Finite Group Databasebeta

← C13×#15169 #15701508

Subgroups — C13×#15169 #15701508

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#400C211yesmaximal, characteristic, complemented
2C2×C13×#397C211yesmaximal, characteristic
3C13×#1443C211yesmaximal, characteristic, complemented
4C13×#1443C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1440C211yesmaximal, characteristic
7C13×#1439C211yesmaximal, characteristic
8C13×#1439C211yesmaximal, characteristic
9C13×#1437C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C13×#400—24no—
30C13×#397—24no—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
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
53C25×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—41no—
93C2×C13×C22⋊C4—41no—
94C2×C13×C22⋊C4—41no—
95C2×C13×C22⋊C4—41no—
96C2×C13×C22⋊C4—41no—
97C2×C13×C22⋊C4—41no—
98C2×C42×C13—22no—
99C2×C42×C13—22no—
100C2×C42×C13—22no—
101C2×C42×C13—41no—
102C2×C42×C13—41no—
103C2×C42×C13—41no—
104C2×C42×C13—41no—
105C2×C42×C13—41no—
106C2×C42×C13—41no—
107C13×#95—22no—
108C13×#95—22no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—41no—
126C13×#95—41no—
127C13×#95—41no—
128C13×#95D414yes—
129#15169C1311yesmaximal, characteristic, direct product factor, Sylow
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13#4112yes—
145C24×C13C2411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—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×C13C2×D412yes—
233C22×C4×C13C2×D412yes—
234C22×C4×C13C2×D412yes—
235C22×C4×C13#4112yes—
236C22×C4×C13#4112yes—
237C22×C4×C13#4112yes—
238C22×C4×C13#4112yes—
239C22×C4×C13#4112yes—
240C22×C4×C13#4112yes—
241C22×C4×C13#4112yes—
242C22×C4×C13#4112yes—
243C22×C4×C13#4112yes—
244C13×C4⋊C4—44no—
245C13×C4⋊C4—44no—
246C13×C4⋊C4—44no—
247C13×C22⋊C4—44no—
248C13×C22⋊C4—44no—
249C13×C22⋊C4—44no—
250C13×C22⋊C4—44no—
251C13×C22⋊C4—44no—
252C13×C22⋊C4—44no—
253C13×C22⋊C4—44no—
254C42×C13—44no—
255C42×C13—44no—
256C42×C13—44no—
257C2×#400C2×C1311yescharacteristic, complemented
258C2×#397C2×C1311yescharacteristic
259#1443C2×C1311yescharacteristic, complemented
260#1443C2×C1311yescharacteristic, complemented
261#1442C2×C1311yescharacteristic, complemented
262#1440C2×C1311yescharacteristic
263#1439C2×C1311yescharacteristic
264#1439C2×C1311yescharacteristic
265#1437C2×C1311yescharacteristic
266#1437C2×C1311yescharacteristic
267#1437C2×C1311yescharacteristic
268#1436C2×C1311yescharacteristic, complemented
269#1436C2×C1311yescharacteristic, complemented
270#1436C2×C1311yescharacteristic, complemented
271C4×#95C2×C1311yescharacteristic, complemented
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13C22×D411yescharacteristic
308C23×C13C2×#4111yescharacteristic
309C23×C13C2×#4111yescharacteristic
310C23×C13C2×#4111yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C132−1+411yescharacteristic
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13#12614yes—
420C22×C4⋊C4C22×C1311yescharacteristic
421C22×C4⋊C4C22×C1311yescharacteristic
422C22×C4⋊C4C22×C1311yescharacteristic
423C22×C22⋊C4C22×C1311yescharacteristic
424C22×C22⋊C4C22×C1311yescharacteristic
425C22×C22⋊C4C22×C1311yescharacteristic
426C22×C22⋊C4C22×C1311yescharacteristic
427C22×C22⋊C4C22×C1311yescharacteristic
428C22×C22⋊C4C22×C1311yescharacteristic
429C22×C22⋊C4C22×C1311yescharacteristic
430C22×C42C22×C1311yescharacteristic
431C22×C42C22×C1311yescharacteristic
432C22×C42C22×C1311yescharacteristic
433#400—24no—
434#397—24no—
435C2×#95C22×C1311yescharacteristic
436C2×#95C22×C1311yescharacteristic
437C2×#95C22×C1311yescharacteristic
438C2×#95C22×C1311yescharacteristic
439C2×#95C22×C1311yescharacteristic
440C2×#95C22×C1311yescharacteristic
441C2×#95C22×C1311yescharacteristic
442C2×#95C22×C1311yescharacteristic
443C2×#95C22×C1311yescharacteristic
444C2×#95C22×C1311yescharacteristic
445C2×#95C22×C1311yescharacteristic
446C2×#95C22×C1311yescharacteristic
447C2×#95C22×C1311yescharacteristic
448C2×#95C22×C1311yescharacteristic
449C2×#95C22×C1311yescharacteristic
450C2×#95C22×C1311yescharacteristic
451C2×#95C22×C1311yescharacteristic
452C2×#95C22×C1311yescharacteristic
453C2×#95C22×C1311yescharacteristic
454C2×#95C22×C1311yescharacteristic
455C2×#95C22×C1311yescharacteristic
456C2×#95C22×C1311yescharacteristic
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—81no—
465C22×C13—81no—
466C22×C13—81no—
467C22×C13—81no—
468C22×C13—81no—
469C22×C13—81no—
470C22×C13—81no—
471C22×C13—81no—
472C22×C13C2×#12611yescharacteristic
473C22×C13#52911yescharacteristic
474C22×C13#52911yescharacteristic
475C22×C13#52911yescharacteristic
476C22×C13#52911yescharacteristic
477C22×C13#52911yescharacteristic
478C22×C13#52911yescharacteristic
479C22×C13#52911yescharacteristic
480C22×C13#52911yescharacteristic
481C22×C13#52911yescharacteristic
482C22×C13#53211yescharacteristic
483C22×C13#53211yescharacteristic
484C22×C13#53211yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53811yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#53911yescharacteristic
491C22×C13#54611yescharacteristic
492C22×C13#54611yescharacteristic
493C22×C13#54611yescharacteristic
494C22×C13#54811yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55211yescharacteristic
499C22×C13#55211yescharacteristic
500C22×C13#55311yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55611yescharacteristic
505C22×C13#55911yescharacteristic
506C22×C13#55911yescharacteristic
507C4×C13—24no—
508C4×C13—42no—
509C4×C13—42no—
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—42no—
514C4×C13—42no—
515C4×C13—42no—
516C4×C13—42no—
517C4×C13—81no—
518C4×C13—81no—
519C4×C13—81no—
520C4×C13—81no—
521C25C23×C1311yescharacteristic
522C23×C4C23×C1311yescharacteristic
523C23×C4C23×C1311yescharacteristic
524C23×C4C23×C1311yescharacteristic
525C23×C4C23×C1311yescharacteristic
526C23×C4C23×C1311yescharacteristic
527C23×C4C23×C1311yescharacteristic
528C23×C4C23×C1311yescharacteristic
529C23×C4C23×C1311yescharacteristic
530C23×C4C23×C1311yescharacteristic
531C23×C4C23×C1311yescharacteristic
532C23×C4C23×C1311yescharacteristic
533C23×C4C23×C1311yescharacteristic
534C23×C4C23×C1311yescharacteristic
535C23×C4C23×C1311yescharacteristic
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42—41no—
574C2×C42—41no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95D4×C1314yes—
597C2×C13—82no—
598C2×C13#240111yescharacteristic
599C2×C13#255711yescharacteristic
600C2×C13#255711yescharacteristic
601C2×C13#255811yescharacteristic
602C2×C13#255811yescharacteristic
603C2×C13#255911yescharacteristic
604C2×C13#256011yescharacteristic
605C2×C13#257511yescharacteristic
606C2×C13#257711yescharacteristic
607C2×C13#257811yescharacteristic
608C2×C13#259511yescharacteristic
609C2×C13#259611yescharacteristic
610C2×C13#259711yescharacteristic
611C2×C13#264311yescharacteristic
612C2×C13#286011yescharacteristic
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24C13×#4112yes—
628C24C24×C1311yescharacteristic
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4C2×D4×C1312yes—
716C22×C4C2×D4×C1312yes—
717C22×C4C2×D4×C1312yes—
718C22×C4C13×#4112yes—
719C22×C4C13×#4112yes—
720C22×C4C13×#4112yes—
721C22×C4C13×#4112yes—
722C22×C4C13×#4112yes—
723C22×C4C13×#4112yes—
724C22×C4C13×#4112yes—
725C22×C4C13×#4112yes—
726C22×C4C13×#4112yes—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C42—44no—
738C42—44no—
739C42—44no—
740C13#1516911yescharacteristic, direct product factor, Sylow
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23C22×D4×C1311yescharacteristic
777C23C2×C13×#4111yescharacteristic
778C23C2×C13×#4111yescharacteristic
779C23C2×C13×#4111yescharacteristic
780C23C2×C13×#4111yescharacteristic
781C23C2×C13×#4111yescharacteristic
782C23C2×C13×#4111yescharacteristic
783C23C2×C13×#4111yescharacteristic
784C23C2×C13×#4111yescharacteristic
785C23C2×C13×#4111yescharacteristic
786C23C2×C13×#4111yescharacteristic
787C23C13×H(5,𝔽2)11yescharacteristic
788C23C13×H(5,𝔽2)11yescharacteristic
789C23C13×H(5,𝔽2)11yescharacteristic
790C23C13×2−1+411yescharacteristic
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4C13×#12614yes—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22C2×C13×#12611yescharacteristic
905C22C13×#52911yescharacteristic
906C22C13×#52911yescharacteristic
907C22C13×#52911yescharacteristic
908C22C13×#52911yescharacteristic
909C22C13×#52911yescharacteristic
910C22C13×#52911yescharacteristic
911C22C13×#52911yescharacteristic
912C22C13×#52911yescharacteristic
913C22C13×#52911yescharacteristic
914C22C13×#53211yescharacteristic
915C22C13×#53211yescharacteristic
916C22C13×#53211yescharacteristic
917C22C13×#53811yescharacteristic
918C22C13×#53811yescharacteristic
919C22C13×#53811yescharacteristic
920C22C13×#53911yescharacteristic
921C22C13×#53911yescharacteristic
922C22C13×#53911yescharacteristic
923C22C13×#54611yescharacteristic
924C22C13×#54611yescharacteristic
925C22C13×#54611yescharacteristic
926C22C13×#54811yescharacteristic
927C22C13×#55111yescharacteristic
928C22C13×#55111yescharacteristic
929C22C13×#55111yescharacteristic
930C22C13×#55211yescharacteristic
931C22C13×#55211yescharacteristic
932C22C13×#55311yescharacteristic
933C22C13×#55311yescharacteristic
934C22C13×#55311yescharacteristic
935C22C13×#55311yescharacteristic
936C22C13×#55611yescharacteristic
937C22C13×#55911yescharacteristic
938C22C13×#55911yescharacteristic
939C4—24no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4—81no—
952C4—81no—
953C2—82no—
954C2C13×#240111yescharacteristic
955C2C13×#255711yescharacteristic
956C2C13×#255711yescharacteristic
957C2C13×#255811yescharacteristic
958C2C13×#255811yescharacteristic
959C2C13×#255911yescharacteristic
960C2C13×#256011yescharacteristic
961C2C13×#257511yescharacteristic
962C2C13×#257711yescharacteristic
963C2C13×#257811yescharacteristic
964C2C13×#259511yescharacteristic
965C2C13×#259611yescharacteristic
966C2C13×#259711yescharacteristic
967C2C13×#264311yescharacteristic
968C2C13×#286011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#400C2semidirect
3. C13×#1443C2semidirect
4. C13×#1443C2semidirect
5. C13×#1442C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C4×C13×#95C2semidirect
129. #15169C13direct (N × H)
257. C2×#400C2×C13semidirect
259. #1443C2×C13semidirect
260. #1443C2×C13semidirect
261. #1442C2×C13semidirect
268. #1436C2×C13semidirect
269. #1436C2×C13semidirect
270. #1436C2×C13semidirect
271. C4×#95C2×C13semidirect
740. C13#15169direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4002
C2×C13×#3972
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C4×C13×#952
#1516913