Finite Group Databasebeta

← C13×#15328 #15701667

Subgroups — C13×#15328 #15701667

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C211yesmaximal, characteristic, complemented
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic, complemented
5C13×#1445C211yesmaximal, characteristic, complemented
6C13×#1443C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1438C211yesmaximal, characteristic
13C13×C22⋊#95C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊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
33C13×#396—24no—
34C13×#386—24no—
35C13×#386—24no—
36C13×#385—24no—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C25×C13C2311yescharacteristic
56C25×C13C2311yescharacteristic
57C22×D4×C13—22no—
58C22×D4×C13—22no—
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—41no—
62C22×D4×C13—41no—
63C22×D4×C13Q814yes—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13—41no—
74C23×C4×C13—41no—
75C23×C4×C13—41no—
76C23×C4×C13—41no—
77C23×C4×C13—41no—
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
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
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—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
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—41no—
120C2×C13×C22⋊C4—41no—
121C2×C13×C22⋊C4—41no—
122C2×C13×C22⋊C4—41no—
123C2×C13×C22⋊C4—41no—
124C2×C13×C22⋊C4—41no—
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×C13×C22⋊C4D414yes—
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—41no—
143C13×#95—41no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95—41no—
147C13×#95—41no—
148C13×#95—41no—
149C13×#95—41no—
150C13×#95—41no—
151#15328C1311yesmaximal, characteristic, direct product factor, Sylow
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×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×C13C2×D412yes—
177C24×C13C2×D412yes—
178C24×C13C2×Q812yes—
179C24×C13C2×Q812yes—
180C24×C13#4112yes—
181C24×C13#4112yes—
182C24×C13C2411yescharacteristic
183C2×D4×C13—28no—
184C2×D4×C13—28no—
185C2×D4×C13—44no—
186C2×D4×C13—44no—
187C2×D4×C13—44no—
188C2×D4×C13—44no—
189C2×D4×C13—44no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—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×C13—44no—
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×C13—44no—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×Q812yes—
291C22×C4×C13#4112yes—
292C22×C4×C13#4112yes—
293C22×C4×C13#4112yes—
294C22×C4×C13#4112yes—
295C13×C4⋊C4—44no—
296C13×C4⋊C4—44no—
297C13×C4⋊C4—44no—
298C13×C4⋊C4—44no—
299C13×C22⋊C4—28no—
300C13×C22⋊C4—44no—
301C13×C22⋊C4—44no—
302C13×C22⋊C4—44no—
303C13×C22⋊C4—44no—
304C13×C22⋊C4—44no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4—44no—
307C13×C22⋊C4—44no—
308C13×C22⋊C4—44no—
309C2×#396C2×C1311yescharacteristic, complemented
310C2×#386C2×C1311yescharacteristic
311C2×#386C2×C1311yescharacteristic
312C2×#385C2×C1311yescharacteristic, complemented
313#1445C2×C1311yescharacteristic, complemented
314#1443C2×C1311yescharacteristic, complemented
315#1442C2×C1311yescharacteristic, complemented
316#1441C2×C1311yescharacteristic, complemented
317#1439C2×C1311yescharacteristic, complemented
318#1439C2×C1311yescharacteristic, complemented
319#1439C2×C1311yescharacteristic, complemented
320#1438C2×C1311yescharacteristic
321C22⋊#95C2×C1311yescharacteristic, complemented
322C22⋊#95C2×C1311yescharacteristic, complemented
323C22⋊#95C2×C1311yescharacteristic, complemented
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—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—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×C13C22⋊Q814yes—
393C23×C13C22⋊Q814yes—
394C23×C13C22×D411yescharacteristic
395C23×C13C22×D411yescharacteristic
396C23×C13C22×Q811yescharacteristic
397C23×C13C2×#4111yescharacteristic
398C23×C13C2×#4111yescharacteristic
399C23×C13C2×#4111yescharacteristic
400C23×C13C2×#4111yescharacteristic
401C23×C13C2×#4111yescharacteristic
402C23×C13C2×#4111yescharacteristic
403C23×C13H(5,𝔽2)11yescharacteristic
404C23×C13H(5,𝔽2)11yescharacteristic
405C23×C13H(5,𝔽2)11yescharacteristic
406C23×C13H(5,𝔽2)11yescharacteristic
407C23×C13H(5,𝔽2)11yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409D4×C13—416no—
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—416no—
438C2×C4×C13—416no—
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—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—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C23×D4C22×C1311yescharacteristic
504C24×C4C22×C1311yescharacteristic
505C24×C4C22×C1311yescharacteristic
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
520#396—24no—
521#386—24no—
522#386—24no—
523#385—24no—
524C2×#95C22×C1311yescharacteristic
525C2×#95C22×C1311yescharacteristic
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—24no—
546C22×C13—24no—
547C22×C13—24no—
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—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13C2×C22⋊Q811yescharacteristic
573C22×C13C2×C22⋊Q811yescharacteristic
574C22×C13#52511yescharacteristic
575C22×C13#52911yescharacteristic
576C22×C13#52911yescharacteristic
577C22×C13#53211yescharacteristic
578C22×C13#53411yescharacteristic
579C22×C13#53411yescharacteristic
580C22×C13#53811yescharacteristic
581C22×C13#53811yescharacteristic
582C22×C13#53811yescharacteristic
583C22×C13#53811yescharacteristic
584C22×C13#54011yescharacteristic
585C22×C13#54011yescharacteristic
586C22×C13#54311yescharacteristic
587C22×C13D4211yescharacteristic
588C22×C13#54611yescharacteristic
589C22×C13#54611yescharacteristic
590C22×C13#54611yescharacteristic
591C22×C13#54611yescharacteristic
592C22×C13#54611yescharacteristic
593C22×C13#54611yescharacteristic
594C22×C13#55111yescharacteristic
595C22×C13#55111yescharacteristic
596C22×C13#55111yescharacteristic
597C22×C13#55311yescharacteristic
598C22×C13#55311yescharacteristic
599C22×C13#55311yescharacteristic
600C22×C13#55311yescharacteristic
601C22×C13#55411yescharacteristic
602C22×C13#55411yescharacteristic
603C22×C13#55411yescharacteristic
604C22×C13#55411yescharacteristic
605C22×C13#56011yescharacteristic
606C22×C13#56011yescharacteristic
607C4×C13—42no—
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—81no—
617C4×C13—81no—
618C4×C13—81no—
619C4×C13—81no—
620C25C23×C1311yescharacteristic
621C25C23×C1311yescharacteristic
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4Q8×C1314yes—
629C23×C4—22no—
630C23×C4—22no—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4C23×C1311yescharacteristic
644C23×C4C23×C1311yescharacteristic
645C23×C4C23×C1311yescharacteristic
646C23×C4C23×C1311yescharacteristic
647C23×C4C23×C1311yescharacteristic
648C23×C4C23×C1311yescharacteristic
649C23×C4C23×C1311yescharacteristic
650C23×C4C23×C1311yescharacteristic
651C23×C4C23×C1311yescharacteristic
652C23×C4C23×C1311yescharacteristic
653C23×C4C23×C1311yescharacteristic
654C23×C4C23×C1311yescharacteristic
655C23×C4C23×C1311yescharacteristic
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
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—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
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⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4D4×C1314yes—
697C2×C22⋊C4D4×C1314yes—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716C2×C13—44no—
717C2×C13—44no—
718C2×C13#243711yescharacteristic
719C2×C13#245011yescharacteristic
720C2×C13#245011yescharacteristic
721C2×C13#245711yescharacteristic
722C2×C13#246411yescharacteristic
723C2×C13#255911yescharacteristic
724C2×C13#256411yescharacteristic
725C2×C13#257611yescharacteristic
726C2×C13#257911yescharacteristic
727C2×C13#266811yescharacteristic
728C2×C13#268811yescharacteristic
729C2×C13#269711yescharacteristic
730C2×C13#274911yescharacteristic
731C2×C13#278011yescharacteristic
732C2×C13#278011yescharacteristic
733C24—21no—
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—
757C24C2×D4×C1312yes—
758C24C2×D4×C1312yes—
759C24C2×Q8×C1312yes—
760C24C2×Q8×C1312yes—
761C24C13×#4112yes—
762C24C13×#4112yes—
763C24C24×C1311yescharacteristic
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
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—21no—
852C22×C4—21no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4C2×D4×C1312yes—
868C22×C4C2×D4×C1312yes—
869C22×C4C2×D4×C1312yes—
870C22×C4C2×D4×C1312yes—
871C22×C4C2×Q8×C1312yes—
872C22×C4C13×#4112yes—
873C22×C4C13×#4112yes—
874C22×C4C13×#4112yes—
875C22×C4C13×#4112yes—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C13#1532811yescharacteristic, direct product factor, Sylow
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—22no—
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—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—
957C23—41no—
958C23—41no—
959C23C13×C22⋊Q814yes—
960C23C13×C22⋊Q814yes—
961C23C22×D4×C1311yescharacteristic
962C23C22×D4×C1311yescharacteristic
963C23C22×Q8×C1311yescharacteristic
964C23C2×C13×#4111yescharacteristic
965C23C2×C13×#4111yescharacteristic
966C23C2×C13×#4111yescharacteristic
967C23C2×C13×#4111yescharacteristic
968C23C2×C13×#4111yescharacteristic
969C23C2×C13×#4111yescharacteristic
970C23C13×H(5,𝔽2)11yescharacteristic
971C23C13×H(5,𝔽2)11yescharacteristic
972C23C13×H(5,𝔽2)11yescharacteristic
973C23C13×H(5,𝔽2)11yescharacteristic
974C23C13×H(5,𝔽2)11yescharacteristic
975C23C13×H(5,𝔽2)11yescharacteristic
976D4—416no—
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—416no—
1005C2×C4—416no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
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×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
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—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22C2×C13×C22⋊Q811yescharacteristic
1101C22C2×C13×C22⋊Q811yescharacteristic
1102C22C13×#52511yescharacteristic
1103C22C13×#52911yescharacteristic
1104C22C13×#52911yescharacteristic
1105C22C13×#53211yescharacteristic
1106C22C13×#53411yescharacteristic
1107C22C13×#53411yescharacteristic
1108C22C13×#53811yescharacteristic
1109C22C13×#53811yescharacteristic
1110C22C13×#53811yescharacteristic
1111C22C13×#53811yescharacteristic
1112C22C13×#54011yescharacteristic
1113C22C13×#54011yescharacteristic
1114C22C13×#54311yescharacteristic
1115C22D42×C1311yescharacteristic
1116C22C13×#54611yescharacteristic
1117C22C13×#54611yescharacteristic
1118C22C13×#54611yescharacteristic
1119C22C13×#54611yescharacteristic
1120C22C13×#54611yescharacteristic
1121C22C13×#54611yescharacteristic
1122C22C13×#55111yescharacteristic
1123C22C13×#55111yescharacteristic
1124C22C13×#55111yescharacteristic
1125C22C13×#55311yescharacteristic
1126C22C13×#55311yescharacteristic
1127C22C13×#55311yescharacteristic
1128C22C13×#55311yescharacteristic
1129C22C13×#55411yescharacteristic
1130C22C13×#55411yescharacteristic
1131C22C13×#55411yescharacteristic
1132C22C13×#55411yescharacteristic
1133C22C13×#56011yescharacteristic
1134C22C13×#56011yescharacteristic
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C2—44no—
1149C2—44no—
1150C2C13×#243711yescharacteristic
1151C2C13×#245011yescharacteristic
1152C2C13×#245011yescharacteristic
1153C2C13×#245711yescharacteristic
1154C2C13×#246411yescharacteristic
1155C2C13×#255911yescharacteristic
1156C2C13×#256411yescharacteristic
1157C2C13×#257611yescharacteristic
1158C2C13×#257911yescharacteristic
1159C2C13×#266811yescharacteristic
1160C2C13×#268811yescharacteristic
1161C2C13×#269711yescharacteristic
1162C2C13×#274911yescharacteristic
1163C2C13×#278011yescharacteristic
1164C2C13×#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
4. C2×C13×#385C2semidirect
5. C13×#1445C2semidirect
6. C13×#1443C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
13. C13×C22⋊#95C2semidirect
14. C13×C22⋊#95C2semidirect
15. C13×C22⋊#95C2semidirect
151. #15328C13direct (N × H)
309. C2×#396C2×C13semidirect
312. C2×#385C2×C13semidirect
313. #1445C2×C13semidirect
314. #1443C2×C13semidirect
315. #1442C2×C13semidirect
316. #1441C2×C13semidirect
317. #1439C2×C13semidirect
318. #1439C2×C13semidirect
319. #1439C2×C13semidirect
321. C22⋊#95C2×C13semidirect
322. C22⋊#95C2×C13semidirect
323. C22⋊#95C2×C13semidirect
890. C13#15328direct (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×#3862
C2×C13×#3852
C13×#14452
C13×#14432
C13×#14422
C13×#14412
C13×#14392
C13×#14382
C13×C22⋊#952
#1532813