Finite Group Databasebeta

← C13×#15309 #15701648

Subgroups — C13×#15309 #15701648

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C211yesmaximal, characteristic, complemented
2C2×C13×#396C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic, complemented
4C2×C13×#390C211yesmaximal, characteristic
5C2×C13×#389C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic
7C2×C13×#385C211yesmaximal, characteristic, complemented
8C2×C13×#380C211yesmaximal, characteristic, complemented
9C13×#1444C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×#1438C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×D4×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×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×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic
39C13×#396—24no—
40C13×#396—24no—
41C13×#396—24no—
42C13×#390—24no—
43C13×#389—24no—
44C13×#386—24no—
45C13×#385—24no—
46C13×#380—24no—
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
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—41no—
66C22×D4×C13—41no—
67C22×D4×C13Q814yes—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—22no—
73C23×C4×C13—41no—
74C23×C4×C13—41no—
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
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
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—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—41no—
108C2×C13×C4⋊C4—41no—
109C2×C13×C4⋊C4—41no—
110C2×C13×C4⋊C4—41no—
111C2×C13×C4⋊C4—41no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4D414yescomplemented
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—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—22no—
132C2×C13×C22⋊C4—22no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—22no—
135C2×C13×C22⋊C4—22no—
136C2×C13×C22⋊C4—22no—
137C2×C13×C22⋊C4—41no—
138C2×C13×C22⋊C4—41no—
139C2×C13×C22⋊C4—41no—
140C2×C13×C22⋊C4—41no—
141C2×C13×C22⋊C4—41no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4D414yes—
148C2×C42×C13—22no—
149C2×C42×C13—22no—
150C2×C42×C13—41no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—41no—
160C13×#95—41no—
161C13×#95D414yes—
162C13×#95D414yescomplemented
163#15309C1311yesmaximal, characteristic, direct product factor, Sylow
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13C2×D412yes—
191C24×C13C2×Q812yes—
192C24×C13C2×Q812yes—
193C24×C13#4112yes—
194C24×C13C2411yescharacteristic
195C2×D4×C13—28no—
196C2×D4×C13—28no—
197C2×D4×C13—44no—
198C2×D4×C13—44no—
199C2×D4×C13—44no—
200C2×D4×C13—44no—
201C2×D4×C13—44no—
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—28no—
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×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—44no—
280C22×C4×C13—44no—
281C22×C4×C13—44no—
282C22×C4×C13—44no—
283C22×C4×C13—44no—
284C22×C4×C13—44no—
285C22×C4×C13C2×D412yes—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×D412yes—
291C22×C4×C13C2×D412yes—
292C22×C4×C13C2×D412yes—
293C22×C4×C13C2×D412yes—
294C22×C4×C13C2×D412yes—
295C22×C4×C13C2×D412yes—
296C22×C4×C13C2×Q812yes—
297C22×C4×C13#4112yes—
298C22×C4×C13#4112yes—
299C22×C4×C13#4112yes—
300C13×C4⋊C4—28no—
301C13×C4⋊C4—44no—
302C13×C4⋊C4—44no—
303C13×C4⋊C4—44no—
304C13×C4⋊C4—44no—
305C13×C4⋊C4—44no—
306C13×C4⋊C4—44no—
307C13×C4⋊C4—44no—
308C13×C4⋊C4—44no—
309C13×C22⋊C4—28no—
310C13×C22⋊C4—44no—
311C13×C22⋊C4—44no—
312C13×C22⋊C4—44no—
313C13×C22⋊C4—44no—
314C13×C22⋊C4—44no—
315C13×C22⋊C4—44no—
316C13×C22⋊C4—44no—
317C13×C22⋊C4—44no—
318C13×C22⋊C4—44no—
319C13×C22⋊C4—44no—
320C42×C13—44no—
321C2×#396C2×C1311yescharacteristic, complemented
322C2×#396C2×C1311yescharacteristic, complemented
323C2×#396C2×C1311yescharacteristic, complemented
324C2×#390C2×C1311yescharacteristic
325C2×#389C2×C1311yescharacteristic, complemented
326C2×#386C2×C1311yescharacteristic
327C2×#385C2×C1311yescharacteristic, complemented
328C2×#380C2×C1311yescharacteristic, complemented
329#1444C2×C1311yescharacteristic, complemented
330#1441C2×C1311yescharacteristic, complemented
331#1439C2×C1311yescharacteristic, complemented
332#1439C2×C1311yescharacteristic, complemented
333#1439C2×C1311yescharacteristic, complemented
334#1438C2×C1311yescharacteristic
335#1436C2×C1311yescharacteristic, complemented
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13—41no—
404C23×C13—41no—
405C23×C13C22⋊Q814yes—
406C23×C13C22×D411yescharacteristic
407C23×C13C22×D411yescharacteristic
408C23×C13C22×D411yescharacteristic
409C23×C13C22×D411yescharacteristic
410C23×C13C22×Q811yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4111yescharacteristic
413C23×C13C2×#4111yescharacteristic
414C23×C13C2×#4111yescharacteristic
415C23×C13H(5,𝔽2)11yescharacteristic
416C23×C13H(5,𝔽2)11yescharacteristic
417C23×C13H(5,𝔽2)11yescharacteristic
418C23×C13H(5,𝔽2)11yescharacteristic
419C23×C132−1+411yescharacteristic
420C23×C132−1+411yescharacteristic
421D4×C13—416no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—22no—
458C2×C4×C13—416no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13#12114yes—
512C2×C4×C13#12114yes—
513C2×C4×C13C22⋊Q814yes—
514C23×D4C22×C1311yescharacteristic
515C24×C4C22×C1311yescharacteristic
516C22×C4⋊C4C22×C1311yescharacteristic
517C22×C4⋊C4C22×C1311yescharacteristic
518C22×C4⋊C4C22×C1311yescharacteristic
519C22×C4⋊C4C22×C1311yescharacteristic
520C22×C4⋊C4C22×C1311yescharacteristic
521C22×C4⋊C4C22×C1311yescharacteristic
522C22×C4⋊C4C22×C1311yescharacteristic
523C22×C4⋊C4C22×C1311yescharacteristic
524C22×C4⋊C4C22×C1311yescharacteristic
525C22×C22⋊C4C22×C1311yescharacteristic
526C22×C22⋊C4C22×C1311yescharacteristic
527C22×C22⋊C4C22×C1311yescharacteristic
528C22×C22⋊C4C22×C1311yescharacteristic
529C22×C22⋊C4C22×C1311yescharacteristic
530C22×C22⋊C4C22×C1311yescharacteristic
531C22×C22⋊C4C22×C1311yescharacteristic
532C22×C22⋊C4C22×C1311yescharacteristic
533C22×C22⋊C4C22×C1311yescharacteristic
534C22×C22⋊C4C22×C1311yescharacteristic
535C22×C22⋊C4C22×C1311yescharacteristic
536C22×C42C22×C1311yescharacteristic
537#396—24no—
538#396—24no—
539#396—24no—
540#390—24no—
541#389—24no—
542#386—24no—
543#385—24no—
544#380—24no—
545C2×#95C22×C1311yescharacteristic
546C2×#95C22×C1311yescharacteristic
547C2×#95C22×C1311yescharacteristic
548C2×#95C22×C1311yescharacteristic
549C2×#95C22×C1311yescharacteristic
550C2×#95C22×C1311yescharacteristic
551C2×#95C22×C1311yescharacteristic
552C2×#95C22×C1311yescharacteristic
553C2×#95C22×C1311yescharacteristic
554C2×#95C22×C1311yescharacteristic
555C2×#95C22×C1311yescharacteristic
556C2×#95C22×C1311yescharacteristic
557C22×C13—24no—
558C22×C13—24no—
559C22×C13—24no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—81no—
580C22×C13—81no—
581C22×C13—81no—
582C22×C13—81no—
583C22×C13—81no—
584C22×C13—81no—
585C22×C13—81no—
586C22×C13—81no—
587C22×C13C2×#12111yescharacteristic
588C22×C13C2×#12111yescharacteristic
589C22×C13C2×C22⋊Q811yescharacteristic
590C22×C13C2×C22⋊Q811yescharacteristic
591C22×C13#52511yescharacteristic
592C22×C13#53211yescharacteristic
593C22×C13#53711yescharacteristic
594C22×C13#53711yescharacteristic
595C22×C13#53711yescharacteristic
596C22×C13#53711yescharacteristic
597C22×C13#53811yescharacteristic
598C22×C13#53911yescharacteristic
599C22×C13#54011yescharacteristic
600C22×C13#54211yescharacteristic
601C22×C13#54311yescharacteristic
602C22×C13D4211yescharacteristic
603C22×C13D4211yescharacteristic
604C22×C13D4211yescharacteristic
605C22×C13D4211yescharacteristic
606C22×C13#54611yescharacteristic
607C22×C13#54611yescharacteristic
608C22×C13#54611yescharacteristic
609C22×C13#54711yescharacteristic
610C22×C13#54811yescharacteristic
611C22×C13D4×Q811yescharacteristic
612C22×C13D4×Q811yescharacteristic
613C22×C13#55011yescharacteristic
614C22×C13#55111yescharacteristic
615C22×C13#55211yescharacteristic
616C22×C13#55311yescharacteristic
617C22×C13#55411yescharacteristic
618C22×C13#55411yescharacteristic
619C22×C13#55611yescharacteristic
620C22×C13#56011yescharacteristic
621C22×C13#56311yescharacteristic
622C4×C13—24no—
623C4×C13—24no—
624C4×C13—24no—
625C4×C13—42no—
626C4×C13—42no—
627C4×C13—42no—
628C4×C13—42no—
629C4×C13—42no—
630C4×C13—42no—
631C4×C13—81no—
632C4×C13—81no—
633C4×C13—81no—
634C4×C13—81no—
635C25C23×C1311yescharacteristic
636C25C23×C1311yescharacteristic
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—41no—
642C22×D4—41no—
643C22×D4Q8×C1314yes—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4C23×C1311yescharacteristic
652C23×C4C23×C1311yescharacteristic
653C23×C4C23×C1311yescharacteristic
654C23×C4C23×C1311yescharacteristic
655C23×C4C23×C1311yescharacteristic
656C23×C4C23×C1311yescharacteristic
657C23×C4C23×C1311yescharacteristic
658C23×C4C23×C1311yescharacteristic
659C23×C4C23×C1311yescharacteristic
660C23×C4C23×C1311yescharacteristic
661C23×C4C23×C1311yescharacteristic
662C23×C4C23×C1311yescharacteristic
663C23×C4C23×C1311yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4D4×C1314yescomplemented
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4D4×C1314yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—41no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—41no—
736#95—41no—
737#95D4×C1314yes—
738#95D4×C1314yescomplemented
739C2×C13—44no—
740C2×C13—82no—
741C2×C13#241611yescharacteristic
742C2×C13#241711yescharacteristic
743C2×C13#242411yescharacteristic
744C2×C13#242811yescharacteristic
745C2×C13#243711yescharacteristic
746C2×C13#244911yescharacteristic
747C2×C13#245211yescharacteristic
748C2×C13#253811yescharacteristic
749C2×C13#260111yescharacteristic
750C2×C13#267511yescharacteristic
751C2×C13#268311yescharacteristic
752C2×C13#270511yescharacteristic
753C2×C13#270711yescharacteristic
754C2×C13#271511yescharacteristic
755C2×C13#278011yescharacteristic
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24C2×D4×C1312yes—
783C24C2×Q8×C1312yes—
784C24C2×Q8×C1312yes—
785C24C13×#4112yes—
786C24C24×C1311yescharacteristic
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—28no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4C2×D4×C1312yes—
878C22×C4C2×D4×C1312yes—
879C22×C4C2×D4×C1312yes—
880C22×C4C2×D4×C1312yes—
881C22×C4C2×D4×C1312yes—
882C22×C4C2×D4×C1312yes—
883C22×C4C2×D4×C1312yes—
884C22×C4C2×D4×C1312yes—
885C22×C4C2×D4×C1312yes—
886C22×C4C2×D4×C1312yes—
887C22×C4C2×D4×C1312yes—
888C22×C4C2×Q8×C1312yes—
889C22×C4C13×#4112yes—
890C22×C4C13×#4112yes—
891C22×C4C13×#4112yes—
892C4⋊C4—28no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C42—44no—
913C13#1530911yescharacteristic, direct product factor, Sylow
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23C13×C22⋊Q814yes—
984C23C22×D4×C1311yescharacteristic
985C23C22×D4×C1311yescharacteristic
986C23C22×D4×C1311yescharacteristic
987C23C22×D4×C1311yescharacteristic
988C23C22×Q8×C1311yescharacteristic
989C23C2×C13×#4111yescharacteristic
990C23C2×C13×#4111yescharacteristic
991C23C2×C13×#4111yescharacteristic
992C23C2×C13×#4111yescharacteristic
993C23C13×H(5,𝔽2)11yescharacteristic
994C23C13×H(5,𝔽2)11yescharacteristic
995C23C13×H(5,𝔽2)11yescharacteristic
996C23C13×H(5,𝔽2)11yescharacteristic
997C23C13×2−1+411yescharacteristic
998C23C13×2−1+411yescharacteristic
999D4—416no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—416no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4C13×#12114yes—
1090C2×C4C13×#12114yes—
1091C2×C4C13×C22⋊Q814yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×C13×#12111yescharacteristic
1123C22C2×C13×#12111yescharacteristic
1124C22C2×C13×C22⋊Q811yescharacteristic
1125C22C2×C13×C22⋊Q811yescharacteristic
1126C22C13×#52511yescharacteristic
1127C22C13×#53211yescharacteristic
1128C22C13×#53711yescharacteristic
1129C22C13×#53711yescharacteristic
1130C22C13×#53711yescharacteristic
1131C22C13×#53711yescharacteristic
1132C22C13×#53811yescharacteristic
1133C22C13×#53911yescharacteristic
1134C22C13×#54011yescharacteristic
1135C22C13×#54211yescharacteristic
1136C22C13×#54311yescharacteristic
1137C22D42×C1311yescharacteristic
1138C22D42×C1311yescharacteristic
1139C22D42×C1311yescharacteristic
1140C22D42×C1311yescharacteristic
1141C22C13×#54611yescharacteristic
1142C22C13×#54611yescharacteristic
1143C22C13×#54611yescharacteristic
1144C22C13×#54711yescharacteristic
1145C22C13×#54811yescharacteristic
1146C22D4×Q8×C1311yescharacteristic
1147C22D4×Q8×C1311yescharacteristic
1148C22C13×#55011yescharacteristic
1149C22C13×#55111yescharacteristic
1150C22C13×#55211yescharacteristic
1151C22C13×#55311yescharacteristic
1152C22C13×#55411yescharacteristic
1153C22C13×#55411yescharacteristic
1154C22C13×#55611yescharacteristic
1155C22C13×#56011yescharacteristic
1156C22C13×#56311yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—24no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C13×#241611yescharacteristic
1173C2C13×#241711yescharacteristic
1174C2C13×#242411yescharacteristic
1175C2C13×#242811yescharacteristic
1176C2C13×#243711yescharacteristic
1177C2C13×#244911yescharacteristic
1178C2C13×#245211yescharacteristic
1179C2C13×#253811yescharacteristic
1180C2C13×#260111yescharacteristic
1181C2C13×#267511yescharacteristic
1182C2C13×#268311yescharacteristic
1183C2C13×#270511yescharacteristic
1184C2C13×#270711yescharacteristic
1185C2C13×#271511yescharacteristic
1186C2C13×#278011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#396C2semidirect
2. C2×C13×#396C2semidirect
3. C2×C13×#396C2semidirect
5. C2×C13×#389C2semidirect
7. C2×C13×#385C2semidirect
8. C2×C13×#380C2semidirect
9. C13×#1444C2semidirect
10. C13×#1441C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1439C2semidirect
15. C13×#1436C2semidirect
114. C2×C13×C4⋊C4D4semidirect
162. C13×#95D4semidirect
163. #15309C13direct (N × H)
321. C2×#396C2×C13semidirect
322. C2×#396C2×C13semidirect
323. C2×#396C2×C13semidirect
325. C2×#389C2×C13semidirect
327. C2×#385C2×C13semidirect
328. C2×#380C2×C13semidirect
329. #1444C2×C13semidirect
330. #1441C2×C13semidirect
331. #1439C2×C13semidirect
332. #1439C2×C13semidirect
333. #1439C2×C13semidirect
335. #1436C2×C13semidirect
690. C2×C4⋊C4D4×C13semidirect
738. #95D4×C13semidirect
913. C13#15309direct (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×#3902
C2×C13×#3892
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14442
C13×#14412
C13×#14392
C13×#14382
C13×#14362
#1530913