Finite Group Databasebeta

← C13×#33808 #15720147

Subgroups — C13×#33808 #15720147

Order 3328.

442 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3177C211yesmaximal, characteristic
2C13×#3164C211yesmaximal, characteristic
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2253C211yesmaximal, characteristic, complemented
5C13×#2245C211yesmaximal, characteristic, complemented
6C13×#2241C211yesmaximal, characteristic, complemented
7C13×#2237C211yesmaximal, characteristic
8C13×#2237C211yesmaximal, characteristic
9C13×#2236C211yesmaximal, characteristic
10C13×#2235C211yesmaximal, characteristic
11C13×#2229C211yesmaximal, characteristic, complemented
12C13×#2229C211yesmaximal, characteristic, complemented
13C13×#2227C211yesmaximal, characteristic, complemented
14C13×#2225C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic
16C13×#544—21no—
17C13×#541—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#499C2211yescharacteristic
25C13×#494C2211yescharacteristic
26C13×#491—21no—
27C13×#470—21no—
28C13×#467C2211yescharacteristic
29C13×#467C2211yescharacteristic
30C13×#441—21no—
31C4×C13×Q16C2211yescharacteristic
32C4×C13×Q16C2211yescharacteristic
33C13×#428—21no—
34C13×#427C2211yescharacteristic
35C2×C13×#107C2211yescharacteristic
36C13×#405C2211yescharacteristic
37C13×#367C2211yescharacteristic
38C13×#367C2211yescharacteristic
39C13×#367C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#358C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#358C2211yescharacteristic
54C13×#358C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16—21no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×Q16C2311yescharacteristic
62C2×C13×M16D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—41no—
68C13×#126—41no—
69C13×#126—41no—
70C13×#125—21no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—41no—
74C13×#125—41no—
75C13×#125—41no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—21no—
78C13×C22⋊Q8—41no—
79C13×C22⋊Q8—41no—
80C4×Q8×C13—21no—
81C4×Q8×C13—21no—
82C13×#117—21no—
83C13×#117D411yescharacteristic
84C2×C13×C4⋊C4—21no—
85C2×C13×C16C2311yescharacteristic
86C2×C13×C16C2311yescharacteristic
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C13×#107—21no—
90C13×#107—21no—
91C13×#107—21no—
92C13×#107C2311yescharacteristic
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#106—21no—
99C13×#106—21no—
100C13×#106—21no—
101C13×#106—21no—
102C13×#103—21no—
103C13×#103—21no—
104C13×#103—21no—
105C13×#103—21no—
106C13×#97D411yescharacteristic
107C13×#97D411yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#33808C1311yesmaximal, characteristic, direct product factor, Sylow
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—41no—
114C2×Q8×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13C2×D411yescharacteristic
117C13×Q16—21no—
118C13×Q16—21no—
119C13×Q16—21no—
120C13×Q16—21no—
121C13×Q16—42no—
122C13×M16—22no—
123C2×C8×C13—21no—
124C2×C8×C13—21no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2411yescharacteristic
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
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⋊C4—41no—
150C13×C4⋊C4D811yescharacteristic
151C13×C4⋊C4D811yescharacteristic
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4D811yescharacteristic
156C13×C22⋊C4D811yescharacteristic
157C42×C13—41no—
158C42×C13—41no—
159C42×C13—41no—
160C42×C13C2×D411yescharacteristic
161C42×C13C2×D411yescharacteristic
162C13×C16—21no—
163C13×C16—21no—
164C13×C16—21no—
165C13×C16—21no—
166#3177C2×C1311yescharacteristic
167#3164C2×C1311yescharacteristic
168#2255C2×C1311yescharacteristic, complemented
169#2253C2×C1311yescharacteristic, complemented
170#2245C2×C1311yescharacteristic, complemented
171#2241C2×C1311yescharacteristic, complemented
172#2237C2×C1311yescharacteristic
173#2237C2×C1311yescharacteristic
174#2236C2×C1311yescharacteristic
175#2235C2×C1311yescharacteristic
176#2229C2×C1311yescharacteristic, complemented
177#2229C2×C1311yescharacteristic, complemented
178#2227C2×C1311yescharacteristic, complemented
179#2225C2×C1311yescharacteristic, complemented
180#2164C2×C1311yescharacteristic
181C23×C13C2×D811yescharacteristic
182Q8×C13—41no—
183Q8×C13—41no—
184Q8×C13—41no—
185Q8×C13—41no—
186Q8×C13—161no—
187Q8×C13—161no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—161no—
199C2×C4×C13C2×D811yescharacteristic
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C22×D411yescharacteristic
205C8×C13—21no—
206C8×C13—21no—
207C8×C13#13712yes—
208C8×C132−1+411yescharacteristic
209C8×C132−1+411yescharacteristic
210#544—21no—
211#541—21no—
212#501—21no—
213#501—21no—
214#500C22×C1311yescharacteristic
215#500C22×C1311yescharacteristic
216#499C22×C1311yescharacteristic
217#499C22×C1311yescharacteristic
218#499C22×C1311yescharacteristic
219#494C22×C1311yescharacteristic
220#491—21no—
221#470—21no—
222#467C22×C1311yescharacteristic
223#467C22×C1311yescharacteristic
224#441—21no—
225C4×Q16C22×C1311yescharacteristic
226C4×Q16C22×C1311yescharacteristic
227#428—21no—
228#427C22×C1311yescharacteristic
229C2×#107C22×C1311yescharacteristic
230#405C22×C1311yescharacteristic
231#367C22×C1311yescharacteristic
232#367C22×C1311yescharacteristic
233#367C22×C1311yescharacteristic
234#367C22×C1311yescharacteristic
235#366C22×C1311yescharacteristic
236#366C22×C1311yescharacteristic
237#366C22×C1311yescharacteristic
238#366C22×C1311yescharacteristic
239C4⋊C16C22×C1311yescharacteristic
240C4⋊C16C22×C1311yescharacteristic
241#358C22×C1311yescharacteristic
242#358C22×C1311yescharacteristic
243#358C22×C1311yescharacteristic
244#358C22×C1311yescharacteristic
245#358C22×C1311yescharacteristic
246#358C22×C1311yescharacteristic
247#358C22×C1311yescharacteristic
248#358C22×C1311yescharacteristic
249C22⋊C16C22×C1311yescharacteristic
250C22⋊C16C22×C1311yescharacteristic
251#346C22×C1311yescharacteristic
252C4×C16C22×C1311yescharacteristic
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13C22×D811yescharacteristic
257C4×C13—21no—
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—81no—
263C4×C13—81no—
264C4×C13—81no—
265C4×C13—81no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13—81no—
269C4×C13—81no—
270C4×C13#53611yescharacteristic
271C4×C13C2×#13711yescharacteristic
272C2×Q16—21no—
273C2×Q16C23×C1311yescharacteristic
274C2×Q16C23×C1311yescharacteristic
275C2×M16D4×C1311yescharacteristic
276C22×C8C23×C1311yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—41no—
281#126—41no—
282#126—41no—
283#125—21no—
284#125—21no—
285#125—21no—
286#125—41no—
287#125—41no—
288#125—41no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—41no—
292C22⋊Q8—41no—
293C4×Q8—21no—
294C4×Q8—21no—
295#117—21no—
296#117D4×C1311yescharacteristic
297C2×C4⋊C4—21no—
298C2×C16C23×C1311yescharacteristic
299C2×C16C23×C1311yescharacteristic
300C2×C16C23×C1311yescharacteristic
301C2×C16C23×C1311yescharacteristic
302#107—21no—
303#107—21no—
304#107—21no—
305#107C23×C1311yescharacteristic
306#107C23×C1311yescharacteristic
307#107C23×C1311yescharacteristic
308#107C23×C1311yescharacteristic
309#107C23×C1311yescharacteristic
310#107C23×C1311yescharacteristic
311#106—21no—
312#106—21no—
313#106—21no—
314#106—21no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—21no—
319#97D4×C1311yescharacteristic
320#97D4×C1311yescharacteristic
321C4×C8C23×C1311yescharacteristic
322C4×C8C23×C1311yescharacteristic
323C2×C13—41no—
324C2×C13#322611yescharacteristic
325C2×C13#341611yescharacteristic
326C2×C13#341711yescharacteristic
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—41no—
330C2×Q8—41no—
331C22×C4—41no—
332C22×C4C2×D4×C1311yescharacteristic
333Q16—21no—
334Q16—21no—
335Q16—21no—
336Q16—21no—
337Q16—42no—
338M16—22no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8C2×D4×C1311yescharacteristic
342C2×C8C2×D4×C1311yescharacteristic
343C2×C8C2×D4×C1311yescharacteristic
344C2×C8C24×C1311yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4C13×D811yescharacteristic
367C4⋊C4C13×D811yescharacteristic
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4C13×D811yescharacteristic
372C22⋊C4C13×D811yescharacteristic
373C42—41no—
374C42—41no—
375C42—41no—
376C42C2×D4×C1311yescharacteristic
377C42C2×D4×C1311yescharacteristic
378C16—21no—
379C16—21no—
380C16—21no—
381C16—21no—
382C13#3380811yescharacteristic, direct product factor, Sylow
383C23C2×C13×D811yescharacteristic
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388Q8—161no—
389Q8—161no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—161no—
401C2×C4C2×C13×D811yescharacteristic
402C2×C4C2×C13×D811yescharacteristic
403C2×C4C2×C13×D811yescharacteristic
404C2×C4C2×C13×D811yescharacteristic
405C2×C4C2×C13×D811yescharacteristic
406C2×C4C22×D4×C1311yescharacteristic
407C8—21no—
408C8—21no—
409C8C13×#13712yes—
410C8C13×2−1+411yescharacteristic
411C8C13×2−1+411yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22C22×C13×D811yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4C13×#53611yescharacteristic
430C4C2×C13×#13711yescharacteristic
431C2—41no—
432C2C13×#322611yescharacteristic
433C2C13×#341611yescharacteristic
434C2C13×#341711yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC23×C13C2×D8
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
3. C13×#2255C2semidirect
4. C13×#2253C2semidirect
5. C13×#2245C2semidirect
6. C13×#2241C2semidirect
11. C13×#2229C2semidirect
12. C13×#2229C2semidirect
13. C13×#2227C2semidirect
14. C13×#2225C2semidirect
110. #33808C13direct (N × H)
168. #2255C2×C13semidirect
169. #2253C2×C13semidirect
170. #2245C2×C13semidirect
171. #2241C2×C13semidirect
176. #2229C2×C13semidirect
177. #2229C2×C13semidirect
178. #2227C2×C13semidirect
179. #2225C2×C13semidirect
382. C13#33808direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31772
C13×#31642
C13×#22552
C13×#22532
C13×#22452
C13×#22412
C13×#22372
C13×#22362
C13×#22352
C13×#22292
C13×#22272
C13×#22252
C13×#21642
#3380813