Finite Group Databasebeta

← C13×#10243 #15696582

Subgroups — C13×#10243 #15696582

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3226C211yesmaximal, characteristic
2C13×#3037C211yesmaximal, characteristic
3C13×#2546C211yesmaximal, characteristic, complemented
4C13×#1546C211yesmaximal, characteristic, complemented
5C13×#1502C211yesmaximal, characteristic
6C13×#1479C211yesmaximal, characteristic, complemented
7C13×#1303C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C13×#532C2211yescharacteristic
10C2×C13×C4⋊Q8—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C13C2211yescharacteristic
13C13×#500—21no—
14C13×#486—21no—
15C13×#480—22no—
16C13×#474—22no—
17C13×#464—22no—
18C13×#462—21no—
19C13×#460—21no—
20C13×#431C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C13×#417—21no—
24C13×#398—22no—
25C13×#391—21no—
26C13×#389—22no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C13×#332—22no—
29C13×#327—22no—
30C13×Q8⋊C8—22no—
31C2×C13×#41—21no—
32C22×Q8×C13—21no—
33C22×Q8×C13D411yescharacteristic
34C13×#137—42no—
35C13×#137—42no—
36C2×C13×Q16—22no—
37C2×C13×SD16—22no—
38C2×C13×M16—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—42no—
44C13×C4⋊Q8—42no—
45C13×C4⋊Q8D411yescharacteristic
46C13×#127D411yescharacteristic
47C13×#124—21no—
48C13×#121—21no—
49C13×#121—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×D4×C13—21no—
55C4×D4×C13—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4D412yes—
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C42×C13—21no—
63C2×C42×C13—21no—
64C2×C42×C13C2311yescharacteristic
65C13×#107—24no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8D412yes—
69C13×C4⋊C8D412yes—
70C13×#103—22no—
71C13×#102—22no—
72C13×#102—24no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8—21no—
75C4×C8×C13—21no—
76C4×C8×C13—21no—
77C13×#95—24no—
78C13×#95D412yes—
79#10243C1311yesmaximal, characteristic, direct product factor, Sylow
80C13×#41—41no—
81C13×#41—41no—
82C13×#41—41no—
83C13×#41—41no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—41no—
91C2×Q8×C13—41no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×Q8×C13—41no—
95C2×Q8×C13—41no—
96C2×Q8×C13D812yes—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—41no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—41no—
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C13×Q16—44no—
110C13×SD16—44no—
111C13×M16—41no—
112C13×M16—41no—
113C2×C8×C13—22no—
114C2×C8×C13—22no—
115C2×C8×C13—41no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—48no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C42×C13—41no—
131C42×C13—41no—
132C42×C13—41no—
133C42×C13—41no—
134C42×C13C2×D411yescharacteristic
135C42×C13C2×D411yescharacteristic
136C42×C13C2×D411yescharacteristic
137C42×C13#4111yescharacteristic
138#3226C2×C1311yescharacteristic
139#3037C2×C1311yescharacteristic
140#2546C2×C1311yescharacteristic, complemented
141#1546C2×C1311yescharacteristic, complemented
142#1502C2×C1311yescharacteristic
143#1479C2×C1311yescharacteristic, complemented
144#1303C2×C1311yescharacteristic, complemented
145C23×C13—41no—
146C23×C13#12011yescharacteristic
147Q8×C13—22no—
148Q8×C13—22no—
149Q8×C13—41no—
150Q8×C13—41no—
151Q8×C13—41no—
152Q8×C13—41no—
153Q8×C13—81no—
154Q8×C13—81no—
155Q8×C13—81no—
156Q8×C13—81no—
157D4×C13—41no—
158D4×C13—41no—
159D4×C13—42no—
160D4×C13—81no—
161D4×C13—81no—
162D4×C13—81no—
163C2×C4×C13—22no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13#12011yescharacteristic
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12711yescharacteristic
185C2×C4×C13C2×D811yescharacteristic
186C2×C4×C13#13511yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
189C8×C13—42no—
190C8×C13—42no—
191C8×C13—81no—
192C2×#137—21no—
193#532C22×C1311yescharacteristic
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8C22×C1311yescharacteristic
196C2×C4×Q8C22×C1311yescharacteristic
197#500—21no—
198#486—21no—
199#480—22no—
200#474—22no—
201#464—22no—
202#462—21no—
203#460—21no—
204#431C22×C1311yescharacteristic
205#431C22×C1311yescharacteristic
206#423C22×C1311yescharacteristic
207#417—21no—
208#398—22no—
209#391—21no—
210#389—22no—
211C4×C4⋊C4C22×C1311yescharacteristic
212#332—22no—
213#327—22no—
214Q8⋊C8—22no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13—81no—
220C22×C13#39211yescharacteristic
221C22×C13#44711yescharacteristic
222C22×C13#44911yescharacteristic
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—21no—
226C4×C13—44no—
227C4×C13—42no—
228C4×C13—82no—
229C4×C13—81no—
230C4×C13—81no—
231C4×C13#44711yescharacteristic
232C4×C13#44911yescharacteristic
233C4×C13#45612yes—
234C4×C13#46611yescharacteristic
235C4×C13#46911yescharacteristic
236C2×#41—21no—
237C22×Q8—21no—
238C22×Q8D4×C1311yescharacteristic
239#137—42no—
240#137—42no—
241C2×Q16—22no—
242C2×SD16—22no—
243C2×M16—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—42no—
249C4⋊Q8—42no—
250C4⋊Q8D4×C1311yescharacteristic
251#127D4×C1311yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×D4—21no—
260C4×D4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C1311yescharacteristic
266C2×C4⋊C4D4×C1312yes—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42C23×C1311yescharacteristic
270#107—24no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C1312yes—
274C4⋊C8D4×C1312yes—
275#103—22no—
276#102—22no—
277#102—24no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C4×C8—21no—
281C4×C8—21no—
282#95—24no—
283#95D4×C1312yes—
284C2×C13—21no—
285C2×C13—21no—
286C2×C13—161no—
287C2×C13#199911yescharacteristic
288C2×C13#200511yescharacteristic
289C2×C13#200911yescharacteristic
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8C13×D812yes—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—41no—
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318C22×C4C2×D4×C1311yescharacteristic
319Q16—44no—
320SD16—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—48no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C42—41no—
341C42—41no—
342C42—41no—
343C42—41no—
344C42C2×D4×C1311yescharacteristic
345C42C2×D4×C1311yescharacteristic
346C42C2×D4×C1311yescharacteristic
347C42C13×#4111yescharacteristic
348C13#1024311yescharacteristic, direct product factor, Sylow
349C23—41no—
350C23C13×#12011yescharacteristic
351Q8—22no—
352Q8—22no—
353Q8—41no—
354Q8—41no—
355Q8—41no—
356Q8—41no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361D4—41no—
362D4—41no—
363D4—42no—
364D4—81no—
365D4—81no—
366D4—81no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C13×#12011yescharacteristic
384C2×C4C13×#12011yescharacteristic
385C2×C4C13×#12111yescharacteristic
386C2×C4C13×#12111yescharacteristic
387C2×C4C13×#12111yescharacteristic
388C2×C4C13×#12711yescharacteristic
389C2×C4C2×C13×D811yescharacteristic
390C2×C4C13×#13511yescharacteristic
391C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
392C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
393C8—42no—
394C8—42no—
395C8—81no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22C13×#39211yescharacteristic
402C22C13×#44711yescharacteristic
403C22C13×#44911yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—44no—
408C4—42no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4C13×#44711yescharacteristic
413C4C13×#44911yescharacteristic
414C4C13×#45612yes—
415C4C13×#46611yescharacteristic
416C4C13×#46911yescharacteristic
417C2—21no—
418C2—21no—
419C2—161no—
420C2C13×#199911yescharacteristic
421C2C13×#200511yescharacteristic
422C2C13×#200911yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2546C2semidirect
4. C13×#1546C2semidirect
6. C13×#1479C2semidirect
7. C13×#1303C2semidirect
79. #10243C13direct (N × H)
140. #2546C2×C13semidirect
141. #1546C2×C13semidirect
143. #1479C2×C13semidirect
144. #1303C2×C13semidirect
348. C13#10243direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#32262
C13×#30372
C13×#25462
C13×#15462
C13×#15022
C13×#14792
C13×#13032
#1024313