Finite Group Databasebeta

← C13×#9960 #15696299

Subgroups — C13×#9960 #15696299

Order 3328.

650 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×#3187C211yesmaximal, characteristic
2C2×C13×#483C211yesmaximal, characteristic, complemented
3C13×#2501C211yesmaximal, characteristic
4C13×#1996C211yesmaximal, characteristic, complemented
5C13×#1823C211yesmaximal, characteristic, complemented
6C13×#1519C211yesmaximal, characteristic
7C13×#1282C211yesmaximal, characteristic, complemented
8C2×C13×#123—22no—
9C2×C13×C22⋊Q8C2211yescharacteristic
10C2×C13×#121C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C13×#483—22no—
13C13×#483—21no—
14C13×#483—22no—
15C13×#481—21no—
16C13×#465—22no—
17C13×#450—21no—
18C13×#448—21no—
19C2×C13×#106—21no—
20C2×C13×#103—21no—
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C13×#399—22no—
24C13×#390—21no—
25C13×#384—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C22⋊C4C2211yescharacteristic
28C13×#342—22no—
29C13×#340—22no—
30C13×#327—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C2×C13×SD16—22no—
37C22×C8×C13—21no—
38C22×C8×C13D412yes—
39C13×#123—44no—
40C13×#123—44no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C13×#121—21no—
46C13×#121—21no—
47C13×#121—21no—
48C13×#121—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4D412yes—
65C2×C42×C13—21no—
66C13×#106—24no—
67C13×#106—22no—
68C13×#103—24no—
69C13×#103—22no—
70C13×#102—22no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×C22⋊C8D412yes—
75C13×#95—21no—
76C13×#95—21no—
77#9960C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—42no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—42no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—42no—
89C2×D4×C13—42no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—42no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—41no—
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C13×SD16—82no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C2×C8×C13—42no—
111C2×C8×C13—42no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—48no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C22⋊C4—22no—
125C13×C22⋊C4—48no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4SD1614yescomplemented
132C42×C13—42no—
133#3187C2×C1311yescharacteristic
134C2×#483C2×C1311yescharacteristic, complemented
135#2501C2×C1311yescharacteristic
136#1996C2×C1311yescharacteristic, complemented
137#1823C2×C1311yescharacteristic, complemented
138#1519C2×C1311yescharacteristic
139#1282C2×C1311yescharacteristic, complemented
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13#12011yescharacteristic
147C23×C13#12111yescharacteristic
148C23×C13#12711yescharacteristic
149C23×C13C2×SD1612yes—
150C23×C13AGL(1,ℤ/8)12yes—
151Q8×C13—42no—
152Q8×C13—42no—
153D4×C13—42no—
154D4×C13—81no—
155D4×C13—82no—
156D4×C13—81no—
157D4×C13—81no—
158C2×C4×C13—22no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—24no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—44no—
172C2×C4×C13—42no—
173C2×C4×C13—82no—
174C2×C4×C13—81no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13—81no—
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13#12011yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12111yescharacteristic
185C8×C13—42no—
186C8×C13—42no—
187C2×#123—22no—
188C2×C22⋊Q8C22×C1311yescharacteristic
189C2×#121C22×C1311yescharacteristic
190C22×C4⋊C4C22×C1311yescharacteristic
191#483—22no—
192#483—21no—
193#483—22no—
194#481—21no—
195#465—22no—
196#450—21no—
197#448—21no—
198C2×#106—21no—
199C2×#103—21no—
200C2×C22⋊C8C22×C1311yescharacteristic
201C2×C22⋊C8C22×C1311yescharacteristic
202#399—22no—
203#390—21no—
204#384—21no—
205#380C22×C1311yescharacteristic
206C4×C22⋊C4C22×C1311yescharacteristic
207#342—22no—
208#340—22no—
209#327—22no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—42no—
217C22×C13—42no—
218C22×C13—84no—
219C22×C13—81no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13#39211yescharacteristic
223C22×C13#45012yes—
224C22×C13#46012yes—
225C22×C13#49211yescharacteristic
226C22×C13#49611yescharacteristic
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—44no—
231C4×C13—81no—
232C4×C13—82no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—161no—
236C4×C13#45812yes—
237C22×Q8D4×C1311yescharacteristic
238C22×D4—21no—
239C22×D4D4×C1311yescharacteristic
240C23×C4—21no—
241C23×C4C23×C1311yescharacteristic
242C2×SD16—22no—
243C22×C8—21no—
244C22×C8D4×C1312yes—
245#123—44no—
246#123—44no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C1312yes—
264C2×C4⋊C4D4×C1311yescharacteristic
265C2×C4⋊C4D4×C1311yescharacteristic
266C2×C22⋊C4—24no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4D4×C1312yes—
271C2×C42—21no—
272#106—24no—
273#106—22no—
274#103—24no—
275#103—22no—
276#102—22no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8D4×C1312yes—
281#95—21no—
282#95—21no—
283C2×C13—22no—
284C2×C13—21no—
285C2×C13—22no—
286C2×C13—21no—
287C2×C13—161no—
288C2×C13#200911yescharacteristic
289C2×C13#201411yescharacteristic
290C2×C13#202211yescharacteristic
291C24—21no—
292C24C2×D4×C1311yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4C2×D4×C1311yescharacteristic
315C22×C4C2×D4×C1311yescharacteristic
316C22×C4C2×D4×C1311yescharacteristic
317C22×C4C2×D4×C1311yescharacteristic
318C22×C4C2×D4×C1311yescharacteristic
319C22×C4C13×#4111yescharacteristic
320SD16—82no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C2×C8—42no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—48no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C22⋊C4—22no—
338C22⋊C4—48no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—42no—
344C22⋊C4C13×SD1614yescomplemented
345C42—42no—
346C13#996011yescharacteristic, direct product factor, Sylow
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—42no—
353C23C13×#12011yescharacteristic
354C23C13×#12111yescharacteristic
355C23C13×#12711yescharacteristic
356C23C2×C13×SD1612yes—
357C23C13×AGL(1,ℤ/8)12yes—
358Q8—42no—
359Q8—42no—
360D4—42no—
361D4—81no—
362D4—82no—
363D4—81no—
364D4—81no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4C13×#12011yescharacteristic
389C2×C4C13×#12011yescharacteristic
390C2×C4C13×#12111yescharacteristic
391C2×C4C13×#12111yescharacteristic
392C8—42no—
393C8—42no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C13×#39211yescharacteristic
407C22C13×#45012yes—
408C22C13×#46012yes—
409C22C13×#49211yescharacteristic
410C22C13×#49611yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—44no—
415C4—81no—
416C4—82no—
417C4—81no—
418C4—81no—
419C4—161no—
420C4C13×#45812yes—
421C2—22no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—161no—
426C2C13×#200911yescharacteristic
427C2C13×#201411yescharacteristic
428C2C13×#202211yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#483C2semidirect
4. C13×#1996C2semidirect
5. C13×#1823C2semidirect
7. C13×#1282C2semidirect
77. #9960C13direct (N × H)
131. C13×C22⋊C4SD16semidirect
134. C2×#483C2×C13semidirect
136. #1996C2×C13semidirect
137. #1823C2×C13semidirect
139. #1282C2×C13semidirect
344. C22⋊C4C13×SD16semidirect
346. C13#9960direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31872
C2×C13×#4832
C13×#25012
C13×#19962
C13×#18232
C13×#15192
C13×#12822
#996013