Finite Group Databasebeta

← C13×#33798 #15720137

Subgroups — C13×#33798 #15720137

Order 3328.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3168C211yesmaximal, characteristic
2C2×C13×#499C211yesmaximal, characteristic, complemented
3C13×#2253C212yesmaximal, complemented
4C13×#2242C212yesmaximal, complemented
5C13×#2236C211yesmaximal, characteristic, complemented
6C13×#2235C211yesmaximal, characteristic, complemented
7C13×#2233C211yesmaximal, characteristic
8C13×#2232C211yesmaximal, characteristic
9C13×#2229C212yesmaximal, complemented
10C13×#2228C212yesmaximal, complemented
11C13×#2162C211yesmaximal, characteristic, complemented
12C13×#529—21no—
13C2×C13×#125—21no—
14C13×#499—21no—
15C13×#499—21no—
16C13×#499C2212yes—
17C13×#499C2211yescharacteristic
18C13×#499C2212yes—
19C13×#495C2211yescharacteristic
20C13×#488—21no—
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#465—21no—
24C4×C13×Q16C2211yescharacteristic
25C4×C13×SD16—21no—
26C4×C13×D8C2211yescharacteristic
27C2×C13×#107C2211yescharacteristic
28C2×C13×#107C2211yescharacteristic
29C2×C13×#106—21no—
30C2×C4×C8×C13C2211yescharacteristic
31C13×#367C2212yes—
32C13×#367C2212yes—
33C13×#366C2212yes—
34C13×#366C2212yes—
35C13×C4⋊C16C2212yes—
36C13×#358C2212yes—
37C13×#358C2212yes—
38C13×#357C2212yes—
39C13×#357C2212yes—
40C13×C22⋊C16C2211yescharacteristic
41C13×C22⋊C16C2211yescharacteristic
42C4×C13×C16C2212yes—
43C2×C13×Q16C2311yescharacteristic
44C2×C13×SD16—21no—
45C2×C13×D8C2311yescharacteristic
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×#126—41no—
49C13×#125—21no—
50C13×#125—22no—
51C13×#125—22no—
52C13×#125—41no—
53C13×#125—41no—
54C13×#124—21no—
55C13×#123—41no—
56C13×C22⋊Q8—21no—
57C13×#121—21no—
58C4×Q8×C13—21no—
59C4×D4×C13—21no—
60C4×D4×C13—41no—
61C13×#117—41no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—41no—
65C2×C13×C4⋊C4—41no—
66C2×C42×C13D411yescharacteristic
67C2×C13×C16C2312yes—
68C2×C13×C16C2312yes—
69C13×#107—21no—
70C13×#107—21no—
71C13×#107C2312yes—
72C13×#107C2312yes—
73C13×#107C2311yescharacteristic
74C13×#107C2311yescharacteristic
75C13×#106—22no—
76C13×#106—22no—
77C13×#106—21no—
78C13×#103—21no—
79C13×#103—21no—
80C13×#102—21no—
81C13×#102—21no—
82C4×C8×C13D411yescharacteristic
83C4×C8×C13D411yescharacteristic
84C4×C8×C13C2311yescharacteristic
85C4×C8×C13C2311yescharacteristic
86#33798C1311yesmaximal, characteristic, direct product factor, Sylow
87C2×Q8×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13D811yescharacteristic
94C22×C4×C13D811yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C13×Q16—22no—
97C13×SD16—42no—
98C13×D8—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C2×C8×C13C2411yescharacteristic
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—42no—
114C13×C4⋊C4—42no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C42×C13—41no—
125C42×C13D811yescharacteristic
126C42×C13D811yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13C2×D411yescharacteristic
129C13×C16—22no—
130C13×C16—22no—
131#3168C2×C1311yescharacteristic
132C2×#499C2×C1311yescharacteristic, complemented
133#2253C2×C1312yescomplemented
134#2242C2×C1312yescomplemented
135#2236C2×C1311yescharacteristic, complemented
136#2235C2×C1311yescharacteristic, complemented
137#2233C2×C1311yescharacteristic
138#2232C2×C1311yescharacteristic
139#2229C2×C1312yescomplemented
140#2228C2×C1312yescomplemented
141#2162C2×C1311yescharacteristic, complemented
142C23×C13—41no—
143C23×C13C2×D811yescharacteristic
144Q8×C13—41no—
145Q8×C13—41no—
146D4×C13—41no—
147D4×C13—41no—
148D4×C13—82no—
149C2×C4×C13—22no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—82no—
159C2×C4×C13—82no—
160C2×C4×C13—82no—
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C2×D811yescharacteristic
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C22×D411yescharacteristic
167C8×C13—21no—
168C8×C13—21no—
169C8×C13#13712yes—
170C8×C132−1+412yes—
171#529—21no—
172C2×#125—21no—
173#499—21no—
174#499—21no—
175#499C22×C1312yes—
176#499C22×C1312yes—
177#499C22×C1311yescharacteristic
178#495C22×C1311yescharacteristic
179#488—21no—
180#467C22×C1311yescharacteristic
181#466C22×C1311yescharacteristic
182#465—21no—
183C4×Q16C22×C1311yescharacteristic
184C4×SD16—21no—
185C4×D8C22×C1311yescharacteristic
186C2×#107C22×C1311yescharacteristic
187C2×#107C22×C1311yescharacteristic
188C2×#106—21no—
189C2×C4×C8C22×C1311yescharacteristic
190#367C22×C1312yes—
191#367C22×C1312yes—
192#366C22×C1312yes—
193#366C22×C1312yes—
194C4⋊C16C22×C1312yes—
195#358C22×C1312yes—
196#358C22×C1312yes—
197#357C22×C1312yes—
198#357C22×C1312yes—
199C22⋊C16C22×C1311yescharacteristic
200C22⋊C16C22×C1311yescharacteristic
201C4×C16C22×C1312yes—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13#50812yes—
208C22×C13C22×D811yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—82no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—82no—
218C4×C13—81no—
219C4×C13#53611yescharacteristic
220C4×C13C2×#13711yescharacteristic
221C2×Q16C23×C1311yescharacteristic
222C2×SD16—21no—
223C2×D8C23×C1311yescharacteristic
224C22×C8D4×C1311yescharacteristic
225C22×C8C23×C1311yescharacteristic
226#126—41no—
227#125—22no—
228#125—22no—
229#125—21no—
230#125—41no—
231#125—41no—
232#124—21no—
233#123—41no—
234C22⋊Q8—21no—
235#121—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—41no—
239#117—41no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—41no—
244C2×C42D4×C1311yescharacteristic
245C2×C16C23×C1312yes—
246C2×C16C23×C1312yes—
247#107—21no—
248#107—21no—
249#107C23×C1312yes—
250#107C23×C1312yes—
251#107C23×C1311yescharacteristic
252#107C23×C1311yescharacteristic
253#106—22no—
254#106—22no—
255#106—21no—
256#103—21no—
257#103—21no—
258#102—21no—
259#102—21no—
260C4×C8D4×C1311yescharacteristic
261C4×C8D4×C1311yescharacteristic
262C4×C8C23×C1311yescharacteristic
263C4×C8C23×C1311yescharacteristic
264C2×C13—22no—
265C2×C13—161no—
266C2×C13#322611yescharacteristic
267C2×C13C2×#50811yescharacteristic
268C2×C13#341411yescharacteristic
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C13×D811yescharacteristic
276C22×C4C13×D811yescharacteristic
277C22×C4C2×D4×C1311yescharacteristic
278Q16—22no—
279SD16—42no—
280D8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8C2×D4×C1311yescharacteristic
284C2×C8C2×D4×C1311yescharacteristic
285C2×C8C2×D4×C1311yescharacteristic
286C2×C8C24×C1311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42C13×D811yescharacteristic
308C42C13×D811yescharacteristic
309C42C2×D4×C1311yescharacteristic
310C42C2×D4×C1311yescharacteristic
311C16—22no—
312C16—22no—
313C13#3379811yescharacteristic, direct product factor, Sylow
314C23—41no—
315C23C2×C13×D811yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4C2×C13×D811yescharacteristic
334C2×C4C2×C13×D811yescharacteristic
335C2×C4C2×C13×D811yescharacteristic
336C2×C4C2×C13×D811yescharacteristic
337C2×C4C2×C13×D811yescharacteristic
338C2×C4C22×D4×C1311yescharacteristic
339C8—21no—
340C8—21no—
341C8C13×#13712yes—
342C8C13×2−1+412yes—
343C22—21no—
344C22—21no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C13×#50812yes—
349C22C22×C13×D811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—81no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4C13×#53611yescharacteristic
361C4C2×C13×#13711yescharacteristic
362C2—22no—
363C2—161no—
364C2C13×#322611yescharacteristic
365C2C2×C13×#50811yescharacteristic
366C2C13×#341411yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#499C2semidirect
3. C13×#2253C2semidirect
4. C13×#2242C2semidirect
5. C13×#2236C2semidirect
6. C13×#2235C2semidirect
9. C13×#2229C2semidirect
10. C13×#2228C2semidirect
11. C13×#2162C2semidirect
86. #33798C13direct (N × H)
132. C2×#499C2×C13semidirect
133. #2253C2×C13semidirect
134. #2242C2×C13semidirect
135. #2236C2×C13semidirect
136. #2235C2×C13semidirect
139. #2229C2×C13semidirect
140. #2228C2×C13semidirect
141. #2162C2×C13semidirect
313. C13#33798direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31682
C2×C13×#4992
C13×#22532
C13×#22422
C13×#22362
C13×#22352
C13×#22332
C13×#22322
C13×#22292
C13×#22282
C13×#21622
#3379813