Finite Group Databasebeta

← C13×#33955 #15720294

Subgroups — C13×#33955 #15720294

Order 3328.

458 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3383C211yesmaximal, characteristic, complemented
2C13×#3380C211yesmaximal, characteristic
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2255C211yesmaximal, characteristic, complemented
5C13×#2253C211yesmaximal, characteristic, complemented
6C13×#2229C211yesmaximal, characteristic, complemented
7C13×#2229C211yesmaximal, characteristic, complemented
8C13×#2228C211yesmaximal, characteristic
9C13×#2228C211yesmaximal, characteristic
10C13×#2226C211yesmaximal, characteristic
11C13×#2225C211yesmaximal, characteristic, complemented
12C13×#2183C211yesmaximal, characteristic, complemented
13C13×#2175C211yesmaximal, characteristic
14C13×#2175C211yesmaximal, characteristic
15C4×C13×SD32C211yesmaximal, characteristic
16C13×#557—21no—
17C13×#554—21no—
18C2×C13×SD32C2211yescharacteristic
19C13×#500C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#499C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#499C2211yescharacteristic
25C13×#479—21no—
26C13×#479—21no—
27C13×#478—21no—
28C13×#478—21no—
29C13×#476—21no—
30C13×#475—21no—
31C8×Q8×C13C2211yescharacteristic
32C4×C13×Q16C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×Q16C2211yescharacteristic
35C4×C13×D8C2211yescharacteristic
36C4×C13×D8C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C13×#367C2211yescharacteristic
39C13×#367C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×#366C2211yescharacteristic
46C13×#366C2211yescharacteristic
47C13×C4⋊C16C2211yescharacteristic
48C13×C4⋊C16C2211yescharacteristic
49C13×C4⋊C16C2211yescharacteristic
50C13×#358C2211yescharacteristic
51C13×#358C2211yescharacteristic
52C13×#358C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×#357C2211yescharacteristic
56C13×#346C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×D8C2311yescharacteristic
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—41no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—21no—
67C13×#125—21no—
68C13×#125—41no—
69C13×#125—41no—
70C13×C22⋊Q8—41no—
71C13×C22⋊Q8—41no—
72C13×C22⋊Q8—41no—
73C4×Q8×C13—21no—
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13—41no—
77C4×Q8×C13D411yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13—21no—
80C4×D4×C13—21no—
81C2×C13×C4⋊C4—41no—
82C13×SD32Q814yescomplemented
83C2×C13×C16C2311yescharacteristic
84C2×C13×C16C2311yescharacteristic
85C2×C13×C16C2311yescharacteristic
86C2×C13×C16C2311yescharacteristic
87C13×#107—21no—
88C13×#107—21no—
89C13×#107C2311yescharacteristic
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#107C2311yescharacteristic
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#106—21no—
96C13×#106—21no—
97C13×#106—21no—
98C13×#106—21no—
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8D411yescharacteristic
102C13×#103—21no—
103C13×#103—21no—
104C13×#103—21no—
105C13×#102—21no—
106C13×#102—21no—
107C13×#102—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#33955C1311yesmaximal, characteristic, direct product factor, Sylow
112C2×Q8×C13—21no—
113C2×Q8×C13—41no—
114C2×Q8×C13—41no—
115C2×Q8×C13D811yescharacteristic
116C2×D4×C13—21no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C13×Q16—21no—
121C13×Q16C2×Q812yes—
122C13×D8—21no—
123C13×D8C2×Q812yes—
124C2×C8×C13C2×D411yescharacteristic
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2411yescharacteristic
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—41no—
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⋊C4D811yescharacteristic
148C13×C4⋊C4D811yescharacteristic
149C13×C4⋊C4D811yescharacteristic
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C42×C13—41no—
154C42×C13—41no—
155C42×C13—41no—
156C42×C13C2×D411yescharacteristic
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C13×C16—21no—
160C13×C16—21no—
161C13×C16—21no—
162C13×C16C2×Q812yes—
163#3383C2×C1311yescharacteristic, complemented
164#3380C2×C1311yescharacteristic
165#2255C2×C1311yescharacteristic, complemented
166#2255C2×C1311yescharacteristic, complemented
167#2253C2×C1311yescharacteristic, complemented
168#2229C2×C1311yescharacteristic, complemented
169#2229C2×C1311yescharacteristic, complemented
170#2228C2×C1311yescharacteristic
171#2228C2×C1311yescharacteristic
172#2226C2×C1311yescharacteristic
173#2225C2×C1311yescharacteristic, complemented
174#2183C2×C1311yescharacteristic, complemented
175#2175C2×C1311yescharacteristic
176#2175C2×C1311yescharacteristic
177C4×SD32C2×C1311yescharacteristic
178C23×C13—41no—
179Q8×C13—22no—
180Q8×C13—41no—
181Q8×C13—41no—
182Q8×C13—82no—
183Q8×C13—161no—
184D4×C13—22no—
185D4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—82no—
194C2×C4×C13—161no—
195C2×C4×C13—161no—
196C2×C4×C13C2×D811yescharacteristic
197C2×C4×C13C2×D811yescharacteristic
198C2×C4×C13C2×D811yescharacteristic
199C2×C4×C13C2×D811yescharacteristic
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13C22×D411yescharacteristic
203C8×C13—21no—
204C8×C13—21no—
205C8×C13—21no—
206C8×C13C22×Q811yescharacteristic
207C8×C132−1+411yescharacteristic
208#557—21no—
209#554—21no—
210C2×SD32C22×C1311yescharacteristic
211#500C22×C1311yescharacteristic
212#500C22×C1311yescharacteristic
213#499C22×C1311yescharacteristic
214#499C22×C1311yescharacteristic
215#499C22×C1311yescharacteristic
216#499C22×C1311yescharacteristic
217#479—21no—
218#479—21no—
219#478—21no—
220#478—21no—
221#476—21no—
222#475—21no—
223C8×Q8C22×C1311yescharacteristic
224C4×Q16C22×C1311yescharacteristic
225C4×Q16C22×C1311yescharacteristic
226C4×Q16C22×C1311yescharacteristic
227C4×D8C22×C1311yescharacteristic
228C4×D8C22×C1311yescharacteristic
229C4×D8C22×C1311yescharacteristic
230#367C22×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
241C4⋊C16C22×C1311yescharacteristic
242#358C22×C1311yescharacteristic
243#358C22×C1311yescharacteristic
244#358C22×C1311yescharacteristic
245#357C22×C1311yescharacteristic
246#357C22×C1311yescharacteristic
247#357C22×C1311yescharacteristic
248#346C22×C1311yescharacteristic
249#346C22×C1311yescharacteristic
250C4×C16C22×C1311yescharacteristic
251C22×C13—42no—
252C22×C13—81no—
253C22×C13—81no—
254C22×C13C22×D811yescharacteristic
255C4×C13—21no—
256C4×C13—21no—
257C4×C13—21no—
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—42no—
262C4×C13—81no—
263C4×C13—81no—
264C4×C13—81no—
265C4×C13—81no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13D4×Q811yescharacteristic
269C4×C13#57811yescharacteristic
270C2×Q16C23×C1311yescharacteristic
271C2×D8C23×C1311yescharacteristic
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—41no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#125—41no—
280#125—41no—
281C22⋊Q8—41no—
282C22⋊Q8—41no—
283C22⋊Q8—41no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8—41no—
288C4×Q8D4×C1311yescharacteristic
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C2×C4⋊C4—41no—
293SD32Q8×C1314yescomplemented
294C2×C16C23×C1311yescharacteristic
295C2×C16C23×C1311yescharacteristic
296C2×C16C23×C1311yescharacteristic
297C2×C16C23×C1311yescharacteristic
298#107—21no—
299#107—21no—
300#107C23×C1311yescharacteristic
301#107C23×C1311yescharacteristic
302#107C23×C1311yescharacteristic
303#107C23×C1311yescharacteristic
304#107C23×C1311yescharacteristic
305#107C23×C1311yescharacteristic
306#106—21no—
307#106—21no—
308#106—21no—
309#106—21no—
310C4⋊C8D4×C1311yescharacteristic
311C4⋊C8D4×C1311yescharacteristic
312C4⋊C8D4×C1311yescharacteristic
313#103—21no—
314#103—21no—
315#103—21no—
316#102—21no—
317#102—21no—
318#102—21no—
319C4×C8C23×C1311yescharacteristic
320C4×C8C23×C1311yescharacteristic
321C4×C8C23×C1311yescharacteristic
322C2×C13—82no—
323C2×C13Q8×D811yescharacteristic
324C2×C13#341411yescharacteristic
325C2×C13#341611yescharacteristic
326C2×Q8—21no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8C13×D811yescharacteristic
330C2×D4—21no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334Q16—21no—
335Q16C2×Q8×C1312yes—
336D8—21no—
337D8C2×Q8×C1312yes—
338C2×C8C2×D4×C1311yescharacteristic
339C2×C8C2×D4×C1311yescharacteristic
340C2×C8C2×D4×C1311yescharacteristic
341C2×C8C24×C1311yescharacteristic
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
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⋊C4C13×D811yescharacteristic
362C4⋊C4C13×D811yescharacteristic
363C4⋊C4C13×D811yescharacteristic
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42—41no—
368C42—41no—
369C42—41no—
370C42C2×D4×C1311yescharacteristic
371C42C2×D4×C1311yescharacteristic
372C42C2×D4×C1311yescharacteristic
373C16—21no—
374C16—21no—
375C16—21no—
376C16C2×Q8×C1312yes—
377C13#3395511yescharacteristic, direct product factor, Sylow
378C23—41no—
379Q8—22no—
380Q8—41no—
381Q8—41no—
382Q8—82no—
383Q8—161no—
384D4—22no—
385D4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—82no—
394C2×C4—161no—
395C2×C4—161no—
396C2×C4C2×C13×D811yescharacteristic
397C2×C4C2×C13×D811yescharacteristic
398C2×C4C2×C13×D811yescharacteristic
399C2×C4C2×C13×D811yescharacteristic
400C2×C4C2×C13×D811yescharacteristic
401C2×C4C2×C13×D811yescharacteristic
402C2×C4C22×D4×C1311yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8C22×Q8×C1311yescharacteristic
407C8C13×2−1+411yescharacteristic
408C22—42no—
409C22—81no—
410C22—81no—
411C22C22×C13×D811yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—42no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4D4×Q8×C1311yescharacteristic
426C4C13×#57811yescharacteristic
427C2—82no—
428C2Q8×C13×D811yescharacteristic
429C2C13×#341411yescharacteristic
430C2C13×#341611yescharacteristic
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
1. C13×#3383C2semidirect
3. C13×#2255C2semidirect
4. C13×#2255C2semidirect
5. C13×#2253C2semidirect
6. C13×#2229C2semidirect
7. C13×#2229C2semidirect
11. C13×#2225C2semidirect
12. C13×#2183C2semidirect
82. C13×SD32Q8semidirect
111. #33955C13direct (N × H)
163. #3383C2×C13semidirect
165. #2255C2×C13semidirect
166. #2255C2×C13semidirect
167. #2253C2×C13semidirect
168. #2229C2×C13semidirect
169. #2229C2×C13semidirect
173. #2225C2×C13semidirect
174. #2183C2×C13semidirect
293. SD32Q8×C13semidirect
377. C13#33955direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33832
C13×#33802
C13×#22552
C13×#22532
C13×#22292
C13×#22282
C13×#22262
C13×#22252
C13×#21832
C13×#21752
C4×C13×SD322
#3395513