Finite Group Databasebeta

← C13×#33679 #15720018

Subgroups — C13×#33679 #15720018

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3176C211yesmaximal, characteristic, complemented
2C13×#2951C211yesmaximal, characteristic, complemented
3C13×#2233C211yesmaximal, characteristic, complemented
4C13×#2232C211yesmaximal, characteristic, complemented
5C13×#2229C211yesmaximal, characteristic, complemented
6C13×#2228C211yesmaximal, characteristic, complemented
7C13×#2207C211yesmaximal, characteristic, complemented
8C13×#2206C211yesmaximal, characteristic, complemented
9C13×#2186C211yesmaximal, characteristic, complemented
10C13×#2186C211yesmaximal, characteristic, complemented
11C13×#2177C211yesmaximal, characteristic, complemented
12C13×#2175C211yesmaximal, characteristic, complemented
13C4×C13×SD32C211yesmaximal, characteristic, complemented
14C4×C13×D16C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C13×#540—21no—
18C13×#520—21no—
19C2×C13×SD32C2211yescharacteristic
20C2×C13×SD32C2211yescharacteristic
21C2×C13×D16C2211yescharacteristic
22C2×C13×D16C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#493C2211yescharacteristic
25C13×#490—21no—
26C13×#469—21no—
27C13×#466C2211yescharacteristic
28C13×#466C2211yescharacteristic
29C13×#442—21no—
30C13×#440—21no—
31C13×#440—21no—
32C4×C13×Q16C2211yescharacteristic
33C4×C13×Q16C2211yescharacteristic
34C4×C13×D8C2211yescharacteristic
35C4×C13×D8C2211yescharacteristic
36C4×C13×D8C2211yescharacteristic
37C4×C13×D8C2211yescharacteristic
38C2×C13×#107C2211yescharacteristic
39C13×#417—21no—
40C13×#405C2211yescharacteristic
41C13×#367C2211yescharacteristic
42C13×#367C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#358C2211yescharacteristic
48C13×#358C2211yescharacteristic
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×#41—21no—
60C13×#135—22no—
61C13×#135—22no—
62C2×C13×Q16C2311yescharacteristic
63C2×C13×SD16—21no—
64C2×C13×D8—21no—
65C2×C13×D8C2311yescharacteristic
66C2×C13×D8C2311yescharacteristic
67C2×C13×D8C2311yescharacteristic
68C2×C13×M16D411yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×#127—21no—
71C13×#125—21no—
72C13×#123—41no—
73C13×#123—41no—
74C13×#121—21no—
75C13×#121—21no—
76C13×#121—41no—
77C13×#121—41no—
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13—41no—
85C4×D4×C13—41no—
86C13×#117—41no—
87C13×#117D411yescharacteristic
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—41no—
90C13×SD32—22no—
91C13×SD32—22no—
92C13×D16—22no—
93C13×D16—22no—
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C2×C13×C16C2311yescharacteristic
97C2×C13×C16C2311yescharacteristic
98C13×#107—21no—
99C13×#107C2311yescharacteristic
100C13×#107C2311yescharacteristic
101C13×#107C2311yescharacteristic
102C13×#107C2311yescharacteristic
103C13×#106—21no—
104C13×#103—21no—
105C13×#103—21no—
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×#102—21no—
110C13×#102—21no—
111C13×#102—21no—
112C13×#97D411yescharacteristic
113C13×#97D411yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#33679C1311yesmaximal, characteristic, direct product factor, Sylow
117C13×#41—24no—
118C13×#41—42no—
119C2×Q8×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C2×D4×C13—41no—
126C2×D4×C13—41no—
127C2×D4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13C2×D411yescharacteristic
135C13×Q16—21no—
136C13×Q16#4112yes—
137C13×SD16—24no—
138C13×D8—21no—
139C13×D8—21no—
140C13×D8—21no—
141C13×D8—21no—
142C13×D8—21no—
143C13×D8—42no—
144C13×D8#4112yes—
145C13×M16—41no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13C2×D411yescharacteristic
149C2×C8×C13C2×D411yescharacteristic
150C2×C8×C13C2×D411yescharacteristic
151C2×C8×C13C2411yescharacteristic
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4D811yescharacteristic
162C13×C4⋊C4D811yescharacteristic
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4D811yescharacteristic
170C13×C22⋊C4D811yescharacteristic
171C42×C13—41no—
172C42×C13—41no—
173C42×C13C2×D411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C13×C16—21no—
176C13×C16—21no—
177C13×C16—21no—
178C13×C16—21no—
179#3176C2×C1311yescharacteristic, complemented
180#2951C2×C1311yescharacteristic, complemented
181#2233C2×C1311yescharacteristic, complemented
182#2232C2×C1311yescharacteristic, complemented
183#2229C2×C1311yescharacteristic, complemented
184#2228C2×C1311yescharacteristic, complemented
185#2207C2×C1311yescharacteristic, complemented
186#2206C2×C1311yescharacteristic, complemented
187#2186C2×C1311yescharacteristic, complemented
188#2186C2×C1311yescharacteristic, complemented
189#2177C2×C1311yescharacteristic, complemented
190#2175C2×C1311yescharacteristic, complemented
191C4×SD32C2×C1311yescharacteristic, complemented
192C4×D16C2×C1311yescharacteristic, complemented
193#2164C2×C1311yescharacteristic, complemented
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13C2×D811yescharacteristic
198Q8×C13—22no—
199Q8×C13—41no—
200D4×C13—22no—
201D4×C13—44no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—161no—
208D4×C13—161no—
209D4×C13—161no—
210D4×C13—161no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—44no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—161no—
220C2×C4×C13—161no—
221C2×C4×C13—161no—
222C2×C4×C13—161no—
223C2×C4×C13—161no—
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C2×D811yescharacteristic
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C8×C13—21no—
231C8×C13—21no—
232C8×C13—21no—
233C8×C13C2×#4111yescharacteristic
234C8×C13C2×#4111yescharacteristic
235C2×#135C22×C1311yescharacteristic
236#540—21no—
237#520—21no—
238C2×SD32C22×C1311yescharacteristic
239C2×SD32C22×C1311yescharacteristic
240C2×D16C22×C1311yescharacteristic
241C2×D16C22×C1311yescharacteristic
242#499C22×C1311yescharacteristic
243#493C22×C1311yescharacteristic
244#490—21no—
245#469—21no—
246#466C22×C1311yescharacteristic
247#466C22×C1311yescharacteristic
248#442—21no—
249#440—21no—
250#440—21no—
251C4×Q16C22×C1311yescharacteristic
252C4×Q16C22×C1311yescharacteristic
253C4×D8C22×C1311yescharacteristic
254C4×D8C22×C1311yescharacteristic
255C4×D8C22×C1311yescharacteristic
256C4×D8C22×C1311yescharacteristic
257C2×#107C22×C1311yescharacteristic
258#417—21no—
259#405C22×C1311yescharacteristic
260#367C22×C1311yescharacteristic
261#367C22×C1311yescharacteristic
262#366C22×C1311yescharacteristic
263#366C22×C1311yescharacteristic
264C4⋊C16C22×C1311yescharacteristic
265C4⋊C16C22×C1311yescharacteristic
266#358C22×C1311yescharacteristic
267#358C22×C1311yescharacteristic
268#357C22×C1311yescharacteristic
269#357C22×C1311yescharacteristic
270#357C22×C1311yescharacteristic
271#357C22×C1311yescharacteristic
272#357C22×C1311yescharacteristic
273#357C22×C1311yescharacteristic
274C22⋊C16C22×C1311yescharacteristic
275C22⋊C16C22×C1311yescharacteristic
276#346C22×C1311yescharacteristic
277C4×C16C22×C1311yescharacteristic
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—42no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13C22×D811yescharacteristic
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—42no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13—81no—
301C4×C13#52511yescharacteristic
302C4×C13#57511yescharacteristic
303C2×#41—21no—
304#135—22no—
305#135—22no—
306C2×Q16C23×C1311yescharacteristic
307C2×SD16—21no—
308C2×D8—21no—
309C2×D8C23×C1311yescharacteristic
310C2×D8C23×C1311yescharacteristic
311C2×D8C23×C1311yescharacteristic
312C2×M16D4×C1311yescharacteristic
313C22×C8C23×C1311yescharacteristic
314#127—21no—
315#125—21no—
316#123—41no—
317#123—41no—
318#121—21no—
319#121—21no—
320#121—41no—
321#121—41no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—41no—
329C4×D4—41no—
330#117—41no—
331#117D4×C1311yescharacteristic
332C2×C4⋊C4—21no—
333C2×C4⋊C4—41no—
334SD32—22no—
335SD32—22no—
336D16—22no—
337D16—22no—
338C2×C16C23×C1311yescharacteristic
339C2×C16C23×C1311yescharacteristic
340C2×C16C23×C1311yescharacteristic
341C2×C16C23×C1311yescharacteristic
342#107—21no—
343#107C23×C1311yescharacteristic
344#107C23×C1311yescharacteristic
345#107C23×C1311yescharacteristic
346#107C23×C1311yescharacteristic
347#106—21no—
348#103—21no—
349#103—21no—
350#102—21no—
351#102—21no—
352#102—21no—
353#102—21no—
354#102—21no—
355#102—21no—
356#97D4×C1311yescharacteristic
357#97D4×C1311yescharacteristic
358C4×C8C23×C1311yescharacteristic
359C4×C8C23×C1311yescharacteristic
360C2×C13—41no—
361C2×C13—82no—
362C2×C13—161no—
363C2×C13—161no—
364C2×C13#310011yescharacteristic
365C2×C13#341511yescharacteristic
366C2×C13#341611yescharacteristic
367#41—24no—
368#41—42no—
369C2×Q8—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4C2×D4×C1311yescharacteristic
385Q16—21no—
386Q16C13×#4112yes—
387SD16—24no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8—42no—
394D8C13×#4112yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×D4×C1311yescharacteristic
399C2×C8C2×D4×C1311yescharacteristic
400C2×C8C2×D4×C1311yescharacteristic
401C2×C8C24×C1311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4C13×D811yescharacteristic
412C4⋊C4C13×D811yescharacteristic
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4C13×D811yescharacteristic
420C22⋊C4C13×D811yescharacteristic
421C42—41no—
422C42—41no—
423C42C2×D4×C1311yescharacteristic
424C42C2×D4×C1311yescharacteristic
425C16—21no—
426C16—21no—
427C16—21no—
428C16—21no—
429C13#3367911yescharacteristic, direct product factor, Sylow
430C23—41no—
431C23—41no—
432C23—41no—
433C23C2×C13×D811yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—161no—
444D4—161no—
445D4—161no—
446D4—161no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—161no—
458C2×C4—161no—
459C2×C4—161no—
460C2×C4C2×C13×D811yescharacteristic
461C2×C4C2×C13×D811yescharacteristic
462C2×C4C2×C13×D811yescharacteristic
463C2×C4C2×C13×D811yescharacteristic
464C2×C4C2×C13×D811yescharacteristic
465C2×C4C22×D4×C1311yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×C13×#4111yescharacteristic
470C8C2×C13×#4111yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C22×C13×D811yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4C13×#52511yescharacteristic
495C4C13×#57511yescharacteristic
496C2—41no—
497C2—82no—
498C2—161no—
499C2—161no—
500C2C13×#310011yescharacteristic
501C2C13×#341511yescharacteristic
502C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3176C2semidirect
2. C13×#2951C2semidirect
3. C13×#2233C2semidirect
4. C13×#2232C2semidirect
5. C13×#2229C2semidirect
6. C13×#2228C2semidirect
7. C13×#2207C2semidirect
8. C13×#2206C2semidirect
9. C13×#2186C2semidirect
10. C13×#2186C2semidirect
11. C13×#2177C2semidirect
12. C13×#2175C2semidirect
13. C4×C13×SD32C2semidirect
14. C4×C13×D16C2semidirect
15. C13×#2164C2semidirect
116. #33679C13direct (N × H)
179. #3176C2×C13semidirect
180. #2951C2×C13semidirect
181. #2233C2×C13semidirect
182. #2232C2×C13semidirect
183. #2229C2×C13semidirect
184. #2228C2×C13semidirect
185. #2207C2×C13semidirect
186. #2206C2×C13semidirect
187. #2186C2×C13semidirect
188. #2186C2×C13semidirect
189. #2177C2×C13semidirect
190. #2175C2×C13semidirect
191. C4×SD32C2×C13semidirect
192. C4×D16C2×C13semidirect
193. #2164C2×C13semidirect
429. C13#33679direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31762
C13×#29512
C13×#22332
C13×#22322
C13×#22292
C13×#22282
C13×#22072
C13×#22062
C13×#21862
C13×#21772
C13×#21752
C4×C13×SD322
C4×C13×D162
C13×#21642
#3367913