Finite Group Databasebeta

← C29×#24404 #20319304

Subgroups — C29×#24404 #20319304

Order 7424.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3484C211yesmaximal, characteristic, complemented
2C2×C29×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×C29×#99C211yesmaximal, characteristic, complemented
4C29×#2410C212yesmaximal, complemented
5C29×#2403C211yesmaximal, characteristic, complemented
6C29×#2044C212yesmaximal, complemented
7C29×#2021C212yesmaximal, complemented
8C29×#1898C212yesmaximal, complemented
9C29×#1889C211yesmaximal, characteristic, complemented
10C29×#1867C211yesmaximal, characteristic, complemented
11C29×#1790C211yesmaximal, characteristic, complemented
12C2×C29×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C29C2211yescharacteristic
14C23×D4×C29C2211yescharacteristic, complemented
15C29×#546—22no—
16C29×#546—22no—
17D42×C29—22no—
18D42×C29—22no—
19C29×#535—21no—
20C29×#534—21no—
21C29×#534C2212yes—
22C29×#525—21no—
23C2×C29×#121—22no—
24C2×C29×#120—21no—
25C2×C29×#120—21no—
26C2×C29×#120C2211yescharacteristic
27C2×C29×#120C2212yes—
28C2×C29×#120C2212yescomplemented
29C2×C29×#120C2211yescharacteristic, complemented
30C29×#518C2211yescharacteristic
31C22×C22⋊C4×C29C2212yescomplemented
32C29×B(4,𝔽2)—24no—
33C2×C29×#99—24no—
34C2×C29×#99C2211yescharacteristic
35C2×C29×#99C2211yescharacteristic
36C2×C29×#99C2212yescomplemented
37C2×C29×#99C2212yescomplemented
38C2×C29×#99C2212yescomplemented
39C29×#394—22no—
40C29×#392—21no—
41C29×#392—21no—
42C29×#392—22no—
43C29×#386—21no—
44C29×#386—22no—
45C29×#386C2211yescharacteristic
46C29×#386C2211yescharacteristic, complemented
47C29×#386C2212yescomplemented
48C29×#385C2212yescomplemented
49C29×#379C2212yescomplemented
50C29×#379C2211yescharacteristic, complemented
51C29×#342C2212yescomplemented
52C29×#342C2212yescomplemented
53C25×C29D411yescharacteristic, complemented
54C25×C29C2311yescharacteristic
55C25×C29C2311yescharacteristic
56C29×H(5,𝔽2)—22no—
57C29×H(5,𝔽2)—22no—
58C29×H(5,𝔽2)—42no—
59C2×#41×C29—21no—
60C2×#41×C29—22no—
61C22×D4×C29—21no—
62C22×D4×C29—21no—
63C22×D4×C29—22no—
64C22×D4×C29—22no—
65C22×D4×C29—22no—
66C22×D4×C29—22no—
67C22×D4×C29—21no—
68C22×D4×C29—21no—
69C22×D4×C29—22no—
70C22×D4×C29—22no—
71C22×D4×C29—21no—
72C22×D4×C29—22no—
73C22×D4×C29—21no—
74C22×D4×C29—21no—
75C22×D4×C29—22no—
76C22×D4×C29—44no—
77C22×D4×C29—42no—
78C22×D4×C29D411yescharacteristic, complemented
79C22×D4×C29D411yescharacteristic, complemented
80C22×D4×C29D412yescomplemented
81C22×D4×C29D412yescomplemented
82C22×D4×C29C2312yes—
83C22×D4×C29C2311yescharacteristic
84C22×D4×C29C2311yescharacteristic
85C23×C4×C29—22no—
86C23×C4×C29D411yescharacteristic, complemented
87C23×C4×C29C2311yescharacteristic
88C29×#127—22no—
89C29×#124—22no—
90C29×#123—22no—
91C29×#123—22no—
92C29×#123—22no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×#121—21no—
96C29×#121—21no—
97C29×#121—22no—
98C29×#121—22no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121—22no—
102C29×#121—22no—
103C29×#121—48no—
104C29×#120—22no—
105C29×#120—22no—
106C29×#120—22no—
107C29×#120—22no—
108C29×#120—22no—
109C29×#120—22no—
110C29×#120—22no—
111C29×#120—22no—
112C29×#120—22no—
113C29×#120—22no—
114C29×#120—22no—
115C29×#120—24no—
116C29×#120—42no—
117C29×#120—42no—
118C29×#120—44no—
119C4×D4×C29—22no—
120C4×D4×C29—22no—
121C4×D4×C29—22no—
122C4×D4×C29—22no—
123C29×#117—21no—
124C2×C4⋊C4×C29—22no—
125C2×C22⋊C4×C29—21no—
126C2×C22⋊C4×C29—21no—
127C2×C22⋊C4×C29—21no—
128C2×C22⋊C4×C29—24no—
129C2×C22⋊C4×C29—22no—
130C2×C22⋊C4×C29—21no—
131C2×C22⋊C4×C29—21no—
132C2×C22⋊C4×C29—21no—
133C2×C22⋊C4×C29—22no—
134C2×C22⋊C4×C29—21no—
135C2×C22⋊C4×C29—21no—
136C2×C22⋊C4×C29—22no—
137C2×C22⋊C4×C29—22no—
138C2×C22⋊C4×C29—21no—
139C2×C22⋊C4×C29—22no—
140C2×C22⋊C4×C29—42no—
141C2×C22⋊C4×C29D412yescomplemented
142C2×C22⋊C4×C29D412yescomplemented
143C2×C22⋊C4×C29C2312yes—
144C2×C22⋊C4×C29C2311yescharacteristic
145C2×C22⋊C4×C29C2311yescharacteristic
146C2×C22⋊C4×C29C2312yes—
147C2×C22⋊C4×C29C2312yes—
148C29×#99—22no—
149C29×#99—24no—
150C29×#99—24no—
151C29×#99—42no—
152C29×#99D414yescomplemented
153C29×#95—22no—
154C29×#95—21no—
155C29×#95—21no—
156C29×#95—22no—
157C24×C29—21no—
158C24×C29—21no—
159C24×C29—22no—
160C24×C29—21no—
161C24×C29—22no—
162C24×C29—21no—
163C24×C29—21no—
164C24×C29—21no—
165C24×C29—22no—
166C24×C29—21no—
167C24×C29—21no—
168C24×C29—22no—
169C24×C29—41no—
170C24×C29—42no—
171C24×C29—42no—
172C24×C29—42no—
173C24×C29—81no—
174C24×C29—81no—
175C24×C29—81no—
176C24×C29C2×D411yescharacteristic
177C24×C29C2×D412yes—
178C24×C29C2×D411yescharacteristic
179C24×C29C2×D412yes—
180C24×C29C2×D412yes—
181C24×C29C2×D411yescharacteristic
182C24×C29C2×D411yescharacteristic
183C24×C29C2411yescharacteristic
184#41×C29—44no—
185#41×C29—44no—
186#41×C29—42no—
187#41×C29—42no—
188C2×Q8×C29—21no—
189C2×D4×C29—22no—
190C2×D4×C29—22no—
191C2×D4×C29—22no—
192C2×D4×C29—24no—
193C2×D4×C29—21no—
194C2×D4×C29—28no—
195C2×D4×C29—22no—
196C2×D4×C29—22no—
197C2×D4×C29—22no—
198C2×D4×C29—22no—
199C2×D4×C29—22no—
200C2×D4×C29—22no—
201C2×D4×C29—22no—
202C2×D4×C29—22no—
203C2×D4×C29—22no—
204C2×D4×C29—21no—
205C2×D4×C29—21no—
206C2×D4×C29—22no—
207C2×D4×C29—22no—
208C2×D4×C29—22no—
209C2×D4×C29—22no—
210C2×D4×C29—22no—
211C2×D4×C29—22no—
212C2×D4×C29—22no—
213C2×D4×C29—22no—
214C2×D4×C29—22no—
215C2×D4×C29—41no—
216C2×D4×C29—41no—
217C2×D4×C29—42no—
218C2×D4×C29—44no—
219C2×D4×C29—44no—
220C2×D4×C29—44no—
221C2×D4×C29—44no—
222C2×D4×C29—44no—
223C2×D4×C29—44no—
224C2×D4×C29—44no—
225C2×D4×C29—44no—
226C2×D4×C29—44no—
227C2×D4×C29—42no—
228C2×D4×C29—42no—
229C2×D4×C29—44no—
230C2×D4×C29—42no—
231C2×D4×C29—41no—
232C2×D4×C29—42no—
233C2×D4×C29—41no—
234C2×D4×C29—42no—
235C2×D4×C29—44no—
236C2×D4×C29—42no—
237C2×D4×C29—42no—
238C2×D4×C29—42no—
239C2×D4×C29—44no—
240C2×D4×C29—42no—
241C2×D4×C29—82no—
242C2×D4×C29—82no—
243C2×D4×C29—81no—
244C2×D4×C29—81no—
245C2×D4×C29—82no—
246C2×D4×C29—82no—
247C2×D4×C29C2×D412yes—
248C2×D4×C29#4112yes—
249C22×C4×C29—21no—
250C22×C4×C29—22no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—22no—
254C22×C4×C29—21no—
255C22×C4×C29—22no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—22no—
259C22×C4×C29—22no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—42no—
263C22×C4×C29—41no—
264C22×C4×C29—44no—
265C22×C4×C29—44no—
266C22×C4×C29—82no—
267C22×C4×C29C2×D412yes—
268C22×C4×C29C2×D411yescharacteristic
269C22×C4×C29C2×D411yescharacteristic
270C22×C4×C29C2×D412yes—
271C22×C4×C29C2×D412yes—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—22no—
275C4⋊C4×C29—22no—
276C4⋊C4×C29—44no—
277C22⋊C4×C29—22no—
278C22⋊C4×C29—22no—
279C22⋊C4×C29—22no—
280C22⋊C4×C29—22no—
281C22⋊C4×C29—22no—
282C22⋊C4×C29—22no—
283C22⋊C4×C29—22no—
284C22⋊C4×C29—22no—
285C22⋊C4×C29—22no—
286C22⋊C4×C29—22no—
287C22⋊C4×C29—22no—
288C22⋊C4×C29—22no—
289C22⋊C4×C29—22no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—22no—
293C22⋊C4×C29—22no—
294C22⋊C4×C29—44no—
295C22⋊C4×C29—44no—
296C22⋊C4×C29—42no—
297C22⋊C4×C29—42no—
298C22⋊C4×C29—42no—
299C22⋊C4×C29—44no—
300C22⋊C4×C29—42no—
301C22⋊C4×C29—44no—
302C22⋊C4×C29—42no—
303C22⋊C4×C29—82no—
304C22⋊C4×C29—81no—
305C22⋊C4×C29C2×D414yescomplemented
306C42×C29—22no—
307#24404C2911yesmaximal, characteristic, direct product factor, Sylow
308C23×C29—21no—
309C23×C29—21no—
310C23×C29—21no—
311C23×C29—22no—
312C23×C29—22no—
313C23×C29—22no—
314C23×C29—24no—
315C23×C29—21no—
316C23×C29—21no—
317C23×C29—21no—
318C23×C29—22no—
319C23×C29—22no—
320C23×C29—24no—
321C23×C29—22no—
322C23×C29—21no—
323C23×C29—22no—
324C23×C29—21no—
325C23×C29—21no—
326C23×C29—22no—
327C23×C29—22no—
328C23×C29—41no—
329C23×C29—42no—
330C23×C29—41no—
331C23×C29—41no—
332C23×C29—41no—
333C23×C29—42no—
334C23×C29—41no—
335C23×C29—42no—
336C23×C29—42no—
337C23×C29—42no—
338C23×C29—41no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—42no—
343C23×C29—42no—
344C23×C29—41no—
345C23×C29—42no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—42no—
349C23×C29—42no—
350C23×C29—42no—
351C23×C29—42no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—42no—
356C23×C29—42no—
357C23×C29—42no—
358C23×C29—81no—
359C23×C29—81no—
360C23×C29—82no—
361C23×C29—82no—
362C23×C29—82no—
363C23×C29—82no—
364C23×C29—84no—
365C23×C29—84no—
366C23×C29—81no—
367C23×C29—81no—
368C23×C29—84no—
369C23×C29—84no—
370C23×C29#12011yescharacteristic
371C23×C29#12012yes—
372C23×C29#12011yescharacteristic
373C23×C29#12112yescomplemented
374C23×C29C22×D411yescharacteristic
375C23×C29C22×D412yes—
376C23×C29C22×D411yescharacteristic
377C23×C29C2×#4111yescharacteristic
378C23×C29H(5,𝔽2)12yes—
379Q8×C29—42no—
380D4×C29—24no—
381D4×C29—24no—
382D4×C29—44no—
383D4×C29—42no—
384D4×C29—44no—
385D4×C29—48no—
386D4×C29—44no—
387D4×C29—44no—
388D4×C29—44no—
389D4×C29—42no—
390D4×C29—42no—
391D4×C29—42no—
392D4×C29—42no—
393D4×C29—42no—
394D4×C29—42no—
395D4×C29—44no—
396D4×C29—44no—
397D4×C29—82no—
398D4×C29—82no—
399D4×C29—82no—
400D4×C29—82no—
401D4×C29—88no—
402D4×C29—84no—
403D4×C29—84no—
404C2×C4×C29—21no—
405C2×C4×C29—21no—
406C2×C4×C29—22no—
407C2×C4×C29—24no—
408C2×C4×C29—22no—
409C2×C4×C29—22no—
410C2×C4×C29—22no—
411C2×C4×C29—21no—
412C2×C4×C29—21no—
413C2×C4×C29—21no—
414C2×C4×C29—24no—
415C2×C4×C29—22no—
416C2×C4×C29—22no—
417C2×C4×C29—42no—
418C2×C4×C29—42no—
419C2×C4×C29—44no—
420C2×C4×C29—42no—
421C2×C4×C29—42no—
422C2×C4×C29—41no—
423C2×C4×C29—42no—
424C2×C4×C29—42no—
425C2×C4×C29—41no—
426C2×C4×C29—42no—
427C2×C4×C29—42no—
428C2×C4×C29—42no—
429C2×C4×C29—41no—
430C2×C4×C29—41no—
431C2×C4×C29—42no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—41no—
436C2×C4×C29—42no—
437C2×C4×C29—81no—
438C2×C4×C29—81no—
439C2×C4×C29—88no—
440C2×C4×C29#12112yescomplemented
441#3484C2×C2911yescharacteristic, complemented
442C2×B(4,𝔽2)C2×C2911yescharacteristic, complemented
443C22×#99C2×C2911yescharacteristic, complemented
444#2410C2×C2912yescomplemented
445#2403C2×C2911yescharacteristic, complemented
446#2044C2×C2912yescomplemented
447#2021C2×C2912yescomplemented
448#1898C2×C2912yescomplemented
449#1889C2×C2911yescharacteristic, complemented
450#1867C2×C2911yescharacteristic, complemented
451#1790C2×C2911yescharacteristic, complemented
452C22×C29—21no—
453C22×C29—22no—
454C22×C29—21no—
455C22×C29—22no—
456C22×C29—21no—
457C22×C29—21no—
458C22×C29—21no—
459C22×C29—22no—
460C22×C29—22no—
461C22×C29—22no—
462C22×C29—21no—
463C22×C29—21no—
464C22×C29—22no—
465C22×C29—41no—
466C22×C29—41no—
467C22×C29—42no—
468C22×C29—44no—
469C22×C29—44no—
470C22×C29—42no—
471C22×C29—42no—
472C22×C29—42no—
473C22×C29—44no—
474C22×C29—42no—
475C22×C29—42no—
476C22×C29—42no—
477C22×C29—44no—
478C22×C29—41no—
479C22×C29—41no—
480C22×C29—42no—
481C22×C29—41no—
482C22×C29—42no—
483C22×C29—42no—
484C22×C29—41no—
485C22×C29—42no—
486C22×C29—41no—
487C22×C29—82no—
488C22×C29—81no—
489C22×C29—81no—
490C22×C29—81no—
491C22×C29—82no—
492C22×C29—84no—
493C22×C29—82no—
494C22×C29—82no—
495C22×C29—81no—
496C22×C29—82no—
497C22×C29—81no—
498C22×C29—81no—
499C22×C29—82no—
500C22×C29—84no—
501C22×C29—81no—
502C22×C29—81no—
503C22×C29—162no—
504C22×C29B(4,𝔽2)12yescomplemented
505C22×C29C2×#12011yescharacteristic
506C22×C29C2×#12111yescharacteristic
507C22×C29#53411yescharacteristic
508C22×C29D4212yes—
509C22×C29#54612yes—
510C4×C29—22no—
511C4×C29—44no—
512C4×C29—41no—
513C4×C29—42no—
514C4×C29—42no—
515C4×C29—42no—
516C4×C29—42no—
517C4×C29—82no—
518C4×C29—81no—
519C4×C29—81no—
520C2×H(5,𝔽2)C22×C2911yescharacteristic
521C23×D4C22×C2911yescharacteristic
522C23×D4C22×C2911yescharacteristic, complemented
523#546—22no—
524#546—22no—
525D42—22no—
526D42—22no—
527#535—21no—
528#534—21no—
529#534C22×C2912yes—
530#525—21no—
531C2×#121—22no—
532C2×#120—21no—
533C2×#120—21no—
534C2×#120C22×C2911yescharacteristic
535C2×#120C22×C2912yes—
536C2×#120C22×C2912yescomplemented
537C2×#120C22×C2911yescharacteristic, complemented
538#518C22×C2911yescharacteristic
539C22×C22⋊C4C22×C2912yescomplemented
540B(4,𝔽2)—24no—
541C2×#99—24no—
542C2×#99C22×C2911yescharacteristic
543C2×#99C22×C2911yescharacteristic
544C2×#99C22×C2912yescomplemented
545C2×#99C22×C2912yescomplemented
546C2×#99C22×C2912yescomplemented
547#394—22no—
548#392—21no—
549#392—21no—
550#392—22no—
551#386—21no—
552#386—22no—
553#386C22×C2911yescharacteristic
554#386C22×C2911yescharacteristic, complemented
555#386C22×C2912yescomplemented
556#385C22×C2912yescomplemented
557#379C22×C2912yescomplemented
558#379C22×C2911yescharacteristic, complemented
559#342C22×C2912yescomplemented
560#342C22×C2912yescomplemented
561C2×C29—22no—
562C2×C29—21no—
563C2×C29—21no—
564C2×C29—22no—
565C2×C29—22no—
566C2×C29—42no—
567C2×C29—41no—
568C2×C29—42no—
569C2×C29—82no—
570C2×C29—81no—
571C2×C29—82no—
572C2×C29#241011yescharacteristic
573C2×C29C2×B(4,𝔽2)11yescharacteristic
574C2×C29#302611yescharacteristic
575C25D4×C2911yescharacteristic, complemented
576C25C23×C2911yescharacteristic
577C25C23×C2911yescharacteristic
578H(5,𝔽2)—22no—
579H(5,𝔽2)—22no—
580H(5,𝔽2)—42no—
581C2×#41—21no—
582C2×#41—22no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—22no—
598C22×D4—44no—
599C22×D4—42no—
600C22×D4D4×C2911yescharacteristic, complemented
601C22×D4D4×C2911yescharacteristic, complemented
602C22×D4D4×C2912yescomplemented
603C22×D4D4×C2912yescomplemented
604C22×D4C23×C2912yes—
605C22×D4C23×C2911yescharacteristic
606C22×D4C23×C2911yescharacteristic
607C23×C4—22no—
608C23×C4D4×C2911yescharacteristic, complemented
609C23×C4C23×C2911yescharacteristic
610#127—22no—
611#124—22no—
612#123—22no—
613#123—22no—
614#123—22no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617#121—21no—
618#121—21no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—48no—
626#120—22no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—24no—
638#120—42no—
639#120—42no—
640#120—44no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—21no—
646C2×C4⋊C4—22no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—42no—
663C2×C22⋊C4D4×C2912yescomplemented
664C2×C22⋊C4D4×C2912yescomplemented
665C2×C22⋊C4C23×C2912yes—
666C2×C22⋊C4C23×C2911yescharacteristic
667C2×C22⋊C4C23×C2911yescharacteristic
668C2×C22⋊C4C23×C2912yes—
669C2×C22⋊C4C23×C2912yes—
670#99—22no—
671#99—24no—
672#99—24no—
673#99—42no—
674#99D4×C2914yescomplemented
675#95—22no—
676#95—21no—
677#95—21no—
678#95—22no—
679C29#2440411yescharacteristic, direct product factor, Sylow
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C2911yescharacteristic
700C24C2×D4×C2912yes—
701C24C2×D4×C2911yescharacteristic
702C24C2×D4×C2912yes—
703C24C2×D4×C2912yes—
704C24C2×D4×C2911yescharacteristic
705C24C2×D4×C2911yescharacteristic
706C24C24×C2911yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C2912yes—
771C2×D4#41×C2912yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C2912yes—
791C22×C4C2×D4×C2911yescharacteristic
792C22×C4C2×D4×C2911yescharacteristic
793C22×C4C2×D4×C2912yes—
794C22×C4C2×D4×C2912yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C2914yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23C29×#12011yescharacteristic
893C23C29×#12012yes—
894C23C29×#12011yescharacteristic
895C23C29×#12112yescomplemented
896C23C22×D4×C2911yescharacteristic
897C23C22×D4×C2912yes—
898C23C22×D4×C2911yescharacteristic
899C23C2×#41×C2911yescharacteristic
900C23C29×H(5,𝔽2)12yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4C29×#12112yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C29×B(4,𝔽2)12yescomplemented
1016C22C2×C29×#12011yescharacteristic
1017C22C2×C29×#12111yescharacteristic
1018C22C29×#53411yescharacteristic
1019C22D42×C2912yes—
1020C22C29×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C29×#241011yescharacteristic
1043C2C2×C29×B(4,𝔽2)11yescharacteristic
1044C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3484C2semidirect
2. C2×C29×B(4,𝔽2)C2semidirect
3. C22×C29×#99C2semidirect
4. C29×#2410C2semidirect
5. C29×#2403C2semidirect
6. C29×#2044C2semidirect
7. C29×#2021C2semidirect
8. C29×#1898C2semidirect
9. C29×#1889C2semidirect
10. C29×#1867C2semidirect
11. C29×#1790C2semidirect
14. C23×D4×C29C22semidirect
28. C2×C29×#120C22semidirect
29. C2×C29×#120C22semidirect
31. C22×C22⋊C4×C29C22semidirect
36. C2×C29×#99C22semidirect
37. C2×C29×#99C22semidirect
38. C2×C29×#99C22semidirect
46. C29×#386C22semidirect
47. C29×#386C22semidirect
48. C29×#385C22semidirect
49. C29×#379C22semidirect
50. C29×#379C22semidirect
51. C29×#342C22semidirect
52. C29×#342C22semidirect
53. C25×C29D4semidirect
78. C22×D4×C29D4semidirect
79. C22×D4×C29D4semidirect
80. C22×D4×C29D4semidirect
81. C22×D4×C29D4semidirect
86. C23×C4×C29D4semidirect
141. C2×C22⋊C4×C29D4semidirect
142. C2×C22⋊C4×C29D4semidirect
152. C29×#99D4semidirect
305. C22⋊C4×C29C2×D4semidirect
307. #24404C29direct (N × H)
373. C23×C29#121semidirect
440. C2×C4×C29#121semidirect
441. #3484C2×C29semidirect
442. C2×B(4,𝔽2)C2×C29semidirect
443. C22×#99C2×C29semidirect
444. #2410C2×C29semidirect
445. #2403C2×C29semidirect
446. #2044C2×C29semidirect
447. #2021C2×C29semidirect
448. #1898C2×C29semidirect
449. #1889C2×C29semidirect
450. #1867C2×C29semidirect
451. #1790C2×C29semidirect
504. C22×C29B(4,𝔽2)semidirect
522. C23×D4C22×C29semidirect
536. C2×#120C22×C29semidirect
537. C2×#120C22×C29semidirect
539. C22×C22⋊C4C22×C29semidirect
544. C2×#99C22×C29semidirect
545. C2×#99C22×C29semidirect
546. C2×#99C22×C29semidirect
554. #386C22×C29semidirect
555. #386C22×C29semidirect
556. #385C22×C29semidirect
557. #379C22×C29semidirect
558. #379C22×C29semidirect
559. #342C22×C29semidirect
560. #342C22×C29semidirect
575. C25D4×C29semidirect
600. C22×D4D4×C29semidirect
601. C22×D4D4×C29semidirect
602. C22×D4D4×C29semidirect
603. C22×D4D4×C29semidirect
608. C23×C4D4×C29semidirect
663. C2×C22⋊C4D4×C29semidirect
664. C2×C22⋊C4D4×C29semidirect
674. #99D4×C29semidirect
679. C29#24404direct (N × H)
828. C22⋊C4C2×D4×C29semidirect
895. C23C29×#121semidirect
962. C2×C4C29×#121semidirect
1015. C22C29×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C29×#34842
C2×C29×B(4,𝔽2)2
C22×C29×#992
C29×#24102
C29×#24032
C29×#20442
C29×#20212
C29×#18982
C29×#18892
C29×#18672
C29×#17902
#2440429