Finite Group Databasebeta

← C13×#15370 #15701709

Subgroups — C13×#15370 #15701709

Order 3328.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic, complemented
2C2×C13×#399C211yesmaximal, characteristic, complemented
3C2×C13×#394C211yesmaximal, characteristic, complemented
4C2×C13×#394C211yesmaximal, characteristic, complemented
5C2×C13×#392C211yesmaximal, characteristic
6C2×C13×#390C211yesmaximal, characteristic, complemented
7C2×C13×#386C211yesmaximal, characteristic, complemented
8C2×C13×#385C211yesmaximal, characteristic, complemented
9C13×#1444C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic, complemented
14C13×#1437C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C2×C13×#123—24no—
21C2×C13×#123—24no—
22C2×C13×#123—24no—
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
39C22×C13×C22⋊C4C2211yescharacteristic
40C22×C13×C22⋊C4C2211yescharacteristic
41C22×C13×C22⋊C4C2211yescharacteristic
42C22×C13×C22⋊C4C2211yescharacteristic
43C22×C42×C13C2211yescharacteristic
44C13×#399—24no—
45C13×#394—24no—
46C13×#394—24no—
47C13×#392—24no—
48C13×#390—24no—
49C13×#386—24no—
50C13×#385—24no—
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C2×C13×#95C2211yescharacteristic
60C2×C13×#95C2211yescharacteristic
61C25×C13C2311yescharacteristic
62C25×C13C2311yescharacteristic
63C25×C13C2311yescharacteristic
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—22no—
75C22×D4×C13—22no—
76C22×D4×C13—22no—
77C22×D4×C13—22no—
78C22×D4×C13—22no—
79C22×D4×C13—41no—
80C22×D4×C13—41no—
81C22×D4×C13—41no—
82C22×D4×C13—41no—
83C22×D4×C13—41no—
84C22×D4×C13—41no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—22no—
88C23×C4×C13—22no—
89C23×C4×C13—22no—
90C23×C4×C13—41no—
91C23×C4×C13—41no—
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C13×#123—232no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4—22no—
118C2×C13×C4⋊C4—41no—
119C2×C13×C4⋊C4—41no—
120C2×C13×C4⋊C4—41no—
121C2×C13×C4⋊C4—41no—
122C2×C13×C4⋊C4D414yescomplemented
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—22no—
138C2×C13×C22⋊C4—22no—
139C2×C13×C22⋊C4—22no—
140C2×C13×C22⋊C4—22no—
141C2×C13×C22⋊C4—22no—
142C2×C13×C22⋊C4—22no—
143C2×C13×C22⋊C4—22no—
144C2×C13×C22⋊C4—22no—
145C2×C13×C22⋊C4—22no—
146C2×C13×C22⋊C4—22no—
147C2×C13×C22⋊C4—22no—
148C2×C13×C22⋊C4—22no—
149C2×C13×C22⋊C4—22no—
150C2×C13×C22⋊C4—22no—
151C2×C13×C22⋊C4—41no—
152C2×C13×C22⋊C4—41no—
153C2×C13×C22⋊C4—41no—
154C2×C13×C22⋊C4—41no—
155C2×C13×C22⋊C4—41no—
156C2×C13×C22⋊C4—41no—
157C2×C13×C22⋊C4—41no—
158C2×C13×C22⋊C4—41no—
159C2×C13×C22⋊C4—41no—
160C2×C13×C22⋊C4—41no—
161C2×C13×C22⋊C4D414yes—
162C2×C13×C22⋊C4D414yescomplemented
163C2×C13×C22⋊C4D414yescomplemented
164C2×C13×C22⋊C4D414yescomplemented
165C2×C42×C13—22no—
166C2×C42×C13—22no—
167C2×C42×C13—41no—
168C13×#95—22no—
169C13×#95—22no—
170C13×#95—22no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95—22no—
174C13×#95—22no—
175C13×#95—22no—
176C13×#95—22no—
177C13×#95—41no—
178#15370C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
191C24×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—21no—
203C24×C13—21no—
204C24×C13—21no—
205C24×C13—21no—
206C24×C13—21no—
207C24×C13—21no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13—21no—
211C24×C13—21no—
212C24×C13—21no—
213C24×C13—21no—
214C24×C13—21no—
215C24×C13—21no—
216C24×C13—21no—
217C24×C13—21no—
218C24×C13—21no—
219C24×C13C2×D412yes—
220C24×C13C2×D412yes—
221C24×C13C2×D412yes—
222C24×C13C2×D412yes—
223C24×C13#4112yes—
224C24×C13C2411yescharacteristic
225C2×D4×C13—28no—
226C2×D4×C13—28no—
227C2×D4×C13—28no—
228C2×D4×C13—44no—
229C2×D4×C13—44no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C2×D4×C13—44no—
233C2×D4×C13—44no—
234C2×D4×C13—44no—
235C2×D4×C13—44no—
236C2×D4×C13—44no—
237C2×D4×C13—44no—
238C2×D4×C13—44no—
239C2×D4×C13—44no—
240C2×D4×C13—44no—
241C2×D4×C13—44no—
242C2×D4×C13—44no—
243C2×D4×C13—44no—
244C2×D4×C13—44no—
245C2×D4×C13—44no—
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—28no—
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—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13—21no—
308C22×C4×C13—21no—
309C22×C4×C13—21no—
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—21no—
315C22×C4×C13—21no—
316C22×C4×C13—21no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
319C22×C4×C13—44no—
320C22×C4×C13—44no—
321C22×C4×C13—44no—
322C22×C4×C13—44no—
323C22×C4×C13C2×D412yes—
324C22×C4×C13C2×D412yes—
325C22×C4×C13C2×D412yes—
326C22×C4×C13C2×D412yes—
327C22×C4×C13C2×D412yes—
328C22×C4×C13C2×D412yes—
329C22×C4×C13C2×D412yes—
330C22×C4×C13C2×D412yes—
331C22×C4×C13C2×D412yes—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D412yes—
334C22×C4×C13#4112yes—
335C22×C4×C13#4112yes—
336C22×C4×C13#4112yes—
337C13×C4⋊C4—28no—
338C13×C4⋊C4—28no—
339C13×C4⋊C4—44no—
340C13×C4⋊C4—44no—
341C13×C4⋊C4—44no—
342C13×C4⋊C4—44no—
343C13×C22⋊C4—28no—
344C13×C22⋊C4—28no—
345C13×C22⋊C4—28no—
346C13×C22⋊C4—28no—
347C13×C22⋊C4—44no—
348C13×C22⋊C4—44no—
349C13×C22⋊C4—44no—
350C13×C22⋊C4—44no—
351C13×C22⋊C4—44no—
352C13×C22⋊C4—44no—
353C13×C22⋊C4—44no—
354C13×C22⋊C4—44no—
355C13×C22⋊C4—44no—
356C13×C22⋊C4—44no—
357C42×C13—44no—
358C22×#123C2×C1311yescharacteristic, complemented
359C2×#399C2×C1311yescharacteristic, complemented
360C2×#394C2×C1311yescharacteristic, complemented
361C2×#394C2×C1311yescharacteristic, complemented
362C2×#392C2×C1311yescharacteristic
363C2×#390C2×C1311yescharacteristic, complemented
364C2×#386C2×C1311yescharacteristic, complemented
365C2×#385C2×C1311yescharacteristic, complemented
366#1444C2×C1311yescharacteristic, complemented
367#1439C2×C1311yescharacteristic, complemented
368#1439C2×C1311yescharacteristic, complemented
369#1439C2×C1311yescharacteristic, complemented
370#1438C2×C1311yescharacteristic, complemented
371#1437C2×C1311yescharacteristic, complemented
372C4⋊#95C2×C1311yescharacteristic, complemented
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—22no—
396C23×C13—22no—
397C23×C13—22no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—22no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13—22no—
405C23×C13—41no—
406C23×C13—41no—
407C23×C13—41no—
408C23×C13—41no—
409C23×C13—41no—
410C23×C13—41no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13—41no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13—41no—
460C23×C13—41no—
461C23×C13—41no—
462C23×C13—41no—
463C23×C13—41no—
464C23×C13—41no—
465C23×C13—41no—
466C23×C13—41no—
467C23×C13—41no—
468C23×C13—41no—
469C23×C13—41no—
470C23×C13—41no—
471C23×C13—41no—
472C23×C13—41no—
473C23×C13—41no—
474C23×C13—41no—
475C23×C13—41no—
476C23×C13—41no—
477C23×C13#12714yes—
478C23×C13C22×D411yescharacteristic
479C23×C13C22×D411yescharacteristic
480C23×C13C22×D411yescharacteristic
481C23×C13C22×D411yescharacteristic
482C23×C13C22×D411yescharacteristic
483C23×C13C2×#4111yescharacteristic
484C23×C13C2×#4111yescharacteristic
485C23×C13C2×#4111yescharacteristic
486C23×C13C2×#4111yescharacteristic
487C23×C13H(5,𝔽2)11yescharacteristic
488C23×C13H(5,𝔽2)11yescharacteristic
489C23×C13H(5,𝔽2)11yescharacteristic
490C23×C13H(5,𝔽2)11yescharacteristic
491C23×C132−1+411yescharacteristic
492C23×C132−1+411yescharacteristic
493D4×C13—416no—
494D4×C13—416no—
495D4×C13—416no—
496C2×C4×C13—22no—
497C2×C4×C13—22no—
498C2×C4×C13—22no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—22no—
512C2×C4×C13—22no—
513C2×C4×C13—22no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—22no—
518C2×C4×C13—22no—
519C2×C4×C13—22no—
520C2×C4×C13—22no—
521C2×C4×C13—22no—
522C2×C4×C13—22no—
523C2×C4×C13—22no—
524C2×C4×C13—22no—
525C2×C4×C13—22no—
526C2×C4×C13—22no—
527C2×C4×C13—22no—
528C2×C4×C13—22no—
529C2×C4×C13—22no—
530C2×C4×C13—22no—
531C2×C4×C13—22no—
532C2×C4×C13—416no—
533C2×C4×C13—41no—
534C2×C4×C13—41no—
535C2×C4×C13—41no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—41no—
541C2×C4×C13—41no—
542C2×C4×C13—41no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13—41no—
563C2×C4×C13—41no—
564C2×C4×C13—41no—
565C2×C4×C13—41no—
566C2×C4×C13—41no—
567C2×C4×C13—41no—
568C2×C4×C13—41no—
569C2×C4×C13—41no—
570C2×C4×C13—41no—
571C2×C4×C13—41no—
572C2×C4×C13—41no—
573C2×C4×C13—41no—
574C2×C4×C13—41no—
575C2×C4×C13—41no—
576C2×C4×C13—41no—
577C2×C4×C13—41no—
578C2×C4×C13—41no—
579C2×C4×C13#12014yes—
580C2×C4×C13#12314yescomplemented
581C23×D4C22×C1311yescharacteristic
582C23×D4C22×C1311yescharacteristic
583C23×D4C22×C1311yescharacteristic
584C24×C4C22×C1311yescharacteristic
585C2×#123—24no—
586C2×#123—24no—
587C2×#123—24no—
588C22×C4⋊C4C22×C1311yescharacteristic
589C22×C4⋊C4C22×C1311yescharacteristic
590C22×C4⋊C4C22×C1311yescharacteristic
591C22×C4⋊C4C22×C1311yescharacteristic
592C22×C4⋊C4C22×C1311yescharacteristic
593C22×C4⋊C4C22×C1311yescharacteristic
594C22×C22⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598C22×C22⋊C4C22×C1311yescharacteristic
599C22×C22⋊C4C22×C1311yescharacteristic
600C22×C22⋊C4C22×C1311yescharacteristic
601C22×C22⋊C4C22×C1311yescharacteristic
602C22×C22⋊C4C22×C1311yescharacteristic
603C22×C22⋊C4C22×C1311yescharacteristic
604C22×C22⋊C4C22×C1311yescharacteristic
605C22×C22⋊C4C22×C1311yescharacteristic
606C22×C22⋊C4C22×C1311yescharacteristic
607C22×C22⋊C4C22×C1311yescharacteristic
608C22×C42C22×C1311yescharacteristic
609#399—24no—
610#394—24no—
611#394—24no—
612#392—24no—
613#390—24no—
614#386—24no—
615#385—24no—
616C2×#95C22×C1311yescharacteristic
617C2×#95C22×C1311yescharacteristic
618C2×#95C22×C1311yescharacteristic
619C2×#95C22×C1311yescharacteristic
620C2×#95C22×C1311yescharacteristic
621C2×#95C22×C1311yescharacteristic
622C2×#95C22×C1311yescharacteristic
623C2×#95C22×C1311yescharacteristic
624C2×#95C22×C1311yescharacteristic
625C2×#95C22×C1311yescharacteristic
626C22×C13—24no—
627C22×C13—24no—
628C22×C13—24no—
629C22×C13—42no—
630C22×C13—42no—
631C22×C13—42no—
632C22×C13—42no—
633C22×C13—42no—
634C22×C13—42no—
635C22×C13—42no—
636C22×C13—42no—
637C22×C13—42no—
638C22×C13—42no—
639C22×C13—42no—
640C22×C13—42no—
641C22×C13—42no—
642C22×C13—42no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—42no—
650C22×C13—42no—
651C22×C13—42no—
652C22×C13—42no—
653C22×C13—42no—
654C22×C13—42no—
655C22×C13—81no—
656C22×C13—81no—
657C22×C13—81no—
658C22×C13—81no—
659C22×C13—81no—
660C22×C13—81no—
661C22×C13—81no—
662C22×C13—81no—
663C22×C13—81no—
664C22×C13—81no—
665C22×C13—81no—
666C22×C13—81no—
667C22×C13—81no—
668C22×C13—81no—
669C22×C13—81no—
670C22×C13—81no—
671C22×C13C2×#12011yescharacteristic
672C22×C13C2×#12311yescharacteristic
673C22×C13#52511yescharacteristic
674C22×C13#52511yescharacteristic
675C22×C13C2×#12711yescharacteristic
676C22×C13#53211yescharacteristic
677C22×C13#53411yescharacteristic
678C22×C13#53511yescharacteristic
679C22×C13#53611yescharacteristic
680C22×C13#53711yescharacteristic
681C22×C13#53711yescharacteristic
682C22×C13#53811yescharacteristic
683C22×C13#53911yescharacteristic
684C22×C13#54011yescharacteristic
685C22×C13#54211yescharacteristic
686C22×C13D4211yescharacteristic
687C22×C13D4211yescharacteristic
688C22×C13D4211yescharacteristic
689C22×C13D4211yescharacteristic
690C22×C13#54611yescharacteristic
691C22×C13#54611yescharacteristic
692C22×C13#54611yescharacteristic
693C22×C13#54611yescharacteristic
694C22×C13#54611yescharacteristic
695C22×C13#54711yescharacteristic
696C22×C13#54711yescharacteristic
697C22×C13#54711yescharacteristic
698C22×C13#54711yescharacteristic
699C22×C13#54711yescharacteristic
700C22×C13#54811yescharacteristic
701C22×C13#55011yescharacteristic
702C22×C13#55111yescharacteristic
703C22×C13#55911yescharacteristic
704C22×C13#56211yescharacteristic
705C22×C13#56211yescharacteristic
706C4×C13—24no—
707C4×C13—24no—
708C4×C13—42no—
709C4×C13—42no—
710C4×C13—42no—
711C4×C13—42no—
712C4×C13—42no—
713C4×C13—42no—
714C4×C13—42no—
715C4×C13—42no—
716C4×C13—81no—
717C4×C13—81no—
718C25C23×C1311yescharacteristic
719C25C23×C1311yescharacteristic
720C25C23×C1311yescharacteristic
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C23×C4—22no—
743C23×C4—22no—
744C23×C4—22no—
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—41no—
748C23×C4—41no—
749C23×C4C23×C1311yescharacteristic
750C23×C4C23×C1311yescharacteristic
751C23×C4C23×C1311yescharacteristic
752C23×C4C23×C1311yescharacteristic
753C23×C4C23×C1311yescharacteristic
754C23×C4C23×C1311yescharacteristic
755C23×C4C23×C1311yescharacteristic
756C23×C4C23×C1311yescharacteristic
757C23×C4C23×C1311yescharacteristic
758C23×C4C23×C1311yescharacteristic
759C23×C4C23×C1311yescharacteristic
760C23×C4C23×C1311yescharacteristic
761#123—232no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4D4×C1314yescomplemented
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4D4×C1314yes—
819C2×C22⋊C4D4×C1314yescomplemented
820C2×C22⋊C4D4×C1314yescomplemented
821C2×C22⋊C4D4×C1314yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—41no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—41no—
835C2×C13—44no—
836C2×C13—82no—
837C2×C13—82no—
838C2×C13#240711yescharacteristic
839C2×C13#241811yescharacteristic
840C2×C13#243011yescharacteristic
841C2×C13#243311yescharacteristic
842C2×C13#244511yescharacteristic
843C2×C13#245511yescharacteristic
844C2×C13#246111yescharacteristic
845C2×C13#250111yescharacteristic
846C2×C13#253911yescharacteristic
847C2×C13#267111yescharacteristic
848C2×C13#267211yescharacteristic
849C2×C13#268111yescharacteristic
850C2×C13#268211yescharacteristic
851C2×C13#270611yescharacteristic
852C2×C13#271011yescharacteristic
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24C2×D4×C1312yes—
894C24C2×D4×C1312yes—
895C24C2×D4×C1312yes—
896C24C2×D4×C1312yes—
897C24C13×#4112yes—
898C24C24×C1311yescharacteristic
899C2×D4—28no—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—28no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4C2×D4×C1312yes—
998C22×C4C2×D4×C1312yes—
999C22×C4C2×D4×C1312yes—
1000C22×C4C2×D4×C1312yes—
1001C22×C4C2×D4×C1312yes—
1002C22×C4C2×D4×C1312yes—
1003C22×C4C2×D4×C1312yes—
1004C22×C4C2×D4×C1312yes—
1005C22×C4C2×D4×C1312yes—
1006C22×C4C2×D4×C1312yes—
1007C22×C4C2×D4×C1312yes—
1008C22×C4C13×#4112yes—
1009C22×C4C13×#4112yes—
1010C22×C4C13×#4112yes—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C42—44no—
1032C13#1537011yescharacteristic, direct product factor, Sylow
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23C13×#12714yes—
1138C23C22×D4×C1311yescharacteristic
1139C23C22×D4×C1311yescharacteristic
1140C23C22×D4×C1311yescharacteristic
1141C23C22×D4×C1311yescharacteristic
1142C23C22×D4×C1311yescharacteristic
1143C23C2×C13×#4111yescharacteristic
1144C23C2×C13×#4111yescharacteristic
1145C23C2×C13×#4111yescharacteristic
1146C23C2×C13×#4111yescharacteristic
1147C23C13×H(5,𝔽2)11yescharacteristic
1148C23C13×H(5,𝔽2)11yescharacteristic
1149C23C13×H(5,𝔽2)11yescharacteristic
1150C23C13×H(5,𝔽2)11yescharacteristic
1151C23C13×2−1+411yescharacteristic
1152C23C13×2−1+411yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—416no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4C13×#12014yes—
1240C2×C4C13×#12314yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×C13×#12011yescharacteristic
1287C22C2×C13×#12311yescharacteristic
1288C22C13×#52511yescharacteristic
1289C22C13×#52511yescharacteristic
1290C22C2×C13×#12711yescharacteristic
1291C22C13×#53211yescharacteristic
1292C22C13×#53411yescharacteristic
1293C22C13×#53511yescharacteristic
1294C22C13×#53611yescharacteristic
1295C22C13×#53711yescharacteristic
1296C22C13×#53711yescharacteristic
1297C22C13×#53811yescharacteristic
1298C22C13×#53911yescharacteristic
1299C22C13×#54011yescharacteristic
1300C22C13×#54211yescharacteristic
1301C22D42×C1311yescharacteristic
1302C22D42×C1311yescharacteristic
1303C22D42×C1311yescharacteristic
1304C22D42×C1311yescharacteristic
1305C22C13×#54611yescharacteristic
1306C22C13×#54611yescharacteristic
1307C22C13×#54611yescharacteristic
1308C22C13×#54611yescharacteristic
1309C22C13×#54611yescharacteristic
1310C22C13×#54711yescharacteristic
1311C22C13×#54711yescharacteristic
1312C22C13×#54711yescharacteristic
1313C22C13×#54711yescharacteristic
1314C22C13×#54711yescharacteristic
1315C22C13×#54811yescharacteristic
1316C22C13×#55011yescharacteristic
1317C22C13×#55111yescharacteristic
1318C22C13×#55911yescharacteristic
1319C22C13×#56211yescharacteristic
1320C22C13×#56211yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C13×#240711yescharacteristic
1337C2C13×#241811yescharacteristic
1338C2C13×#243011yescharacteristic
1339C2C13×#243311yescharacteristic
1340C2C13×#244511yescharacteristic
1341C2C13×#245511yescharacteristic
1342C2C13×#246111yescharacteristic
1343C2C13×#250111yescharacteristic
1344C2C13×#253911yescharacteristic
1345C2C13×#267111yescharacteristic
1346C2C13×#267211yescharacteristic
1347C2C13×#268111yescharacteristic
1348C2C13×#268211yescharacteristic
1349C2C13×#270611yescharacteristic
1350C2C13×#271011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×#123C2semidirect
2. C2×C13×#399C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#394C2semidirect
6. C2×C13×#390C2semidirect
7. C2×C13×#386C2semidirect
8. C2×C13×#385C2semidirect
9. C13×#1444C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1438C2semidirect
14. C13×#1437C2semidirect
15. C13×C4⋊#95C2semidirect
122. C2×C13×C4⋊C4D4semidirect
162. C2×C13×C22⋊C4D4semidirect
163. C2×C13×C22⋊C4D4semidirect
164. C2×C13×C22⋊C4D4semidirect
178. #15370C13direct (N × H)
358. C22×#123C2×C13semidirect
359. C2×#399C2×C13semidirect
360. C2×#394C2×C13semidirect
361. C2×#394C2×C13semidirect
363. C2×#390C2×C13semidirect
364. C2×#386C2×C13semidirect
365. C2×#385C2×C13semidirect
366. #1444C2×C13semidirect
367. #1439C2×C13semidirect
368. #1439C2×C13semidirect
369. #1439C2×C13semidirect
370. #1438C2×C13semidirect
371. #1437C2×C13semidirect
372. C4⋊#95C2×C13semidirect
580. C2×C4×C13#123semidirect
779. C2×C4⋊C4D4×C13semidirect
819. C2×C22⋊C4D4×C13semidirect
820. C2×C22⋊C4D4×C13semidirect
821. C2×C22⋊C4D4×C13semidirect
1032. C13#15370direct (N × H)
1240. C2×C4C13×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3992
C2×C13×#3942
C2×C13×#3922
C2×C13×#3902
C2×C13×#3862
C2×C13×#3852
C13×#14442
C13×#14392
C13×#14382
C13×#14372
C13×C4⋊#952
#1537013