Finite Group Databasebeta

← C13×#9999 #15696338

Subgroups — C13×#9999 #15696338

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3103C211yesmaximal, characteristic
2C13×#3037C211yesmaximal, characteristic
3C13×#2581C211yesmaximal, characteristic, complemented
4C13×#1517C211yesmaximal, characteristic
5C13×#1487C211yesmaximal, characteristic, complemented
6C13×#1479C211yesmaximal, characteristic, complemented
7C13×#1286C211yesmaximal, characteristic, complemented
8C2×C13×#137—21no—
9C13×#532C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C2×C4×Q8×C13C2211yescharacteristic
12C13×#481—21no—
13C13×#475—21no—
14C13×#464—22no—
15C13×#462—21no—
16C13×#460—21no—
17C13×#460—21no—
18C13×#448—21no—
19C4×C13×SD16—22no—
20C13×#431C2211yescharacteristic
21C13×#431C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C13×#417—21no—
24C13×#400—21no—
25C13×#395—21no—
26C13×#391—21no—
27C13×#389—21no—
28C13×#387—22no—
29C13×#382C2211yescharacteristic
30C13×#327—22no—
31C13×Q8⋊C8—22no—
32C13×Q8⋊C8—22no—
33C2×C13×#41—21no—
34C22×Q8×C13D411yescharacteristic
35C22×Q8×C13D411yescharacteristic
36C13×#137—42no—
37C13×#137—42no—
38C2×C13×Q16—22no—
39C2×C13×SD16—22no—
40C2×C13×SD16—22no—
41C2×C13×M16—21no—
42C13×C4⋊Q8D411yescharacteristic
43C13×#127D411yescharacteristic
44C13×#124—21no—
45C13×#121—21no—
46C13×#121—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13—21no—
52C4×Q8×C13—21no—
53C4×Q8×C13—21no—
54C4×Q8×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C13×C4⋊C4D411yescharacteristic
63C2×C42×C13—21no—
64C2×C42×C13—21no—
65C2×C42×C13C2311yescharacteristic
66C13×#106—22no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8—21no—
70C13×C4⋊C8D412yes—
71C13×#103—22no—
72C13×#103—22no—
73C13×#102—22no—
74C13×#102—22no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C4×C8×C13—21no—
78C4×C8×C13D412yes—
79C13×#95—22no—
80C13×#95—22no—
81C13×#95—22no—
82C13×#95—21no—
83C13×#95D412yes—
84#9999C1311yesmaximal, characteristic, direct product factor, Sylow
85C13×#41—41no—
86C13×#41—41no—
87C13×#41—41no—
88C13×#41—41no—
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13—21no—
92C2×Q8×C13—21no—
93C2×Q8×C13—21no—
94C2×Q8×C13—21no—
95C2×Q8×C13—21no—
96C2×Q8×C13—21no—
97C2×Q8×C13—42no—
98C2×Q8×C13SD1612yescomplemented
99C2×D4×C13—21no—
100C2×D4×C13—21no—
101C2×D4×C13—21no—
102C2×D4×C13—41no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—41no—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C13×Q16—44no—
113C13×SD16—44no—
114C13×SD16—44no—
115C13×M16—41no—
116C13×M16—41no—
117C2×C8×C13—22no—
118C2×C8×C13—22no—
119C2×C8×C13—41no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—44no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C42×C13—41no—
136C42×C13—41no—
137C42×C13—41no—
138C42×C13—41no—
139C42×C13C2×D411yescharacteristic
140C42×C13C2×D411yescharacteristic
141C42×C13C2×D411yescharacteristic
142C42×C13#4111yescharacteristic
143#3103C2×C1311yescharacteristic
144#3037C2×C1311yescharacteristic
145#2581C2×C1311yescharacteristic, complemented
146#1517C2×C1311yescharacteristic
147#1487C2×C1311yescharacteristic, complemented
148#1479C2×C1311yescharacteristic, complemented
149#1286C2×C1311yescharacteristic, complemented
150C23×C13—41no—
151C23×C13#12011yescharacteristic
152Q8×C13—22no—
153Q8×C13—22no—
154Q8×C13—22no—
155Q8×C13—22no—
156Q8×C13—41no—
157Q8×C13—41no—
158Q8×C13—41no—
159Q8×C13—41no—
160Q8×C13—41no—
161Q8×C13—41no—
162D4×C13—42no—
163D4×C13—41no—
164D4×C13—41no—
165D4×C13—81no—
166D4×C13—81no—
167D4×C13—81no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—81no—
185C2×C4×C13—81no—
186C2×C4×C13#12011yescharacteristic
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#12111yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#12111yescharacteristic
191C2×C4×C13#12711yescharacteristic
192C2×C4×C13C2×SD1611yescharacteristic
193C2×C4×C13#13511yescharacteristic
194C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C13#13711yescharacteristic
196C8×C13—42no—
197C8×C13—42no—
198C8×C13—81no—
199C2×#137—21no—
200#532C22×C1311yescharacteristic
201C2×C4×Q8C22×C1311yescharacteristic
202C2×C4×Q8C22×C1311yescharacteristic
203#481—21no—
204#475—21no—
205#464—22no—
206#462—21no—
207#460—21no—
208#460—21no—
209#448—21no—
210C4×SD16—22no—
211#431C22×C1311yescharacteristic
212#431C22×C1311yescharacteristic
213#423C22×C1311yescharacteristic
214#417—21no—
215#400—21no—
216#395—21no—
217#391—21no—
218#389—21no—
219#387—22no—
220#382C22×C1311yescharacteristic
221#327—22no—
222Q8⋊C8—22no—
223Q8⋊C8—22no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13#39211yescharacteristic
230C22×C13#44811yescharacteristic
231C22×C13#44911yescharacteristic
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—42no—
237C4×C13—42no—
238C4×C13—82no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13#45011yescharacteristic
243C4×C13#45211yescharacteristic
244C4×C13#46511yescharacteristic
245C4×C13#46811yescharacteristic
246C2×#41—21no—
247C22×Q8D4×C1311yescharacteristic
248C22×Q8D4×C1311yescharacteristic
249#137—42no—
250#137—42no—
251C2×Q16—22no—
252C2×SD16—22no—
253C2×SD16—22no—
254C2×M16—21no—
255C4⋊Q8D4×C1311yescharacteristic
256#127D4×C1311yescharacteristic
257#124—21no—
258#121—21no—
259#121—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×D4—21no—
269C4×D4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1311yescharacteristic
275C2×C4⋊C4D4×C1311yescharacteristic
276C2×C42—21no—
277C2×C42—21no—
278C2×C42C23×C1311yescharacteristic
279#106—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8D4×C1312yes—
284#103—22no—
285#103—22no—
286#102—22no—
287#102—22no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C4×C8—21no—
291C4×C8D4×C1312yes—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—21no—
296#95D4×C1312yes—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—161no—
300C2×C13#200011yescharacteristic
301C2×C13#200911yescharacteristic
302C2×C13#201011yescharacteristic
303#41—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—42no—
316C2×Q8C13×SD1612yescomplemented
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4C2×D4×C1311yescharacteristic
328C22×C4C2×D4×C1311yescharacteristic
329C22×C4C2×D4×C1311yescharacteristic
330Q16—44no—
331SD16—44no—
332SD16—44no—
333M16—41no—
334M16—41no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—41no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—44no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42—41no—
357C42C2×D4×C1311yescharacteristic
358C42C2×D4×C1311yescharacteristic
359C42C2×D4×C1311yescharacteristic
360C42C13×#4111yescharacteristic
361C13#999911yescharacteristic, direct product factor, Sylow
362C23—41no—
363C23C13×#12011yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—41no—
371Q8—41no—
372Q8—41no—
373Q8—41no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—81no—
378D4—81no—
379D4—81no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C13×#12011yescharacteristic
399C2×C4C13×#12011yescharacteristic
400C2×C4C13×#12111yescharacteristic
401C2×C4C13×#12111yescharacteristic
402C2×C4C13×#12111yescharacteristic
403C2×C4C13×#12711yescharacteristic
404C2×C4C2×C13×SD1611yescharacteristic
405C2×C4C13×#13511yescharacteristic
406C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C13×#13711yescharacteristic
408C8—42no—
409C8—42no—
410C8—81no—
411C22—21no—
412C22—21no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C13×#39211yescharacteristic
417C22C13×#44811yescharacteristic
418C22C13×#44911yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4C13×#45011yescharacteristic
430C4C13×#45211yescharacteristic
431C4C13×#46511yescharacteristic
432C4C13×#46811yescharacteristic
433C2—21no—
434C2—21no—
435C2—161no—
436C2C13×#200011yescharacteristic
437C2C13×#200911yescharacteristic
438C2C13×#201011yescharacteristic
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×#2581C2semidirect
5. C13×#1487C2semidirect
6. C13×#1479C2semidirect
7. C13×#1286C2semidirect
84. #9999C13direct (N × H)
98. C2×Q8×C13SD16semidirect
145. #2581C2×C13semidirect
147. #1487C2×C13semidirect
148. #1479C2×C13semidirect
149. #1286C2×C13semidirect
316. C2×Q8C13×SD16semidirect
361. C13#9999direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31032
C13×#30372
C13×#25812
C13×#15172
C13×#14872
C13×#14792
C13×#12862
#999913