Finite Group Databasebeta

← C13×#9942 #15696281

Subgroups — C13×#9942 #15696281

Order 3328.

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

normal subgroups only

This group has 894 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×#3007C211yesmaximal, characteristic, complemented
2C13×#2561C211yesmaximal, characteristic, complemented
3C13×#2404C211yesmaximal, characteristic
4C13×#1789C211yesmaximal, characteristic, complemented
5C13×#1511C211yesmaximal, characteristic, complemented
6C13×#1462C211yesmaximal, characteristic, complemented
7C13×#1284C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#120—21no—
12C22×C13×C22⋊C4C2211yescharacteristic
13C13×#452—22no—
14C13×#451—21no—
15C13×#450—21no—
16C2×C13×#104—22no—
17C13×#417—21no—
18C13×#407C2211yescharacteristic
19C13×#407C2211yescharacteristic
20C13×#397—21no—
21C13×#393—21no—
22C13×#393—21no—
23C13×#392—21no—
24C13×#388—22no—
25C13×#386—21no—
26C13×#386—22no—
27C13×#381—21no—
28C13×#381C2211yescharacteristic
29C13×#379—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31C13×#328—22no—
32C13×#323—22no—
33C25×C13D411yescharacteristic
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—44no—
39C22×Q8×C13D411yescharacteristic
40C22×Q8×C13D411yescharacteristic, complemented
41C22×D4×C13—21no—
42C22×D4×C13—22no—
43C22×D4×C13D411yescharacteristic
44C23×C4×C13—21no—
45C23×C4×C13D411yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C13×#137—44no—
48C2×C13×Q16—22no—
49C2×C13×SD16—22no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×#120—44no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4D411yescharacteristic, complemented
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C42×C13D412yescomplemented
73C13×#104—44no—
74C13×#103—22no—
75C13×#102—22no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8D412yescomplemented
80C13×#95—22no—
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—21no—
84C13×#95—21no—
85C13×#95D412yes—
86#9942C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—42no—
92C24×C13—42no—
93C24×C13—42no—
94C24×C13C2×D411yescharacteristic
95C13×#41—24no—
96C13×#41—24no—
97C13×#41—42no—
98C13×#41—42no—
99C13×#41—42no—
100C13×#41—42no—
101C13×#41—42no—
102C13×#41—42no—
103C2×Q8×C13—21no—
104C2×Q8×C13—21no—
105C2×Q8×C13—21no—
106C2×Q8×C13—21no—
107C2×Q8×C13—42no—
108C2×Q8×C13—42no—
109C2×D4×C13—24no—
110C2×D4×C13—21no—
111C2×D4×C13—21no—
112C2×D4×C13—42no—
113C2×D4×C13—42no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—44no—
117C2×D4×C13—44no—
118C2×D4×C13—82no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—42no—
130C22×C4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—42no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13#4111yescharacteristic
139C13×Q16—44no—
140C13×SD16—44no—
141C13×M16—42no—
142C13×M16—42no—
143C2×C8×C13—22no—
144C2×C8×C13—41no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C22⋊C4—44no—
150C13×C22⋊C4—42no—
151C13×C22⋊C4—44no—
152C13×C22⋊C4—42no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—82no—
160C13×C22⋊C4—82no—
161C42×C13—42no—
162#3007C2×C1311yescharacteristic, complemented
163#2561C2×C1311yescharacteristic, complemented
164#2404C2×C1311yescharacteristic
165#1789C2×C1311yescharacteristic, complemented
166#1511C2×C1311yescharacteristic, complemented
167#1462C2×C1311yescharacteristic, complemented
168#1284C2×C1311yescharacteristic, complemented
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13—41no—
176C23×C13—42no—
177C23×C13—41no—
178C23×C13—42no—
179C23×C13—42no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13—88no—
191C23×C13#12011yescharacteristic
192C23×C13#12011yescharacteristic
193C23×C13#12111yescharacteristic
194Q8×C13—22no—
195Q8×C13—22no—
196Q8×C13—41no—
197Q8×C13—41no—
198Q8×C13—42no—
199Q8×C13—81no—
200D4×C13—22no—
201D4×C13—22no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—44no—
205D4×C13—44no—
206D4×C13—88no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—44no—
215C2×C4×C13—44no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—81no—
232C2×C4×C13#12011yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C2×C4×C13#12711yescharacteristic
236C8×C13—42no—
237C8×C13—81no—
238C22×#41C22×C1311yescharacteristic
239C2×#137—21no—
240C2×C22⋊Q8C22×C1311yescharacteristic
241C2×#120—21no—
242C22×C22⋊C4C22×C1311yescharacteristic
243#452—22no—
244#451—21no—
245#450—21no—
246C2×#104—22no—
247#417—21no—
248#407C22×C1311yescharacteristic
249#407C22×C1311yescharacteristic
250#397—21no—
251#393—21no—
252#393—21no—
253#392—21no—
254#388—22no—
255#386—21no—
256#386—22no—
257#381—21no—
258#381C22×C1311yescharacteristic
259#379—21no—
260C4×C22⋊C4C22×C1311yescharacteristic
261#328—22no—
262#323—22no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—44no—
271C22×C13—44no—
272C22×C13—44no—
273C22×C13—44no—
274C22×C13—42no—
275C22×C13—42no—
276C22×C13—82no—
277C22×C13—82no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13—82no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13#39211yescharacteristic
286C22×C13#45512yes—
287C22×C13B(4,𝔽2)12yes—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—42no—
293C4×C13—82no—
294C4×C13—82no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13—81no—
298C25D4×C1311yescharacteristic
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—44no—
304C22×Q8D4×C1311yescharacteristic
305C22×Q8D4×C1311yescharacteristic, complemented
306C22×D4—21no—
307C22×D4—22no—
308C22×D4D4×C1311yescharacteristic
309C23×C4—21no—
310C23×C4D4×C1311yescharacteristic
311C23×C4C23×C1311yescharacteristic
312#137—44no—
313C2×Q16—22no—
314C2×SD16—22no—
315C2×M16—21no—
316C2×M16—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321#120—44no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C1311yescharacteristic, complemented
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C42D4×C1312yescomplemented
338#104—44no—
339#103—22no—
340#102—22no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8D4×C1312yescomplemented
345#95—22no—
346#95—22no—
347#95—22no—
348#95—21no—
349#95—21no—
350#95D4×C1312yes—
351C2×C13—22no—
352C2×C13—22no—
353C2×C13—41no—
354C2×C13—82no—
355C2×C13—82no—
356C2×C13#200411yescharacteristic
357C2×C13#201011yescharacteristic
358C2×C13#202111yescharacteristic
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24C2×D4×C1311yescharacteristic
367#41—24no—
368#41—24no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—42no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—42no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—82no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—42no—
405C22×C4C2×D4×C1311yescharacteristic
406C22×C4C2×D4×C1311yescharacteristic
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C13×#4111yescharacteristic
411Q16—44no—
412SD16—44no—
413M16—42no—
414M16—42no—
415C2×C8—22no—
416C2×C8—41no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C22⋊C4—44no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—44no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—82no—
432C22⋊C4—82no—
433C42—42no—
434C13#994211yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—81no—
455C23—81no—
456C23—88no—
457C23C13×#12011yescharacteristic
458C23C13×#12011yescharacteristic
459C23C13×#12111yescharacteristic
460Q8—22no—
461Q8—22no—
462Q8—41no—
463Q8—41no—
464Q8—42no—
465Q8—81no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—44no—
471D4—44no—
472D4—88no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—81no—
498C2×C4C13×#12011yescharacteristic
499C2×C4C13×#12111yescharacteristic
500C2×C4C13×#12111yescharacteristic
501C2×C4C13×#12711yescharacteristic
502C8—42no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22C13×#39211yescharacteristic
527C22C13×#45512yes—
528C22C13×B(4,𝔽2)12yes—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—82no—
535C4—82no—
536C4—81no—
537C4—81no—
538C4—81no—
539C2—22no—
540C2—22no—
541C2—41no—
542C2—82no—
543C2—82no—
544C2C13×#200411yescharacteristic
545C2C13×#201011yescharacteristic
546C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2404C2
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×#3007C2semidirect
2. C13×#2561C2semidirect
4. C13×#1789C2semidirect
5. C13×#1511C2semidirect
6. C13×#1462C2semidirect
7. C13×#1284C2semidirect
40. C22×Q8×C13D4semidirect
58. C2×C13×C4⋊C4D4semidirect
72. C2×C42×C13D4semidirect
79. C13×C22⋊C8D4semidirect
86. #9942C13direct (N × H)
162. #3007C2×C13semidirect
163. #2561C2×C13semidirect
165. #1789C2×C13semidirect
166. #1511C2×C13semidirect
167. #1462C2×C13semidirect
168. #1284C2×C13semidirect
305. C22×Q8D4×C13semidirect
323. C2×C4⋊C4D4×C13semidirect
337. C2×C42D4×C13semidirect
344. C22⋊C8D4×C13semidirect
434. C13#9942direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30072
C13×#25612
C13×#24042
C13×#17892
C13×#15112
C13×#14622
C13×#12842
#994213