Finite Group Databasebeta

← C13×#18252 #15704591

Subgroups — C13×#18252 #15704591

Order 3328.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3534C211yesmaximal, characteristic, complemented
2C13×#3006C211yesmaximal, characteristic, complemented
3C13×#3002C211yesmaximal, characteristic, complemented
4C13×#2430C211yesmaximal, characteristic, complemented
5C13×#1606C211yesmaximal, characteristic, complemented
6C13×#1604C211yesmaximal, characteristic, complemented
7C13×#1603C211yesmaximal, characteristic, complemented
8C13×#1601C211yesmaximal, characteristic, complemented
9C13×#1600C211yesmaximal, characteristic, complemented
10C13×#1598C211yesmaximal, characteristic, complemented
11C13×#1597C211yesmaximal, characteristic, complemented
12C13×#1595C211yesmaximal, characteristic, complemented
13C13×#1504C211yesmaximal, characteristic, complemented
14C2×C13×#327C211yesmaximal, characteristic, complemented
15C13×#1468C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic, complemented
17C2×C13×AGL(1,ℤ/8)—21no—
18C2×C13×#135—21no—
19C13×#562—21no—
20C13×#560—21no—
21C13×#553—21no—
22C13×#551—21no—
23C13×#546—21no—
24C13×#546—21no—
25C13×#546—21no—
26D42×C13—21no—
27C13×#540—21no—
28C13×#539—21no—
29C13×#539C2211yescharacteristic
30C13×#538—21no—
31C13×#538C2211yescharacteristic
32C13×#537C2211yescharacteristic
33C13×#534—21no—
34C13×#534C2211yescharacteristic
35C13×#525C2211yescharacteristic
36C2×C13×#123C2211yescharacteristic
37C2×C13×#121—21no—
38C2×C13×#121C2211yescharacteristic
39C13×#452—21no—
40C13×#451C2211yescharacteristic, complemented
41C13×#450C2211yescharacteristic, complemented
42C13×#449—21no—
43C13×#449—21no—
44C13×#449—21no—
45C13×#448C2211yescharacteristic
46C13×#448C2211yescharacteristic, complemented
47C13×#448C2211yescharacteristic, complemented
48C13×#447C2211yescharacteristic
49C13×#447C2211yescharacteristic, complemented
50C13×#447C2211yescharacteristic, complemented
51C13×#417—21no—
52C13×#416—21no—
53C13×#407C2211yescharacteristic, complemented
54C2×C13×C22⋊C8C2211yescharacteristic, complemented
55C13×#395C2211yescharacteristic, complemented
56C13×#394C2211yescharacteristic, complemented
57C13×#393C2211yescharacteristic, complemented
58C13×#392C2211yescharacteristic, complemented
59C13×#386—21no—
60C13×#386—21no—
61C13×#385—21no—
62C2×C13×#95C2211yescharacteristic, complemented
63C13×#328C2211yescharacteristic, complemented
64C13×#328C2211yescharacteristic, complemented
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic, complemented
68C13×#327C2211yescharacteristic, complemented
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#324C2211yescharacteristic, complemented
72C13×#324C2211yescharacteristic, complemented
73C13×#323C2211yescharacteristic, complemented
74C13×#323C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41—21no—
77C2×C13×#41—21no—
78C2×C13×#41—21no—
79C2×C13×#41—21no—
80C2×C13×#41—44no—
81C2×C13×#41D411yescharacteristic, complemented
82C22×Q8×C13C2311yescharacteristic
83C22×D4×C13—21no—
84C22×D4×C13—21no—
85C22×D4×C13—21no—
86C22×D4×C13—21no—
87C22×D4×C13—21no—
88C22×D4×C13D411yescharacteristic
89C22×D4×C13D411yescharacteristic, complemented
90C22×D4×C13C2311yescharacteristic
91C23×C4×C13—21no—
92C23×C4×C13—21no—
93C23×C4×C13C2311yescharacteristic
94C13×AGL(1,ℤ/8)—44no—
95C13×#135—44no—
96C2×C13×Q16—21no—
97C2×C13×SD16—21no—
98C2×C13×SD16—21no—
99C2×C13×SD16—21no—
100C2×C13×SD16—21no—
101C2×C13×D8—21no—
102C2×C13×D8—21no—
103C2×C13×D8—21no—
104C2×C13×M16—21no—
105C22×C8×C13—21no—
106C13×#127—21no—
107C13×#126—21no—
108C13×#126—21no—
109C13×#126—21no—
110C13×#126—21no—
111C13×#125—21no—
112C13×#125—21no—
113C13×#124—21no—
114C13×#124—21no—
115C13×#124—21no—
116C13×#123—21no—
117C13×#123—21no—
118C13×#123—21no—
119C13×#123—21no—
120C13×#123—21no—
121C13×#123—21no—
122C13×#123—21no—
123C13×#123—21no—
124C13×#123—21no—
125C13×#123—21no—
126C13×#123—21no—
127C13×#123—21no—
128C13×#123—21no—
129C13×#123—21no—
130C13×C22⋊Q8—21no—
131C13×C22⋊Q8—21no—
132C13×C22⋊Q8—21no—
133C13×C22⋊Q8—21no—
134C13×C22⋊Q8—21no—
135C13×C22⋊Q8D411yescharacteristic, complemented
136C13×C22⋊Q8C2311yescharacteristic
137C13×#121—21no—
138C13×#121—21no—
139C13×#121—21no—
140C13×#121—21no—
141C13×#121—21no—
142C13×#121—21no—
143C13×#121—21no—
144C13×#121—21no—
145C13×#121—21no—
146C13×#121—21no—
147C13×#121—21no—
148C13×#121—21no—
149C13×#121—21no—
150C13×#121—21no—
151C13×#121—21no—
152C13×#121—44no—
153C13×#121D411yescharacteristic, complemented
154C13×#121D411yescharacteristic, complemented
155C13×#121D411yescharacteristic, complemented
156C13×#121C2311yescharacteristic
157C13×#121C2311yescharacteristic
158C13×#121C2311yescharacteristic
159C13×#120—21no—
160C13×#120—21no—
161C13×#120—21no—
162C13×#120—21no—
163C13×#120—21no—
164C13×#120—21no—
165C13×#120—21no—
166C13×#120—21no—
167C4×D4×C13—21no—
168C4×D4×C13—21no—
169C4×D4×C13—21no—
170C4×D4×C13—21no—
171C4×D4×C13—21no—
172C4×D4×C13—21no—
173C4×D4×C13—21no—
174C4×D4×C13—21no—
175C13×#117—21no—
176C13×#117D411yescharacteristic, complemented
177C2×C13×C4⋊C4—21no—
178C2×C13×C4⋊C4D411yescharacteristic
179C2×C13×C4⋊C4D411yescharacteristic, complemented
180C2×C13×C4⋊C4C2311yescharacteristic
181C2×C13×C22⋊C4—21no—
182C2×C13×C22⋊C4—21no—
183C2×C13×C22⋊C4—21no—
184C2×C13×C22⋊C4—21no—
185C2×C13×C22⋊C4—21no—
186C2×C13×C22⋊C4—21no—
187C2×C13×C22⋊C4—21no—
188C2×C13×C22⋊C4D411yescharacteristic
189C2×C13×C22⋊C4D411yescharacteristic
190C2×C13×C22⋊C4C2311yescharacteristic
191C13×#103—21no—
192C13×#103—21no—
193C13×#103—21no—
194C13×#103—21no—
195C13×#102—21no—
196C13×#102—21no—
197C13×#102—21no—
198C13×#102—21no—
199C13×C22⋊C8—21no—
200C13×C22⋊C8—21no—
201C13×C22⋊C8C2311yescharacteristic
202C13×C22⋊C8C2311yescharacteristic
203C13×C22⋊C8C2311yescharacteristic
204C13×C22⋊C8C2311yescharacteristic
205C13×#95—21no—
206C13×#95—21no—
207C13×#95—21no—
208C13×#95C2311yescharacteristic
209C13×#95C2311yescharacteristic
210#18252C1311yesmaximal, characteristic, direct product factor, Sylow
211C24×C13—21no—
212C24×C13—21no—
213C24×C13—21no—
214C24×C13C2×D411yescharacteristic
215C24×C13C2×D411yescharacteristic
216C13×#41—24no—
217C13×#41—24no—
218C13×#41—42no—
219C13×#41—42no—
220C13×#41—42no—
221C13×#41—42no—
222C13×#41—42no—
223C13×#41—42no—
224C13×#41—42no—
225C13×#41—81no—
226C13×#41—81no—
227C2×Q8×C13—21no—
228C2×Q8×C13—21no—
229C2×Q8×C13—21no—
230C2×Q8×C13—42no—
231C2×Q8×C13C2×D411yescharacteristic
232C2×D4×C13—24no—
233C2×D4×C13—21no—
234C2×D4×C13—21no—
235C2×D4×C13—21no—
236C2×D4×C13—21no—
237C2×D4×C13—21no—
238C2×D4×C13—21no—
239C2×D4×C13—21no—
240C2×D4×C13—21no—
241C2×D4×C13—21no—
242C2×D4×C13—21no—
243C2×D4×C13—21no—
244C2×D4×C13—21no—
245C2×D4×C13—21no—
246C2×D4×C13—21no—
247C2×D4×C13—21no—
248C2×D4×C13—21no—
249C2×D4×C13—21no—
250C2×D4×C13—21no—
251C2×D4×C13—21no—
252C2×D4×C13—42no—
253C2×D4×C13—42no—
254C2×D4×C13—42no—
255C2×D4×C13—42no—
256C2×D4×C13—41no—
257C2×D4×C13—41no—
258C2×D4×C13—42no—
259C2×D4×C13—42no—
260C2×D4×C13—81no—
261C2×D4×C13—81no—
262C2×D4×C13—81no—
263C2×D4×C13—81no—
264C2×D4×C13—81no—
265C2×D4×C13—82no—
266C2×D4×C13C2×D411yescharacteristic
267C2×D4×C13C2×D411yescharacteristic
268C2×D4×C13C2×D411yescharacteristic
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—42no—
280C22×C4×C13—42no—
281C22×C4×C13—42no—
282C22×C4×C13—42no—
283C22×C4×C13—41no—
284C22×C4×C13—41no—
285C22×C4×C13—42no—
286C22×C4×C13—81no—
287C22×C4×C13C2×D411yescharacteristic
288C22×C4×C13C2×D411yescharacteristic
289C22×C4×C13C2×D411yescharacteristic
290C22×C4×C13C2×D411yescharacteristic
291C22×C4×C13C2×D411yescharacteristic
292C22×C4×C13C2×D411yescharacteristic
293C22×C4×C13C2×D411yescharacteristic
294C22×C4×C13C2×D411yescharacteristic
295C22×C4×C13C2411yescharacteristic
296C13×Q16—42no—
297C13×SD16—42no—
298C13×SD16—42no—
299C13×SD16—42no—
300C13×SD16—42no—
301C13×D8—42no—
302C13×D8—42no—
303C13×D8—42no—
304C13×M16—42no—
305C2×C8×C13—21no—
306C2×C8×C13—21no—
307C2×C8×C13—21no—
308C2×C8×C13—21no—
309C2×C8×C13—42no—
310C13×C4⋊C4—21no—
311C13×C4⋊C4—21no—
312C13×C4⋊C4—21no—
313C13×C4⋊C4—21no—
314C13×C4⋊C4—21no—
315C13×C4⋊C4—21no—
316C13×C4⋊C4—21no—
317C13×C4⋊C4—21no—
318C13×C4⋊C4—21no—
319C13×C4⋊C4—21no—
320C13×C4⋊C4—21no—
321C13×C4⋊C4—21no—
322C13×C4⋊C4—21no—
323C13×C4⋊C4—42no—
324C13×C4⋊C4C2×D411yescharacteristic
325C13×C4⋊C4C2×D411yescharacteristic
326C13×C4⋊C4C2×D411yescharacteristic
327C13×C4⋊C4C2×D411yescharacteristic
328C13×C22⋊C4—21no—
329C13×C22⋊C4—21no—
330C13×C22⋊C4—21no—
331C13×C22⋊C4—21no—
332C13×C22⋊C4—21no—
333C13×C22⋊C4—21no—
334C13×C22⋊C4—21no—
335C13×C22⋊C4—21no—
336C13×C22⋊C4—21no—
337C13×C22⋊C4—21no—
338C13×C22⋊C4—21no—
339C13×C22⋊C4—21no—
340C13×C22⋊C4—21no—
341C13×C22⋊C4—21no—
342C13×C22⋊C4—21no—
343C13×C22⋊C4—21no—
344C13×C22⋊C4—21no—
345C13×C22⋊C4—21no—
346C13×C22⋊C4—21no—
347C13×C22⋊C4—21no—
348C13×C22⋊C4—21no—
349C13×C22⋊C4—21no—
350C13×C22⋊C4—21no—
351C13×C22⋊C4—21no—
352C13×C22⋊C4—21no—
353C13×C22⋊C4—42no—
354C13×C22⋊C4—42no—
355C13×C22⋊C4—42no—
356C13×C22⋊C4—81no—
357C42×C13—21no—
358C42×C13—21no—
359C42×C13—21no—
360#3534C2×C1311yescharacteristic, complemented
361#3006C2×C1311yescharacteristic, complemented
362#3002C2×C1311yescharacteristic, complemented
363#2430C2×C1311yescharacteristic, complemented
364#1606C2×C1311yescharacteristic, complemented
365#1604C2×C1311yescharacteristic, complemented
366#1603C2×C1311yescharacteristic, complemented
367#1601C2×C1311yescharacteristic, complemented
368#1600C2×C1311yescharacteristic, complemented
369#1598C2×C1311yescharacteristic, complemented
370#1597C2×C1311yescharacteristic, complemented
371#1595C2×C1311yescharacteristic, complemented
372#1504C2×C1311yescharacteristic, complemented
373C2×#327C2×C1311yescharacteristic, complemented
374#1468C2×C1311yescharacteristic, complemented
375C23×C13—21no—
376C23×C13—21no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—21no—
380C23×C13—21no—
381C23×C13—21no—
382C23×C13—21no—
383C23×C13—21no—
384C23×C13—21no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—42no—
395C23×C13—81no—
396C23×C13—81no—
397C23×C13—81no—
398C23×C13—81no—
399C23×C13—81no—
400C23×C13#12011yescharacteristic
401C23×C13#12011yescharacteristic
402C23×C13C22×D411yescharacteristic
403Q8×C13—22no—
404Q8×C13—22no—
405Q8×C13—41no—
406Q8×C13—41no—
407Q8×C13—41no—
408Q8×C13—81no—
409D4×C13—22no—
410D4×C13—22no—
411D4×C13—41no—
412D4×C13—41no—
413D4×C13—41no—
414D4×C13—41no—
415D4×C13—41no—
416D4×C13—44no—
417D4×C13—41no—
418D4×C13—41no—
419D4×C13—41no—
420D4×C13—41no—
421D4×C13—41no—
422D4×C13—41no—
423D4×C13—44no—
424D4×C13—42no—
425D4×C13—42no—
426D4×C13—81no—
427D4×C13—81no—
428D4×C13—81no—
429D4×C13—81no—
430D4×C13—81no—
431D4×C13—81no—
432D4×C13—81no—
433D4×C13—81no—
434D4×C13—81no—
435D4×C13—81no—
436D4×C13—81no—
437D4×C13—81no—
438D4×C13—84no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—21no—
444C2×C4×C13—21no—
445C2×C4×C13—21no—
446C2×C4×C13—21no—
447C2×C4×C13—21no—
448C2×C4×C13—21no—
449C2×C4×C13—21no—
450C2×C4×C13—21no—
451C2×C4×C13—21no—
452C2×C4×C13—21no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—44no—
458C2×C4×C13—44no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—81no—
469C2×C4×C13—81no—
470C2×C4×C13—81no—
471C2×C4×C13—81no—
472C2×C4×C13—81no—
473C2×C4×C13—81no—
474C2×C4×C13—81no—
475C2×C4×C13—84no—
476C2×C4×C13#12011yescharacteristic
477C2×C4×C13#12011yescharacteristic
478C2×C4×C13C22×D411yescharacteristic
479C2×C4×C13C22×D411yescharacteristic
480C8×C13—41no—
481C8×C13—41no—
482C8×C13—41no—
483C8×C13—41no—
484C22×#41C22×C1311yescharacteristic, complemented
485C2×AGL(1,ℤ/8)—21no—
486C2×#135—21no—
487#562—21no—
488#560—21no—
489#553—21no—
490#551—21no—
491#546—21no—
492#546—21no—
493#546—21no—
494D42—21no—
495#540—21no—
496#539—21no—
497#539C22×C1311yescharacteristic
498#538—21no—
499#538C22×C1311yescharacteristic
500#537C22×C1311yescharacteristic
501#534—21no—
502#534C22×C1311yescharacteristic
503#525C22×C1311yescharacteristic
504C2×#123C22×C1311yescharacteristic
505C2×#121—21no—
506C2×#121C22×C1311yescharacteristic
507#452—21no—
508#451C22×C1311yescharacteristic, complemented
509#450C22×C1311yescharacteristic, complemented
510#449—21no—
511#449—21no—
512#449—21no—
513#448C22×C1311yescharacteristic
514#448C22×C1311yescharacteristic, complemented
515#448C22×C1311yescharacteristic, complemented
516#447C22×C1311yescharacteristic
517#447C22×C1311yescharacteristic, complemented
518#447C22×C1311yescharacteristic, complemented
519#417—21no—
520#416—21no—
521#407C22×C1311yescharacteristic, complemented
522C2×C22⋊C8C22×C1311yescharacteristic, complemented
523#395C22×C1311yescharacteristic, complemented
524#394C22×C1311yescharacteristic, complemented
525#393C22×C1311yescharacteristic, complemented
526#392C22×C1311yescharacteristic, complemented
527#386—21no—
528#386—21no—
529#385—21no—
530C2×#95C22×C1311yescharacteristic, complemented
531#328C22×C1311yescharacteristic, complemented
532#328C22×C1311yescharacteristic, complemented
533#327C22×C1311yescharacteristic
534#327C22×C1311yescharacteristic
535#327C22×C1311yescharacteristic, complemented
536#327C22×C1311yescharacteristic, complemented
537#327C22×C1311yescharacteristic, complemented
538#327C22×C1311yescharacteristic, complemented
539#324C22×C1311yescharacteristic, complemented
540#324C22×C1311yescharacteristic, complemented
541#323C22×C1311yescharacteristic, complemented
542#323C22×C1311yescharacteristic, complemented
543C22×C13—21no—
544C22×C13—21no—
545C22×C13—21no—
546C22×C13—21no—
547C22×C13—21no—
548C22×C13—21no—
549C22×C13—21no—
550C22×C13—42no—
551C22×C13—42no—
552C22×C13—42no—
553C22×C13—42no—
554C22×C13—41no—
555C22×C13—41no—
556C22×C13—41no—
557C22×C13—41no—
558C22×C13—41no—
559C22×C13—41no—
560C22×C13—41no—
561C22×C13—41no—
562C22×C13—42no—
563C22×C13—41no—
564C22×C13—41no—
565C22×C13—41no—
566C22×C13—41no—
567C22×C13—81no—
568C22×C13—81no—
569C22×C13—81no—
570C22×C13—81no—
571C22×C13—81no—
572C22×C13—81no—
573C22×C13—162no—
574C22×C13—162no—
575C22×C13B(4,𝔽2)12yes—
576C22×C13C2×#12011yescharacteristic
577C22×C13#57611yescharacteristic
578C22×C13#57711yescharacteristic
579C4×C13—21no—
580C4×C13—21no—
581C4×C13—21no—
582C4×C13—21no—
583C4×C13—42no—
584C4×C13—41no—
585C4×C13—41no—
586C4×C13—41no—
587C4×C13—41no—
588C4×C13—41no—
589C4×C13—41no—
590C4×C13—42no—
591C4×C13—41no—
592C4×C13—41no—
593C4×C13—81no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—44no—
600C2×#41D4×C1311yescharacteristic, complemented
601C22×Q8C23×C1311yescharacteristic
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—21no—
605C22×D4—21no—
606C22×D4—21no—
607C22×D4D4×C1311yescharacteristic
608C22×D4D4×C1311yescharacteristic, complemented
609C22×D4C23×C1311yescharacteristic
610C23×C4—21no—
611C23×C4—21no—
612C23×C4C23×C1311yescharacteristic
613AGL(1,ℤ/8)—44no—
614#135—44no—
615C2×Q16—21no—
616C2×SD16—21no—
617C2×SD16—21no—
618C2×SD16—21no—
619C2×SD16—21no—
620C2×D8—21no—
621C2×D8—21no—
622C2×D8—21no—
623C2×M16—21no—
624C22×C8—21no—
625#127—21no—
626#126—21no—
627#126—21no—
628#126—21no—
629#126—21no—
630#125—21no—
631#125—21no—
632#124—21no—
633#124—21no—
634#124—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640#123—21no—
641#123—21no—
642#123—21no—
643#123—21no—
644#123—21no—
645#123—21no—
646#123—21no—
647#123—21no—
648#123—21no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8D4×C1311yescharacteristic, complemented
655C22⋊Q8C23×C1311yescharacteristic
656#121—21no—
657#121—21no—
658#121—21no—
659#121—21no—
660#121—21no—
661#121—21no—
662#121—21no—
663#121—21no—
664#121—21no—
665#121—21no—
666#121—21no—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121—44no—
672#121D4×C1311yescharacteristic, complemented
673#121D4×C1311yescharacteristic, complemented
674#121D4×C1311yescharacteristic, complemented
675#121C23×C1311yescharacteristic
676#121C23×C1311yescharacteristic
677#121C23×C1311yescharacteristic
678#120—21no—
679#120—21no—
680#120—21no—
681#120—21no—
682#120—21no—
683#120—21no—
684#120—21no—
685#120—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4—21no—
692C4×D4—21no—
693C4×D4—21no—
694#117—21no—
695#117D4×C1311yescharacteristic, complemented
696C2×C4⋊C4—21no—
697C2×C4⋊C4D4×C1311yescharacteristic
698C2×C4⋊C4D4×C1311yescharacteristic, complemented
699C2×C4⋊C4C23×C1311yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4D4×C1311yescharacteristic
708C2×C22⋊C4D4×C1311yescharacteristic
709C2×C22⋊C4C23×C1311yescharacteristic
710#103—21no—
711#103—21no—
712#103—21no—
713#103—21no—
714#102—21no—
715#102—21no—
716#102—21no—
717#102—21no—
718C22⋊C8—21no—
719C22⋊C8—21no—
720C22⋊C8C23×C1311yescharacteristic
721C22⋊C8C23×C1311yescharacteristic
722C22⋊C8C23×C1311yescharacteristic
723C22⋊C8C23×C1311yescharacteristic
724#95—21no—
725#95—21no—
726#95—21no—
727#95C23×C1311yescharacteristic
728#95C23×C1311yescharacteristic
729C2×C13—21no—
730C2×C13—21no—
731C2×C13—22no—
732C2×C13—41no—
733C2×C13—82no—
734C2×C13—81no—
735C2×C13—81no—
736C2×C13—81no—
737C2×C13—81no—
738C2×C13#301211yescharacteristic
739C2×C13#301811yescharacteristic
740C2×C13C2×B(4,𝔽2)11yescharacteristic
741C24—21no—
742C24—21no—
743C24—21no—
744C24C2×D4×C1311yescharacteristic
745C24C2×D4×C1311yescharacteristic
746#41—24no—
747#41—24no—
748#41—42no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—81no—
756#41—81no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—42no—
761C2×Q8C2×D4×C1311yescharacteristic
762C2×D4—24no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—82no—
796C2×D4C2×D4×C1311yescharacteristic
797C2×D4C2×D4×C1311yescharacteristic
798C2×D4C2×D4×C1311yescharacteristic
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—42no—
816C22×C4—81no—
817C22×C4C2×D4×C1311yescharacteristic
818C22×C4C2×D4×C1311yescharacteristic
819C22×C4C2×D4×C1311yescharacteristic
820C22×C4C2×D4×C1311yescharacteristic
821C22×C4C2×D4×C1311yescharacteristic
822C22×C4C2×D4×C1311yescharacteristic
823C22×C4C2×D4×C1311yescharacteristic
824C22×C4C2×D4×C1311yescharacteristic
825C22×C4C24×C1311yescharacteristic
826Q16—42no—
827SD16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831D8—42no—
832D8—42no—
833D8—42no—
834M16—42no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—42no—
854C4⋊C4C2×D4×C1311yescharacteristic
855C4⋊C4C2×D4×C1311yescharacteristic
856C4⋊C4C2×D4×C1311yescharacteristic
857C4⋊C4C2×D4×C1311yescharacteristic
858C22⋊C4—21no—
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—81no—
887C42—21no—
888C42—21no—
889C42—21no—
890C13#1825211yescharacteristic, direct product factor, Sylow
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23C13×#12011yescharacteristic
917C23C13×#12011yescharacteristic
918C23C22×D4×C1311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4C13×#12011yescharacteristic
993C2×C4C13×#12011yescharacteristic
994C2×C4C22×D4×C1311yescharacteristic
995C2×C4C22×D4×C1311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C13×B(4,𝔽2)12yes—
1033C22C2×C13×#12011yescharacteristic
1034C22C13×#57611yescharacteristic
1035C22C13×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C13×#301211yescharacteristic
1061C2C13×#301811yescharacteristic
1062C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3534C2semidirect
2. C13×#3006C2semidirect
3. C13×#3002C2semidirect
4. C13×#2430C2semidirect
5. C13×#1606C2semidirect
6. C13×#1604C2semidirect
7. C13×#1603C2semidirect
8. C13×#1601C2semidirect
9. C13×#1600C2semidirect
10. C13×#1598C2semidirect
11. C13×#1597C2semidirect
12. C13×#1595C2semidirect
13. C13×#1504C2semidirect
14. C2×C13×#327C2semidirect
15. C13×#1468C2semidirect
16. C22×C13×#41C22semidirect
40. C13×#451C22semidirect
41. C13×#450C22semidirect
46. C13×#448C22semidirect
47. C13×#448C22semidirect
49. C13×#447C22semidirect
50. C13×#447C22semidirect
53. C13×#407C22semidirect
54. C2×C13×C22⋊C8C22semidirect
55. C13×#395C22semidirect
56. C13×#394C22semidirect
57. C13×#393C22semidirect
58. C13×#392C22semidirect
62. C2×C13×#95C22semidirect
63. C13×#328C22semidirect
64. C13×#328C22semidirect
67. C13×#327C22semidirect
68. C13×#327C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#324C22semidirect
72. C13×#324C22semidirect
73. C13×#323C22semidirect
74. C13×#323C22semidirect
81. C2×C13×#41D4semidirect
89. C22×D4×C13D4semidirect
135. C13×C22⋊Q8D4semidirect
153. C13×#121D4semidirect
154. C13×#121D4semidirect
155. C13×#121D4semidirect
176. C13×#117D4semidirect
179. C2×C13×C4⋊C4D4semidirect
210. #18252C13direct (N × H)
360. #3534C2×C13semidirect
361. #3006C2×C13semidirect
362. #3002C2×C13semidirect
363. #2430C2×C13semidirect
364. #1606C2×C13semidirect
365. #1604C2×C13semidirect
366. #1603C2×C13semidirect
367. #1601C2×C13semidirect
368. #1600C2×C13semidirect
369. #1598C2×C13semidirect
370. #1597C2×C13semidirect
371. #1595C2×C13semidirect
372. #1504C2×C13semidirect
373. C2×#327C2×C13semidirect
374. #1468C2×C13semidirect
484. C22×#41C22×C13semidirect
508. #451C22×C13semidirect
509. #450C22×C13semidirect
514. #448C22×C13semidirect
515. #448C22×C13semidirect
517. #447C22×C13semidirect
518. #447C22×C13semidirect
521. #407C22×C13semidirect
522. C2×C22⋊C8C22×C13semidirect
523. #395C22×C13semidirect
524. #394C22×C13semidirect
525. #393C22×C13semidirect
526. #392C22×C13semidirect
530. C2×#95C22×C13semidirect
531. #328C22×C13semidirect
532. #328C22×C13semidirect
535. #327C22×C13semidirect
536. #327C22×C13semidirect
537. #327C22×C13semidirect
538. #327C22×C13semidirect
539. #324C22×C13semidirect
540. #324C22×C13semidirect
541. #323C22×C13semidirect
542. #323C22×C13semidirect
600. C2×#41D4×C13semidirect
608. C22×D4D4×C13semidirect
654. C22⋊Q8D4×C13semidirect
672. #121D4×C13semidirect
673. #121D4×C13semidirect
674. #121D4×C13semidirect
695. #117D4×C13semidirect
698. C2×C4⋊C4D4×C13semidirect
890. C13#18252direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35342
C13×#30062
C13×#30022
C13×#24302
C13×#16062
C13×#16042
C13×#16032
C13×#16012
C13×#16002
C13×#15982
C13×#15972
C13×#15952
C13×#15042
C2×C13×#3272
C13×#14682
#1825213