Finite Group Databasebeta

← C13×#15220 #15701559

Subgroups — C13×#15220 #15701559

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#389C211yesmaximal, characteristic, complemented
3C2×C13×#382C211yesmaximal, characteristic, complemented
4C2×C13×#380C211yesmaximal, characteristic
5C2×C13×#380C211yesmaximal, characteristic
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C13×#1443C212yesmaximal, complemented
8C13×#1441C212yesmaximal, complemented
9C13×#1439C212yesmaximal
10C13×#1439C212yesmaximal
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C13×C22⋊C4C2212yes—
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C13×#389—24no—
26C13×#389—24no—
27C13×#382—24no—
28C13×#380—24no—
29C13×#380—24no—
30C4×C13×C22⋊C4—24no—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13Q814yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—42no—
73C2×C13×C4⋊C4—42no—
74C2×C13×C4⋊C4—42no—
75C2×C13×C4⋊C4D414yes—
76C2×C13×C4⋊C4D414yes—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—24no—
84C2×C13×C22⋊C4—24no—
85C2×C13×C22⋊C4—24no—
86C2×C13×C22⋊C4—24no—
87C2×C13×C22⋊C4—42no—
88C2×C13×C22⋊C4—42no—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—22no—
93C2×C42×C13—22no—
94C2×C42×C13D414yes—
95C13×#95—22no—
96C13×#95—22no—
97C13×#95—24no—
98C13×#95—24no—
99C13×#95—24no—
100C13×#95—24no—
101C13×#95—24no—
102C13×#95—24no—
103C13×#95—24no—
104C13×#95—42no—
105#15220C1311yesmaximal, characteristic, direct product factor, Sylow
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13C2×Q812yes—
119C24×C13#4112yes—
120C24×C13#4112yes—
121C24×C13C2411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—28no—
165C22×C4×C13—28no—
166C22×C4×C13—28no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—44no—
182C22×C4×C13—44no—
183C22×C4×C13—44no—
184C22×C4×C13—44no—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×Q812yes—
193C22×C4×C13C2×Q812yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C13×C4⋊C4—28no—
200C13×C4⋊C4—28no—
201C13×C4⋊C4—48no—
202C13×C4⋊C4—48no—
203C13×C4⋊C4—44no—
204C13×C4⋊C4—44no—
205C13×C22⋊C4—28no—
206C13×C22⋊C4—28no—
207C13×C22⋊C4—48no—
208C13×C22⋊C4—48no—
209C42×C13—28no—
210C42×C13—44no—
211C2×#389C2×C1311yescharacteristic, complemented
212C2×#389C2×C1311yescharacteristic, complemented
213C2×#382C2×C1311yescharacteristic, complemented
214C2×#380C2×C1311yescharacteristic
215C2×#380C2×C1311yescharacteristic
216C2×C4×C22⋊C4C2×C1311yescharacteristic
217#1443C2×C1312yescomplemented
218#1441C2×C1312yescomplemented
219#1439C2×C1312yes—
220#1439C2×C1312yes—
221C4⋊#95C2×C1311yescharacteristic, complemented
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13#12514yes—
257C23×C13C22×D411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×D411yescharacteristic
260C23×C13C22×Q811yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C13H(5,𝔽2)11yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—24no—
275C2×C4×C13—24no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—42no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—42no—
317C2×C4×C13—41no—
318C2×C4×C13—42no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—416no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13#12114yes—
337C2×C4×C13#12114yes—
338C2×C4×C13#12114yes—
339C2×C4×C13C22⋊Q814yes—
340C2×C4×C13C22⋊Q814yes—
341C2×C4×C13C22⋊Q814yes—
342C2×C4×C13#12614yes—
343C24×C4C22×C1311yescharacteristic
344C22×C4⋊C4C22×C1311yescharacteristic
345C22×C4⋊C4C22×C1311yescharacteristic
346C22×C4⋊C4C22×C1312yes—
347C22×C4⋊C4C22×C1311yescharacteristic
348C22×C4⋊C4C22×C1311yescharacteristic
349C22×C4⋊C4C22×C1312yes—
350C22×C22⋊C4C22×C1311yescharacteristic
351C22×C22⋊C4C22×C1311yescharacteristic
352C22×C22⋊C4C22×C1312yes—
353C22×C22⋊C4C22×C1312yes—
354C22×C42C22×C1311yescharacteristic
355C22×C42C22×C1311yescharacteristic
356#389—24no—
357#389—24no—
358#382—24no—
359#380—24no—
360#380—24no—
361C4×C22⋊C4—24no—
362C2×#95C22×C1312yes—
363C2×#95C22×C1312yes—
364C2×#95C22×C1312yes—
365C2×#95C22×C1312yes—
366C2×#95C22×C1312yes—
367C2×#95C22×C1311yescharacteristic
368C2×#95C22×C1312yes—
369C2×#95C22×C1312yes—
370C2×#95C22×C1311yescharacteristic
371C2×#95C22×C1312yes—
372C22×C13—24no—
373C22×C13—24no—
374C22×C13—24no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13C2×#12111yescharacteristic
388C22×C13C2×#12111yescharacteristic
389C22×C13C2×#12111yescharacteristic
390C22×C13C2×C22⋊Q811yescharacteristic
391C22×C13C2×C22⋊Q811yescharacteristic
392C22×C13C2×C22⋊Q811yescharacteristic
393C22×C13#52511yescharacteristic
394C22×C13#52511yescharacteristic
395C22×C13C2×#12511yescharacteristic
396C22×C13C2×#12611yescharacteristic
397C22×C13#52911yescharacteristic
398C22×C13#52911yescharacteristic
399C22×C13#53311yescharacteristic
400C22×C13#53511yescharacteristic
401C22×C13#53611yescharacteristic
402C22×C13#54211yescharacteristic
403C22×C13#54211yescharacteristic
404C22×C13#54411yescharacteristic
405C22×C13#54411yescharacteristic
406C22×C13#54611yescharacteristic
407C22×C13#54611yescharacteristic
408C22×C13#54611yescharacteristic
409C22×C13#54711yescharacteristic
410C22×C13#54811yescharacteristic
411C22×C13#54811yescharacteristic
412C22×C13#54811yescharacteristic
413C22×C13#55011yescharacteristic
414C22×C13#55211yescharacteristic
415C22×C13#55211yescharacteristic
416C22×C13#55211yescharacteristic
417C22×C13#55311yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55311yescharacteristic
420C22×C13#55511yescharacteristic
421C22×C13#55611yescharacteristic
422C4×C13—42no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—44no—
426C4×C13—44no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13—82no—
430C4×C13—82no—
431C4×C13#39618yes—
432C25C23×C1311yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4Q8×C1314yes—
440C23×C4C23×C1312yes—
441C23×C4C23×C1312yes—
442C23×C4C23×C1312yes—
443C23×C4C23×C1312yes—
444C23×C4C23×C1311yescharacteristic
445C23×C4C23×C1311yescharacteristic
446C23×C4C23×C1311yescharacteristic
447C23×C4C23×C1311yescharacteristic
448C23×C4C23×C1311yescharacteristic
449C23×C4C23×C1311yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4D4×C1314yes—
467C2×C4⋊C4D4×C1314yes—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42D4×C1314yes—
486#95—22no—
487#95—22no—
488#95—24no—
489#95—24no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—24no—
494#95—24no—
495#95—42no—
496C2×C13—44no—
497C2×C13C2×#39611yescharacteristic
498C2×C13#241411yescharacteristic
499C2×C13#241511yescharacteristic
500C2×C13#242611yescharacteristic
501C2×C13#242711yescharacteristic
502C2×C13#243911yescharacteristic
503C2×C13#244111yescharacteristic
504C2×C13#244211yescharacteristic
505C2×C13#244211yescharacteristic
506C2×C13#249411yescharacteristic
507C2×C13#249511yescharacteristic
508C2×C13#253511yescharacteristic
509C2×C13#253611yescharacteristic
510C2×C13#262811yescharacteristic
511C2×C13#285111yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24C2×Q8×C1312yes—
525C24C13×#4112yes—
526C24C13×#4112yes—
527C24C24×C1311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C2×D4×C1312yes—
592C22×C4C2×D4×C1314yes—
593C22×C4C2×D4×C1314yes—
594C22×C4C2×D4×C1312yes—
595C22×C4C2×D4×C1312yes—
596C22×C4C2×D4×C1312yes—
597C22×C4C2×D4×C1312yes—
598C22×C4C2×Q8×C1312yes—
599C22×C4C2×Q8×C1312yes—
600C22×C4C13×#4112yes—
601C22×C4C13×#4112yes—
602C22×C4C13×#4112yes—
603C22×C4C13×#4112yes—
604C22×C4C13×#4112yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C42—28no—
616C42—44no—
617C13#1522011yescharacteristic, direct product factor, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C13×#12514yes—
653C23C22×D4×C1311yescharacteristic
654C23C22×D4×C1311yescharacteristic
655C23C22×D4×C1311yescharacteristic
656C23C22×Q8×C1311yescharacteristic
657C23C2×C13×#4111yescharacteristic
658C23C2×C13×#4111yescharacteristic
659C23C2×C13×#4111yescharacteristic
660C23C2×C13×#4111yescharacteristic
661C23C2×C13×#4111yescharacteristic
662C23C2×C13×#4111yescharacteristic
663C23C2×C13×#4111yescharacteristic
664C23C13×H(5,𝔽2)11yescharacteristic
665C23C13×H(5,𝔽2)11yescharacteristic
666C23C13×2−1+411yescharacteristic
667C23C13×2−1+411yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4C13×#12114yes—
733C2×C4C13×#12114yes—
734C2×C4C13×#12114yes—
735C2×C4C13×C22⋊Q814yes—
736C2×C4C13×C22⋊Q814yes—
737C2×C4C13×C22⋊Q814yes—
738C2×C4C13×#12614yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C13×#12111yescharacteristic
755C22C2×C13×#12111yescharacteristic
756C22C2×C13×#12111yescharacteristic
757C22C2×C13×C22⋊Q811yescharacteristic
758C22C2×C13×C22⋊Q811yescharacteristic
759C22C2×C13×C22⋊Q811yescharacteristic
760C22C13×#52511yescharacteristic
761C22C13×#52511yescharacteristic
762C22C2×C13×#12511yescharacteristic
763C22C2×C13×#12611yescharacteristic
764C22C13×#52911yescharacteristic
765C22C13×#52911yescharacteristic
766C22C13×#53311yescharacteristic
767C22C13×#53511yescharacteristic
768C22C13×#53611yescharacteristic
769C22C13×#54211yescharacteristic
770C22C13×#54211yescharacteristic
771C22C13×#54411yescharacteristic
772C22C13×#54411yescharacteristic
773C22C13×#54611yescharacteristic
774C22C13×#54611yescharacteristic
775C22C13×#54611yescharacteristic
776C22C13×#54711yescharacteristic
777C22C13×#54811yescharacteristic
778C22C13×#54811yescharacteristic
779C22C13×#54811yescharacteristic
780C22C13×#55011yescharacteristic
781C22C13×#55211yescharacteristic
782C22C13×#55211yescharacteristic
783C22C13×#55211yescharacteristic
784C22C13×#55311yescharacteristic
785C22C13×#55311yescharacteristic
786C22C13×#55311yescharacteristic
787C22C13×#55511yescharacteristic
788C22C13×#55611yescharacteristic
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4C13×#39618yes—
799C2—44no—
800C2C2×C13×#39611yescharacteristic
801C2C13×#241411yescharacteristic
802C2C13×#241511yescharacteristic
803C2C13×#242611yescharacteristic
804C2C13×#242711yescharacteristic
805C2C13×#243911yescharacteristic
806C2C13×#244111yescharacteristic
807C2C13×#244211yescharacteristic
808C2C13×#244211yescharacteristic
809C2C13×#249411yescharacteristic
810C2C13×#249511yescharacteristic
811C2C13×#253511yescharacteristic
812C2C13×#253611yescharacteristic
813C2C13×#262811yescharacteristic
814C2C13×#285111yescharacteristic
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
1. C2×C13×#389C2semidirect
2. C2×C13×#389C2semidirect
3. C2×C13×#382C2semidirect
7. C13×#1443C2semidirect
8. C13×#1441C2semidirect
11. C13×C4⋊#95C2semidirect
105. #15220C13direct (N × H)
211. C2×#389C2×C13semidirect
212. C2×#389C2×C13semidirect
213. C2×#382C2×C13semidirect
217. #1443C2×C13semidirect
218. #1441C2×C13semidirect
221. C4⋊#95C2×C13semidirect
617. C13#15220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3892
C2×C13×#3822
C2×C13×#3802
C2×C4×C13×C22⋊C42
C13×#14432
C13×#14412
C13×#14392
C13×C4⋊#952
#1522013