Finite Group Databasebeta

← C13×#63045 #15749384

Subgroups — C13×#63045 #15749384

Order 3328.

7484 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C2112yesmaximal, complemented
2C13×#3558C216yesmaximal, complemented
3C13×#3549C213yesmaximal, complemented
4C13×#3545C216yesmaximal, complemented
5C13×#3540C216yesmaximal, complemented
6C13×#3532C2112yesmaximal, complemented
7C13×#3529C211yesmaximal, characteristic, complemented
8C2×C13×H(3,𝔽4)C212yesmaximal, complemented
9C13×#3514C216yesmaximal, complemented
10C13×#3500C213yesmaximal, complemented
11C13×#3484C216yesmaximal, complemented
12C2×C13×2−1+4C2211yescharacteristic, complemented
13C2×C13×H(5,𝔽2)C2213yescomplemented
14C23×D4×C13C2212yescomplemented
15C13×#563C2213yescomplemented
16C13×#562C2216yescomplemented
17C13×#562C22112yescomplemented
18C13×H(3,𝔽4)C2211yescharacteristic, complemented
19C13×H(3,𝔽4)C22112yescomplemented
20C13×H(3,𝔽4)C2216yescomplemented
21C13×H(3,𝔽4)C22112yescomplemented
22C13×H(3,𝔽4)C2216yescomplemented
23C13×#560C2216yescomplemented
24C13×#560C22112yescomplemented
25C13×#559C22112yescomplemented
26C13×#559C2216yescomplemented
27C13×#556C2216yescomplemented
28C13×#555C22112yescomplemented
29C13×#555C2216yescomplemented
30C13×#551C22112yescomplemented
31C13×#551C22124yescomplemented
32D4×Q8×C13C2212yescomplemented
33C13×#548C22112yescomplemented
34C13×#548C22112yescomplemented
35C13×#546C22112yescomplemented
36C13×#546C22112yescomplemented
37C13×#546C22124yescomplemented
38C13×#546C22112yescomplemented
39C13×#546C22124yescomplemented
40C13×#546C22124yescomplemented
41D42×C13C2216yescomplemented
42D42×C13C22124yescomplemented
43D42×C13C2216yescomplemented
44D42×C13C22112yescomplemented
45C13×#542C22124yescomplemented
46C13×#542C22112yescomplemented
47C13×#538C22124yescomplemented
48C13×#538C22124yescomplemented
49C13×#538C22124yescomplemented
50C13×#538C22112yescomplemented
51C13×#536C2213yescomplemented
52C13×#536C2216yescomplemented
53C13×#535C2216yescomplemented
54C13×#535C2216yescomplemented
55C13×#535C2216yescomplemented
56C13×#535C22124yescomplemented
57C13×#535C2213yescomplemented
58C13×#534C22112yescomplemented
59C13×#534C22112yescomplemented
60C13×#534C22112yescomplemented
61C13×#532C2213yescomplemented
62C13×#532C2216yescomplemented
63C13×#532C2216yescomplemented
64C13×#529C2216yescomplemented
65C13×#529C22112yescomplemented
66C2×C13×#124C2216yescomplemented
67C2×C13×#124C22112yescomplemented
68C2×C13×#124C2213yescomplemented
69C13×#525C2216yescomplemented
70C13×#525C2216yescomplemented
71C2×C13×#120C22112yescomplemented
72C2×C13×#120C22112yescomplemented
73C13×#518C2216yescomplemented
74C4×C13×#41C2213yescomplemented
75C25×C13C2314yescomplemented
76C13×2−1+4—44no—
77C13×H(5,𝔽2)—412no—
78C2×C13×#41C2313yes—
79C2×C13×#41C2313yes—
80C2×C13×#41C2316yes—
81C2×C13×#41C2316yes—
82C2×C13×#41C2311yescharacteristic, complemented
83C2×C13×#41C2316yescomplemented
84C2×C13×#41C23112yescomplemented
85C22×Q8×C13C2312yescomplemented
86C22×Q8×C13C2313yescomplemented
87C22×Q8×C13C2314yescomplemented
88C22×D4×C13—48no—
89C22×D4×C13C2316yes—
90C22×D4×C13C2316yes—
91C22×D4×C13C23112yes—
92C22×D4×C13C2313yes—
93C22×D4×C13C23112yes—
94C22×D4×C13C23112yescomplemented
95C22×D4×C13C2316yescomplemented
96C22×D4×C13C23124yescomplemented
97C23×C4×C13C2312yescomplemented
98C13×C4⋊Q8C2316yescomplemented
99C13×C4⋊Q8C2313yescomplemented
100C13×C4⋊Q8C2316yescomplemented
101C13×#127C2316yes—
102C13×#127C2313yes—
103C13×#127C23112yes—
104C13×#127C2316yescomplemented
105C13×#126C23124yescomplemented
106C13×#126C23112yescomplemented
107C13×#126C23124yescomplemented
108C13×#125C2316yescomplemented
109C13×#124C2316yes—
110C13×#124C2313yes—
111C13×#124C2316yes—
112C13×#124C23112yes—
113C13×#124C2316yescomplemented
114C13×#124C23112yescomplemented
115C13×#124C2316yescomplemented
116C13×#124C2316yescomplemented
117C13×#124C23112yescomplemented
118C13×#124C23124yescomplemented
119C13×#124C23112yescomplemented
120C13×#124C23124yescomplemented
121C13×#124C23124yescomplemented
122C13×#124C2313yescomplemented
123C13×#124C23124yescomplemented
124C13×#124C23112yescomplemented
125C13×#123C2316yes—
126C13×#123C23112yescomplemented
127C13×#123C2316yescomplemented
128C13×#123C23124yescomplemented
129C13×#123C23112yescomplemented
130C13×#123C23124yescomplemented
131C13×#123C23124yescomplemented
132C13×#123C23124yescomplemented
133C13×#123C23112yescomplemented
134C13×C22⋊Q8C23112yescomplemented
135C13×C22⋊Q8C23112yescomplemented
136C13×C22⋊Q8C23112yescomplemented
137C13×C22⋊Q8C2316yescomplemented
138C13×C22⋊Q8C23124yescomplemented
139C13×C22⋊Q8C23124yescomplemented
140C13×#121C23112yes—
141C13×#121C23112yes—
142C13×#121C23112yes—
143C13×#121C2316yes—
144C13×#121C23124yes—
145C13×#121C23112yescomplemented
146C13×#121C23124yescomplemented
147C13×#121C23112yescomplemented
148C13×#121C23112yescomplemented
149C13×#121C23124yescomplemented
150C13×#121C23124yescomplemented
151C13×#121C23124yescomplemented
152C13×#121C23124yescomplemented
153C13×#120C2316yes—
154C13×#120C23112yes—
155C13×#120C23124yes—
156C13×#120C23124yes—
157C13×#120C2316yescomplemented
158C13×#120C23112yescomplemented
159C13×#120C23112yescomplemented
160C13×#120C23112yescomplemented
161C13×#120C23112yescomplemented
162C13×#120C23124yescomplemented
163C13×#120C23124yescomplemented
164C13×#120C23124yescomplemented
165C13×#120C23112yescomplemented
166C4×Q8×C13C2316yescomplemented
167C4×Q8×C13C2312yescomplemented
168C4×Q8×C13C23112yescomplemented
169C4×D4×C13C2316yes—
170C4×D4×C13C2316yes—
171C4×D4×C13C23112yescomplemented
172C4×D4×C13C23124yescomplemented
173C4×D4×C13C23112yescomplemented
174C4×D4×C13C23112yescomplemented
175C4×D4×C13C23124yescomplemented
176C4×D4×C13C23112yescomplemented
177C4×D4×C13C23112yescomplemented
178C4×D4×C13C23124yescomplemented
179C13×#117C2316yescomplemented
180C13×#117C2313yescomplemented
181C13×#117C2316yescomplemented
182C13×#117C2316yescomplemented
183C13×#117C23124yescomplemented
184C2×C13×C22⋊C4C23112yescomplemented
185C2×C13×C22⋊C4C23112yescomplemented
186C2×C13×C22⋊C4C23124yescomplemented
187C2×C13×C22⋊C4C23124yescomplemented
188C2×C13×C22⋊C4C23112yescomplemented
189C2×C42×C13C2316yescomplemented
190C2×C42×C13C2313yescomplemented
191#63045C1311yesmaximal, characteristic, direct product factor, Sylow
192C24×C13—48no—
193C24×C13—88no—
194C24×C13C24112yes—
195C24×C13C24112yes—
196C24×C13C2416yes—
197C24×C13C2412yes—
198C13×#41—212no—
199C13×#41—46no—
200C13×#41—42no—
201C13×#41—412no—
202C13×#41—412no—
203C13×#41—412no—
204C13×#41—812no—
205C2×Q8×C13—44no—
206C2×Q8×C13—46no—
207C2×Q8×C13—84no—
208C2×Q8×C13C2413yes—
209C2×Q8×C13C2412yes—
210C2×Q8×C13C24112yes—
211C2×Q8×C13C2416yes—
212C2×Q8×C13C2413yes—
213C2×Q8×C13C2411yescharacteristic
214C2×D4×C13—224no—
215C2×D4×C13—412no—
216C2×D4×C13—46no—
217C2×D4×C13—412no—
218C2×D4×C13—424no—
219C2×D4×C13—424no—
220C2×D4×C13—812no—
221C2×D4×C13—824no—
222C2×D4×C13C24112yes—
223C2×D4×C13C2416yes—
224C2×D4×C13C2416yes—
225C2×D4×C13C2416yes—
226C2×D4×C13C24124yes—
227C2×D4×C13C24112yes—
228C2×D4×C13C24112yes—
229C2×D4×C13C24124yes—
230C2×D4×C13C24112yes—
231C2×D4×C13C2413yes—
232C2×D4×C13C24112yes—
233C2×D4×C13C2416yes—
234C2×D4×C13C2413yes—
235C2×D4×C13C2416yes—
236C2×D4×C13C24112yes—
237C2×D4×C13C2411yescharacteristic
238C22×C4×C13—44no—
239C22×C4×C13C2416yes—
240C22×C4×C13C2413yes—
241C22×C4×C13C2416yes—
242C22×C4×C13C24112yes—
243C22×C4×C13C2416yes—
244C22×C4×C13C24124yes—
245C22×C4×C13C2416yes—
246C22×C4×C13C24112yes—
247C22×C4×C13C2416yes—
248C13×C4⋊C4C2416yes—
249C13×C4⋊C4C24112yes—
250C13×C4⋊C4C24112yes—
251C13×C4⋊C4C24112yes—
252C13×C4⋊C4C24112yes—
253C13×C4⋊C4C2416yes—
254C13×C4⋊C4C24124yes—
255C13×C4⋊C4C2416yes—
256C13×C22⋊C4C24112yes—
257C13×C22⋊C4C24112yes—
258C13×C22⋊C4C2416yes—
259C13×C22⋊C4C2416yes—
260C13×C22⋊C4C24112yes—
261C13×C22⋊C4C24124yes—
262C13×C22⋊C4C24112yes—
263C13×C22⋊C4C24124yes—
264C13×C22⋊C4C24124yes—
265C13×C22⋊C4C24124yes—
266C13×C22⋊C4C24124yes—
267C13×C22⋊C4C24124yes—
268C13×C22⋊C4C2416yes—
269C13×C22⋊C4C24112yes—
270C42×C13C2413yes—
271C42×C13C2416yes—
272C42×C13C2416yes—
273C42×C13C2413yes—
274C42×C13C24112yes—
275C42×C13C24112yes—
276#3558C2×C13112yescomplemented
277#3558C2×C1316yescomplemented
278#3549C2×C1313yescomplemented
279#3545C2×C1316yescomplemented
280#3540C2×C1316yescomplemented
281#3532C2×C13112yescomplemented
282#3529C2×C1311yescharacteristic, complemented
283C2×H(3,𝔽4)C2×C1312yescomplemented
284#3514C2×C1316yescomplemented
285#3500C2×C1313yescomplemented
286#3484C2×C1316yescomplemented
287C23×C13—224no—
288C23×C13—42no—
289C23×C13—44no—
290C23×C13—412no—
291C23×C13—424no—
292C23×C13—424no—
293C23×C13—46no—
294C23×C13—412no—
295C23×C13—832no—
296C23×C13C2516yes—
297C23×C13C25112yes—
298C23×C13C2513yes—
299C23×C13C2512yes—
300Q8×C13—26no—
301Q8×C13—41no—
302Q8×C13—46no—
303Q8×C13—42no—
304Q8×C13—412no—
305Q8×C13—43no—
306D4×C13—224no—
307D4×C13—212no—
308D4×C13—212no—
309D4×C13—412no—
310D4×C13—43no—
311D4×C13—46no—
312D4×C13—46no—
313D4×C13—412no—
314D4×C13—412no—
315D4×C13—412no—
316D4×C13—424no—
317D4×C13—46no—
318D4×C13—424no—
319D4×C13—412no—
320D4×C13—43no—
321D4×C13H(5,𝔽2)14yes—
322C2×C4×C13—212no—
323C2×C4×C13—212no—
324C2×C4×C13—26no—
325C2×C4×C13—46no—
326C2×C4×C13—412no—
327C2×C4×C13—412no—
328C2×C4×C13—424no—
329C2×C4×C13—46no—
330C2×C4×C13—46no—
331C2×C4×C13C2516yes—
332C2×C4×C13C25112yes—
333C2×C4×C13C2513yes—
334C2×C4×C13C2516yes—
335C2×C4×C13C2516yes—
336C2×C4×C13C2516yes—
337C2×C4×C13C2511yescharacteristic
338C2×2−1+4C22×C1311yescharacteristic, complemented
339C2×H(5,𝔽2)C22×C1313yescomplemented
340C23×D4C22×C1312yescomplemented
341#563C22×C1313yescomplemented
342#562C22×C1316yescomplemented
343#562C22×C13112yescomplemented
344H(3,𝔽4)C22×C1311yescharacteristic, complemented
345H(3,𝔽4)C22×C13112yescomplemented
346H(3,𝔽4)C22×C1316yescomplemented
347H(3,𝔽4)C22×C13112yescomplemented
348H(3,𝔽4)C22×C1316yescomplemented
349#560C22×C1316yescomplemented
350#560C22×C13112yescomplemented
351#559C22×C1316yescomplemented
352#559C22×C13112yescomplemented
353#556C22×C1316yescomplemented
354#555C22×C13112yescomplemented
355#555C22×C1316yescomplemented
356#551C22×C13112yescomplemented
357#551C22×C13124yescomplemented
358D4×Q8C22×C1312yescomplemented
359#548C22×C13112yescomplemented
360#548C22×C13112yescomplemented
361#546C22×C13112yescomplemented
362#546C22×C13112yescomplemented
363#546C22×C13124yescomplemented
364#546C22×C13112yescomplemented
365#546C22×C13124yescomplemented
366#546C22×C13124yescomplemented
367D42C22×C1316yescomplemented
368D42C22×C13124yescomplemented
369D42C22×C1316yescomplemented
370D42C22×C13112yescomplemented
371#542C22×C13112yescomplemented
372#542C22×C13124yescomplemented
373#538C22×C13124yescomplemented
374#538C22×C13124yescomplemented
375#538C22×C13124yescomplemented
376#538C22×C13112yescomplemented
377#536C22×C1313yescomplemented
378#536C22×C1316yescomplemented
379#535C22×C1316yescomplemented
380#535C22×C1316yescomplemented
381#535C22×C1316yescomplemented
382#535C22×C13124yescomplemented
383#535C22×C1313yescomplemented
384#534C22×C13112yescomplemented
385#534C22×C13112yescomplemented
386#534C22×C13112yescomplemented
387#532C22×C1313yescomplemented
388#532C22×C1316yescomplemented
389#532C22×C1316yescomplemented
390#529C22×C1316yescomplemented
391#529C22×C13112yescomplemented
392C2×#124C22×C1316yescomplemented
393C2×#124C22×C13112yescomplemented
394C2×#124C22×C1313yescomplemented
395#525C22×C1316yescomplemented
396#525C22×C1316yescomplemented
397C2×#120C22×C13112yescomplemented
398C2×#120C22×C13112yescomplemented
399#518C22×C1316yescomplemented
400C4×#41C22×C1313yescomplemented
401C22×C13—24no—
402C22×C13—23no—
403C22×C13—26no—
404C22×C13—212no—
405C22×C13—26no—
406C22×C13—224no—
407C22×C13—212no—
408C22×C13—48no—
409C22×C13—824no—
410C22×C13—824no—
411C22×C13—166no—
412C22×C13C2×H(5,𝔽2)14yes—
413C22×C13C2611yescharacteristic
414C4×C13—23no—
415C4×C13—26no—
416C4×C13—26no—
417C4×C13—26no—
418C4×C13—212no—
419C4×C13—26no—
420C4×C13C2×H(5,𝔽2)12yes—
421C25C23×C1314yescomplemented
4222−1+4—44no—
423H(5,𝔽2)—412no—
424C2×#41C23×C1313yes—
425C2×#41C23×C1313yes—
426C2×#41C23×C1316yes—
427C2×#41C23×C1316yes—
428C2×#41C23×C1311yescharacteristic, complemented
429C2×#41C23×C1316yescomplemented
430C2×#41C23×C13112yescomplemented
431C22×Q8C23×C1312yescomplemented
432C22×Q8C23×C1313yescomplemented
433C22×Q8C23×C1314yescomplemented
434C22×D4—48no—
435C22×D4C23×C1316yes—
436C22×D4C23×C1316yes—
437C22×D4C23×C13112yes—
438C22×D4C23×C1313yes—
439C22×D4C23×C13112yes—
440C22×D4C23×C13112yescomplemented
441C22×D4C23×C1316yescomplemented
442C22×D4C23×C13124yescomplemented
443C23×C4C23×C1312yescomplemented
444C4⋊Q8C23×C1316yescomplemented
445C4⋊Q8C23×C1313yescomplemented
446C4⋊Q8C23×C1316yescomplemented
447#127C23×C1316yes—
448#127C23×C1313yes—
449#127C23×C13112yes—
450#127C23×C1316yescomplemented
451#126C23×C13124yescomplemented
452#126C23×C13112yescomplemented
453#126C23×C13124yescomplemented
454#125C23×C1316yescomplemented
455#124C23×C1316yes—
456#124C23×C1313yes—
457#124C23×C1316yes—
458#124C23×C13112yes—
459#124C23×C1316yescomplemented
460#124C23×C13112yescomplemented
461#124C23×C1316yescomplemented
462#124C23×C1316yescomplemented
463#124C23×C13112yescomplemented
464#124C23×C13124yescomplemented
465#124C23×C13112yescomplemented
466#124C23×C13124yescomplemented
467#124C23×C13124yescomplemented
468#124C23×C1313yescomplemented
469#124C23×C13124yescomplemented
470#124C23×C13112yescomplemented
471#123C23×C1316yes—
472#123C23×C13112yescomplemented
473#123C23×C1316yescomplemented
474#123C23×C13124yescomplemented
475#123C23×C13112yescomplemented
476#123C23×C13124yescomplemented
477#123C23×C13124yescomplemented
478#123C23×C13124yescomplemented
479#123C23×C13112yescomplemented
480C22⋊Q8C23×C13112yescomplemented
481C22⋊Q8C23×C13112yescomplemented
482C22⋊Q8C23×C13112yescomplemented
483C22⋊Q8C23×C1316yescomplemented
484C22⋊Q8C23×C13124yescomplemented
485C22⋊Q8C23×C13124yescomplemented
486#121C23×C13112yes—
487#121C23×C13112yes—
488#121C23×C13112yes—
489#121C23×C1316yes—
490#121C23×C13124yes—
491#121C23×C13112yescomplemented
492#121C23×C13124yescomplemented
493#121C23×C13112yescomplemented
494#121C23×C13112yescomplemented
495#121C23×C13124yescomplemented
496#121C23×C13124yescomplemented
497#121C23×C13124yescomplemented
498#121C23×C13124yescomplemented
499#120C23×C1316yes—
500#120C23×C13112yes—
501#120C23×C13124yes—
502#120C23×C13124yes—
503#120C23×C1316yescomplemented
504#120C23×C13112yescomplemented
505#120C23×C13112yescomplemented
506#120C23×C13112yescomplemented
507#120C23×C13112yescomplemented
508#120C23×C13124yescomplemented
509#120C23×C13124yescomplemented
510#120C23×C13124yescomplemented
511#120C23×C13112yescomplemented
512C4×Q8C23×C1316yescomplemented
513C4×Q8C23×C1312yescomplemented
514C4×Q8C23×C13112yescomplemented
515C4×D4C23×C1316yes—
516C4×D4C23×C1316yes—
517C4×D4C23×C13112yescomplemented
518C4×D4C23×C13124yescomplemented
519C4×D4C23×C13112yescomplemented
520C4×D4C23×C13112yescomplemented
521C4×D4C23×C13124yescomplemented
522C4×D4C23×C13112yescomplemented
523C4×D4C23×C13112yescomplemented
524C4×D4C23×C13124yescomplemented
525#117C23×C1316yescomplemented
526#117C23×C1313yescomplemented
527#117C23×C1316yescomplemented
528#117C23×C1316yescomplemented
529#117C23×C13124yescomplemented
530C2×C22⋊C4C23×C13112yescomplemented
531C2×C22⋊C4C23×C13112yescomplemented
532C2×C22⋊C4C23×C13124yescomplemented
533C2×C22⋊C4C23×C13124yescomplemented
534C2×C22⋊C4C23×C13112yescomplemented
535C2×C42C23×C1316yescomplemented
536C2×C42C23×C1313yescomplemented
537C2×C13—24no—
538C2×C13—46no—
539C2×C13—412no—
540C2×C13—43no—
541C2×C13C22×H(5,𝔽2)11yescharacteristic
542C2×C13H(7,𝔽2)12yes—
543C24—48no—
544C24—88no—
545C24C24×C13112yes—
546C24C24×C13112yes—
547C24C24×C1316yes—
548C24C24×C1312yes—
549#41—212no—
550#41—46no—
551#41—42no—
552#41—412no—
553#41—412no—
554#41—412no—
555#41—812no—
556C2×Q8—44no—
557C2×Q8—46no—
558C2×Q8—84no—
559C2×Q8C24×C1313yes—
560C2×Q8C24×C1312yes—
561C2×Q8C24×C13112yes—
562C2×Q8C24×C1316yes—
563C2×Q8C24×C1313yes—
564C2×Q8C24×C1311yescharacteristic
565C2×D4—224no—
566C2×D4—412no—
567C2×D4—46no—
568C2×D4—412no—
569C2×D4—424no—
570C2×D4—424no—
571C2×D4—812no—
572C2×D4—824no—
573C2×D4C24×C13112yes—
574C2×D4C24×C1316yes—
575C2×D4C24×C1316yes—
576C2×D4C24×C1316yes—
577C2×D4C24×C13124yes—
578C2×D4C24×C13112yes—
579C2×D4C24×C13112yes—
580C2×D4C24×C13124yes—
581C2×D4C24×C13112yes—
582C2×D4C24×C1313yes—
583C2×D4C24×C13112yes—
584C2×D4C24×C1316yes—
585C2×D4C24×C1313yes—
586C2×D4C24×C1316yes—
587C2×D4C24×C13112yes—
588C2×D4C24×C1311yescharacteristic
589C22×C4—44no—
590C22×C4C24×C1316yes—
591C22×C4C24×C1313yes—
592C22×C4C24×C1316yes—
593C22×C4C24×C13112yes—
594C22×C4C24×C1316yes—
595C22×C4C24×C13124yes—
596C22×C4C24×C1316yes—
597C22×C4C24×C13112yes—
598C22×C4C24×C1316yes—
599C4⋊C4C24×C1316yes—
600C4⋊C4C24×C13112yes—
601C4⋊C4C24×C13112yes—
602C4⋊C4C24×C13112yes—
603C4⋊C4C24×C13112yes—
604C4⋊C4C24×C1316yes—
605C4⋊C4C24×C13124yes—
606C4⋊C4C24×C1316yes—
607C22⋊C4C24×C13112yes—
608C22⋊C4C24×C13112yes—
609C22⋊C4C24×C1316yes—
610C22⋊C4C24×C1316yes—
611C22⋊C4C24×C13112yes—
612C22⋊C4C24×C13124yes—
613C22⋊C4C24×C13112yes—
614C22⋊C4C24×C13124yes—
615C22⋊C4C24×C13124yes—
616C22⋊C4C24×C13124yes—
617C22⋊C4C24×C13124yes—
618C22⋊C4C24×C13124yes—
619C22⋊C4C24×C1316yes—
620C22⋊C4C24×C13112yes—
621C42C24×C1313yes—
622C42C24×C1316yes—
623C42C24×C1316yes—
624C42C24×C1313yes—
625C42C24×C13112yes—
626C42C24×C13112yes—
627C13#6304511yescharacteristic, direct product factor, Sylow
628C23—224no—
629C23—42no—
630C23—44no—
631C23—412no—
632C23—424no—
633C23—424no—
634C23—46no—
635C23—412no—
636C23—832no—
637C23C25×C1316yes—
638C23C25×C13112yes—
639C23C25×C1313yes—
640C23C25×C1312yes—
641Q8—26no—
642Q8—41no—
643Q8—46no—
644Q8—42no—
645Q8—412no—
646Q8—43no—
647D4—224no—
648D4—212no—
649D4—212no—
650D4—412no—
651D4—43no—
652D4—46no—
653D4—46no—
654D4—412no—
655D4—412no—
656D4—412no—
657D4—424no—
658D4—46no—
659D4—424no—
660D4—412no—
661D4—43no—
662D4C13×H(5,𝔽2)14yes—
663C2×C4—212no—
664C2×C4—212no—
665C2×C4—26no—
666C2×C4—46no—
667C2×C4—412no—
668C2×C4—412no—
669C2×C4—424no—
670C2×C4—46no—
671C2×C4—46no—
672C2×C4C25×C1316yes—
673C2×C4C25×C13112yes—
674C2×C4C25×C1313yes—
675C2×C4C25×C1316yes—
676C2×C4C25×C1316yes—
677C2×C4C25×C1316yes—
678C2×C4C25×C1311yescharacteristic
679C22—24no—
680C22—23no—
681C22—26no—
682C22—212no—
683C22—26no—
684C22—224no—
685C22—212no—
686C22—48no—
687C22—824no—
688C22—824no—
689C22—166no—
690C22C2×C13×H(5,𝔽2)14yes—
691C22C26×C1311yescharacteristic
692C4—23no—
693C4—26no—
694C4—26no—
695C4—26no—
696C4—212no—
697C4—26no—
698C4C2×C13×H(5,𝔽2)12yes—
699C2—24no—
700C2—46no—
701C2—412no—
702C2—43no—
703C2C22×C13×H(5,𝔽2)11yescharacteristic
704C2C13×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3558C2semidirect
2. C13×#3558C2semidirect
3. C13×#3549C2semidirect
4. C13×#3545C2semidirect
5. C13×#3540C2semidirect
6. C13×#3532C2semidirect
7. C13×#3529C2semidirect
8. C2×C13×H(3,𝔽4)C2semidirect
9. C13×#3514C2semidirect
10. C13×#3500C2semidirect
11. C13×#3484C2semidirect
12. C2×C13×2−1+4C22semidirect
13. C2×C13×H(5,𝔽2)C22semidirect
14. C23×D4×C13C22semidirect
15. C13×#563C22semidirect
16. C13×#562C22semidirect
17. C13×#562C22semidirect
18. C13×H(3,𝔽4)C22semidirect
19. C13×H(3,𝔽4)C22semidirect
20. C13×H(3,𝔽4)C22semidirect
21. C13×H(3,𝔽4)C22semidirect
22. C13×H(3,𝔽4)C22semidirect
23. C13×#560C22semidirect
24. C13×#560C22semidirect
25. C13×#559C22semidirect
26. C13×#559C22semidirect
27. C13×#556C22semidirect
28. C13×#555C22semidirect
29. C13×#555C22semidirect
30. C13×#551C22semidirect
31. C13×#551C22semidirect
32. D4×Q8×C13C22semidirect
33. C13×#548C22semidirect
34. C13×#548C22semidirect
35. C13×#546C22semidirect
36. C13×#546C22semidirect
37. C13×#546C22semidirect
38. C13×#546C22semidirect
39. C13×#546C22semidirect
40. C13×#546C22semidirect
41. D42×C13C22semidirect
42. D42×C13C22semidirect
43. D42×C13C22semidirect
44. D42×C13C22semidirect
45. C13×#542C22semidirect
46. C13×#542C22semidirect
47. C13×#538C22semidirect
48. C13×#538C22semidirect
49. C13×#538C22semidirect
50. C13×#538C22semidirect
51. C13×#536C22semidirect
52. C13×#536C22semidirect
53. C13×#535C22semidirect
54. C13×#535C22semidirect
55. C13×#535C22semidirect
56. C13×#535C22semidirect
57. C13×#535C22semidirect
58. C13×#534C22semidirect
59. C13×#534C22semidirect
60. C13×#534C22semidirect
61. C13×#532C22semidirect
62. C13×#532C22semidirect
63. C13×#532C22semidirect
64. C13×#529C22semidirect
65. C13×#529C22semidirect
66. C2×C13×#124C22semidirect
67. C2×C13×#124C22semidirect
68. C2×C13×#124C22semidirect
69. C13×#525C22semidirect
70. C13×#525C22semidirect
71. C2×C13×#120C22semidirect
72. C2×C13×#120C22semidirect
73. C13×#518C22semidirect
74. C4×C13×#41C22semidirect
75. C25×C13C23semidirect
82. C2×C13×#41C23semidirect
83. C2×C13×#41C23semidirect
84. C2×C13×#41C23semidirect
85. C22×Q8×C13C23semidirect
86. C22×Q8×C13C23semidirect
87. C22×Q8×C13C23semidirect
94. C22×D4×C13C23semidirect
95. C22×D4×C13C23semidirect
96. C22×D4×C13C23semidirect
97. C23×C4×C13C23semidirect
98. C13×C4⋊Q8C23semidirect
99. C13×C4⋊Q8C23semidirect
100. C13×C4⋊Q8C23semidirect
104. C13×#127C23semidirect
105. C13×#126C23semidirect
106. C13×#126C23semidirect
107. C13×#126C23semidirect
108. C13×#125C23semidirect
113. C13×#124C23semidirect
114. C13×#124C23semidirect
115. C13×#124C23semidirect
116. C13×#124C23semidirect
117. C13×#124C23semidirect
118. C13×#124C23semidirect
119. C13×#124C23semidirect
120. C13×#124C23semidirect
121. C13×#124C23semidirect
122. C13×#124C23semidirect
123. C13×#124C23semidirect
124. C13×#124C23semidirect
126. C13×#123C23semidirect
127. C13×#123C23semidirect
128. C13×#123C23semidirect
129. C13×#123C23semidirect
130. C13×#123C23semidirect
131. C13×#123C23semidirect
132. C13×#123C23semidirect
133. C13×#123C23semidirect
134. C13×C22⋊Q8C23semidirect
135. C13×C22⋊Q8C23semidirect
136. C13×C22⋊Q8C23semidirect
137. C13×C22⋊Q8C23semidirect
138. C13×C22⋊Q8C23semidirect
139. C13×C22⋊Q8C23semidirect
145. C13×#121C23semidirect
146. C13×#121C23semidirect
147. C13×#121C23semidirect
148. C13×#121C23semidirect
149. C13×#121C23semidirect
150. C13×#121C23semidirect
151. C13×#121C23semidirect
152. C13×#121C23semidirect
157. C13×#120C23semidirect
158. C13×#120C23semidirect
159. C13×#120C23semidirect
160. C13×#120C23semidirect
161. C13×#120C23semidirect
162. C13×#120C23semidirect
163. C13×#120C23semidirect
164. C13×#120C23semidirect
165. C13×#120C23semidirect
166. C4×Q8×C13C23semidirect
167. C4×Q8×C13C23semidirect
168. C4×Q8×C13C23semidirect
171. C4×D4×C13C23semidirect
172. C4×D4×C13C23semidirect
173. C4×D4×C13C23semidirect
174. C4×D4×C13C23semidirect
175. C4×D4×C13C23semidirect
176. C4×D4×C13C23semidirect
177. C4×D4×C13C23semidirect
178. C4×D4×C13C23semidirect
179. C13×#117C23semidirect
180. C13×#117C23semidirect
181. C13×#117C23semidirect
182. C13×#117C23semidirect
183. C13×#117C23semidirect
184. C2×C13×C22⋊C4C23semidirect
185. C2×C13×C22⋊C4C23semidirect
186. C2×C13×C22⋊C4C23semidirect
187. C2×C13×C22⋊C4C23semidirect
188. C2×C13×C22⋊C4C23semidirect
189. C2×C42×C13C23semidirect
190. C2×C42×C13C23semidirect
191. #63045C13direct (N × H)
276. #3558C2×C13semidirect
277. #3558C2×C13semidirect
278. #3549C2×C13semidirect
279. #3545C2×C13semidirect
280. #3540C2×C13semidirect
281. #3532C2×C13semidirect
282. #3529C2×C13semidirect
283. C2×H(3,𝔽4)C2×C13semidirect
284. #3514C2×C13semidirect
285. #3500C2×C13semidirect
286. #3484C2×C13semidirect
338. C2×2−1+4C22×C13semidirect
339. C2×H(5,𝔽2)C22×C13semidirect
340. C23×D4C22×C13semidirect
341. #563C22×C13semidirect
342. #562C22×C13semidirect
343. #562C22×C13semidirect
344. H(3,𝔽4)C22×C13semidirect
345. H(3,𝔽4)C22×C13semidirect
346. H(3,𝔽4)C22×C13semidirect
347. H(3,𝔽4)C22×C13semidirect
348. H(3,𝔽4)C22×C13semidirect
349. #560C22×C13semidirect
350. #560C22×C13semidirect
351. #559C22×C13semidirect
352. #559C22×C13semidirect
353. #556C22×C13semidirect
354. #555C22×C13semidirect
355. #555C22×C13semidirect
356. #551C22×C13semidirect
357. #551C22×C13semidirect
358. D4×Q8C22×C13semidirect
359. #548C22×C13semidirect
360. #548C22×C13semidirect
361. #546C22×C13semidirect
362. #546C22×C13semidirect
363. #546C22×C13semidirect
364. #546C22×C13semidirect
365. #546C22×C13semidirect
366. #546C22×C13semidirect
367. D42C22×C13semidirect
368. D42C22×C13semidirect
369. D42C22×C13semidirect
370. D42C22×C13semidirect
371. #542C22×C13semidirect
372. #542C22×C13semidirect
373. #538C22×C13semidirect
374. #538C22×C13semidirect
375. #538C22×C13semidirect
376. #538C22×C13semidirect
377. #536C22×C13semidirect
378. #536C22×C13semidirect
379. #535C22×C13semidirect
380. #535C22×C13semidirect
381. #535C22×C13semidirect
382. #535C22×C13semidirect
383. #535C22×C13semidirect
384. #534C22×C13semidirect
385. #534C22×C13semidirect
386. #534C22×C13semidirect
387. #532C22×C13semidirect
388. #532C22×C13semidirect
389. #532C22×C13semidirect
390. #529C22×C13semidirect
391. #529C22×C13semidirect
392. C2×#124C22×C13semidirect
393. C2×#124C22×C13semidirect
394. C2×#124C22×C13semidirect
395. #525C22×C13semidirect
396. #525C22×C13semidirect
397. C2×#120C22×C13semidirect
398. C2×#120C22×C13semidirect
399. #518C22×C13semidirect
400. C4×#41C22×C13semidirect
421. C25C23×C13semidirect
428. C2×#41C23×C13semidirect
429. C2×#41C23×C13semidirect
430. C2×#41C23×C13semidirect
431. C22×Q8C23×C13semidirect
432. C22×Q8C23×C13semidirect
433. C22×Q8C23×C13semidirect
440. C22×D4C23×C13semidirect
441. C22×D4C23×C13semidirect
442. C22×D4C23×C13semidirect
443. C23×C4C23×C13semidirect
444. C4⋊Q8C23×C13semidirect
445. C4⋊Q8C23×C13semidirect
446. C4⋊Q8C23×C13semidirect
450. #127C23×C13semidirect
451. #126C23×C13semidirect
452. #126C23×C13semidirect
453. #126C23×C13semidirect
454. #125C23×C13semidirect
459. #124C23×C13semidirect
460. #124C23×C13semidirect
461. #124C23×C13semidirect
462. #124C23×C13semidirect
463. #124C23×C13semidirect
464. #124C23×C13semidirect
465. #124C23×C13semidirect
466. #124C23×C13semidirect
467. #124C23×C13semidirect
468. #124C23×C13semidirect
469. #124C23×C13semidirect
470. #124C23×C13semidirect
472. #123C23×C13semidirect
473. #123C23×C13semidirect
474. #123C23×C13semidirect
475. #123C23×C13semidirect
476. #123C23×C13semidirect
477. #123C23×C13semidirect
478. #123C23×C13semidirect
479. #123C23×C13semidirect
480. C22⋊Q8C23×C13semidirect
481. C22⋊Q8C23×C13semidirect
482. C22⋊Q8C23×C13semidirect
483. C22⋊Q8C23×C13semidirect
484. C22⋊Q8C23×C13semidirect
485. C22⋊Q8C23×C13semidirect
491. #121C23×C13semidirect
492. #121C23×C13semidirect
493. #121C23×C13semidirect
494. #121C23×C13semidirect
495. #121C23×C13semidirect
496. #121C23×C13semidirect
497. #121C23×C13semidirect
498. #121C23×C13semidirect
503. #120C23×C13semidirect
504. #120C23×C13semidirect
505. #120C23×C13semidirect
506. #120C23×C13semidirect
507. #120C23×C13semidirect
508. #120C23×C13semidirect
509. #120C23×C13semidirect
510. #120C23×C13semidirect
511. #120C23×C13semidirect
512. C4×Q8C23×C13semidirect
513. C4×Q8C23×C13semidirect
514. C4×Q8C23×C13semidirect
517. C4×D4C23×C13semidirect
518. C4×D4C23×C13semidirect
519. C4×D4C23×C13semidirect
520. C4×D4C23×C13semidirect
521. C4×D4C23×C13semidirect
522. C4×D4C23×C13semidirect
523. C4×D4C23×C13semidirect
524. C4×D4C23×C13semidirect
525. #117C23×C13semidirect
526. #117C23×C13semidirect
527. #117C23×C13semidirect
528. #117C23×C13semidirect
529. #117C23×C13semidirect
530. C2×C22⋊C4C23×C13semidirect
531. C2×C22⋊C4C23×C13semidirect
532. C2×C22⋊C4C23×C13semidirect
533. C2×C22⋊C4C23×C13semidirect
534. C2×C22⋊C4C23×C13semidirect
535. C2×C42C23×C13semidirect
536. C2×C42C23×C13semidirect
627. C13#63045direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35582
C13×#35492
C13×#35452
C13×#35402
C13×#35322
C13×#35292
C2×C13×H(3,𝔽4)2
C13×#35142
C13×#35002
C13×#34842
#6304513