Finite Group Databasebeta

← C13×#9522 #15695861

Subgroups — C13×#9522 #15695861

Order 3328.

472 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3092C211yesmaximal, characteristic
2C13×#2976C211yesmaximal, characteristic
3C13×#1823C211yesmaximal, characteristic, complemented
4C13×#1821C211yesmaximal, characteristic, complemented
5C13×#1513C211yesmaximal, characteristic
6C13×#1305C211yesmaximal, characteristic, complemented
7C13×#1293C211yesmaximal, characteristic, complemented
8C13×#525C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#484C412yescomplemented
11C13×#483—21no—
12C13×#481C412yescomplemented
13C13×#480—21no—
14C13×#436—21no—
15C13×#435—21no—
16C13×#435—21no—
17C8×D4×C13—21no—
18C13×#433—21no—
19C13×#428—21no—
20C13×#417—21no—
21C13×#408—21no—
22C13×#407C2211yescharacteristic
23C13×#407C2211yescharacteristic
24C13×#407C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#343—21no—
28C13×#343—21no—
29C13×#340—21no—
30C13×#340—21no—
31C13×#328—21no—
32C13×#327—21no—
33C2×C13×#41D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C2×C13×M16—21no—
37C2×C13×M16—21no—
38C2×C13×M16—21no—
39C2×C13×M16D411yescharacteristic
40C2×C13×M16D411yescharacteristic
41C22×C8×C13—21no—
42C22×C8×C13D411yescharacteristic
43C22×C8×C13D411yescharacteristic
44C13×#123—21no—
45C13×C22⋊Q8C2×C411yescharacteristic
46C13×C22⋊Q8D411yescharacteristic
47C13×#121C2×C411yescharacteristic
48C13×#121D411yescharacteristic
49C13×#120—21no—
50C4×D4×C13—21no—
51C4×D4×C13—21no—
52C13×#117D411yescharacteristic
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4C2×C412yes—
60C2×C13×C22⋊C4—21no—
61C13×#107—22no—
62C13×#106—22no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8—21no—
65C13×#103—22no—
66C13×#102—22no—
67C13×C22⋊C8—21no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8C2×C412yes—
77C13×#97—21no—
78C4×C8×C13—21no—
79C13×#95—21no—
80#9522C1311yesmaximal, characteristic, direct product factor, Sylow
81C24×C13#4111yescharacteristic
82C13×#41—41no—
83C13×#41—41no—
84C2×Q8×C13C22⋊C411yescharacteristic
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13C22⋊C411yescharacteristic
89C22×C4×C13—21no—
90C22×C4×C13—22no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—81no—
97C22×C4×C13—81no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C13×M16—41no—
105C13×M16—41no—
106C13×M16—41no—
107C13×M16—41no—
108C13×M16—41no—
109C13×M16—41no—
110C13×M16—81no—
111C2×C8×C13—22no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13—21no—
115C2×C8×C13—21no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13—41no—
119C2×C8×C13—81no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4C22⋊C411yescharacteristic
129C13×C4⋊C4C22⋊C411yescharacteristic
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C13×C22⋊C4—21no—
134C13×C22⋊C4—21no—
135C13×C22⋊C4—81no—
136C42×C13—21no—
137#3092C2×C1311yescharacteristic
138#2976C2×C1311yescharacteristic
139#1823C2×C1311yescharacteristic, complemented
140#1821C2×C1311yescharacteristic, complemented
141#1513C2×C1311yescharacteristic
142#1305C2×C1311yescharacteristic, complemented
143#1293C2×C1311yescharacteristic, complemented
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13C4×D411yescharacteristic
150C23×C13#12111yescharacteristic
151C23×C13#12311yescharacteristic
152Q8×C13—41no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—41no—
156D4×C13—81no—
157D4×C13—81no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—42no—
173C2×C4×C13—82no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13—82no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13C2×C22⋊C411yescharacteristic
181C2×C4×C13C4×D411yescharacteristic
182C2×C4×C13#12011yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C8×C13—42no—
185C8×C13—41no—
186C8×C13—41no—
187C8×C13—41no—
188C8×C13—41no—
189C8×C13—81no—
190#525C22×C1311yescharacteristic
191C22×C4⋊C4C22×C1311yescharacteristic
192#484C4×C1312yescomplemented
193#483—21no—
194#481C4×C1312yescomplemented
195#480—21no—
196#436—21no—
197#435—21no—
198#435—21no—
199C8×D4—21no—
200#433—21no—
201#428—21no—
202#417—21no—
203#408—21no—
204#407C22×C1311yescharacteristic
205#407C22×C1311yescharacteristic
206#407C22×C1311yescharacteristic
207C2×C22⋊C8C22×C1311yescharacteristic
208#380C22×C1311yescharacteristic
209#343—21no—
210#343—21no—
211#340—21no—
212#340—21no—
213#328—21no—
214#327—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—42no—
224C22×C13—42no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13#38611yescharacteristic
229C22×C13#47111yescharacteristic
230C22×C13#47211yescharacteristic
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—82no—
238C4×C13—161no—
239C4×C13#45811yescharacteristic
240C4×C13#45811yescharacteristic
241C2×#41D4×C1311yescharacteristic
242C23×C4—21no—
243C23×C4C23×C1311yescharacteristic
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16D4×C1311yescharacteristic
248C2×M16D4×C1311yescharacteristic
249C22×C8—21no—
250C22×C8D4×C1311yescharacteristic
251C22×C8D4×C1311yescharacteristic
252#123—21no—
253C22⋊Q8C2×C4×C1311yescharacteristic
254C22⋊Q8D4×C1311yescharacteristic
255#121C2×C4×C1311yescharacteristic
256#121D4×C1311yescharacteristic
257#120—21no—
258C4×D4—21no—
259C4×D4—21no—
260#117D4×C1311yescharacteristic
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C2×C4×C1312yes—
268C2×C22⋊C4—21no—
269#107—22no—
270#106—22no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273#103—22no—
274#102—22no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8C2×C4×C1312yes—
285#97—21no—
286C4×C8—21no—
287#95—21no—
288C2×C13—21no—
289C2×C13—21no—
290C2×C13—41no—
291C2×C13—41no—
292C2×C13—81no—
293C2×C13#189011yescharacteristic
294C2×C13#190211yescharacteristic
295C2×C13#190711yescharacteristic
296C24C13×#4111yescharacteristic
297#41—41no—
298#41—41no—
299C2×Q8C13×C22⋊C411yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4C13×C22⋊C411yescharacteristic
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4C22×C4×C1311yescharacteristic
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318C22×C4C13×#4111yescharacteristic
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—81no—
326C2×C8—22no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—81no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C13×C22⋊C411yescharacteristic
344C4⋊C4C13×C22⋊C411yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—81no—
351C42—21no—
352C13#952211yescharacteristic, direct product factor, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23C4×D4×C1311yescharacteristic
359C23C13×#12111yescharacteristic
360C23C13×#12311yescharacteristic
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C2×C13×C22⋊C411yescharacteristic
390C2×C4C4×D4×C1311yescharacteristic
391C2×C4C13×#12011yescharacteristic
392C2×C4C13×#12111yescharacteristic
393C8—42no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—41no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22C13×#38611yescharacteristic
413C22C13×#47111yescharacteristic
414C22C13×#47211yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—161no—
423C4C13×#45811yescharacteristic
424C4C13×#45811yescharacteristic
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2C13×#189011yescharacteristic
431C2C13×#190211yescharacteristic
432C2C13×#190711yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1823C2semidirect
4. C13×#1821C2semidirect
6. C13×#1305C2semidirect
7. C13×#1293C2semidirect
10. C13×#484C4semidirect
12. C13×#481C4semidirect
80. #9522C13direct (N × H)
139. #1823C2×C13semidirect
140. #1821C2×C13semidirect
142. #1305C2×C13semidirect
143. #1293C2×C13semidirect
192. #484C4×C13semidirect
194. #481C4×C13semidirect
352. C13#9522direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30922
C13×#29762
C13×#18232
C13×#18212
C13×#15132
C13×#13052
C13×#12932
#952213