Finite Group Databasebeta

← C13×#15276 #15701615

Subgroups — C13×#15276 #15701615

Order 3328.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#396C211yesmaximal, characteristic
3C2×C13×#395C211yesmaximal, characteristic, complemented
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C2×C13×#389C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic
13C13×#1439C211yesmaximal, characteristic
14C13×#1437C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×C22⋊Q8—24no—
19C2×C13×C22⋊Q8—24no—
20C2×C13×C22⋊Q8—24no—
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×C13×C4⋊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×C42×C13C2211yescharacteristic
38C13×#396—24no—
39C13×#395—24no—
40C13×#391—24no—
41C13×#389—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
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—41no—
65C22×Q8×C13—41no—
66C22×Q8×C13D414yes—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—41no—
73C23×C4×C13—41no—
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
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C13×C22⋊Q8—232no—
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—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4—41no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4—41no—
117C2×C13×C4⋊C4—41no—
118C2×C13×C4⋊C4D414yes—
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—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4D414yes—
135C2×C13×C22⋊C4Q814yescomplemented
136C2×C13×C22⋊C4Q814yescomplemented
137C2×C42×C13—22no—
138C2×C42×C13—22no—
139C2×C42×C13—41no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
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—41no—
152C13×#95—41no—
153C13×#95—41no—
154C13×#95—41no—
155C13×#95D414yes—
156#15276C1311yesmaximal, characteristic, direct product factor, Sylow
157C24×C13—21no—
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×C13C2×D412yes—
170C24×C13C2×Q812yes—
171C24×C13C2×Q812yes—
172C24×C13C2411yescharacteristic
173C2×Q8×C13—28no—
174C2×Q8×C13—28no—
175C2×Q8×C13—44no—
176C2×Q8×C13—44no—
177C2×Q8×C13—44no—
178C2×Q8×C13—44no—
179C2×Q8×C13—44no—
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—28no—
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×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—44no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13—44no—
265C22×C4×C13—44no—
266C22×C4×C13—44no—
267C22×C4×C13C2×D412yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D412yes—
270C22×C4×C13C2×D412yes—
271C22×C4×C13C2×D412yes—
272C22×C4×C13C2×D412yes—
273C22×C4×C13C2×D412yes—
274C22×C4×C13C2×D412yes—
275C22×C4×C13C2×D412yes—
276C22×C4×C13C2×D412yes—
277C22×C4×C13C2×D412yes—
278C22×C4×C13C2×Q812yes—
279C22×C4×C13C2×Q812yes—
280C22×C4×C13C2×Q812yes—
281C22×C4×C13C2×Q812yes—
282C22×C4×C13#4112yes—
283C22×C4×C13#4112yes—
284C22×C4×C13#4112yes—
285C13×C4⋊C4—28no—
286C13×C4⋊C4—28no—
287C13×C4⋊C4—28no—
288C13×C4⋊C4—28no—
289C13×C4⋊C4—44no—
290C13×C4⋊C4—44no—
291C13×C4⋊C4—44no—
292C13×C4⋊C4—44no—
293C13×C4⋊C4—44no—
294C13×C4⋊C4—44no—
295C13×C22⋊C4—28no—
296C13×C22⋊C4—28no—
297C13×C22⋊C4—28no—
298C13×C22⋊C4—44no—
299C13×C22⋊C4—44no—
300C13×C22⋊C4—44no—
301C42×C13—44no—
302C22×C22⋊Q8C2×C1311yescharacteristic
303C2×#396C2×C1311yescharacteristic
304C2×#395C2×C1311yescharacteristic, complemented
305C2×#391C2×C1311yescharacteristic, complemented
306C2×#389C2×C1311yescharacteristic, complemented
307C2×#385C2×C1311yescharacteristic
308#1444C2×C1311yescharacteristic, complemented
309#1444C2×C1311yescharacteristic, complemented
310#1441C2×C1311yescharacteristic, complemented
311#1441C2×C1311yescharacteristic, complemented
312#1441C2×C1311yescharacteristic, complemented
313#1439C2×C1311yescharacteristic
314#1439C2×C1311yescharacteristic
315#1437C2×C1311yescharacteristic
316C22⋊#95C2×C1311yescharacteristic
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—41no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13C4⋊Q814yes—
352C23×C13C22×D411yescharacteristic
353C23×C13C22×D411yescharacteristic
354C23×C13C22×D411yescharacteristic
355C23×C13C22×D411yescharacteristic
356C23×C13C22×Q811yescharacteristic
357C23×C13C22×Q811yescharacteristic
358C23×C13C2×#4111yescharacteristic
359C23×C13C2×#4111yescharacteristic
360C23×C13C2×#4111yescharacteristic
361C23×C13H(5,𝔽2)11yescharacteristic
362C23×C13H(5,𝔽2)11yescharacteristic
363C23×C13H(5,𝔽2)11yescharacteristic
364C23×C132−1+411yescharacteristic
365C23×C132−1+411yescharacteristic
366C23×C132−1+411yescharacteristic
367Q8×C13—416no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—416no—
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—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
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#12014yes—
465C2×C4×C13#12114yes—
466C2×C4×C13C22⋊Q814yescomplemented
467C23×Q8C22×C1311yescharacteristic
468C24×C4C22×C1311yescharacteristic
469C2×C22⋊Q8—24no—
470C2×C22⋊Q8—24no—
471C2×C22⋊Q8—24no—
472C22×C4⋊C4C22×C1311yescharacteristic
473C22×C4⋊C4C22×C1311yescharacteristic
474C22×C4⋊C4C22×C1311yescharacteristic
475C22×C4⋊C4C22×C1311yescharacteristic
476C22×C4⋊C4C22×C1311yescharacteristic
477C22×C4⋊C4C22×C1311yescharacteristic
478C22×C4⋊C4C22×C1311yescharacteristic
479C22×C4⋊C4C22×C1311yescharacteristic
480C22×C4⋊C4C22×C1311yescharacteristic
481C22×C4⋊C4C22×C1311yescharacteristic
482C22×C22⋊C4C22×C1311yescharacteristic
483C22×C22⋊C4C22×C1311yescharacteristic
484C22×C22⋊C4C22×C1311yescharacteristic
485C22×C22⋊C4C22×C1311yescharacteristic
486C22×C22⋊C4C22×C1311yescharacteristic
487C22×C22⋊C4C22×C1311yescharacteristic
488C22×C42C22×C1311yescharacteristic
489#396—24no—
490#395—24no—
491#391—24no—
492#389—24no—
493#385—24no—
494C2×#95C22×C1311yescharacteristic
495C2×#95C22×C1311yescharacteristic
496C2×#95C22×C1311yescharacteristic
497C2×#95C22×C1311yescharacteristic
498C2×#95C22×C1311yescharacteristic
499C2×#95C22×C1311yescharacteristic
500C2×#95C22×C1311yescharacteristic
501C2×#95C22×C1311yescharacteristic
502C2×#95C22×C1311yescharacteristic
503C2×#95C22×C1311yescharacteristic
504C2×#95C22×C1311yescharacteristic
505C2×#95C22×C1311yescharacteristic
506C2×#95C22×C1311yescharacteristic
507C2×#95C22×C1311yescharacteristic
508C2×#95C22×C1311yescharacteristic
509C2×#95C22×C1311yescharacteristic
510C22×C13—24no—
511C22×C13—24no—
512C22×C13—24no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13—42no—
520C22×C13—42no—
521C22×C13—42no—
522C22×C13—42no—
523C22×C13—42no—
524C22×C13—42no—
525C22×C13C2×#12011yescharacteristic
526C22×C13C2×#12111yescharacteristic
527C22×C13C2×C22⋊Q811yescharacteristic
528C22×C13#52511yescharacteristic
529C22×C13C2×C4⋊Q811yescharacteristic
530C22×C13#53311yescharacteristic
531C22×C13#53411yescharacteristic
532C22×C13#53611yescharacteristic
533C22×C13#53711yescharacteristic
534C22×C13#53711yescharacteristic
535C22×C13#53911yescharacteristic
536C22×C13#54111yescharacteristic
537C22×C13#54211yescharacteristic
538C22×C13#54311yescharacteristic
539C22×C13#54411yescharacteristic
540C22×C13D4211yescharacteristic
541C22×C13D4211yescharacteristic
542C22×C13#54611yescharacteristic
543C22×C13#54611yescharacteristic
544C22×C13#54611yescharacteristic
545C22×C13#54711yescharacteristic
546C22×C13#54711yescharacteristic
547C22×C13#54811yescharacteristic
548C22×C13D4×Q811yescharacteristic
549C22×C13D4×Q811yescharacteristic
550C22×C13D4×Q811yescharacteristic
551C22×C13D4×Q811yescharacteristic
552C22×C13D4×Q811yescharacteristic
553C22×C13#55011yescharacteristic
554C22×C13#55411yescharacteristic
555C22×C13#55411yescharacteristic
556C22×C13#55411yescharacteristic
557C22×C13#55611yescharacteristic
558C22×C13#56211yescharacteristic
559C22×C13#56311yescharacteristic
560C4×C13—24no—
561C4×C13—24no—
562C4×C13—24no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—42no—
568C4×C13—42no—
569C4×C13—42no—
570C4×C13—42no—
571C4×C13—42no—
572C4×C13—81no—
573C4×C13—81no—
574C25C23×C1311yescharacteristic
575C22×Q8—22no—
576C22×Q8—22no—
577C22×Q8—22no—
578C22×Q8—22no—
579C22×Q8—41no—
580C22×Q8—41no—
581C22×Q8D4×C1314yes—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—22no—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—41no—
588C23×C4—41no—
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1311yescharacteristic
597C23×C4C23×C1311yescharacteristic
598C23×C4C23×C1311yescharacteristic
599C23×C4C23×C1311yescharacteristic
600C23×C4C23×C1311yescharacteristic
601C23×C4C23×C1311yescharacteristic
602C23×C4C23×C1311yescharacteristic
603C22⋊Q8—232no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4D4×C1314yes—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4D4×C1314yes—
650C2×C22⋊C4Q8×C1314yescomplemented
651C2×C22⋊C4Q8×C1314yescomplemented
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—41no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—41no—
667#95—41no—
668#95—41no—
669#95—41no—
670#95D4×C1314yes—
671C2×C13—44no—
672C2×C13#240711yescharacteristic
673C2×C13#241011yescharacteristic
674C2×C13#242911yescharacteristic
675C2×C13#243411yescharacteristic
676C2×C13#244011yescharacteristic
677C2×C13#244911yescharacteristic
678C2×C13#246511yescharacteristic
679C2×C13#253811yescharacteristic
680C2×C13#254911yescharacteristic
681C2×C13#267211yescharacteristic
682C2×C13#268311yescharacteristic
683C2×C13#268911yescharacteristic
684C2×C13#270411yescharacteristic
685C2×C13#272911yescharacteristic
686C2×C13#273211yescharacteristic
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24C2×D4×C1312yes—
700C24C2×Q8×C1312yes—
701C24C2×Q8×C1312yes—
702C24C24×C1311yescharacteristic
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
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—28no—
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×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
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—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4C2×D4×C1312yes—
798C22×C4C2×D4×C1312yes—
799C22×C4C2×D4×C1312yes—
800C22×C4C2×D4×C1312yes—
801C22×C4C2×D4×C1312yes—
802C22×C4C2×D4×C1312yes—
803C22×C4C2×D4×C1312yes—
804C22×C4C2×D4×C1312yes—
805C22×C4C2×D4×C1312yes—
806C22×C4C2×D4×C1312yes—
807C22×C4C2×D4×C1312yes—
808C22×C4C2×Q8×C1312yes—
809C22×C4C2×Q8×C1312yes—
810C22×C4C2×Q8×C1312yes—
811C22×C4C2×Q8×C1312yes—
812C22×C4C13×#4112yes—
813C22×C4C13×#4112yes—
814C22×C4C13×#4112yes—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C42—44no—
832C13#1527611yescharacteristic, direct product factor, Sylow
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23C13×C4⋊Q814yes—
868C23C22×D4×C1311yescharacteristic
869C23C22×D4×C1311yescharacteristic
870C23C22×D4×C1311yescharacteristic
871C23C22×D4×C1311yescharacteristic
872C23C22×Q8×C1311yescharacteristic
873C23C22×Q8×C1311yescharacteristic
874C23C2×C13×#4111yescharacteristic
875C23C2×C13×#4111yescharacteristic
876C23C2×C13×#4111yescharacteristic
877C23C13×H(5,𝔽2)11yescharacteristic
878C23C13×H(5,𝔽2)11yescharacteristic
879C23C13×H(5,𝔽2)11yescharacteristic
880C23C13×2−1+411yescharacteristic
881C23C13×2−1+411yescharacteristic
882C23C13×2−1+411yescharacteristic
883Q8—416no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—416no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4C13×#12014yes—
981C2×C4C13×#12114yes—
982C2×C4C13×C22⋊Q814yescomplemented
983C22—24no—
984C22—24no—
985C22—24no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22C2×C13×#12011yescharacteristic
999C22C2×C13×#12111yescharacteristic
1000C22C2×C13×C22⋊Q811yescharacteristic
1001C22C13×#52511yescharacteristic
1002C22C2×C13×C4⋊Q811yescharacteristic
1003C22C13×#53311yescharacteristic
1004C22C13×#53411yescharacteristic
1005C22C13×#53611yescharacteristic
1006C22C13×#53711yescharacteristic
1007C22C13×#53711yescharacteristic
1008C22C13×#53911yescharacteristic
1009C22C13×#54111yescharacteristic
1010C22C13×#54211yescharacteristic
1011C22C13×#54311yescharacteristic
1012C22C13×#54411yescharacteristic
1013C22D42×C1311yescharacteristic
1014C22D42×C1311yescharacteristic
1015C22C13×#54611yescharacteristic
1016C22C13×#54611yescharacteristic
1017C22C13×#54611yescharacteristic
1018C22C13×#54711yescharacteristic
1019C22C13×#54711yescharacteristic
1020C22C13×#54811yescharacteristic
1021C22D4×Q8×C1311yescharacteristic
1022C22D4×Q8×C1311yescharacteristic
1023C22D4×Q8×C1311yescharacteristic
1024C22D4×Q8×C1311yescharacteristic
1025C22D4×Q8×C1311yescharacteristic
1026C22C13×#55011yescharacteristic
1027C22C13×#55411yescharacteristic
1028C22C13×#55411yescharacteristic
1029C22C13×#55411yescharacteristic
1030C22C13×#55611yescharacteristic
1031C22C13×#56211yescharacteristic
1032C22C13×#56311yescharacteristic
1033C4—24no—
1034C4—24no—
1035C4—24no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—81no—
1047C2—44no—
1048C2C13×#240711yescharacteristic
1049C2C13×#241011yescharacteristic
1050C2C13×#242911yescharacteristic
1051C2C13×#243411yescharacteristic
1052C2C13×#244011yescharacteristic
1053C2C13×#244911yescharacteristic
1054C2C13×#246511yescharacteristic
1055C2C13×#253811yescharacteristic
1056C2C13×#254911yescharacteristic
1057C2C13×#267211yescharacteristic
1058C2C13×#268311yescharacteristic
1059C2C13×#268911yescharacteristic
1060C2C13×#270411yescharacteristic
1061C2C13×#272911yescharacteristic
1062C2C13×#273211yescharacteristic
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
3. C2×C13×#395C2semidirect
4. C2×C13×#391C2semidirect
5. C2×C13×#389C2semidirect
7. C13×#1444C2semidirect
8. C13×#1444C2semidirect
9. C13×#1441C2semidirect
10. C13×#1441C2semidirect
11. C13×#1441C2semidirect
135. C2×C13×C22⋊C4Q8semidirect
136. C2×C13×C22⋊C4Q8semidirect
156. #15276C13direct (N × H)
304. C2×#395C2×C13semidirect
305. C2×#391C2×C13semidirect
306. C2×#389C2×C13semidirect
308. #1444C2×C13semidirect
309. #1444C2×C13semidirect
310. #1441C2×C13semidirect
311. #1441C2×C13semidirect
312. #1441C2×C13semidirect
466. C2×C4×C13C22⋊Q8semidirect
650. C2×C22⋊C4Q8×C13semidirect
651. C2×C22⋊C4Q8×C13semidirect
832. C13#15276direct (N × H)
982. C2×C4C13×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#3962
C2×C13×#3952
C2×C13×#3912
C2×C13×#3892
C2×C13×#3852
C13×#14442
C13×#14412
C13×#14392
C13×#14372
C13×C22⋊#952
#1527613