Finite Group Databasebeta

← C13×#15358 #15701697

Subgroups — C13×#15358 #15701697

Order 3328.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic, complemented
2C2×C13×#390C211yesmaximal, characteristic
3C2×C13×#389C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×#1438C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊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×C42×C13C2211yescharacteristic
37C13×#399—24no—
38C13×#390—24no—
39C13×#389—24no—
40C13×#386—24no—
41C13×#385—24no—
42C13×#385—24no—
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
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—41no—
64C22×D4×C13—41no—
65C22×D4×C13Q814yes—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—41no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13C2311yescharacteristic
74C23×C4×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
86C2×C13×C4⋊C4—22no—
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—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4—41no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4D414yescomplemented
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—41no—
128C2×C13×C22⋊C4—41no—
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⋊C4D414yes—
140C2×C42×C13—22no—
141C2×C42×C13—22no—
142C2×C42×C13—41no—
143C13×#95—22no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—22no—
149C13×#95—22no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—41no—
153C13×#95—41no—
154C13×#95—41no—
155C13×#95—41no—
156C13×#95D414yes—
157#15358C1311yesmaximal, characteristic, direct product factor, Sylow
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13C2×D412yes—
185C24×C13C2×Q812yes—
186C24×C13C2×Q812yes—
187C24×C13#4112yes—
188C24×C13C2411yescharacteristic
189C2×D4×C13—28no—
190C2×D4×C13—28no—
191C2×D4×C13—44no—
192C2×D4×C13—44no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13—44no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—44no—
275C22×C4×C13—44no—
276C22×C4×C13—44no—
277C22×C4×C13—44no—
278C22×C4×C13—44no—
279C22×C4×C13—44no—
280C22×C4×C13—44no—
281C22×C4×C13C2×D412yes—
282C22×C4×C13C2×D412yes—
283C22×C4×C13C2×D412yes—
284C22×C4×C13C2×D412yes—
285C22×C4×C13C2×D412yes—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×Q812yes—
290C22×C4×C13#4112yes—
291C22×C4×C13#4112yes—
292C22×C4×C13#4112yes—
293C22×C4×C13#4112yes—
294C13×C4⋊C4—28no—
295C13×C4⋊C4—44no—
296C13×C4⋊C4—44no—
297C13×C4⋊C4—44no—
298C13×C4⋊C4—44no—
299C13×C4⋊C4—44no—
300C13×C4⋊C4—44no—
301C13×C22⋊C4—28no—
302C13×C22⋊C4—28no—
303C13×C22⋊C4—44no—
304C13×C22⋊C4—44no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4—44no—
307C13×C22⋊C4—44no—
308C13×C22⋊C4—44no—
309C13×C22⋊C4—44no—
310C13×C22⋊C4—44no—
311C13×C22⋊C4—44no—
312C42×C13—44no—
313C2×#399C2×C1311yescharacteristic, complemented
314C2×#390C2×C1311yescharacteristic
315C2×#389C2×C1311yescharacteristic, complemented
316C2×#386C2×C1311yescharacteristic
317C2×#385C2×C1311yescharacteristic, complemented
318C2×#385C2×C1311yescharacteristic, complemented
319#1442C2×C1311yescharacteristic, complemented
320#1441C2×C1311yescharacteristic, complemented
321#1439C2×C1311yescharacteristic, complemented
322#1439C2×C1311yescharacteristic, complemented
323#1439C2×C1311yescharacteristic, complemented
324#1439C2×C1311yescharacteristic, complemented
325#1439C2×C1311yescharacteristic, complemented
326#1438C2×C1311yescharacteristic
327#1436C2×C1311yescharacteristic, complemented
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—41no—
354C23×C13—41no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13C22⋊Q814yes—
398C23×C13C22×D411yescharacteristic
399C23×C13C22×D411yescharacteristic
400C23×C13C22×D411yescharacteristic
401C23×C13C22×Q811yescharacteristic
402C23×C13C2×#4111yescharacteristic
403C23×C13C2×#4111yescharacteristic
404C23×C13C2×#4111yescharacteristic
405C23×C13C2×#4111yescharacteristic
406C23×C13C2×#4111yescharacteristic
407C23×C13H(5,𝔽2)11yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409C23×C13H(5,𝔽2)11yescharacteristic
410C23×C13H(5,𝔽2)11yescharacteristic
411C23×C13H(5,𝔽2)11yescharacteristic
412C23×C132−1+411yescharacteristic
413D4×C13—416no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—416no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13C22⋊Q814yes—
505C2×C4×C13#12314yes—
506C23×D4C22×C1311yescharacteristic
507C24×C4C22×C1311yescharacteristic
508C22×C4⋊C4C22×C1311yescharacteristic
509C22×C4⋊C4C22×C1311yescharacteristic
510C22×C4⋊C4C22×C1311yescharacteristic
511C22×C4⋊C4C22×C1311yescharacteristic
512C22×C4⋊C4C22×C1311yescharacteristic
513C22×C4⋊C4C22×C1311yescharacteristic
514C22×C4⋊C4C22×C1311yescharacteristic
515C22×C22⋊C4C22×C1311yescharacteristic
516C22×C22⋊C4C22×C1311yescharacteristic
517C22×C22⋊C4C22×C1311yescharacteristic
518C22×C22⋊C4C22×C1311yescharacteristic
519C22×C22⋊C4C22×C1311yescharacteristic
520C22×C22⋊C4C22×C1311yescharacteristic
521C22×C22⋊C4C22×C1311yescharacteristic
522C22×C22⋊C4C22×C1311yescharacteristic
523C22×C22⋊C4C22×C1311yescharacteristic
524C22×C22⋊C4C22×C1311yescharacteristic
525C22×C22⋊C4C22×C1311yescharacteristic
526C22×C42C22×C1311yescharacteristic
527#399—24no—
528#390—24no—
529#389—24no—
530#386—24no—
531#385—24no—
532#385—24no—
533C2×#95C22×C1311yescharacteristic
534C2×#95C22×C1311yescharacteristic
535C2×#95C22×C1311yescharacteristic
536C2×#95C22×C1311yescharacteristic
537C2×#95C22×C1311yescharacteristic
538C2×#95C22×C1311yescharacteristic
539C2×#95C22×C1311yescharacteristic
540C2×#95C22×C1311yescharacteristic
541C2×#95C22×C1311yescharacteristic
542C2×#95C22×C1311yescharacteristic
543C2×#95C22×C1311yescharacteristic
544C2×#95C22×C1311yescharacteristic
545C2×#95C22×C1311yescharacteristic
546C2×#95C22×C1311yescharacteristic
547C22×C13—24no—
548C22×C13—24no—
549C22×C13—24no—
550C22×C13—42no—
551C22×C13—42no—
552C22×C13—42no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—81no—
570C22×C13—81no—
571C22×C13—81no—
572C22×C13—81no—
573C22×C13—81no—
574C22×C13—81no—
575C22×C13—81no—
576C22×C13—81no—
577C22×C13C2×C22⋊Q811yescharacteristic
578C22×C13C2×C22⋊Q811yescharacteristic
579C22×C13C2×#12311yescharacteristic
580C22×C13#52511yescharacteristic
581C22×C13#52511yescharacteristic
582C22×C13#53211yescharacteristic
583C22×C13#53411yescharacteristic
584C22×C13#53511yescharacteristic
585C22×C13#53511yescharacteristic
586C22×C13#53811yescharacteristic
587C22×C13#53911yescharacteristic
588C22×C13#53911yescharacteristic
589C22×C13#54011yescharacteristic
590C22×C13#54211yescharacteristic
591C22×C13#54311yescharacteristic
592C22×C13D4211yescharacteristic
593C22×C13D4211yescharacteristic
594C22×C13D4211yescharacteristic
595C22×C13#54611yescharacteristic
596C22×C13#54611yescharacteristic
597C22×C13#54711yescharacteristic
598C22×C13#54811yescharacteristic
599C22×C13D4×Q811yescharacteristic
600C22×C13#55011yescharacteristic
601C22×C13#55111yescharacteristic
602C22×C13#55311yescharacteristic
603C22×C13#55311yescharacteristic
604C22×C13#55311yescharacteristic
605C22×C13#55411yescharacteristic
606C22×C13#55411yescharacteristic
607C22×C13#55411yescharacteristic
608C22×C13#55911yescharacteristic
609C22×C13#55911yescharacteristic
610C22×C13#56011yescharacteristic
611C22×C13#56211yescharacteristic
612C4×C13—24no—
613C4×C13—24no—
614C4×C13—42no—
615C4×C13—42no—
616C4×C13—42no—
617C4×C13—42no—
618C4×C13—42no—
619C4×C13—42no—
620C4×C13—42no—
621C4×C13—81no—
622C4×C13—81no—
623C4×C13—81no—
624C4×C13—81no—
625C25C23×C1311yescharacteristic
626C25C23×C1311yescharacteristic
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4Q8×C1314yes—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4C23×C1311yescharacteristic
642C23×C4C23×C1311yescharacteristic
643C23×C4C23×C1311yescharacteristic
644C23×C4C23×C1311yescharacteristic
645C23×C4C23×C1311yescharacteristic
646C23×C4C23×C1311yescharacteristic
647C23×C4C23×C1311yescharacteristic
648C23×C4C23×C1311yescharacteristic
649C23×C4C23×C1311yescharacteristic
650C23×C4C23×C1311yescharacteristic
651C23×C4C23×C1311yescharacteristic
652C23×C4C23×C1311yescharacteristic
653C23×C4C23×C1311yescharacteristic
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4D4×C1314yescomplemented
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4D4×C1314yes—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95D4×C1314yes—
725C2×C13—44no—
726C2×C13—82no—
727C2×C13#243711yescharacteristic
728C2×C13#244311yescharacteristic
729C2×C13#244511yescharacteristic
730C2×C13#244911yescharacteristic
731C2×C13#245211yescharacteristic
732C2×C13#245611yescharacteristic
733C2×C13#248711yescharacteristic
734C2×C13#258011yescharacteristic
735C2×C13#260211yescharacteristic
736C2×C13#266911yescharacteristic
737C2×C13#271011yescharacteristic
738C2×C13#271111yescharacteristic
739C2×C13#273211yescharacteristic
740C2×C13#278011yescharacteristic
741C2×C13#279611yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24C2×D4×C1312yes—
769C24C2×Q8×C1312yes—
770C24C2×Q8×C1312yes—
771C24C13×#4112yes—
772C24C24×C1311yescharacteristic
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4C2×D4×C1312yes—
866C22×C4C2×D4×C1312yes—
867C22×C4C2×D4×C1312yes—
868C22×C4C2×D4×C1312yes—
869C22×C4C2×D4×C1312yes—
870C22×C4C2×D4×C1312yes—
871C22×C4C2×D4×C1312yes—
872C22×C4C2×D4×C1312yes—
873C22×C4C2×Q8×C1312yes—
874C22×C4C13×#4112yes—
875C22×C4C13×#4112yes—
876C22×C4C13×#4112yes—
877C22×C4C13×#4112yes—
878C4⋊C4—28no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—44no—
897C13#1535811yescharacteristic, direct product factor, Sylow
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23C13×C22⋊Q814yes—
968C23C22×D4×C1311yescharacteristic
969C23C22×D4×C1311yescharacteristic
970C23C22×D4×C1311yescharacteristic
971C23C22×Q8×C1311yescharacteristic
972C23C2×C13×#4111yescharacteristic
973C23C2×C13×#4111yescharacteristic
974C23C2×C13×#4111yescharacteristic
975C23C2×C13×#4111yescharacteristic
976C23C2×C13×#4111yescharacteristic
977C23C13×H(5,𝔽2)11yescharacteristic
978C23C13×H(5,𝔽2)11yescharacteristic
979C23C13×H(5,𝔽2)11yescharacteristic
980C23C13×H(5,𝔽2)11yescharacteristic
981C23C13×H(5,𝔽2)11yescharacteristic
982C23C13×2−1+411yescharacteristic
983D4—416no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—416no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4C13×C22⋊Q814yes—
1075C2×C4C13×#12314yes—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22C2×C13×C22⋊Q811yescharacteristic
1107C22C2×C13×C22⋊Q811yescharacteristic
1108C22C2×C13×#12311yescharacteristic
1109C22C13×#52511yescharacteristic
1110C22C13×#52511yescharacteristic
1111C22C13×#53211yescharacteristic
1112C22C13×#53411yescharacteristic
1113C22C13×#53511yescharacteristic
1114C22C13×#53511yescharacteristic
1115C22C13×#53811yescharacteristic
1116C22C13×#53911yescharacteristic
1117C22C13×#53911yescharacteristic
1118C22C13×#54011yescharacteristic
1119C22C13×#54211yescharacteristic
1120C22C13×#54311yescharacteristic
1121C22D42×C1311yescharacteristic
1122C22D42×C1311yescharacteristic
1123C22D42×C1311yescharacteristic
1124C22C13×#54611yescharacteristic
1125C22C13×#54611yescharacteristic
1126C22C13×#54711yescharacteristic
1127C22C13×#54811yescharacteristic
1128C22D4×Q8×C1311yescharacteristic
1129C22C13×#55011yescharacteristic
1130C22C13×#55111yescharacteristic
1131C22C13×#55311yescharacteristic
1132C22C13×#55311yescharacteristic
1133C22C13×#55311yescharacteristic
1134C22C13×#55411yescharacteristic
1135C22C13×#55411yescharacteristic
1136C22C13×#55411yescharacteristic
1137C22C13×#55911yescharacteristic
1138C22C13×#55911yescharacteristic
1139C22C13×#56011yescharacteristic
1140C22C13×#56211yescharacteristic
1141C4—24no—
1142C4—24no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C2—44no—
1155C2—82no—
1156C2C13×#243711yescharacteristic
1157C2C13×#244311yescharacteristic
1158C2C13×#244511yescharacteristic
1159C2C13×#244911yescharacteristic
1160C2C13×#245211yescharacteristic
1161C2C13×#245611yescharacteristic
1162C2C13×#248711yescharacteristic
1163C2C13×#258011yescharacteristic
1164C2C13×#260211yescharacteristic
1165C2C13×#266911yescharacteristic
1166C2C13×#271011yescharacteristic
1167C2C13×#271111yescharacteristic
1168C2C13×#273211yescharacteristic
1169C2C13×#278011yescharacteristic
1170C2C13×#279611yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#399C2semidirect
3. C2×C13×#389C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#385C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1439C2semidirect
15. C13×#1436C2semidirect
106. C2×C13×C4⋊C4D4semidirect
157. #15358C13direct (N × H)
313. C2×#399C2×C13semidirect
315. C2×#389C2×C13semidirect
317. C2×#385C2×C13semidirect
318. C2×#385C2×C13semidirect
319. #1442C2×C13semidirect
320. #1441C2×C13semidirect
321. #1439C2×C13semidirect
322. #1439C2×C13semidirect
323. #1439C2×C13semidirect
324. #1439C2×C13semidirect
325. #1439C2×C13semidirect
327. #1436C2×C13semidirect
674. C2×C4⋊C4D4×C13semidirect
897. C13#15358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3992
C2×C13×#3902
C2×C13×#3892
C2×C13×#3862
C2×C13×#3852
C13×#14422
C13×#14412
C13×#14392
C13×#14382
C13×#14362
#1535813