Finite Group Databasebeta

← C13×#15183 #15701522

Subgroups — C13×#15183 #15701522

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#380C211yesmaximal, characteristic
3C2×C13×#380C211yesmaximal, characteristic
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
5C13×#1445C212yesmaximal, complemented
6C13×#1443C212yesmaximal, complemented
7C13×#1440C212yesmaximal
8C13×#1439C212yesmaximal
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C13×C4⋊#95C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2212yes—
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C13×#389—24no—
25C13×#380—24no—
26C13×#380—24no—
27C4×C13×C22⋊C4—24no—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C25×C13C2311yescharacteristic
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13D414yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—42no—
71C2×C13×C4⋊C4D414yes—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4—24no—
79C2×C13×C22⋊C4—24no—
80C2×C13×C22⋊C4—42no—
81C2×C13×C22⋊C4—42no—
82C2×C13×C22⋊C4—42no—
83C2×C13×C22⋊C4Q814yes—
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C13×#95—22no—
91C13×#95—22no—
92C13×#95—24no—
93C13×#95—24no—
94C13×#95—24no—
95C13×#95—24no—
96C13×#95—42no—
97C13×#95—42no—
98C13×#95—42no—
99C13×#95—42no—
100C13×#95—42no—
101#15183C1311yesmaximal, characteristic, direct product factor, Sylow
102C24×C13—21no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—21no—
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×C13C2×D412yes—
115C24×C13C2×Q812yes—
116C24×C13#4112yes—
117C24×C13C2411yescharacteristic
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
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—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—28no—
155C22×C4×C13—28no—
156C22×C4×C13—28no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
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—44no—
179C22×C4×C13—44no—
180C22×C4×C13—44no—
181C22×C4×C13—44no—
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2×D414yes—
184C22×C4×C13C2×D412yes—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×Q812yes—
187C22×C4×C13C2×Q812yes—
188C22×C4×C13#4112yes—
189C22×C4×C13#4112yes—
190C22×C4×C13#4112yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
193C22×C4×C13#4112yes—
194C22×C4×C13#4112yes—
195C13×C4⋊C4—28no—
196C13×C4⋊C4—48no—
197C13×C4⋊C4—44no—
198C13×C4⋊C4—44no—
199C13×C4⋊C4—44no—
200C13×C22⋊C4—28no—
201C13×C22⋊C4—28no—
202C13×C22⋊C4—48no—
203C13×C22⋊C4—48no—
204C42×C13—44no—
205C42×C13—44no—
206C2×#389C2×C1311yescharacteristic, complemented
207C2×#380C2×C1311yescharacteristic
208C2×#380C2×C1311yescharacteristic
209C2×C4×C22⋊C4C2×C1311yescharacteristic
210#1445C2×C1312yescomplemented
211#1443C2×C1312yescomplemented
212#1440C2×C1312yes—
213#1439C2×C1312yes—
214C4⋊#95C2×C1311yescharacteristic, complemented
215C4⋊#95C2×C1311yescharacteristic, complemented
216C4⋊#95C2×C1311yescharacteristic, complemented
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
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—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
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×C13C22⋊Q814yes—
252C23×C13C22×D411yescharacteristic
253C23×C13C22×D411yescharacteristic
254C23×C13C22×Q811yescharacteristic
255C23×C13C2×#4111yescharacteristic
256C23×C13C2×#4111yescharacteristic
257C23×C13C2×#4111yescharacteristic
258C23×C13C2×#4111yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13H(5,𝔽2)11yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C13H(5,𝔽2)11yescharacteristic
266C23×C132−1+411yescharacteristic
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—24no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—24no—
276C2×C4×C13—22no—
277C2×C4×C13—24no—
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—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—42no—
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—41no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—42no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—416no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
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#12114yes—
332C2×C4×C13#12314yes—
333C2×C4×C13#12314yes—
334C2×C4×C13#12314yes—
335C2×C4×C13#12414yes—
336C2×C4×C13#12614yes—
337C2×C4×C13#12614yes—
338C24×C4C22×C1311yescharacteristic
339C22×C4⋊C4C22×C1311yescharacteristic
340C22×C4⋊C4C22×C1311yescharacteristic
341C22×C4⋊C4C22×C1311yescharacteristic
342C22×C4⋊C4C22×C1312yes—
343C22×C4⋊C4C22×C1311yescharacteristic
344C22×C22⋊C4C22×C1311yescharacteristic
345C22×C22⋊C4C22×C1312yes—
346C22×C22⋊C4C22×C1311yescharacteristic
347C22×C22⋊C4C22×C1312yes—
348C22×C42C22×C1311yescharacteristic
349C22×C42C22×C1311yescharacteristic
350#389—24no—
351#380—24no—
352#380—24no—
353C4×C22⋊C4—24no—
354C2×#95C22×C1312yes—
355C2×#95C22×C1312yes—
356C2×#95C22×C1311yescharacteristic
357C2×#95C22×C1312yes—
358C2×#95C22×C1312yes—
359C2×#95C22×C1311yescharacteristic
360C2×#95C22×C1312yes—
361C2×#95C22×C1312yes—
362C2×#95C22×C1312yes—
363C2×#95C22×C1312yes—
364C2×#95C22×C1312yes—
365C22×C13—24no—
366C22×C13—24no—
367C22×C13—24no—
368C22×C13—42no—
369C22×C13—42no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13C2×#12111yescharacteristic
381C22×C13C2×C22⋊Q811yescharacteristic
382C22×C13C2×#12311yescharacteristic
383C22×C13C2×#12311yescharacteristic
384C22×C13C2×#12311yescharacteristic
385C22×C13#52511yescharacteristic
386C22×C13C2×#12411yescharacteristic
387C22×C13C2×#12611yescharacteristic
388C22×C13C2×#12611yescharacteristic
389C22×C13#52911yescharacteristic
390C22×C13#52911yescharacteristic
391C22×C13#53311yescharacteristic
392C22×C13#53311yescharacteristic
393C22×C13#53511yescharacteristic
394C22×C13#53711yescharacteristic
395C22×C13#54011yescharacteristic
396C22×C13#54011yescharacteristic
397C22×C13#54211yescharacteristic
398C22×C13#54211yescharacteristic
399C22×C13#54611yescharacteristic
400C22×C13#54611yescharacteristic
401C22×C13D4×Q811yescharacteristic
402C22×C13#55011yescharacteristic
403C22×C13#55211yescharacteristic
404C22×C13#55211yescharacteristic
405C22×C13#55311yescharacteristic
406C22×C13#55311yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55411yescharacteristic
410C22×C13#55411yescharacteristic
411C22×C13#55411yescharacteristic
412C22×C13#55511yescharacteristic
413C22×C13#55511yescharacteristic
414C22×C13#55611yescharacteristic
415C4×C13—42no—
416C4×C13—42no—
417C4×C13—42no—
418C4×C13—44no—
419C4×C13—42no—
420C4×C13—42no—
421C4×C13—82no—
422C4×C13—82no—
423C4×C13—82no—
424C4×C13#39718yes—
425C25C23×C1311yescharacteristic
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4D4×C1314yes—
433C23×C4C23×C1312yes—
434C23×C4C23×C1312yes—
435C23×C4C23×C1312yes—
436C23×C4C23×C1312yes—
437C23×C4C23×C1311yescharacteristic
438C23×C4C23×C1311yescharacteristic
439C23×C4C23×C1311yescharacteristic
440C23×C4C23×C1311yescharacteristic
441C23×C4C23×C1311yescharacteristic
442C23×C4C23×C1311yescharacteristic
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4D4×C1314yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4Q8×C1314yes—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476#95—22no—
477#95—22no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—24no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—42no—
487C2×C13—44no—
488C2×C13C2×#39711yescharacteristic
489C2×C13#241411yescharacteristic
490C2×C13#241711yescharacteristic
491C2×C13#242011yescharacteristic
492C2×C13#242311yescharacteristic
493C2×C13#248511yescharacteristic
494C2×C13#248711yescharacteristic
495C2×C13#249011yescharacteristic
496C2×C13#249211yescharacteristic
497C2×C13#249411yescharacteristic
498C2×C13#249511yescharacteristic
499C2×C13#249711yescharacteristic
500C2×C13#249711yescharacteristic
501C2×C13#262411yescharacteristic
502C2×C13#285511yescharacteristic
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24C2×D4×C1312yes—
516C24C2×Q8×C1312yes—
517C24C13×#4112yes—
518C24C24×C1311yescharacteristic
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
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—22no—
539C22×C4—22no—
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—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4C2×D4×C1312yes—
584C22×C4C2×D4×C1314yes—
585C22×C4C2×D4×C1312yes—
586C22×C4C2×D4×C1312yes—
587C22×C4C2×Q8×C1312yes—
588C22×C4C2×Q8×C1312yes—
589C22×C4C13×#4112yes—
590C22×C4C13×#4112yes—
591C22×C4C13×#4112yes—
592C22×C4C13×#4112yes—
593C22×C4C13×#4112yes—
594C22×C4C13×#4112yes—
595C22×C4C13×#4112yes—
596C4⋊C4—28no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C42—44no—
606C42—44no—
607C13#1518311yescharacteristic, direct product factor, Sylow
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C13×C22⋊Q814yes—
643C23C22×D4×C1311yescharacteristic
644C23C22×D4×C1311yescharacteristic
645C23C22×Q8×C1311yescharacteristic
646C23C2×C13×#4111yescharacteristic
647C23C2×C13×#4111yescharacteristic
648C23C2×C13×#4111yescharacteristic
649C23C2×C13×#4111yescharacteristic
650C23C2×C13×#4111yescharacteristic
651C23C2×C13×#4111yescharacteristic
652C23C2×C13×#4111yescharacteristic
653C23C2×C13×#4111yescharacteristic
654C23C13×H(5,𝔽2)11yescharacteristic
655C23C13×H(5,𝔽2)11yescharacteristic
656C23C13×H(5,𝔽2)11yescharacteristic
657C23C13×2−1+411yescharacteristic
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—416no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C13×#12114yes—
723C2×C4C13×#12314yes—
724C2×C4C13×#12314yes—
725C2×C4C13×#12314yes—
726C2×C4C13×#12414yes—
727C2×C4C13×#12614yes—
728C2×C4C13×#12614yes—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22C2×C13×#12111yescharacteristic
745C22C2×C13×C22⋊Q811yescharacteristic
746C22C2×C13×#12311yescharacteristic
747C22C2×C13×#12311yescharacteristic
748C22C2×C13×#12311yescharacteristic
749C22C13×#52511yescharacteristic
750C22C2×C13×#12411yescharacteristic
751C22C2×C13×#12611yescharacteristic
752C22C2×C13×#12611yescharacteristic
753C22C13×#52911yescharacteristic
754C22C13×#52911yescharacteristic
755C22C13×#53311yescharacteristic
756C22C13×#53311yescharacteristic
757C22C13×#53511yescharacteristic
758C22C13×#53711yescharacteristic
759C22C13×#54011yescharacteristic
760C22C13×#54011yescharacteristic
761C22C13×#54211yescharacteristic
762C22C13×#54211yescharacteristic
763C22C13×#54611yescharacteristic
764C22C13×#54611yescharacteristic
765C22D4×Q8×C1311yescharacteristic
766C22C13×#55011yescharacteristic
767C22C13×#55211yescharacteristic
768C22C13×#55211yescharacteristic
769C22C13×#55311yescharacteristic
770C22C13×#55311yescharacteristic
771C22C13×#55311yescharacteristic
772C22C13×#55311yescharacteristic
773C22C13×#55411yescharacteristic
774C22C13×#55411yescharacteristic
775C22C13×#55411yescharacteristic
776C22C13×#55511yescharacteristic
777C22C13×#55511yescharacteristic
778C22C13×#55611yescharacteristic
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4C13×#39718yes—
789C2—44no—
790C2C2×C13×#39711yescharacteristic
791C2C13×#241411yescharacteristic
792C2C13×#241711yescharacteristic
793C2C13×#242011yescharacteristic
794C2C13×#242311yescharacteristic
795C2C13×#248511yescharacteristic
796C2C13×#248711yescharacteristic
797C2C13×#249011yescharacteristic
798C2C13×#249211yescharacteristic
799C2C13×#249411yescharacteristic
800C2C13×#249511yescharacteristic
801C2C13×#249711yescharacteristic
802C2C13×#249711yescharacteristic
803C2C13×#262411yescharacteristic
804C2C13×#285511yescharacteristic
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
5. C13×#1445C2semidirect
6. C13×#1443C2semidirect
9. C13×C4⋊#95C2semidirect
10. C13×C4⋊#95C2semidirect
11. C13×C4⋊#95C2semidirect
101. #15183C13direct (N × H)
206. C2×#389C2×C13semidirect
210. #1445C2×C13semidirect
211. #1443C2×C13semidirect
214. C4⋊#95C2×C13semidirect
215. C4⋊#95C2×C13semidirect
216. C4⋊#95C2×C13semidirect
607. C13#15183direct (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×#3802
C2×C4×C13×C22⋊C42
C13×#14452
C13×#14432
C13×#14402
C13×#14392
C13×C4⋊#952
#1518313