Finite Group Databasebeta

← C13×#15297 #15701636

Subgroups — C13×#15297 #15701636

Order 3328.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic, complemented
2C2×C13×#396C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic, complemented
4C2×C13×#379C211yesmaximal, characteristic
5C2×C13×#379C211yesmaximal, characteristic
6C2×C13×#379C211yesmaximal, characteristic
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×#1437C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic, complemented
16C26×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic, complemented
18C22×C13×C4⋊C4C2211yescharacteristic, complemented
19C22×C13×C4⋊C4C2211yescharacteristic, complemented
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×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×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic, complemented
39C13×#397—24no—
40C13×#396—24no—
41C13×#388—24no—
42C13×#379—24no—
43C13×#379—24no—
44C13×#379—24no—
45C2×C13×#95C2211yescharacteristic, complemented
46C2×C13×#95C2211yescharacteristic, complemented
47C2×C13×#95C2211yescharacteristic, complemented
48C2×C13×#95C2211yescharacteristic, complemented
49C2×C13×#95C2211yescharacteristic, complemented
50C2×C13×#95C2211yescharacteristic, complemented
51C2×C13×#95C2211yescharacteristic, complemented
52C2×C13×#95C2211yescharacteristic, complemented
53C2×C13×#95C2211yescharacteristic, complemented
54C2×C13×#95C2211yescharacteristic, complemented
55C2×C13×#95C2211yescharacteristic, complemented
56C2×C13×#95C2211yescharacteristic, complemented
57C25×C13—22no—
58C25×C13—22no—
59C25×C13—22no—
60C25×C13—22no—
61C25×C13—22no—
62C25×C13—22no—
63C25×C13—22no—
64C25×C13—22no—
65C25×C13—22no—
66C25×C13—41no—
67C25×C13—41no—
68C25×C13—41no—
69C25×C13—41no—
70C25×C13—41no—
71C25×C13—41no—
72C25×C13C2311yescharacteristic
73C25×C13C2311yescharacteristic
74C25×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
86C23×C4×C13C2311yescharacteristic
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—41no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4—41no—
95C2×C13×C4⋊C4—41no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
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—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—41no—
130C2×C13×C22⋊C4—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4—41no—
135C2×C13×C22⋊C4—41no—
136C2×C13×C22⋊C4—41no—
137C2×C13×C22⋊C4—41no—
138C2×C13×C22⋊C4—41no—
139C2×C13×C22⋊C4—41no—
140C2×C13×C22⋊C4—41no—
141C2×C13×C22⋊C4—41no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4D414yes—
148C2×C13×C22⋊C4D414yes—
149C2×C13×C22⋊C4D414yes—
150C2×C42×C13—22no—
151C2×C42×C13—41no—
152C2×C42×C13—41no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—41no—
160C13×#95—41no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95—41no—
164C13×#95—41no—
165#15297C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13—21no—
191C24×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—28no—
203C24×C13—28no—
204C24×C13—28no—
205C24×C13—44no—
206C24×C13—44no—
207C24×C13—44no—
208C24×C13—44no—
209C24×C13—44no—
210C24×C13—44no—
211C24×C13—44no—
212C24×C13—44no—
213C24×C13—44no—
214C24×C13—44no—
215C24×C13—44no—
216C24×C13—44no—
217C24×C13—44no—
218C24×C13—44no—
219C24×C13—44no—
220C24×C13—44no—
221C24×C13—44no—
222C24×C13—44no—
223C24×C13—44no—
224C24×C13—44no—
225C24×C13—44no—
226C24×C13—44no—
227C24×C13—44no—
228C24×C13—44no—
229C24×C13—44no—
230C24×C13—44no—
231C24×C13—44no—
232C24×C13—44no—
233C24×C13—44no—
234C24×C13—44no—
235C24×C13—44no—
236C24×C13—44no—
237C24×C13C2×D412yes—
238C24×C13C2×D412yes—
239C24×C13C2×D412yes—
240C24×C13#4112yes—
241C24×C13#4112yes—
242C24×C13#4112yes—
243C24×C13#4112yes—
244C24×C13#4112yes—
245C24×C13#4112yes—
246C24×C13C2411yescharacteristic
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—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13—21no—
308C22×C4×C13—21no—
309C22×C4×C13—21no—
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—21no—
315C22×C4×C13—21no—
316C22×C4×C13—21no—
317C22×C4×C13—21no—
318C22×C4×C13—21no—
319C22×C4×C13—21no—
320C22×C4×C13—21no—
321C22×C4×C13—21no—
322C22×C4×C13—21no—
323C22×C4×C13—21no—
324C22×C4×C13—21no—
325C22×C4×C13C2×D412yes—
326C22×C4×C13C2×D412yes—
327C22×C4×C13C2×D412yes—
328C22×C4×C13C2×D412yes—
329C22×C4×C13C2×D412yes—
330C22×C4×C13C2×D412yes—
331C13×C4⋊C4—44no—
332C13×C4⋊C4—44no—
333C13×C4⋊C4—44no—
334C13×C22⋊C4—28no—
335C13×C22⋊C4—44no—
336C13×C22⋊C4—44no—
337C13×C22⋊C4—44no—
338C13×C22⋊C4—44no—
339C13×C22⋊C4—44no—
340C13×C22⋊C4—44no—
341C13×C22⋊C4—44no—
342C13×C22⋊C4—44no—
343C13×C22⋊C4—44no—
344C13×C22⋊C4—44no—
345C13×C22⋊C4—44no—
346C13×C22⋊C4—44no—
347C13×C22⋊C4—44no—
348C13×C22⋊C4—44no—
349C13×C22⋊C4—44no—
350C13×C22⋊C4—44no—
351C13×C22⋊C4—44no—
352C42×C13—44no—
353C2×#397C2×C1311yescharacteristic, complemented
354C2×#396C2×C1311yescharacteristic, complemented
355C2×#388C2×C1311yescharacteristic, complemented
356C2×#379C2×C1311yescharacteristic
357C2×#379C2×C1311yescharacteristic
358C2×#379C2×C1311yescharacteristic
359#1440C2×C1311yescharacteristic, complemented
360#1440C2×C1311yescharacteristic, complemented
361#1440C2×C1311yescharacteristic, complemented
362#1439C2×C1311yescharacteristic, complemented
363#1439C2×C1311yescharacteristic, complemented
364#1439C2×C1311yescharacteristic, complemented
365#1439C2×C1311yescharacteristic, complemented
366#1437C2×C1311yescharacteristic, complemented
367#1437C2×C1311yescharacteristic, complemented
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—22no—
396C23×C13—22no—
397C23×C13—22no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—22no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13—22no—
405C23×C13—22no—
406C23×C13—22no—
407C23×C13—22no—
408C23×C13—22no—
409C23×C13—22no—
410C23×C13—22no—
411C23×C13—22no—
412C23×C13—22no—
413C23×C13—22no—
414C23×C13—22no—
415C23×C13—22no—
416C23×C13—22no—
417C23×C13—22no—
418C23×C13—22no—
419C23×C13—22no—
420C23×C13—22no—
421C23×C13—22no—
422C23×C13—416no—
423C23×C13—416no—
424C23×C13—416no—
425C23×C13—416no—
426C23×C13—416no—
427C23×C13—416no—
428C23×C13—416no—
429C23×C13—416no—
430C23×C13—416no—
431C23×C13—416no—
432C23×C13—416no—
433C23×C13—416no—
434C23×C13—416no—
435C23×C13—416no—
436C23×C13—416no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13—41no—
460C23×C13—41no—
461C23×C13—41no—
462C23×C13—41no—
463C23×C13—41no—
464C23×C13—41no—
465C23×C13—41no—
466C23×C13—41no—
467C23×C13—41no—
468C23×C13—41no—
469C23×C13—41no—
470C23×C13—41no—
471C23×C13—41no—
472C23×C13—41no—
473C23×C13—41no—
474C23×C13—41no—
475C23×C13—41no—
476C23×C13—41no—
477C23×C13—41no—
478C23×C13—41no—
479C23×C13—41no—
480C23×C13—41no—
481C23×C13—41no—
482C23×C13—41no—
483C23×C13—41no—
484C23×C13—41no—
485C23×C13#12114yes—
486C23×C13#12414yes—
487C23×C13#12614yes—
488C23×C13C22×D411yescharacteristic
489C23×C13C22×D411yescharacteristic
490C23×C13C22×D411yescharacteristic
491C23×C13C2×#4111yescharacteristic
492C23×C13C2×#4111yescharacteristic
493C23×C13C2×#4111yescharacteristic
494C23×C13C2×#4111yescharacteristic
495C23×C13C2×#4111yescharacteristic
496C23×C13C2×#4111yescharacteristic
497C23×C13H(5,𝔽2)11yescharacteristic
498C23×C13H(5,𝔽2)11yescharacteristic
499C23×C13H(5,𝔽2)11yescharacteristic
500C23×C13H(5,𝔽2)11yescharacteristic
501C23×C13H(5,𝔽2)11yescharacteristic
502C23×C13H(5,𝔽2)11yescharacteristic
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—22no—
512C2×C4×C13—22no—
513C2×C4×C13—22no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—22no—
518C2×C4×C13—22no—
519C2×C4×C13—22no—
520C2×C4×C13—22no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13—41no—
524C2×C4×C13—41no—
525C2×C4×C13—41no—
526C2×C4×C13—41no—
527C2×C4×C13—41no—
528C2×C4×C13—41no—
529C2×C4×C13—41no—
530C2×C4×C13—41no—
531C2×C4×C13—41no—
532C2×C4×C13—41no—
533C2×C4×C13—41no—
534C2×C4×C13—41no—
535C2×C4×C13—41no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—41no—
541C2×C4×C13—41no—
542C2×C4×C13—41no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13—41no—
563C2×C4×C13—41no—
564C2×C4×C13—41no—
565C2×C4×C13—41no—
566C2×C4×C13—41no—
567C2×C4×C13—41no—
568C2×C4×C13—41no—
569C2×C4×C13—41no—
570C2×C4×C13—41no—
571C2×C4×C13—41no—
572C2×C4×C13—41no—
573C2×C4×C13—41no—
574C2×C4×C13—41no—
575C2×C4×C13—41no—
576C2×C4×C13—41no—
577C2×C4×C13—41no—
578C2×C4×C13—41no—
579C2×C4×C13—41no—
580C2×C4×C13—41no—
581C2×C4×C13—41no—
582C2×C4×C13—41no—
583C2×C4×C13—41no—
584C2×C4×C13—41no—
585C2×C4×C13—41no—
586C2×C4×C13—41no—
587C26C22×C1311yescharacteristic
588C22×C4⋊C4C22×C1311yescharacteristic, complemented
589C22×C4⋊C4C22×C1311yescharacteristic, complemented
590C22×C4⋊C4C22×C1311yescharacteristic, complemented
591C22×C22⋊C4C22×C1311yescharacteristic
592C22×C22⋊C4C22×C1311yescharacteristic
593C22×C22⋊C4C22×C1311yescharacteristic
594C22×C22⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598C22×C22⋊C4C22×C1311yescharacteristic
599C22×C22⋊C4C22×C1311yescharacteristic
600C22×C22⋊C4C22×C1311yescharacteristic
601C22×C22⋊C4C22×C1311yescharacteristic
602C22×C22⋊C4C22×C1311yescharacteristic
603C22×C22⋊C4C22×C1311yescharacteristic
604C22×C22⋊C4C22×C1311yescharacteristic
605C22×C22⋊C4C22×C1311yescharacteristic
606C22×C22⋊C4C22×C1311yescharacteristic
607C22×C22⋊C4C22×C1311yescharacteristic
608C22×C22⋊C4C22×C1311yescharacteristic
609C22×C42C22×C1311yescharacteristic, complemented
610#397—24no—
611#396—24no—
612#388—24no—
613#379—24no—
614#379—24no—
615#379—24no—
616C2×#95C22×C1311yescharacteristic, complemented
617C2×#95C22×C1311yescharacteristic, complemented
618C2×#95C22×C1311yescharacteristic, complemented
619C2×#95C22×C1311yescharacteristic, complemented
620C2×#95C22×C1311yescharacteristic, complemented
621C2×#95C22×C1311yescharacteristic, complemented
622C2×#95C22×C1311yescharacteristic, complemented
623C2×#95C22×C1311yescharacteristic, complemented
624C2×#95C22×C1311yescharacteristic, complemented
625C2×#95C22×C1311yescharacteristic, complemented
626C2×#95C22×C1311yescharacteristic, complemented
627C2×#95C22×C1311yescharacteristic, complemented
628C22×C13—24no—
629C22×C13—24no—
630C22×C13—24no—
631C22×C13—24no—
632C22×C13—24no—
633C22×C13—24no—
634C22×C13—24no—
635C22×C13—24no—
636C22×C13—24no—
637C22×C13—464no—
638C22×C13—42no—
639C22×C13—42no—
640C22×C13—42no—
641C22×C13—42no—
642C22×C13—42no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—42no—
650C22×C13—42no—
651C22×C13—42no—
652C22×C13—42no—
653C22×C13—42no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—42no—
659C22×C13—42no—
660C22×C13—42no—
661C22×C13—42no—
662C22×C13—42no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13—42no—
666C22×C13—42no—
667C22×C13—42no—
668C22×C13—42no—
669C22×C13—42no—
670C22×C13—42no—
671C22×C13—42no—
672C22×C13—42no—
673C22×C13—42no—
674C22×C13C2×#12111yescharacteristic
675C22×C13#52511yescharacteristic
676C22×C13#52511yescharacteristic
677C22×C13#52511yescharacteristic
678C22×C13C2×#12411yescharacteristic
679C22×C13C2×#12611yescharacteristic
680C22×C13#53411yescharacteristic
681C22×C13#53411yescharacteristic
682C22×C13#53511yescharacteristic
683C22×C13#53811yescharacteristic
684C22×C13#53811yescharacteristic
685C22×C13#53811yescharacteristic
686C22×C13#53811yescharacteristic
687C22×C13#53811yescharacteristic
688C22×C13#53811yescharacteristic
689C22×C13D4211yescharacteristic
690C22×C13D4211yescharacteristic
691C22×C13#54611yescharacteristic
692C22×C13#54611yescharacteristic
693C22×C13#54611yescharacteristic
694C22×C13#54611yescharacteristic
695C22×C13#54611yescharacteristic
696C22×C13#54611yescharacteristic
697C22×C13#54611yescharacteristic
698C22×C13#54611yescharacteristic
699C22×C13#55111yescharacteristic
700C22×C13#55111yescharacteristic
701C22×C13#55111yescharacteristic
702C22×C13#55111yescharacteristic
703C22×C13#55111yescharacteristic
704C22×C13#55111yescharacteristic
705C22×C13#55111yescharacteristic
706C22×C13#55111yescharacteristic
707C22×C13#56011yescharacteristic
708C22×C13#56011yescharacteristic
709C4×C13—42no—
710C4×C13—42no—
711C4×C13—42no—
712C4×C13—42no—
713C4×C13—42no—
714C4×C13—42no—
715C4×C13—81no—
716C4×C13—81no—
717C4×C13—81no—
718C4×C13—81no—
719C4×C13—81no—
720C4×C13—81no—
721C25—22no—
722C25—22no—
723C25—22no—
724C25—22no—
725C25—22no—
726C25—22no—
727C25—22no—
728C25—22no—
729C25—22no—
730C25—41no—
731C25—41no—
732C25—41no—
733C25—41no—
734C25—41no—
735C25—41no—
736C25C23×C1311yescharacteristic
737C25C23×C1311yescharacteristic
738C25C23×C1311yescharacteristic
739C23×C4C23×C1311yescharacteristic
740C23×C4C23×C1311yescharacteristic
741C23×C4C23×C1311yescharacteristic
742C23×C4C23×C1311yescharacteristic
743C23×C4C23×C1311yescharacteristic
744C23×C4C23×C1311yescharacteristic
745C23×C4C23×C1311yescharacteristic
746C23×C4C23×C1311yescharacteristic
747C23×C4C23×C1311yescharacteristic
748C23×C4C23×C1311yescharacteristic
749C23×C4C23×C1311yescharacteristic
750C23×C4C23×C1311yescharacteristic
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—22no—
755C2×C4⋊C4—22no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C4⋊C4—41no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4D4×C1314yes—
812C2×C22⋊C4D4×C1314yes—
813C2×C22⋊C4D4×C1314yes—
814C2×C42—22no—
815C2×C42—41no—
816C2×C42—41no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—22no—
821#95—22no—
822#95—22no—
823#95—41no—
824#95—41no—
825#95—41no—
826#95—41no—
827#95—41no—
828#95—41no—
829C2×C13—44no—
830C2×C13—44no—
831C2×C13—44no—
832C2×C13#241111yescharacteristic
833C2×C13#242411yescharacteristic
834C2×C13#247211yescharacteristic
835C2×C13#247211yescharacteristic
836C2×C13#248011yescharacteristic
837C2×C13#248011yescharacteristic
838C2×C13#248011yescharacteristic
839C2×C13#253411yescharacteristic
840C2×C13#256111yescharacteristic
841C2×C13#266811yescharacteristic
842C2×C13#267811yescharacteristic
843C2×C13#268511yescharacteristic
844C2×C13#269711yescharacteristic
845C2×C13#273511yescharacteristic
846C2×C13#273511yescharacteristic
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—28no—
884C24—28no—
885C24—28no—
886C24—44no—
887C24—44no—
888C24—44no—
889C24—44no—
890C24—44no—
891C24—44no—
892C24—44no—
893C24—44no—
894C24—44no—
895C24—44no—
896C24—44no—
897C24—44no—
898C24—44no—
899C24—44no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—44no—
905C24—44no—
906C24—44no—
907C24—44no—
908C24—44no—
909C24—44no—
910C24—44no—
911C24—44no—
912C24—44no—
913C24—44no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24—44no—
918C24C2×D4×C1312yes—
919C24C2×D4×C1312yes—
920C24C2×D4×C1312yes—
921C24C13×#4112yes—
922C24C13×#4112yes—
923C24C13×#4112yes—
924C24C13×#4112yes—
925C24C13×#4112yes—
926C24C13×#4112yes—
927C24C24×C1311yescharacteristic
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4C2×D4×C1312yes—
1007C22×C4C2×D4×C1312yes—
1008C22×C4C2×D4×C1312yes—
1009C22×C4C2×D4×C1312yes—
1010C22×C4C2×D4×C1312yes—
1011C22×C4C2×D4×C1312yes—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C42—44no—
1034C13#1529711yescharacteristic, direct product factor, Sylow
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—416no—
1090C23—416no—
1091C23—416no—
1092C23—416no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—416no—
1097C23—416no—
1098C23—416no—
1099C23—416no—
1100C23—416no—
1101C23—416no—
1102C23—416no—
1103C23—416no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23C13×#12114yes—
1153C23C13×#12414yes—
1154C23C13×#12614yes—
1155C23C22×D4×C1311yescharacteristic
1156C23C22×D4×C1311yescharacteristic
1157C23C22×D4×C1311yescharacteristic
1158C23C2×C13×#4111yescharacteristic
1159C23C2×C13×#4111yescharacteristic
1160C23C2×C13×#4111yescharacteristic
1161C23C2×C13×#4111yescharacteristic
1162C23C2×C13×#4111yescharacteristic
1163C23C2×C13×#4111yescharacteristic
1164C23C13×H(5,𝔽2)11yescharacteristic
1165C23C13×H(5,𝔽2)11yescharacteristic
1166C23C13×H(5,𝔽2)11yescharacteristic
1167C23C13×H(5,𝔽2)11yescharacteristic
1168C23C13×H(5,𝔽2)11yescharacteristic
1169C23C13×H(5,𝔽2)11yescharacteristic
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—464no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22C2×C13×#12111yescharacteristic
1301C22C13×#52511yescharacteristic
1302C22C13×#52511yescharacteristic
1303C22C13×#52511yescharacteristic
1304C22C2×C13×#12411yescharacteristic
1305C22C2×C13×#12611yescharacteristic
1306C22C13×#53411yescharacteristic
1307C22C13×#53411yescharacteristic
1308C22C13×#53511yescharacteristic
1309C22C13×#53811yescharacteristic
1310C22C13×#53811yescharacteristic
1311C22C13×#53811yescharacteristic
1312C22C13×#53811yescharacteristic
1313C22C13×#53811yescharacteristic
1314C22C13×#53811yescharacteristic
1315C22D42×C1311yescharacteristic
1316C22D42×C1311yescharacteristic
1317C22C13×#54611yescharacteristic
1318C22C13×#54611yescharacteristic
1319C22C13×#54611yescharacteristic
1320C22C13×#54611yescharacteristic
1321C22C13×#54611yescharacteristic
1322C22C13×#54611yescharacteristic
1323C22C13×#54611yescharacteristic
1324C22C13×#54611yescharacteristic
1325C22C13×#55111yescharacteristic
1326C22C13×#55111yescharacteristic
1327C22C13×#55111yescharacteristic
1328C22C13×#55111yescharacteristic
1329C22C13×#55111yescharacteristic
1330C22C13×#55111yescharacteristic
1331C22C13×#55111yescharacteristic
1332C22C13×#55111yescharacteristic
1333C22C13×#56011yescharacteristic
1334C22C13×#56011yescharacteristic
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C2—44no—
1348C2—44no—
1349C2—44no—
1350C2C13×#241111yescharacteristic
1351C2C13×#242411yescharacteristic
1352C2C13×#247211yescharacteristic
1353C2C13×#247211yescharacteristic
1354C2C13×#248011yescharacteristic
1355C2C13×#248011yescharacteristic
1356C2C13×#248011yescharacteristic
1357C2C13×#253411yescharacteristic
1358C2C13×#256111yescharacteristic
1359C2C13×#266811yescharacteristic
1360C2C13×#267811yescharacteristic
1361C2C13×#268511yescharacteristic
1362C2C13×#269711yescharacteristic
1363C2C13×#273511yescharacteristic
1364C2C13×#273511yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC26×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×#397C2semidirect
2. C2×C13×#396C2semidirect
3. C2×C13×#388C2semidirect
7. C13×#1440C2semidirect
8. C13×#1440C2semidirect
9. C13×#1440C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1439C2semidirect
14. C13×#1437C2semidirect
15. C13×#1437C2semidirect
17. C22×C13×C4⋊C4C22semidirect
18. C22×C13×C4⋊C4C22semidirect
19. C22×C13×C4⋊C4C22semidirect
38. C22×C42×C13C22semidirect
45. C2×C13×#95C22semidirect
46. C2×C13×#95C22semidirect
47. C2×C13×#95C22semidirect
48. C2×C13×#95C22semidirect
49. C2×C13×#95C22semidirect
50. C2×C13×#95C22semidirect
51. C2×C13×#95C22semidirect
52. C2×C13×#95C22semidirect
53. C2×C13×#95C22semidirect
54. C2×C13×#95C22semidirect
55. C2×C13×#95C22semidirect
56. C2×C13×#95C22semidirect
165. #15297C13direct (N × H)
353. C2×#397C2×C13semidirect
354. C2×#396C2×C13semidirect
355. C2×#388C2×C13semidirect
359. #1440C2×C13semidirect
360. #1440C2×C13semidirect
361. #1440C2×C13semidirect
362. #1439C2×C13semidirect
363. #1439C2×C13semidirect
364. #1439C2×C13semidirect
365. #1439C2×C13semidirect
366. #1437C2×C13semidirect
367. #1437C2×C13semidirect
588. C22×C4⋊C4C22×C13semidirect
589. C22×C4⋊C4C22×C13semidirect
590. C22×C4⋊C4C22×C13semidirect
609. C22×C42C22×C13semidirect
616. C2×#95C22×C13semidirect
617. C2×#95C22×C13semidirect
618. C2×#95C22×C13semidirect
619. C2×#95C22×C13semidirect
620. C2×#95C22×C13semidirect
621. C2×#95C22×C13semidirect
622. C2×#95C22×C13semidirect
623. C2×#95C22×C13semidirect
624. C2×#95C22×C13semidirect
625. C2×#95C22×C13semidirect
626. C2×#95C22×C13semidirect
627. C2×#95C22×C13semidirect
1034. C13#15297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3962
C2×C13×#3882
C2×C13×#3792
C13×#14402
C13×#14392
C13×#14372
#1529713