Finite Group Databasebeta

← C13×#14891 #15701230

Subgroups — C13×#14891 #15701230

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#117C211yesmaximal, characteristic
2C2×C13×#398C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic
4C2×C13×#387C211yesmaximal, characteristic, complemented
5C13×#1444C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×C4⋊#95C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C2×C13×#117—24no—
18C2×C13×#117—24no—
19C2×C13×#117—24no—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C13×#398—24no—
37C13×#396—24no—
38C13×#387—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13Q814yes—
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C13×#117—232no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4D414yes—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—41no—
118C2×C13×C22⋊C4—41no—
119C2×C13×C22⋊C4—41no—
120C2×C13×C22⋊C4—41no—
121C2×C13×C22⋊C4D414yes—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13D414yes—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—41no—
143C13×#95—41no—
144C13×#95—41no—
145C13×#95—41no—
146#14891C1311yesmaximal, characteristic, direct product factor, Sylow
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13C2×D412yes—
160C24×C13C2×Q812yes—
161C24×C13#4112yes—
162C24×C13C2411yescharacteristic
163C22×C4×C13—28no—
164C22×C4×C13—28no—
165C22×C4×C13—28no—
166C22×C4×C13—28no—
167C22×C4×C13—28no—
168C22×C4×C13—21no—
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—28no—
181C22×C4×C13—28no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13C2×D412yes—
256C22×C4×C13C2×D412yes—
257C22×C4×C13C2×D412yes—
258C22×C4×C13C2×D412yes—
259C22×C4×C13C2×D412yes—
260C22×C4×C13C2×Q812yes—
261C22×C4×C13C2×Q812yes—
262C22×C4×C13#4112yes—
263C22×C4×C13#4112yes—
264C22×C4×C13#4112yes—
265C22×C4×C13#4112yes—
266C22×C4×C13#4112yes—
267C22×C4×C13#4112yes—
268C13×C4⋊C4—28no—
269C13×C4⋊C4—28no—
270C13×C4⋊C4—28no—
271C13×C4⋊C4—44no—
272C13×C4⋊C4—44no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4—44no—
276C13×C22⋊C4—28no—
277C13×C22⋊C4—28no—
278C13×C22⋊C4—44no—
279C13×C22⋊C4—44no—
280C13×C22⋊C4—44no—
281C13×C22⋊C4—44no—
282C42×C13—28no—
283C42×C13—28no—
284C22×#117C2×C1311yescharacteristic
285C2×#398C2×C1311yescharacteristic, complemented
286C2×#396C2×C1311yescharacteristic
287C2×#387C2×C1311yescharacteristic, complemented
288#1444C2×C1311yescharacteristic, complemented
289#1442C2×C1311yescharacteristic, complemented
290#1441C2×C1311yescharacteristic, complemented
291#1439C2×C1311yescharacteristic
292#1439C2×C1311yescharacteristic
293#1439C2×C1311yescharacteristic
294#1436C2×C1311yescharacteristic, complemented
295#1436C2×C1311yescharacteristic, complemented
296C4⋊#95C2×C1311yescharacteristic, complemented
297C22⋊#95C2×C1311yescharacteristic
298C22⋊#95C2×C1311yescharacteristic
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13C22⋊Q814yes—
334C23×C13C22×D411yescharacteristic
335C23×C13C22×D411yescharacteristic
336C23×C13C22×D411yescharacteristic
337C23×C13C22×Q811yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C132−1+411yescharacteristic
348C23×C132−1+411yescharacteristic
349C2×C4×C13—232no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13#12014yes—
446C2×C4×C13C22⋊Q814yes—
447C2×C4×C13C22⋊Q814yes—
448C24×C4C22×C1311yescharacteristic
449C2×#117—24no—
450C2×#117—24no—
451C2×#117—24no—
452C22×C4⋊C4C22×C1311yescharacteristic
453C22×C4⋊C4C22×C1311yescharacteristic
454C22×C4⋊C4C22×C1311yescharacteristic
455C22×C4⋊C4C22×C1311yescharacteristic
456C22×C4⋊C4C22×C1311yescharacteristic
457C22×C4⋊C4C22×C1311yescharacteristic
458C22×C4⋊C4C22×C1311yescharacteristic
459C22×C4⋊C4C22×C1311yescharacteristic
460C22×C22⋊C4C22×C1311yescharacteristic
461C22×C22⋊C4C22×C1311yescharacteristic
462C22×C22⋊C4C22×C1311yescharacteristic
463C22×C22⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465C22×C22⋊C4C22×C1311yescharacteristic
466C22×C42C22×C1311yescharacteristic
467C22×C42C22×C1311yescharacteristic
468#398—24no—
469#396—24no—
470#387—24no—
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C2×#95C22×C1311yescharacteristic
482C2×#95C22×C1311yescharacteristic
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C22×C13—24no—
490C22×C13—24no—
491C22×C13—24no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13C2×#12011yescharacteristic
505C22×C13C2×C22⋊Q811yescharacteristic
506C22×C13C2×C22⋊Q811yescharacteristic
507C22×C13C2×C22⋊Q811yescharacteristic
508C22×C13#52511yescharacteristic
509C22×C13#52511yescharacteristic
510C22×C13#52511yescharacteristic
511C22×C13#52511yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#53211yescharacteristic
515C22×C13#53311yescharacteristic
516C22×C13#53311yescharacteristic
517C22×C13#53711yescharacteristic
518C22×C13#53711yescharacteristic
519C22×C13#54011yescharacteristic
520C22×C13#54111yescharacteristic
521C22×C13#54411yescharacteristic
522C22×C13#54411yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#54611yescharacteristic
526C22×C13#54711yescharacteristic
527C22×C13#54711yescharacteristic
528C22×C13#54711yescharacteristic
529C22×C13#54811yescharacteristic
530C22×C13#55011yescharacteristic
531C22×C13#55111yescharacteristic
532C22×C13#55111yescharacteristic
533C22×C13#55211yescharacteristic
534C22×C13#55211yescharacteristic
535C22×C13#55211yescharacteristic
536C22×C13#55311yescharacteristic
537C22×C13#55511yescharacteristic
538C22×C13#55611yescharacteristic
539C4×C13—24no—
540C4×C13—24no—
541C4×C13—24no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—42no—
548C4×C13—42no—
549C4×C13—81no—
550C4×C13—81no—
551C4×C13—81no—
552C4×C13—81no—
553C25C23×C1311yescharacteristic
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4Q8×C1314yes—
561C23×C4C23×C1311yescharacteristic
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1311yescharacteristic
567C23×C4C23×C1311yescharacteristic
568C23×C4C23×C1311yescharacteristic
569C23×C4C23×C1311yescharacteristic
570C23×C4C23×C1311yescharacteristic
571C23×C4C23×C1311yescharacteristic
572C23×C4C23×C1311yescharacteristic
573C23×C4C23×C1311yescharacteristic
574C23×C4C23×C1311yescharacteristic
575#117—232no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4D4×C1314yes—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4D4×C1314yes—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42D4×C1314yes—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—41no—
639#95—41no—
640#95—41no—
641#95—41no—
642C2×C13—44no—
643C2×C13#239611yescharacteristic
644C2×C13#240711yescharacteristic
645C2×C13#243011yescharacteristic
646C2×C13#243811yescharacteristic
647C2×C13#243811yescharacteristic
648C2×C13#243911yescharacteristic
649C2×C13#244111yescharacteristic
650C2×C13#247111yescharacteristic
651C2×C13#247511yescharacteristic
652C2×C13#247611yescharacteristic
653C2×C13#247811yescharacteristic
654C2×C13#260111yescharacteristic
655C2×C13#260911yescharacteristic
656C2×C13#262911yescharacteristic
657C2×C13#284811yescharacteristic
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24C2×D4×C1312yes—
671C24C2×Q8×C1312yes—
672C24C13×#4112yes—
673C24C24×C1311yescharacteristic
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4C2×D4×C1312yes—
764C22×C4C2×D4×C1312yes—
765C22×C4C2×D4×C1312yes—
766C22×C4C2×D4×C1312yes—
767C22×C4C2×D4×C1312yes—
768C22×C4C2×D4×C1312yes—
769C22×C4C2×D4×C1312yes—
770C22×C4C2×D4×C1312yes—
771C22×C4C2×Q8×C1312yes—
772C22×C4C2×Q8×C1312yes—
773C22×C4C13×#4112yes—
774C22×C4C13×#4112yes—
775C22×C4C13×#4112yes—
776C22×C4C13×#4112yes—
777C22×C4C13×#4112yes—
778C22×C4C13×#4112yes—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C42—28no—
794C42—28no—
795C13#1489111yescharacteristic, direct product factor, Sylow
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23C13×C22⋊Q814yes—
831C23C22×D4×C1311yescharacteristic
832C23C22×D4×C1311yescharacteristic
833C23C22×D4×C1311yescharacteristic
834C23C22×Q8×C1311yescharacteristic
835C23C2×C13×#4111yescharacteristic
836C23C2×C13×#4111yescharacteristic
837C23C2×C13×#4111yescharacteristic
838C23C2×C13×#4111yescharacteristic
839C23C2×C13×#4111yescharacteristic
840C23C2×C13×#4111yescharacteristic
841C23C2×C13×#4111yescharacteristic
842C23C13×H(5,𝔽2)11yescharacteristic
843C23C13×H(5,𝔽2)11yescharacteristic
844C23C13×2−1+411yescharacteristic
845C23C13×2−1+411yescharacteristic
846C2×C4—232no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4C13×#12014yes—
943C2×C4C13×C22⋊Q814yes—
944C2×C4C13×C22⋊Q814yes—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22C2×C13×#12011yescharacteristic
961C22C2×C13×C22⋊Q811yescharacteristic
962C22C2×C13×C22⋊Q811yescharacteristic
963C22C2×C13×C22⋊Q811yescharacteristic
964C22C13×#52511yescharacteristic
965C22C13×#52511yescharacteristic
966C22C13×#52511yescharacteristic
967C22C13×#52511yescharacteristic
968C22C13×#52911yescharacteristic
969C22C13×#52911yescharacteristic
970C22C13×#53211yescharacteristic
971C22C13×#53311yescharacteristic
972C22C13×#53311yescharacteristic
973C22C13×#53711yescharacteristic
974C22C13×#53711yescharacteristic
975C22C13×#54011yescharacteristic
976C22C13×#54111yescharacteristic
977C22C13×#54411yescharacteristic
978C22C13×#54411yescharacteristic
979C22C13×#54611yescharacteristic
980C22C13×#54611yescharacteristic
981C22C13×#54611yescharacteristic
982C22C13×#54711yescharacteristic
983C22C13×#54711yescharacteristic
984C22C13×#54711yescharacteristic
985C22C13×#54811yescharacteristic
986C22C13×#55011yescharacteristic
987C22C13×#55111yescharacteristic
988C22C13×#55111yescharacteristic
989C22C13×#55211yescharacteristic
990C22C13×#55211yescharacteristic
991C22C13×#55211yescharacteristic
992C22C13×#55311yescharacteristic
993C22C13×#55511yescharacteristic
994C22C13×#55611yescharacteristic
995C4—24no—
996C4—24no—
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—81no—
1007C4—81no—
1008C4—81no—
1009C2—44no—
1010C2C13×#239611yescharacteristic
1011C2C13×#240711yescharacteristic
1012C2C13×#243011yescharacteristic
1013C2C13×#243811yescharacteristic
1014C2C13×#243811yescharacteristic
1015C2C13×#243911yescharacteristic
1016C2C13×#244111yescharacteristic
1017C2C13×#247111yescharacteristic
1018C2C13×#247511yescharacteristic
1019C2C13×#247611yescharacteristic
1020C2C13×#247811yescharacteristic
1021C2C13×#260111yescharacteristic
1022C2C13×#260911yescharacteristic
1023C2C13×#262911yescharacteristic
1024C2C13×#284811yescharacteristic
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×#398C2semidirect
4. C2×C13×#387C2semidirect
5. C13×#1444C2semidirect
6. C13×#1442C2semidirect
7. C13×#1441C2semidirect
11. C13×#1436C2semidirect
12. C13×#1436C2semidirect
13. C13×C4⋊#95C2semidirect
146. #14891C13direct (N × H)
285. C2×#398C2×C13semidirect
287. C2×#387C2×C13semidirect
288. #1444C2×C13semidirect
289. #1442C2×C13semidirect
290. #1441C2×C13semidirect
294. #1436C2×C13semidirect
295. #1436C2×C13semidirect
296. C4⋊#95C2×C13semidirect
795. C13#14891direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1172
C2×C13×#3982
C2×C13×#3962
C2×C13×#3872
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1489113