Finite Group Databasebeta

← C13×#9997 #15696336

Subgroups — C13×#9997 #15696336

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3100C211yesmaximal, characteristic
2C13×#3037C211yesmaximal, characteristic, complemented
3C13×#2536C211yesmaximal, characteristic, complemented
4C13×#1517C211yesmaximal, characteristic, complemented
5C13×#1486C211yesmaximal, characteristic, complemented
6C13×#1479C211yesmaximal, characteristic, complemented
7C13×#1286C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C13×#532C2211yescharacteristic
10C2×C13×C22⋊Q8—21no—
11C2×C4×Q8×C13C2211yescharacteristic
12C2×C4×D4×C13C2211yescharacteristic
13C13×#480—21no—
14C13×#474—21no—
15C13×#464—22no—
16C13×#462—21no—
17C13×#460—21no—
18C13×#459—21no—
19C13×#447—21no—
20C4×C13×D8—22no—
21C13×#431C2211yescharacteristic
22C13×#431C2211yescharacteristic
23C13×#423C2211yescharacteristic
24C13×#417—21no—
25C13×#398—21no—
26C13×#394—21no—
27C13×#388—22no—
28C13×#382C2211yescharacteristic
29C13×#380—21no—
30C13×#327—22no—
31C13×Q8⋊C8—22no—
32C13×D4⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C23×C4×C13—21no—
37C13×#137—42no—
38C13×#137—42no—
39C2×C13×Q16—22no—
40C2×C13×SD16—22no—
41C2×C13×D8—22no—
42C2×C13×M16—21no—
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#124—21no—
46C13×C22⋊Q8—42no—
47C13×C22⋊Q8—42no—
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—
56C4×D4×C13—21no—
57C4×D4×C13—21no—
58C4×D4×C13—21no—
59C4×D4×C13—21no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4D411yescharacteristic
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—21no—
68C2×C42×C13—21no—
69C2×C42×C13C2311yescharacteristic
70C13×#107—22no—
71C13×C4⋊C8—21no—
72C13×C4⋊C8—21no—
73C13×C4⋊C8—21no—
74C13×C4⋊C8D412yes—
75C13×#103—22no—
76C13×#102—22no—
77C13×#102—22no—
78C13×#102—22no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C4×C8×C13—21no—
82C4×C8×C13D412yes—
83C13×#95—22no—
84C13×#95—21no—
85C13×#95D412yes—
86#9997C1311yesmaximal, characteristic, direct product factor, Sylow
87C24×C13—21no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C13×#41—41no—
92C2×Q8×C13—21no—
93C2×Q8×C13—21no—
94C2×Q8×C13—21no—
95C2×Q8×C13—21no—
96C2×Q8×C13—21no—
97C2×Q8×C13—21no—
98C2×Q8×C13D812yescomplemented
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—21no—
102C2×D4×C13—21no—
103C2×D4×C13—21no—
104C2×D4×C13—42no—
105C2×D4×C13—41no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—41no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C13×Q16—44no—
121C13×SD16—44no—
122C13×D8—44no—
123C13×M16—41no—
124C13×M16—41no—
125C2×C8×C13—22no—
126C2×C8×C13—22no—
127C2×C8×C13—41no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—44no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C22⋊C4—44no—
140C13×C22⋊C4—44no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C42×C13—41no—
146C42×C13—41no—
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C42×C13C2×D411yescharacteristic
150C42×C13#4111yescharacteristic
151#3100C2×C1311yescharacteristic
152#3037C2×C1311yescharacteristic, complemented
153#2536C2×C1311yescharacteristic, complemented
154#1517C2×C1311yescharacteristic, complemented
155#1486C2×C1311yescharacteristic, complemented
156#1479C2×C1311yescharacteristic, complemented
157#1286C2×C1311yescharacteristic, complemented
158C23×C13—22no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13#12011yescharacteristic
167Q8×C13—22no—
168Q8×C13—22no—
169Q8×C13—41no—
170Q8×C13—41no—
171Q8×C13—41no—
172Q8×C13—41no—
173D4×C13—22no—
174D4×C13—22no—
175D4×C13—41no—
176D4×C13—41no—
177D4×C13—42no—
178D4×C13—41no—
179D4×C13—41no—
180D4×C13—81no—
181D4×C13—81no—
182D4×C13—81no—
183C2×C4×C13—22no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—42no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—81no—
198C2×C4×C13—81no—
199C2×C4×C13—81no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13#12011yescharacteristic
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13#12111yescharacteristic
206C2×C4×C13#12111yescharacteristic
207C2×C4×C13#12111yescharacteristic
208C2×C4×C13#12711yescharacteristic
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13#13511yescharacteristic
211C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
213C8×C13—42no—
214C8×C13—42no—
215C8×C13—81no—
216C2×#137—21no—
217#532C22×C1311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C4×Q8C22×C1311yescharacteristic
220C2×C4×D4C22×C1311yescharacteristic
221#480—21no—
222#474—21no—
223#464—22no—
224#462—21no—
225#460—21no—
226#459—21no—
227#447—21no—
228C4×D8—22no—
229#431C22×C1311yescharacteristic
230#431C22×C1311yescharacteristic
231#423C22×C1311yescharacteristic
232#417—21no—
233#398—21no—
234#394—21no—
235#388—22no—
236#382C22×C1311yescharacteristic
237#380—21no—
238#327—22no—
239Q8⋊C8—22no—
240D4⋊C8—22no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—42no—
244C22×C13—42no—
245C22×C13—42no—
246C22×C13—81no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13—81no—
251C22×C13—81no—
252C22×C13—81no—
253C22×C13#39211yescharacteristic
254C22×C13#44711yescharacteristic
255C22×C13#44911yescharacteristic
256C4×C13—21no—
257C4×C13—21no—
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—42no—
261C4×C13—82no—
262C4×C13—81no—
263C4×C13—81no—
264C4×C13—81no—
265C4×C13#44711yescharacteristic
266C4×C13#44911yescharacteristic
267C4×C13#46611yescharacteristic
268C4×C13#46911yescharacteristic
269C2×#41—21no—
270C22×Q8D4×C1311yescharacteristic
271C22×D4D4×C1311yescharacteristic
272C23×C4—21no—
273#137—42no—
274#137—42no—
275C2×Q16—22no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×M16—21no—
279C4⋊Q8D4×C1311yescharacteristic
280#127D4×C1311yescharacteristic
281#124—21no—
282C22⋊Q8—42no—
283C22⋊Q8—42no—
284#121—21no—
285#121—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C1311yescharacteristic
300C2×C4⋊C4D4×C1311yescharacteristic
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C42—21no—
305C2×C42C23×C1311yescharacteristic
306#107—22no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8D4×C1312yes—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C4×C8—21no—
318C4×C8D4×C1312yes—
319#95—22no—
320#95—21no—
321#95D4×C1312yes—
322C2×C13—21no—
323C2×C13—21no—
324C2×C13—82no—
325C2×C13—161no—
326C2×C13#199911yescharacteristic
327C2×C13#200911yescharacteristic
328C2×C13#201011yescharacteristic
329C24—21no—
330#41—41no—
331#41—41no—
332#41—41no—
333#41—41no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8C13×D812yescomplemented
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—42no—
347C2×D4—41no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C1311yescharacteristic
360C22×C4C2×D4×C1311yescharacteristic
361C22×C4C2×D4×C1311yescharacteristic
362Q16—44no—
363SD16—44no—
364D8—44no—
365M16—41no—
366M16—41no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—41no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—44no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C42—41no—
388C42—41no—
389C42C2×D4×C1311yescharacteristic
390C42C2×D4×C1311yescharacteristic
391C42C2×D4×C1311yescharacteristic
392C42C13×#4111yescharacteristic
393C13#999711yescharacteristic, direct product factor, Sylow
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C13×#12011yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—42no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4C13×#12011yescharacteristic
440C2×C4C13×#12011yescharacteristic
441C2×C4C13×#12111yescharacteristic
442C2×C4C13×#12111yescharacteristic
443C2×C4C13×#12111yescharacteristic
444C2×C4C13×#12711yescharacteristic
445C2×C4C2×C13×D811yescharacteristic
446C2×C4C13×#13511yescharacteristic
447C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
448C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
449C8—42no—
450C8—42no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22C13×#39211yescharacteristic
465C22C13×#44711yescharacteristic
466C22C13×#44911yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—81no—
476C4C13×#44711yescharacteristic
477C4C13×#44911yescharacteristic
478C4C13×#46611yescharacteristic
479C4C13×#46911yescharacteristic
480C2—21no—
481C2—21no—
482C2—82no—
483C2—161no—
484C2C13×#199911yescharacteristic
485C2C13×#200911yescharacteristic
486C2C13×#201011yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC2×C42C23×C13
prime radicalC13×#3100C2
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
2. C13×#3037C2semidirect
3. C13×#2536C2semidirect
4. C13×#1517C2semidirect
5. C13×#1486C2semidirect
6. C13×#1479C2semidirect
7. C13×#1286C2semidirect
86. #9997C13direct (N × H)
98. C2×Q8×C13D8semidirect
152. #3037C2×C13semidirect
153. #2536C2×C13semidirect
154. #1517C2×C13semidirect
155. #1486C2×C13semidirect
156. #1479C2×C13semidirect
157. #1286C2×C13semidirect
340. C2×Q8C13×D8semidirect
393. C13#9997direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31002
C13×#30372
C13×#25362
C13×#15172
C13×#14862
C13×#14792
C13×#12862
#999713