Finite Group Databasebeta

← C13×#33944 #15720283

Subgroups — C13×#33944 #15720283

Order 3328.

468 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3393C211yesmaximal, characteristic
2C13×#3383C211yesmaximal, characteristic, complemented
3C13×#2245C211yesmaximal, characteristic, complemented
4C13×#2243C211yesmaximal, characteristic
5C13×#2242C211yesmaximal, characteristic
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2228C211yesmaximal, characteristic
8C13×#2227C211yesmaximal, characteristic, complemented
9C13×#2211C211yesmaximal, characteristic
10C13×#2211C211yesmaximal, characteristic
11C13×#2209C211yesmaximal, characteristic, complemented
12C13×#2183C211yesmaximal, characteristic, complemented
13C13×#2176C211yesmaximal, characteristic, complemented
14C13×#2175C211yesmaximal, characteristic
15C4×C13×Q32C211yesmaximal, characteristic, complemented
16C13×#557—21no—
17C13×#556—21no—
18C2×C13×Q32C2211yescharacteristic
19C2×C13×Q32C2211yescharacteristic
20C2×C13×SD32C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#495C2211yescharacteristic
25C13×#495C2211yescharacteristic
26C13×#494C2211yescharacteristic
27C13×#479—21no—
28C13×#479—21no—
29C13×#475—21no—
30C13×#464—21no—
31C13×#464—21no—
32C13×#461—21no—
33C8×Q8×C13C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C4×C13×Q16C2211yescharacteristic
36C4×C13×Q16C2211yescharacteristic
37C4×C13×Q16C2211yescharacteristic
38C4×C13×Q16C2211yescharacteristic
39C4×C13×D8C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×C4⋊C16C2211yescharacteristic
44C13×C4⋊C16C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×#346C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16—21no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×Q16C2311yescharacteristic
62C2×C13×Q16C2311yescharacteristic
63C2×C13×SD16—21no—
64C2×C13×SD16—21no—
65C2×C13×D8C2311yescharacteristic
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—41no—
69C13×#126—41no—
70C13×#126—41no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—41no—
74C13×#125—41no—
75C13×#124—21no—
76C13×#124—21no—
77C13×C22⋊Q8—41no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13—21no—
81C4×Q8×C13—21no—
82C4×Q8×C13—21no—
83C4×Q8×C13—41no—
84C4×Q8×C13D411yescharacteristic
85C4×D4×C13—21no—
86C13×#117—41no—
87C13×Q32—22no—
88C13×Q32—22no—
89C13×SD32—22no—
90C2×C13×C16C2311yescharacteristic
91C2×C13×C16C2311yescharacteristic
92C2×C13×C16C2311yescharacteristic
93C2×C13×C16C2311yescharacteristic
94C13×#107—21no—
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#106—21no—
100C13×#106—21no—
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×#103—21no—
105C13×#103—21no—
106C13×#103—21no—
107C13×#103—21no—
108C13×#103—21no—
109C13×#102—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33944C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—41no—
118C2×Q8×C13D811yescharacteristic
119C2×D4×C13—21no—
120C22×C4×C13—41no—
121C13×Q16—21no—
122C13×Q16—21no—
123C13×Q16—21no—
124C13×Q16—21no—
125C13×Q16—21no—
126C13×Q16—81no—
127C13×Q16#4112yes—
128C13×SD16—81no—
129C13×SD16—81no—
130C13×D8—21no—
131C13×D8—21no—
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2411yescharacteristic
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4—41no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4D811yescharacteristic
153C13×C4⋊C4D811yescharacteristic
154C13×C4⋊C4D811yescharacteristic
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C42×C13—41no—
161C42×C13—41no—
162C42×C13—41no—
163C42×C13—41no—
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C42×C13C2×D411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C13×C16—21no—
169C13×C16—21no—
170C13×C16—21no—
171C13×C16—21no—
172#3393C2×C1311yescharacteristic
173#3383C2×C1311yescharacteristic, complemented
174#2245C2×C1311yescharacteristic, complemented
175#2243C2×C1311yescharacteristic
176#2242C2×C1311yescharacteristic
177#2229C2×C1311yescharacteristic, complemented
178#2228C2×C1311yescharacteristic
179#2227C2×C1311yescharacteristic, complemented
180#2211C2×C1311yescharacteristic
181#2211C2×C1311yescharacteristic
182#2209C2×C1311yescharacteristic, complemented
183#2183C2×C1311yescharacteristic, complemented
184#2176C2×C1311yescharacteristic, complemented
185#2175C2×C1311yescharacteristic
186C4×Q32C2×C1311yescharacteristic, complemented
187C23×C13—41no—
188Q8×C13—22no—
189Q8×C13—41no—
190Q8×C13—41no—
191Q8×C13—41no—
192Q8×C13—41no—
193Q8×C13—41no—
194Q8×C13—41no—
195Q8×C13—82no—
196D4×C13—41no—
197D4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—82no—
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C8×C13—21no—
214C8×C13—21no—
215C8×C13—21no—
216C8×C13C2×#4111yescharacteristic
217C8×C132−1+411yescharacteristic
218#557—21no—
219#556—21no—
220C2×Q32C22×C1311yescharacteristic
221C2×Q32C22×C1311yescharacteristic
222C2×SD32C22×C1311yescharacteristic
223#500C22×C1311yescharacteristic
224#499C22×C1311yescharacteristic
225#499C22×C1311yescharacteristic
226#495C22×C1311yescharacteristic
227#495C22×C1311yescharacteristic
228#494C22×C1311yescharacteristic
229#479—21no—
230#479—21no—
231#475—21no—
232#464—21no—
233#464—21no—
234#461—21no—
235C8×Q8C22×C1311yescharacteristic
236C4×Q16C22×C1311yescharacteristic
237C4×Q16C22×C1311yescharacteristic
238C4×Q16C22×C1311yescharacteristic
239C4×Q16C22×C1311yescharacteristic
240C4×Q16C22×C1311yescharacteristic
241C4×D8C22×C1311yescharacteristic
242#367C22×C1311yescharacteristic
243#366C22×C1311yescharacteristic
244#366C22×C1311yescharacteristic
245C4⋊C16C22×C1311yescharacteristic
246C4⋊C16C22×C1311yescharacteristic
247C4⋊C16C22×C1311yescharacteristic
248#358C22×C1311yescharacteristic
249#358C22×C1311yescharacteristic
250#358C22×C1311yescharacteristic
251#358C22×C1311yescharacteristic
252#358C22×C1311yescharacteristic
253#358C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255#357C22×C1311yescharacteristic
256#357C22×C1311yescharacteristic
257#357C22×C1311yescharacteristic
258#346C22×C1311yescharacteristic
259#346C22×C1311yescharacteristic
260C4×C16C22×C1311yescharacteristic
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13C22×D811yescharacteristic
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—42no—
272C4×C13—81no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13#54811yescharacteristic
279C4×C13#57711yescharacteristic
280C2×Q16—21no—
281C2×Q16C23×C1311yescharacteristic
282C2×Q16C23×C1311yescharacteristic
283C2×Q16C23×C1311yescharacteristic
284C2×SD16—21no—
285C2×SD16—21no—
286C2×D8C23×C1311yescharacteristic
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—41no—
290#126—41no—
291#126—41no—
292#125—21no—
293#125—21no—
294#125—41no—
295#125—41no—
296#124—21no—
297#124—21no—
298C22⋊Q8—41no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—41no—
305C4×Q8D4×C1311yescharacteristic
306C4×D4—21no—
307#117—41no—
308Q32—22no—
309Q32—22no—
310SD32—22no—
311C2×C16C23×C1311yescharacteristic
312C2×C16C23×C1311yescharacteristic
313C2×C16C23×C1311yescharacteristic
314C2×C16C23×C1311yescharacteristic
315#107—21no—
316#107C23×C1311yescharacteristic
317#107C23×C1311yescharacteristic
318#107C23×C1311yescharacteristic
319#107C23×C1311yescharacteristic
320#106—21no—
321#106—21no—
322C4⋊C8D4×C1311yescharacteristic
323C4⋊C8D4×C1311yescharacteristic
324C4⋊C8D4×C1311yescharacteristic
325#103—21no—
326#103—21no—
327#103—21no—
328#103—21no—
329#103—21no—
330#102—21no—
331C4×C8C23×C1311yescharacteristic
332C4×C8C23×C1311yescharacteristic
333C4×C8C23×C1311yescharacteristic
334C2×C13—161no—
335C2×C13#335811yescharacteristic
336C2×C13#341411yescharacteristic
337C2×C13#341711yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8C13×D811yescharacteristic
343C2×D4—21no—
344C22×C4—41no—
345Q16—21no—
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350Q16—81no—
351Q16C13×#4112yes—
352SD16—81no—
353SD16—81no—
354D8—21no—
355D8—21no—
356C2×C8C2×D4×C1311yescharacteristic
357C2×C8C2×D4×C1311yescharacteristic
358C2×C8C2×D4×C1311yescharacteristic
359C2×C8C24×C1311yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C13×D811yescharacteristic
377C4⋊C4C13×D811yescharacteristic
378C4⋊C4C13×D811yescharacteristic
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C42—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42C2×D4×C1311yescharacteristic
390C42C2×D4×C1311yescharacteristic
391C42C2×D4×C1311yescharacteristic
392C16—21no—
393C16—21no—
394C16—21no—
395C16—21no—
396C13#3394411yescharacteristic, direct product factor, Sylow
397C23—41no—
398Q8—22no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—41no—
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4C2×C13×D811yescharacteristic
417C2×C4C2×C13×D811yescharacteristic
418C2×C4C2×C13×D811yescharacteristic
419C2×C4C2×C13×D811yescharacteristic
420C2×C4C2×C13×D811yescharacteristic
421C2×C4C2×C13×D811yescharacteristic
422C2×C4C22×D4×C1311yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8C2×C13×#4111yescharacteristic
427C8C13×2−1+411yescharacteristic
428C22—81no—
429C22—81no—
430C22—81no—
431C22C22×C13×D811yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4C13×#54811yescharacteristic
446C4C13×#57711yescharacteristic
447C2—161no—
448C2C13×#335811yescharacteristic
449C2C13×#341411yescharacteristic
450C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC2×C13×D8C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3383C2semidirect
3. C13×#2245C2semidirect
6. C13×#2229C2semidirect
8. C13×#2227C2semidirect
11. C13×#2209C2semidirect
12. C13×#2183C2semidirect
13. C13×#2176C2semidirect
15. C4×C13×Q32C2semidirect
113. #33944C13direct (N × H)
173. #3383C2×C13semidirect
174. #2245C2×C13semidirect
177. #2229C2×C13semidirect
179. #2227C2×C13semidirect
182. #2209C2×C13semidirect
183. #2183C2×C13semidirect
184. #2176C2×C13semidirect
186. C4×Q32C2×C13semidirect
396. C13#33944direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33932
C13×#33832
C13×#22452
C13×#22432
C13×#22422
C13×#22292
C13×#22282
C13×#22272
C13×#22112
C13×#22092
C13×#21832
C13×#21762
C13×#21752
C4×C13×Q322
#3394413