Finite Group Databasebeta

← C13×#9521 #15695860

Subgroups — C13×#9521 #15695860

Order 3328.

472 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3092C211yesmaximal, characteristic
2C13×#2976C211yesmaximal, characteristic
3C13×#1824C211yesmaximal, characteristic, complemented
4C13×#1821C211yesmaximal, characteristic, complemented
5C13×#1513C211yesmaximal, characteristic
6C13×#1305C211yesmaximal, characteristic, complemented
7C13×#1293C211yesmaximal, characteristic, complemented
8C13×#525C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#484—21no—
11C13×#483C412yescomplemented
12C13×#481—21no—
13C13×#480C412yescomplemented
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#9521C1311yesmaximal, 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—82no—
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C13×M16—41no—
104C13×M16—41no—
105C13×M16—41no—
106C13×M16—41no—
107C13×M16—41no—
108C13×M16—41no—
109C13×M16—81no—
110C2×C8×C13—22no—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13—21no—
115C2×C8×C13—41no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13—81no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4C22⋊C411yescharacteristic
128C13×C4⋊C4C22⋊C411yescharacteristic
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C13×C22⋊C4—21no—
134C13×C22⋊C4—81no—
135C42×C13—21no—
136#3092C2×C1311yescharacteristic
137#2976C2×C1311yescharacteristic
138#1824C2×C1311yescharacteristic, complemented
139#1821C2×C1311yescharacteristic, complemented
140#1513C2×C1311yescharacteristic
141#1305C2×C1311yescharacteristic, complemented
142#1293C2×C1311yescharacteristic, complemented
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13C4×D411yescharacteristic
149C23×C13#12111yescharacteristic
150C23×C13#12311yescharacteristic
151Q8×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—41no—
155D4×C13—81no—
156D4×C13—81no—
157C2×C4×C13—21no—
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—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—82no—
173C2×C4×C13—82no—
174C2×C4×C13—82no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13C2×C22⋊C411yescharacteristic
179C2×C4×C13C4×D411yescharacteristic
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C8×C13—42no—
183C8×C13—41no—
184C8×C13—41no—
185C8×C13—41no—
186C8×C13—41no—
187C8×C13—81no—
188#525C22×C1311yescharacteristic
189C22×C4⋊C4C22×C1311yescharacteristic
190#484—21no—
191#483C4×C1312yescomplemented
192#481—21no—
193#480C4×C1312yescomplemented
194#436—21no—
195#435—21no—
196#435—21no—
197C8×D4—21no—
198#433—21no—
199#428—21no—
200#417—21no—
201#408—21no—
202#407C22×C1311yescharacteristic
203#407C22×C1311yescharacteristic
204#407C22×C1311yescharacteristic
205C2×C22⋊C8C22×C1311yescharacteristic
206#380C22×C1311yescharacteristic
207#343—21no—
208#343—21no—
209#340—21no—
210#340—21no—
211#328—21no—
212#327—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13#38611yescharacteristic
227C22×C13#47111yescharacteristic
228C22×C13#47311yescharacteristic
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—41no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—82no—
236C4×C13—161no—
237C4×C13#45811yescharacteristic
238C4×C13#45811yescharacteristic
239C2×#41D4×C1311yescharacteristic
240C23×C4—21no—
241C23×C4C23×C1311yescharacteristic
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16D4×C1311yescharacteristic
246C2×M16D4×C1311yescharacteristic
247C22×C8—21no—
248C22×C8D4×C1311yescharacteristic
249C22×C8D4×C1311yescharacteristic
250#123—21no—
251C22⋊Q8C2×C4×C1311yescharacteristic
252C22⋊Q8D4×C1311yescharacteristic
253#121C2×C4×C1311yescharacteristic
254#121D4×C1311yescharacteristic
255#120—21no—
256C4×D4—21no—
257C4×D4—21no—
258#117D4×C1311yescharacteristic
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C1312yes—
266C2×C22⋊C4—21no—
267#107—22no—
268#106—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271#103—22no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8C2×C4×C1312yes—
283#97—21no—
284C4×C8—21no—
285#95—21no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13—41no—
289C2×C13—41no—
290C2×C13—81no—
291C2×C13#189011yescharacteristic
292C2×C13#190311yescharacteristic
293C2×C13#190811yescharacteristic
294C24C13×#4111yescharacteristic
295#41—41no—
296#41—41no—
297C2×Q8C13×C22⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4C13×C22⋊C411yescharacteristic
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4C22×C4×C1311yescharacteristic
311C22×C4C2×D4×C1311yescharacteristic
312C22×C4C2×D4×C1311yescharacteristic
313C22×C4C2×D4×C1311yescharacteristic
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C13×#4111yescharacteristic
316M16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—81no—
323C2×C8—22no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—81no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4C13×C22⋊C411yescharacteristic
341C4⋊C4C13×C22⋊C411yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—81no—
348C42—21no—
349C13#952111yescharacteristic, direct product factor, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23C4×D4×C1311yescharacteristic
356C23C13×#12111yescharacteristic
357C23C13×#12311yescharacteristic
358Q8—41no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—81no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C13×C22⋊C411yescharacteristic
386C2×C4C4×D4×C1311yescharacteristic
387C2×C4C13×#12011yescharacteristic
388C2×C4C13×#12111yescharacteristic
389C8—42no—
390C8—41no—
391C8—41no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C13×#38611yescharacteristic
409C22C13×#47111yescharacteristic
410C22C13×#47311yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—82no—
418C4—161no—
419C4C13×#45811yescharacteristic
420C4C13×#45811yescharacteristic
421C2—21no—
422C2—21no—
423C2—41no—
424C2—41no—
425C2—81no—
426C2C13×#189011yescharacteristic
427C2C13×#190311yescharacteristic
428C2C13×#190811yescharacteristic
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×#1824C2semidirect
4. C13×#1821C2semidirect
6. C13×#1305C2semidirect
7. C13×#1293C2semidirect
11. C13×#483C4semidirect
13. C13×#480C4semidirect
80. #9521C13direct (N × H)
138. #1824C2×C13semidirect
139. #1821C2×C13semidirect
141. #1305C2×C13semidirect
142. #1293C2×C13semidirect
191. #483C4×C13semidirect
193. #480C4×C13semidirect
349. C13#9521direct (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×#18242
C13×#18212
C13×#15132
C13×#13052
C13×#12932
#952113