Finite Group Databasebeta

← C13×#33916 #15720255

Subgroups — C13×#33916 #15720255

Order 3328.

464 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×#3342C211yesmaximal, characteristic
2C13×#3336C211yesmaximal, characteristic
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2237C211yesmaximal, characteristic, complemented
5C13×#2237C211yesmaximal, characteristic, complemented
6C13×#2237C211yesmaximal, characteristic, complemented
7C13×#2236C211yesmaximal, characteristic, complemented
8C13×#2229C211yesmaximal, characteristic, complemented
9C13×#2227C211yesmaximal, characteristic, complemented
10C13×#2219C211yesmaximal, characteristic, complemented
11C13×#2216C211yesmaximal, characteristic, complemented
12C13×#2176C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic
14C13×#2159C211yesmaximal, characteristic, complemented
15C13×#2158C211yesmaximal, characteristic, complemented
16C13×#556—21no—
17C13×#552—21no—
18C2×C13×Q32C2211yescharacteristic
19C2×C13×M32C2211yescharacteristic
20C22×C13×C16C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#485—21no—
24C13×#485—21no—
25C13×#485—21no—
26C13×#483—21no—
27C13×#479—21no—
28C13×#475—21no—
29C13×#467C2211yescharacteristic
30C13×#467C2211yescharacteristic
31C13×#467C2211yescharacteristic
32C13×#467C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C8×D4×C13C2211yescharacteristic
36C13×#427C2211yescharacteristic
37C13×#427C2211yescharacteristic
38C13×#427C2211yescharacteristic
39C2×C13×#107C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#367C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×#366C2211yescharacteristic
48C13×#366C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#358C2211yescharacteristic
54C13×#358C2211yescharacteristic
55C13×#358C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×C22⋊C16C2211yescharacteristic
58C13×#346C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×Q16C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×C4⋊Q8—21no—
64C13×#126—41no—
65C13×#126—41no—
66C13×#126—41no—
67C13×#125—21no—
68C13×#125—41no—
69C13×#124—41no—
70C13×#123—41no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—41no—
78C4×D4×C13D411yescharacteristic
79C13×#117—21no—
80C13×#117—21no—
81C13×#117—21no—
82C13×#117—41no—
83C2×C13×C4⋊C4—21no—
84C13×Q32—22no—
85C13×M32—22no—
86C2×C13×C16—22no—
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C2×C13×C16C2311yescharacteristic
90C2×C13×C16C2311yescharacteristic
91C13×#107—21no—
92C13×#107—21no—
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×#106—21no—
100C13×#106—21no—
101C13×#106—21no—
102C13×#106—21no—
103C13×C4⋊C8D411yescharacteristic
104C13×#103—21no—
105C13×#103—21no—
106C13×#103—21no—
107C13×#103—21no—
108C13×#103—21no—
109C13×#103—21no—
110C13×C22⋊C8D411yescharacteristic
111C13×C22⋊C8D411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#33916C1311yesmaximal, characteristic, direct product factor, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—41no—
117C2×D4×C13D811yescharacteristic
118C22×C4×C13—41no—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C13×Q16—21no—
122C13×Q16—21no—
123C13×Q16—21no—
124C13×Q16—21no—
125C2×C8×C13—21no—
126C2×C8×C13—21no—
127C2×C8×C13—21no—
128C2×C8×C13—21no—
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2411yescharacteristic
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4D811yescharacteristic
158C13×C22⋊C4D811yescharacteristic
159C42×C13—41no—
160C42×C13—41no—
161C42×C13—41no—
162C42×C13—41no—
163C42×C13—41no—
164C42×C13C2×D411yescharacteristic
165C13×C16—21no—
166C13×C16—21no—
167C13×C16—21no—
168C13×C16#4112yes—
169#3342C2×C1311yescharacteristic
170#3336C2×C1311yescharacteristic
171#2255C2×C1311yescharacteristic, complemented
172#2237C2×C1311yescharacteristic, complemented
173#2237C2×C1311yescharacteristic, complemented
174#2237C2×C1311yescharacteristic, complemented
175#2236C2×C1311yescharacteristic, complemented
176#2229C2×C1311yescharacteristic, complemented
177#2227C2×C1311yescharacteristic, complemented
178#2219C2×C1311yescharacteristic, complemented
179#2216C2×C1311yescharacteristic, complemented
180#2176C2×C1311yescharacteristic, complemented
181#2168C2×C1311yescharacteristic
182#2159C2×C1311yescharacteristic, complemented
183#2158C2×C1311yescharacteristic, complemented
184C23×C13C2×D811yescharacteristic
185C23×C13C2×D811yescharacteristic
186Q8×C13—41no—
187Q8×C13—41no—
188Q8×C13—41no—
189Q8×C13—41no—
190Q8×C13—82no—
191D4×C13—41no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—41no—
197C2×C4×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—82no—
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C8×C13—21no—
211C8×C13—21no—
212C8×C13—21no—
213C8×C13C2×#4111yescharacteristic
214C8×C132−1+411yescharacteristic
215#556—21no—
216#552—21no—
217C2×Q32C22×C1311yescharacteristic
218C2×M32C22×C1311yescharacteristic
219C22×C16C22×C1311yescharacteristic
220#500C22×C1311yescharacteristic
221#499C22×C1311yescharacteristic
222#485—21no—
223#485—21no—
224#485—21no—
225#483—21no—
226#479—21no—
227#475—21no—
228#467C22×C1311yescharacteristic
229#467C22×C1311yescharacteristic
230#467C22×C1311yescharacteristic
231#467C22×C1311yescharacteristic
232C4×Q16C22×C1311yescharacteristic
233C4×Q16C22×C1311yescharacteristic
234C8×D4C22×C1311yescharacteristic
235#427C22×C1311yescharacteristic
236#427C22×C1311yescharacteristic
237#427C22×C1311yescharacteristic
238C2×#107C22×C1311yescharacteristic
239#367C22×C1311yescharacteristic
240#367C22×C1311yescharacteristic
241#367C22×C1311yescharacteristic
242#367C22×C1311yescharacteristic
243#366C22×C1311yescharacteristic
244#366C22×C1311yescharacteristic
245#366C22×C1311yescharacteristic
246#366C22×C1311yescharacteristic
247#366C22×C1311yescharacteristic
248C4⋊C16C22×C1311yescharacteristic
249#358C22×C1311yescharacteristic
250#358C22×C1311yescharacteristic
251#358C22×C1311yescharacteristic
252#358C22×C1311yescharacteristic
253#358C22×C1311yescharacteristic
254#358C22×C1311yescharacteristic
255C22⋊C16C22×C1311yescharacteristic
256C22⋊C16C22×C1311yescharacteristic
257#346C22×C1311yescharacteristic
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13C22×D811yescharacteristic
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—21no—
269C4×C13—81no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13—81no—
273C4×C13—81no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13#54711yescharacteristic
278C4×C13#57811yescharacteristic
279C2×Q16C23×C1311yescharacteristic
280C2×Q16C23×C1311yescharacteristic
281C22×C8C23×C1311yescharacteristic
282C22×C8C23×C1311yescharacteristic
283C4⋊Q8—21no—
284#126—41no—
285#126—41no—
286#126—41no—
287#125—21no—
288#125—41no—
289#124—41no—
290#123—41no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—41no—
298C4×D4D4×C1311yescharacteristic
299#117—21no—
300#117—21no—
301#117—21no—
302#117—41no—
303C2×C4⋊C4—21no—
304Q32—22no—
305M32—22no—
306C2×C16—22no—
307C2×C16C23×C1311yescharacteristic
308C2×C16C23×C1311yescharacteristic
309C2×C16C23×C1311yescharacteristic
310C2×C16C23×C1311yescharacteristic
311#107—21no—
312#107—21no—
313#107C23×C1311yescharacteristic
314#107C23×C1311yescharacteristic
315#107C23×C1311yescharacteristic
316#107C23×C1311yescharacteristic
317#107C23×C1311yescharacteristic
318#107C23×C1311yescharacteristic
319#106—21no—
320#106—21no—
321#106—21no—
322#106—21no—
323C4⋊C8D4×C1311yescharacteristic
324#103—21no—
325#103—21no—
326#103—21no—
327#103—21no—
328#103—21no—
329#103—21no—
330C22⋊C8D4×C1311yescharacteristic
331C22⋊C8D4×C1311yescharacteristic
332C4×C8C23×C1311yescharacteristic
333C2×C13—41no—
334C2×C13—41no—
335C2×C13#333411yescharacteristic
336C2×C13#341411yescharacteristic
337C2×C13#341711yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×D4C13×D811yescharacteristic
342C22×C4—41no—
343C22×C4C2×D4×C1311yescharacteristic
344C22×C4C2×D4×C1311yescharacteristic
345Q16—21no—
346Q16—21no—
347Q16—21no—
348Q16—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C2×D4×C1311yescharacteristic
354C2×C8C2×D4×C1311yescharacteristic
355C2×C8C2×D4×C1311yescharacteristic
356C2×C8C24×C1311yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
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⋊C4C13×D811yescharacteristic
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4C13×D811yescharacteristic
382C22⋊C4C13×D811yescharacteristic
383C42—41no—
384C42—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42C2×D4×C1311yescharacteristic
389C16—21no—
390C16—21no—
391C16—21no—
392C16C13×#4112yes—
393C13#3391611yescharacteristic, direct product factor, Sylow
394C23C2×C13×D811yescharacteristic
395C23C2×C13×D811yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—82no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C2×C13×D811yescharacteristic
416C2×C4C2×C13×D811yescharacteristic
417C2×C4C2×C13×D811yescharacteristic
418C2×C4C2×C13×D811yescharacteristic
419C2×C4C22×D4×C1311yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8C2×C13×#4111yescharacteristic
424C8C13×2−1+411yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×C13×D811yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4C13×#54711yescharacteristic
445C4C13×#57811yescharacteristic
446C2—41no—
447C2—41no—
448C2C13×#333411yescharacteristic
449C2C13×#341411yescharacteristic
450C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC2×D4×C13D8
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
3. C13×#2255C2semidirect
4. C13×#2237C2semidirect
5. C13×#2237C2semidirect
6. C13×#2237C2semidirect
7. C13×#2236C2semidirect
8. C13×#2229C2semidirect
9. C13×#2227C2semidirect
10. C13×#2219C2semidirect
11. C13×#2216C2semidirect
12. C13×#2176C2semidirect
14. C13×#2159C2semidirect
15. C13×#2158C2semidirect
113. #33916C13direct (N × H)
171. #2255C2×C13semidirect
172. #2237C2×C13semidirect
173. #2237C2×C13semidirect
174. #2237C2×C13semidirect
175. #2236C2×C13semidirect
176. #2229C2×C13semidirect
177. #2227C2×C13semidirect
178. #2219C2×C13semidirect
179. #2216C2×C13semidirect
180. #2176C2×C13semidirect
182. #2159C2×C13semidirect
183. #2158C2×C13semidirect
393. C13#33916direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33422
C13×#33362
C13×#22552
C13×#22372
C13×#22362
C13×#22292
C13×#22272
C13×#22192
C13×#22162
C13×#21762
C13×#21682
C13×#21592
C13×#21582
#3391613