Finite Group Databasebeta

← C13×#9934 #15696273

Subgroups — C13×#9934 #15696273

Order 3328.

808 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3007C211yesmaximal, characteristic, complemented
3C13×#2615C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1789C211yesmaximal, characteristic, complemented
6C13×#1507C211yesmaximal, characteristic, complemented
7C13×#1305C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#121—21no—
12C2×C13×#121C2211yescharacteristic
13C13×#484—21no—
14C13×#480—21no—
15C13×#468—22no—
16C13×#452—22no—
17C13×#451—21no—
18C13×#450—21no—
19C13×#450—21no—
20C13×#448—21no—
21C2×C13×#104—22no—
22C13×#417—21no—
23C13×#407C2211yescharacteristic
24C13×#407C2211yescharacteristic
25C13×#393—21no—
26C13×#392—21no—
27C13×#392—22no—
28C13×#380—21no—
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C13×#342—22no—
32C13×#327—22no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—44no—
38C22×Q8×C13D411yescharacteristic
39C22×Q8×C13D411yescharacteristic, complemented
40C22×D4×C13—21no—
41C22×D4×C13—22no—
42C22×D4×C13—21no—
43C22×D4×C13D411yescharacteristic
44C22×D4×C13D411yescharacteristic
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C13×#137—44no—
48C2×C13×Q16—22no—
49C2×C13×SD16—22no—
50C2×C13×SD16—22no—
51C2×C13×M16—21no—
52C2×C13×M16D412yescomplemented
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C13×#121—21no—
58C13×#121—21no—
59C13×#121—21no—
60C13×#121—21no—
61C13×#121—44no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4D411yescharacteristic, complemented
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4D412yes—
72C2×C42×C13—21no—
73C13×#107—22no—
74C13×#104—44no—
75C13×#103—22no—
76C13×#103—22no—
77C13×#102—22no—
78C13×#102—22no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8D412yescomplemented
83C13×#95—22no—
84C13×#95—21no—
85C13×#95—21no—
86#9934C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—21no—
88C24×C13—21no—
89C24×C13C2×D411yescharacteristic
90C13×#41—24no—
91C13×#41—24no—
92C13×#41—42no—
93C13×#41—42no—
94C13×#41—42no—
95C13×#41—42no—
96C13×#41—42no—
97C13×#41—42no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—42no—
103C2×Q8×C13—42no—
104C2×D4×C13—21no—
105C2×D4×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—21no—
108C2×D4×C13—42no—
109C2×D4×C13—42no—
110C2×D4×C13—42no—
111C2×D4×C13—42no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—44no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—82no—
118C2×D4×C13—82no—
119C2×D4×C13—82no—
120C22×C4×C13—24no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C13×Q16—44no—
138C13×SD16—44no—
139C13×SD16—82no—
140C13×M16—42no—
141C13×M16—42no—
142C2×C8×C13—22no—
143C2×C8×C13—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—42no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4—41no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—44no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—42no—
159C13×C22⋊C4—82no—
160C42×C13—42no—
161#3193C2×C1311yescharacteristic, complemented
162#3007C2×C1311yescharacteristic, complemented
163#2615C2×C1311yescharacteristic
164#1996C2×C1311yescharacteristic, complemented
165#1789C2×C1311yescharacteristic, complemented
166#1507C2×C1311yescharacteristic, complemented
167#1305C2×C1311yescharacteristic, complemented
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—22no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—42no—
177C23×C13—42no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13#12011yescharacteristic
185C23×C13#12111yescharacteristic
186C23×C13#12711yescharacteristic
187Q8×C13—22no—
188Q8×C13—22no—
189Q8×C13—41no—
190Q8×C13—41no—
191Q8×C13—42no—
192Q8×C13—42no—
193D4×C13—22no—
194D4×C13—22no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—44no—
198D4×C13—44no—
199D4×C13—42no—
200D4×C13—81no—
201D4×C13—82no—
202D4×C13—82no—
203D4×C13—88no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—44no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—44no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—42no—
223C2×C4×C13—81no—
224C2×C4×C13—81no—
225C2×C4×C13—81no—
226C2×C4×C13—81no—
227C2×C4×C13#12011yescharacteristic
228C2×C4×C13#12011yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C8×C13—42no—
232C8×C13—42no—
233C22×#41C22×C1311yescharacteristic
234C2×#137—21no—
235C2×C22⋊Q8C22×C1311yescharacteristic
236C2×#121—21no—
237C2×#121C22×C1311yescharacteristic
238#484—21no—
239#480—21no—
240#468—22no—
241#452—22no—
242#451—21no—
243#450—21no—
244#450—21no—
245#448—21no—
246C2×#104—22no—
247#417—21no—
248#407C22×C1311yescharacteristic
249#407C22×C1311yescharacteristic
250#393—21no—
251#392—21no—
252#392—22no—
253#380—21no—
254#380C22×C1311yescharacteristic
255C4×C22⋊C4C22×C1311yescharacteristic
256#342—22no—
257#327—22no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13—82no—
274C22×C13—82no—
275C22×C13—81no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13—81no—
279C22×C13—81no—
280C22×C13#39211yescharacteristic
281C22×C13#45511yescharacteristic
282C22×C13#45611yescharacteristic
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—42no—
287C4×C13—82no—
288C4×C13—82no—
289C4×C13—81no—
290C4×C13—81no—
291C4×C13—81no—
292C4×C13B(4,𝔽2)12yes—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—44no—
298C22×Q8D4×C1311yescharacteristic
299C22×Q8D4×C1311yescharacteristic, complemented
300C22×D4—21no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4D4×C1311yescharacteristic
304C22×D4D4×C1311yescharacteristic
305C23×C4—21no—
306C23×C4C23×C1311yescharacteristic
307#137—44no—
308C2×Q16—22no—
309C2×SD16—22no—
310C2×SD16—22no—
311C2×M16—21no—
312C2×M16D4×C1312yescomplemented
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—44no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C1311yescharacteristic
325C2×C4⋊C4D4×C1311yescharacteristic, complemented
326C2×C22⋊C4—21no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4D4×C1312yes—
332C2×C42—21no—
333#107—22no—
334#104—44no—
335#103—22no—
336#103—22no—
337#102—22no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8D4×C1312yescomplemented
343#95—22no—
344#95—21no—
345#95—21no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—41no—
349C2×C13—41no—
350C2×C13—82no—
351C2×C13—161no—
352C2×C13#200711yescharacteristic
353C2×C13#200811yescharacteristic
354C2×C13#202111yescharacteristic
355C24—21no—
356C24—21no—
357C24C2×D4×C1311yescharacteristic
358#41—24no—
359#41—24no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—44no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—82no—
386C2×D4—82no—
387C2×D4—82no—
388C22×C4—24no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4C2×D4×C1311yescharacteristic
400C22×C4C2×D4×C1311yescharacteristic
401C22×C4C2×D4×C1311yescharacteristic
402C22×C4C2×D4×C1311yescharacteristic
403C22×C4C2×D4×C1311yescharacteristic
404C22×C4C13×#4111yescharacteristic
405Q16—44no—
406SD16—44no—
407SD16—82no—
408M16—42no—
409M16—42no—
410C2×C8—22no—
411C2×C8—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—42no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—22no—
420C22⋊C4—44no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—42no—
427C22⋊C4—82no—
428C42—42no—
429C13#993411yescharacteristic, direct product factor, Sylow
430C23—21no—
431C23—21no—
432C23—22no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—42no—
439C23—42no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23C13×#12011yescharacteristic
447C23C13×#12111yescharacteristic
448C23C13×#12711yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—41no—
452Q8—41no—
453Q8—42no—
454Q8—42no—
455D4—22no—
456D4—22no—
457D4—41no—
458D4—41no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—81no—
463D4—82no—
464D4—82no—
465D4—88no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4C13×#12011yescharacteristic
490C2×C4C13×#12011yescharacteristic
491C2×C4C13×#12111yescharacteristic
492C2×C4C13×#12111yescharacteristic
493C8—42no—
494C8—42no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—82no—
511C22—82no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C13×#39211yescharacteristic
518C22C13×#45511yescharacteristic
519C22C13×#45611yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—82no—
525C4—82no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4C13×B(4,𝔽2)12yes—
530C2—21no—
531C2—21no—
532C2—41no—
533C2—41no—
534C2—82no—
535C2—161no—
536C2C13×#200711yescharacteristic
537C2C13×#200811yescharacteristic
538C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2615C2
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×#3007C2semidirect
4. C13×#1996C2semidirect
5. C13×#1789C2semidirect
6. C13×#1507C2semidirect
7. C13×#1305C2semidirect
39. C22×Q8×C13D4semidirect
52. C2×C13×M16D4semidirect
65. C2×C13×C4⋊C4D4semidirect
82. C13×C22⋊C8D4semidirect
86. #9934C13direct (N × H)
161. #3193C2×C13semidirect
162. #3007C2×C13semidirect
164. #1996C2×C13semidirect
165. #1789C2×C13semidirect
166. #1507C2×C13semidirect
167. #1305C2×C13semidirect
299. C22×Q8D4×C13semidirect
312. C2×M16D4×C13semidirect
325. C2×C4⋊C4D4×C13semidirect
342. C22⋊C8D4×C13semidirect
429. C13#9934direct (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×#30072
C13×#26152
C13×#19962
C13×#17892
C13×#15072
C13×#13052
#993413