Finite Group Databasebeta

← C13×#15375 #15701714

Subgroups — C13×#15375 #15701714

Order 3328.

2270 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic, complemented
2C2×C13×#392C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1443C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic, complemented
10C13×#1440C211yesmaximal, characteristic, complemented
11C13×#1440C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C22×C13×C4⋊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
35C13×#394—24no—
36C13×#392—24no—
37C13×#386—24no—
38C13×#386—24no—
39C13×#386—24no—
40C13×#386—24no—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—41no—
75C22×D4×C13—41no—
76C22×D4×C13—41no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13D414yes—
81C23×C4×C13—22no—
82C23×C4×C13—22no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—41no—
88C23×C4×C13—41no—
89C23×C4×C13—41no—
90C23×C4×C13—41no—
91C23×C4×C13—41no—
92C23×C4×C13—41no—
93C23×C4×C13—41no—
94C23×C4×C13—41no—
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—41no—
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—22no—
130C2×C13×C22⋊C4—22no—
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⋊C4D414yescomplemented
148C2×C13×C22⋊C4D414yescomplemented
149C13×#95—22no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—41no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95—41no—
164C13×#95—41no—
165#15375C1311yesmaximal, 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—21no—
203C24×C13—21no—
204C24×C13C2×D412yes—
205C24×C13C2×D412yes—
206C24×C13C2×D412yes—
207C24×C13C2×D412yes—
208C24×C13#4112yes—
209C24×C13#4112yes—
210C24×C13#4112yes—
211C24×C13C2411yescharacteristic
212C2×D4×C13—28no—
213C2×D4×C13—28no—
214C2×D4×C13—28no—
215C2×D4×C13—28no—
216C2×D4×C13—44no—
217C2×D4×C13—44no—
218C2×D4×C13—44no—
219C2×D4×C13—44no—
220C2×D4×C13—44no—
221C2×D4×C13—44no—
222C2×D4×C13—44no—
223C2×D4×C13—44no—
224C2×D4×C13—44no—
225C2×D4×C13—44no—
226C2×D4×C13—44no—
227C2×D4×C13—44no—
228C2×D4×C13—44no—
229C2×D4×C13—44no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C2×D4×C13—44no—
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—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—44no—
310C22×C4×C13—44no—
311C22×C4×C13—44no—
312C22×C4×C13—44no—
313C22×C4×C13—44no—
314C22×C4×C13—44no—
315C22×C4×C13—44no—
316C22×C4×C13—44no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
319C22×C4×C13—44no—
320C22×C4×C13—44no—
321C22×C4×C13—44no—
322C22×C4×C13—44no—
323C22×C4×C13C2×D412yes—
324C22×C4×C13C2×D412yes—
325C22×C4×C13C2×D412yes—
326C22×C4×C13C2×D412yes—
327C22×C4×C13C2×D412yes—
328C22×C4×C13#4112yes—
329C22×C4×C13#4112yes—
330C22×C4×C13#4112yes—
331C13×C4⋊C4—44no—
332C13×C22⋊C4—44no—
333C13×C22⋊C4—44no—
334C13×C22⋊C4—44no—
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—
345C2×#394C2×C1311yescharacteristic, complemented
346C2×#392C2×C1311yescharacteristic
347C2×#386C2×C1311yescharacteristic, complemented
348C2×#386C2×C1311yescharacteristic, complemented
349C2×#386C2×C1311yescharacteristic, complemented
350C2×#386C2×C1311yescharacteristic, complemented
351#1445C2×C1311yescharacteristic, complemented
352#1443C2×C1311yescharacteristic, complemented
353#1440C2×C1311yescharacteristic, complemented
354#1440C2×C1311yescharacteristic, complemented
355#1440C2×C1311yescharacteristic, complemented
356#1439C2×C1311yescharacteristic, complemented
357#1438C2×C1311yescharacteristic, complemented
358C22⋊#95C2×C1311yescharacteristic, complemented
359C22⋊#95C2×C1311yescharacteristic, complemented
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
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—41no—
404C23×C13—41no—
405C23×C13—41no—
406C23×C13—41no—
407C23×C13—41no—
408C23×C13—41no—
409C23×C13—41no—
410C23×C13—41no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13—41no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
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#12114yes—
464C23×C13#12314yes—
465C23×C13C22×D411yescharacteristic
466C23×C13C22×D411yescharacteristic
467C23×C13C22×D411yescharacteristic
468C23×C13C2×#4111yescharacteristic
469C23×C13C2×#4111yescharacteristic
470C23×C13C2×#4111yescharacteristic
471C23×C13C2×#4111yescharacteristic
472C23×C13C2×#4111yescharacteristic
473C23×C13C2×#4111yescharacteristic
474C23×C13H(5,𝔽2)11yescharacteristic
475C23×C13H(5,𝔽2)11yescharacteristic
476C23×C13H(5,𝔽2)11yescharacteristic
477C23×C13H(5,𝔽2)11yescharacteristic
478C23×C13H(5,𝔽2)11yescharacteristic
479C23×C13H(5,𝔽2)11yescharacteristic
480D4×C13—416no—
481D4×C13—416no—
482D4×C13—416no—
483C2×C4×C13—22no—
484C2×C4×C13—22no—
485C2×C4×C13—22no—
486C2×C4×C13—22no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—22no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13—22no—
494C2×C4×C13—22no—
495C2×C4×C13—22no—
496C2×C4×C13—22no—
497C2×C4×C13—22no—
498C2×C4×C13—22no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—416no—
508C2×C4×C13—416no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13—41no—
512C2×C4×C13—41no—
513C2×C4×C13—41no—
514C2×C4×C13—41no—
515C2×C4×C13—41no—
516C2×C4×C13—41no—
517C2×C4×C13—41no—
518C2×C4×C13—41no—
519C2×C4×C13—41no—
520C2×C4×C13—41no—
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—
569C23×D4C22×C1311yescharacteristic
570C23×D4C22×C1311yescharacteristic
571C23×D4C22×C1311yescharacteristic
572C24×C4C22×C1311yescharacteristic
573C24×C4C22×C1311yescharacteristic
574C22×C4⋊C4C22×C1311yescharacteristic
575C22×C22⋊C4C22×C1311yescharacteristic
576C22×C22⋊C4C22×C1311yescharacteristic
577C22×C22⋊C4C22×C1311yescharacteristic
578C22×C22⋊C4C22×C1311yescharacteristic
579C22×C22⋊C4C22×C1311yescharacteristic
580C22×C22⋊C4C22×C1311yescharacteristic
581C22×C22⋊C4C22×C1311yescharacteristic
582C22×C22⋊C4C22×C1311yescharacteristic
583C22×C22⋊C4C22×C1311yescharacteristic
584C22×C22⋊C4C22×C1311yescharacteristic
585C22×C22⋊C4C22×C1311yescharacteristic
586C22×C22⋊C4C22×C1311yescharacteristic
587C22×C22⋊C4C22×C1311yescharacteristic
588#394—24no—
589#392—24no—
590#386—24no—
591#386—24no—
592#386—24no—
593#386—24no—
594C2×#95C22×C1311yescharacteristic
595C2×#95C22×C1311yescharacteristic
596C2×#95C22×C1311yescharacteristic
597C2×#95C22×C1311yescharacteristic
598C2×#95C22×C1311yescharacteristic
599C2×#95C22×C1311yescharacteristic
600C2×#95C22×C1311yescharacteristic
601C2×#95C22×C1311yescharacteristic
602C2×#95C22×C1311yescharacteristic
603C2×#95C22×C1311yescharacteristic
604C2×#95C22×C1311yescharacteristic
605C2×#95C22×C1311yescharacteristic
606C2×#95C22×C1311yescharacteristic
607C2×#95C22×C1311yescharacteristic
608C2×#95C22×C1311yescharacteristic
609C2×#95C22×C1311yescharacteristic
610C22×C13—24no—
611C22×C13—24no—
612C22×C13—24no—
613C22×C13—24no—
614C22×C13—24no—
615C22×C13—24no—
616C22×C13—42no—
617C22×C13—42no—
618C22×C13—42no—
619C22×C13—42no—
620C22×C13—42no—
621C22×C13—42no—
622C22×C13—42no—
623C22×C13—42no—
624C22×C13—42no—
625C22×C13—42no—
626C22×C13—42no—
627C22×C13—42no—
628C22×C13—42no—
629C22×C13—42no—
630C22×C13—42no—
631C22×C13—42no—
632C22×C13—42no—
633C22×C13—42no—
634C22×C13—42no—
635C22×C13—42no—
636C22×C13—42no—
637C22×C13—42no—
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—81no—
648C22×C13—81no—
649C22×C13—81no—
650C22×C13—81no—
651C22×C13—81no—
652C22×C13—81no—
653C22×C13—81no—
654C22×C13—81no—
655C22×C13C2×#12111yescharacteristic
656C22×C13C2×#12311yescharacteristic
657C22×C13#52511yescharacteristic
658C22×C13#52511yescharacteristic
659C22×C13#52911yescharacteristic
660C22×C13#53211yescharacteristic
661C22×C13#53411yescharacteristic
662C22×C13#53411yescharacteristic
663C22×C13#53411yescharacteristic
664C22×C13#53811yescharacteristic
665C22×C13#53811yescharacteristic
666C22×C13#53811yescharacteristic
667C22×C13#53811yescharacteristic
668C22×C13#54011yescharacteristic
669C22×C13#54011yescharacteristic
670C22×C13D4211yescharacteristic
671C22×C13D4211yescharacteristic
672C22×C13#54611yescharacteristic
673C22×C13#54611yescharacteristic
674C22×C13#54611yescharacteristic
675C22×C13#54611yescharacteristic
676C22×C13#54611yescharacteristic
677C22×C13#54611yescharacteristic
678C22×C13#54611yescharacteristic
679C22×C13#54611yescharacteristic
680C22×C13#55111yescharacteristic
681C22×C13#55111yescharacteristic
682C22×C13#55111yescharacteristic
683C22×C13#55311yescharacteristic
684C22×C13#55311yescharacteristic
685C22×C13#55311yescharacteristic
686C22×C13#55311yescharacteristic
687C22×C13#55911yescharacteristic
688C22×C13#56011yescharacteristic
689C22×C13#56011yescharacteristic
690C4×C13—42no—
691C4×C13—42no—
692C4×C13—42no—
693C4×C13—42no—
694C4×C13—42no—
695C4×C13—42no—
696C4×C13—42no—
697C4×C13—42no—
698C4×C13—81no—
699C4×C13—81no—
700C4×C13—81no—
701C4×C13—81no—
702C25C23×C1311yescharacteristic
703C25C23×C1311yescharacteristic
704C25C23×C1311yescharacteristic
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4D4×C1314yes—
726C23×C4—22no—
727C23×C4—22no—
728C23×C4—22no—
729C23×C4—22no—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—41no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4—41no—
738C23×C4—41no—
739C23×C4—41no—
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
751C23×C4C23×C1311yescharacteristic
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—41no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
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—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4D4×C1314yescomplemented
793C2×C22⋊C4D4×C1314yescomplemented
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—22no—
802#95—22no—
803#95—22no—
804#95—22no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95—41no—
810C2×C13—44no—
811C2×C13—44no—
812C2×C13—82no—
813C2×C13#241211yescharacteristic
814C2×C13#241811yescharacteristic
815C2×C13#242411yescharacteristic
816C2×C13#244411yescharacteristic
817C2×C13#245711yescharacteristic
818C2×C13#246411yescharacteristic
819C2×C13#254311yescharacteristic
820C2×C13#255711yescharacteristic
821C2×C13#260011yescharacteristic
822C2×C13#266811yescharacteristic
823C2×C13#266811yescharacteristic
824C2×C13#268811yescharacteristic
825C2×C13#270911yescharacteristic
826C2×C13#274911yescharacteristic
827C2×C13#277811yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
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—
866C24C2×D4×C1312yes—
867C24C2×D4×C1312yes—
868C24C2×D4×C1312yes—
869C24C2×D4×C1312yes—
870C24C13×#4112yes—
871C24C13×#4112yes—
872C24C13×#4112yes—
873C24C24×C1311yescharacteristic
874C2×D4—28no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
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—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4C2×D4×C1312yes—
986C22×C4C2×D4×C1312yes—
987C22×C4C2×D4×C1312yes—
988C22×C4C2×D4×C1312yes—
989C22×C4C2×D4×C1312yes—
990C22×C4C13×#4112yes—
991C22×C4C13×#4112yes—
992C22×C4C13×#4112yes—
993C4⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C13#1537511yescharacteristic, direct product factor, Sylow
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
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—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C13×#12114yes—
1112C23C13×#12314yes—
1113C23C22×D4×C1311yescharacteristic
1114C23C22×D4×C1311yescharacteristic
1115C23C22×D4×C1311yescharacteristic
1116C23C2×C13×#4111yescharacteristic
1117C23C2×C13×#4111yescharacteristic
1118C23C2×C13×#4111yescharacteristic
1119C23C2×C13×#4111yescharacteristic
1120C23C2×C13×#4111yescharacteristic
1121C23C2×C13×#4111yescharacteristic
1122C23C13×H(5,𝔽2)11yescharacteristic
1123C23C13×H(5,𝔽2)11yescharacteristic
1124C23C13×H(5,𝔽2)11yescharacteristic
1125C23C13×H(5,𝔽2)11yescharacteristic
1126C23C13×H(5,𝔽2)11yescharacteristic
1127C23C13×H(5,𝔽2)11yescharacteristic
1128D4—416no—
1129D4—416no—
1130D4—416no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
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—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22C2×C13×#12111yescharacteristic
1263C22C2×C13×#12311yescharacteristic
1264C22C13×#52511yescharacteristic
1265C22C13×#52511yescharacteristic
1266C22C13×#52911yescharacteristic
1267C22C13×#53211yescharacteristic
1268C22C13×#53411yescharacteristic
1269C22C13×#53411yescharacteristic
1270C22C13×#53411yescharacteristic
1271C22C13×#53811yescharacteristic
1272C22C13×#53811yescharacteristic
1273C22C13×#53811yescharacteristic
1274C22C13×#53811yescharacteristic
1275C22C13×#54011yescharacteristic
1276C22C13×#54011yescharacteristic
1277C22D42×C1311yescharacteristic
1278C22D42×C1311yescharacteristic
1279C22C13×#54611yescharacteristic
1280C22C13×#54611yescharacteristic
1281C22C13×#54611yescharacteristic
1282C22C13×#54611yescharacteristic
1283C22C13×#54611yescharacteristic
1284C22C13×#54611yescharacteristic
1285C22C13×#54611yescharacteristic
1286C22C13×#54611yescharacteristic
1287C22C13×#55111yescharacteristic
1288C22C13×#55111yescharacteristic
1289C22C13×#55111yescharacteristic
1290C22C13×#55311yescharacteristic
1291C22C13×#55311yescharacteristic
1292C22C13×#55311yescharacteristic
1293C22C13×#55311yescharacteristic
1294C22C13×#55911yescharacteristic
1295C22C13×#56011yescharacteristic
1296C22C13×#56011yescharacteristic
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C2—44no—
1310C2—44no—
1311C2—82no—
1312C2C13×#241211yescharacteristic
1313C2C13×#241811yescharacteristic
1314C2C13×#242411yescharacteristic
1315C2C13×#244411yescharacteristic
1316C2C13×#245711yescharacteristic
1317C2C13×#246411yescharacteristic
1318C2C13×#254311yescharacteristic
1319C2C13×#255711yescharacteristic
1320C2C13×#260011yescharacteristic
1321C2C13×#266811yescharacteristic
1322C2C13×#266811yescharacteristic
1323C2C13×#268811yescharacteristic
1324C2C13×#270911yescharacteristic
1325C2C13×#274911yescharacteristic
1326C2C13×#277811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#394C2semidirect
3. C2×C13×#386C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#386C2semidirect
7. C13×#1445C2semidirect
8. C13×#1443C2semidirect
9. C13×#1440C2semidirect
10. C13×#1440C2semidirect
11. C13×#1440C2semidirect
12. C13×#1439C2semidirect
13. C13×#1438C2semidirect
14. C13×C22⋊#95C2semidirect
15. C13×C22⋊#95C2semidirect
147. C2×C13×C22⋊C4D4semidirect
148. C2×C13×C22⋊C4D4semidirect
165. #15375C13direct (N × H)
345. C2×#394C2×C13semidirect
347. C2×#386C2×C13semidirect
348. C2×#386C2×C13semidirect
349. C2×#386C2×C13semidirect
350. C2×#386C2×C13semidirect
351. #1445C2×C13semidirect
352. #1443C2×C13semidirect
353. #1440C2×C13semidirect
354. #1440C2×C13semidirect
355. #1440C2×C13semidirect
356. #1439C2×C13semidirect
357. #1438C2×C13semidirect
358. C22⋊#95C2×C13semidirect
359. C22⋊#95C2×C13semidirect
792. C2×C22⋊C4D4×C13semidirect
793. C2×C22⋊C4D4×C13semidirect
1007. C13#15375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3942
C2×C13×#3922
C2×C13×#3862
C13×#14452
C13×#14432
C13×#14402
C13×#14392
C13×#14382
C13×C22⋊#952
#1537513