Finite Group Databasebeta

← C29×#29068 #20323968

Subgroups — C29×#29068 #20323968

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2496C211yesmaximal, characteristic, complemented
2C29×#2428C211yesmaximal, characteristic
3C29×#2099C211yesmaximal, characteristic, complemented
4C29×#2041C211yesmaximal, characteristic, complemented
5C29×#2034C211yesmaximal, characteristic, complemented
6C29×#2034C211yesmaximal, characteristic, complemented
7C29×#1957C211yesmaximal, characteristic, complemented
8C29×#1941C211yesmaximal, characteristic, complemented
9C29×#1936C211yesmaximal, characteristic, complemented
10C29×#1926C211yesmaximal, characteristic, complemented
11C29×#1895C211yesmaximal, characteristic, complemented
12C29×#1895C211yesmaximal, characteristic, complemented
13C29×#1864C211yesmaximal, characteristic, complemented
14C29×#1762C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C2×C29×#127C2211yescharacteristic
18C2×C29×#126—21no—
19C2×C29×#121—21no—
20C2×C29×#121C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C2×C4×D4×C29C2211yescharacteristic
23C2×C29×#106C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×C22⋊C8C2211yescharacteristic
34C2×C29×#97C2211yescharacteristic
35C2×C4×C8×C29C2211yescharacteristic
36C29×#400—21no—
37C29×#397—21no—
38C29×#394—21no—
39C29×#392—21no—
40C29×#390C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#387—21no—
45C29×#386—21no—
46C29×#384C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#380C2211yescharacteristic
49C4×C4⋊C4×C29C2211yescharacteristic
50C4×C22⋊C4×C29C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29—21no—
60C22×D4×C29—21no—
61C22×D4×C29—21no—
62C22×D4×C29—21no—
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C23×C4×C29C2311yescharacteristic
67C2×M16×C29—22no—
68C2×M16×C29—41no—
69C2×M16×C29—41no—
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×#127—22no—
75C29×#127—41no—
76C29×#126—44no—
77C29×#121—22no—
78C29×#121—22no—
79C29×#121—44no—
80C29×#121—41no—
81C29×#121—41no—
82C4×D4×C29—22no—
83C4×D4×C29—41no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29D411yescharacteristic
103C2×C22⋊C4×C29D411yescharacteristic
104C2×C42×C29—21no—
105C2×C42×C29C2311yescharacteristic
106C2×C42×C29C2311yescharacteristic
107C29×#106—22no—
108C29×#106—41no—
109C29×#102—22no—
110C29×#102—22no—
111C29×#102—22no—
112C29×#102—22no—
113C29×#102—22no—
114C29×#102—41no—
115C29×#102—41no—
116C29×#102—41no—
117C29×C22⋊C8—22no—
118C29×#97—41no—
119C4×C8×C29—41no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C29×#95D411yescharacteristic
127C29×#95D411yescharacteristic
128C24×C29—21no—
129C24×C29—21no—
130C24×C29C2×D411yescharacteristic
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29—21no—
137C2×D4×C29—21no—
138C2×D4×C29—21no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—42no—
143C2×D4×C29—42no—
144C2×D4×C29—42no—
145C2×D4×C29—42no—
146C2×D4×C29—42no—
147C2×D4×C29—42no—
148C2×D4×C29—42no—
149C2×D4×C29—42no—
150C2×D4×C29—81no—
151C2×D4×C29—81no—
152C2×D4×C29—81no—
153C2×D4×C29—81no—
154C2×D4×C29#4112yes—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—42no—
168C22×C4×C29—42no—
169C22×C4×C29—81no—
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2411yescharacteristic
176M16×C29—44no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29#4112yes—
188C2×C8×C29#4112yes—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—42no—
201C4⋊C4×C29—42no—
202C4⋊C4×C29—42no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—42no—
205C4⋊C4×C29#4112yes—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—42no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—81no—
215C42×C29—21no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—21no—
219C42×C29—42no—
220#29068C2911yesmaximal, characteristic, direct product factor, Sylow
221C23×C29—21no—
222C23×C29—22no—
223C23×C29—21no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29C22×D411yescharacteristic
243D4×C29—22no—
244D4×C29—22no—
245D4×C29—41no—
246D4×C29—41no—
247D4×C29—41no—
248D4×C29—41no—
249D4×C29—41no—
250D4×C29—41no—
251D4×C29—84no—
252D4×C29—84no—
253D4×C29—84no—
254D4×C29—84no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—21no—
262C2×C4×C29—22no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—41no—
277C2×C4×C29—41no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
280C2×C4×C29—41no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
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—84no—
291C2×C4×C29AGL(1,ℤ/8)12yes—
292C2×C4×C29AGL(1,ℤ/8)12yes—
293C2×C4×C29C2×#4111yescharacteristic
294C2×C4×C29C2×#4111yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29C2×#4111yescharacteristic
297C2×C4×C29H(5,𝔽2)11yescharacteristic
298C2×C4×C29H(5,𝔽2)11yescharacteristic
299C8×C29—22no—
300C8×C29—22no—
301C8×C29—41no—
302C8×C29—41no—
303#2496C2×C2911yescharacteristic, complemented
304#2428C2×C2911yescharacteristic
305#2099C2×C2911yescharacteristic, complemented
306#2041C2×C2911yescharacteristic, complemented
307#2034C2×C2911yescharacteristic, complemented
308#2034C2×C2911yescharacteristic, complemented
309#1957C2×C2911yescharacteristic, complemented
310#1941C2×C2911yescharacteristic, complemented
311#1936C2×C2911yescharacteristic, complemented
312#1926C2×C2911yescharacteristic, complemented
313#1895C2×C2911yescharacteristic, complemented
314#1895C2×C2911yescharacteristic, complemented
315#1864C2×C2911yescharacteristic, complemented
316#1762C2×C2911yescharacteristic, complemented
317#1753C2×C2911yescharacteristic, complemented
318C22×C29—41no—
319C22×C29—41no—
320C22×C29—41no—
321C22×C29—42no—
322C22×C29—41no—
323C22×C29—41no—
324C22×C29—42no—
325C22×C29—41no—
326C22×C29—41no—
327C22×C29—42no—
328C22×C29—81no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29#53211yescharacteristic
340C22×C29#54611yescharacteristic
341C22×C29#54611yescharacteristic
342C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C29#57711yescharacteristic
345C22×C29#57711yescharacteristic
346C4×C29—22no—
347C4×C29—22no—
348C4×C29—41no—
349C4×C29—41no—
350C4×C29—42no—
351C4×C29—41no—
352C4×C29—81no—
353C4×C29—81no—
354C4×C29—81no—
355C4×C29—81no—
356C4×C29—81no—
357C4×C29#52911yescharacteristic
358C4×C29#53811yescharacteristic
359C4×C29#55311yescharacteristic
360C4×C29#55311yescharacteristic
361C22×M16C22×C2911yescharacteristic
362C2×#127C22×C2911yescharacteristic
363C2×#126—21no—
364C2×#121—21no—
365C2×#121C22×C2911yescharacteristic
366C2×#121C22×C2911yescharacteristic
367C2×C4×D4C22×C2911yescharacteristic
368C2×#106C22×C2911yescharacteristic
369C2×#106C22×C2911yescharacteristic
370C2×#102C22×C2911yescharacteristic
371C2×#102C22×C2911yescharacteristic
372C2×#102C22×C2911yescharacteristic
373C2×#102C22×C2911yescharacteristic
374C2×#102C22×C2911yescharacteristic
375C2×#102C22×C2911yescharacteristic
376C2×#102C22×C2911yescharacteristic
377C2×#102C22×C2911yescharacteristic
378C2×C22⋊C8C22×C2911yescharacteristic
379C2×#97C22×C2911yescharacteristic
380C2×C4×C8C22×C2911yescharacteristic
381#400—21no—
382#397—21no—
383#394—21no—
384#392—21no—
385#390C22×C2911yescharacteristic
386#389C22×C2911yescharacteristic
387#389C22×C2911yescharacteristic
388#389C22×C2911yescharacteristic
389#387—21no—
390#386—21no—
391#384C22×C2911yescharacteristic
392#380C22×C2911yescharacteristic
393#380C22×C2911yescharacteristic
394C4×C4⋊C4C22×C2911yescharacteristic
395C4×C22⋊C4C22×C2911yescharacteristic
396#340C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#340C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#340C22×C2911yescharacteristic
402#336C22×C2911yescharacteristic
403#336C22×C2911yescharacteristic
404C2×C29—81no—
405C2×C29—82no—
406C2×C29—161no—
407C2×C29#255911yescharacteristic
408C2×C29#317411yescharacteristic
409C2×C29#318411yescharacteristic
410C2×C29#330611yescharacteristic
411C2×C29#331011yescharacteristic
412C2×C29#332411yescharacteristic
413C2×C29#333211yescharacteristic
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C2911yescharacteristic
419C22×D4C23×C2911yescharacteristic
420C23×C4—21no—
421C23×C4C23×C2911yescharacteristic
422C2×M16—22no—
423C2×M16—41no—
424C2×M16—41no—
425C22×C8C23×C2911yescharacteristic
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428C22×C8C23×C2911yescharacteristic
429#127—22no—
430#127—41no—
431#126—44no—
432#121—22no—
433#121—22no—
434#121—44no—
435#121—41no—
436#121—41no—
437C4×D4—22no—
438C4×D4—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C23×C2911yescharacteristic
445C2×C4⋊C4C23×C2911yescharacteristic
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C2911yescharacteristic
458C2×C22⋊C4D4×C2911yescharacteristic
459C2×C42—21no—
460C2×C42C23×C2911yescharacteristic
461C2×C42C23×C2911yescharacteristic
462#106—22no—
463#106—41no—
464#102—22no—
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—41no—
470#102—41no—
471#102—41no—
472C22⋊C8—22no—
473#97—41no—
474C4×C8—41no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C2911yescharacteristic
482#95D4×C2911yescharacteristic
483C29#2906811yescharacteristic, direct product factor, Sylow
484C24—21no—
485C24—21no—
486C24C2×D4×C2911yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4#41×C2912yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4C2×D4×C2911yescharacteristic
530C22×C4C2×D4×C2911yescharacteristic
531C22×C4C24×C2911yescharacteristic
532M16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8#41×C2912yes—
544C2×C8#41×C2912yes—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4#41×C2912yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C23—21no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×D4×C2911yescharacteristic
598D4—22no—
599D4—22no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4C29×AGL(1,ℤ/8)12yes—
647C2×C4C29×AGL(1,ℤ/8)12yes—
648C2×C4C2×#41×C2911yescharacteristic
649C2×C4C2×#41×C2911yescharacteristic
650C2×C4C2×#41×C2911yescharacteristic
651C2×C4C2×#41×C2911yescharacteristic
652C2×C4C29×H(5,𝔽2)11yescharacteristic
653C2×C4C29×H(5,𝔽2)11yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—41no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C29×#53211yescharacteristic
680C22C29×#54611yescharacteristic
681C22C29×#54611yescharacteristic
682C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
683C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
684C22C29×#57711yescharacteristic
685C22C29×#57711yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C29×#52911yescharacteristic
698C4C29×#53811yescharacteristic
699C4C29×#55311yescharacteristic
700C4C29×#55311yescharacteristic
701C2—81no—
702C2—82no—
703C2—161no—
704C2C29×#255911yescharacteristic
705C2C29×#317411yescharacteristic
706C2C29×#318411yescharacteristic
707C2C29×#330611yescharacteristic
708C2C29×#331011yescharacteristic
709C2C29×#332411yescharacteristic
710C2C29×#333211yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2496C2semidirect
3. C29×#2099C2semidirect
4. C29×#2041C2semidirect
5. C29×#2034C2semidirect
6. C29×#2034C2semidirect
7. C29×#1957C2semidirect
8. C29×#1941C2semidirect
9. C29×#1936C2semidirect
10. C29×#1926C2semidirect
11. C29×#1895C2semidirect
12. C29×#1895C2semidirect
13. C29×#1864C2semidirect
14. C29×#1762C2semidirect
15. C29×#1753C2semidirect
220. #29068C29direct (N × H)
303. #2496C2×C29semidirect
305. #2099C2×C29semidirect
306. #2041C2×C29semidirect
307. #2034C2×C29semidirect
308. #2034C2×C29semidirect
309. #1957C2×C29semidirect
310. #1941C2×C29semidirect
311. #1936C2×C29semidirect
312. #1926C2×C29semidirect
313. #1895C2×C29semidirect
314. #1895C2×C29semidirect
315. #1864C2×C29semidirect
316. #1762C2×C29semidirect
317. #1753C2×C29semidirect
483. C29#29068direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24962
C29×#24282
C29×#20992
C29×#20412
C29×#20342
C29×#19572
C29×#19412
C29×#19362
C29×#19262
C29×#18952
C29×#18642
C29×#17622
C29×#17532
#2906829