Finite Group Databasebeta

← C13×#13316 #15699655

Subgroups — C13×#13316 #15699655

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic, complemented
2C13×#3054C211yesmaximal, characteristic, complemented
3C2×C13×#469C211yesmaximal, characteristic, complemented
4C2×C13×#360C211yesmaximal, characteristic, complemented
5C13×#2140C211yesmaximal, characteristic, complemented
6C2×C13×#349C211yesmaximal, characteristic, complemented
7C13×#1386C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C22×C13×D8C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C13×#525—21no—
12C2×C13×#121—21no—
13C13×#509—22no—
14C13×#509—22no—
15C2×C13×SD32—21no—
16C2×C13×D16—21no—
17C2×C13×M32C2211yescharacteristic
18C2×C13×M32C2211yescharacteristic
19C13×#470—21no—
20C13×#469—22no—
21C13×#469—21no—
22C13×#469—22no—
23C13×#468—22no—
24C13×#427C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C13×#416—21no—
27C2×C13×#102—21no—
28C13×#360—22no—
29C13×#357—22no—
30C13×#349—22no—
31C2×C13×#41—21no—
32C22×D4×C13—21no—
33C22×D4×C13—41no—
34C23×C4×C13D411yescharacteristic
35C13×#135—21no—
36C13×#135—21no—
37C13×#135—21no—
38C13×#135—21no—
39C2×C13×Q16D411yescharacteristic, complemented
40C2×C13×SD16—21no—
41C2×C13×D8—21no—
42C2×C13×D8—21no—
43C2×C13×D8—21no—
44C2×C13×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8D411yescharacteristic, complemented
47C2×C13×D8D412yescomplemented
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C22×C8×C13D411yescharacteristic
55C22×C8×C13C2311yescharacteristic
56C13×#123—41no—
57C13×C22⋊Q8—22no—
58C13×#121—22no—
59C13×#121—24no—
60C13×#121—42no—
61C13×#120—41no—
62C4×D4×C13—42no—
63C13×#117—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C22⋊C4—41no—
66C13×SD32—24no—
67C13×D16—24no—
68C13×M32—21no—
69C13×M32—21no—
70C13×M32—21no—
71C13×M32D412yescomplemented
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#107D412yescomplemented
75C13×#106—21no—
76C13×#106—21no—
77C13×#106D412yescomplemented
78C13×#103—22no—
79C13×#102—24no—
80C13×#102—22no—
81#13316C1311yesmaximal, characteristic, direct product factor, Sylow
82C24×C13—41no—
83C24×C13D811yescharacteristic
84C13×#41—41no—
85C13×#41—41no—
86C13×#41—41no—
87C13×#41—41no—
88C2×Q8×C13—21no—
89C2×D4×C13—22no—
90C2×D4×C13—21no—
91C2×D4×C13—42no—
92C2×D4×C13—44no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—84no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13D811yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C13×Q16—21no—
111C13×Q16—21no—
112C13×SD16—41no—
113C13×SD16—41no—
114C13×D8—21no—
115C13×D8—22no—
116C13×D8—22no—
117C13×D8—21no—
118C13×D8—41no—
119C13×D8—41no—
120C13×M16—41no—
121C13×M16—41no—
122C13×M16—41no—
123C13×M16—41no—
124C2×C8×C13—21no—
125C2×C8×C13—21no—
126C2×C8×C13—21no—
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13#4111yescharacteristic
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—42no—
136C13×C4⋊C4—41no—
137C13×C22⋊C4—44no—
138C13×C22⋊C4—42no—
139C13×C22⋊C4—42no—
140C13×C22⋊C4—41no—
141C42×C13—41no—
142C13×C16—22no—
143C13×C16—41no—
144C2×#509C2×C1311yescharacteristic, complemented
145#3054C2×C1311yescharacteristic, complemented
146C2×#469C2×C1311yescharacteristic, complemented
147C2×#360C2×C1311yescharacteristic, complemented
148#2140C2×C1311yescharacteristic, complemented
149C2×#349C2×C1311yescharacteristic, complemented
150#1386C2×C1311yescharacteristic, complemented
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—42no—
155C23×C13—42no—
156C23×C13—41no—
157C23×C13—82no—
158C23×C13—82no—
159C23×C13—81no—
160C23×C13—81no—
161C23×C13C2×D811yescharacteristic
162Q8×C13—41no—
163Q8×C13—41no—
164D4×C13—42no—
165D4×C13—41no—
166D4×C13—42no—
167D4×C13—41no—
168D4×C13—84no—
169D4×C13—88no—
170D4×C13—81no—
171D4×C13—81no—
172D4×C13—81no—
173D4×C13—81no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—42no—
183C2×C4×C13—41no—
184C2×C4×C13—82no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13#12011yescharacteristic
188C2×C4×C13#12011yescharacteristic
189C2×C4×C13#12111yescharacteristic
190C2×C4×C13#13511yescharacteristic
191C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
193C8×C13—41no—
194C8×C13#12011yescharacteristic
195C8×C13#12111yescharacteristic
196C8×C13#12111yescharacteristic
197C8×C13#12711yescharacteristic
198C2×#135C22×C1311yescharacteristic
199C22×D8C22×C1311yescharacteristic
200C22×M16C22×C1311yescharacteristic
201#525—21no—
202C2×#121—21no—
203#509—22no—
204#509—22no—
205C2×SD32—21no—
206C2×D16—21no—
207C2×M32C22×C1311yescharacteristic
208C2×M32C22×C1311yescharacteristic
209#470—21no—
210#469—22no—
211#469—21no—
212#469—22no—
213#468—22no—
214#427C22×C1311yescharacteristic
215C2×#106C22×C1311yescharacteristic
216#416—21no—
217C2×#102—21no—
218#360—22no—
219#357—22no—
220#349—22no—
221C22×C13—22no—
222C22×C13—42no—
223C22×C13—42no—
224C22×C13—41no—
225C22×C13—81no—
226C22×C13—82no—
227C22×C13—82no—
228C22×C13—82no—
229C22×C13—81no—
230C22×C13—82no—
231C22×C13—162no—
232C22×C13—162no—
233C22×C13#44711yescharacteristic
234C22×C13#44711yescharacteristic
235C22×C13#46611yescharacteristic
236C4×C13—41no—
237C4×C13—82no—
238C4×C13—82no—
239C4×C13—81no—
240C4×C13#39211yescharacteristic
241C4×C13#44911yescharacteristic
242C4×C13#44911yescharacteristic
243C4×C13#46911yescharacteristic
244C2×#41—21no—
245C22×D4—21no—
246C22×D4—41no—
247C23×C4D4×C1311yescharacteristic
248#135—21no—
249#135—21no—
250#135—21no—
251#135—21no—
252C2×Q16D4×C1311yescharacteristic, complemented
253C2×SD16—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8D4×C1312yescomplemented
260C2×D8D4×C1311yescharacteristic, complemented
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C22×C8D4×C1311yescharacteristic
268C22×C8C23×C1311yescharacteristic
269#123—41no—
270C22⋊Q8—22no—
271#121—24no—
272#121—22no—
273#121—42no—
274#120—41no—
275C4×D4—42no—
276#117—21no—
277C2×C4⋊C4—21no—
278C2×C22⋊C4—41no—
279SD32—24no—
280D16—24no—
281M32—21no—
282M32—21no—
283M32—21no—
284M32D4×C1312yescomplemented
285C2×C16—21no—
286C2×C16—21no—
287#107D4×C1312yescomplemented
288#106—21no—
289#106—21no—
290#106D4×C1312yescomplemented
291#103—22no—
292#102—24no—
293#102—22no—
294C2×C13—21no—
295C2×C13—21no—
296C2×C13—81no—
297C2×C13—161no—
298C2×C13—162no—
299C2×C13#199911yescharacteristic
300C2×C13#219012yes—
301C24—41no—
302C24C13×D811yescharacteristic
303#41—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307C2×Q8—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—42no—
311C2×D4—44no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—84no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4C13×D811yescharacteristic
328C22×C4C2×D4×C1311yescharacteristic
329Q16—21no—
330Q16—21no—
331SD16—41no—
332SD16—41no—
333D8—21no—
334D8—22no—
335D8—22no—
336D8—21no—
337D8—41no—
338D8—41no—
339M16—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8C2×D4×C1311yescharacteristic
347C2×C8C2×D4×C1311yescharacteristic
348C2×C8C2×D4×C1311yescharacteristic
349C2×C8C2×D4×C1311yescharacteristic
350C2×C8C2×D4×C1311yescharacteristic
351C2×C8C13×#4111yescharacteristic
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C22⋊C4—44no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—41no—
360C42—41no—
361C16—22no—
362C16—41no—
363C13#1331611yescharacteristic, direct product factor, Sylow
364C23—21no—
365C23—21no—
366C23—21no—
367C23—42no—
368C23—41no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—81no—
373C23—81no—
374C23C2×C13×D811yescharacteristic
375Q8—41no—
376Q8—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—88no—
382D4—84no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4C13×#12011yescharacteristic
401C2×C4C13×#12011yescharacteristic
402C2×C4C13×#12111yescharacteristic
403C2×C4C13×#13511yescharacteristic
404C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
406C8—41no—
407C8C13×#12011yescharacteristic
408C8C13×#12111yescharacteristic
409C8C13×#12111yescharacteristic
410C8C13×#12711yescharacteristic
411C22—22no—
412C22—42no—
413C22—41no—
414C22—42no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—81no—
419C22—82no—
420C22—82no—
421C22—162no—
422C22—162no—
423C22C13×#44711yescharacteristic
424C22C13×#44711yescharacteristic
425C22C13×#46611yescharacteristic
426C4—41no—
427C4—82no—
428C4—81no—
429C4—82no—
430C4C13×#39211yescharacteristic
431C4C13×#44911yescharacteristic
432C4C13×#44911yescharacteristic
433C4C13×#46911yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2—161no—
439C2C13×#199911yescharacteristic
440C2C13×#219012yes—
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#509C2semidirect
2. C13×#3054C2semidirect
3. C2×C13×#469C2semidirect
4. C2×C13×#360C2semidirect
5. C13×#2140C2semidirect
6. C2×C13×#349C2semidirect
7. C13×#1386C2semidirect
39. C2×C13×Q16D4semidirect
46. C2×C13×D8D4semidirect
47. C2×C13×D8D4semidirect
71. C13×M32D4semidirect
74. C13×#107D4semidirect
77. C13×#106D4semidirect
81. #13316C13direct (N × H)
144. C2×#509C2×C13semidirect
145. #3054C2×C13semidirect
146. C2×#469C2×C13semidirect
147. C2×#360C2×C13semidirect
148. #2140C2×C13semidirect
149. C2×#349C2×C13semidirect
150. #1386C2×C13semidirect
252. C2×Q16D4×C13semidirect
259. C2×D8D4×C13semidirect
260. C2×D8D4×C13semidirect
284. M32D4×C13semidirect
287. #107D4×C13semidirect
290. #106D4×C13semidirect
363. C13#13316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5092
C13×#30542
C2×C13×#4692
C2×C13×#3602
C13×#21402
C2×C13×#3492
C13×#13862
#1331613