Finite Group Databasebeta

← C13×#33943 #15720282

Subgroups — C13×#33943 #15720282

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3393C211yesmaximal, characteristic, complemented
2C13×#3380C211yesmaximal, characteristic, complemented
3C13×#2245C211yesmaximal, characteristic, complemented
4C13×#2243C211yesmaximal, characteristic, complemented
5C13×#2242C211yesmaximal, characteristic, complemented
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2228C211yesmaximal, characteristic, complemented
8C13×#2225C211yesmaximal, characteristic, complemented
9C13×#2210C211yesmaximal, characteristic
10C13×#2210C211yesmaximal, characteristic
11C13×#2208C211yesmaximal, characteristic, complemented
12C13×#2183C211yesmaximal, characteristic, complemented
13C13×#2177C211yesmaximal, characteristic
14C13×#2175C211yesmaximal, characteristic, complemented
15C4×C13×SD32C211yesmaximal, characteristic, complemented
16C13×#556—21no—
17C13×#554—21no—
18C2×C13×SD32C2211yescharacteristic
19C2×C13×SD32C2211yescharacteristic
20C2×C13×D16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#495C2211yescharacteristic
25C13×#495C2211yescharacteristic
26C13×#494C2211yescharacteristic
27C13×#478—21no—
28C13×#478—21no—
29C13×#476—21no—
30C13×#464—21no—
31C13×#464—21no—
32C13×#461—21no—
33C8×Q8×C13C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C4×C13×Q16C2211yescharacteristic
36C4×C13×D8C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic
39C4×C13×D8C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×C4⋊C16C2211yescharacteristic
44C13×C4⋊C16C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×#358C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#357C2211yescharacteristic
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×SD16—21no—
63C2×C13×SD16—21no—
64C2×C13×D8C2311yescharacteristic
65C2×C13×D8C2311yescharacteristic
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×#126—41no—
69C13×#126—41no—
70C13×#125—21no—
71C13×#125—21no—
72C13×#124—21no—
73C13×#124—21no—
74C13×C22⋊Q8—41no—
75C13×C22⋊Q8—41no—
76C13×C22⋊Q8—41no—
77C13×C22⋊Q8—41no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13D411yescharacteristic
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13—21no—
85C13×#117—41no—
86C2×C13×C4⋊C4—41no—
87C13×SD32—22no—
88C13×SD32—22no—
89C13×D16—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×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33943C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—41no—
117C2×Q8×C13D811yescharacteristic
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C13×Q16—21no—
125C13×Q16—21no—
126C13×Q16—21no—
127C13×Q16—21no—
128C13×Q16—81no—
129C13×SD16—81no—
130C13×SD16—81no—
131C13×D8—21no—
132C13×D8—21no—
133C13×D8—21no—
134C13×D8#4112yes—
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2411yescharacteristic
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
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—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—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, complemented
173#3380C2×C1311yescharacteristic, complemented
174#2245C2×C1311yescharacteristic, complemented
175#2243C2×C1311yescharacteristic, complemented
176#2242C2×C1311yescharacteristic, complemented
177#2229C2×C1311yescharacteristic, complemented
178#2228C2×C1311yescharacteristic, complemented
179#2225C2×C1311yescharacteristic, complemented
180#2210C2×C1311yescharacteristic
181#2210C2×C1311yescharacteristic
182#2208C2×C1311yescharacteristic, complemented
183#2183C2×C1311yescharacteristic, complemented
184#2177C2×C1311yescharacteristic
185#2175C2×C1311yescharacteristic, complemented
186C4×SD32C2×C1311yescharacteristic, complemented
187C23×C13—41no—
188C23×C13—41no—
189Q8×C13—41no—
190Q8×C13—41no—
191Q8×C13—41no—
192Q8×C13—41no—
193Q8×C13—41no—
194Q8×C13—161no—
195D4×C13—22no—
196D4×C13—41no—
197D4×C13—41no—
198D4×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×C13—82no—
207C2×C4×C13—161no—
208C2×C4×C13—161no—
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C22×D411yescharacteristic
216C8×C13—21no—
217C8×C13—21no—
218C8×C13—21no—
219C8×C13C2×#4111yescharacteristic
220C8×C132−1+411yescharacteristic
221#556—21no—
222#554—21no—
223C2×SD32C22×C1311yescharacteristic
224C2×SD32C22×C1311yescharacteristic
225C2×D16C22×C1311yescharacteristic
226#500C22×C1311yescharacteristic
227#499C22×C1311yescharacteristic
228#499C22×C1311yescharacteristic
229#495C22×C1311yescharacteristic
230#495C22×C1311yescharacteristic
231#494C22×C1311yescharacteristic
232#478—21no—
233#478—21no—
234#476—21no—
235#464—21no—
236#464—21no—
237#461—21no—
238C8×Q8C22×C1311yescharacteristic
239C4×Q16C22×C1311yescharacteristic
240C4×Q16C22×C1311yescharacteristic
241C4×D8C22×C1311yescharacteristic
242C4×D8C22×C1311yescharacteristic
243C4×D8C22×C1311yescharacteristic
244C4×D8C22×C1311yescharacteristic
245#367C22×C1311yescharacteristic
246#367C22×C1311yescharacteristic
247#366C22×C1311yescharacteristic
248C4⋊C16C22×C1311yescharacteristic
249C4⋊C16C22×C1311yescharacteristic
250C4⋊C16C22×C1311yescharacteristic
251#358C22×C1311yescharacteristic
252#358C22×C1311yescharacteristic
253#358C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255#358C22×C1311yescharacteristic
256#358C22×C1311yescharacteristic
257#357C22×C1311yescharacteristic
258#357C22×C1311yescharacteristic
259#357C22×C1311yescharacteristic
260#357C22×C1311yescharacteristic
261#346C22×C1311yescharacteristic
262#346C22×C1311yescharacteristic
263C4×C16C22×C1311yescharacteristic
264C22×C13—42no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13C22×D811yescharacteristic
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13#54811yescharacteristic
284C4×C13#57711yescharacteristic
285C2×Q16—21no—
286C2×Q16C23×C1311yescharacteristic
287C2×Q16C23×C1311yescharacteristic
288C2×SD16—21no—
289C2×SD16—21no—
290C2×D8C23×C1311yescharacteristic
291C2×D8C23×C1311yescharacteristic
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294#126—41no—
295#126—41no—
296#125—21no—
297#125—21no—
298#124—21no—
299#124—21no—
300C22⋊Q8—41no—
301C22⋊Q8—41no—
302C22⋊Q8—41no—
303C22⋊Q8—41no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C1311yescharacteristic
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311#117—41no—
312C2×C4⋊C4—41no—
313SD32—22no—
314SD32—22no—
315D16—22no—
316C2×C16C23×C1311yescharacteristic
317C2×C16C23×C1311yescharacteristic
318C2×C16C23×C1311yescharacteristic
319C2×C16C23×C1311yescharacteristic
320#107—21no—
321#107C23×C1311yescharacteristic
322#107C23×C1311yescharacteristic
323#107C23×C1311yescharacteristic
324#107C23×C1311yescharacteristic
325#106—21no—
326#106—21no—
327C4⋊C8D4×C1311yescharacteristic
328C4⋊C8D4×C1311yescharacteristic
329C4⋊C8D4×C1311yescharacteristic
330#103—21no—
331#103—21no—
332#102—21no—
333#102—21no—
334#102—21no—
335#102—21no—
336C4×C8C23×C1311yescharacteristic
337C4×C8C23×C1311yescharacteristic
338C4×C8C23×C1311yescharacteristic
339C2×C13—82no—
340C2×C13—161no—
341C2×C13#335811yescharacteristic
342C2×C13#341411yescharacteristic
343C2×C13#341611yescharacteristic
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8C13×D811yescharacteristic
348C2×D4—21no—
349C2×D4—21no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354Q16—21no—
355Q16—21no—
356Q16—21no—
357Q16—21no—
358Q16—81no—
359SD16—81no—
360SD16—81no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8C13×#4112yes—
365C2×C8C2×D4×C1311yescharacteristic
366C2×C8C2×D4×C1311yescharacteristic
367C2×C8C2×D4×C1311yescharacteristic
368C2×C8C24×C1311yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4C13×D811yescharacteristic
383C4⋊C4C13×D811yescharacteristic
384C4⋊C4C13×D811yescharacteristic
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C42—41no—
394C42—41no—
395C42C2×D4×C1311yescharacteristic
396C42C2×D4×C1311yescharacteristic
397C42C2×D4×C1311yescharacteristic
398C16—21no—
399C16—21no—
400C16—21no—
401C16—21no—
402C13#3394311yescharacteristic, direct product factor, Sylow
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—161no—
411D4—22no—
412D4—41no—
413D4—41no—
414D4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—161no—
424C2×C4—161no—
425C2×C4C2×C13×D811yescharacteristic
426C2×C4C2×C13×D811yescharacteristic
427C2×C4C2×C13×D811yescharacteristic
428C2×C4C2×C13×D811yescharacteristic
429C2×C4C2×C13×D811yescharacteristic
430C2×C4C2×C13×D811yescharacteristic
431C2×C4C22×D4×C1311yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×C13×#4111yescharacteristic
436C8C13×2−1+411yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×C13×D811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4C13×#54811yescharacteristic
457C4C13×#57711yescharacteristic
458C2—82no—
459C2—161no—
460C2C13×#335811yescharacteristic
461C2C13×#341411yescharacteristic
462C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC2×C13×D16C22
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
1. C13×#3393C2semidirect
2. C13×#3380C2semidirect
3. C13×#2245C2semidirect
4. C13×#2243C2semidirect
5. C13×#2242C2semidirect
6. C13×#2229C2semidirect
7. C13×#2228C2semidirect
8. C13×#2225C2semidirect
11. C13×#2208C2semidirect
12. C13×#2183C2semidirect
14. C13×#2175C2semidirect
15. C4×C13×SD32C2semidirect
113. #33943C13direct (N × H)
172. #3393C2×C13semidirect
173. #3380C2×C13semidirect
174. #2245C2×C13semidirect
175. #2243C2×C13semidirect
176. #2242C2×C13semidirect
177. #2229C2×C13semidirect
178. #2228C2×C13semidirect
179. #2225C2×C13semidirect
182. #2208C2×C13semidirect
183. #2183C2×C13semidirect
185. #2175C2×C13semidirect
186. C4×SD32C2×C13semidirect
402. C13#33943direct (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×#33802
C13×#22452
C13×#22432
C13×#22422
C13×#22292
C13×#22282
C13×#22252
C13×#22102
C13×#22082
C13×#21832
C13×#21772
C13×#21752
C4×C13×SD322
#3394313