Finite Group Databasebeta

← C13×#33790 #15720129

Subgroups — C13×#33790 #15720129

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3175C211yesmaximal, characteristic, complemented
2C13×#3155C211yesmaximal, characteristic, complemented
3C13×#2250C211yesmaximal, characteristic, complemented
4C13×#2249C211yesmaximal, characteristic, complemented
5C13×#2243C211yesmaximal, characteristic, complemented
6C13×#2240C211yesmaximal, characteristic, complemented
7C13×#2211C211yesmaximal, characteristic, complemented
8C13×#2210C211yesmaximal, characteristic, complemented
9C13×#2207C211yesmaximal, characteristic, complemented
10C13×#2206C211yesmaximal, characteristic, complemented
11C13×#2189C211yesmaximal, characteristic, complemented
12C13×#2187C211yesmaximal, characteristic, complemented
13C13×#2186C211yesmaximal, characteristic, complemented
14C13×#2184C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C2×C13×AGL(1,ℤ/8)—21no—
17C2×C13×#135C2211yescharacteristic
18C22×C13×D8C2211yescharacteristic
19C13×#542—21no—
20C13×#535—21no—
21C2×C13×Q32C2211yescharacteristic, complemented
22C2×C13×SD32C2211yescharacteristic
23C2×C13×SD32C2211yescharacteristic
24C2×C13×SD32C2211yescharacteristic, complemented
25C2×C13×SD32C2211yescharacteristic, complemented
26C2×C13×D16C2211yescharacteristic
27C2×C13×D16C2211yescharacteristic
28C2×C13×D16C2211yescharacteristic, complemented
29C13×#500C2211yescharacteristic, complemented
30C13×#496—21no—
31C13×#496—21no—
32C13×#495C2211yescharacteristic
33C13×#495C2211yescharacteristic
34C13×#495C2211yescharacteristic, complemented
35C13×#493C2211yescharacteristic
36C13×#493C2211yescharacteristic
37C13×#489—21no—
38C13×#468—21no—
39C13×#467C2211yescharacteristic
40C13×#466C2211yescharacteristic
41C13×#440—21no—
42C4×C13×Q16C2211yescharacteristic, complemented
43C4×C13×D8C2211yescharacteristic, complemented
44C13×#405C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic, complemented
46C13×C4⋊C16C2211yescharacteristic, complemented
47C13×#358C2211yescharacteristic, complemented
48C13×#358C2211yescharacteristic, complemented
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic, complemented
54C13×#357C2211yescharacteristic, complemented
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic, complemented
58C4×C13×C16C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C22×D4×C13—21no—
61C13×AGL(1,ℤ/8)—44no—
62C13×#135—41no—
63C13×#135—41no—
64C2×C13×Q16C2311yescharacteristic
65C2×C13×Q16C2311yescharacteristic
66C2×C13×SD16—21no—
67C2×C13×SD16—21no—
68C2×C13×SD16—21no—
69C2×C13×SD16—21no—
70C2×C13×D8—21no—
71C2×C13×D8—21no—
72C2×C13×D8—21no—
73C2×C13×D8—41no—
74C2×C13×D8—41no—
75C2×C13×D8C2311yescharacteristic
76C2×C13×D8C2311yescharacteristic
77C2×C13×D8C2311yescharacteristic
78C2×C13×D8C2311yescharacteristic
79C2×C13×M16D411yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C13×C4⋊Q8—21no—
82C13×#127—21no—
83C13×#127—21no—
84C13×#126—41no—
85C13×#124—21no—
86C13×#124—21no—
87C13×#124—21no—
88C13×#124—41no—
89C13×#123—41no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—41no—
92C13×#121—21no—
93C13×#121—41no—
94C13×#121—41no—
95C13×#120—41no—
96C13×#120—41no—
97C4×Q8×C13—21no—
98C4×D4×C13—21no—
99C13×#117D411yescharacteristic
100C13×Q32—41no—
101C13×SD32—41no—
102C13×SD32—41no—
103C13×SD32—41no—
104C13×SD32—41no—
105C13×D16—41no—
106C13×D16—41no—
107C13×D16—41no—
108C2×C13×C16C2311yescharacteristic
109C2×C13×C16C2311yescharacteristic
110C2×C13×C16C2311yescharacteristic
111C2×C13×C16C2311yescharacteristic
112C13×#107—21no—
113C13×#107C2311yescharacteristic
114C13×#107C2311yescharacteristic
115C13×#103—21no—
116C13×#103—21no—
117C13×#102—21no—
118C13×#102—21no—
119C13×#97D411yescharacteristic
120C13×#97D411yescharacteristic
121C4×C8×C13C2311yescharacteristic
122C4×C8×C13C2311yescharacteristic
123#33790C1311yesmaximal, characteristic, direct product factor, Sylow
124C24×C13—41no—
125C13×#41—42no—
126C13×#41—42no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—41no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—42no—
135C2×D4×C13—42no—
136C2×D4×C13—41no—
137C2×D4×C13—41no—
138C2×D4×C13—41no—
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13C2×D411yescharacteristic
146C13×Q16—21no—
147C13×Q16—21no—
148C13×Q16—21no—
149C13×Q16—21no—
150C13×SD16—42no—
151C13×SD16—42no—
152C13×SD16—42no—
153C13×SD16—42no—
154C13×D8—21no—
155C13×D8—21no—
156C13×D8—21no—
157C13×D8—21no—
158C13×D8—21no—
159C13×D8—21no—
160C13×D8—21no—
161C13×D8—21no—
162C13×D8—42no—
163C13×D8—42no—
164C13×D8—42no—
165C13×M16—22no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4D811yescharacteristic
178C13×C4⋊C4D811yescharacteristic
179C13×C22⋊C4—41no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—41no—
183C13×C22⋊C4—41no—
184C13×C22⋊C4—41no—
185C13×C22⋊C4—41no—
186C13×C22⋊C4—41no—
187C13×C22⋊C4—41no—
188C13×C22⋊C4D811yescharacteristic
189C13×C22⋊C4D811yescharacteristic
190C42×C13—41no—
191C42×C13C2×D411yescharacteristic
192C42×C13C2×D411yescharacteristic
193C13×C16—21no—
194C13×C16—21no—
195C13×C16—21no—
196C13×C16—21no—
197#3175C2×C1311yescharacteristic, complemented
198#3155C2×C1311yescharacteristic, complemented
199#2250C2×C1311yescharacteristic, complemented
200#2249C2×C1311yescharacteristic, complemented
201#2243C2×C1311yescharacteristic, complemented
202#2240C2×C1311yescharacteristic, complemented
203#2211C2×C1311yescharacteristic, complemented
204#2210C2×C1311yescharacteristic, complemented
205#2207C2×C1311yescharacteristic, complemented
206#2206C2×C1311yescharacteristic, complemented
207#2189C2×C1311yescharacteristic, complemented
208#2187C2×C1311yescharacteristic, complemented
209#2186C2×C1311yescharacteristic, complemented
210#2184C2×C1311yescharacteristic, complemented
211#2164C2×C1311yescharacteristic, complemented
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—82no—
217C23×C13—161no—
218C23×C13—161no—
219C23×C13C2×D811yescharacteristic
220Q8×C13—41no—
221Q8×C13—41no—
222Q8×C13—41no—
223Q8×C13—41no—
224Q8×C13—161no—
225D4×C13—41no—
226D4×C13—41no—
227D4×C13—41no—
228D4×C13—41no—
229D4×C13—41no—
230D4×C13—41no—
231D4×C13—41no—
232D4×C13—41no—
233D4×C13—82no—
234D4×C13—82no—
235D4×C13—161no—
236D4×C13—161no—
237D4×C13—161no—
238D4×C13—161no—
239D4×C13—161no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—82no—
247C2×C4×C13—161no—
248C2×C4×C13C2×D811yescharacteristic
249C2×C4×C13C2×D811yescharacteristic
250C2×C4×C13C2×D811yescharacteristic
251C2×C4×C13C2×D811yescharacteristic
252C2×C4×C13C2×D811yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C8×C13—21no—
255C8×C13—21no—
256C8×C13AGL(1,ℤ/8)12yes—
257C8×C13H(5,𝔽2)11yescharacteristic
258C8×C13H(5,𝔽2)11yescharacteristic
259C2×AGL(1,ℤ/8)—21no—
260C2×#135C22×C1311yescharacteristic
261C22×D8C22×C1311yescharacteristic
262#542—21no—
263#535—21no—
264C2×Q32C22×C1311yescharacteristic, complemented
265C2×SD32C22×C1311yescharacteristic
266C2×SD32C22×C1311yescharacteristic
267C2×SD32C22×C1311yescharacteristic, complemented
268C2×SD32C22×C1311yescharacteristic, complemented
269C2×D16C22×C1311yescharacteristic
270C2×D16C22×C1311yescharacteristic
271C2×D16C22×C1311yescharacteristic, complemented
272#500C22×C1311yescharacteristic, complemented
273#496—21no—
274#496—21no—
275#495C22×C1311yescharacteristic
276#495C22×C1311yescharacteristic
277#495C22×C1311yescharacteristic, complemented
278#493C22×C1311yescharacteristic
279#493C22×C1311yescharacteristic
280#489—21no—
281#468—21no—
282#467C22×C1311yescharacteristic
283#466C22×C1311yescharacteristic
284#440—21no—
285C4×Q16C22×C1311yescharacteristic, complemented
286C4×D8C22×C1311yescharacteristic, complemented
287#405C22×C1311yescharacteristic
288C4⋊C16C22×C1311yescharacteristic, complemented
289C4⋊C16C22×C1311yescharacteristic, complemented
290#358C22×C1311yescharacteristic, complemented
291#358C22×C1311yescharacteristic, complemented
292#357C22×C1311yescharacteristic
293#357C22×C1311yescharacteristic
294#357C22×C1311yescharacteristic
295#357C22×C1311yescharacteristic
296#357C22×C1311yescharacteristic, complemented
297#357C22×C1311yescharacteristic, complemented
298C22⋊C16C22×C1311yescharacteristic
299C22⋊C16C22×C1311yescharacteristic
300#346C22×C1311yescharacteristic, complemented
301C4×C16C22×C1311yescharacteristic, complemented
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13—81no—
306C22×C13—81no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—164no—
318C22×C13C22×D811yescharacteristic
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—81no—
325C4×C13—81no—
326C4×C13—81no—
327C4×C13—81no—
328C4×C13#53511yescharacteristic
329C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
330C2×#41—21no—
331C22×D4—21no—
332AGL(1,ℤ/8)—44no—
333#135—41no—
334#135—41no—
335C2×Q16C23×C1311yescharacteristic
336C2×Q16C23×C1311yescharacteristic
337C2×SD16—21no—
338C2×SD16—21no—
339C2×SD16—21no—
340C2×SD16—21no—
341C2×D8—21no—
342C2×D8—21no—
343C2×D8—21no—
344C2×D8—41no—
345C2×D8—41no—
346C2×D8C23×C1311yescharacteristic
347C2×D8C23×C1311yescharacteristic
348C2×D8C23×C1311yescharacteristic
349C2×D8C23×C1311yescharacteristic
350C2×M16D4×C1311yescharacteristic
351C22×C8C23×C1311yescharacteristic
352C4⋊Q8—21no—
353#127—21no—
354#127—21no—
355#126—41no—
356#124—21no—
357#124—21no—
358#124—21no—
359#124—41no—
360#123—41no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363#121—21no—
364#121—41no—
365#121—41no—
366#120—41no—
367#120—41no—
368C4×Q8—21no—
369C4×D4—21no—
370#117D4×C1311yescharacteristic
371Q32—41no—
372SD32—41no—
373SD32—41no—
374SD32—41no—
375SD32—41no—
376D16—41no—
377D16—41no—
378D16—41no—
379C2×C16C23×C1311yescharacteristic
380C2×C16C23×C1311yescharacteristic
381C2×C16C23×C1311yescharacteristic
382C2×C16C23×C1311yescharacteristic
383#107—21no—
384#107C23×C1311yescharacteristic
385#107C23×C1311yescharacteristic
386#103—21no—
387#103—21no—
388#102—21no—
389#102—21no—
390#97D4×C1311yescharacteristic
391#97D4×C1311yescharacteristic
392C4×C8C23×C1311yescharacteristic
393C4×C8C23×C1311yescharacteristic
394C2×C13—41no—
395C2×C13—161no—
396C2×C13—161no—
397C2×C13—161no—
398C2×C13—161no—
399C2×C13#320511yescharacteristic
400C2×C13#341511yescharacteristic
401C2×C13#341611yescharacteristic
402C24—41no—
403#41—42no—
404#41—42no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—41no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4C2×D4×C1311yescharacteristic
424Q16—21no—
425Q16—21no—
426Q16—21no—
427Q16—21no—
428SD16—42no—
429SD16—42no—
430SD16—42no—
431SD16—42no—
432D8—21no—
433D8—21no—
434D8—21no—
435D8—21no—
436D8—21no—
437D8—21no—
438D8—21no—
439D8—21no—
440D8—42no—
441D8—42no—
442D8—42no—
443M16—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8C2×D4×C1311yescharacteristic
447C2×C8C2×D4×C1311yescharacteristic
448C2×C8C2×D4×C1311yescharacteristic
449C2×C8C24×C1311yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4C13×D811yescharacteristic
456C4⋊C4C13×D811yescharacteristic
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4C13×D811yescharacteristic
467C22⋊C4C13×D811yescharacteristic
468C42—41no—
469C42C2×D4×C1311yescharacteristic
470C42C2×D4×C1311yescharacteristic
471C16—21no—
472C16—21no—
473C16—21no—
474C16—21no—
475C13#3379011yescharacteristic, direct product factor, Sylow
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—82no—
481C23—161no—
482C23—161no—
483C23C2×C13×D811yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—161no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—82no—
498D4—82no—
499D4—161no—
500D4—161no—
501D4—161no—
502D4—161no—
503D4—161no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—82no—
511C2×C4—161no—
512C2×C4C2×C13×D811yescharacteristic
513C2×C4C2×C13×D811yescharacteristic
514C2×C4C2×C13×D811yescharacteristic
515C2×C4C2×C13×D811yescharacteristic
516C2×C4C2×C13×D811yescharacteristic
517C2×C4C22×D4×C1311yescharacteristic
518C8—21no—
519C8—21no—
520C8C13×AGL(1,ℤ/8)12yes—
521C8C13×H(5,𝔽2)11yescharacteristic
522C8C13×H(5,𝔽2)11yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—164no—
539C22C22×C13×D811yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4C13×#53511yescharacteristic
550C4C2×C13×AGL(1,ℤ/8)11yescharacteristic
551C2—41no—
552C2—161no—
553C2—161no—
554C2—161no—
555C2—161no—
556C2C13×#320511yescharacteristic
557C2C13×#341511yescharacteristic
558C2C13×#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×#3175C2semidirect
2. C13×#3155C2semidirect
3. C13×#2250C2semidirect
4. C13×#2249C2semidirect
5. C13×#2243C2semidirect
6. C13×#2240C2semidirect
7. C13×#2211C2semidirect
8. C13×#2210C2semidirect
9. C13×#2207C2semidirect
10. C13×#2206C2semidirect
11. C13×#2189C2semidirect
12. C13×#2187C2semidirect
13. C13×#2186C2semidirect
14. C13×#2184C2semidirect
15. C13×#2164C2semidirect
21. C2×C13×Q32C22semidirect
24. C2×C13×SD32C22semidirect
25. C2×C13×SD32C22semidirect
28. C2×C13×D16C22semidirect
29. C13×#500C22semidirect
34. C13×#495C22semidirect
42. C4×C13×Q16C22semidirect
43. C4×C13×D8C22semidirect
45. C13×C4⋊C16C22semidirect
46. C13×C4⋊C16C22semidirect
47. C13×#358C22semidirect
48. C13×#358C22semidirect
53. C13×#357C22semidirect
54. C13×#357C22semidirect
57. C13×#346C22semidirect
58. C4×C13×C16C22semidirect
123. #33790C13direct (N × H)
197. #3175C2×C13semidirect
198. #3155C2×C13semidirect
199. #2250C2×C13semidirect
200. #2249C2×C13semidirect
201. #2243C2×C13semidirect
202. #2240C2×C13semidirect
203. #2211C2×C13semidirect
204. #2210C2×C13semidirect
205. #2207C2×C13semidirect
206. #2206C2×C13semidirect
207. #2189C2×C13semidirect
208. #2187C2×C13semidirect
209. #2186C2×C13semidirect
210. #2184C2×C13semidirect
211. #2164C2×C13semidirect
264. C2×Q32C22×C13semidirect
267. C2×SD32C22×C13semidirect
268. C2×SD32C22×C13semidirect
271. C2×D16C22×C13semidirect
272. #500C22×C13semidirect
277. #495C22×C13semidirect
285. C4×Q16C22×C13semidirect
286. C4×D8C22×C13semidirect
288. C4⋊C16C22×C13semidirect
289. C4⋊C16C22×C13semidirect
290. #358C22×C13semidirect
291. #358C22×C13semidirect
296. #357C22×C13semidirect
297. #357C22×C13semidirect
300. #346C22×C13semidirect
301. C4×C16C22×C13semidirect
475. C13#33790direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31752
C13×#31552
C13×#22502
C13×#22492
C13×#22432
C13×#22402
C13×#22112
C13×#22102
C13×#22072
C13×#22062
C13×#21892
C13×#21872
C13×#21862
C13×#21842
C13×#21642
#3379013