Finite Group Databasebeta

← C13×#15004 #15701343

Subgroups — C13×#15004 #15701343

Order 3328.

1466 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#400C211yesmaximal, characteristic, complemented
2C2×C13×#393C211yesmaximal, characteristic
3C2×C13×#391C211yesmaximal, characteristic, complemented
4C2×C13×#388C211yesmaximal, characteristic
5C13×#1446C211yesmaximal, characteristic, complemented
6C13×#1443C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic
9C13×#1440C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1437C211yesmaximal, characteristic
13C13×#1434C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
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×#393—24no—
31C13×#391—24no—
32C13×#388—24no—
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
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C25×C13C2311yescharacteristic
56C22×Q8×C13—22no—
57C22×Q8×C13—22no—
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—41no—
62C22×Q8×C13—41no—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
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—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—41no—
101C2×C13×C22⋊C4—41no—
102C2×C13×C22⋊C4—41no—
103C2×C13×C22⋊C4—41no—
104C2×C42×C13—22no—
105C2×C42×C13—22no—
106C2×C42×C13—22no—
107C2×C42×C13—22no—
108C2×C42×C13—22no—
109C2×C42×C13—22no—
110C2×C42×C13—22no—
111C2×C42×C13—41no—
112C2×C42×C13—41no—
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—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—41no—
132C13×#95—41no—
133C13×#95D414yes—
134C13×#95D414yes—
135#15004C1311yesmaximal, characteristic, direct product factor, Sylow
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—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13#4112yes—
151C24×C13C2411yescharacteristic
152C2×Q8×C13—28no—
153C2×Q8×C13—44no—
154C2×Q8×C13—44no—
155C2×Q8×C13—44no—
156C2×Q8×C13—44no—
157C2×Q8×C13—44no—
158C2×Q8×C13—44no—
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×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×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13#4112yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C13×C4⋊C4—44no—
258C13×C4⋊C4—44no—
259C13×C22⋊C4—28no—
260C13×C22⋊C4—44no—
261C13×C22⋊C4—44no—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4—44no—
266C42×C13—44no—
267C42×C13—44no—
268C42×C13—44no—
269C2×#400C2×C1311yescharacteristic, complemented
270C2×#393C2×C1311yescharacteristic
271C2×#391C2×C1311yescharacteristic, complemented
272C2×#388C2×C1311yescharacteristic
273#1446C2×C1311yescharacteristic, complemented
274#1443C2×C1311yescharacteristic, complemented
275#1442C2×C1311yescharacteristic, complemented
276#1440C2×C1311yescharacteristic
277#1440C2×C1311yescharacteristic
278#1439C2×C1311yescharacteristic
279#1437C2×C1311yescharacteristic
280#1437C2×C1311yescharacteristic
281#1434C2×C1311yescharacteristic, complemented
282#1434C2×C1311yescharacteristic, complemented
283C4×#95C2×C1311yescharacteristic, complemented
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
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×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13C22×D411yescharacteristic
320C23×C13C22×D411yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13H(5,𝔽2)11yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C132−1+411yescharacteristic
333C23×C132−1+411yescharacteristic
334Q8×C13—416no—
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—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
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—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13#12414yes—
432C2×C4×C13#12414yes—
433C23×Q8C22×C1311yescharacteristic
434C22×C4⋊C4C22×C1311yescharacteristic
435C22×C4⋊C4C22×C1311yescharacteristic
436C22×C22⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1311yescharacteristic
439C22×C22⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1311yescharacteristic
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1311yescharacteristic
443C22×C42C22×C1311yescharacteristic
444C22×C42C22×C1311yescharacteristic
445C22×C42C22×C1311yescharacteristic
446#400—24no—
447#393—24no—
448#391—24no—
449#388—24no—
450C2×#95C22×C1311yescharacteristic
451C2×#95C22×C1311yescharacteristic
452C2×#95C22×C1311yescharacteristic
453C2×#95C22×C1311yescharacteristic
454C2×#95C22×C1311yescharacteristic
455C2×#95C22×C1311yescharacteristic
456C2×#95C22×C1311yescharacteristic
457C2×#95C22×C1311yescharacteristic
458C2×#95C22×C1311yescharacteristic
459C2×#95C22×C1311yescharacteristic
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—81no—
480C22×C13—81no—
481C22×C13—81no—
482C22×C13—81no—
483C22×C13—81no—
484C22×C13—81no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13#52511yescharacteristic
488C22×C13#52511yescharacteristic
489C22×C13C2×#12411yescharacteristic
490C22×C13C2×#12411yescharacteristic
491C22×C13#52911yescharacteristic
492C22×C13#52911yescharacteristic
493C22×C13#52911yescharacteristic
494C22×C13#52911yescharacteristic
495C22×C13#52911yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13#52911yescharacteristic
498C22×C13#53211yescharacteristic
499C22×C13#53211yescharacteristic
500C22×C13#53811yescharacteristic
501C22×C13#53911yescharacteristic
502C22×C13#54111yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13#54211yescharacteristic
506C22×C13D4211yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13#54711yescharacteristic
511C22×C13#54811yescharacteristic
512C22×C13#54811yescharacteristic
513C22×C13#55111yescharacteristic
514C22×C13#55111yescharacteristic
515C22×C13#55111yescharacteristic
516C22×C13#55111yescharacteristic
517C22×C13#55211yescharacteristic
518C22×C13#55211yescharacteristic
519C22×C13#55511yescharacteristic
520C22×C13#55611yescharacteristic
521C22×C13#55611yescharacteristic
522C4×C13—24no—
523C4×C13—24no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—42no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—81no—
533C4×C13—81no—
534C4×C13—81no—
535C4×C13—81no—
536C25C23×C1311yescharacteristic
537C22×Q8—22no—
538C22×Q8—22no—
539C22×Q8—22no—
540C22×Q8—22no—
541C22×Q8—22no—
542C22×Q8—41no—
543C22×Q8—41no—
544C23×C4C23×C1311yescharacteristic
545C23×C4C23×C1311yescharacteristic
546C23×C4C23×C1311yescharacteristic
547C23×C4C23×C1311yescharacteristic
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C23×C4C23×C1311yescharacteristic
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—41no—
593C2×C42—41no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—41no—
614#95D4×C1314yes—
615#95D4×C1314yes—
616C2×C13—82no—
617C2×C13#239811yescharacteristic
618C2×C13#246111yescharacteristic
619C2×C13#246911yescharacteristic
620C2×C13#247211yescharacteristic
621C2×C13#247711yescharacteristic
622C2×C13#248811yescharacteristic
623C2×C13#248911yescharacteristic
624C2×C13#249111yescharacteristic
625C2×C13#252111yescharacteristic
626C2×C13#252711yescharacteristic
627C2×C13#253211yescharacteristic
628C2×C13#256011yescharacteristic
629C2×C13#257211yescharacteristic
630C2×C13#265011yescharacteristic
631C2×C13#286111yescharacteristic
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24C13×#4112yes—
647C24C24×C1311yescharacteristic
648C2×Q8—28no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—44no—
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×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4C2×D4×C1312yes—
740C22×C4C2×D4×C1312yes—
741C22×C4C2×D4×C1312yes—
742C22×C4C2×D4×C1312yes—
743C22×C4C2×D4×C1312yes—
744C22×C4C2×D4×C1312yes—
745C22×C4C13×#4112yes—
746C22×C4C13×#4112yes—
747C22×C4C13×#4112yes—
748C22×C4C13×#4112yes—
749C22×C4C13×#4112yes—
750C22×C4C13×#4112yes—
751C22×C4C13×#4112yes—
752C22×C4C13×#4112yes—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C42—44no—
763C42—44no—
764C42—44no—
765C13#1500411yescharacteristic, direct product factor, Sylow
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23C22×D4×C1311yescharacteristic
802C23C22×D4×C1311yescharacteristic
803C23C2×C13×#4111yescharacteristic
804C23C2×C13×#4111yescharacteristic
805C23C2×C13×#4111yescharacteristic
806C23C2×C13×#4111yescharacteristic
807C23C2×C13×#4111yescharacteristic
808C23C2×C13×#4111yescharacteristic
809C23C2×C13×#4111yescharacteristic
810C23C2×C13×#4111yescharacteristic
811C23C2×C13×#4111yescharacteristic
812C23C13×H(5,𝔽2)11yescharacteristic
813C23C13×H(5,𝔽2)11yescharacteristic
814C23C13×2−1+411yescharacteristic
815C23C13×2−1+411yescharacteristic
816Q8—416no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
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×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4C13×#12414yes—
914C2×C4C13×#12414yes—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22C13×#52511yescharacteristic
931C22C13×#52511yescharacteristic
932C22C2×C13×#12411yescharacteristic
933C22C2×C13×#12411yescharacteristic
934C22C13×#52911yescharacteristic
935C22C13×#52911yescharacteristic
936C22C13×#52911yescharacteristic
937C22C13×#52911yescharacteristic
938C22C13×#52911yescharacteristic
939C22C13×#52911yescharacteristic
940C22C13×#52911yescharacteristic
941C22C13×#53211yescharacteristic
942C22C13×#53211yescharacteristic
943C22C13×#53811yescharacteristic
944C22C13×#53911yescharacteristic
945C22C13×#54111yescharacteristic
946C22C13×#54211yescharacteristic
947C22C13×#54211yescharacteristic
948C22C13×#54211yescharacteristic
949C22D42×C1311yescharacteristic
950C22C13×#54611yescharacteristic
951C22C13×#54611yescharacteristic
952C22C13×#54711yescharacteristic
953C22C13×#54711yescharacteristic
954C22C13×#54811yescharacteristic
955C22C13×#54811yescharacteristic
956C22C13×#55111yescharacteristic
957C22C13×#55111yescharacteristic
958C22C13×#55111yescharacteristic
959C22C13×#55111yescharacteristic
960C22C13×#55211yescharacteristic
961C22C13×#55211yescharacteristic
962C22C13×#55511yescharacteristic
963C22C13×#55611yescharacteristic
964C22C13×#55611yescharacteristic
965C4—24no—
966C4—24no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C4—81no—
978C4—81no—
979C2—82no—
980C2C13×#239811yescharacteristic
981C2C13×#246111yescharacteristic
982C2C13×#246911yescharacteristic
983C2C13×#247211yescharacteristic
984C2C13×#247711yescharacteristic
985C2C13×#248811yescharacteristic
986C2C13×#248911yescharacteristic
987C2C13×#249111yescharacteristic
988C2C13×#252111yescharacteristic
989C2C13×#252711yescharacteristic
990C2C13×#253211yescharacteristic
991C2C13×#256011yescharacteristic
992C2C13×#257211yescharacteristic
993C2C13×#265011yescharacteristic
994C2C13×#286111yescharacteristic
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. C2×C13×#391C2semidirect
5. C13×#1446C2semidirect
6. C13×#1443C2semidirect
7. C13×#1442C2semidirect
13. C13×#1434C2semidirect
14. C13×#1434C2semidirect
15. C4×C13×#95C2semidirect
135. #15004C13direct (N × H)
269. C2×#400C2×C13semidirect
271. C2×#391C2×C13semidirect
273. #1446C2×C13semidirect
274. #1443C2×C13semidirect
275. #1442C2×C13semidirect
281. #1434C2×C13semidirect
282. #1434C2×C13semidirect
283. C4×#95C2×C13semidirect
765. C13#15004direct (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×#3932
C2×C13×#3912
C2×C13×#3882
C13×#14462
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14372
C13×#14342
C4×C13×#952
#1500413