Finite Group Databasebeta

← C13×#13351 #15699690

Subgroups — C13×#13351 #15699690

Order 3328.

710 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3200C211yesmaximal, characteristic, complemented
2C13×#3028C211yesmaximal, characteristic, complemented
3C13×#3027C211yesmaximal, characteristic
4C13×#2129C211yesmaximal, characteristic, complemented
5C13×#2128C211yesmaximal, characteristic, complemented
6C13×#1794C211yesmaximal, characteristic, complemented
7C13×#1391C211yesmaximal, characteristic, complemented
8C13×#585C2211yescharacteristic
9C13×#536—21no—
10C13×#536C2211yescharacteristic
11C13×#535—21no—
12C13×#535C2211yescharacteristic
13C13×#485—21no—
14C13×#482—21no—
15C13×#468—21no—
16C13×#465—21no—
17C13×#458—22no—
18C13×#458—22no—
19C13×B(4,𝔽2)—22no—
20C13×B(4,𝔽2)—22no—
21C13×#450—21no—
22C13×#448—21no—
23C13×#421—21no—
24C13×#416—21no—
25C13×#410—21no—
26C13×#410—21no—
27C13×#410C2211yescharacteristic
28C13×#410C2211yescharacteristic
29C13×#410C2211yescharacteristic
30C13×#408C2211yescharacteristic
31C13×#354—22no—
32C13×#353—22no—
33C13×2−1+4—21no—
34C13×2−1+4—41no—
35C13×H(5,𝔽2)—21no—
36C13×H(5,𝔽2)—21no—
37C13×H(5,𝔽2)—41no—
38C13×H(5,𝔽2)D412yes—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—42no—
43C2×C13×#41C2311yescharacteristic
44C22×Q8×C13D411yescharacteristic, complemented
45C22×D4×C13D411yescharacteristic
46C2×C13×SD16—21no—
47C2×C13×SD16—21no—
48C2×C13×M16D411yescharacteristic, complemented
49C22×C8×C13D411yescharacteristic, complemented
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8—41no—
52C13×#127—21no—
53C13×#127—41no—
54C13×#124—21no—
55C13×#124—21no—
56C13×#124—41no—
57C13×#124—41no—
58C13×#123—24no—
59C13×#123—21no—
60C13×#123—21no—
61C13×C22⋊Q8—21no—
62C13×C22⋊Q8—21no—
63C13×C22⋊Q8—42no—
64C13×#121—21no—
65C13×#121—21no—
66C13×#121—42no—
67C13×#120—24no—
68C13×#120—21no—
69C13×#120—21no—
70C13×#117—21no—
71C13×#117—21no—
72C13×#117—21no—
73C13×#117D411yescharacteristic
74C13×#117D411yescharacteristic, complemented
75C13×#107—21no—
76C13×#106—21no—
77C13×#104—42no—
78C13×#103—21no—
79C13×#103—21no—
80C13×#103—41no—
81C13×#102—21no—
82C13×#102—21no—
83C13×#102—41no—
84C13×#99—24no—
85C13×#99—24no—
86C13×#99—21no—
87C13×#99—21no—
88C13×#99—21no—
89C13×#99—21no—
90C13×#99D412yes—
91C13×#99D412yescomplemented
92C13×C22⋊C8—21no—
93C13×C22⋊C8—21no—
94#13351C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—21no—
96C13×#41—22no—
97C13×#41—22no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—42no—
101C13×#41—41no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—41no—
106C13×#41—42no—
107C13×#41—42no—
108C13×#41—42no—
109C13×#41—41no—
110C13×#41—41no—
111C13×#41—41no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—41no—
118C2×Q8×C13—41no—
119C2×Q8×C13—42no—
120C2×Q8×C13#4111yescharacteristic
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—42no—
131C2×D4×C13—42no—
132C2×D4×C13—42no—
133C2×D4×C13—41no—
134C2×D4×C13—44no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C2×D4×C13C2×D411yescharacteristic
138C2×D4×C13C2×D411yescharacteristic
139C2×D4×C13C2×D411yescharacteristic
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—41no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C13×SD16—81no—
148C13×SD16—81no—
149C13×M16—41no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—41no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—44no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C22⋊C4—21no—
162C13×C22⋊C4—21no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—44no—
166C13×C22⋊C4—44no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—41no—
175C42×C13—41no—
176C42×C13—41no—
177#3200C2×C1311yescharacteristic, complemented
178#3028C2×C1311yescharacteristic, complemented
179#3027C2×C1311yescharacteristic
180#2129C2×C1311yescharacteristic, complemented
181#2128C2×C1311yescharacteristic, complemented
182#1794C2×C1311yescharacteristic, complemented
183#1391C2×C1311yescharacteristic, complemented
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—41no—
187C23×C13—42no—
188C23×C13—41no—
189C23×C13—161no—
190C23×C13#12011yescharacteristic
191C23×C13#12011yescharacteristic
192C23×C13#12711yescharacteristic
193Q8×C13—22no—
194Q8×C13—41no—
195Q8×C13—41no—
196Q8×C13—41no—
197Q8×C13—41no—
198Q8×C13—41no—
199Q8×C13—41no—
200Q8×C13—81no—
201D4×C13—22no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—42no—
208D4×C13—42no—
209D4×C13—42no—
210D4×C13—42no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—81no—
215D4×C13—161no—
216D4×C13—161no—
217D4×C13—164no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—81no—
238C2×C4×C13#12011yescharacteristic
239C2×C4×C13#12111yescharacteristic
240C2×C4×C13#12111yescharacteristic
241C2×C4×C13#12111yescharacteristic
242C8×C13—41no—
243C8×C13—41no—
244#585C22×C1311yescharacteristic
245#536—21no—
246#536C22×C1311yescharacteristic
247#535—21no—
248#535C22×C1311yescharacteristic
249#485—21no—
250#482—21no—
251#468—21no—
252#465—21no—
253#458—22no—
254#458—22no—
255B(4,𝔽2)—22no—
256B(4,𝔽2)—22no—
257#450—21no—
258#448—21no—
259#421—21no—
260#416—21no—
261#410—21no—
262#410—21no—
263#410C22×C1311yescharacteristic
264#410C22×C1311yescharacteristic
265#410C22×C1311yescharacteristic
266#408C22×C1311yescharacteristic
267#354—22no—
268#353—22no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—42no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13—84no—
281C22×C13—81no—
282C22×C13—161no—
283C22×C13#39211yescharacteristic
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—42no—
288C4×C13—81no—
289C4×C13—81no—
290C4×C13—82no—
291C4×C13—82no—
292C4×C13—81no—
293C4×C13—161no—
294C4×C13B(4,𝔽2)11yescharacteristic
295C4×C13B(4,𝔽2)11yescharacteristic
2962−1+4—21no—
2972−1+4—41no—
298H(5,𝔽2)—21no—
299H(5,𝔽2)—21no—
300H(5,𝔽2)—41no—
301H(5,𝔽2)D4×C1312yes—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—42no—
306C2×#41C23×C1311yescharacteristic
307C22×Q8D4×C1311yescharacteristic, complemented
308C22×D4D4×C1311yescharacteristic
309C2×SD16—21no—
310C2×SD16—21no—
311C2×M16D4×C1311yescharacteristic, complemented
312C22×C8D4×C1311yescharacteristic, complemented
313C4⋊Q8—21no—
314C4⋊Q8—41no—
315#127—21no—
316#127—41no—
317#124—21no—
318#124—21no—
319#124—41no—
320#124—41no—
321#123—24no—
322#123—21no—
323#123—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—42no—
327#121—21no—
328#121—21no—
329#121—42no—
330#120—24no—
331#120—21no—
332#120—21no—
333#117—21no—
334#117—21no—
335#117—21no—
336#117D4×C1311yescharacteristic
337#117D4×C1311yescharacteristic, complemented
338#107—21no—
339#106—21no—
340#104—42no—
341#103—21no—
342#103—21no—
343#103—41no—
344#102—21no—
345#102—21no—
346#102—41no—
347#99—24no—
348#99—24no—
349#99—21no—
350#99—21no—
351#99—21no—
352#99—21no—
353#99D4×C1312yes—
354#99D4×C1312yescomplemented
355C22⋊C8—21no—
356C22⋊C8—21no—
357C2×C13—21no—
358C2×C13—41no—
359C2×C13—41no—
360C2×C13—41no—
361C2×C13—82no—
362C2×C13—161no—
363C2×C13#202111yescharacteristic
364C24—21no—
365#41—22no—
366#41—22no—
367#41—41no—
368#41—41no—
369#41—42no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—42no—
376#41—42no—
377#41—42no—
378#41—41no—
379#41—41no—
380#41—41no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—42no—
389C2×Q8C13×#4111yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—44no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4C2×D4×C1311yescharacteristic
407C2×D4C2×D4×C1311yescharacteristic
408C2×D4C2×D4×C1311yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4C2×D4×C1311yescharacteristic
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1311yescharacteristic
416SD16—81no—
417SD16—81no—
418M16—41no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—44no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—44no—
435C22⋊C4—44no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C42—21no—
442C42—21no—
443C42—41no—
444C42—41no—
445C42—41no—
446C13#1335111yescharacteristic, direct product factor, Sylow
447C23—22no—
448C23—22no—
449C23—41no—
450C23—42no—
451C23—41no—
452C23—161no—
453C23C13×#12011yescharacteristic
454C23C13×#12011yescharacteristic
455C23C13×#12711yescharacteristic
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—41no—
460Q8—41no—
461Q8—41no—
462Q8—41no—
463Q8—81no—
464D4—22no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—81no—
478D4—161no—
479D4—161no—
480D4—164no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—81no—
501C2×C4C13×#12011yescharacteristic
502C2×C4C13×#12111yescharacteristic
503C2×C4C13×#12111yescharacteristic
504C2×C4C13×#12111yescharacteristic
505C8—41no—
506C8—41no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22—84no—
519C22—81no—
520C22—161no—
521C22C13×#39211yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—42no—
526C4—81no—
527C4—81no—
528C4—82no—
529C4—82no—
530C4—81no—
531C4—161no—
532C4C13×B(4,𝔽2)11yescharacteristic
533C4C13×B(4,𝔽2)11yescharacteristic
534C2—21no—
535C2—41no—
536C2—41no—
537C2—41no—
538C2—82no—
539C2—161no—
540C2C13×#202111yescharacteristic
subgroupG/H
center, socleC2×C13#2021
commutator, Frattini, cosocleC2×#41C23×C13
prime radicalC13×#3027C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3200C2semidirect
2. C13×#3028C2semidirect
4. C13×#2129C2semidirect
5. C13×#2128C2semidirect
6. C13×#1794C2semidirect
7. C13×#1391C2semidirect
44. C22×Q8×C13D4semidirect
48. C2×C13×M16D4semidirect
49. C22×C8×C13D4semidirect
74. C13×#117D4semidirect
91. C13×#99D4semidirect
94. #13351C13direct (N × H)
177. #3200C2×C13semidirect
178. #3028C2×C13semidirect
180. #2129C2×C13semidirect
181. #2128C2×C13semidirect
182. #1794C2×C13semidirect
183. #1391C2×C13semidirect
307. C22×Q8D4×C13semidirect
311. C2×M16D4×C13semidirect
312. C22×C8D4×C13semidirect
337. #117D4×C13semidirect
354. #99D4×C13semidirect
446. C13#13351direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32002
C13×#30282
C13×#30272
C13×#21292
C13×#21282
C13×#17942
C13×#13912
#1335113