Finite Group Databasebeta

← C29×#25514 #20320414

Subgroups — C29×#25514 #20320414

Order 7424.

1092 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#542C211yesmaximal, characteristic
2C2×C29×#468C211yesmaximal, characteristic
3C2×C29×#467C211yesmaximal, characteristic, complemented
4C29×#2625C211yesmaximal, characteristic, complemented
5C29×#2057C211yesmaximal, characteristic, complemented
6C29×#2042C211yesmaximal, characteristic, complemented
7C29×#2024C211yesmaximal, characteristic, complemented
8C29×#2015C211yesmaximal, characteristic, complemented
9C29×#1894C211yesmaximal, characteristic, complemented
10C29×#1893C211yesmaximal, characteristic
11C29×#1878C211yesmaximal, characteristic, complemented
12C29×#1877C211yesmaximal, characteristic, complemented
13C29×#1863C211yesmaximal, characteristic, complemented
14C29×#1862C211yesmaximal, characteristic, complemented
15C29×#1729C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C23×C8×C29C2211yescharacteristic
20C29×#542—24no—
21C29×#542—24no—
22C2×C29×C4⋊Q8C2211yescharacteristic
23C2×C29×#126—21no—
24C2×C29×#124—21no—
25C2×C29×#124C2211yescharacteristic
26C2×C29×#123—21no—
27C2×C29×C22⋊Q8—21no—
28C2×C29×C22⋊Q8C2211yescharacteristic
29C2×C29×C22⋊Q8C2211yescharacteristic
30C2×C29×#121C2211yescharacteristic
31C2×C4×Q8×C29C2211yescharacteristic
32C2×C4×D4×C29C2211yescharacteristic
33C2×C29×#117C2211yescharacteristic
34C29×#468—24no—
35C29×#467—24no—
36C2×C29×#107C2211yescharacteristic
37C2×C29×#107C2211yescharacteristic
38C2×C29×#103C2211yescharacteristic
39C2×C29×#103C2211yescharacteristic
40C2×C29×#103C2211yescharacteristic
41C2×C29×#103C2211yescharacteristic
42C2×C29×#103C2211yescharacteristic
43C2×C29×#102C2211yescharacteristic
44C2×C29×#102C2211yescharacteristic
45C2×C29×#102C2211yescharacteristic
46C29×#400—21no—
47C29×#398—21no—
48C29×#397—21no—
49C29×#397—21no—
50C29×#391C2211yescharacteristic
51C29×#391C2211yescharacteristic
52C29×#389C2211yescharacteristic
53C29×#389C2211yescharacteristic
54C29×#380C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C29×#336C2211yescharacteristic
62C29×#336C2211yescharacteristic
63C22×Q8×C29—21no—
64C22×Q8×C29C2311yescharacteristic
65C22×Q8×C29C2311yescharacteristic
66C22×D4×C29—21no—
67C22×D4×C29C2311yescharacteristic
68C23×C4×C29—21no—
69C23×C4×C29C2311yescharacteristic
70C2×Q16×C29—22no—
71C2×Q16×C29—22no—
72C2×Q16×C29—41no—
73C2×SD16×C29—22no—
74C2×SD16×C29—22no—
75C2×SD16×C29—41no—
76C2×M16×C29—22no—
77C2×M16×C29—22no—
78C2×M16×C29—41no—
79C22×C8×C29—22no—
80C22×C8×C29—22no—
81C22×C8×C29—41no—
82C22×C8×C29C2311yescharacteristic
83C22×C8×C29C2311yescharacteristic
84C22×C8×C29C2311yescharacteristic
85C22×C8×C29C2311yescharacteristic
86C29×C4⋊Q8—22no—
87C29×C4⋊Q8—22no—
88C29×#126—28no—
89C29×#124—28no—
90C29×#124—22no—
91C29×#124—22no—
92C29×#123—28no—
93C29×C22⋊Q8—28no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8—22no—
97C29×C22⋊Q8D414yes—
98C29×#121—22no—
99C29×#121D414yes—
100C4×Q8×C29—22no—
101C4×Q8×C29—22no—
102C4×D4×C29—22no—
103C4×D4×C29—22no—
104C29×#117—22no—
105C29×#117—22no—
106C2×C4⋊C4×C29—21no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29—21no—
111C2×C4⋊C4×C29—21no—
112C2×C4⋊C4×C29D411yescharacteristic
113C2×C4⋊C4×C29D411yescharacteristic
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C4⋊C4×C29C2311yescharacteristic
117C2×C4⋊C4×C29C2311yescharacteristic
118C2×C4⋊C4×C29C2311yescharacteristic
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29—21no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—21no—
126C2×C22⋊C4×C29D411yescharacteristic
127C2×C22⋊C4×C29D411yescharacteristic
128C2×C42×C29—21no—
129C2×C42×C29C2311yescharacteristic
130C2×C42×C29C2311yescharacteristic
131C29×#107—22no—
132C29×#107—22no—
133C29×#103—22no—
134C29×#103—22no—
135C29×#103—22no—
136C29×#103—22no—
137C29×#103—41no—
138C29×#102—22no—
139C29×#102—22no—
140C29×#102—41no—
141C29×#95—21no—
142C29×#95—21no—
143C29×#95—21no—
144C29×#95—21no—
145C29×#95—21no—
146C29×#95—21no—
147C29×#95—21no—
148C24×C29—21no—
149C24×C29C2×D411yescharacteristic
150C2×Q8×C29—24no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—21no—
154C2×Q8×C29—21no—
155C2×Q8×C29—21no—
156C2×Q8×C29—21no—
157C2×Q8×C29—21no—
158C2×Q8×C29—21no—
159C2×Q8×C29—21no—
160C2×Q8×C29—21no—
161C2×Q8×C29—21no—
162C2×Q8×C29—81no—
163C2×Q8×C29—81no—
164C2×Q8×C29C2×D412yes—
165C2×D4×C29—24no—
166C2×D4×C29—21no—
167C2×D4×C29—21no—
168C2×D4×C29—21no—
169C2×D4×C29—21no—
170C2×D4×C29—21no—
171C2×D4×C29—81no—
172C2×D4×C29—81no—
173C2×D4×C29C2×D412yes—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—24no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—81no—
187C22×C4×C29—81no—
188C22×C4×C29C2×D411yescharacteristic
189C22×C4×C29C2×D411yescharacteristic
190C22×C4×C29C2×D411yescharacteristic
191C22×C4×C29C2×D411yescharacteristic
192C22×C4×C29C2×D411yescharacteristic
193C22×C4×C29C2×D412yes—
194C22×C4×C29C2×D412yes—
195C22×C4×C29C2411yescharacteristic
196Q16×C29—44no—
197SD16×C29—44no—
198M16×C29—44no—
199C2×C8×C29—21no—
200C2×C8×C29—21no—
201C2×C8×C29—21no—
202C2×C8×C29—21no—
203C2×C8×C29—21no—
204C2×C8×C29—21no—
205C2×C8×C29—21no—
206C2×C8×C29—21no—
207C2×C8×C29—21no—
208C2×C8×C29—21no—
209C2×C8×C29—44no—
210C2×C8×C29#4112yes—
211C2×C8×C29#4112yes—
212C4⋊C4×C29—24no—
213C4⋊C4×C29—24no—
214C4⋊C4×C29—24no—
215C4⋊C4×C29—22no—
216C4⋊C4×C29—22no—
217C4⋊C4×C29—21no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—21no—
223C4⋊C4×C29—21no—
224C4⋊C4×C29—21no—
225C4⋊C4×C29—42no—
226C4⋊C4×C29—81no—
227C4⋊C4×C29—81no—
228C4⋊C4×C29C2×D412yes—
229C4⋊C4×C29C2×D412yes—
230C22⋊C4×C29—24no—
231C22⋊C4×C29—24no—
232C22⋊C4×C29—24no—
233C22⋊C4×C29—24no—
234C22⋊C4×C29—22no—
235C22⋊C4×C29—22no—
236C22⋊C4×C29—24no—
237C22⋊C4×C29—42no—
238C22⋊C4×C29—81no—
239C42×C29—24no—
240C42×C29—21no—
241C42×C29—21no—
242C42×C29—21no—
243C42×C29—21no—
244#25514C2911yesmaximal, characteristic, direct product factor, Sylow
245C23×C29—21no—
246C23×C29—21no—
247C23×C29—21no—
248C23×C29—21no—
249C23×C29—21no—
250C23×C29—21no—
251C23×C29—22no—
252C23×C29—41no—
253C23×C29—41no—
254C23×C29—41no—
255C23×C29—41no—
256C23×C29—41no—
257C23×C29—41no—
258C23×C29#12012yes—
259C23×C29C22×D411yescharacteristic
260Q8×C29—22no—
261Q8×C29—22no—
262Q8×C29—41no—
263Q8×C29—41no—
264Q8×C29—41no—
265Q8×C29—41no—
266Q8×C29—41no—
267Q8×C29—41no—
268Q8×C29—84no—
269D4×C29—22no—
270D4×C29—22no—
271D4×C29—41no—
272D4×C29—41no—
273D4×C29—84no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—22no—
277C2×C4×C29—22no—
278C2×C4×C29—22no—
279C2×C4×C29—22no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—22no—
283C2×C4×C29—21no—
284C2×C4×C29—21no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—21no—
288C2×C4×C29—21no—
289C2×C4×C29—21no—
290C2×C4×C29—21no—
291C2×C4×C29—21no—
292C2×C4×C29—21no—
293C2×C4×C29—21no—
294C2×C4×C29—21no—
295C2×C4×C29—41no—
296C2×C4×C29—41no—
297C2×C4×C29—41no—
298C2×C4×C29—41no—
299C2×C4×C29—41no—
300C2×C4×C29—41no—
301C2×C4×C29—41no—
302C2×C4×C29—41no—
303C2×C4×C29—41no—
304C2×C4×C29—41no—
305C2×C4×C29—41no—
306C2×C4×C29—41no—
307C2×C4×C29—41no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—84no—
314C2×C4×C29#12012yes—
315C2×C4×C29C22×D411yescharacteristic
316C2×C4×C29C22×D411yescharacteristic
317C2×C4×C29C2×#4111yescharacteristic
318C2×C4×C29C2×#4111yescharacteristic
319C2×C4×C29H(5,𝔽2)11yescharacteristic
320C2×C4×C292−1+411yescharacteristic
321C8×C29—22no—
322C8×C29—22no—
323C8×C29—41no—
324C8×C29—41no—
325C2×#542C2×C2911yescharacteristic
326C2×#468C2×C2911yescharacteristic
327C2×#467C2×C2911yescharacteristic, complemented
328#2625C2×C2911yescharacteristic, complemented
329#2057C2×C2911yescharacteristic, complemented
330#2042C2×C2911yescharacteristic, complemented
331#2024C2×C2911yescharacteristic, complemented
332#2015C2×C2911yescharacteristic, complemented
333#1894C2×C2911yescharacteristic, complemented
334#1893C2×C2911yescharacteristic
335#1878C2×C2911yescharacteristic, complemented
336#1877C2×C2911yescharacteristic, complemented
337#1863C2×C2911yescharacteristic, complemented
338#1862C2×C2911yescharacteristic, complemented
339#1729C2×C2911yescharacteristic, complemented
340C22×C29—22no—
341C22×C29—22no—
342C22×C29—22no—
343C22×C29—41no—
344C22×C29—41no—
345C22×C29—41no—
346C22×C29—41no—
347C22×C29—42no—
348C22×C29—42no—
349C22×C29—42no—
350C22×C29—81no—
351C22×C29—81no—
352C22×C29—81no—
353C22×C29—81no—
354C22×C29C2×#12011yescharacteristic
355C22×C29#53211yescharacteristic
356C22×C29#53711yescharacteristic
357C22×C29#57611yescharacteristic
358C22×C29#57711yescharacteristic
359C22×C29#57811yescharacteristic
360C22×C29#57811yescharacteristic
361C4×C29—22no—
362C4×C29—42no—
363C4×C29—41no—
364C4×C29—41no—
365C4×C29—41no—
366C4×C29—41no—
367C4×C29—42no—
368C4×C29—42no—
369C4×C29—81no—
370C4×C29—81no—
371C4×C29—81no—
372C4×C29—81no—
373C4×C29#54611yescharacteristic
374C4×C29#54611yescharacteristic
375C4×C29#54711yescharacteristic
376C4×C29#54711yescharacteristic
377C22×Q16C22×C2911yescharacteristic
378C22×SD16C22×C2911yescharacteristic
379C22×M16C22×C2911yescharacteristic
380C23×C8C22×C2911yescharacteristic
381#542—24no—
382#542—24no—
383C2×C4⋊Q8C22×C2911yescharacteristic
384C2×#126—21no—
385C2×#124—21no—
386C2×#124C22×C2911yescharacteristic
387C2×#123—21no—
388C2×C22⋊Q8—21no—
389C2×C22⋊Q8C22×C2911yescharacteristic
390C2×C22⋊Q8C22×C2911yescharacteristic
391C2×#121C22×C2911yescharacteristic
392C2×C4×Q8C22×C2911yescharacteristic
393C2×C4×D4C22×C2911yescharacteristic
394C2×#117C22×C2911yescharacteristic
395#468—24no—
396#467—24no—
397C2×#107C22×C2911yescharacteristic
398C2×#107C22×C2911yescharacteristic
399C2×#103C22×C2911yescharacteristic
400C2×#103C22×C2911yescharacteristic
401C2×#103C22×C2911yescharacteristic
402C2×#103C22×C2911yescharacteristic
403C2×#103C22×C2911yescharacteristic
404C2×#102C22×C2911yescharacteristic
405C2×#102C22×C2911yescharacteristic
406C2×#102C22×C2911yescharacteristic
407#400—21no—
408#398—21no—
409#397—21no—
410#397—21no—
411#391C22×C2911yescharacteristic
412#391C22×C2911yescharacteristic
413#389C22×C2911yescharacteristic
414#389C22×C2911yescharacteristic
415#380C22×C2911yescharacteristic
416#340C22×C2911yescharacteristic
417#340C22×C2911yescharacteristic
418#340C22×C2911yescharacteristic
419#340C22×C2911yescharacteristic
420#336C22×C2911yescharacteristic
421#336C22×C2911yescharacteristic
422#336C22×C2911yescharacteristic
423#336C22×C2911yescharacteristic
424C2×C29—42no—
425C2×C29—82no—
426C2×C29#243011yescharacteristic
427C2×C29#301111yescharacteristic
428C2×C29#301211yescharacteristic
429C2×C29#317511yescharacteristic
430C2×C29#317811yescharacteristic
431C2×C29#325811yescharacteristic
432C2×C29#326211yescharacteristic
433C22×Q8—21no—
434C22×Q8C23×C2911yescharacteristic
435C22×Q8C23×C2911yescharacteristic
436C22×D4—21no—
437C22×D4C23×C2911yescharacteristic
438C23×C4—21no—
439C23×C4C23×C2911yescharacteristic
440C2×Q16—22no—
441C2×Q16—22no—
442C2×Q16—41no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—41no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—41no—
452C22×C8C23×C2911yescharacteristic
453C22×C8C23×C2911yescharacteristic
454C22×C8C23×C2911yescharacteristic
455C22×C8C23×C2911yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458#126—28no—
459#124—28no—
460#124—22no—
461#124—22no—
462#123—28no—
463C22⋊Q8—28no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8D4×C2914yes—
468#121—22no—
469#121D4×C2914yes—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4D4×C2911yescharacteristic
483C2×C4⋊C4D4×C2911yescharacteristic
484C2×C4⋊C4C23×C2911yescharacteristic
485C2×C4⋊C4C23×C2911yescharacteristic
486C2×C4⋊C4C23×C2911yescharacteristic
487C2×C4⋊C4C23×C2911yescharacteristic
488C2×C4⋊C4C23×C2911yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4D4×C2911yescharacteristic
497C2×C22⋊C4D4×C2911yescharacteristic
498C2×C42—21no—
499C2×C42C23×C2911yescharacteristic
500C2×C42C23×C2911yescharacteristic
501#107—22no—
502#107—22no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—41no—
508#102—22no—
509#102—22no—
510#102—41no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518C29#2551411yescharacteristic, direct product factor, Sylow
519C24—21no—
520C24C2×D4×C2911yescharacteristic
521C2×Q8—24no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—81no—
534C2×Q8—81no—
535C2×Q8C2×D4×C2912yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4C2×D4×C2912yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D4×C2911yescharacteristic
560C22×C4C2×D4×C2911yescharacteristic
561C22×C4C2×D4×C2911yescharacteristic
562C22×C4C2×D4×C2911yescharacteristic
563C22×C4C2×D4×C2911yescharacteristic
564C22×C4C2×D4×C2912yes—
565C22×C4C2×D4×C2912yes—
566C22×C4C24×C2911yescharacteristic
567Q16—44no—
568SD16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—44no—
581C2×C8#41×C2912yes—
582C2×C8#41×C2912yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—81no—
598C4⋊C4—81no—
599C4⋊C4C2×D4×C2912yes—
600C4⋊C4C2×D4×C2912yes—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C42—24no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C29×#12012yes—
629C23C22×D4×C2911yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—84no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4C29×#12012yes—
685C2×C4C22×D4×C2911yescharacteristic
686C2×C4C22×D4×C2911yescharacteristic
687C2×C4C2×#41×C2911yescharacteristic
688C2×C4C2×#41×C2911yescharacteristic
689C2×C4C29×H(5,𝔽2)11yescharacteristic
690C2×C4C29×2−1+411yescharacteristic
691C8—22no—
692C8—22no—
693C8—41no—
694C8—41no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×C29×#12011yescharacteristic
710C22C29×#53211yescharacteristic
711C22C29×#53711yescharacteristic
712C22C29×#57611yescharacteristic
713C22C29×#57711yescharacteristic
714C22C29×#57811yescharacteristic
715C22C29×#57811yescharacteristic
716C4—22no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4C29×#54611yescharacteristic
729C4C29×#54611yescharacteristic
730C4C29×#54711yescharacteristic
731C4C29×#54711yescharacteristic
732C2—42no—
733C2—82no—
734C2C29×#243011yescharacteristic
735C2C29×#301111yescharacteristic
736C2C29×#301211yescharacteristic
737C2C29×#317511yescharacteristic
738C2C29×#317811yescharacteristic
739C2C29×#325811yescharacteristic
740C2C29×#326211yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#467C2semidirect
4. C29×#2625C2semidirect
5. C29×#2057C2semidirect
6. C29×#2042C2semidirect
7. C29×#2024C2semidirect
8. C29×#2015C2semidirect
9. C29×#1894C2semidirect
11. C29×#1878C2semidirect
12. C29×#1877C2semidirect
13. C29×#1863C2semidirect
14. C29×#1862C2semidirect
15. C29×#1729C2semidirect
244. #25514C29direct (N × H)
327. C2×#467C2×C29semidirect
328. #2625C2×C29semidirect
329. #2057C2×C29semidirect
330. #2042C2×C29semidirect
331. #2024C2×C29semidirect
332. #2015C2×C29semidirect
333. #1894C2×C29semidirect
335. #1878C2×C29semidirect
336. #1877C2×C29semidirect
337. #1863C2×C29semidirect
338. #1862C2×C29semidirect
339. #1729C2×C29semidirect
518. C29#25514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5422
C2×C29×#4682
C2×C29×#4672
C29×#26252
C29×#20572
C29×#20422
C29×#20242
C29×#20152
C29×#18942
C29×#18932
C29×#18782
C29×#18772
C29×#18632
C29×#18622
C29×#17292
#2551429