Finite Group Databasebeta

← C13×#15354 #15701693

Subgroups — C13×#15354 #15701693

Order 3328.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#395C211yesmaximal, characteristic, complemented
3C2×C13×#389C211yesmaximal, characteristic, complemented
4C2×C13×#388C211yesmaximal, characteristic
5C2×C13×#387C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic
7C13×#1446C211yesmaximal, characteristic, complemented
8C13×#1445C211yesmaximal, characteristic, complemented
9C13×#1444C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1440C211yesmaximal, characteristic
13C13×#1439C211yesmaximal, characteristic
14C13×#1439C211yesmaximal, 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×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C13×#395—24no—
37C13×#389—24no—
38C13×#388—24no—
39C13×#387—24no—
40C13×#385—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
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—22no—
65C22×Q8×C13—41no—
66C22×Q8×C13—41no—
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—41no—
108C2×C13×C4⋊C4—41no—
109C2×C13×C4⋊C4—41no—
110C2×C13×C4⋊C4D414yes—
111C2×C13×C4⋊C4D414yes—
112C2×C13×C4⋊C4D414yes—
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⋊C4D414yes—
130C2×C13×C22⋊C4Q814yescomplemented
131C2×C42×C13—22no—
132C2×C42×C13—22no—
133C2×C42×C13—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
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—41no—
150C13×#95—41no—
151C13×#95—41no—
152#15354C1311yesmaximal, characteristic, direct product factor, Sylow
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
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×C13C2×D412yes—
166C24×C13C2×Q812yes—
167C24×C13#4112yes—
168C24×C13C2411yescharacteristic
169C2×Q8×C13—28no—
170C2×Q8×C13—44no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—44no—
175C2×Q8×C13—44no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—28no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×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—44no—
260C22×C4×C13—44no—
261C22×C4×C13—44no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13—44no—
265C22×C4×C13C2×D412yes—
266C22×C4×C13C2×D412yes—
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×Q812yes—
277C22×C4×C13C2×Q812yes—
278C22×C4×C13#4112yes—
279C22×C4×C13#4112yes—
280C22×C4×C13#4112yes—
281C13×C4⋊C4—28no—
282C13×C4⋊C4—28no—
283C13×C4⋊C4—28no—
284C13×C4⋊C4—28no—
285C13×C4⋊C4—28no—
286C13×C4⋊C4—44no—
287C13×C4⋊C4—44no—
288C13×C4⋊C4—44no—
289C13×C22⋊C4—28no—
290C13×C22⋊C4—28no—
291C13×C22⋊C4—28no—
292C13×C22⋊C4—28no—
293C13×C22⋊C4—44no—
294C13×C22⋊C4—44no—
295C42×C13—44no—
296C22×C22⋊Q8C2×C1311yescharacteristic
297C2×#395C2×C1311yescharacteristic, complemented
298C2×#389C2×C1311yescharacteristic, complemented
299C2×#388C2×C1311yescharacteristic
300C2×#387C2×C1311yescharacteristic, complemented
301C2×#385C2×C1311yescharacteristic
302#1446C2×C1311yescharacteristic, complemented
303#1445C2×C1311yescharacteristic, complemented
304#1444C2×C1311yescharacteristic, complemented
305#1442C2×C1311yescharacteristic, complemented
306#1441C2×C1311yescharacteristic, complemented
307#1440C2×C1311yescharacteristic
308#1439C2×C1311yescharacteristic
309#1439C2×C1311yescharacteristic
310C22⋊#95C2×C1311yescharacteristic
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
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—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
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×C13C22⋊Q814yes—
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×D411yescharacteristic
350C23×C13C22×Q811yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13H(5,𝔽2)11yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C132−1+411yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
360C23×C132−1+411yescharacteristic
361Q8×C13—416no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—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—416no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—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#12014yes—
460C2×C4×C13#12114yes—
461C23×Q8C22×C1311yescharacteristic
462C24×C4C22×C1311yescharacteristic
463C2×C22⋊Q8—24no—
464C2×C22⋊Q8—24no—
465C2×C22⋊Q8—24no—
466C22×C4⋊C4C22×C1311yescharacteristic
467C22×C4⋊C4C22×C1311yescharacteristic
468C22×C4⋊C4C22×C1311yescharacteristic
469C22×C4⋊C4C22×C1311yescharacteristic
470C22×C4⋊C4C22×C1311yescharacteristic
471C22×C4⋊C4C22×C1311yescharacteristic
472C22×C4⋊C4C22×C1311yescharacteristic
473C22×C4⋊C4C22×C1311yescharacteristic
474C22×C22⋊C4C22×C1311yescharacteristic
475C22×C22⋊C4C22×C1311yescharacteristic
476C22×C22⋊C4C22×C1311yescharacteristic
477C22×C22⋊C4C22×C1311yescharacteristic
478C22×C22⋊C4C22×C1311yescharacteristic
479C22×C22⋊C4C22×C1311yescharacteristic
480C22×C42C22×C1311yescharacteristic
481#395—24no—
482#389—24no—
483#388—24no—
484#387—24no—
485#385—24no—
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
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
504C22×C13—24no—
505C22×C13—24no—
506C22×C13—24no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13C2×#12011yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13#52511yescharacteristic
523C22×C13#52511yescharacteristic
524C22×C13#53311yescharacteristic
525C22×C13#53511yescharacteristic
526C22×C13#53611yescharacteristic
527C22×C13#53611yescharacteristic
528C22×C13#53611yescharacteristic
529C22×C13#53911yescharacteristic
530C22×C13#53911yescharacteristic
531C22×C13#54111yescharacteristic
532C22×C13#54211yescharacteristic
533C22×C13#54411yescharacteristic
534C22×C13D4211yescharacteristic
535C22×C13D4211yescharacteristic
536C22×C13#54611yescharacteristic
537C22×C13#54611yescharacteristic
538C22×C13#54711yescharacteristic
539C22×C13#54711yescharacteristic
540C22×C13#54711yescharacteristic
541C22×C13#54711yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13#54811yescharacteristic
544C22×C13#54811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13D4×Q811yescharacteristic
547C22×C13D4×Q811yescharacteristic
548C22×C13#55111yescharacteristic
549C22×C13#55211yescharacteristic
550C22×C13#55411yescharacteristic
551C22×C13#55611yescharacteristic
552C22×C13#56311yescharacteristic
553C22×C13#56311yescharacteristic
554C4×C13—24no—
555C4×C13—24no—
556C4×C13—42no—
557C4×C13—42no—
558C4×C13—42no—
559C4×C13—42no—
560C4×C13—42no—
561C4×C13—42no—
562C4×C13—42no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—81no—
567C4×C13—81no—
568C25C23×C1311yescharacteristic
569C22×Q8—22no—
570C22×Q8—22no—
571C22×Q8—22no—
572C22×Q8—22no—
573C22×Q8—22no—
574C22×Q8—41no—
575C22×Q8—41no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C23×C4C23×C1311yescharacteristic
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1311yescharacteristic
597C22⋊Q8—232no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
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—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4D4×C1314yes—
620C2×C4⋊C4D4×C1314yes—
621C2×C4⋊C4D4×C1314yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—41no—
637C2×C22⋊C4—41no—
638C2×C22⋊C4D4×C1314yes—
639C2×C22⋊C4Q8×C1314yescomplemented
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—41no—
659#95—41no—
660#95—41no—
661C2×C13—44no—
662C2×C13#240611yescharacteristic
663C2×C13#240811yescharacteristic
664C2×C13#240911yescharacteristic
665C2×C13#241511yescharacteristic
666C2×C13#242911yescharacteristic
667C2×C13#243811yescharacteristic
668C2×C13#244911yescharacteristic
669C2×C13#246311yescharacteristic
670C2×C13#246511yescharacteristic
671C2×C13#267411yescharacteristic
672C2×C13#267711yescharacteristic
673C2×C13#268911yescharacteristic
674C2×C13#269011yescharacteristic
675C2×C13#272011yescharacteristic
676C2×C13#272311yescharacteristic
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24C2×D4×C1312yes—
690C24C2×Q8×C1312yes—
691C24C13×#4112yes—
692C24C24×C1311yescharacteristic
693C2×Q8—28no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—28no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×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—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4C2×D4×C1312yes—
790C22×C4C2×D4×C1312yes—
791C22×C4C2×D4×C1312yes—
792C22×C4C2×D4×C1312yes—
793C22×C4C2×D4×C1312yes—
794C22×C4C2×D4×C1312yes—
795C22×C4C2×D4×C1312yes—
796C22×C4C2×D4×C1312yes—
797C22×C4C2×D4×C1312yes—
798C22×C4C2×D4×C1312yes—
799C22×C4C2×D4×C1312yes—
800C22×C4C2×Q8×C1312yes—
801C22×C4C2×Q8×C1312yes—
802C22×C4C13×#4112yes—
803C22×C4C13×#4112yes—
804C22×C4C13×#4112yes—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C42—44no—
820C13#1535411yescharacteristic, direct product factor, Sylow
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23C13×C22⋊Q814yes—
856C23C22×D4×C1311yescharacteristic
857C23C22×D4×C1311yescharacteristic
858C23C22×D4×C1311yescharacteristic
859C23C22×D4×C1311yescharacteristic
860C23C22×Q8×C1311yescharacteristic
861C23C2×C13×#4111yescharacteristic
862C23C2×C13×#4111yescharacteristic
863C23C2×C13×#4111yescharacteristic
864C23C2×C13×#4111yescharacteristic
865C23C13×H(5,𝔽2)11yescharacteristic
866C23C13×H(5,𝔽2)11yescharacteristic
867C23C13×2−1+411yescharacteristic
868C23C13×2−1+411yescharacteristic
869C23C13×2−1+411yescharacteristic
870C23C13×2−1+411yescharacteristic
871Q8—416no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
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—416no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
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×C4C13×#12014yes—
970C2×C4C13×#12114yes—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22C2×C13×#12011yescharacteristic
987C22C2×C13×#12111yescharacteristic
988C22C2×C13×C22⋊Q811yescharacteristic
989C22C13×#52511yescharacteristic
990C22C13×#52511yescharacteristic
991C22C13×#53311yescharacteristic
992C22C13×#53511yescharacteristic
993C22C13×#53611yescharacteristic
994C22C13×#53611yescharacteristic
995C22C13×#53611yescharacteristic
996C22C13×#53911yescharacteristic
997C22C13×#53911yescharacteristic
998C22C13×#54111yescharacteristic
999C22C13×#54211yescharacteristic
1000C22C13×#54411yescharacteristic
1001C22D42×C1311yescharacteristic
1002C22D42×C1311yescharacteristic
1003C22C13×#54611yescharacteristic
1004C22C13×#54611yescharacteristic
1005C22C13×#54711yescharacteristic
1006C22C13×#54711yescharacteristic
1007C22C13×#54711yescharacteristic
1008C22C13×#54711yescharacteristic
1009C22C13×#54811yescharacteristic
1010C22C13×#54811yescharacteristic
1011C22C13×#54811yescharacteristic
1012C22D4×Q8×C1311yescharacteristic
1013C22D4×Q8×C1311yescharacteristic
1014C22D4×Q8×C1311yescharacteristic
1015C22C13×#55111yescharacteristic
1016C22C13×#55211yescharacteristic
1017C22C13×#55411yescharacteristic
1018C22C13×#55611yescharacteristic
1019C22C13×#56311yescharacteristic
1020C22C13×#56311yescharacteristic
1021C4—24no—
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—81no—
1034C4—81no—
1035C2—44no—
1036C2C13×#240611yescharacteristic
1037C2C13×#240811yescharacteristic
1038C2C13×#240911yescharacteristic
1039C2C13×#241511yescharacteristic
1040C2C13×#242911yescharacteristic
1041C2C13×#243811yescharacteristic
1042C2C13×#244911yescharacteristic
1043C2C13×#246311yescharacteristic
1044C2C13×#246511yescharacteristic
1045C2C13×#267411yescharacteristic
1046C2C13×#267711yescharacteristic
1047C2C13×#268911yescharacteristic
1048C2C13×#269011yescharacteristic
1049C2C13×#272011yescharacteristic
1050C2C13×#272311yescharacteristic
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
2. C2×C13×#395C2semidirect
3. C2×C13×#389C2semidirect
5. C2×C13×#387C2semidirect
7. C13×#1446C2semidirect
8. C13×#1445C2semidirect
9. C13×#1444C2semidirect
10. C13×#1442C2semidirect
11. C13×#1441C2semidirect
130. C2×C13×C22⋊C4Q8semidirect
152. #15354C13direct (N × H)
297. C2×#395C2×C13semidirect
298. C2×#389C2×C13semidirect
300. C2×#387C2×C13semidirect
302. #1446C2×C13semidirect
303. #1445C2×C13semidirect
304. #1444C2×C13semidirect
305. #1442C2×C13semidirect
306. #1441C2×C13semidirect
639. C2×C22⋊C4Q8×C13semidirect
820. C13#15354direct (N × H)

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×#3952
C2×C13×#3892
C2×C13×#3882
C2×C13×#3872
C2×C13×#3852
C13×#14462
C13×#14452
C13×#14442
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×C22⋊#952
#1535413