Finite Group Databasebeta

← C13×#33888 #15720227

Subgroups — C13×#33888 #15720227

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3341C211yesmaximal, characteristic, complemented
2C13×#3285C211yesmaximal, characteristic, complemented
3C13×#2243C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2234C211yesmaximal, characteristic, complemented
6C13×#2225C211yesmaximal, characteristic, complemented
7C13×#2218C211yesmaximal, characteristic, complemented
8C13×#2217C211yesmaximal, characteristic, complemented
9C13×#2210C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic, complemented
11C13×#2185C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2141C211yesmaximal, characteristic, complemented
15C13×#2138C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C13×#555—21no—
19C13×#548—21no—
20C2×C13×SD32C2211yescharacteristic
21C2×C13×SD32C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C2×C13×M32C2211yescharacteristic
24C22×C13×C16C2211yescharacteristic
25C13×#500C2211yescharacteristic
26C13×#495C2211yescharacteristic
27C13×#482—21no—
28C13×#482—21no—
29C13×#476—21no—
30C13×#467C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic
33C13×#466C2211yescharacteristic
34C13×#464—21no—
35C13×#452—21no—
36C13×#448—21no—
37C4×C13×Q16C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic
41C13×#427C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×#41—21no—
60C22×Q8×C13—21no—
61C13×#135—22no—
62C13×#135—41no—
63C2×C13×Q16—22no—
64C2×C13×Q16—21no—
65C2×C13×Q16—41no—
66C2×C13×Q16C2311yescharacteristic
67C2×C13×Q16C2311yescharacteristic
68C2×C13×SD16—21no—
69C2×C13×SD16—21no—
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×C4⋊Q8—21no—
75C13×#124—21no—
76C13×#124—41no—
77C13×#124—41no—
78C13×#124—41no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—41no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—21no—
84C13×#121—41no—
85C13×#121—41no—
86C4×Q8×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13—41no—
89C4×D4×C13D411yescharacteristic
90C13×#117—21no—
91C13×#117—21no—
92C13×#117—41no—
93C13×SD32—22no—
94C13×SD32—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×#103—21no—
112C13×#102—21no—
113C13×#102—21no—
114C13×#102—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33888C1311yesmaximal, characteristic, direct product factor, Sylow
120C13×#41—42no—
121C13×#41—81no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—42no—
125C2×Q8×C13—41no—
126C2×Q8×C13—41no—
127C2×Q8×C13—81no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13D811yescharacteristic
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C13×Q16—21no—
141C13×Q16—21no—
142C13×Q16—21no—
143C13×Q16—42no—
144C13×Q16#4112yes—
145C13×SD16—42no—
146C13×SD16—81no—
147C13×D8—21no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C2×D411yescharacteristic
156C2×C8×C13C2×D411yescharacteristic
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2411yescharacteristic
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C4⋊C4D811yescharacteristic
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4—41no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—41no—
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4D811yescharacteristic
177C13×C22⋊C4D811yescharacteristic
178C42×C13—41no—
179C42×C13—41no—
180C42×C13—41no—
181C42×C13C2×D411yescharacteristic
182C13×C16—21no—
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186#3341C2×C1311yescharacteristic, complemented
187#3285C2×C1311yescharacteristic, complemented
188#2243C2×C1311yescharacteristic, complemented
189#2237C2×C1311yescharacteristic, complemented
190#2234C2×C1311yescharacteristic, complemented
191#2225C2×C1311yescharacteristic, complemented
192#2218C2×C1311yescharacteristic, complemented
193#2217C2×C1311yescharacteristic, complemented
194#2210C2×C1311yescharacteristic, complemented
195#2186C2×C1311yescharacteristic, complemented
196#2185C2×C1311yescharacteristic, complemented
197#2175C2×C1311yescharacteristic, complemented
198#2168C2×C1311yescharacteristic, complemented
199#2141C2×C1311yescharacteristic, complemented
200#2138C2×C1311yescharacteristic, complemented
201C23×C13—41no—
202C23×C13—41no—
203C23×C13C2×D811yescharacteristic
204C23×C13C2×D811yescharacteristic
205Q8×C13—22no—
206Q8×C13—41no—
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—82no—
210Q8×C13—161no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—41no—
216D4×C13—82no—
217D4×C13—82no—
218D4×C13—161no—
219D4×C13—161no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—82no—
231C2×C4×C13—82no—
232C2×C4×C13—82no—
233C2×C4×C13C2×D811yescharacteristic
234C2×C4×C13C2×D811yescharacteristic
235C2×C4×C13C2×D811yescharacteristic
236C2×C4×C13C2×D811yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C8×C13—21no—
239C8×C13—21no—
240C8×C13—21no—
241C8×C13C2×#4111yescharacteristic
242C8×C13H(5,𝔽2)11yescharacteristic
243C2×#135C22×C1311yescharacteristic
244C22×Q16C22×C1311yescharacteristic
245#555—21no—
246#548—21no—
247C2×SD32C22×C1311yescharacteristic
248C2×SD32C22×C1311yescharacteristic
249C2×D16C22×C1311yescharacteristic
250C2×M32C22×C1311yescharacteristic
251C22×C16C22×C1311yescharacteristic
252#500C22×C1311yescharacteristic
253#495C22×C1311yescharacteristic
254#482—21no—
255#482—21no—
256#476—21no—
257#467C22×C1311yescharacteristic
258#466C22×C1311yescharacteristic
259#466C22×C1311yescharacteristic
260#466C22×C1311yescharacteristic
261#464—21no—
262#452—21no—
263#448—21no—
264C4×Q16C22×C1311yescharacteristic
265C4×D8C22×C1311yescharacteristic
266C8×D4C22×C1311yescharacteristic
267#427C22×C1311yescharacteristic
268#427C22×C1311yescharacteristic
269#367C22×C1311yescharacteristic
270#367C22×C1311yescharacteristic
271#366C22×C1311yescharacteristic
272C4⋊C16C22×C1311yescharacteristic
273#358C22×C1311yescharacteristic
274#358C22×C1311yescharacteristic
275#358C22×C1311yescharacteristic
276#358C22×C1311yescharacteristic
277#358C22×C1311yescharacteristic
278#358C22×C1311yescharacteristic
279#357C22×C1311yescharacteristic
280#357C22×C1311yescharacteristic
281#357C22×C1311yescharacteristic
282#357C22×C1311yescharacteristic
283C22⋊C16C22×C1311yescharacteristic
284C22⋊C16C22×C1311yescharacteristic
285#346C22×C1311yescharacteristic
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13—81no—
298C22×C13C22×D811yescharacteristic
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—42no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13—81no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13#54611yescharacteristic
310C4×C13#57711yescharacteristic
311C2×#41—21no—
312C22×Q8—21no—
313#135—22no—
314#135—41no—
315C2×Q16—22no—
316C2×Q16—21no—
317C2×Q16—41no—
318C2×Q16C23×C1311yescharacteristic
319C2×Q16C23×C1311yescharacteristic
320C2×SD16—21no—
321C2×SD16—21no—
322C2×D8C23×C1311yescharacteristic
323C2×D8C23×C1311yescharacteristic
324C22×C8C23×C1311yescharacteristic
325C22×C8C23×C1311yescharacteristic
326C4⋊Q8—21no—
327#124—21no—
328#124—41no—
329#124—41no—
330#124—41no—
331C22⋊Q8—21no—
332C22⋊Q8—41no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—41no—
337#121—41no—
338C4×Q8—21no—
339C4×D4—21no—
340C4×D4—41no—
341C4×D4D4×C1311yescharacteristic
342#117—21no—
343#117—21no—
344#117—41no—
345SD32—22no—
346SD32—41no—
347D16—41no—
348M32—41no—
349C2×C16—41no—
350C2×C16C23×C1311yescharacteristic
351C2×C16C23×C1311yescharacteristic
352C2×C16C23×C1311yescharacteristic
353C2×C16C23×C1311yescharacteristic
354#107—21no—
355#107C23×C1311yescharacteristic
356#107C23×C1311yescharacteristic
357#107C23×C1311yescharacteristic
358#107C23×C1311yescharacteristic
359#106—21no—
360#106—21no—
361C4⋊C8D4×C1311yescharacteristic
362#103—21no—
363#103—21no—
364#102—21no—
365#102—21no—
366#102—21no—
367#102—21no—
368C22⋊C8D4×C1311yescharacteristic
369C22⋊C8D4×C1311yescharacteristic
370C4×C8C23×C1311yescharacteristic
371C2×C13—41no—
372C2×C13—41no—
373C2×C13—161no—
374C2×C13—161no—
375C2×C13#329411yescharacteristic
376C2×C13#341411yescharacteristic
377C2×C13#341611yescharacteristic
378#41—42no—
379#41—81no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—81no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4C13×D811yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4C2×D4×C1311yescharacteristic
397C22×C4C2×D4×C1311yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—21no—
401Q16—42no—
402Q16C13×#4112yes—
403SD16—42no—
404SD16—81no—
405D8—21no—
406D8—21no—
407D8—21no—
408D8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×D4×C1311yescharacteristic
414C2×C8C2×D4×C1311yescharacteristic
415C2×C8C2×D4×C1311yescharacteristic
416C2×C8C24×C1311yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4C13×D811yescharacteristic
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4C13×D811yescharacteristic
435C22⋊C4C13×D811yescharacteristic
436C42—41no—
437C42—41no—
438C42—41no—
439C42C2×D4×C1311yescharacteristic
440C16—21no—
441C16—21no—
442C16—21no—
443C16—21no—
444C13#3388811yescharacteristic, direct product factor, Sylow
445C23—41no—
446C23—41no—
447C23C2×C13×D811yescharacteristic
448C23C2×C13×D811yescharacteristic
449Q8—22no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453Q8—82no—
454Q8—161no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—82no—
461D4—82no—
462D4—161no—
463D4—161no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4C2×C13×D811yescharacteristic
478C2×C4C2×C13×D811yescharacteristic
479C2×C4C2×C13×D811yescharacteristic
480C2×C4C2×C13×D811yescharacteristic
481C2×C4C22×D4×C1311yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×C13×#4111yescharacteristic
486C8C13×H(5,𝔽2)11yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C22×C13×D811yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4C13×#54611yescharacteristic
511C4C13×#57711yescharacteristic
512C2—41no—
513C2—41no—
514C2—161no—
515C2—161no—
516C2C13×#329411yescharacteristic
517C2C13×#341411yescharacteristic
518C2C13×#341611yescharacteristic
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×#3341C2semidirect
2. C13×#3285C2semidirect
3. C13×#2243C2semidirect
4. C13×#2237C2semidirect
5. C13×#2234C2semidirect
6. C13×#2225C2semidirect
7. C13×#2218C2semidirect
8. C13×#2217C2semidirect
9. C13×#2210C2semidirect
10. C13×#2186C2semidirect
11. C13×#2185C2semidirect
12. C13×#2175C2semidirect
13. C13×#2168C2semidirect
14. C13×#2141C2semidirect
15. C13×#2138C2semidirect
119. #33888C13direct (N × H)
186. #3341C2×C13semidirect
187. #3285C2×C13semidirect
188. #2243C2×C13semidirect
189. #2237C2×C13semidirect
190. #2234C2×C13semidirect
191. #2225C2×C13semidirect
192. #2218C2×C13semidirect
193. #2217C2×C13semidirect
194. #2210C2×C13semidirect
195. #2186C2×C13semidirect
196. #2185C2×C13semidirect
197. #2175C2×C13semidirect
198. #2168C2×C13semidirect
199. #2141C2×C13semidirect
200. #2138C2×C13semidirect
444. C13#33888direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33412
C13×#32852
C13×#22432
C13×#22372
C13×#22342
C13×#22252
C13×#22182
C13×#22172
C13×#22102
C13×#21862
C13×#21852
C13×#21752
C13×#21682
C13×#21412
C13×#21382
#3388813