Finite Group Databasebeta

← C13×#24786 #15711125

Subgroups — C13×#24786 #15711125

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#468C211yesmaximal, characteristic, complemented
2C2×C13×#465C211yesmaximal, characteristic, complemented
3C2×C13×#435C211yesmaximal, characteristic, complemented
4C2×C13×#427C211yesmaximal, characteristic, complemented
5C13×#2415C211yesmaximal, characteristic, complemented
6C13×#2414C211yesmaximal, characteristic
7C13×#2066C211yesmaximal, characteristic, complemented
8C13×#2065C211yesmaximal, characteristic, complemented
9C13×#2035C211yesmaximal, characteristic, complemented
10C13×#2034C211yesmaximal, characteristic, complemented
11C13×#1973C211yesmaximal, characteristic, complemented
12C13×#1943C211yesmaximal, characteristic, complemented
13C13×#1875C211yesmaximal, characteristic, complemented
14C13×#1873C211yesmaximal, characteristic, complemented
15C13×#1809C211yesmaximal, characteristic, complemented
16C22×C13×SD16C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C13×#121C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×C13×#117C2211yescharacteristic
26C13×#468—24no—
27C13×#465—24no—
28C13×#435—24no—
29C13×#427—24no—
30C2×C13×#107C2211yescharacteristic
31C2×C13×#107C2211yescharacteristic
32C2×C13×#106C2211yescharacteristic
33C2×C13×#106C2211yescharacteristic
34C2×C13×#106C2211yescharacteristic
35C2×C13×C4⋊C8C2211yescharacteristic
36C2×C13×#103C2211yescharacteristic
37C2×C13×#103C2211yescharacteristic
38C2×C13×#103C2211yescharacteristic
39C2×C13×#102C2211yescharacteristic
40C2×C13×#102C2211yescharacteristic
41C2×C13×#102C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C2×C13×C22⋊C8C2211yescharacteristic
44C2×C13×#97C2211yescharacteristic
45C13×#397—21no—
46C13×#394—21no—
47C13×#394—21no—
48C13×#392—21no—
49C13×#391C2211yescharacteristic
50C13×#390—21no—
51C13×#390C2211yescharacteristic
52C13×#389—21no—
53C13×#389C2211yescharacteristic
54C13×#389C2211yescharacteristic
55C13×#388—21no—
56C13×#388—21no—
57C13×#380C2211yescharacteristic
58C13×#380C2211yescharacteristic
59C13×#340C2211yescharacteristic
60C13×#340C2211yescharacteristic
61C13×#340C2211yescharacteristic
62C13×#340C2211yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C22×D4×C13—21no—
65C22×D4×C13—21no—
66C22×D4×C13D411yescharacteristic
67C22×D4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C2×C13×SD16—22no—
71C2×C13×SD16—22no—
72C2×C13×SD16—22no—
73C2×C13×M16—22no—
74C2×C13×M16—22no—
75C2×C13×M16—22no—
76C22×C8×C13—22no—
77C22×C8×C13—22no—
78C22×C8×C13D414yescomplemented
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—41no—
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121—41no—
91C4×D4×C13—22no—
92C4×D4×C13—22no—
93C13×#117—22no—
94C13×#117—22no—
95C13×#117—41no—
96C13×#117—41no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4D411yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C42×C13—21no—
121C2×C42×C13—21no—
122C2×C42×C13C2311yescharacteristic
123C13×#107—22no—
124C13×#107D414yescomplemented
125C13×#106—22no—
126C13×#106—22no—
127C13×#106—22no—
128C13×C4⋊C8—22no—
129C13×#103—22no—
130C13×#103—22no—
131C13×#103—41no—
132C13×#102—22no—
133C13×#102—22no—
134C13×#102—41no—
135C13×C22⋊C8—22no—
136C13×C22⋊C8—22no—
137C13×#97—22no—
138C13×#95—21no—
139C13×#95—21no—
140C13×#95—21no—
141C13×#95—21no—
142C13×#95—21no—
143C13×#95—21no—
144#24786C1311yesmaximal, characteristic, direct product factor, Sylow
145C24×C13—21no—
146C24×C13C2×D411yescharacteristic
147C24×C13C2×D411yescharacteristic
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×D4×C13—22no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—41no—
162C2×D4×C13—41no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13—42no—
166C2×D4×C13—81no—
167C2×D4×C13—81no—
168C2×D4×C13—81no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D412yes—
191C22×C4×C13#4112yes—
192C22×C4×C13C2411yescharacteristic
193C13×SD16—44no—
194C13×M16—44no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—28no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13C2×D412yes—
205C2×C8×C13C2×D412yes—
206C2×C8×C13C2×D412yes—
207C2×C8×C13#4112yes—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—42no—
220C13×C4⋊C4—42no—
221C13×C4⋊C4—42no—
222C13×C4⋊C4—81no—
223C13×C4⋊C4C2×D412yes—
224C13×C4⋊C4C2×D412yes—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—22no—
227C13×C22⋊C4—42no—
228C13×C22⋊C4—42no—
229C13×C22⋊C4—42no—
230C13×C22⋊C4—42no—
231C13×C22⋊C4—42no—
232C13×C22⋊C4—42no—
233C13×C22⋊C4—42no—
234C13×C22⋊C4—42no—
235C13×C22⋊C4—81no—
236C13×C22⋊C4—81no—
237C42×C13—21no—
238C42×C13—21no—
239C42×C13—42no—
240C42×C13—42no—
241C2×#468C2×C1311yescharacteristic, complemented
242C2×#465C2×C1311yescharacteristic, complemented
243C2×#435C2×C1311yescharacteristic, complemented
244C2×#427C2×C1311yescharacteristic, complemented
245#2415C2×C1311yescharacteristic, complemented
246#2414C2×C1311yescharacteristic
247#2066C2×C1311yescharacteristic, complemented
248#2065C2×C1311yescharacteristic, complemented
249#2035C2×C1311yescharacteristic, complemented
250#2034C2×C1311yescharacteristic, complemented
251#1973C2×C1311yescharacteristic, complemented
252#1943C2×C1311yescharacteristic, complemented
253#1875C2×C1311yescharacteristic, complemented
254#1873C2×C1311yescharacteristic, complemented
255#1809C2×C1311yescharacteristic, complemented
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13#12112yes—
277C23×C13C22×D411yescharacteristic
278Q8×C13—41no—
279Q8×C13—41no—
280Q8×C13—41no—
281Q8×C13—41no—
282D4×C13—44no—
283D4×C13—41no—
284D4×C13—41no—
285D4×C13—41no—
286D4×C13—41no—
287D4×C13—84no—
288D4×C13—84no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13#12112yes—
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C22×D411yescharacteristic
332C2×C4×C13C2×#4111yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13H(5,𝔽2)11yescharacteristic
335C2×C4×C132−1+411yescharacteristic
336C8×C13—22no—
337C8×C13—41no—
338C8×C13—41no—
339C8×C13#12114yes—
340C22×SD16C22×C1311yescharacteristic
341C22×M16C22×C1311yescharacteristic
342C23×C8C22×C1311yescharacteristic
343C2×C22⋊Q8C22×C1311yescharacteristic
344C2×C22⋊Q8C22×C1311yescharacteristic
345C2×#121C22×C1311yescharacteristic
346C2×#121C22×C1311yescharacteristic
347C2×C4×D4C22×C1311yescharacteristic
348C2×#117C22×C1311yescharacteristic
349C2×#117C22×C1311yescharacteristic
350#468—24no—
351#465—24no—
352#435—24no—
353#427—24no—
354C2×#107C22×C1311yescharacteristic
355C2×#107C22×C1311yescharacteristic
356C2×#106C22×C1311yescharacteristic
357C2×#106C22×C1311yescharacteristic
358C2×#106C22×C1311yescharacteristic
359C2×C4⋊C8C22×C1311yescharacteristic
360C2×#103C22×C1311yescharacteristic
361C2×#103C22×C1311yescharacteristic
362C2×#103C22×C1311yescharacteristic
363C2×#102C22×C1311yescharacteristic
364C2×#102C22×C1311yescharacteristic
365C2×#102C22×C1311yescharacteristic
366C2×C22⋊C8C22×C1311yescharacteristic
367C2×C22⋊C8C22×C1311yescharacteristic
368C2×#97C22×C1311yescharacteristic
369#397—21no—
370#394—21no—
371#394—21no—
372#392—21no—
373#391C22×C1311yescharacteristic
374#390—21no—
375#390C22×C1311yescharacteristic
376#389—21no—
377#389C22×C1311yescharacteristic
378#389C22×C1311yescharacteristic
379#388—21no—
380#388—21no—
381#380C22×C1311yescharacteristic
382#380C22×C1311yescharacteristic
383#340C22×C1311yescharacteristic
384#340C22×C1311yescharacteristic
385#340C22×C1311yescharacteristic
386#340C22×C1311yescharacteristic
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—81no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13—81no—
405C22×C13—81no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13C2×#12111yescharacteristic
409C22×C13D4211yescharacteristic
410C22×C13#54711yescharacteristic
411C22×C13#57511yescharacteristic
412C22×C13#57511yescharacteristic
413C22×C13#57711yescharacteristic
414C22×C13#57711yescharacteristic
415C4×C13—22no—
416C4×C13—41no—
417C4×C13—42no—
418C4×C13—42no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—81no—
422C4×C13—81no—
423C4×C13—81no—
424C4×C13—81no—
425C4×C13—81no—
426C4×C13C2×#12111yescharacteristic
427C4×C13#53711yescharacteristic
428C4×C13#54811yescharacteristic
429C4×C13#55311yescharacteristic
430C22×Q8C23×C1311yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4D4×C1311yescharacteristic
434C22×D4C23×C1311yescharacteristic
435C23×C4C23×C1311yescharacteristic
436C23×C4C23×C1311yescharacteristic
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—22no—
443C22×C8—22no—
444C22×C8—22no—
445C22×C8D4×C1314yescomplemented
446C22×C8C23×C1311yescharacteristic
447C22×C8C23×C1311yescharacteristic
448C22×C8C23×C1311yescharacteristic
449C22×C8C23×C1311yescharacteristic
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—41no—
454#121—22no—
455#121—22no—
456#121—22no—
457#121—41no—
458C4×D4—22no—
459C4×D4—22no—
460#117—22no—
461#117—22no—
462#117—41no—
463#117—41no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4D4×C1311yescharacteristic
469C2×C4⋊C4C23×C1311yescharacteristic
470C2×C4⋊C4C23×C1311yescharacteristic
471C2×C4⋊C4C23×C1311yescharacteristic
472C2×C4⋊C4C23×C1311yescharacteristic
473C2×C4⋊C4C23×C1311yescharacteristic
474C2×C4⋊C4C23×C1311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4D4×C1311yescharacteristic
486C2×C22⋊C4D4×C1311yescharacteristic
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C23×C1311yescharacteristic
490#107—22no—
491#107D4×C1314yescomplemented
492#106—22no—
493#106—22no—
494#106—22no—
495C4⋊C8—22no—
496#103—22no—
497#103—22no—
498#103—41no—
499#102—22no—
500#102—22no—
501#102—41no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504#97—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511C2×C13—42no—
512C2×C13—81no—
513C2×C13—161no—
514C2×C13#241611yescharacteristic
515C2×C13#305411yescharacteristic
516C2×C13#305711yescharacteristic
517C2×C13#326711yescharacteristic
518C2×C13#327111yescharacteristic
519C2×C13#334811yescharacteristic
520C2×C13#335011yescharacteristic
521C24—21no—
522C24C2×D4×C1311yescharacteristic
523C24C2×D4×C1311yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4C2×D4×C1311yescharacteristic
563C22×C4C2×D4×C1311yescharacteristic
564C22×C4C2×D4×C1311yescharacteristic
565C22×C4C2×D4×C1311yescharacteristic
566C22×C4C2×D4×C1312yes—
567C22×C4C13×#4112yes—
568C22×C4C24×C1311yescharacteristic
569SD16—44no—
570M16—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—28no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8C2×D4×C1312yes—
581C2×C8C2×D4×C1312yes—
582C2×C8C2×D4×C1312yes—
583C2×C8C13×#4112yes—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—81no—
599C4⋊C4C2×D4×C1312yes—
600C4⋊C4C2×D4×C1312yes—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—42no—
617C13#2478611yescharacteristic, direct product factor, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C13×#12112yes—
639C23C22×D4×C1311yescharacteristic
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644D4—44no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650D4—84no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4C13×#12112yes—
692C2×C4C22×D4×C1311yescharacteristic
693C2×C4C22×D4×C1311yescharacteristic
694C2×C4C2×C13×#4111yescharacteristic
695C2×C4C2×C13×#4111yescharacteristic
696C2×C4C13×H(5,𝔽2)11yescharacteristic
697C2×C4C13×2−1+411yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8C13×#12114yes—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×C13×#12111yescharacteristic
724C22D42×C1311yescharacteristic
725C22C13×#54711yescharacteristic
726C22C13×#57511yescharacteristic
727C22C13×#57511yescharacteristic
728C22C13×#57711yescharacteristic
729C22C13×#57711yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4C2×C13×#12111yescharacteristic
742C4C13×#53711yescharacteristic
743C4C13×#54811yescharacteristic
744C4C13×#55311yescharacteristic
745C2—42no—
746C2—81no—
747C2—161no—
748C2C13×#241611yescharacteristic
749C2C13×#305411yescharacteristic
750C2C13×#305711yescharacteristic
751C2C13×#326711yescharacteristic
752C2C13×#327111yescharacteristic
753C2C13×#334811yescharacteristic
754C2C13×#335011yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#468C2semidirect
2. C2×C13×#465C2semidirect
3. C2×C13×#435C2semidirect
4. C2×C13×#427C2semidirect
5. C13×#2415C2semidirect
7. C13×#2066C2semidirect
8. C13×#2065C2semidirect
9. C13×#2035C2semidirect
10. C13×#2034C2semidirect
11. C13×#1973C2semidirect
12. C13×#1943C2semidirect
13. C13×#1875C2semidirect
14. C13×#1873C2semidirect
15. C13×#1809C2semidirect
78. C22×C8×C13D4semidirect
124. C13×#107D4semidirect
144. #24786C13direct (N × H)
241. C2×#468C2×C13semidirect
242. C2×#465C2×C13semidirect
243. C2×#435C2×C13semidirect
244. C2×#427C2×C13semidirect
245. #2415C2×C13semidirect
247. #2066C2×C13semidirect
248. #2065C2×C13semidirect
249. #2035C2×C13semidirect
250. #2034C2×C13semidirect
251. #1973C2×C13semidirect
252. #1943C2×C13semidirect
253. #1875C2×C13semidirect
254. #1873C2×C13semidirect
255. #1809C2×C13semidirect
445. C22×C8D4×C13semidirect
491. #107D4×C13semidirect
617. C13#24786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4682
C2×C13×#4652
C2×C13×#4352
C2×C13×#4272
C13×#24152
C13×#24142
C13×#20662
C13×#20652
C13×#20352
C13×#20342
C13×#19732
C13×#19432
C13×#18752
C13×#18732
C13×#18092
#2478613