Finite Group Databasebeta

← C13×#33876 #15720215

Subgroups — C13×#33876 #15720215

Order 3328.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3339C211yesmaximal, characteristic, complemented
2C13×#3287C211yesmaximal, characteristic, complemented
3C13×#2244C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2232C211yesmaximal, characteristic, complemented
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2218C211yesmaximal, characteristic, complemented
8C13×#2215C211yesmaximal, characteristic, complemented
9C13×#2206C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic, complemented
11C13×#2186C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2139C211yesmaximal, characteristic, complemented
15C13×#2138C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C13×#553—21no—
19C13×#550—21no—
20C2×C13×SD32C2211yescharacteristic
21C2×C13×D16C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C22×C13×C16C2211yescharacteristic
25C13×#499C2211yescharacteristic
26C13×#493C2211yescharacteristic
27C13×#482—21no—
28C13×#481—21no—
29C13×#478—21no—
30C13×#466C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C13×#466C2211yescharacteristic
34C13×#460—21no—
35C13×#449—21no—
36C13×#449—21no—
37C4×C13×Q16C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic
41C2×C13×#107C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×#41—21no—
60C2×C13×#41—21no—
61C13×#135—22no—
62C13×#135—22no—
63C13×#135—41no—
64C13×#135—41no—
65C2×C13×Q16C2311yescharacteristic
66C2×C13×SD16—21no—
67C2×C13×SD16—21no—
68C2×C13×D8—21no—
69C2×C13×D8C2311yescharacteristic
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×#127—21no—
75C13×#127—41no—
76C13×#126—41no—
77C13×#125—21no—
78C13×#123—41no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—41no—
84C13×#121—41no—
85C13×#121—41no—
86C4×Q8×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13—41no—
89C4×D4×C13—41no—
90C4×D4×C13D411yescharacteristic
91C13×#117—21no—
92C2×C13×C4⋊C4—21no—
93C13×SD32—22no—
94C13×D16—41no—
95C13×D16—41no—
96C13×M32—41no—
97C2×C13×C16—41no—
98C2×C13×C16C2311yescharacteristic
99C2×C13×C16C2311yescharacteristic
100C2×C13×C16C2311yescharacteristic
101C2×C13×C16C2311yescharacteristic
102C13×#107—21no—
103C13×#107C2311yescharacteristic
104C13×#107C2311yescharacteristic
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#106—21no—
108C13×#106—21no—
109C13×C4⋊C8D411yescharacteristic
110C13×#103—21no—
111C13×#102—21no—
112C13×#102—21no—
113C13×#102—21no—
114C13×#102—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33876C1311yesmaximal, characteristic, direct product factor, Sylow
120C13×#41—42no—
121C13×#41—42no—
122C13×#41—81no—
123C13×#41—81no—
124C2×Q8×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13D811yescharacteristic
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C13×Q16—21no—
144C13×Q16#4112yes—
145C13×SD16—42no—
146C13×SD16—42no—
147C13×D8—21no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—21no—
151C13×D8—21no—
152C13×D8—21no—
153C13×D8—81no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2411yescharacteristic
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4—41no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C4⋊C4D811yescharacteristic
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4D811yescharacteristic
178C13×C22⋊C4D811yescharacteristic
179C42×C13—41no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C13×C16—21no—
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186#3339C2×C1311yescharacteristic, complemented
187#3287C2×C1311yescharacteristic, complemented
188#2244C2×C1311yescharacteristic, complemented
189#2234C2×C1311yescharacteristic, complemented
190#2232C2×C1311yescharacteristic, complemented
191#2229C2×C1311yescharacteristic, complemented
192#2218C2×C1311yescharacteristic, complemented
193#2215C2×C1311yescharacteristic, complemented
194#2206C2×C1311yescharacteristic, complemented
195#2186C2×C1311yescharacteristic, complemented
196#2186C2×C1311yescharacteristic, complemented
197#2175C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic, complemented
199#2139C2×C1311yescharacteristic, complemented
200#2138C2×C1311yescharacteristic, complemented
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13C2×D811yescharacteristic
205C23×C13C2×D811yescharacteristic
206Q8×C13—22no—
207Q8×C13—41no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—41no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—82no—
216D4×C13—82no—
217D4×C13—82no—
218D4×C13—82no—
219D4×C13—161no—
220D4×C13—161no—
221D4×C13—161no—
222D4×C13—161no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—82no—
233C2×C4×C13—82no—
234C2×C4×C13—161no—
235C2×C4×C13—161no—
236C2×C4×C13C2×D811yescharacteristic
237C2×C4×C13C2×D811yescharacteristic
238C2×C4×C13C2×D811yescharacteristic
239C2×C4×C13C2×D811yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135C22×C1311yescharacteristic
247C2×#135C22×C1311yescharacteristic
248#553—21no—
249#550—21no—
250C2×SD32C22×C1311yescharacteristic
251C2×D16C22×C1311yescharacteristic
252C2×D16C22×C1311yescharacteristic
253C2×M32C22×C1311yescharacteristic
254C22×C16C22×C1311yescharacteristic
255#499C22×C1311yescharacteristic
256#493C22×C1311yescharacteristic
257#482—21no—
258#481—21no—
259#478—21no—
260#466C22×C1311yescharacteristic
261#466C22×C1311yescharacteristic
262#466C22×C1311yescharacteristic
263#466C22×C1311yescharacteristic
264#460—21no—
265#449—21no—
266#449—21no—
267C4×Q16C22×C1311yescharacteristic
268C4×D8C22×C1311yescharacteristic
269C8×D4C22×C1311yescharacteristic
270#427C22×C1311yescharacteristic
271C2×#107C22×C1311yescharacteristic
272#367C22×C1311yescharacteristic
273#366C22×C1311yescharacteristic
274#366C22×C1311yescharacteristic
275C4⋊C16C22×C1311yescharacteristic
276#358C22×C1311yescharacteristic
277#358C22×C1311yescharacteristic
278#358C22×C1311yescharacteristic
279#357C22×C1311yescharacteristic
280#357C22×C1311yescharacteristic
281#357C22×C1311yescharacteristic
282#357C22×C1311yescharacteristic
283#357C22×C1311yescharacteristic
284#357C22×C1311yescharacteristic
285#357C22×C1311yescharacteristic
286C22⋊C16C22×C1311yescharacteristic
287C22⋊C16C22×C1311yescharacteristic
288#346C22×C1311yescharacteristic
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13—81no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13C22×D811yescharacteristic
305C4×C13—21no—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—42no—
310C4×C13—81no—
311C4×C13—81no—
312C4×C13—81no—
313C4×C13—81no—
314C4×C13#54611yescharacteristic
315C4×C13#57711yescharacteristic
316C2×#41—21no—
317C2×#41—21no—
318#135—22no—
319#135—22no—
320#135—41no—
321#135—41no—
322C2×Q16C23×C1311yescharacteristic
323C2×SD16—21no—
324C2×SD16—21no—
325C2×D8—21no—
326C2×D8C23×C1311yescharacteristic
327C2×D8C23×C1311yescharacteristic
328C2×D8C23×C1311yescharacteristic
329C22×C8C23×C1311yescharacteristic
330C22×C8C23×C1311yescharacteristic
331#127—21no—
332#127—41no—
333#126—41no—
334#125—21no—
335#123—41no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—41no—
341#121—41no—
342#121—41no—
343C4×Q8—21no—
344C4×D4—21no—
345C4×D4—41no—
346C4×D4—41no—
347C4×D4D4×C1311yescharacteristic
348#117—21no—
349C2×C4⋊C4—21no—
350SD32—22no—
351D16—41no—
352D16—41no—
353M32—41no—
354C2×C16—41no—
355C2×C16C23×C1311yescharacteristic
356C2×C16C23×C1311yescharacteristic
357C2×C16C23×C1311yescharacteristic
358C2×C16C23×C1311yescharacteristic
359#107—21no—
360#107C23×C1311yescharacteristic
361#107C23×C1311yescharacteristic
362#107C23×C1311yescharacteristic
363#107C23×C1311yescharacteristic
364#106—21no—
365#106—21no—
366C4⋊C8D4×C1311yescharacteristic
367#103—21no—
368#102—21no—
369#102—21no—
370#102—21no—
371#102—21no—
372#102—21no—
373C22⋊C8D4×C1311yescharacteristic
374C22⋊C8D4×C1311yescharacteristic
375C4×C8C23×C1311yescharacteristic
376C2×C13—41no—
377C2×C13—41no—
378C2×C13—161no—
379C2×C13—161no—
380C2×C13—161no—
381C2×C13#329411yescharacteristic
382C2×C13#341411yescharacteristic
383C2×C13#341511yescharacteristic
384#41—42no—
385#41—42no—
386#41—81no—
387#41—81no—
388C2×Q8—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4C13×D811yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C1311yescharacteristic
406C22×C4C2×D4×C1311yescharacteristic
407Q16—21no—
408Q16C13×#4112yes—
409SD16—42no—
410SD16—42no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—81no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D4×C1311yescharacteristic
423C2×C8C2×D4×C1311yescharacteristic
424C2×C8C2×D4×C1311yescharacteristic
425C2×C8C24×C1311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4C13×D811yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4C13×D811yescharacteristic
442C22⋊C4C13×D811yescharacteristic
443C42—41no—
444C42—41no—
445C42C2×D4×C1311yescharacteristic
446C16—21no—
447C16—21no—
448C16—21no—
449C16—21no—
450C13#3387611yescharacteristic, direct product factor, Sylow
451C23—41no—
452C23—41no—
453C23—41no—
454C23C2×C13×D811yescharacteristic
455C23C2×C13×D811yescharacteristic
456Q8—22no—
457Q8—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—82no—
467D4—82no—
468D4—82no—
469D4—161no—
470D4—161no—
471D4—161no—
472D4—161no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—161no—
485C2×C4—161no—
486C2×C4C2×C13×D811yescharacteristic
487C2×C4C2×C13×D811yescharacteristic
488C2×C4C2×C13×D811yescharacteristic
489C2×C4C2×C13×D811yescharacteristic
490C2×C4C22×D4×C1311yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8C2×C13×#4111yescharacteristic
495C8C13×H(5,𝔽2)11yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22C22×C13×D811yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4C13×#54611yescharacteristic
522C4C13×#57711yescharacteristic
523C2—41no—
524C2—41no—
525C2—161no—
526C2—161no—
527C2—161no—
528C2C13×#329411yescharacteristic
529C2C13×#341411yescharacteristic
530C2C13×#341511yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3339C2semidirect
2. C13×#3287C2semidirect
3. C13×#2244C2semidirect
4. C13×#2234C2semidirect
5. C13×#2232C2semidirect
6. C13×#2229C2semidirect
7. C13×#2218C2semidirect
8. C13×#2215C2semidirect
9. C13×#2206C2semidirect
10. C13×#2186C2semidirect
11. C13×#2186C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2139C2semidirect
15. C13×#2138C2semidirect
119. #33876C13direct (N × H)
186. #3339C2×C13semidirect
187. #3287C2×C13semidirect
188. #2244C2×C13semidirect
189. #2234C2×C13semidirect
190. #2232C2×C13semidirect
191. #2229C2×C13semidirect
192. #2218C2×C13semidirect
193. #2215C2×C13semidirect
194. #2206C2×C13semidirect
195. #2186C2×C13semidirect
196. #2186C2×C13semidirect
197. #2175C2×C13semidirect
198. #2168C2×C13semidirect
199. #2139C2×C13semidirect
200. #2138C2×C13semidirect
450. C13#33876direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33392
C13×#32872
C13×#22442
C13×#22342
C13×#22322
C13×#22292
C13×#22182
C13×#22152
C13×#22062
C13×#21862
C13×#21752
C13×#21682
C13×#21392
C13×#21382
#3387613