Finite Group Databasebeta

← C13×#16520 #15702859

Subgroups — C13×#16520 #15702859

Order 3328.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C211yesmaximal, characteristic
2C2×C13×#395C211yesmaximal, characteristic, complemented
3C2×C13×#393C211yesmaximal, characteristic
4C2×C13×#380C211yesmaximal, characteristic
5C13×#1446C211yesmaximal, characteristic, complemented
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic
13C13×#1439C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C13×#396—24no—
32C13×#395—24no—
33C13×#393—24no—
34C13×#380—24no—
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
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
55C25×C13C2311yescharacteristic
56C22×Q8×C13—22no—
57C22×Q8×C13—22no—
58C22×Q8×C13—22no—
59C22×Q8×C13—41no—
60C22×Q8×C13—41no—
61C22×Q8×C13—41no—
62C22×Q8×C13—41no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—41no—
66C23×C4×C13—41no—
67C23×C4×C13—41no—
68C23×C4×C13—41no—
69C23×C4×C13Q814yescomplemented
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
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
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—41no—
94C2×C13×C4⋊C4—41no—
95C2×C13×C4⋊C4—41no—
96C2×C13×C4⋊C4—41no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4D414yes—
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—41no—
114C2×C13×C22⋊C4—41no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4—41no—
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×C13×C22⋊C4Q814yescomplemented
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95—41no—
141C13×#95—41no—
142C13×#95—41no—
143#16520C1311yesmaximal, characteristic, direct product factor, Sylow
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
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×C13C2×D412yes—
157C24×C13C2×Q812yes—
158C24×C13C2×Q812yes—
159C24×C13C2411yescharacteristic
160C2×Q8×C13—44no—
161C2×Q8×C13—44no—
162C2×Q8×C13—44no—
163C2×Q8×C13—44no—
164C2×Q8×C13—44no—
165C2×Q8×C13—44no—
166C2×Q8×C13—44no—
167C22×C4×C13—21no—
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—21no—
181C22×C4×C13—21no—
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—28no—
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×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×C13C2×D412yes—
261C22×C4×C13C2×D412yes—
262C22×C4×C13C2×D412yes—
263C22×C4×C13C2×D412yes—
264C22×C4×C13C2×D412yes—
265C22×C4×C13C2×Q812yes—
266C22×C4×C13C2×Q812yes—
267C22×C4×C13C2×Q812yes—
268C22×C4×C13C2×Q812yes—
269C22×C4×C13#4112yes—
270C22×C4×C13#4112yes—
271C22×C4×C13#4112yes—
272C13×C4⋊C4—44no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4—44no—
276C13×C4⋊C4—44no—
277C13×C4⋊C4—44no—
278C13×C4⋊C4—44no—
279C13×C22⋊C4—44no—
280C13×C22⋊C4—44no—
281C13×C22⋊C4—44no—
282C13×C22⋊C4—44no—
283C13×C22⋊C4—44no—
284C13×C22⋊C4—44no—
285C2×#396C2×C1311yescharacteristic
286C2×#395C2×C1311yescharacteristic, complemented
287C2×#393C2×C1311yescharacteristic
288C2×#380C2×C1311yescharacteristic
289#1446C2×C1311yescharacteristic, complemented
290#1445C2×C1311yescharacteristic, complemented
291#1444C2×C1311yescharacteristic, complemented
292#1442C2×C1311yescharacteristic, complemented
293#1441C2×C1311yescharacteristic, complemented
294#1441C2×C1311yescharacteristic, complemented
295#1441C2×C1311yescharacteristic, complemented
296#1439C2×C1311yescharacteristic
297#1439C2×C1311yescharacteristic
298C22⋊#95C2×C1311yescharacteristic
299C22⋊#95C2×C1311yescharacteristic
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—22no—
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×C13—41no—
334C23×C13C4⋊Q814yes—
335C23×C13C22×D411yescharacteristic
336C23×C13C22×D411yescharacteristic
337C23×C13C22×Q811yescharacteristic
338C23×C13C22×Q811yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13H(5,𝔽2)11yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C132−1+411yescharacteristic
349C23×C132−1+411yescharacteristic
350Q8×C13—416no—
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—416no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
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—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13C22⋊Q814yes—
450C23×Q8C22×C1311yescharacteristic
451C24×C4C22×C1311yescharacteristic
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×C22⋊C4C22×C1311yescharacteristic
460C22×C22⋊C4C22×C1311yescharacteristic
461C22×C22⋊C4C22×C1311yescharacteristic
462C22×C22⋊C4C22×C1311yescharacteristic
463C22×C22⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465#396—24no—
466#395—24no—
467#393—24no—
468#380—24no—
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
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×C22⋊Q811yescharacteristic
505C22×C13C2×C4⋊Q811yescharacteristic
506C22×C13#53311yescharacteristic
507C22×C13#53411yescharacteristic
508C22×C13#53411yescharacteristic
509C22×C13#53511yescharacteristic
510C22×C13#53711yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53811yescharacteristic
513C22×C13#53811yescharacteristic
514C22×C13#53811yescharacteristic
515C22×C13#54211yescharacteristic
516C22×C13#54211yescharacteristic
517C22×C13#54311yescharacteristic
518C22×C13#54311yescharacteristic
519C22×C13#54311yescharacteristic
520C22×C13#54411yescharacteristic
521C22×C13#54411yescharacteristic
522C22×C13#54411yescharacteristic
523C22×C13D4211yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#54611yescharacteristic
526C22×C13#54611yescharacteristic
527C22×C13#54711yescharacteristic
528C22×C13#54811yescharacteristic
529C22×C13D4×Q811yescharacteristic
530C22×C13#55411yescharacteristic
531C22×C13#55411yescharacteristic
532C22×C13#55411yescharacteristic
533C22×C13#55511yescharacteristic
534C22×C13#55611yescharacteristic
535C22×C13#56011yescharacteristic
536C22×C13#56211yescharacteristic
537C22×C13#56211yescharacteristic
538C22×C13#56311yescharacteristic
539C4×C13—24no—
540C4×C13—42no—
541C4×C13—42no—
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
554C22×Q8—22no—
555C22×Q8—22no—
556C22×Q8—22no—
557C22×Q8—41no—
558C22×Q8—41no—
559C22×Q8—41no—
560C22×Q8—41no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4Q8×C1314yescomplemented
568C23×C4C23×C1311yescharacteristic
569C23×C4C23×C1311yescharacteristic
570C23×C4C23×C1311yescharacteristic
571C23×C4C23×C1311yescharacteristic
572C23×C4C23×C1311yescharacteristic
573C23×C4C23×C1311yescharacteristic
574C23×C4C23×C1311yescharacteristic
575C23×C4C23×C1311yescharacteristic
576C23×C4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C23×C4C23×C1311yescharacteristic
581C23×C4C23×C1311yescharacteristic
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—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4D4×C1314yes—
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—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4D4×C1314yes—
620C2×C22⋊C4Q8×C1314yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
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—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95—41no—
640#95—41no—
641C2×C13—44no—
642C2×C13#243911yescharacteristic
643C2×C13#244011yescharacteristic
644C2×C13#254911yescharacteristic
645C2×C13#262611yescharacteristic
646C2×C13#265911yescharacteristic
647C2×C13#266511yescharacteristic
648C2×C13#266811yescharacteristic
649C2×C13#267611yescharacteristic
650C2×C13#268611yescharacteristic
651C2×C13#269211yescharacteristic
652C2×C13#271511yescharacteristic
653C2×C13#272911yescharacteristic
654C2×C13#278411yescharacteristic
655C2×C13#278811yescharacteristic
656C2×C13#284111yescharacteristic
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24C2×D4×C1312yes—
670C24C2×Q8×C1312yes—
671C24C2×Q8×C1312yes—
672C24C24×C1311yescharacteristic
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
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—21no—
692C22×C4—21no—
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—28no—
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×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4C2×D4×C1312yes—
774C22×C4C2×D4×C1312yes—
775C22×C4C2×D4×C1312yes—
776C22×C4C2×D4×C1312yes—
777C22×C4C2×D4×C1312yes—
778C22×C4C2×Q8×C1312yes—
779C22×C4C2×Q8×C1312yes—
780C22×C4C2×Q8×C1312yes—
781C22×C4C2×Q8×C1312yes—
782C22×C4C13×#4112yes—
783C22×C4C13×#4112yes—
784C22×C4C13×#4112yes—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C13#1652011yescharacteristic, direct product factor, Sylow
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—22no—
815C23—22no—
816C23—22no—
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—
830C23—41no—
831C23—41no—
832C23—41no—
833C23C13×C4⋊Q814yes—
834C23C22×D4×C1311yescharacteristic
835C23C22×D4×C1311yescharacteristic
836C23C22×Q8×C1311yescharacteristic
837C23C22×Q8×C1311yescharacteristic
838C23C2×C13×#4111yescharacteristic
839C23C2×C13×#4111yescharacteristic
840C23C2×C13×#4111yescharacteristic
841C23C13×H(5,𝔽2)11yescharacteristic
842C23C13×H(5,𝔽2)11yescharacteristic
843C23C13×H(5,𝔽2)11yescharacteristic
844C23C13×H(5,𝔽2)11yescharacteristic
845C23C13×H(5,𝔽2)11yescharacteristic
846C23C13×H(5,𝔽2)11yescharacteristic
847C23C13×2−1+411yescharacteristic
848C23C13×2−1+411yescharacteristic
849Q8—416no—
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—416no—
884C2×C4—41no—
885C2×C4—41no—
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×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4C13×C22⋊Q814yes—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22C2×C13×C22⋊Q811yescharacteristic
965C22C2×C13×C4⋊Q811yescharacteristic
966C22C13×#53311yescharacteristic
967C22C13×#53411yescharacteristic
968C22C13×#53411yescharacteristic
969C22C13×#53511yescharacteristic
970C22C13×#53711yescharacteristic
971C22C13×#53811yescharacteristic
972C22C13×#53811yescharacteristic
973C22C13×#53811yescharacteristic
974C22C13×#53811yescharacteristic
975C22C13×#54211yescharacteristic
976C22C13×#54211yescharacteristic
977C22C13×#54311yescharacteristic
978C22C13×#54311yescharacteristic
979C22C13×#54311yescharacteristic
980C22C13×#54411yescharacteristic
981C22C13×#54411yescharacteristic
982C22C13×#54411yescharacteristic
983C22D42×C1311yescharacteristic
984C22C13×#54611yescharacteristic
985C22C13×#54611yescharacteristic
986C22C13×#54611yescharacteristic
987C22C13×#54711yescharacteristic
988C22C13×#54811yescharacteristic
989C22D4×Q8×C1311yescharacteristic
990C22C13×#55411yescharacteristic
991C22C13×#55411yescharacteristic
992C22C13×#55411yescharacteristic
993C22C13×#55511yescharacteristic
994C22C13×#55611yescharacteristic
995C22C13×#56011yescharacteristic
996C22C13×#56211yescharacteristic
997C22C13×#56211yescharacteristic
998C22C13×#56311yescharacteristic
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C2—44no—
1014C2C13×#243911yescharacteristic
1015C2C13×#244011yescharacteristic
1016C2C13×#254911yescharacteristic
1017C2C13×#262611yescharacteristic
1018C2C13×#265911yescharacteristic
1019C2C13×#266511yescharacteristic
1020C2C13×#266811yescharacteristic
1021C2C13×#267611yescharacteristic
1022C2C13×#268611yescharacteristic
1023C2C13×#269211yescharacteristic
1024C2C13×#271511yescharacteristic
1025C2C13×#272911yescharacteristic
1026C2C13×#278411yescharacteristic
1027C2C13×#278811yescharacteristic
1028C2C13×#284111yescharacteristic
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×#395C2semidirect
5. C13×#1446C2semidirect
6. C13×#1445C2semidirect
7. C13×#1444C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
10. C13×#1441C2semidirect
11. C13×#1441C2semidirect
69. C23×C4×C13Q8semidirect
122. C2×C13×C22⋊C4Q8semidirect
143. #16520C13direct (N × H)
286. C2×#395C2×C13semidirect
289. #1446C2×C13semidirect
290. #1445C2×C13semidirect
291. #1444C2×C13semidirect
292. #1442C2×C13semidirect
293. #1441C2×C13semidirect
294. #1441C2×C13semidirect
295. #1441C2×C13semidirect
567. C23×C4Q8×C13semidirect
620. C2×C22⋊C4Q8×C13semidirect
798. C13#16520direct (N × H)

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×#3952
C2×C13×#3932
C2×C13×#3802
C13×#14462
C13×#14452
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×C22⋊#952
#1652013