Finite Group Databasebeta

← C13×#15322 #15701661

Subgroups — C13×#15322 #15701661

Order 3328.

1830 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#396C211yesmaximal, characteristic
3C2×C13×#393C211yesmaximal, characteristic
4C2×C13×#393C211yesmaximal, characteristic
5C2×C13×#391C211yesmaximal, characteristic, complemented
6C2×C13×#388C211yesmaximal, characteristic
7C13×#1446C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic
12C13×#1439C211yesmaximal, characteristic
13C13×#1437C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×Q8×C13C2211yescharacteristic
18C2×C13×C4⋊Q8—24no—
19C2×C13×C4⋊Q8—24no—
20C2×C13×C4⋊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×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C13×#396—24no—
37C13×#393—24no—
38C13×#393—24no—
39C13×#391—24no—
40C13×#388—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—22no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—22no—
69C22×Q8×C13—41no—
70C22×Q8×C13—41no—
71C22×Q8×C13—41no—
72C22×Q8×C13—41no—
73C22×Q8×C13D414yes—
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×C4⋊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—41no—
105C2×C13×C4⋊C4D414yes—
106C2×C13×C4⋊C4D414yes—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
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—41no—
124C2×C13×C22⋊C4—41no—
125C2×C13×C22⋊C4—41no—
126C2×C13×C22⋊C4—41no—
127C2×C13×C22⋊C4Q814yescomplemented
128C2×C42×C13—22no—
129C2×C42×C13—22no—
130C2×C42×C13—22no—
131C2×C42×C13—22no—
132C2×C42×C13—22no—
133C2×C42×C13—41no—
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×#95D414yes—
152#15322C1311yesmaximal, 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×C13—21no—
166C24×C13—21no—
167C24×C13C2×Q812yes—
168C24×C13C2411yescharacteristic
169C2×Q8×C13—28no—
170C2×Q8×C13—28no—
171C2×Q8×C13—28no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—44no—
175C2×Q8×C13—44no—
176C2×Q8×C13—44no—
177C2×Q8×C13—44no—
178C2×Q8×C13—44no—
179C2×Q8×C13—44no—
180C2×Q8×C13—44no—
181C2×Q8×C13—44no—
182C2×Q8×C13—44no—
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—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—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13C2×D412yes—
264C22×C4×C13C2×D412yes—
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×Q812yes—
276C22×C4×C13C2×Q812yes—
277C22×C4×C13#4112yes—
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—44no—
286C13×C4⋊C4—44no—
287C13×C22⋊C4—28no—
288C13×C22⋊C4—44no—
289C13×C22⋊C4—44no—
290C13×C22⋊C4—44no—
291C13×C22⋊C4—44no—
292C13×C22⋊C4—44no—
293C13×C22⋊C4—44no—
294C42×C13—28no—
295C42×C13—44no—
296C22×C4⋊Q8C2×C1311yescharacteristic, complemented
297C2×#396C2×C1311yescharacteristic
298C2×#393C2×C1311yescharacteristic
299C2×#393C2×C1311yescharacteristic
300C2×#391C2×C1311yescharacteristic, complemented
301C2×#388C2×C1311yescharacteristic
302#1446C2×C1311yescharacteristic, complemented
303#1442C2×C1311yescharacteristic, complemented
304#1441C2×C1311yescharacteristic, complemented
305#1441C2×C1311yescharacteristic, complemented
306#1439C2×C1311yescharacteristic
307#1439C2×C1311yescharacteristic
308#1437C2×C1311yescharacteristic
309#1436C2×C1311yescharacteristic, complemented
310#1436C2×C1311yescharacteristic, complemented
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
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×C13—41no—
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—
362Q8×C13—416no—
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—22no—
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#12014yes—
458C2×C4×C13#12114yes—
459C2×C4×C13C22⋊Q814yes—
460C2×C4×C13#12414yes—
461C23×Q8C22×C1311yescharacteristic
462C23×Q8C22×C1311yescharacteristic
463C2×C4⋊Q8—24no—
464C2×C4⋊Q8—24no—
465C2×C4⋊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×C22⋊C4C22×C1311yescharacteristic
473C22×C22⋊C4C22×C1311yescharacteristic
474C22×C22⋊C4C22×C1311yescharacteristic
475C22×C22⋊C4C22×C1311yescharacteristic
476C22×C22⋊C4C22×C1311yescharacteristic
477C22×C22⋊C4C22×C1311yescharacteristic
478C22×C22⋊C4C22×C1311yescharacteristic
479C22×C42C22×C1311yescharacteristic
480C22×C42C22×C1311yescharacteristic
481#396—24no—
482#393—24no—
483#393—24no—
484#391—24no—
485#388—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—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—81no—
512C22×C13—81no—
513C22×C13—81no—
514C22×C13—81no—
515C22×C13—81no—
516C22×C13—81no—
517C22×C13—81no—
518C22×C13—81no—
519C22×C13C2×#12011yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×#12411yescharacteristic
523C22×C13#53211yescharacteristic
524C22×C13#53311yescharacteristic
525C22×C13#53411yescharacteristic
526C22×C13#53611yescharacteristic
527C22×C13#53611yescharacteristic
528C22×C13#53611yescharacteristic
529C22×C13#54111yescharacteristic
530C22×C13#54211yescharacteristic
531C22×C13#54211yescharacteristic
532C22×C13#54211yescharacteristic
533C22×C13#54411yescharacteristic
534C22×C13D4211yescharacteristic
535C22×C13D4211yescharacteristic
536C22×C13#54611yescharacteristic
537C22×C13#54611yescharacteristic
538C22×C13#54711yescharacteristic
539C22×C13#54811yescharacteristic
540C22×C13#54811yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13#54811yescharacteristic
544C22×C13#54811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13D4×Q811yescharacteristic
547C22×C13D4×Q811yescharacteristic
548C22×C13#55411yescharacteristic
549C22×C13#55511yescharacteristic
550C22×C13#55611yescharacteristic
551C22×C13#55611yescharacteristic
552C22×C13#56311yescharacteristic
553C22×C13#56311yescharacteristic
554C4×C13—24no—
555C4×C13—24no—
556C4×C13—24no—
557C4×C13—24no—
558C4×C13—42no—
559C4×C13—42no—
560C4×C13—42no—
561C4×C13—42no—
562C4×C13—42no—
563C4×C13—42no—
564C4×C13—81no—
565C4×C13—81no—
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—22no—
575C22×Q8—22no—
576C22×Q8—22no—
577C22×Q8—22no—
578C22×Q8—41no—
579C22×Q8—41no—
580C22×Q8—41no—
581C22×Q8—41no—
582C22×Q8D4×C1314yes—
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
597C4⋊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—41no—
614C2×C4⋊C4D4×C1314yes—
615C2×C4⋊C4D4×C1314yes—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
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—41no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4Q8×C1314yescomplemented
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—41no—
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#95D4×C1314yes—
661C2×C13—82no—
662C2×C13#240911yescharacteristic
663C2×C13#241011yescharacteristic
664C2×C13#242911yescharacteristic
665C2×C13#243611yescharacteristic
666C2×C13#243911yescharacteristic
667C2×C13#245211yescharacteristic
668C2×C13#249111yescharacteristic
669C2×C13#249211yescharacteristic
670C2×C13#254511yescharacteristic
671C2×C13#267411yescharacteristic
672C2×C13#267711yescharacteristic
673C2×C13#271611yescharacteristic
674C2×C13#271611yescharacteristic
675C2×C13#272911yescharacteristic
676C2×C13#273111yescharacteristic
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24C2×Q8×C1312yes—
692C24C24×C1311yescharacteristic
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—44no—
706C2×Q8—44no—
707C22×C4—21no—
708C22×C4—21no—
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—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4C2×D4×C1312yes—
788C22×C4C2×D4×C1312yes—
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×Q8×C1312yes—
800C22×C4C2×Q8×C1312yes—
801C22×C4C13×#4112yes—
802C22×C4C13×#4112yes—
803C22×C4C13×#4112yes—
804C22×C4C13×#4112yes—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C22⋊C4—28no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—44no—
818C42—28no—
819C42—44no—
820C13#1532211yescharacteristic, direct product factor, Sylow
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
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—
855C23—41no—
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—
872Q8—416no—
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—22no—
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×C4C13×#12014yes—
968C2×C4C13×#12114yes—
969C2×C4C13×C22⋊Q814yes—
970C2×C4C13×#12414yes—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—81no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22C2×C13×#12011yescharacteristic
987C22C2×C13×#12111yescharacteristic
988C22C2×C13×C22⋊Q811yescharacteristic
989C22C2×C13×#12411yescharacteristic
990C22C13×#53211yescharacteristic
991C22C13×#53311yescharacteristic
992C22C13×#53411yescharacteristic
993C22C13×#53611yescharacteristic
994C22C13×#53611yescharacteristic
995C22C13×#53611yescharacteristic
996C22C13×#54111yescharacteristic
997C22C13×#54211yescharacteristic
998C22C13×#54211yescharacteristic
999C22C13×#54211yescharacteristic
1000C22C13×#54411yescharacteristic
1001C22D42×C1311yescharacteristic
1002C22D42×C1311yescharacteristic
1003C22C13×#54611yescharacteristic
1004C22C13×#54611yescharacteristic
1005C22C13×#54711yescharacteristic
1006C22C13×#54811yescharacteristic
1007C22C13×#54811yescharacteristic
1008C22C13×#54811yescharacteristic
1009C22C13×#54811yescharacteristic
1010C22C13×#54811yescharacteristic
1011C22C13×#54811yescharacteristic
1012C22D4×Q8×C1311yescharacteristic
1013C22D4×Q8×C1311yescharacteristic
1014C22D4×Q8×C1311yescharacteristic
1015C22C13×#55411yescharacteristic
1016C22C13×#55511yescharacteristic
1017C22C13×#55611yescharacteristic
1018C22C13×#55611yescharacteristic
1019C22C13×#56311yescharacteristic
1020C22C13×#56311yescharacteristic
1021C4—24no—
1022C4—24no—
1023C4—24no—
1024C4—24no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—81no—
1032C4—81no—
1033C4—81no—
1034C4—81no—
1035C2—82no—
1036C2C13×#240911yescharacteristic
1037C2C13×#241011yescharacteristic
1038C2C13×#242911yescharacteristic
1039C2C13×#243611yescharacteristic
1040C2C13×#243911yescharacteristic
1041C2C13×#245211yescharacteristic
1042C2C13×#249111yescharacteristic
1043C2C13×#249211yescharacteristic
1044C2C13×#254511yescharacteristic
1045C2C13×#267411yescharacteristic
1046C2C13×#267711yescharacteristic
1047C2C13×#271611yescharacteristic
1048C2C13×#271611yescharacteristic
1049C2C13×#272911yescharacteristic
1050C2C13×#273111yescharacteristic
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. C22×C13×C4⋊Q8C2semidirect
5. C2×C13×#391C2semidirect
7. C13×#1446C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
10. C13×#1441C2semidirect
14. C13×#1436C2semidirect
15. C13×#1436C2semidirect
127. C2×C13×C22⋊C4Q8semidirect
152. #15322C13direct (N × H)
296. C22×C4⋊Q8C2×C13semidirect
300. C2×#391C2×C13semidirect
302. #1446C2×C13semidirect
303. #1442C2×C13semidirect
304. #1441C2×C13semidirect
305. #1441C2×C13semidirect
309. #1436C2×C13semidirect
310. #1436C2×C13semidirect
636. C2×C22⋊C4Q8×C13semidirect
820. C13#15322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊Q82
C2×C13×#3962
C2×C13×#3932
C2×C13×#3912
C2×C13×#3882
C13×#14462
C13×#14422
C13×#14412
C13×#14392
C13×#14372
C13×#14362
#1532213