Finite Group Databasebeta

← C13×#33885 #15720224

Subgroups — C13×#33885 #15720224

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3339C211yesmaximal, characteristic, complemented
2D4×C13×D8C211yesmaximal, characteristic, complemented
3C13×#2244C211yesmaximal, characteristic, complemented
4C13×#2234C211yesmaximal, characteristic, complemented
5C13×#2233C211yesmaximal, characteristic, complemented
6C13×#2228C211yesmaximal, characteristic, complemented
7C13×#2218C211yesmaximal, characteristic, complemented
8C13×#2215C211yesmaximal, characteristic, complemented
9C13×#2206C211yesmaximal, characteristic, complemented
10C13×#2184C211yesmaximal, characteristic, complemented
11C13×#2184C211yesmaximal, characteristic, complemented
12C13×#2177C211yesmaximal, characteristic, complemented
13C13×#2168C211yesmaximal, characteristic, complemented
14C13×#2140C211yesmaximal, characteristic, complemented
15C2×C13×#357C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#553—21no—
19D42×C13—21no—
20C2×C13×D16C2211yescharacteristic
21C2×C13×D16C2211yescharacteristic, complemented
22C2×C13×D16C2211yescharacteristic, complemented
23C2×C13×M32C2211yescharacteristic, complemented
24C22×C13×C16C2211yescharacteristic, complemented
25C13×#499C2211yescharacteristic, complemented
26C13×#493C2211yescharacteristic
27C13×#482—21no—
28C13×#481—21no—
29C13×#478—21no—
30C13×#466C2211yescharacteristic
31C13×#466C2211yescharacteristic
32C13×#466C2211yescharacteristic, complemented
33C13×#466C2211yescharacteristic, complemented
34C13×#459—21no—
35C13×#447—21no—
36C13×#447—21no—
37C4×C13×D8C2211yescharacteristic
38C4×C13×D8C2211yescharacteristic, complemented
39C8×D4×C13C2211yescharacteristic
40C13×#427C2211yescharacteristic, complemented
41C2×C13×#107C2211yescharacteristic, complemented
42C13×#367C2211yescharacteristic, complemented
43C13×#367C2211yescharacteristic, complemented
44C13×#366C2211yescharacteristic, complemented
45C13×C4⋊C16C2211yescharacteristic, complemented
46C13×#357C2211yescharacteristic
47C13×#357C2211yescharacteristic
48C13×#357C2211yescharacteristic
49C13×#357C2211yescharacteristic, complemented
50C13×#357C2211yescharacteristic, complemented
51C13×#357C2211yescharacteristic, complemented
52C13×#357C2211yescharacteristic, complemented
53C13×#357C2211yescharacteristic, complemented
54C13×#357C2211yescharacteristic, complemented
55C13×#357C2211yescharacteristic, complemented
56C13×C22⋊C16C2211yescharacteristic, complemented
57C13×C22⋊C16C2211yescharacteristic, complemented
58C13×#346C2211yescharacteristic, complemented
59C22×D4×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13—41no—
62C2×C13×D8—22no—
63C2×C13×D8—22no—
64C2×C13×D8—21no—
65C2×C13×D8—21no—
66C2×C13×D8—21no—
67C2×C13×D8—41no—
68C2×C13×D8—41no—
69C2×C13×D8C2311yescharacteristic
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C2×C13×D8C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×#127—21no—
76C13×#126—41no—
77C13×#125—21no—
78C13×#123—41no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#121—21no—
83C13×#121—41no—
84C13×#121—41no—
85C13×#120—41no—
86C13×#120—41no—
87C4×D4×C13—21no—
88C4×D4×C13—21no—
89C4×D4×C13—41no—
90C4×D4×C13D411yescharacteristic
91C13×#117—21no—
92C2×C13×C4⋊C4—21no—
93C13×D16—22no—
94C13×D16—41no—
95C13×D16—41no—
96C13×M32—41no—
97C2×C13×C16—41no—
98C2×C13×C16C2311yescharacteristic
99C2×C13×C16C2311yescharacteristic
100C2×C13×C16C2311yescharacteristic
101C2×C13×C16C2311yescharacteristic
102C13×#107—21no—
103C13×#107C2311yescharacteristic
104C13×#107C2311yescharacteristic
105C13×#107C2311yescharacteristic
106C13×#107C2311yescharacteristic
107C13×#106—21no—
108C13×#106—21no—
109C13×C4⋊C8D411yescharacteristic
110C13×#102—21no—
111C13×#102—21no—
112C13×#102—21no—
113C13×#102—21no—
114C13×#102—21no—
115C13×#102—21no—
116C13×C22⋊C8D411yescharacteristic
117C13×C22⋊C8D411yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#33885C1311yesmaximal, characteristic, direct product factor, Sylow
120C24×C13—41no—
121C24×C13—41no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13—81no—
137C2×D4×C13—81no—
138C2×D4×C13—84no—
139C2×D4×C13D811yescharacteristic
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C13×D8—21no—
146C13×D8—21no—
147C13×D8—21no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—21no—
151C13×D8—21no—
152C13×D8—42no—
153C13×D8—42no—
154C13×D8—81no—
155C13×D8#4112yes—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2411yescharacteristic
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—41no—
170C13×C4⋊C4—41no—
171C13×C4⋊C4D811yescharacteristic
172C13×C22⋊C4—41no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—41no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4D811yescharacteristic
180C13×C22⋊C4D811yescharacteristic
181C42×C13—41no—
182C42×C13C2×D411yescharacteristic
183C13×C16—21no—
184C13×C16—21no—
185C13×C16—21no—
186C13×C16—21no—
187#3339C2×C1311yescharacteristic, complemented
188D4×D8C2×C1311yescharacteristic, complemented
189#2244C2×C1311yescharacteristic, complemented
190#2234C2×C1311yescharacteristic, complemented
191#2233C2×C1311yescharacteristic, complemented
192#2228C2×C1311yescharacteristic, complemented
193#2218C2×C1311yescharacteristic, complemented
194#2215C2×C1311yescharacteristic, complemented
195#2206C2×C1311yescharacteristic, complemented
196#2184C2×C1311yescharacteristic, complemented
197#2184C2×C1311yescharacteristic, complemented
198#2177C2×C1311yescharacteristic, complemented
199#2168C2×C1311yescharacteristic, complemented
200#2140C2×C1311yescharacteristic, complemented
201C2×#357C2×C1311yescharacteristic, complemented
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—82no—
207C23×C13—82no—
208C23×C13—82no—
209C23×C13—82no—
210C23×C13—161no—
211C23×C13—161no—
212C23×C13C2×D811yescharacteristic
213C23×C13C2×D811yescharacteristic
214D4×C13—22no—
215D4×C13—22no—
216D4×C13—41no—
217D4×C13—41no—
218D4×C13—41no—
219D4×C13—41no—
220D4×C13—41no—
221D4×C13—41no—
222D4×C13—41no—
223D4×C13—82no—
224D4×C13—82no—
225D4×C13—82no—
226D4×C13—82no—
227D4×C13—82no—
228D4×C13—82no—
229D4×C13—161no—
230D4×C13—161no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—82no—
240C2×C4×C13—161no—
241C2×C4×C13—161no—
242C2×C4×C13C2×D811yescharacteristic
243C2×C4×C13C2×D811yescharacteristic
244C2×C4×C13C2×D811yescharacteristic
245C2×C4×C13C2×D811yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C8×C13—21no—
248C8×C13—21no—
249C8×C13—21no—
250C8×C13C2×#4111yescharacteristic
251C8×C13H(5,𝔽2)11yescharacteristic
252C22×D8C22×C1311yescharacteristic
253C22×D8C22×C1311yescharacteristic
254#553—21no—
255D42—21no—
256C2×D16C22×C1311yescharacteristic
257C2×D16C22×C1311yescharacteristic, complemented
258C2×D16C22×C1311yescharacteristic, complemented
259C2×M32C22×C1311yescharacteristic, complemented
260C22×C16C22×C1311yescharacteristic, complemented
261#499C22×C1311yescharacteristic, complemented
262#493C22×C1311yescharacteristic
263#482—21no—
264#481—21no—
265#478—21no—
266#466C22×C1311yescharacteristic
267#466C22×C1311yescharacteristic
268#466C22×C1311yescharacteristic, complemented
269#466C22×C1311yescharacteristic, complemented
270#459—21no—
271#447—21no—
272#447—21no—
273C4×D8C22×C1311yescharacteristic
274C4×D8C22×C1311yescharacteristic, complemented
275C8×D4C22×C1311yescharacteristic
276#427C22×C1311yescharacteristic, complemented
277C2×#107C22×C1311yescharacteristic, complemented
278#367C22×C1311yescharacteristic, complemented
279#367C22×C1311yescharacteristic, complemented
280#366C22×C1311yescharacteristic, complemented
281C4⋊C16C22×C1311yescharacteristic, complemented
282#357C22×C1311yescharacteristic
283#357C22×C1311yescharacteristic
284#357C22×C1311yescharacteristic
285#357C22×C1311yescharacteristic, complemented
286#357C22×C1311yescharacteristic, complemented
287#357C22×C1311yescharacteristic, complemented
288#357C22×C1311yescharacteristic, complemented
289#357C22×C1311yescharacteristic, complemented
290#357C22×C1311yescharacteristic, complemented
291#357C22×C1311yescharacteristic, complemented
292C22⋊C16C22×C1311yescharacteristic, complemented
293C22⋊C16C22×C1311yescharacteristic, complemented
294#346C22×C1311yescharacteristic, complemented
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—42no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13—81no—
305C22×C13—81no—
306C22×C13—81no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—164no—
313C22×C13—164no—
314C22×C13#50912yes—
315C22×C13C22×D811yescharacteristic
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—81no—
321C4×C13—81no—
322C4×C13—81no—
323C4×C13—81no—
324C4×C13#54611yescharacteristic
325C4×C13#57711yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—41no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—21no—
332C2×D8—21no—
333C2×D8—21no—
334C2×D8—41no—
335C2×D8—41no—
336C2×D8C23×C1311yescharacteristic
337C2×D8C23×C1311yescharacteristic
338C2×D8C23×C1311yescharacteristic
339C2×D8C23×C1311yescharacteristic
340C22×C8C23×C1311yescharacteristic
341C22×C8C23×C1311yescharacteristic
342#127—21no—
343#126—41no—
344#125—21no—
345#123—41no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—41no—
351#121—41no—
352#120—41no—
353#120—41no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—41no—
357C4×D4D4×C1311yescharacteristic
358#117—21no—
359C2×C4⋊C4—21no—
360D16—22no—
361D16—41no—
362D16—41no—
363M32—41no—
364C2×C16—41no—
365C2×C16C23×C1311yescharacteristic
366C2×C16C23×C1311yescharacteristic
367C2×C16C23×C1311yescharacteristic
368C2×C16C23×C1311yescharacteristic
369#107—21no—
370#107C23×C1311yescharacteristic
371#107C23×C1311yescharacteristic
372#107C23×C1311yescharacteristic
373#107C23×C1311yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8D4×C1311yescharacteristic
377#102—21no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—21no—
382#102—21no—
383C22⋊C8D4×C1311yescharacteristic
384C22⋊C8D4×C1311yescharacteristic
385C4×C8C23×C1311yescharacteristic
386C2×C13—22no—
387C2×C13—41no—
388C2×C13—82no—
389C2×C13—161no—
390C2×C13—161no—
391C2×C13—161no—
392C2×C13#329411yescharacteristic
393C2×C13C2×#50911yescharacteristic
394C2×C13#341511yescharacteristic
395C24—41no—
396C24—41no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—84no—
414C2×D4C13×D811yescharacteristic
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4C2×D4×C1311yescharacteristic
419C22×C4C2×D4×C1311yescharacteristic
420D8—21no—
421D8—21no—
422D8—21no—
423D8—21no—
424D8—21no—
425D8—21no—
426D8—21no—
427D8—42no—
428D8—42no—
429D8—81no—
430D8C13×#4112yes—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8C2×D4×C1311yescharacteristic
436C2×C8C2×D4×C1311yescharacteristic
437C2×C8C2×D4×C1311yescharacteristic
438C2×C8C24×C1311yescharacteristic
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4C13×D811yescharacteristic
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4C13×D811yescharacteristic
455C22⋊C4C13×D811yescharacteristic
456C42—41no—
457C42C2×D4×C1311yescharacteristic
458C16—21no—
459C16—21no—
460C16—21no—
461C16—21no—
462C13#3388511yescharacteristic, direct product factor, Sylow
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—82no—
468C23—82no—
469C23—82no—
470C23—82no—
471C23—161no—
472C23—161no—
473C23C2×C13×D811yescharacteristic
474C23C2×C13×D811yescharacteristic
475D4—22no—
476D4—22no—
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486D4—82no—
487D4—82no—
488D4—82no—
489D4—82no—
490D4—161no—
491D4—161no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—82no—
501C2×C4—161no—
502C2×C4—161no—
503C2×C4C2×C13×D811yescharacteristic
504C2×C4C2×C13×D811yescharacteristic
505C2×C4C2×C13×D811yescharacteristic
506C2×C4C2×C13×D811yescharacteristic
507C2×C4C22×D4×C1311yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8C2×C13×#4111yescharacteristic
512C8C13×H(5,𝔽2)11yescharacteristic
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—42no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—164no—
531C22—164no—
532C22C13×#50912yes—
533C22C22×C13×D811yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4C13×#54611yescharacteristic
543C4C13×#57711yescharacteristic
544C2—22no—
545C2—41no—
546C2—82no—
547C2—161no—
548C2—161no—
549C2—161no—
550C2C13×#329411yescharacteristic
551C2C2×C13×#50911yescharacteristic
552C2C13×#341511yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3339C2semidirect
2. D4×C13×D8C2semidirect
3. C13×#2244C2semidirect
4. C13×#2234C2semidirect
5. C13×#2233C2semidirect
6. C13×#2228C2semidirect
7. C13×#2218C2semidirect
8. C13×#2215C2semidirect
9. C13×#2206C2semidirect
10. C13×#2184C2semidirect
11. C13×#2184C2semidirect
12. C13×#2177C2semidirect
13. C13×#2168C2semidirect
14. C13×#2140C2semidirect
15. C2×C13×#357C2semidirect
21. C2×C13×D16C22semidirect
22. C2×C13×D16C22semidirect
23. C2×C13×M32C22semidirect
24. C22×C13×C16C22semidirect
25. C13×#499C22semidirect
32. C13×#466C22semidirect
33. C13×#466C22semidirect
38. C4×C13×D8C22semidirect
40. C13×#427C22semidirect
41. C2×C13×#107C22semidirect
42. C13×#367C22semidirect
43. C13×#367C22semidirect
44. C13×#366C22semidirect
45. C13×C4⋊C16C22semidirect
49. C13×#357C22semidirect
50. C13×#357C22semidirect
51. C13×#357C22semidirect
52. C13×#357C22semidirect
53. C13×#357C22semidirect
54. C13×#357C22semidirect
55. C13×#357C22semidirect
56. C13×C22⋊C16C22semidirect
57. C13×C22⋊C16C22semidirect
58. C13×#346C22semidirect
119. #33885C13direct (N × H)
187. #3339C2×C13semidirect
188. D4×D8C2×C13semidirect
189. #2244C2×C13semidirect
190. #2234C2×C13semidirect
191. #2233C2×C13semidirect
192. #2228C2×C13semidirect
193. #2218C2×C13semidirect
194. #2215C2×C13semidirect
195. #2206C2×C13semidirect
196. #2184C2×C13semidirect
197. #2184C2×C13semidirect
198. #2177C2×C13semidirect
199. #2168C2×C13semidirect
200. #2140C2×C13semidirect
201. C2×#357C2×C13semidirect
257. C2×D16C22×C13semidirect
258. C2×D16C22×C13semidirect
259. C2×M32C22×C13semidirect
260. C22×C16C22×C13semidirect
261. #499C22×C13semidirect
268. #466C22×C13semidirect
269. #466C22×C13semidirect
274. C4×D8C22×C13semidirect
276. #427C22×C13semidirect
277. C2×#107C22×C13semidirect
278. #367C22×C13semidirect
279. #367C22×C13semidirect
280. #366C22×C13semidirect
281. C4⋊C16C22×C13semidirect
285. #357C22×C13semidirect
286. #357C22×C13semidirect
287. #357C22×C13semidirect
288. #357C22×C13semidirect
289. #357C22×C13semidirect
290. #357C22×C13semidirect
291. #357C22×C13semidirect
292. C22⋊C16C22×C13semidirect
293. C22⋊C16C22×C13semidirect
294. #346C22×C13semidirect
462. C13#33885direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33392
D4×C13×D82
C13×#22442
C13×#22342
C13×#22332
C13×#22282
C13×#22182
C13×#22152
C13×#22062
C13×#21842
C13×#21772
C13×#21682
C13×#21402
C2×C13×#3572
#3388513