Finite Group Databasebeta

← C13×#15131 #15701470

Subgroups — C13×#15131 #15701470

Order 3328.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C212yesmaximal
2C2×C13×#389C211yesmaximal, characteristic, complemented
3C2×C13×#389C211yesmaximal, characteristic, complemented
4C2×C13×#384C211yesmaximal, characteristic, complemented
5C2×C13×#380C211yesmaximal, characteristic
6C2×C13×#380C211yesmaximal, characteristic
7C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
8C13×#1441C212yesmaximal, complemented
9C13×#1441C212yesmaximal, complemented
10C13×#1439C212yesmaximal
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2212yes—
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C13×C22⋊C4C2212yes—
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C13×#396—28no—
28C13×#389—24no—
29C13×#389—24no—
30C13×#384—24no—
31C13×#380—24no—
32C13×#380—24no—
33C4×C13×C22⋊C4—24no—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C25×C13C2311yescharacteristic
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13Q814yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—42no—
80C2×C13×C4⋊C4—42no—
81C2×C13×C4⋊C4—42no—
82C2×C13×C4⋊C4D414yes—
83C2×C13×C4⋊C4D414yes—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—24no—
89C2×C13×C22⋊C4—24no—
90C2×C13×C22⋊C4—24no—
91C2×C13×C22⋊C4—24no—
92C2×C13×C22⋊C4—42no—
93C2×C13×C22⋊C4—42no—
94C2×C13×C22⋊C4D414yes—
95C2×C13×C22⋊C4Q814yes—
96C2×C42×C13—22no—
97C2×C42×C13—22no—
98C2×C42×C13—22no—
99C2×C42×C13—22no—
100C2×C42×C13—22no—
101C2×C42×C13D414yes—
102C13×#95—22no—
103C13×#95—22no—
104C13×#95—24no—
105C13×#95—24no—
106C13×#95—24no—
107C13×#95—24no—
108C13×#95—24no—
109C13×#95—42no—
110#15131C1311yesmaximal, characteristic, direct product factor, Sylow
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13C2×D412yes—
124C24×C13C2×Q812yes—
125C24×C13C2×Q812yes—
126C24×C13C2411yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—21no—
165C22×C4×C13—28no—
166C22×C4×C13—28no—
167C22×C4×C13—28no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—44no—
183C22×C4×C13—44no—
184C22×C4×C13—44no—
185C22×C4×C13—44no—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D414yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×Q812yes—
196C22×C4×C13C2×Q812yes—
197C22×C4×C13C2×Q812yes—
198C22×C4×C13C2×Q812yes—
199C22×C4×C13#4112yes—
200C22×C4×C13#4112yes—
201C22×C4×C13#4112yes—
202C22×C4×C13#4112yes—
203C22×C4×C13#4112yes—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—28no—
206C13×C4⋊C4—48no—
207C13×C4⋊C4—48no—
208C13×C4⋊C4—48no—
209C13×C4⋊C4—48no—
210C13×C4⋊C4—44no—
211C13×C4⋊C4—44no—
212C13×C22⋊C4—28no—
213C13×C22⋊C4—28no—
214C13×C22⋊C4—48no—
215C13×C22⋊C4—48no—
216C42×C13—28no—
217C42×C13—44no—
218C2×#396C2×C1312yes—
219C2×#389C2×C1311yescharacteristic, complemented
220C2×#389C2×C1311yescharacteristic, complemented
221C2×#384C2×C1311yescharacteristic, complemented
222C2×#380C2×C1311yescharacteristic
223C2×#380C2×C1311yescharacteristic
224C2×C4×C22⋊C4C2×C1311yescharacteristic
225#1441C2×C1312yescomplemented
226#1441C2×C1312yescomplemented
227#1439C2×C1312yes—
228C4⋊#95C2×C1311yescharacteristic, complemented
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13C4⋊Q814yes—
264C23×C13C22×D411yescharacteristic
265C23×C13C22×D411yescharacteristic
266C23×C13C22×D411yescharacteristic
267C23×C13C22×D411yescharacteristic
268C23×C13C22×Q811yescharacteristic
269C23×C13C22×Q811yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13C2×#4111yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13H(5,𝔽2)11yescharacteristic
276C23×C13H(5,𝔽2)11yescharacteristic
277C23×C132−1+411yescharacteristic
278C23×C132−1+411yescharacteristic
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—24no—
299C2×C4×C13—24no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—24no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—42no—
314C2×C4×C13—41no—
315C2×C4×C13—42no—
316C2×C4×C13—41no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—41no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—42no—
325C2×C4×C13—41no—
326C2×C4×C13—416no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13#12114yes—
342C2×C4×C13#12114yes—
343C2×C4×C13#12114yes—
344C2×C4×C13#12114yes—
345C2×C4×C13C22⋊Q814yes—
346C2×C4×C13C22⋊Q814yes—
347C2×C4×C13C22⋊Q814yes—
348C2×C4×C13C22⋊Q814yes—
349C2×C4×C13#12614yes—
350C24×C4C22×C1311yescharacteristic
351C22×C4⋊C4C22×C1312yes—
352C22×C4⋊C4C22×C1311yescharacteristic
353C22×C4⋊C4C22×C1311yescharacteristic
354C22×C4⋊C4C22×C1312yes—
355C22×C4⋊C4C22×C1312yes—
356C22×C4⋊C4C22×C1312yes—
357C22×C4⋊C4C22×C1311yescharacteristic
358C22×C4⋊C4C22×C1311yescharacteristic
359C22×C22⋊C4C22×C1312yes—
360C22×C22⋊C4C22×C1312yes—
361C22×C22⋊C4C22×C1311yescharacteristic
362C22×C22⋊C4C22×C1311yescharacteristic
363C22×C42C22×C1311yescharacteristic
364C22×C42C22×C1311yescharacteristic
365#396—28no—
366#389—24no—
367#389—24no—
368#384—24no—
369#380—24no—
370#380—24no—
371C4×C22⋊C4—24no—
372C2×#95C22×C1312yes—
373C2×#95C22×C1312yes—
374C2×#95C22×C1312yes—
375C2×#95C22×C1311yescharacteristic
376C2×#95C22×C1311yescharacteristic
377C2×#95C22×C1312yes—
378C2×#95C22×C1312yes—
379C2×#95C22×C1312yes—
380C22×C13—24no—
381C22×C13—24no—
382C22×C13—24no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—42no—
393C22×C13—42no—
394C22×C13—42no—
395C22×C13C2×#12111yescharacteristic
396C22×C13C2×#12111yescharacteristic
397C22×C13C2×#12111yescharacteristic
398C22×C13C2×#12111yescharacteristic
399C22×C13C2×C22⋊Q811yescharacteristic
400C22×C13C2×C22⋊Q811yescharacteristic
401C22×C13C2×C22⋊Q811yescharacteristic
402C22×C13C2×C22⋊Q811yescharacteristic
403C22×C13C2×#12611yescharacteristic
404C22×C13C2×C4⋊Q811yescharacteristic
405C22×C13#53211yescharacteristic
406C22×C13#53311yescharacteristic
407C22×C13#53311yescharacteristic
408C22×C13#53711yescharacteristic
409C22×C13#53711yescharacteristic
410C22×C13#54011yescharacteristic
411C22×C13#54111yescharacteristic
412C22×C13#54411yescharacteristic
413C22×C13#54411yescharacteristic
414C22×C13D4211yescharacteristic
415C22×C13D4211yescharacteristic
416C22×C13#54611yescharacteristic
417C22×C13#54711yescharacteristic
418C22×C13#54711yescharacteristic
419C22×C13#54711yescharacteristic
420C22×C13#54811yescharacteristic
421C22×C13D4×Q811yescharacteristic
422C22×C13D4×Q811yescharacteristic
423C22×C13#55011yescharacteristic
424C22×C13#55211yescharacteristic
425C22×C13#55311yescharacteristic
426C22×C13#55411yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55511yescharacteristic
429C22×C13#55611yescharacteristic
430C4×C13—24no—
431C4×C13—24no—
432C4×C13—42no—
433C4×C13—44no—
434C4×C13—42no—
435C4×C13—44no—
436C4×C13—42no—
437C4×C13—82no—
438C4×C13—82no—
439C4×C13#39618yescomplemented
440C25C23×C1311yescharacteristic
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4Q8×C1314yes—
448C23×C4C23×C1312yes—
449C23×C4C23×C1312yes—
450C23×C4C23×C1312yes—
451C23×C4C23×C1312yes—
452C23×C4C23×C1311yescharacteristic
453C23×C4C23×C1311yescharacteristic
454C23×C4C23×C1311yescharacteristic
455C23×C4C23×C1311yescharacteristic
456C23×C4C23×C1311yescharacteristic
457C23×C4C23×C1311yescharacteristic
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4D4×C1314yes—
481C2×C4⋊C4D4×C1314yes—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4D4×C1314yes—
493C2×C22⋊C4Q8×C1314yes—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42D4×C1314yes—
500#95—22no—
501#95—22no—
502#95—24no—
503#95—24no—
504#95—24no—
505#95—24no—
506#95—24no—
507#95—42no—
508C2×C13—44no—
509C2×C13C2×#39611yescharacteristic
510C2×C13#241611yescharacteristic
511C2×C13#241711yescharacteristic
512C2×C13#242811yescharacteristic
513C2×C13#242911yescharacteristic
514C2×C13#243911yescharacteristic
515C2×C13#244011yescharacteristic
516C2×C13#244011yescharacteristic
517C2×C13#244111yescharacteristic
518C2×C13#249611yescharacteristic
519C2×C13#249711yescharacteristic
520C2×C13#253711yescharacteristic
521C2×C13#253811yescharacteristic
522C2×C13#262911yescharacteristic
523C2×C13#285711yescharacteristic
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24C2×D4×C1312yes—
537C24C2×Q8×C1312yes—
538C24C2×Q8×C1312yes—
539C24C24×C1311yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
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—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C2×D4×C1314yes—
600C22×C4C2×D4×C1312yes—
601C22×C4C2×D4×C1314yes—
602C22×C4C2×D4×C1312yes—
603C22×C4C2×D4×C1312yes—
604C22×C4C2×D4×C1312yes—
605C22×C4C2×D4×C1312yes—
606C22×C4C2×D4×C1312yes—
607C22×C4C2×D4×C1312yes—
608C22×C4C2×Q8×C1312yes—
609C22×C4C2×Q8×C1312yes—
610C22×C4C2×Q8×C1312yes—
611C22×C4C2×Q8×C1312yes—
612C22×C4C13×#4112yes—
613C22×C4C13×#4112yes—
614C22×C4C13×#4112yes—
615C22×C4C13×#4112yes—
616C22×C4C13×#4112yes—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C42—28no—
630C42—44no—
631C13#1513111yescharacteristic, direct product factor, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C13×C4⋊Q814yes—
667C23C22×D4×C1311yescharacteristic
668C23C22×D4×C1311yescharacteristic
669C23C22×D4×C1311yescharacteristic
670C23C22×D4×C1311yescharacteristic
671C23C22×Q8×C1311yescharacteristic
672C23C22×Q8×C1311yescharacteristic
673C23C2×C13×#4111yescharacteristic
674C23C2×C13×#4111yescharacteristic
675C23C2×C13×#4111yescharacteristic
676C23C2×C13×#4111yescharacteristic
677C23C2×C13×#4111yescharacteristic
678C23C13×H(5,𝔽2)11yescharacteristic
679C23C13×H(5,𝔽2)11yescharacteristic
680C23C13×2−1+411yescharacteristic
681C23C13×2−1+411yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4C13×#12114yes—
745C2×C4C13×#12114yes—
746C2×C4C13×#12114yes—
747C2×C4C13×#12114yes—
748C2×C4C13×C22⋊Q814yes—
749C2×C4C13×C22⋊Q814yes—
750C2×C4C13×C22⋊Q814yes—
751C2×C4C13×C22⋊Q814yes—
752C2×C4C13×#12614yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×C13×#12111yescharacteristic
769C22C2×C13×#12111yescharacteristic
770C22C2×C13×#12111yescharacteristic
771C22C2×C13×#12111yescharacteristic
772C22C2×C13×C22⋊Q811yescharacteristic
773C22C2×C13×C22⋊Q811yescharacteristic
774C22C2×C13×C22⋊Q811yescharacteristic
775C22C2×C13×C22⋊Q811yescharacteristic
776C22C2×C13×#12611yescharacteristic
777C22C2×C13×C4⋊Q811yescharacteristic
778C22C13×#53211yescharacteristic
779C22C13×#53311yescharacteristic
780C22C13×#53311yescharacteristic
781C22C13×#53711yescharacteristic
782C22C13×#53711yescharacteristic
783C22C13×#54011yescharacteristic
784C22C13×#54111yescharacteristic
785C22C13×#54411yescharacteristic
786C22C13×#54411yescharacteristic
787C22D42×C1311yescharacteristic
788C22D42×C1311yescharacteristic
789C22C13×#54611yescharacteristic
790C22C13×#54711yescharacteristic
791C22C13×#54711yescharacteristic
792C22C13×#54711yescharacteristic
793C22C13×#54811yescharacteristic
794C22D4×Q8×C1311yescharacteristic
795C22D4×Q8×C1311yescharacteristic
796C22C13×#55011yescharacteristic
797C22C13×#55211yescharacteristic
798C22C13×#55311yescharacteristic
799C22C13×#55411yescharacteristic
800C22C13×#55411yescharacteristic
801C22C13×#55511yescharacteristic
802C22C13×#55611yescharacteristic
803C4—24no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—82no—
812C4C13×#39618yescomplemented
813C2—44no—
814C2C2×C13×#39611yescharacteristic
815C2C13×#241611yescharacteristic
816C2C13×#241711yescharacteristic
817C2C13×#242811yescharacteristic
818C2C13×#242911yescharacteristic
819C2C13×#243911yescharacteristic
820C2C13×#244011yescharacteristic
821C2C13×#244011yescharacteristic
822C2C13×#244111yescharacteristic
823C2C13×#249611yescharacteristic
824C2C13×#249711yescharacteristic
825C2C13×#253711yescharacteristic
826C2C13×#253811yescharacteristic
827C2C13×#262911yescharacteristic
828C2C13×#285711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#389C2semidirect
3. C2×C13×#389C2semidirect
4. C2×C13×#384C2semidirect
8. C13×#1441C2semidirect
9. C13×#1441C2semidirect
11. C13×C4⋊#95C2semidirect
110. #15131C13direct (N × H)
219. C2×#389C2×C13semidirect
220. C2×#389C2×C13semidirect
221. C2×#384C2×C13semidirect
225. #1441C2×C13semidirect
226. #1441C2×C13semidirect
228. C4⋊#95C2×C13semidirect
439. C4×C13#396semidirect
631. C13#15131direct (N × H)
812. C4C13×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#3962
C2×C13×#3892
C2×C13×#3842
C2×C13×#3802
C2×C4×C13×C22⋊C42
C13×#14412
C13×#14392
C13×C4⋊#952
#1513113