Finite Group Databasebeta

← C29×#25529 #20320429

Subgroups — C29×#25529 #20320429

Order 7424.

1014 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3495C211yesmaximal, characteristic
2C29×#3095C211yesmaximal, characteristic, complemented
3C29×#3056C211yesmaximal, characteristic
4C29×#2621C211yesmaximal, characteristic, complemented
5C29×#2061C211yesmaximal, characteristic, complemented
6C29×#2038C211yesmaximal, characteristic, complemented
7C29×#2028C211yesmaximal, characteristic, complemented
8C29×#2005C211yesmaximal, characteristic, complemented
9C29×#1901C211yesmaximal, characteristic, complemented
10C29×#1897C211yesmaximal, characteristic
11C29×#1886C211yesmaximal, characteristic, complemented
12C29×#1882C211yesmaximal, characteristic, complemented
13C29×#1860C211yesmaximal, characteristic, complemented
14C29×#1857C211yesmaximal, characteristic, complemented
15C29×#1733C211yesmaximal, characteristic, complemented
16C2×C29×#137C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C29×#556—21no—
19C29×#554—21no—
20C29×#552—21no—
21C29×#552—22no—
22C29×#552—21no—
23C29×#551—22no—
24C29×#544C2211yescharacteristic
25C29×#542—21no—
26C29×#541—21no—
27C29×#536C2211yescharacteristic
28C29×#533—21no—
29C2×C29×C4⋊Q8C2211yescharacteristic
30C29×#529—21no—
31C29×#525C2211yescharacteristic
32C2×C29×C22⋊Q8C2211yescharacteristic
33C2×C29×C22⋊Q8C2211yescharacteristic
34C29×#520C2211yescharacteristic
35C29×#519C2211yescharacteristic
36C2×C29×#117C2211yescharacteristic
37C2×C29×#117C2211yescharacteristic
38C29×#485—21no—
39C29×#485—21no—
40C29×#484—21no—
41C29×#483—21no—
42C29×#470—21no—
43C29×#468—21no—
44C29×#467—21no—
45C29×#465—21no—
46C29×#428C2211yescharacteristic
47C29×#428C2211yescharacteristic
48C29×#428C2211yescharacteristic
49C2×C29×#104C2211yescharacteristic
50C2×C29×#104C2211yescharacteristic
51C29×#419C2211yescharacteristic
52C29×#419C2211yescharacteristic
53C29×#419C2211yescharacteristic
54C29×#417C2211yescharacteristic
55C2×C29×#101C2211yescharacteristic
56C2×C29×#101C2211yescharacteristic
57C29×#407C2211yescharacteristic
58C29×#398—22no—
59C29×#397—22no—
60C29×#391C2211yescharacteristic
61C29×#391C2211yescharacteristic
62C29×#382C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#339C2211yescharacteristic
66C29×#339C2211yescharacteristic
67C29×#339C2211yescharacteristic
68C29×#339C2211yescharacteristic
69C29×#339C2211yescharacteristic
70C29×#339C2211yescharacteristic
71C2×#41×C29C2311yescharacteristic
72C22×Q8×C29C2311yescharacteristic
73C22×Q8×C29C2311yescharacteristic
74C23×C4×C29C2311yescharacteristic
75C29×#137—22no—
76C29×#137—41no—
77C2×Q16×C29—21no—
78C2×SD16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29—22no—
81C2×M16×C29—41no—
82C2×M16×C29C2311yescharacteristic
83C2×M16×C29C2311yescharacteristic
84C2×M16×C29C2311yescharacteristic
85C2×M16×C29C2311yescharacteristic
86C22×C8×C29—21no—
87C29×C4⋊Q8—21no—
88C29×C4⋊Q8—21no—
89C29×C4⋊Q8—21no—
90C29×C4⋊Q8—22no—
91C29×C4⋊Q8—41no—
92C29×#126—22no—
93C29×#126—22no—
94C29×#126—22no—
95C29×#126—22no—
96C29×#125—22no—
97C29×#125—22no—
98C29×#125—22no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#124—22no—
102C29×#124—21no—
103C29×#123—22no—
104C29×#123—22no—
105C29×#123—21no—
106C29×#123—22no—
107C29×C22⋊Q8—22no—
108C29×C22⋊Q8—22no—
109C29×C22⋊Q8—21no—
110C29×C22⋊Q8—21no—
111C29×C22⋊Q8—21no—
112C29×C22⋊Q8—21no—
113C29×C22⋊Q8—22no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8—21no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8D411yescharacteristic
121C29×C22⋊Q8D411yescharacteristic
122C29×#121D411yescharacteristic
123C29×#121D411yescharacteristic
124C29×#120—21no—
125C4×Q8×C29—22no—
126C4×Q8×C29—21no—
127C4×Q8×C29—21no—
128C4×Q8×C29—21no—
129C4×Q8×C29—21no—
130C4×Q8×C29—21no—
131C4×D4×C29—22no—
132C4×D4×C29—21no—
133C4×D4×C29—22no—
134C4×D4×C29—21no—
135C4×D4×C29—21no—
136C29×#117—22no—
137C29×#117—22no—
138C29×#117—21no—
139C29×#117—21no—
140C29×#117—22no—
141C29×#117—21no—
142C29×#117—22no—
143C29×#117—41no—
144C29×#117D411yescharacteristic
145C29×#117D411yescharacteristic
146C29×#117C2311yescharacteristic
147C29×#117C2311yescharacteristic
148C29×#117C2311yescharacteristic
149C2×C4⋊C4×C29—21no—
150C2×C4⋊C4×C29—21no—
151C2×C4⋊C4×C29—21no—
152C2×C4⋊C4×C29—22no—
153C2×C4⋊C4×C29D412yes—
154C2×C4⋊C4×C29D411yescharacteristic
155C2×C4⋊C4×C29D411yescharacteristic
156C2×C4⋊C4×C29C2311yescharacteristic
157C2×C4⋊C4×C29C2311yescharacteristic
158C2×C22⋊C4×C29—21no—
159C2×C22⋊C4×C29—21no—
160C2×C22⋊C4×C29—21no—
161C2×C22⋊C4×C29D412yes—
162C2×C42×C29—21no—
163C2×C42×C29C2311yescharacteristic
164C2×C42×C29C2311yescharacteristic
165C29×#107—21no—
166C29×#107—21no—
167C29×#107—21no—
168C29×#106—21no—
169C29×#106—21no—
170C29×#106—21no—
171C29×#104—22no—
172C29×#104—41no—
173C29×#103—21no—
174C29×#103—21no—
175C29×#103—21no—
176C29×#103—21no—
177C29×#103—21no—
178C29×#103—21no—
179C29×#103—21no—
180C29×#102—21no—
181C29×#101—22no—
182C29×#101—41no—
183C29×C22⋊C8—21no—
184C29×C22⋊C8—21no—
185C29×#95—22no—
186C29×#95—22no—
187C29×#95—22no—
188C24×C29C2×D411yescharacteristic
189#41×C29—21no—
190#41×C29—21no—
191#41×C29—21no—
192#41×C29—21no—
193C2×Q8×C29—22no—
194C2×Q8×C29—21no—
195C2×Q8×C29—21no—
196C2×Q8×C29—21no—
197C2×Q8×C29—21no—
198C2×Q8×C29—21no—
199C2×Q8×C29—21no—
200C2×Q8×C29—21no—
201C2×Q8×C29—21no—
202C2×Q8×C29—21no—
203C2×Q8×C29—21no—
204C2×Q8×C29—21no—
205C2×Q8×C29—21no—
206C2×Q8×C29C2×D411yescharacteristic
207C2×D4×C29—21no—
208C2×D4×C29—21no—
209C2×D4×C29—21no—
210C2×D4×C29C2×D411yescharacteristic
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—21no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—22no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29C2×D412yes—
224C22×C4×C29C2×D411yescharacteristic
225C22×C4×C29C2×D411yescharacteristic
226C22×C4×C29C2×D411yescharacteristic
227C22×C4×C29C2×D411yescharacteristic
228C22×C4×C29C2×D411yescharacteristic
229C22×C4×C29C2×D412yes—
230C22×C4×C29C2411yescharacteristic
231Q16×C29—42no—
232SD16×C29—42no—
233M16×C29—21no—
234M16×C29—21no—
235M16×C29—21no—
236M16×C29—21no—
237M16×C29—21no—
238M16×C29—21no—
239M16×C29—21no—
240M16×C29—42no—
241M16×C29#4112yes—
242C2×C8×C29—21no—
243C2×C8×C29—21no—
244C2×C8×C29—21no—
245C2×C8×C29—21no—
246C2×C8×C29—42no—
247C4⋊C4×C29—22no—
248C4⋊C4×C29—22no—
249C4⋊C4×C29—22no—
250C4⋊C4×C29—22no—
251C4⋊C4×C29—22no—
252C4⋊C4×C29—22no—
253C4⋊C4×C29—22no—
254C4⋊C4×C29—22no—
255C4⋊C4×C29—21no—
256C4⋊C4×C29—21no—
257C4⋊C4×C29—22no—
258C4⋊C4×C29—22no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—42no—
266C4⋊C4×C29—44no—
267C4⋊C4×C29—41no—
268C4⋊C4×C29—41no—
269C4⋊C4×C29C2×D411yescharacteristic
270C4⋊C4×C29C2×D411yescharacteristic
271C4⋊C4×C29C2×D411yescharacteristic
272C4⋊C4×C29C2×D411yescharacteristic
273C4⋊C4×C29C2×D411yescharacteristic
274C4⋊C4×C29C2×D411yescharacteristic
275C22⋊C4×C29—22no—
276C22⋊C4×C29—22no—
277C22⋊C4×C29—22no—
278C22⋊C4×C29—21no—
279C22⋊C4×C29—21no—
280C22⋊C4×C29—22no—
281C22⋊C4×C29—22no—
282C22⋊C4×C29—21no—
283C22⋊C4×C29—21no—
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—42no—
290C22⋊C4×C29—41no—
291C22⋊C4×C29—41no—
292C42×C29—22no—
293C42×C29—22no—
294C42×C29—22no—
295C42×C29—21no—
296C42×C29—21no—
297C42×C29—21no—
298C42×C29—21no—
299C42×C29—21no—
300C42×C29—21no—
301C42×C29—21no—
302C42×C29—21no—
303C42×C29#4112yes—
304#25529C2911yesmaximal, characteristic, direct product factor, Sylow
305C23×C29—21no—
306C23×C29—21no—
307C23×C29—21no—
308C23×C29—41no—
309C23×C29—41no—
310C23×C29#12011yescharacteristic
311C23×C29#12011yescharacteristic
312C23×C29C22×D411yescharacteristic
313Q8×C29—21no—
314Q8×C29—21no—
315Q8×C29—41no—
316Q8×C29—41no—
317Q8×C29—41no—
318Q8×C29—41no—
319Q8×C29—41no—
320Q8×C29—41no—
321Q8×C29—41no—
322Q8×C29—41no—
323Q8×C29—82no—
324D4×C29—21no—
325D4×C29—21no—
326D4×C29—42no—
327D4×C29—41no—
328D4×C29—41no—
329D4×C29—81no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—21no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—21no—
336C2×C4×C29—21no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
339C2×C4×C29—21no—
340C2×C4×C29—21no—
341C2×C4×C29—21no—
342C2×C4×C29—21no—
343C2×C4×C29—21no—
344C2×C4×C29—21no—
345C2×C4×C29—22no—
346C2×C4×C29—21no—
347C2×C4×C29—21no—
348C2×C4×C29—22no—
349C2×C4×C29—22no—
350C2×C4×C29—22no—
351C2×C4×C29—22no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—42no—
355C2×C4×C29—41no—
356C2×C4×C29—41no—
357C2×C4×C29—42no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—42no—
361C2×C4×C29—41no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—81no—
367C2×C4×C29—82no—
368C2×C4×C29#12011yescharacteristic
369C2×C4×C29#12011yescharacteristic
370C2×C4×C29C22×D411yescharacteristic
371C2×C4×C29C22×D411yescharacteristic
372C2×C4×C29C2×#4111yescharacteristic
373C2×C4×C29C2×#4111yescharacteristic
374C2×C4×C29H(5,𝔽2)11yescharacteristic
375C2×C4×C292−1+411yescharacteristic
376C8×C29—22no—
377C8×C29—41no—
378C8×C29—41no—
379C8×C29—41no—
380#3495C2×C2911yescharacteristic
381#3095C2×C2911yescharacteristic, complemented
382#3056C2×C2911yescharacteristic
383#2621C2×C2911yescharacteristic, complemented
384#2061C2×C2911yescharacteristic, complemented
385#2038C2×C2911yescharacteristic, complemented
386#2028C2×C2911yescharacteristic, complemented
387#2005C2×C2911yescharacteristic, complemented
388#1901C2×C2911yescharacteristic, complemented
389#1897C2×C2911yescharacteristic
390#1886C2×C2911yescharacteristic, complemented
391#1882C2×C2911yescharacteristic, complemented
392#1860C2×C2911yescharacteristic, complemented
393#1857C2×C2911yescharacteristic, complemented
394#1733C2×C2911yescharacteristic, complemented
395C22×C29—21no—
396C22×C29—21no—
397C22×C29—21no—
398C22×C29—21no—
399C22×C29—21no—
400C22×C29—21no—
401C22×C29—21no—
402C22×C29—21no—
403C22×C29—41no—
404C22×C29—41no—
405C22×C29—41no—
406C22×C29—81no—
407C22×C29—81no—
408C22×C29C2×#12011yescharacteristic
409C22×C29#54611yescharacteristic
410C22×C29#54711yescharacteristic
411C4×C29—21no—
412C4×C29—21no—
413C4×C29—42no—
414C4×C29—42no—
415C4×C29—41no—
416C4×C29—41no—
417C4×C29—41no—
418C4×C29—41no—
419C4×C29—42no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—41no—
423C4×C29—81no—
424C4×C29—81no—
425C4×C29—81no—
426C4×C29#53211yescharacteristic
427C4×C29#53711yescharacteristic
428C4×C29#54611yescharacteristic
429C4×C29#54711yescharacteristic
430C2×#137C22×C2911yescharacteristic
431C22×M16C22×C2911yescharacteristic
432#556—21no—
433#554—21no—
434#552—21no—
435#552—22no—
436#552—21no—
437#551—22no—
438#544C22×C2911yescharacteristic
439#542—21no—
440#541—21no—
441#536C22×C2911yescharacteristic
442#533—21no—
443C2×C4⋊Q8C22×C2911yescharacteristic
444#529—21no—
445#525C22×C2911yescharacteristic
446C2×C22⋊Q8C22×C2911yescharacteristic
447C2×C22⋊Q8C22×C2911yescharacteristic
448#520C22×C2911yescharacteristic
449#519C22×C2911yescharacteristic
450C2×#117C22×C2911yescharacteristic
451C2×#117C22×C2911yescharacteristic
452#485—21no—
453#485—21no—
454#484—21no—
455#483—21no—
456#470—21no—
457#468—21no—
458#467—21no—
459#465—21no—
460#428C22×C2911yescharacteristic
461#428C22×C2911yescharacteristic
462#428C22×C2911yescharacteristic
463C2×#104C22×C2911yescharacteristic
464C2×#104C22×C2911yescharacteristic
465#419C22×C2911yescharacteristic
466#419C22×C2911yescharacteristic
467#419C22×C2911yescharacteristic
468#417C22×C2911yescharacteristic
469C2×#101C22×C2911yescharacteristic
470C2×#101C22×C2911yescharacteristic
471#407C22×C2911yescharacteristic
472#398—22no—
473#397—22no—
474#391C22×C2911yescharacteristic
475#391C22×C2911yescharacteristic
476#382C22×C2911yescharacteristic
477#343C22×C2911yescharacteristic
478#343C22×C2911yescharacteristic
479#339C22×C2911yescharacteristic
480#339C22×C2911yescharacteristic
481#339C22×C2911yescharacteristic
482#339C22×C2911yescharacteristic
483#339C22×C2911yescharacteristic
484#339C22×C2911yescharacteristic
485C2×C29—21no—
486C2×C29—21no—
487C2×C29—41no—
488C2×C29—41no—
489C2×C29—81no—
490C2×C29#243011yescharacteristic
491C2×C29#302011yescharacteristic
492C2×C29#302211yescharacteristic
493C2×#41C23×C2911yescharacteristic
494C22×Q8C23×C2911yescharacteristic
495C22×Q8C23×C2911yescharacteristic
496C23×C4C23×C2911yescharacteristic
497#137—22no—
498#137—41no—
499C2×Q16—21no—
500C2×SD16—21no—
501C2×M16—21no—
502C2×M16—22no—
503C2×M16—41no—
504C2×M16C23×C2911yescharacteristic
505C2×M16C23×C2911yescharacteristic
506C2×M16C23×C2911yescharacteristic
507C2×M16C23×C2911yescharacteristic
508C22×C8—21no—
509C4⋊Q8—21no—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8—22no—
513C4⋊Q8—41no—
514#126—22no—
515#126—22no—
516#126—22no—
517#126—22no—
518#125—22no—
519#125—22no—
520#125—22no—
521#125—21no—
522#125—21no—
523#124—22no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123—21no—
528#123—22no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—22no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8D4×C2911yescharacteristic
543C22⋊Q8D4×C2911yescharacteristic
544#121D4×C2911yescharacteristic
545#121D4×C2911yescharacteristic
546#120—21no—
547C4×Q8—22no—
548C4×Q8—21no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×D4—22no—
554C4×D4—21no—
555C4×D4—22no—
556C4×D4—21no—
557C4×D4—21no—
558#117—22no—
559#117—22no—
560#117—21no—
561#117—21no—
562#117—22no—
563#117—21no—
564#117—22no—
565#117—41no—
566#117D4×C2911yescharacteristic
567#117D4×C2911yescharacteristic
568#117C23×C2911yescharacteristic
569#117C23×C2911yescharacteristic
570#117C23×C2911yescharacteristic
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4D4×C2912yes—
576C2×C4⋊C4D4×C2911yescharacteristic
577C2×C4⋊C4D4×C2911yescharacteristic
578C2×C4⋊C4C23×C2911yescharacteristic
579C2×C4⋊C4C23×C2911yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4D4×C2912yes—
584C2×C42—21no—
585C2×C42C23×C2911yescharacteristic
586C2×C42C23×C2911yescharacteristic
587#107—21no—
588#107—21no—
589#107—21no—
590#106—21no—
591#106—21no—
592#106—21no—
593#104—22no—
594#104—41no—
595#103—21no—
596#103—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#102—21no—
603#101—22no—
604#101—41no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607#95—22no—
608#95—22no—
609#95—22no—
610C29#2552911yescharacteristic, direct product factor, Sylow
611C24C2×D4×C2911yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—22no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8C2×D4×C2911yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C2×D4×C2911yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4C2×D4×C2912yes—
647C22×C4C2×D4×C2911yescharacteristic
648C22×C4C2×D4×C2911yescharacteristic
649C22×C4C2×D4×C2911yescharacteristic
650C22×C4C2×D4×C2911yescharacteristic
651C22×C4C2×D4×C2911yescharacteristic
652C22×C4C2×D4×C2912yes—
653C22×C4C24×C2911yescharacteristic
654Q16—42no—
655SD16—42no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16—21no—
663M16—42no—
664M16#41×C2912yes—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—42no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—44no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4C2×D4×C2911yescharacteristic
693C4⋊C4C2×D4×C2911yescharacteristic
694C4⋊C4C2×D4×C2911yescharacteristic
695C4⋊C4C2×D4×C2911yescharacteristic
696C4⋊C4C2×D4×C2911yescharacteristic
697C4⋊C4C2×D4×C2911yescharacteristic
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—42no—
713C22⋊C4—41no—
714C22⋊C4—41no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42#41×C2912yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23C29×#12011yescharacteristic
733C23C29×#12011yescharacteristic
734C23C22×D4×C2911yescharacteristic
735Q8—21no—
736Q8—21no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—82no—
746D4—21no—
747D4—21no—
748D4—42no—
749D4—41no—
750D4—41no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—81no—
789C2×C4—82no—
790C2×C4C29×#12011yescharacteristic
791C2×C4C29×#12011yescharacteristic
792C2×C4C22×D4×C2911yescharacteristic
793C2×C4C22×D4×C2911yescharacteristic
794C2×C4C2×#41×C2911yescharacteristic
795C2×C4C2×#41×C2911yescharacteristic
796C2×C4C29×H(5,𝔽2)11yescharacteristic
797C2×C4C29×2−1+411yescharacteristic
798C8—22no—
799C8—41no—
800C8—41no—
801C8—41no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—81no—
814C22—81no—
815C22C2×C29×#12011yescharacteristic
816C22C29×#54611yescharacteristic
817C22C29×#54711yescharacteristic
818C4—21no—
819C4—21no—
820C4—42no—
821C4—42no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4C29×#53211yescharacteristic
834C4C29×#53711yescharacteristic
835C4C29×#54611yescharacteristic
836C4C29×#54711yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2C29×#243011yescharacteristic
843C2C29×#302011yescharacteristic
844C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3095C2semidirect
4. C29×#2621C2semidirect
5. C29×#2061C2semidirect
6. C29×#2038C2semidirect
7. C29×#2028C2semidirect
8. C29×#2005C2semidirect
9. C29×#1901C2semidirect
11. C29×#1886C2semidirect
12. C29×#1882C2semidirect
13. C29×#1860C2semidirect
14. C29×#1857C2semidirect
15. C29×#1733C2semidirect
304. #25529C29direct (N × H)
381. #3095C2×C29semidirect
383. #2621C2×C29semidirect
384. #2061C2×C29semidirect
385. #2038C2×C29semidirect
386. #2028C2×C29semidirect
387. #2005C2×C29semidirect
388. #1901C2×C29semidirect
390. #1886C2×C29semidirect
391. #1882C2×C29semidirect
392. #1860C2×C29semidirect
393. #1857C2×C29semidirect
394. #1733C2×C29semidirect
610. C29#25529direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34952
C29×#30952
C29×#30562
C29×#26212
C29×#20612
C29×#20382
C29×#20282
C29×#20052
C29×#19012
C29×#18972
C29×#18862
C29×#18822
C29×#18602
C29×#18572
C29×#17332
#2552929