Finite Group Databasebeta

← C29×#25216 #20320116

Subgroups — C29×#25216 #20320116

Order 7424.

900 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#482C211yesmaximal, characteristic
2C2×C29×#468C211yesmaximal, characteristic
3C29×#2499C211yesmaximal, characteristic, complemented
4C29×#2361C211yesmaximal, characteristic
5C29×#2083C211yesmaximal, characteristic, complemented
6C29×#2073C211yesmaximal, characteristic, complemented
7C29×#2066C211yesmaximal, characteristic, complemented
8C29×#2055C211yesmaximal, characteristic, complemented
9C29×#1949C211yesmaximal, characteristic, complemented
10C29×#1928C211yesmaximal, characteristic, complemented
11C29×#1877C211yesmaximal, characteristic, complemented
12C29×#1872C211yesmaximal, characteristic, complemented
13C29×#1851C211yesmaximal, characteristic, complemented
14C29×#1802C211yesmaximal, characteristic, complemented
15C29×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C2×C29×C22⋊Q8C2211yescharacteristic
19C2×C29×#121C2211yescharacteristic
20C2×C4×D4×C29—21no—
21C2×C4×D4×C29C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C29×#482—24no—
25C29×#468—24no—
26C2×C29×#107C2211yescharacteristic
27C2×C29×#107C2211yescharacteristic
28C2×C29×#106C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×C4⋊C8C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×C22⋊C8C2211yescharacteristic
38C29×#397—21no—
39C29×#397—21no—
40C29×#391C2211yescharacteristic
41C29×#391C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#388—21no—
45C29×#387—21no—
46C29×#387—21no—
47C29×#386—21no—
48C29×#385—21no—
49C29×#384C2211yescharacteristic
50C29×#382C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
52C4×C22⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×D4×C29—21no—
63C22×D4×C29C2311yescharacteristic
64C23×C4×C29—21no—
65C23×C4×C29—21no—
66C23×C4×C29C2311yescharacteristic
67C2×SD16×C29—22no—
68C2×SD16×C29—22no—
69C2×SD16×C29—41no—
70C2×M16×C29—22no—
71C2×M16×C29—22no—
72C2×M16×C29—41no—
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C29×C22⋊Q8—22no—
78C29×C22⋊Q8—22no—
79C29×#121—22no—
80C29×#121D414yes—
81C4×D4×C29—22no—
82C4×D4×C29—41no—
83C4×D4×C29—44no—
84C29×#117—22no—
85C29×#117—22no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—41no—
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—21no—
105C2×C22⋊C4×C29D411yescharacteristic
106C2×C22⋊C4×C29D411yescharacteristic
107C2×C42×C29—21no—
108C2×C42×C29—21no—
109C2×C42×C29C2311yescharacteristic
110C2×C42×C29C2311yescharacteristic
111C29×#107—22no—
112C29×#107—22no—
113C29×#106—22no—
114C29×C4⋊C8—22no—
115C29×C4⋊C8—41no—
116C29×#103—22no—
117C29×#103—22no—
118C29×#103—41no—
119C29×#102—22no—
120C29×#102—22no—
121C29×#102—22no—
122C29×C22⋊C8—22no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C29×#95—21no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95D411yescharacteristic
132C29×#95D411yescharacteristic
133C24×C29—21no—
134C24×C29C2×D411yescharacteristic
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—21no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×D4×C29—24no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—42no—
148C2×D4×C29—42no—
149C2×D4×C29C2×D412yes—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
154C22×C4×C29—21no—
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—42no—
162C22×C4×C29—42no—
163C22×C4×C29—42no—
164C22×C4×C29—42no—
165C22×C4×C29—81no—
166C22×C4×C29—81no—
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D412yes—
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29#4112yes—
174C22×C4×C29C2411yescharacteristic
175SD16×C29—44no—
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—21no—
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—42no—
200C4⋊C4×C29—42no—
201C4⋊C4×C29—42no—
202C4⋊C4×C29—42no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29C2×D412yes—
205C4⋊C4×C29#4112yes—
206C22⋊C4×C29—24no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—81no—
214C42×C29—21no—
215C42×C29—21no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—42no—
219C42×C29—42no—
220#25216C2911yesmaximal, characteristic, direct product factor, Sylow
221C23×C29—21no—
222C23×C29—21no—
223C23×C29—21no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—22no—
228C23×C29—41no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—41no—
234C23×C29#12112yes—
235C23×C29C22×D411yescharacteristic
236Q8×C29—41no—
237Q8×C29—41no—
238Q8×C29—41no—
239Q8×C29—41no—
240D4×C29—22no—
241D4×C29—22no—
242D4×C29—48no—
243D4×C29—41no—
244D4×C29—41no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—22no—
250C2×C4×C29—22no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
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—21no—
263C2×C4×C29—21no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
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—84no—
284C2×C4×C29—84no—
285C2×C4×C29#12112yes—
286C2×C4×C29AGL(1,ℤ/8)12yes—
287C2×C4×C29C22×D411yescharacteristic
288C2×C4×C29C2×#4111yescharacteristic
289C2×C4×C29C2×#4111yescharacteristic
290C2×C4×C29C2×#4111yescharacteristic
291C2×C4×C29H(5,𝔽2)11yescharacteristic
292C2×C4×C292−1+411yescharacteristic
293C8×C29—22no—
294C8×C29—41no—
295C8×C29—41no—
296C8×C29—41no—
297C2×#482C2×C2911yescharacteristic
298C2×#468C2×C2911yescharacteristic
299#2499C2×C2911yescharacteristic, complemented
300#2361C2×C2911yescharacteristic
301#2083C2×C2911yescharacteristic, complemented
302#2073C2×C2911yescharacteristic, complemented
303#2066C2×C2911yescharacteristic, complemented
304#2055C2×C2911yescharacteristic, complemented
305#1949C2×C2911yescharacteristic, complemented
306#1928C2×C2911yescharacteristic, complemented
307#1877C2×C2911yescharacteristic, complemented
308#1872C2×C2911yescharacteristic, complemented
309#1851C2×C2911yescharacteristic, complemented
310#1802C2×C2911yescharacteristic, complemented
311#1736C2×C2911yescharacteristic, complemented
312C22×C29—22no—
313C22×C29—22no—
314C22×C29—22no—
315C22×C29—41no—
316C22×C29—41no—
317C22×C29—41no—
318C22×C29—41no—
319C22×C29—42no—
320C22×C29—42no—
321C22×C29—42no—
322C22×C29—81no—
323C22×C29—81no—
324C22×C29—81no—
325C22×C29—81no—
326C22×C29C2×#12111yescharacteristic
327C22×C29#54611yescharacteristic
328C22×C29#54711yescharacteristic
329C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C29#57511yescharacteristic
331C22×C29#57711yescharacteristic
332C22×C29#57811yescharacteristic
333C4×C29—22no—
334C4×C29—22no—
335C4×C29—41no—
336C4×C29—41no—
337C4×C29—42no—
338C4×C29—42no—
339C4×C29—41no—
340C4×C29—81no—
341C4×C29—81no—
342C4×C29—81no—
343C4×C29—81no—
344C4×C29—81no—
345C4×C29#52911yescharacteristic
346C4×C29#53911yescharacteristic
347C4×C29#54611yescharacteristic
348C4×C29#54711yescharacteristic
349C22×SD16C22×C2911yescharacteristic
350C22×M16C22×C2911yescharacteristic
351C2×C22⋊Q8C22×C2911yescharacteristic
352C2×#121C22×C2911yescharacteristic
353C2×C4×D4—21no—
354C2×C4×D4C22×C2911yescharacteristic
355C2×#117C22×C2911yescharacteristic
356C22×C4⋊C4C22×C2911yescharacteristic
357#482—24no—
358#468—24no—
359C2×#107C22×C2911yescharacteristic
360C2×#107C22×C2911yescharacteristic
361C2×#106C22×C2911yescharacteristic
362C2×C4⋊C8C22×C2911yescharacteristic
363C2×C4⋊C8C22×C2911yescharacteristic
364C2×#103C22×C2911yescharacteristic
365C2×#103C22×C2911yescharacteristic
366C2×#103C22×C2911yescharacteristic
367C2×#102C22×C2911yescharacteristic
368C2×#102C22×C2911yescharacteristic
369C2×#102C22×C2911yescharacteristic
370C2×C22⋊C8C22×C2911yescharacteristic
371#397—21no—
372#397—21no—
373#391C22×C2911yescharacteristic
374#391C22×C2911yescharacteristic
375#390C22×C2911yescharacteristic
376#389C22×C2911yescharacteristic
377#388—21no—
378#387—21no—
379#387—21no—
380#386—21no—
381#385—21no—
382#384C22×C2911yescharacteristic
383#382C22×C2911yescharacteristic
384C4×C4⋊C4C22×C2911yescharacteristic
385C4×C22⋊C4C22×C2911yescharacteristic
386#340C22×C2911yescharacteristic
387#340C22×C2911yescharacteristic
388#340C22×C2911yescharacteristic
389#340C22×C2911yescharacteristic
390#340C22×C2911yescharacteristic
391#340C22×C2911yescharacteristic
392#336C22×C2911yescharacteristic
393#336C22×C2911yescharacteristic
394C2×C29—42no—
395C2×C29—82no—
396C2×C29#242511yescharacteristic
397C2×C29#303611yescharacteristic
398C2×C29#304611yescharacteristic
399C2×C29#331011yescharacteristic
400C2×C29#332711yescharacteristic
401C2×C29#335011yescharacteristic
402C2×C29#335311yescharacteristic
403C22×Q8C23×C2911yescharacteristic
404C22×D4—21no—
405C22×D4C23×C2911yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C2911yescharacteristic
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—41no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—41no—
415C22×C8C23×C2911yescharacteristic
416C22×C8C23×C2911yescharacteristic
417C22×C8C23×C2911yescharacteristic
418C22×C8C23×C2911yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421#121—22no—
422#121D4×C2914yes—
423C4×D4—22no—
424C4×D4—41no—
425C4×D4—44no—
426#117—22no—
427#117—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4C23×C2911yescharacteristic
436C2×C4⋊C4C23×C2911yescharacteristic
437C2×C4⋊C4C23×C2911yescharacteristic
438C2×C4⋊C4C23×C2911yescharacteristic
439C2×C4⋊C4C23×C2911yescharacteristic
440C2×C4⋊C4C23×C2911yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C2911yescharacteristic
448C2×C22⋊C4D4×C2911yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C2911yescharacteristic
452C2×C42C23×C2911yescharacteristic
453#107—22no—
454#107—22no—
455#106—22no—
456C4⋊C8—22no—
457C4⋊C8—41no—
458#103—22no—
459#103—22no—
460#103—41no—
461#102—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95D4×C2911yescharacteristic
474#95D4×C2911yescharacteristic
475C29#2521611yescharacteristic, direct product factor, Sylow
476C24—21no—
477C24C2×D4×C2911yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C2×D4×C2912yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4C2×D4×C2911yescharacteristic
511C22×C4C2×D4×C2911yescharacteristic
512C22×C4C2×D4×C2911yescharacteristic
513C22×C4C2×D4×C2911yescharacteristic
514C22×C4C2×D4×C2912yes—
515C22×C4C2×D4×C2911yescharacteristic
516C22×C4#41×C2912yes—
517C22×C4C24×C2911yescharacteristic
518SD16—44no—
519M16—44no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8#41×C2912yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4C2×D4×C2912yes—
548C4⋊C4#41×C2912yes—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C42—42no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23C29×#12112yes—
577C23C22×D4×C2911yescharacteristic
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—48no—
585D4—41no—
586D4—41no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—84no—
627C2×C4C29×#12112yes—
628C2×C4C29×AGL(1,ℤ/8)12yes—
629C2×C4C22×D4×C2911yescharacteristic
630C2×C4C2×#41×C2911yescharacteristic
631C2×C4C2×#41×C2911yescharacteristic
632C2×C4C2×#41×C2911yescharacteristic
633C2×C4C29×H(5,𝔽2)11yescharacteristic
634C2×C4C29×2−1+411yescharacteristic
635C8—22no—
636C8—41no—
637C8—41no—
638C8—41no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×C29×#12111yescharacteristic
654C22C29×#54611yescharacteristic
655C22C29×#54711yescharacteristic
656C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
657C22C29×#57511yescharacteristic
658C22C29×#57711yescharacteristic
659C22C29×#57811yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C29×#52911yescharacteristic
673C4C29×#53911yescharacteristic
674C4C29×#54611yescharacteristic
675C4C29×#54711yescharacteristic
676C2—42no—
677C2—82no—
678C2C29×#242511yescharacteristic
679C2C29×#303611yescharacteristic
680C2C29×#304611yescharacteristic
681C2C29×#331011yescharacteristic
682C2C29×#332711yescharacteristic
683C2C29×#335011yescharacteristic
684C2C29×#335311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
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
3. C29×#2499C2semidirect
5. C29×#2083C2semidirect
6. C29×#2073C2semidirect
7. C29×#2066C2semidirect
8. C29×#2055C2semidirect
9. C29×#1949C2semidirect
10. C29×#1928C2semidirect
11. C29×#1877C2semidirect
12. C29×#1872C2semidirect
13. C29×#1851C2semidirect
14. C29×#1802C2semidirect
15. C29×#1736C2semidirect
220. #25216C29direct (N × H)
299. #2499C2×C29semidirect
301. #2083C2×C29semidirect
302. #2073C2×C29semidirect
303. #2066C2×C29semidirect
304. #2055C2×C29semidirect
305. #1949C2×C29semidirect
306. #1928C2×C29semidirect
307. #1877C2×C29semidirect
308. #1872C2×C29semidirect
309. #1851C2×C29semidirect
310. #1802C2×C29semidirect
311. #1736C2×C29semidirect
475. C29#25216direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4822
C2×C29×#4682
C29×#24992
C29×#23612
C29×#20832
C29×#20732
C29×#20662
C29×#20552
C29×#19492
C29×#19282
C29×#18772
C29×#18722
C29×#18512
C29×#18022
C29×#17362
#2521629