no—
375C2×C8—22no—
376C2×C8—41no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C22⋊C4—24no—
384C22⋊C4—48no—
385C22⋊C4—48no—
386C22⋊C4—42no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—84no—
392C42—42no—
393C42—42no—
394C13#1032911yescharacteristic, direct product factor, Sylow
395C23—22no—
396C23—22no—
397C23—24no—
398C23—24no—
399C23—24no—
400C23—41no—
401C23—44no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—44no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—44no—
410C23—44no—
411C23—41no—
412C23—42no—
413C23—82no—
414C23—82no—
415C23—816no—
416C23C13×#12011yescharacteristic
417C23C13×#12011yescharacteristic
418C23C13×#12111yescharacteristic
419Q8—42no—
420Q8—81no—
421D4—44no—
422D4—44no—
423D4—44no—
424D4—44no—
425D4—42no—
426D4—81no—
427D4—816no—
428D4—82no—
429D4—82no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4C13×#12011yescharacteristic
449C2×C4C13×#12111yescharacteristic
450C2×C4C13×#12111yescharacteristic
451C2×C4C13×#12711yescharacteristic
452C8—42no—
453C8—81no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—44no—
462C22—48no—
463C22—48no—
464C22—44no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—84no—
470C22—82no—
471C22—82no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22C13×#39211yescharacteristic
476C22C13×#45312yes—
477C22C13×#45512yes—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—82no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4C13×B(4,𝔽2)12yes—
487C2—22no—
488C2—22no—
489C2—41no—
490C2—84no—
491C2—161no—
492C2C13×#200211yescharacteristic
493C2C13×#200411yescharacteristic
494C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2433C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3193C2semidirect
2. C13×#2435C2semidirect
4. C13×#1783C2semidirect
5. C13×#1508C2semidirect
6. C13×#1507C2semidirect
7. C13×#1297C2semidirect
32. C22×Q8×C13D4semidirect
46. C2×C13×M16D4semidirect
60. C2×C13×C4⋊C4D4semidirect
79. C13×#95D4semidirect
80. #10329C13direct (N × H)
148. #3193C2×C13semidirect
149. #2435C2×C13semidirect
151. #1783C2×C13semidirect
152. #1508C2×C13semidirect
153. #1507C2×C13semidirect
154. #1297C2×C13semidirect
271. C22×Q8D4×C13semidirect
285. C2×M16D4×C13semidirect
299. C2×C4⋊C4D4×C13semidirect
318. #95D4×C13semidirect
394. C13#10329direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31932
C13×#24352
C13×#24332
C13×#17832
C13×#15082
C13×#15072
C13×#12972
#1032913