Finite Group Databasebeta

← C29×#25916 #20320816

Subgroups — C29×#25916 #20320816

Order 7424.

1052 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#544C211yesmaximal, characteristic, complemented
2C2×C29×#489C211yesmaximal, characteristic, complemented
3C2×C29×#488C211yesmaximal, characteristic, complemented
4C29×#2620C211yesmaximal, characteristic
5C29×#2026C211yesmaximal, characteristic, complemented
6C29×#2025C211yesmaximal, characteristic, complemented
7C29×#2024C211yesmaximal, characteristic, complemented
8C29×#2023C211yesmaximal, characteristic, complemented
9C29×#1992C211yesmaximal, characteristic, complemented
10C29×#1990C211yesmaximal, characteristic, complemented
11C29×#1875C211yesmaximal, characteristic
12C29×#1874C211yesmaximal, characteristic
13C29×#1873C211yesmaximal, characteristic, complemented
14C29×#1872C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic, complemented
16C29×#544—24no—
17C29×#544—24no—
18C2×C29×C4⋊Q8—21no—
19C2×C29×C4⋊Q8C2211yescharacteristic
20C2×C29×C4⋊Q8C2211yescharacteristic
21C2×C29×#125—21no—
22C2×C29×#125C2211yescharacteristic
23C2×C29×#125C2211yescharacteristic
24C2×C29×#124C2211yescharacteristic
25C2×C29×C22⋊Q8—21no—
26C2×C29×C22⋊Q8—21no—
27C2×C29×C22⋊Q8C2211yescharacteristic
28C2×C29×#121C2211yescharacteristic
29C2×C29×#117C2211yescharacteristic
30C2×C29×#117C2211yescharacteristic
31C22×C4⋊C4×C29C2211yescharacteristic
32C29×#489—24no—
33C29×#488—24no—
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#103C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#102C2211yescharacteristic
42C2×C29×C22⋊C8C2211yescharacteristic
43C2×C29×C22⋊C8C2211yescharacteristic
44C2×C29×#97C2211yescharacteristic
45C2×C4×C8×C29C2211yescharacteristic
46C29×#396—21no—
47C29×#396—21no—
48C29×#394—21no—
49C29×#394—21no—
50C29×#391C2211yescharacteristic
51C29×#390C2211yescharacteristic
52C29×#384C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C29×#336C2211yescharacteristic
62C29×#336C2211yescharacteristic
63C22×Q8×C29—21no—
64C22×Q8×C29—21no—
65C22×Q8×C29C2311yescharacteristic
66C22×D4×C29—21no—
67C22×D4×C29C2311yescharacteristic
68C23×C4×C29—21no—
69C23×C4×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×C4⋊Q8—28no—
75C29×C4⋊Q8—22no—
76C29×C4⋊Q8—22no—
77C29×C4⋊Q8—22no—
78C29×C4⋊Q8D414yescomplemented
79C29×#125—28no—
80C29×#125—22no—
81C29×#125—22no—
82C29×#125—22no—
83C29×#125D414yescomplemented
84C29×#124—22no—
85C29×#124—22no—
86C29×C22⋊Q8—28no—
87C29×C22⋊Q8—28no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—22no—
90C29×#121—22no—
91C29×#121—22no—
92C29×#117—22no—
93C29×#117—22no—
94C29×#117—22no—
95C29×#117—22no—
96C2×C4⋊C4×C29—21no—
97C2×C4⋊C4×C29—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29—21no—
101C2×C4⋊C4×C29—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29—22no—
104C2×C4⋊C4×C29—22no—
105C2×C4⋊C4×C29—21no—
106C2×C4⋊C4×C29—21no—
107C2×C4⋊C4×C29—21no—
108C2×C4⋊C4×C29D411yescharacteristic
109C2×C4⋊C4×C29D411yescharacteristic
110C2×C4⋊C4×C29C2311yescharacteristic
111C2×C4⋊C4×C29C2311yescharacteristic
112C2×C4⋊C4×C29C2311yescharacteristic
113C2×C4⋊C4×C29C2311yescharacteristic
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C22⋊C4×C29—21no—
117C2×C22⋊C4×C29—21no—
118C2×C22⋊C4×C29—21no—
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29D411yescharacteristic
124C2×C22⋊C4×C29D411yescharacteristic
125C2×C42×C29—21no—
126C2×C42×C29C2311yescharacteristic
127C2×C42×C29C2311yescharacteristic
128C29×#103—22no—
129C29×#103—22no—
130C29×#103—22no—
131C29×#103—22no—
132C29×#102—22no—
133C29×#102—22no—
134C29×#102—22no—
135C29×#102—22no—
136C29×C22⋊C8—22no—
137C29×C22⋊C8—22no—
138C29×#97—22no—
139C4×C8×C29—22no—
140C29×#95—21no—
141C29×#95—21no—
142C24×C29—21no—
143C24×C29C2×D411yescharacteristic
144C2×Q8×C29—24no—
145C2×Q8×C29—24no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—81no—
153C2×Q8×C29—81no—
154C2×Q8×C29—81no—
155C2×Q8×C29—81no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—42no—
163C2×D4×C29—81no—
164C2×D4×C29—81no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—24no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—81no—
178C22×C4×C29—81no—
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2×D411yescharacteristic
181C22×C4×C29C2×D411yescharacteristic
182C22×C4×C29C2×D411yescharacteristic
183C22×C4×C29C2×D411yescharacteristic
184C22×C4×C29#4112yes—
185C22×C4×C29#4112yes—
186C22×C4×C29C2411yescharacteristic
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29—21no—
195C2×C8×C29—21no—
196C2×C8×C29—21no—
197C2×C8×C29—21no—
198C2×C8×C29—21no—
199C4⋊C4×C29—24no—
200C4⋊C4×C29—24no—
201C4⋊C4×C29—24no—
202C4⋊C4×C29—24no—
203C4⋊C4×C29—24no—
204C4⋊C4×C29—24no—
205C4⋊C4×C29—24no—
206C4⋊C4×C29—22no—
207C4⋊C4×C29—22no—
208C4⋊C4×C29—21no—
209C4⋊C4×C29—21no—
210C4⋊C4×C29—21no—
211C4⋊C4×C29—21no—
212C4⋊C4×C29—21no—
213C4⋊C4×C29—21no—
214C4⋊C4×C29—21no—
215C4⋊C4×C29—21no—
216C4⋊C4×C29—42no—
217C4⋊C4×C29—81no—
218C4⋊C4×C29—81no—
219C4⋊C4×C29C2×D412yes—
220C4⋊C4×C29C2×D412yes—
221C4⋊C4×C29C2×D412yes—
222C4⋊C4×C29C2×D412yes—
223C22⋊C4×C29—24no—
224C22⋊C4×C29—22no—
225C22⋊C4×C29—22no—
226C22⋊C4×C29—42no—
227C22⋊C4×C29—42no—
228C22⋊C4×C29—42no—
229C22⋊C4×C29—42no—
230C22⋊C4×C29—81no—
231C22⋊C4×C29—81no—
232C42×C29—24no—
233C42×C29—21no—
234C42×C29—21no—
235C42×C29C2×D412yes—
236C42×C29C2×D412yes—
237#25916C2911yesmaximal, characteristic, direct product factor, Sylow
238C23×C29—21no—
239C23×C29—21no—
240C23×C29—21no—
241C23×C29—21no—
242C23×C29—21no—
243C23×C29—21no—
244C23×C29—41no—
245C23×C29—41no—
246C23×C29—41no—
247C23×C29—41no—
248C23×C29—41no—
249C23×C29—41no—
250C23×C29—41no—
251C23×C29#12412yes—
252C23×C29C22×D411yescharacteristic
253Q8×C29—41no—
254Q8×C29—41no—
255Q8×C29—41no—
256Q8×C29—41no—
257Q8×C29—84no—
258Q8×C29—84no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—41no—
262D4×C29—41no—
263D4×C29—84no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—22no—
271C2×C4×C29—22no—
272C2×C4×C29—22no—
273C2×C4×C29—22no—
274C2×C4×C29—21no—
275C2×C4×C29—22no—
276C2×C4×C29—21no—
277C2×C4×C29—22no—
278C2×C4×C29—22no—
279C2×C4×C29—22no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—21no—
283C2×C4×C29—21no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—41no—
294C2×C4×C29—41no—
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—84no—
302C2×C4×C29#12012yes—
303C2×C4×C29#12012yes—
304C2×C4×C29#12412yes—
305C2×C4×C29C22×D411yescharacteristic
306C2×C4×C29C22×D411yescharacteristic
307C2×C4×C29C2×#4111yescharacteristic
308C2×C4×C29C2×#4111yescharacteristic
309C2×C4×C292−1+411yescharacteristic
310C2×C4×C292−1+411yescharacteristic
311C8×C29—41no—
312C8×C29—41no—
313C8×C29—41no—
314C8×C29—41no—
315C2×#544C2×C2911yescharacteristic, complemented
316C2×#489C2×C2911yescharacteristic, complemented
317C2×#488C2×C2911yescharacteristic, complemented
318#2620C2×C2911yescharacteristic
319#2026C2×C2911yescharacteristic, complemented
320#2025C2×C2911yescharacteristic, complemented
321#2024C2×C2911yescharacteristic, complemented
322#2023C2×C2911yescharacteristic, complemented
323#1992C2×C2911yescharacteristic, complemented
324#1990C2×C2911yescharacteristic, complemented
325#1875C2×C2911yescharacteristic
326#1874C2×C2911yescharacteristic
327#1873C2×C2911yescharacteristic, complemented
328#1872C2×C2911yescharacteristic, complemented
329#1750C2×C2911yescharacteristic, complemented
330C22×C29—22no—
331C22×C29—22no—
332C22×C29—22no—
333C22×C29—41no—
334C22×C29—41no—
335C22×C29—41no—
336C22×C29—41no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29—81no—
340C22×C29—81no—
341C22×C29—81no—
342C22×C29—81no—
343C22×C29—81no—
344C22×C29C2×#12011yescharacteristic
345C22×C29C2×#12411yescharacteristic
346C22×C29#53611yescharacteristic
347C22×C29#57611yescharacteristic
348C22×C29#57711yescharacteristic
349C22×C29#57711yescharacteristic
350C22×C29#57811yescharacteristic
351C4×C29—22no—
352C4×C29—22no—
353C4×C29—22no—
354C4×C29—41no—
355C4×C29—42no—
356C4×C29—42no—
357C4×C29—42no—
358C4×C29—41no—
359C4×C29—42no—
360C4×C29—81no—
361C4×C29—81no—
362C4×C29—81no—
363C4×C29#54811yescharacteristic
364C4×C29#54811yescharacteristic
365C4×C29#54811yescharacteristic
366C4×C29#54811yescharacteristic
367#544—24no—
368#544—24no—
369C2×C4⋊Q8—21no—
370C2×C4⋊Q8C22×C2911yescharacteristic
371C2×C4⋊Q8C22×C2911yescharacteristic
372C2×#125—21no—
373C2×#125C22×C2911yescharacteristic
374C2×#125C22×C2911yescharacteristic
375C2×#124C22×C2911yescharacteristic
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8C22×C2911yescharacteristic
379C2×#121C22×C2911yescharacteristic
380C2×#117C22×C2911yescharacteristic
381C2×#117C22×C2911yescharacteristic
382C22×C4⋊C4C22×C2911yescharacteristic
383#489—24no—
384#488—24no—
385C2×#103C22×C2911yescharacteristic
386C2×#103C22×C2911yescharacteristic
387C2×#103C22×C2911yescharacteristic
388C2×#103C22×C2911yescharacteristic
389C2×#102C22×C2911yescharacteristic
390C2×#102C22×C2911yescharacteristic
391C2×#102C22×C2911yescharacteristic
392C2×#102C22×C2911yescharacteristic
393C2×C22⋊C8C22×C2911yescharacteristic
394C2×C22⋊C8C22×C2911yescharacteristic
395C2×#97C22×C2911yescharacteristic
396C2×C4×C8C22×C2911yescharacteristic
397#396—21no—
398#396—21no—
399#394—21no—
400#394—21no—
401#391C22×C2911yescharacteristic
402#390C22×C2911yescharacteristic
403#384C22×C2911yescharacteristic
404#340C22×C2911yescharacteristic
405#340C22×C2911yescharacteristic
406#340C22×C2911yescharacteristic
407#340C22×C2911yescharacteristic
408#340C22×C2911yescharacteristic
409#340C22×C2911yescharacteristic
410#340C22×C2911yescharacteristic
411#340C22×C2911yescharacteristic
412#336C22×C2911yescharacteristic
413#336C22×C2911yescharacteristic
414C2×C29—42no—
415C2×C29—161no—
416C2×C29#243611yescharacteristic
417C2×C29#301211yescharacteristic
418C2×C29#301311yescharacteristic
419C2×C29#313611yescharacteristic
420C2×C29#313711yescharacteristic
421C2×C29#324311yescharacteristic
422C2×C29#324411yescharacteristic
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8C23×C2911yescharacteristic
426C22×D4—21no—
427C22×D4C23×C2911yescharacteristic
428C23×C4—21no—
429C23×C4C23×C2911yescharacteristic
430C22×C8C23×C2911yescharacteristic
431C22×C8C23×C2911yescharacteristic
432C22×C8C23×C2911yescharacteristic
433C22×C8C23×C2911yescharacteristic
434C4⋊Q8—28no—
435C4⋊Q8—22no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438C4⋊Q8D4×C2914yescomplemented
439#125—28no—
440#125—22no—
441#125—22no—
442#125—22no—
443#125D4×C2914yescomplemented
444#124—22no—
445#124—22no—
446C22⋊Q8—28no—
447C22⋊Q8—28no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450#121—22no—
451#121—22no—
452#117—22no—
453#117—22no—
454#117—22no—
455#117—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4D4×C2911yescharacteristic
469C2×C4⋊C4D4×C2911yescharacteristic
470C2×C4⋊C4C23×C2911yescharacteristic
471C2×C4⋊C4C23×C2911yescharacteristic
472C2×C4⋊C4C23×C2911yescharacteristic
473C2×C4⋊C4C23×C2911yescharacteristic
474C2×C4⋊C4C23×C2911yescharacteristic
475C2×C4⋊C4C23×C2911yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C2911yescharacteristic
484C2×C22⋊C4D4×C2911yescharacteristic
485C2×C42—21no—
486C2×C42C23×C2911yescharacteristic
487C2×C42C23×C2911yescharacteristic
488#103—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498#97—22no—
499C4×C8—22no—
500#95—21no—
501#95—21no—
502C29#2591611yescharacteristic, direct product factor, Sylow
503C24—21no—
504C24C2×D4×C2911yescharacteristic
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—81no—
514C2×Q8—81no—
515C2×Q8—81no—
516C2×Q8—81no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
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—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C2911yescharacteristic
541C22×C4C2×D4×C2911yescharacteristic
542C22×C4C2×D4×C2911yescharacteristic
543C22×C4C2×D4×C2911yescharacteristic
544C22×C4C2×D4×C2911yescharacteristic
545C22×C4#41×C2912yes—
546C22×C4#41×C2912yes—
547C22×C4C24×C2911yescharacteristic
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C2912yes—
581C4⋊C4C2×D4×C2912yes—
582C4⋊C4C2×D4×C2912yes—
583C4⋊C4C2×D4×C2912yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—24no—
594C42—21no—
595C42—21no—
596C42C2×D4×C2912yes—
597C42C2×D4×C2912yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C29×#12412yes—
612C23C22×D4×C2911yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—84no—
618Q8—84no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4C29×#12012yes—
663C2×C4C29×#12012yes—
664C2×C4C29×#12412yes—
665C2×C4C22×D4×C2911yescharacteristic
666C2×C4C22×D4×C2911yescharacteristic
667C2×C4C2×#41×C2911yescharacteristic
668C2×C4C2×#41×C2911yescharacteristic
669C2×C4C29×2−1+411yescharacteristic
670C2×C4C29×2−1+411yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C29×#12011yescharacteristic
690C22C2×C29×#12411yescharacteristic
691C22C29×#53611yescharacteristic
692C22C29×#57611yescharacteristic
693C22C29×#57711yescharacteristic
694C22C29×#57711yescharacteristic
695C22C29×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C29×#54811yescharacteristic
709C4C29×#54811yescharacteristic
710C4C29×#54811yescharacteristic
711C4C29×#54811yescharacteristic
712C2—42no—
713C2—161no—
714C2C29×#243611yescharacteristic
715C2C29×#301211yescharacteristic
716C2C29×#301311yescharacteristic
717C2C29×#313611yescharacteristic
718C2C29×#313711yescharacteristic
719C2C29×#324311yescharacteristic
720C2C29×#324411yescharacteristic
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
1. C2×C29×#544C2semidirect
2. C2×C29×#489C2semidirect
3. C2×C29×#488C2semidirect
5. C29×#2026C2semidirect
6. C29×#2025C2semidirect
7. C29×#2024C2semidirect
8. C29×#2023C2semidirect
9. C29×#1992C2semidirect
10. C29×#1990C2semidirect
13. C29×#1873C2semidirect
14. C29×#1872C2semidirect
15. C29×#1750C2semidirect
78. C29×C4⋊Q8D4semidirect
83. C29×#125D4semidirect
237. #25916C29direct (N × H)
315. C2×#544C2×C29semidirect
316. C2×#489C2×C29semidirect
317. C2×#488C2×C29semidirect
319. #2026C2×C29semidirect
320. #2025C2×C29semidirect
321. #2024C2×C29semidirect
322. #2023C2×C29semidirect
323. #1992C2×C29semidirect
324. #1990C2×C29semidirect
327. #1873C2×C29semidirect
328. #1872C2×C29semidirect
329. #1750C2×C29semidirect
438. C4⋊Q8D4×C29semidirect
443. #125D4×C29semidirect
502. C29#25916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5442
C2×C29×#4892
C2×C29×#4882
C29×#26202
C29×#20262
C29×#20252
C29×#20242
C29×#20232
C29×#19922
C29×#19902
C29×#18752
C29×#18742
C29×#18732
C29×#18722
C29×#17502
#2591629