Finite Group Databasebeta

← C13×#13307 #15699646

Subgroups — C13×#13307 #15699646

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#509C211yesmaximal, characteristic, complemented
2C2×C13×#472C211yesmaximal, characteristic, complemented
3C13×#3061C211yesmaximal, characteristic, complemented
4C2×C13×#359C211yesmaximal, characteristic, complemented
5C2×C13×#357C211yesmaximal, characteristic, complemented
6C2×C13×#350C211yesmaximal, characteristic, complemented
7C13×#1387C211yesmaximal, characteristic, complemented
8C2×C13×AGL(1,ℤ/8)—21no—
9C2×C13×#135C2211yescharacteristic
10C22×C13×D8C2211yescharacteristic
11C2×C13×#131C2211yescharacteristic
12C13×#537—21no—
13C13×#509—22no—
14C13×#509—22no—
15C2×C13×SD32—21no—
16C2×C13×D16—21no—
17C2×C13×M32C2211yescharacteristic
18C22×C13×C16C2211yescharacteristic
19C13×#472—22no—
20C13×#472—22no—
21C13×#468—22no—
22C13×#467—21no—
23C13×#466—21no—
24C2×C13×#108C2211yescharacteristic
25C2×C13×#107C2211yescharacteristic
26C13×#417—21no—
27C2×C13×#100—21no—
28C13×#359—22no—
29C13×#357—22no—
30C13×#350—22no—
31C2×C13×#41—21no—
32C2×C13×#41D411yescharacteristic
33C22×D4×C13—21no—
34C13×AGL(1,ℤ/8)—24no—
35C13×AGL(1,ℤ/8)—42no—
36C13×#135—21no—
37C13×#135—21no—
38C13×#135—21no—
39C13×#135—21no—
40C2×C13×Q16D411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×SD16—41no—
43C2×C13×D8—21no—
44C2×C13×D8—21no—
45C2×C13×D8—21no—
46C2×C13×D8—21no—
47C2×C13×D8—21no—
48C2×C13×D8—41no—
49C2×C13×D8D411yescharacteristic
50C2×C13×D8D412yescomplemented
51C13×#131—21no—
52C13×#131—21no—
53C13×#131—21no—
54C13×#131—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16D411yescharacteristic
58C22×C8×C13—21no—
59C22×C8×C13C2311yescharacteristic
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—41no—
62C13×#121—22no—
63C13×#121—42no—
64C13×#121—41no—
65C2×C13×C4⋊C4—21no—
66C13×SD32—24no—
67C13×D16—24no—
68C13×M32—21no—
69C13×M32D412yescomplemented
70C2×C13×C16—21no—
71C2×C13×C16—21no—
72C2×C13×C16—21no—
73C2×C13×C16—21no—
74C13×#108—21no—
75C13×#108D412yescomplemented
76C13×#107—21no—
77C13×#107D412yes—
78C13×#103—22no—
79C13×#102—22no—
80C13×#100—24no—
81#13307C1311yesmaximal, characteristic, direct product factor, Sylow
82C24×C13—41no—
83C13×#41—21no—
84C13×#41—21no—
85C13×#41—21no—
86C13×#41—21no—
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C2×Q8×C13—21no—
92C2×Q8×C13D811yescharacteristic
93C2×D4×C13—21no—
94C2×D4×C13—22no—
95C2×D4×C13—21no—
96C2×D4×C13—41no—
97C2×D4×C13—42no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13D811yescharacteristic
104C22×C4×C13—21no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13C2×D411yescharacteristic
108C13×Q16—21no—
109C13×Q16—21no—
110C13×SD16—44no—
111C13×SD16—41no—
112C13×SD16—41no—
113C13×D8—21no—
114C13×D8—22no—
115C13×D8—22no—
116C13×D8—21no—
117C13×D8—44no—
118C13×D8—41no—
119C13×D8—41no—
120C13×M16—21no—
121C13×M16—22no—
122C13×M16—21no—
123C13×M16—41no—
124C13×M16—41no—
125C13×M16—41no—
126C2×C8×C13—21no—
127C2×C8×C13—41no—
128C2×C8×C13—41no—
129C2×C8×C13—41no—
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13#4111yescharacteristic
136C13×C4⋊C4—22no—
137C13×C4⋊C4—42no—
138C13×C4⋊C4—41no—
139C13×C22⋊C4—42no—
140C13×C22⋊C4—42no—
141C13×C16—22no—
142C13×C16—41no—
143C2×#509C2×C1311yescharacteristic, complemented
144C2×#472C2×C1311yescharacteristic, complemented
145#3061C2×C1311yescharacteristic, complemented
146C2×#359C2×C1311yescharacteristic, complemented
147C2×#357C2×C1311yescharacteristic, complemented
148C2×#350C2×C1311yescharacteristic, complemented
149#1387C2×C1311yescharacteristic, complemented
150C23×C13—21no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—161no—
156C23×C13—161no—
157C23×C13AGL(1,ℤ/8)11yescharacteristic
158Q8×C13—21no—
159Q8×C13—21no—
160Q8×C13—41no—
161Q8×C13—41no—
162D4×C13—21no—
163D4×C13—21no—
164D4×C13—41no—
165D4×C13—41no—
166D4×C13—42no—
167D4×C13—41no—
168D4×C13—42no—
169D4×C13—41no—
170D4×C13—81no—
171D4×C13—81no—
172D4×C13—81no—
173D4×C13—81no—
174D4×C13—162no—
175C2×C4×C13—21no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—81no—
181C2×C4×C13—81no—
182C2×C4×C13—161no—
183C2×C4×C13#12011yescharacteristic
184C2×C4×C13#12011yescharacteristic
185C2×C4×C13#12111yescharacteristic
186C2×C4×C13C2×D811yescharacteristic
187C2×C4×C13#13511yescharacteristic
188C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
189C8×C13—41no—
190C8×C13—42no—
191C8×C13#12011yescharacteristic
192C8×C13#12111yescharacteristic
193C8×C13#12111yescharacteristic
194C8×C13#12711yescharacteristic
195C2×AGL(1,ℤ/8)—21no—
196C2×#135C22×C1311yescharacteristic
197C22×D8C22×C1311yescharacteristic
198C2×#131C22×C1311yescharacteristic
199#537—21no—
200#509—22no—
201#509—22no—
202C2×SD32—21no—
203C2×D16—21no—
204C2×M32C22×C1311yescharacteristic
205C22×C16C22×C1311yescharacteristic
206#472—22no—
207#472—22no—
208#468—22no—
209#467—21no—
210#466—21no—
211C2×#108C22×C1311yescharacteristic
212C2×#107C22×C1311yescharacteristic
213#417—21no—
214C2×#100—21no—
215#359—22no—
216#357—22no—
217#350—22no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—82no—
227C22×C13—162no—
228C22×C13—162no—
229C22×C13—161no—
230C22×C13—161no—
231C22×C13#44711yescharacteristic
232C22×C13#44911yescharacteristic
233C22×C13#46911yescharacteristic
234C4×C13—41no—
235C4×C13—82no—
236C4×C13—81no—
237C4×C13#39211yescharacteristic
238C4×C13#44711yescharacteristic
239C4×C13#44911yescharacteristic
240C4×C13#46611yescharacteristic
241C2×#41—21no—
242C2×#41D4×C1311yescharacteristic
243C22×D4—21no—
244AGL(1,ℤ/8)—24no—
245AGL(1,ℤ/8)—42no—
246#135—21no—
247#135—21no—
248#135—21no—
249#135—21no—
250C2×Q16D4×C1311yescharacteristic
251C2×SD16—21no—
252C2×SD16—41no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—41no—
259C2×D8D4×C1311yescharacteristic
260C2×D8D4×C1312yescomplemented
261#131—21no—
262#131—21no—
263#131—21no—
264#131—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16D4×C1311yescharacteristic
268C22×C8—21no—
269C22×C8C23×C1311yescharacteristic
270C22⋊Q8—22no—
271C22⋊Q8—41no—
272#121—22no—
273#121—42no—
274#121—41no—
275C2×C4⋊C4—21no—
276SD32—24no—
277D16—24no—
278M32—21no—
279M32D4×C1312yescomplemented
280C2×C16—21no—
281C2×C16—21no—
282C2×C16—21no—
283C2×C16—21no—
284#108—21no—
285#108D4×C1312yescomplemented
286#107—21no—
287#107D4×C1312yes—
288#103—22no—
289#102—22no—
290#100—24no—
291C2×C13—21no—
292C2×C13—21no—
293C2×C13—81no—
294C2×C13—161no—
295C2×C13—162no—
296C2×C13#199911yescharacteristic
297C2×C13#219211yescharacteristic
298C2×C13#219311yescharacteristic
299C24—41no—
300#41—21no—
301#41—21no—
302#41—21no—
303#41—21no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×Q8C13×D811yescharacteristic
310C2×D4—21no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4C13×D811yescharacteristic
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4C2×D4×C1311yescharacteristic
325Q16—21no—
326Q16—21no—
327SD16—44no—
328SD16—41no—
329SD16—41no—
330D8—21no—
331D8—22no—
332D8—22no—
333D8—21no—
334D8—44no—
335D8—41no—
336D8—41no—
337M16—21no—
338M16—22no—
339M16—21no—
340M16—41no—
341M16—41no—
342M16—41no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8C2×D4×C1311yescharacteristic
348C2×C8C2×D4×C1311yescharacteristic
349C2×C8C2×D4×C1311yescharacteristic
350C2×C8C2×D4×C1311yescharacteristic
351C2×C8C2×D4×C1311yescharacteristic
352C2×C8C13×#4111yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C16—22no—
359C16—41no—
360C13#1330711yescharacteristic, direct product factor, Sylow
361C23—21no—
362C23—41no—
363C23—42no—
364C23—81no—
365C23—81no—
366C23—161no—
367C23—161no—
368C23C13×AGL(1,ℤ/8)11yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—41no—
372Q8—41no—
373D4—21no—
374D4—21no—
375D4—41no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—162no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—161no—
394C2×C4C13×#12011yescharacteristic
395C2×C4C13×#12011yescharacteristic
396C2×C4C13×#12111yescharacteristic
397C2×C4C2×C13×D811yescharacteristic
398C2×C4C13×#13511yescharacteristic
399C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
400C8—41no—
401C8—42no—
402C8C13×#12011yescharacteristic
403C8C13×#12111yescharacteristic
404C8C13×#12111yescharacteristic
405C8C13×#12711yescharacteristic
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—162no—
416C22—162no—
417C22—161no—
418C22—161no—
419C22C13×#44711yescharacteristic
420C22C13×#44911yescharacteristic
421C22C13×#46911yescharacteristic
422C4—41no—
423C4—81no—
424C4—82no—
425C4C13×#39211yescharacteristic
426C4C13×#44711yescharacteristic
427C4C13×#44911yescharacteristic
428C4C13×#46611yescharacteristic
429C2—21no—
430C2—21no—
431C2—81no—
432C2—161no—
433C2—162no—
434C2C13×#199911yescharacteristic
435C2C13×#219211yescharacteristic
436C2C13×#219311yescharacteristic
subgroupG/H
center, socleC22×C13#447
commutator, Frattini, cosocleC22×C8C23×C13
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#509C2semidirect
2. C2×C13×#472C2semidirect
3. C13×#3061C2semidirect
4. C2×C13×#359C2semidirect
5. C2×C13×#357C2semidirect
6. C2×C13×#350C2semidirect
7. C13×#1387C2semidirect
50. C2×C13×D8D4semidirect
69. C13×M32D4semidirect
75. C13×#108D4semidirect
81. #13307C13direct (N × H)
143. C2×#509C2×C13semidirect
144. C2×#472C2×C13semidirect
145. #3061C2×C13semidirect
146. C2×#359C2×C13semidirect
147. C2×#357C2×C13semidirect
148. C2×#350C2×C13semidirect
149. #1387C2×C13semidirect
260. C2×D8D4×C13semidirect
279. M32D4×C13semidirect
285. #108D4×C13semidirect
360. C13#13307direct (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
C2×C13×#4722
C13×#30612
C2×C13×#3592
C2×C13×#3572
C2×C13×#3502
C13×#13872
#1330713