Finite Group Databasebeta

← C13×#8897 #15695236

Subgroups — C13×#8897 #15695236

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2354C211yesmaximal, characteristic
2C13×#1947C211yesmaximal, characteristic, complemented
3C13×#1834C211yesmaximal, characteristic, complemented
4C13×#1802C211yesmaximal, characteristic
5C2×C13×D4⋊C8C211yesmaximal, characteristic
6C13×#1296C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D4×C13C2211yescharacteristic
9C2×C13×#117—21no—
10C2×C13×#107—21no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×#102—21no—
14C2×C4×C8×C13C2211yescharacteristic
15C13×#390—21no—
16C13×#388—22no—
17C13×#384C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C13×#380—21no—
20C4×C13×C4⋊C4—21no—
21C4×C13×C4⋊C4C2211yescharacteristic
22C13×#340—21no—
23C13×#340—22no—
24C13×#340—21no—
25C13×D4⋊C8C414yescomplemented
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13—21no—
33C4×D4×C13C2×C412yes—
34C4×D4×C13Q812yes—
35C13×#117—42no—
36C13×#117—42no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C13×C4⋊C4D412yes—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—22no—
49C2×C42×C13—22no—
50C2×C42×C13—21no—
51C2×C42×C13C2311yescharacteristic
52C13×#107—42no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8C2×C412yes—
57C13×#102—42no—
58C4×C8×C13—21no—
59C4×C8×C13C2×C412yes—
60C13×#95—22no—
61C13×#95—21no—
62#8897C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13C4⋊C412yes—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—21no—
75C22×C4×C13—22no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4C4⋊C412yes—
108C13×C4⋊C4D812yes—
109C13×C22⋊C4—22no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—44no—
112C13×C22⋊C4—82no—
113C42×C13—44no—
114C42×C13—41no—
115C42×C13—41no—
116C42×C13C22×C411yescharacteristic
117C42×C13C2×Q811yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13#4111yescharacteristic
120#2354C2×C1311yescharacteristic
121#1947C2×C1311yescharacteristic, complemented
122#1834C2×C1311yescharacteristic, complemented
123#1802C2×C1311yescharacteristic
124C2×D4⋊C8C2×C1311yescharacteristic
125#1296C2×C1311yescharacteristic, complemented
126#1279C2×C1311yescharacteristic, complemented
127C23×C13—22no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13#12011yescharacteristic
135D4×C13—22no—
136D4×C13—22no—
137D4×C13—41no—
138D4×C13—41no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13C2×C4⋊C411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13C4×D411yescharacteristic
163C2×C4×C13C22⋊Q811yescharacteristic
164C2×C4×C13C22⋊Q811yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13#13511yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C8×C13—42no—
175C8×C13—42no—
176C8×C13—81no—
177C2×C4×D4C22×C1311yescharacteristic
178C2×#117—21no—
179C2×#107—21no—
180C2×C4⋊C8C22×C1311yescharacteristic
181C2×C4⋊C8C22×C1311yescharacteristic
182C2×#102—21no—
183C2×C4×C8C22×C1311yescharacteristic
184#390—21no—
185#388—22no—
186#384C22×C1311yescharacteristic
187#384C22×C1311yescharacteristic
188#380—21no—
189C4×C4⋊C4—21no—
190C4×C4⋊C4C22×C1311yescharacteristic
191#340—21no—
192#340—22no—
193#340—21no—
194D4⋊C8C4×C1314yescomplemented
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13#38511yescharacteristic
203C22×C13#44711yescharacteristic
204C22×C13#44911yescharacteristic
205C22×C13#45211yescharacteristic
206C22×C13#45211yescharacteristic
207C22×C13#45411yescharacteristic
208C22×C13#45511yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—42no—
212C4×C13—42no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13—161no—
216C4×C13#42711yescharacteristic
217C4×C13#42811yescharacteristic
218C4×C13C4×D811yescharacteristic
219C4×C13#44011yescharacteristic
220C4×C13#47411yescharacteristic
221C4×C13#47811yescharacteristic
222C4×C13#48211yescharacteristic
223C4×C13#48511yescharacteristic
224C22×D4D4×C1311yescharacteristic
225C23×C4—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4C2×C4×C1312yes—
232C4×D4Q8×C1312yes—
233#117—42no—
234#117—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4D4×C1311yescharacteristic
241C2×C4⋊C4D4×C1311yescharacteristic
242C2×C4⋊C4D4×C1311yescharacteristic
243C2×C4⋊C4D4×C1312yes—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C42—22no—
248C2×C42—21no—
249C2×C42C23×C1311yescharacteristic
250#107—42no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8C2×C4×C1312yes—
255#102—42no—
256C4×C8—21no—
257C4×C8C2×C4×C1312yes—
258#95—22no—
259#95—21no—
260C2×C13—82no—
261C2×C13#162511yescharacteristic
262C2×C13#163811yescharacteristic
263C2×C13#164111yescharacteristic
264C2×C13#164611yescharacteristic
265C2×C13#185411yescharacteristic
266C2×C13#186011yescharacteristic
267C2×C13#186211yescharacteristic
268C24—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4C13×C4⋊C412yes—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C1311yescharacteristic
287C22×C4C2×D4×C1311yescharacteristic
288C22×C4C2×D4×C1311yescharacteristic
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C13×C4⋊C412yes—
313C4⋊C4C13×D812yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—44no—
317C22⋊C4—82no—
318C42—44no—
319C42—41no—
320C42—41no—
321C42C22×C4×C1311yescharacteristic
322C42C2×Q8×C1311yescharacteristic
323C42C13×#4111yescharacteristic
324C42C13×#4111yescharacteristic
325C13#889711yescharacteristic, direct product factor, Sylow
326C23—22no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23C13×#12011yescharacteristic
334D4—22no—
335D4—22no—
336D4—41no—
337D4—41no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C13×C4⋊C411yescharacteristic
360C2×C4C4×D4×C1311yescharacteristic
361C2×C4C4×D4×C1311yescharacteristic
362C2×C4C13×C22⋊Q811yescharacteristic
363C2×C4C13×C22⋊Q811yescharacteristic
364C2×C4C13×#12311yescharacteristic
365C2×C4C2×C13×D811yescharacteristic
366C2×C4C13×#13511yescharacteristic
367C2×C4C13×#13511yescharacteristic
368C2×C4C13×#13511yescharacteristic
369C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
370C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
371C2×C4C13×#13711yescharacteristic
372C2×C4C13×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C13×#38511yescharacteristic
384C22C13×#44711yescharacteristic
385C22C13×#44911yescharacteristic
386C22C13×#45211yescharacteristic
387C22C13×#45211yescharacteristic
388C22C13×#45411yescharacteristic
389C22C13×#45511yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4—161no—
397C4C13×#42711yescharacteristic
398C4C13×#42811yescharacteristic
399C4C4×C13×D811yescharacteristic
400C4C13×#44011yescharacteristic
401C4C13×#47411yescharacteristic
402C4C13×#47811yescharacteristic
403C4C13×#48211yescharacteristic
404C4C13×#48511yescharacteristic
405C2—82no—
406C2C13×#162511yescharacteristic
407C2C13×#163811yescharacteristic
408C2C13×#164111yescharacteristic
409C2C13×#164611yescharacteristic
410C2C13×#185411yescharacteristic
411C2C13×#186011yescharacteristic
412C2C13×#186211yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1947C2semidirect
3. C13×#1834C2semidirect
6. C13×#1296C2semidirect
7. C13×#1279C2semidirect
25. C13×D4⋊C8C4semidirect
62. #8897C13direct (N × H)
121. #1947C2×C13semidirect
122. #1834C2×C13semidirect
125. #1296C2×C13semidirect
126. #1279C2×C13semidirect
194. D4⋊C8C4×C13semidirect
325. C13#8897direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23542
C13×#19472
C13×#18342
C13×#18022
C2×C13×D4⋊C82
C13×#12962
C13×#12792
#889713