Finite Group Databasebeta

← C13×#14771 #15701110

Subgroups — C13×#14771 #15701110

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C2×C13×#398C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic
4C2×C13×#389C211yesmaximal, characteristic, complemented
5C2×C13×#380C211yesmaximal, characteristic
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C4⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C13×#399—24no—
36C13×#398—24no—
37C13×#396—24no—
38C13×#389—24no—
39C13×#380—24no—
40C4×C13×C22⋊C4—24no—
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—41no—
63C23×C4×C13—41no—
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
79C2×C13×C4⋊C4—22no—
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—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4—41no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4—41no—
107C2×C13×C4⋊C4—41no—
108C2×C13×C4⋊C4—41no—
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—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—41no—
122C2×C13×C22⋊C4—41no—
123C2×C13×C22⋊C4—41no—
124C2×C13×C22⋊C4—41no—
125C2×C13×C22⋊C4D414yes—
126C2×C13×C22⋊C4Q814yes—
127C2×C42×C13—22no—
128C2×C42×C13—22no—
129C2×C42×C13—22no—
130C2×C42×C13—22no—
131C2×C42×C13—41no—
132C2×C42×C13—41no—
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—22no—
143C13×#95—22no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95—41no—
147C13×#95D414yes—
148C13×#95D414yes—
149#14771C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13C2×D412yes—
163C24×C13C2×Q812yes—
164C24×C13C2×Q812yes—
165C24×C13C2411yescharacteristic
166C22×C4×C13—21no—
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—28no—
219C22×C4×C13—28no—
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—44no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13—44no—
252C22×C4×C13—44no—
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×D412yes—
261C22×C4×C13C2×Q812yes—
262C22×C4×C13C2×Q812yes—
263C22×C4×C13C2×Q812yes—
264C22×C4×C13C2×Q812yes—
265C22×C4×C13#4112yes—
266C22×C4×C13#4112yes—
267C22×C4×C13#4112yes—
268C22×C4×C13#4112yes—
269C22×C4×C13#4112yes—
270C22×C4×C13#4112yes—
271C13×C4⋊C4—28no—
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×C4⋊C4—44no—
280C13×C4⋊C4—44no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—44no—
284C13×C22⋊C4—44no—
285C13×C22⋊C4—44no—
286C13×C22⋊C4—44no—
287C42×C13—44no—
288C42×C13—44no—
289C2×#399C2×C1311yescharacteristic
290C2×#398C2×C1311yescharacteristic, complemented
291C2×#396C2×C1311yescharacteristic
292C2×#389C2×C1311yescharacteristic, complemented
293C2×#380C2×C1311yescharacteristic
294C2×C4×C22⋊C4C2×C1311yescharacteristic
295#1444C2×C1311yescharacteristic, complemented
296#1444C2×C1311yescharacteristic, complemented
297#1441C2×C1311yescharacteristic, complemented
298#1439C2×C1311yescharacteristic
299#1439C2×C1311yescharacteristic
300#1436C2×C1311yescharacteristic, complemented
301#1436C2×C1311yescharacteristic, complemented
302C4⋊#95C2×C1311yescharacteristic, complemented
303C22⋊#95C2×C1311yescharacteristic
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—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
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×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13C4⋊Q814yes—
339C23×C13C22×D411yescharacteristic
340C23×C13C22×D411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×Q811yescharacteristic
343C23×C13C22×Q811yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13H(5,𝔽2)11yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C132−1+411yescharacteristic
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—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—416no—
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×C13#12114yes—
450C2×C4×C13C22⋊Q814yes—
451C2×C4×C13C22⋊Q814yes—
452C2×C4×C13C22⋊Q814yes—
453C24×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×C4⋊C4C22×C1311yescharacteristic
461C22×C4⋊C4C22×C1311yescharacteristic
462C22×C4⋊C4C22×C1311yescharacteristic
463C22×C4⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465C22×C22⋊C4C22×C1311yescharacteristic
466C22×C22⋊C4C22×C1311yescharacteristic
467C22×C22⋊C4C22×C1311yescharacteristic
468C22×C22⋊C4C22×C1311yescharacteristic
469C22×C22⋊C4C22×C1311yescharacteristic
470C22×C42C22×C1311yescharacteristic
471C22×C42C22×C1311yescharacteristic
472#399—24no—
473#398—24no—
474#396—24no—
475#389—24no—
476#380—24no—
477C4×C22⋊C4—24no—
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
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
494C22×C13—24no—
495C22×C13—24no—
496C22×C13—24no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13C2×#12111yescharacteristic
510C22×C13C2×C22⋊Q811yescharacteristic
511C22×C13C2×C22⋊Q811yescharacteristic
512C22×C13C2×C22⋊Q811yescharacteristic
513C22×C13#52511yescharacteristic
514C22×C13#52911yescharacteristic
515C22×C13#52911yescharacteristic
516C22×C13C2×C4⋊Q811yescharacteristic
517C22×C13#53211yescharacteristic
518C22×C13#53211yescharacteristic
519C22×C13#53311yescharacteristic
520C22×C13#53311yescharacteristic
521C22×C13#53311yescharacteristic
522C22×C13#53911yescharacteristic
523C22×C13#53911yescharacteristic
524C22×C13#54011yescharacteristic
525C22×C13#54011yescharacteristic
526C22×C13#54311yescharacteristic
527C22×C13#54411yescharacteristic
528C22×C13D4211yescharacteristic
529C22×C13D4211yescharacteristic
530C22×C13#54611yescharacteristic
531C22×C13#54611yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54611yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13D4×Q811yescharacteristic
537C22×C13#55011yescharacteristic
538C22×C13#55111yescharacteristic
539C22×C13#55211yescharacteristic
540C22×C13#55311yescharacteristic
541C22×C13#55411yescharacteristic
542C22×C13#55411yescharacteristic
543C22×C13#55411yescharacteristic
544C4×C13—24no—
545C4×C13—24no—
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552C4×C13—42no—
553C4×C13—42no—
554C4×C13—81no—
555C4×C13—81no—
556C4×C13—81no—
557C4×C13—81no—
558C25C23×C1311yescharacteristic
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4Q8×C1314yes—
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
575C23×C4C23×C1311yescharacteristic
576C23×C4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
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—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4D4×C1314yes—
627C2×C22⋊C4Q8×C1314yes—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—41no—
633C2×C42—41no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95D4×C1314yes—
649#95D4×C1314yes—
650C2×C13—44no—
651C2×C13#239611yescharacteristic
652C2×C13#242511yescharacteristic
653C2×C13#242811yescharacteristic
654C2×C13#243711yescharacteristic
655C2×C13#244011yescharacteristic
656C2×C13#244111yescharacteristic
657C2×C13#244911yescharacteristic
658C2×C13#245411yescharacteristic
659C2×C13#246411yescharacteristic
660C2×C13#252211yescharacteristic
661C2×C13#254911yescharacteristic
662C2×C13#255311yescharacteristic
663C2×C13#255611yescharacteristic
664C2×C13#266711yescharacteristic
665C2×C13#285711yescharacteristic
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C2×D4×C1312yes—
679C24C2×Q8×C1312yes—
680C24C2×Q8×C1312yes—
681C24C24×C1311yescharacteristic
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—28no—
735C22×C4—28no—
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×C4—21no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4C2×D4×C1312yes—
770C22×C4C2×D4×C1312yes—
771C22×C4C2×D4×C1312yes—
772C22×C4C2×D4×C1312yes—
773C22×C4C2×D4×C1312yes—
774C22×C4C2×D4×C1312yes—
775C22×C4C2×D4×C1312yes—
776C22×C4C2×D4×C1312yes—
777C22×C4C2×Q8×C1312yes—
778C22×C4C2×Q8×C1312yes—
779C22×C4C2×Q8×C1312yes—
780C22×C4C2×Q8×C1312yes—
781C22×C4C13×#4112yes—
782C22×C4C13×#4112yes—
783C22×C4C13×#4112yes—
784C22×C4C13×#4112yes—
785C22×C4C13×#4112yes—
786C22×C4C13×#4112yes—
787C4⋊C4—28no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C42—44no—
804C42—44no—
805C13#1477111yescharacteristic, direct product factor, Sylow
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23C13×C4⋊Q814yes—
841C23C22×D4×C1311yescharacteristic
842C23C22×D4×C1311yescharacteristic
843C23C22×D4×C1311yescharacteristic
844C23C22×Q8×C1311yescharacteristic
845C23C22×Q8×C1311yescharacteristic
846C23C2×C13×#4111yescharacteristic
847C23C2×C13×#4111yescharacteristic
848C23C2×C13×#4111yescharacteristic
849C23C2×C13×#4111yescharacteristic
850C23C2×C13×#4111yescharacteristic
851C23C2×C13×#4111yescharacteristic
852C23C13×H(5,𝔽2)11yescharacteristic
853C23C13×H(5,𝔽2)11yescharacteristic
854C23C13×H(5,𝔽2)11yescharacteristic
855C23C13×2−1+411yescharacteristic
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—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—416no—
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×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4C13×#12114yes—
952C2×C4C13×C22⋊Q814yes—
953C2×C4C13×C22⋊Q814yes—
954C2×C4C13×C22⋊Q814yes—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22C2×C13×#12111yescharacteristic
971C22C2×C13×C22⋊Q811yescharacteristic
972C22C2×C13×C22⋊Q811yescharacteristic
973C22C2×C13×C22⋊Q811yescharacteristic
974C22C13×#52511yescharacteristic
975C22C13×#52911yescharacteristic
976C22C13×#52911yescharacteristic
977C22C2×C13×C4⋊Q811yescharacteristic
978C22C13×#53211yescharacteristic
979C22C13×#53211yescharacteristic
980C22C13×#53311yescharacteristic
981C22C13×#53311yescharacteristic
982C22C13×#53311yescharacteristic
983C22C13×#53911yescharacteristic
984C22C13×#53911yescharacteristic
985C22C13×#54011yescharacteristic
986C22C13×#54011yescharacteristic
987C22C13×#54311yescharacteristic
988C22C13×#54411yescharacteristic
989C22D42×C1311yescharacteristic
990C22D42×C1311yescharacteristic
991C22C13×#54611yescharacteristic
992C22C13×#54611yescharacteristic
993C22C13×#54611yescharacteristic
994C22C13×#54611yescharacteristic
995C22C13×#54711yescharacteristic
996C22C13×#54711yescharacteristic
997C22D4×Q8×C1311yescharacteristic
998C22C13×#55011yescharacteristic
999C22C13×#55111yescharacteristic
1000C22C13×#55211yescharacteristic
1001C22C13×#55311yescharacteristic
1002C22C13×#55411yescharacteristic
1003C22C13×#55411yescharacteristic
1004C22C13×#55411yescharacteristic
1005C4—24no—
1006C4—24no—
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—81no—
1016C4—81no—
1017C4—81no—
1018C4—81no—
1019C2—44no—
1020C2C13×#239611yescharacteristic
1021C2C13×#242511yescharacteristic
1022C2C13×#242811yescharacteristic
1023C2C13×#243711yescharacteristic
1024C2C13×#244011yescharacteristic
1025C2C13×#244111yescharacteristic
1026C2C13×#244911yescharacteristic
1027C2C13×#245411yescharacteristic
1028C2C13×#246411yescharacteristic
1029C2C13×#252211yescharacteristic
1030C2C13×#254911yescharacteristic
1031C2C13×#255311yescharacteristic
1032C2C13×#255611yescharacteristic
1033C2C13×#266711yescharacteristic
1034C2C13×#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×#398C2semidirect
4. C2×C13×#389C2semidirect
7. C13×#1444C2semidirect
8. C13×#1444C2semidirect
9. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×C4⋊#95C2semidirect
149. #14771C13direct (N × H)
290. C2×#398C2×C13semidirect
292. C2×#389C2×C13semidirect
295. #1444C2×C13semidirect
296. #1444C2×C13semidirect
297. #1441C2×C13semidirect
300. #1436C2×C13semidirect
301. #1436C2×C13semidirect
302. C4⋊#95C2×C13semidirect
805. C13#14771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3992
C2×C13×#3982
C2×C13×#3962
C2×C13×#3892
C2×C13×#3802
C2×C4×C13×C22⋊C42
C13×#14442
C13×#14412
C13×#14392
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1477113