Finite Group Databasebeta

← C13×#33823 #15720162

Subgroups — C13×#33823 #15720162

Order 3328.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3176C211yesmaximal, characteristic, complemented
2C13×#3175C211yesmaximal, characteristic, complemented
3C13×#2229C211yesmaximal, characteristic, complemented
4C13×#2228C211yesmaximal, characteristic, complemented
5C13×#2226C211yesmaximal, characteristic, complemented
6C13×#2224C211yesmaximal, characteristic, complemented
7C13×#2220C211yesmaximal, characteristic, complemented
8C13×#2218C211yesmaximal, characteristic, complemented
9C13×#2217C211yesmaximal, characteristic, complemented
10C13×#2215C211yesmaximal, characteristic, complemented
11C13×#2210C211yesmaximal, characteristic, complemented
12C13×#2210C211yesmaximal, characteristic, complemented
13C13×#2207C211yesmaximal, characteristic, complemented
14C13×#2206C211yesmaximal, characteristic, complemented
15C13×#2151C211yesmaximal, characteristic, complemented
16C13×#542—21no—
17C13×#540—21no—
18C2×C13×SD32C2211yescharacteristic
19C2×C13×SD32C2211yescharacteristic
20C2×C13×D16C2211yescharacteristic
21C2×C13×D16C2211yescharacteristic
22C2×C13×M32C2211yescharacteristic
23C22×C13×C16C2211yescharacteristic
24C13×#500C2211yescharacteristic
25C13×#499C2211yescharacteristic
26C13×#495C2211yescharacteristic
27C13×#493C2211yescharacteristic
28C13×#490—21no—
29C13×#489—21no—
30C13×#469—21no—
31C13×#468—21no—
32C13×#467C2211yescharacteristic
33C13×#466C2211yescharacteristic
34C13×#466C2211yescharacteristic
35C13×#466C2211yescharacteristic
36C13×#442—21no—
37C13×#440—21no—
38C4×C13×Q16C2211yescharacteristic
39C4×C13×D8C2211yescharacteristic
40C4×C13×D8C2211yescharacteristic
41C4×C13×D8C2211yescharacteristic
42C13×#405C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#367C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×C4⋊C16C2211yescharacteristic
48C13×C4⋊C16C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×C4⋊C16C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×#357C2211yescharacteristic
57C13×#357C2211yescharacteristic
58C13×#357C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×D8—21no—
62C2×C13×D8C2311yescharacteristic
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C2×C13×M16D411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×C4⋊Q8—21no—
68C13×#127—21no—
69C13×#126—41no—
70C13×#125—21no—
71C13×#124—21no—
72C13×#124—41no—
73C13×#123—41no—
74C13×#123—41no—
75C13×#123—41no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—41no—
78C13×#121—21no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—41no—
82C13×#121—41no—
83C4×Q8×C13—21no—
84C4×D4×C13—21no—
85C4×D4×C13—21no—
86C4×D4×C13—21no—
87C13×#117D411yescharacteristic
88C13×SD32—41no—
89C13×SD32—41no—
90C13×D16—41no—
91C13×D16—41no—
92C13×M32—41no—
93C2×C13×C16—41no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C2×C13×C16C2311yescharacteristic
97C2×C13×C16C2311yescharacteristic
98C13×#107—21no—
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#107C2311yescharacteristic
102C13×#107C2311yescharacteristic
103C13×#106—21no—
104C13×#103—21no—
105C13×#103—21no—
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×#102—21no—
111C13×#102—21no—
112C13×#97D411yescharacteristic
113C13×#97D411yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#33823C1311yesmaximal, characteristic, direct product factor, Sylow
117C2×Q8×C13—21no—
118C2×Q8×C13—41no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C2×D4×C13—41no—
126C2×D4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C2×D411yescharacteristic
131C13×Q16—21no—
132C13×Q16—21no—
133C13×SD16—42no—
134C13×D8—21no—
135C13×D8—21no—
136C13×D8—21no—
137C13×D8—21no—
138C13×D8—21no—
139C13×D8—21no—
140C13×D8—42no—
141C13×M16—41no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2411yescharacteristic
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C4⋊C4D811yescharacteristic
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4D811yescharacteristic
169C13×C22⋊C4D811yescharacteristic
170C42×C13—41no—
171C42×C13C2×D411yescharacteristic
172C42×C13C2×D411yescharacteristic
173C13×C16—21no—
174C13×C16—21no—
175C13×C16—21no—
176C13×C16—21no—
177#3176C2×C1311yescharacteristic, complemented
178#3175C2×C1311yescharacteristic, complemented
179#2229C2×C1311yescharacteristic, complemented
180#2228C2×C1311yescharacteristic, complemented
181#2226C2×C1311yescharacteristic, complemented
182#2224C2×C1311yescharacteristic, complemented
183#2220C2×C1311yescharacteristic, complemented
184#2218C2×C1311yescharacteristic, complemented
185#2217C2×C1311yescharacteristic, complemented
186#2215C2×C1311yescharacteristic, complemented
187#2210C2×C1311yescharacteristic, complemented
188#2210C2×C1311yescharacteristic, complemented
189#2207C2×C1311yescharacteristic, complemented
190#2206C2×C1311yescharacteristic, complemented
191#2151C2×C1311yescharacteristic, complemented
192C23×C13—41no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13C2×D811yescharacteristic
196Q8×C13—41no—
197Q8×C13—41no—
198Q8×C13—161no—
199D4×C13—41no—
200D4×C13—41no—
201D4×C13—41no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—161no—
206D4×C13—161no—
207D4×C13—161no—
208D4×C13—161no—
209D4×C13—161no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—161no—
218C2×C4×C13—161no—
219C2×C4×C13—161no—
220C2×C4×C13C2×D811yescharacteristic
221C2×C4×C13C2×D811yescharacteristic
222C2×C4×C13C2×D811yescharacteristic
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C8×C13—21no—
227C8×C13—21no—
228C8×C13—21no—
229C8×C13H(5,𝔽2)11yescharacteristic
230C8×C132−1+411yescharacteristic
231#542—21no—
232#540—21no—
233C2×SD32C22×C1311yescharacteristic
234C2×SD32C22×C1311yescharacteristic
235C2×D16C22×C1311yescharacteristic
236C2×D16C22×C1311yescharacteristic
237C2×M32C22×C1311yescharacteristic
238C22×C16C22×C1311yescharacteristic
239#500C22×C1311yescharacteristic
240#499C22×C1311yescharacteristic
241#495C22×C1311yescharacteristic
242#493C22×C1311yescharacteristic
243#490—21no—
244#489—21no—
245#469—21no—
246#468—21no—
247#467C22×C1311yescharacteristic
248#466C22×C1311yescharacteristic
249#466C22×C1311yescharacteristic
250#466C22×C1311yescharacteristic
251#442—21no—
252#440—21no—
253C4×Q16C22×C1311yescharacteristic
254C4×D8C22×C1311yescharacteristic
255C4×D8C22×C1311yescharacteristic
256C4×D8C22×C1311yescharacteristic
257#405C22×C1311yescharacteristic
258#367C22×C1311yescharacteristic
259#367C22×C1311yescharacteristic
260#366C22×C1311yescharacteristic
261#366C22×C1311yescharacteristic
262C4⋊C16C22×C1311yescharacteristic
263C4⋊C16C22×C1311yescharacteristic
264C4⋊C16C22×C1311yescharacteristic
265C4⋊C16C22×C1311yescharacteristic
266#358C22×C1311yescharacteristic
267#358C22×C1311yescharacteristic
268#357C22×C1311yescharacteristic
269#357C22×C1311yescharacteristic
270#357C22×C1311yescharacteristic
271#357C22×C1311yescharacteristic
272#357C22×C1311yescharacteristic
273#357C22×C1311yescharacteristic
274C22×C13—21no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—81no—
278C22×C13—81no—
279C22×C13—81no—
280C22×C13—81no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13C22×D811yescharacteristic
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—81no—
293C4×C13—81no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13#53711yescharacteristic
298C4×C13#57511yescharacteristic
299C2×Q16C23×C1311yescharacteristic
300C2×SD16—21no—
301C2×D8—21no—
302C2×D8C23×C1311yescharacteristic
303C2×D8C23×C1311yescharacteristic
304C2×D8C23×C1311yescharacteristic
305C2×M16D4×C1311yescharacteristic
306C22×C8C23×C1311yescharacteristic
307C4⋊Q8—21no—
308#127—21no—
309#126—41no—
310#125—21no—
311#124—21no—
312#124—41no—
313#123—41no—
314#123—41no—
315#123—41no—
316C22⋊Q8—21no—
317C22⋊Q8—41no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—41no—
322#121—41no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327#117D4×C1311yescharacteristic
328SD32—41no—
329SD32—41no—
330D16—41no—
331D16—41no—
332M32—41no—
333C2×C16—41no—
334C2×C16C23×C1311yescharacteristic
335C2×C16C23×C1311yescharacteristic
336C2×C16C23×C1311yescharacteristic
337C2×C16C23×C1311yescharacteristic
338#107—21no—
339#107C23×C1311yescharacteristic
340#107C23×C1311yescharacteristic
341#107C23×C1311yescharacteristic
342#107C23×C1311yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348#102—21no—
349#102—21no—
350#102—21no—
351#102—21no—
352#97D4×C1311yescharacteristic
353#97D4×C1311yescharacteristic
354C4×C8C23×C1311yescharacteristic
355C4×C8C23×C1311yescharacteristic
356C2×C13—41no—
357C2×C13—161no—
358C2×C13—161no—
359C2×C13—161no—
360C2×C13#324511yescharacteristic
361C2×C13#341511yescharacteristic
362C2×C13#341611yescharacteristic
363C2×Q8—21no—
364C2×Q8—41no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C1311yescharacteristic
377Q16—21no—
378Q16—21no—
379SD16—42no—
380D8—21no—
381D8—21no—
382D8—21no—
383D8—21no—
384D8—21no—
385D8—21no—
386D8—42no—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D4×C1311yescharacteristic
391C2×C8C2×D4×C1311yescharacteristic
392C2×C8C2×D4×C1311yescharacteristic
393C2×C8C24×C1311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C13×D811yescharacteristic
404C4⋊C4C13×D811yescharacteristic
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4C13×D811yescharacteristic
415C22⋊C4C13×D811yescharacteristic
416C42—41no—
417C42C2×D4×C1311yescharacteristic
418C42C2×D4×C1311yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C13#3382311yescharacteristic, direct product factor, Sylow
424C23—41no—
425C23—41no—
426C23—41no—
427C23C2×C13×D811yescharacteristic
428Q8—41no—
429Q8—41no—
430Q8—161no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—161no—
438D4—161no—
439D4—161no—
440D4—161no—
441D4—161no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—161no—
450C2×C4—161no—
451C2×C4—161no—
452C2×C4C2×C13×D811yescharacteristic
453C2×C4C2×C13×D811yescharacteristic
454C2×C4C2×C13×D811yescharacteristic
455C2×C4C2×C13×D811yescharacteristic
456C2×C4C2×C13×D811yescharacteristic
457C2×C4C22×D4×C1311yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8C13×H(5,𝔽2)11yescharacteristic
462C8C13×2−1+411yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22C22×C13×D811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4C13×#53711yescharacteristic
487C4C13×#57511yescharacteristic
488C2—41no—
489C2—161no—
490C2—161no—
491C2—161no—
492C2C13×#324511yescharacteristic
493C2C13×#341511yescharacteristic
494C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3176C2semidirect
2. C13×#3175C2semidirect
3. C13×#2229C2semidirect
4. C13×#2228C2semidirect
5. C13×#2226C2semidirect
6. C13×#2224C2semidirect
7. C13×#2220C2semidirect
8. C13×#2218C2semidirect
9. C13×#2217C2semidirect
10. C13×#2215C2semidirect
11. C13×#2210C2semidirect
12. C13×#2210C2semidirect
13. C13×#2207C2semidirect
14. C13×#2206C2semidirect
15. C13×#2151C2semidirect
116. #33823C13direct (N × H)
177. #3176C2×C13semidirect
178. #3175C2×C13semidirect
179. #2229C2×C13semidirect
180. #2228C2×C13semidirect
181. #2226C2×C13semidirect
182. #2224C2×C13semidirect
183. #2220C2×C13semidirect
184. #2218C2×C13semidirect
185. #2217C2×C13semidirect
186. #2215C2×C13semidirect
187. #2210C2×C13semidirect
188. #2210C2×C13semidirect
189. #2207C2×C13semidirect
190. #2206C2×C13semidirect
191. #2151C2×C13semidirect
423. C13#33823direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31762
C13×#31752
C13×#22292
C13×#22282
C13×#22262
C13×#22242
C13×#22202
C13×#22182
C13×#22172
C13×#22152
C13×#22102
C13×#22072
C13×#22062
C13×#21512
#3382313