Finite Group Databasebeta

← C13×#33595 #15719934

Subgroups — C13×#33595 #15719934

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3414C211yesmaximal, characteristic, complemented
2C2×C13×#509C211yesmaximal, characteristic, complemented
3C13×#3155C211yesmaximal, characteristic, complemented
4C13×#2957C211yesmaximal, characteristic, complemented
5C13×#2213C214yesmaximal, complemented
6C13×#2212C214yesmaximal, complemented
7C13×#2153C211yesmaximal, characteristic, complemented
8C13×#2148C211yesmaximal, characteristic, complemented
9C2×C13×#361C211yesmaximal, characteristic, complemented
10C2×C13×AGL(1,ℤ/8)—21no—
11C2×C13×#135C2211yescharacteristic
12C2×C13×#135C2211yescharacteristic
13C22×C13×D8C2211yescharacteristic
14C13×#568—21no—
15C13×#535—21no—
16C13×#510—21no—
17C13×#510C2212yescomplemented
18C13×#509—22no—
19C13×#509—21no—
20C13×#509C2214yes—
21C13×#509C2212yescomplemented
22C13×#508—22no—
23C2×C13×SD32—21no—
24C2×C13×D16—21no—
25C2×C13×M32C2211yescharacteristic
26C2×C13×M32C2211yescharacteristic
27C13×#496—22no—
28C13×#495C2212yescomplemented
29C13×#493C2212yescomplemented
30C13×#444—22no—
31C13×#443C2214yescomplemented
32C2×C13×#108C2211yescharacteristic
33C13×#421—21no—
34C13×#405C2211yescharacteristic
35C13×#364C2214yescomplemented
36C13×#362C2212yescomplemented
37C13×#361C2214yescomplemented
38C13×#361C2212yescomplemented
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C22×D4×C13—21no—
42C13×AGL(1,ℤ/8)—42no—
43C13×AGL(1,ℤ/8)—42no—
44C13×#135—21no—
45C13×#135—21no—
46C13×#135—21no—
47C13×#135—21no—
48C13×#135—21no—
49C13×#135—21no—
50C13×#135D412yescomplemented
51C13×#135C2312yes—
52C2×C13×Q16D411yescharacteristic, complemented
53C2×C13×Q16C2311yescharacteristic
54C2×C13×SD16—22no—
55C2×C13×SD16—21no—
56C2×C13×SD16—21no—
57C2×C13×D8—21no—
58C2×C13×D8—21no—
59C2×C13×D8—22no—
60C2×C13×D8—21no—
61C2×C13×D8—21no—
62C2×C13×D8—21no—
63C2×C13×D8D411yescharacteristic, complemented
64C2×C13×D8C2311yescharacteristic
65C2×C13×D8C2312yes—
66C13×#131—24no—
67C13×#131—42no—
68C2×C13×M16—21no—
69C2×C13×M16—42no—
70C2×C13×M16D411yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#127—22no—
73C13×#124—22no—
74C13×#121—42no—
75C13×#120—42no—
76C13×#117D411yescharacteristic
77C13×Q32—22no—
78C13×SD32—24no—
79C13×SD32—22no—
80C13×SD32—22no—
81C13×D16—24no—
82C13×D16—22no—
83C13×M32—21no—
84C13×M32—21no—
85C13×M32C2312yes—
86C13×M32C2312yes—
87C2×C13×C16—21no—
88C2×C13×C16—21no—
89C13×#108—21no—
90C13×#108C2312yes—
91C13×#104—24no—
92C13×#97D412yes—
93C4×C8×C13C2312yes—
94#33595C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—41no—
96C13×#41—22no—
97C13×#41—22no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41—41no—
102C13×#41—41no—
103C13×#41—41no—
104C2×Q8×C13—21no—
105C2×Q8×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—22no—
108C2×D4×C13—21no—
109C2×D4×C13—44no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13C2×D411yescharacteristic
120C13×Q16—21no—
121C13×Q16—21no—
122C13×Q16—21no—
123C13×Q16C2×D412yes—
124C13×SD16—22no—
125C13×SD16—22no—
126C13×SD16—41no—
127C13×SD16—41no—
128C13×SD16—44no—
129C13×D8—21no—
130C13×D8—22no—
131C13×D8—21no—
132C13×D8—22no—
133C13×D8—21no—
134C13×D8—41no—
135C13×D8—41no—
136C13×D8—44no—
137C13×D8C2×D412yes—
138C13×M16—22no—
139C13×M16—41no—
140C13×M16—44no—
141C13×M16D812yes—
142C13×M16D812yes—
143C2×C8×C13—41no—
144C2×C8×C13—44no—
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2×D411yescharacteristic
148C2×C8×C13C2×D412yes—
149C2×C8×C13#4111yescharacteristic
150C2×C8×C13#4111yescharacteristic
151C2×C8×C13C2411yescharacteristic
152C13×C4⋊C4—21no—
153C13×C22⋊C4—21no—
154C13×C22⋊C4—44no—
155C42×C13C2×D412yes—
156C13×C16—22no—
157C13×C16—22no—
158#3414C2×C1311yescharacteristic, complemented
159C2×#509C2×C1311yescharacteristic, complemented
160#3155C2×C1311yescharacteristic, complemented
161#2957C2×C1311yescharacteristic, complemented
162#2213C2×C1314yescomplemented
163#2212C2×C1314yescomplemented
164#2153C2×C1311yescharacteristic, complemented
165#2148C2×C1311yescharacteristic, complemented
166C2×#361C2×C1311yescharacteristic, complemented
167C23×C13—41no—
168C23×C13—42no—
169C23×C13—41no—
170C23×C13—81no—
171C23×C13—81no—
172C23×C13—162no—
173C23×C13AGL(1,ℤ/8)11yescharacteristic
174Q8×C13—22no—
175Q8×C13—41no—
176Q8×C13—41no—
177Q8×C13—41no—
178D4×C13—22no—
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—42no—
182D4×C13—41no—
183D4×C13—41no—
184D4×C13—42no—
185D4×C13—41no—
186D4×C13—81no—
187D4×C13—81no—
188D4×C13—81no—
189D4×C13—81no—
190D4×C13—164no—
191C2×C4×C13—22no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—41no—
196C2×C4×C13—81no—
197C2×C4×C13—81no—
198C2×C4×C13#12111yescharacteristic
199C2×C4×C13#12111yescharacteristic
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C13C22×D411yescharacteristic
204C8×C13—42no—
205C8×C13#12111yescharacteristic
206C8×C13#12111yescharacteristic
207C8×C13C2×D814yes—
208C8×C13C22×D411yescharacteristic
209C8×C13C2×#4111yescharacteristic
210C2×AGL(1,ℤ/8)—21no—
211C2×#135C22×C1311yescharacteristic
212C2×#135C22×C1311yescharacteristic
213C22×D8C22×C1311yescharacteristic
214#568—21no—
215#535—21no—
216#510—21no—
217#510C22×C1312yescomplemented
218#509—22no—
219#509—21no—
220#509C22×C1314yes—
221#509C22×C1312yescomplemented
222#508—22no—
223C2×SD32—21no—
224C2×D16—21no—
225C2×M32C22×C1311yescharacteristic
226C2×M32C22×C1311yescharacteristic
227#496—22no—
228#495C22×C1312yescomplemented
229#493C22×C1312yescomplemented
230#444—22no—
231#443C22×C1314yescomplemented
232C2×#108C22×C1311yescharacteristic
233#421—21no—
234#405C22×C1311yescharacteristic
235#364C22×C1314yescomplemented
236#362C22×C1312yescomplemented
237#361C22×C1314yescomplemented
238#361C22×C1312yescomplemented
239C22×C13—41no—
240C22×C13—42no—
241C22×C13—82no—
242C22×C13—84no—
243C22×C13—81no—
244C22×C13—82no—
245C22×C13—161no—
246C22×C13—162no—
247C22×C13—162no—
248C22×C13#45911yescharacteristic
249C22×C13#45911yescharacteristic
250C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C13—42no—
252C4×C13—42no—
253C4×C13—81no—
254C4×C13#45911yescharacteristic
255C4×C13#45911yescharacteristic
256C4×C13C2×#12111yescharacteristic
257C4×C13C22×D811yescharacteristic
258C2×#41—21no—
259C2×#41—21no—
260C22×D4—21no—
261AGL(1,ℤ/8)—42no—
262AGL(1,ℤ/8)—42no—
263#135—21no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—21no—
268#135—21no—
269#135D4×C1312yescomplemented
270#135C23×C1312yes—
271C2×Q16D4×C1311yescharacteristic, complemented
272C2×Q16C23×C1311yescharacteristic
273C2×SD16—21no—
274C2×SD16—22no—
275C2×SD16—21no—
276C2×D8—21no—
277C2×D8—21no—
278C2×D8—21no—
279C2×D8—22no—
280C2×D8—21no—
281C2×D8—21no—
282C2×D8D4×C1311yescharacteristic, complemented
283C2×D8C23×C1312yes—
284C2×D8C23×C1311yescharacteristic
285#131—24no—
286#131—42no—
287C2×M16—21no—
288C2×M16—42no—
289C2×M16D4×C1311yescharacteristic
290C22×C8C23×C1311yescharacteristic
291#127—22no—
292#124—22no—
293#121—42no—
294#120—42no—
295#117D4×C1311yescharacteristic
296Q32—22no—
297SD32—24no—
298SD32—22no—
299SD32—22no—
300D16—24no—
301D16—22no—
302M32—21no—
303M32—21no—
304M32C23×C1312yes—
305M32C23×C1312yes—
306C2×C16—21no—
307C2×C16—21no—
308#108—21no—
309#108C23×C1312yes—
310#104—24no—
311#97D4×C1312yes—
312C4×C8C23×C1312yes—
313C2×C13—21no—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—82no—
317C2×C13—161no—
318C2×C13—162no—
319C2×C13C2×#45911yescharacteristic
320C24—41no—
321#41—22no—
322#41—22no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×D4—21no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—44no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×D4×C1311yescharacteristic
345Q16—21no—
346Q16—21no—
347Q16—21no—
348Q16C2×D4×C1312yes—
349SD16—22no—
350SD16—22no—
351SD16—41no—
352SD16—41no—
353SD16—44no—
354D8—21no—
355D8—22no—
356D8—21no—
357D8—22no—
358D8—21no—
359D8—41no—
360D8—41no—
361D8—44no—
362D8C2×D4×C1312yes—
363M16—22no—
364M16—41no—
365M16—44no—
366M16C13×D812yes—
367M16C13×D812yes—
368C2×C8—41no—
369C2×C8—44no—
370C2×C8C2×D4×C1311yescharacteristic
371C2×C8C2×D4×C1311yescharacteristic
372C2×C8C2×D4×C1311yescharacteristic
373C2×C8C2×D4×C1312yes—
374C2×C8C13×#4111yescharacteristic
375C2×C8C13×#4111yescharacteristic
376C2×C8C24×C1311yescharacteristic
377C4⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—44no—
380C42C2×D4×C1312yes—
381C16—22no—
382C16—22no—
383C13#3359511yescharacteristic, direct product factor, Sylow
384C23—41no—
385C23—42no—
386C23—41no—
387C23—81no—
388C23—81no—
389C23—162no—
390C23C13×AGL(1,ℤ/8)11yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—41no—
401D4—41no—
402D4—42no—
403D4—81no—
404D4—81no—
405D4—81no—
406D4—81no—
407D4—164no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4C13×#12111yescharacteristic
416C2×C4C13×#12111yescharacteristic
417C2×C4C2×C13×D811yescharacteristic
418C2×C4C2×C13×D811yescharacteristic
419C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
420C2×C4C22×D4×C1311yescharacteristic
421C8—42no—
422C8C13×#12111yescharacteristic
423C8C13×#12111yescharacteristic
424C8C2×C13×D814yes—
425C8C22×D4×C1311yescharacteristic
426C8C2×C13×#4111yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—84no—
431C22—81no—
432C22—82no—
433C22—161no—
434C22—162no—
435C22—162no—
436C22C13×#45911yescharacteristic
437C22C13×#45911yescharacteristic
438C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
439C4—42no—
440C4—42no—
441C4—81no—
442C4C13×#45911yescharacteristic
443C4C13×#45911yescharacteristic
444C4C2×C13×#12111yescharacteristic
445C4C22×C13×D811yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—162no—
451C2—161no—
452C2C2×C13×#45911yescharacteristic
subgroupG/H
center, socleC2×C13C2×#459
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3414C2semidirect
2. C2×C13×#509C2semidirect
3. C13×#3155C2semidirect
4. C13×#2957C2semidirect
5. C13×#2213C2semidirect
6. C13×#2212C2semidirect
7. C13×#2153C2semidirect
8. C13×#2148C2semidirect
9. C2×C13×#361C2semidirect
17. C13×#510C22semidirect
21. C13×#509C22semidirect
28. C13×#495C22semidirect
29. C13×#493C22semidirect
31. C13×#443C22semidirect
35. C13×#364C22semidirect
36. C13×#362C22semidirect
37. C13×#361C22semidirect
38. C13×#361C22semidirect
50. C13×#135D4semidirect
52. C2×C13×Q16D4semidirect
63. C2×C13×D8D4semidirect
94. #33595C13direct (N × H)
158. #3414C2×C13semidirect
159. C2×#509C2×C13semidirect
160. #3155C2×C13semidirect
161. #2957C2×C13semidirect
162. #2213C2×C13semidirect
163. #2212C2×C13semidirect
164. #2153C2×C13semidirect
165. #2148C2×C13semidirect
166. C2×#361C2×C13semidirect
217. #510C22×C13semidirect
221. #509C22×C13semidirect
228. #495C22×C13semidirect
229. #493C22×C13semidirect
231. #443C22×C13semidirect
235. #364C22×C13semidirect
236. #362C22×C13semidirect
237. #361C22×C13semidirect
238. #361C22×C13semidirect
269. #135D4×C13semidirect
271. C2×Q16D4×C13semidirect
282. C2×D8D4×C13semidirect
383. C13#33595direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34142
C2×C13×#5092
C13×#31552
C13×#29572
C13×#22132
C13×#22122
C13×#21532
C13×#21482
C2×C13×#3612
#3359513