Finite Group Databasebeta

← C13×#14917 #15701256

Subgroups — C13×#14917 #15701256

Order 3328.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#126C211yesmaximal, characteristic, complemented
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#385C211yesmaximal, characteristic, complemented
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic
12C13×#1438C211yesmaximal, characteristic
13C13×#1437C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#126—24no—
19C2×C13×#126—24no—
20C2×C13×#126—24no—
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
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C42×C13C2211yescharacteristic
37C22×C42×C13C2211yescharacteristic
38C13×#386—24no—
39C13×#385—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
58C25×C13C2311yescharacteristic
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—41no—
65C22×D4×C13—41no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
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
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C13×#126—232no—
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—41no—
98C2×C13×C4⋊C4D414yescomplemented
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—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—41no—
126C2×C13×C22⋊C4—41no—
127C2×C13×C22⋊C4—41no—
128C2×C13×C22⋊C4—41no—
129C2×C13×C22⋊C4—41no—
130C2×C13×C22⋊C4—41no—
131C2×C13×C22⋊C4D414yes—
132C2×C42×C13—22no—
133C2×C42×C13—22no—
134C2×C42×C13—22no—
135C2×C42×C13—41no—
136C2×C42×C13—41no—
137C2×C42×C13D414yescomplemented
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—22no—
149C13×#95—41no—
150C13×#95—41no—
151C13×#95—41no—
152C13×#95—41no—
153C13×#95—41no—
154#14917C1311yesmaximal, characteristic, direct product factor, Sylow
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
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×C13C2×D412yes—
182C24×C13#4112yes—
183C24×C13#4112yes—
184C24×C13#4112yes—
185C24×C13C2411yescharacteristic
186C2×D4×C13—28no—
187C2×D4×C13—44no—
188C2×D4×C13—44no—
189C2×D4×C13—44no—
190C2×D4×C13—44no—
191C2×D4×C13—44no—
192C2×D4×C13—44no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—28no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×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—44no—
273C22×C4×C13—44no—
274C22×C4×C13—44no—
275C22×C4×C13—44no—
276C22×C4×C13—44no—
277C22×C4×C13—44no—
278C22×C4×C13C2×D412yes—
279C22×C4×C13C2×D412yes—
280C22×C4×C13C2×D412yes—
281C22×C4×C13C2×D412yes—
282C22×C4×C13C2×D412yes—
283C22×C4×C13C2×D412yes—
284C22×C4×C13C2×D412yes—
285C22×C4×C13C2×D412yes—
286C22×C4×C13#4112yes—
287C22×C4×C13#4112yes—
288C22×C4×C13#4112yes—
289C22×C4×C13#4112yes—
290C22×C4×C13#4112yes—
291C13×C4⋊C4—28no—
292C13×C4⋊C4—28no—
293C13×C4⋊C4—28no—
294C13×C4⋊C4—44no—
295C13×C22⋊C4—28no—
296C13×C22⋊C4—28no—
297C13×C22⋊C4—28no—
298C13×C22⋊C4—28no—
299C13×C22⋊C4—28no—
300C13×C22⋊C4—28no—
301C13×C22⋊C4—44no—
302C13×C22⋊C4—44no—
303C13×C22⋊C4—44no—
304C13×C22⋊C4—44no—
305C13×C22⋊C4—44no—
306C42×C13—28no—
307C42×C13—44no—
308C22×#126C2×C1311yescharacteristic, complemented
309C2×#386C2×C1311yescharacteristic
310C2×#385C2×C1311yescharacteristic, complemented
311C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
312#1442C2×C1311yescharacteristic, complemented
313#1441C2×C1311yescharacteristic, complemented
314#1440C2×C1311yescharacteristic, complemented
315#1439C2×C1311yescharacteristic, complemented
316#1439C2×C1311yescharacteristic, complemented
317#1439C2×C1311yescharacteristic, complemented
318#1438C2×C1311yescharacteristic
319#1438C2×C1311yescharacteristic
320#1437C2×C1311yescharacteristic, complemented
321#1436C2×C1311yescharacteristic, complemented
322#1434C2×C1311yescharacteristic, complemented
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
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—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13—41no—
353C23×C13—41no—
354C23×C13—41no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
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#12614yescomplemented
393C23×C13C22×D411yescharacteristic
394C23×C13C22×D411yescharacteristic
395C23×C13C22×D411yescharacteristic
396C23×C13C2×#4111yescharacteristic
397C23×C13C2×#4111yescharacteristic
398C23×C13C2×#4111yescharacteristic
399C23×C13C2×#4111yescharacteristic
400C23×C13C2×#4111yescharacteristic
401C23×C13C2×#4111yescharacteristic
402C23×C13C2×#4111yescharacteristic
403C23×C13C2×#4111yescharacteristic
404C23×C13H(5,𝔽2)11yescharacteristic
405C23×C13H(5,𝔽2)11yescharacteristic
406C23×C13H(5,𝔽2)11yescharacteristic
407C23×C132−1+411yescharacteristic
408D4×C13—416no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
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—416no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
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#12014yes—
501C23×D4C22×C1311yescharacteristic
502C24×C4C22×C1311yescharacteristic
503C2×#126—24no—
504C2×#126—24no—
505C2×#126—24no—
506C22×C4⋊C4C22×C1311yescharacteristic
507C22×C4⋊C4C22×C1311yescharacteristic
508C22×C4⋊C4C22×C1311yescharacteristic
509C22×C4⋊C4C22×C1311yescharacteristic
510C22×C22⋊C4C22×C1311yescharacteristic
511C22×C22⋊C4C22×C1311yescharacteristic
512C22×C22⋊C4C22×C1311yescharacteristic
513C22×C22⋊C4C22×C1311yescharacteristic
514C22×C22⋊C4C22×C1311yescharacteristic
515C22×C22⋊C4C22×C1311yescharacteristic
516C22×C22⋊C4C22×C1311yescharacteristic
517C22×C22⋊C4C22×C1311yescharacteristic
518C22×C22⋊C4C22×C1311yescharacteristic
519C22×C22⋊C4C22×C1311yescharacteristic
520C22×C22⋊C4C22×C1311yescharacteristic
521C22×C42C22×C1311yescharacteristic
522C22×C42C22×C1311yescharacteristic
523#386—24no—
524#385—24no—
525C4×C22⋊C4—24no—
526C2×#95C22×C1311yescharacteristic
527C2×#95C22×C1311yescharacteristic
528C2×#95C22×C1311yescharacteristic
529C2×#95C22×C1311yescharacteristic
530C2×#95C22×C1311yescharacteristic
531C2×#95C22×C1311yescharacteristic
532C2×#95C22×C1311yescharacteristic
533C2×#95C22×C1311yescharacteristic
534C2×#95C22×C1311yescharacteristic
535C2×#95C22×C1311yescharacteristic
536C2×#95C22×C1311yescharacteristic
537C2×#95C22×C1311yescharacteristic
538C2×#95C22×C1311yescharacteristic
539C2×#95C22×C1311yescharacteristic
540C2×#95C22×C1311yescharacteristic
541C2×#95C22×C1311yescharacteristic
542C22×C13—24no—
543C22×C13—24no—
544C22×C13—24no—
545C22×C13—42no—
546C22×C13—42no—
547C22×C13—42no—
548C22×C13—42no—
549C22×C13—42no—
550C22×C13—42no—
551C22×C13—42no—
552C22×C13—42no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—81no—
565C22×C13—81no—
566C22×C13—81no—
567C22×C13—81no—
568C22×C13—81no—
569C22×C13—81no—
570C22×C13—81no—
571C22×C13—81no—
572C22×C13C2×#12011yescharacteristic
573C22×C13#52511yescharacteristic
574C22×C13#52511yescharacteristic
575C22×C13#52511yescharacteristic
576C22×C13#52511yescharacteristic
577C22×C13#52511yescharacteristic
578C22×C13C2×#12611yescharacteristic
579C22×C13#52911yescharacteristic
580C22×C13#52911yescharacteristic
581C22×C13#52911yescharacteristic
582C22×C13#53211yescharacteristic
583C22×C13#53211yescharacteristic
584C22×C13#53211yescharacteristic
585C22×C13#53511yescharacteristic
586C22×C13#53711yescharacteristic
587C22×C13#53811yescharacteristic
588C22×C13#53811yescharacteristic
589C22×C13#53911yescharacteristic
590C22×C13#53911yescharacteristic
591C22×C13#54611yescharacteristic
592C22×C13#54611yescharacteristic
593C22×C13#54611yescharacteristic
594C22×C13#54611yescharacteristic
595C22×C13#54611yescharacteristic
596C22×C13#54711yescharacteristic
597C22×C13#54811yescharacteristic
598C22×C13#55011yescharacteristic
599C22×C13#55111yescharacteristic
600C22×C13#55111yescharacteristic
601C22×C13#55111yescharacteristic
602C22×C13#55211yescharacteristic
603C22×C13#55311yescharacteristic
604C22×C13#55311yescharacteristic
605C22×C13#55311yescharacteristic
606C22×C13#55611yescharacteristic
607C4×C13—24no—
608C4×C13—42no—
609C4×C13—42no—
610C4×C13—42no—
611C4×C13—42no—
612C4×C13—42no—
613C4×C13—42no—
614C4×C13—42no—
615C4×C13—42no—
616C4×C13—42no—
617C4×C13—42no—
618C4×C13—81no—
619C4×C13—81no—
620C25C23×C1311yescharacteristic
621C25C23×C1311yescharacteristic
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—41no—
628C22×D4—41no—
629C23×C4—22no—
630C23×C4—22no—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4C23×C1311yescharacteristic
637C23×C4C23×C1311yescharacteristic
638C23×C4C23×C1311yescharacteristic
639C23×C4C23×C1311yescharacteristic
640C23×C4C23×C1311yescharacteristic
641C23×C4C23×C1311yescharacteristic
642C23×C4C23×C1311yescharacteristic
643C23×C4C23×C1311yescharacteristic
644C23×C4C23×C1311yescharacteristic
645C23×C4C23×C1311yescharacteristic
646C23×C4C23×C1311yescharacteristic
647C23×C4C23×C1311yescharacteristic
648C23×C4C23×C1311yescharacteristic
649#126—232no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4D4×C1314yescomplemented
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4D4×C1314yes—
695C2×C42—22no—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—41no—
699C2×C42—41no—
700C2×C42D4×C1314yescomplemented
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—22no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717C2×C13—44no—
718C2×C13—82no—
719C2×C13#238811yescharacteristic
720C2×C13#240411yescharacteristic
721C2×C13#240711yescharacteristic
722C2×C13#246611yescharacteristic
723C2×C13#246711yescharacteristic
724C2×C13#248011yescharacteristic
725C2×C13#248111yescharacteristic
726C2×C13#255311yescharacteristic
727C2×C13#255411yescharacteristic
728C2×C13#255911yescharacteristic
729C2×C13#256011yescharacteristic
730C2×C13#260111yescharacteristic
731C2×C13#260311yescharacteristic
732C2×C13#263611yescharacteristic
733C2×C13#285211yescharacteristic
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C2×D4×C1312yes—
761C24C13×#4112yes—
762C24C13×#4112yes—
763C24C13×#4112yes—
764C24C24×C1311yescharacteristic
765C2×D4—28no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—28no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
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—21no—
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—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4C2×D4×C1312yes—
858C22×C4C2×D4×C1312yes—
859C22×C4C2×D4×C1312yes—
860C22×C4C2×D4×C1312yes—
861C22×C4C2×D4×C1312yes—
862C22×C4C2×D4×C1312yes—
863C22×C4C2×D4×C1312yes—
864C22×C4C2×D4×C1312yes—
865C22×C4C13×#4112yes—
866C22×C4C13×#4112yes—
867C22×C4C13×#4112yes—
868C22×C4C13×#4112yes—
869C22×C4C13×#4112yes—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—44no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C42—28no—
886C42—44no—
887C13#1491711yescharacteristic, direct product factor, Sylow
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
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—
957C23C13×#12614yescomplemented
958C23C22×D4×C1311yescharacteristic
959C23C22×D4×C1311yescharacteristic
960C23C22×D4×C1311yescharacteristic
961C23C2×C13×#4111yescharacteristic
962C23C2×C13×#4111yescharacteristic
963C23C2×C13×#4111yescharacteristic
964C23C2×C13×#4111yescharacteristic
965C23C2×C13×#4111yescharacteristic
966C23C2×C13×#4111yescharacteristic
967C23C2×C13×#4111yescharacteristic
968C23C2×C13×#4111yescharacteristic
969C23C13×H(5,𝔽2)11yescharacteristic
970C23C13×H(5,𝔽2)11yescharacteristic
971C23C13×H(5,𝔽2)11yescharacteristic
972C23C13×2−1+411yescharacteristic
973D4—416no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
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—416no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
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×C4C13×#12014yes—
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22C2×C13×#12011yescharacteristic
1097C22C13×#52511yescharacteristic
1098C22C13×#52511yescharacteristic
1099C22C13×#52511yescharacteristic
1100C22C13×#52511yescharacteristic
1101C22C13×#52511yescharacteristic
1102C22C2×C13×#12611yescharacteristic
1103C22C13×#52911yescharacteristic
1104C22C13×#52911yescharacteristic
1105C22C13×#52911yescharacteristic
1106C22C13×#53211yescharacteristic
1107C22C13×#53211yescharacteristic
1108C22C13×#53211yescharacteristic
1109C22C13×#53511yescharacteristic
1110C22C13×#53711yescharacteristic
1111C22C13×#53811yescharacteristic
1112C22C13×#53811yescharacteristic
1113C22C13×#53911yescharacteristic
1114C22C13×#53911yescharacteristic
1115C22C13×#54611yescharacteristic
1116C22C13×#54611yescharacteristic
1117C22C13×#54611yescharacteristic
1118C22C13×#54611yescharacteristic
1119C22C13×#54611yescharacteristic
1120C22C13×#54711yescharacteristic
1121C22C13×#54811yescharacteristic
1122C22C13×#55011yescharacteristic
1123C22C13×#55111yescharacteristic
1124C22C13×#55111yescharacteristic
1125C22C13×#55111yescharacteristic
1126C22C13×#55211yescharacteristic
1127C22C13×#55311yescharacteristic
1128C22C13×#55311yescharacteristic
1129C22C13×#55311yescharacteristic
1130C22C13×#55611yescharacteristic
1131C4—24no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—81no—
1143C4—81no—
1144C2—44no—
1145C2—82no—
1146C2C13×#238811yescharacteristic
1147C2C13×#240411yescharacteristic
1148C2C13×#240711yescharacteristic
1149C2C13×#246611yescharacteristic
1150C2C13×#246711yescharacteristic
1151C2C13×#248011yescharacteristic
1152C2C13×#248111yescharacteristic
1153C2C13×#255311yescharacteristic
1154C2C13×#255411yescharacteristic
1155C2C13×#255911yescharacteristic
1156C2C13×#256011yescharacteristic
1157C2C13×#260111yescharacteristic
1158C2C13×#260311yescharacteristic
1159C2C13×#263611yescharacteristic
1160C2C13×#285211yescharacteristic
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. C22×C13×#126C2semidirect
3. C2×C13×#385C2semidirect
4. C2×C4×C13×C22⋊C4C2semidirect
5. C13×#1442C2semidirect
6. C13×#1441C2semidirect
7. C13×#1440C2semidirect
8. C13×#1439C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
13. C13×#1437C2semidirect
14. C13×#1436C2semidirect
15. C13×#1434C2semidirect
98. C2×C13×C4⋊C4D4semidirect
137. C2×C42×C13D4semidirect
154. #14917C13direct (N × H)
308. C22×#126C2×C13semidirect
310. C2×#385C2×C13semidirect
311. C2×C4×C22⋊C4C2×C13semidirect
312. #1442C2×C13semidirect
313. #1441C2×C13semidirect
314. #1440C2×C13semidirect
315. #1439C2×C13semidirect
316. #1439C2×C13semidirect
317. #1439C2×C13semidirect
320. #1437C2×C13semidirect
321. #1436C2×C13semidirect
322. #1434C2×C13semidirect
392. C23×C13#126semidirect
661. C2×C4⋊C4D4×C13semidirect
700. C2×C42D4×C13semidirect
887. C13#14917direct (N × H)
957. C23C13×#126semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1262
C2×C13×#3862
C2×C13×#3852
C2×C4×C13×C22⋊C42
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×#14342
#1491713