Finite Group Databasebeta

← C29×#25270 #20320170

Subgroups — C29×#25270 #20320170

Order 7424.

776 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3092C211yesmaximal, characteristic, complemented
2C2×C29×#481C211yesmaximal, characteristic, complemented
3C29×#3055C211yesmaximal, characteristic
4C29×#2933C211yesmaximal, characteristic, complemented
5C29×#2090C211yesmaximal, characteristic, complemented
6C29×#2079C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic, complemented
8C29×#2051C211yesmaximal, characteristic, complemented
9C29×#1951C211yesmaximal, characteristic, complemented
10C29×#1931C211yesmaximal, characteristic, complemented
11C29×#1907C211yesmaximal, characteristic, complemented
12C29×#1900C211yesmaximal, characteristic, complemented
13C29×#1855C211yesmaximal, characteristic, complemented
14C29×#1815C211yesmaximal, characteristic, complemented
15C2×C29×#343C211yesmaximal, characteristic, complemented
16C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C29×#131C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C22×M16×C29C2211yescharacteristic
20C29×#525C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C22×C4⋊C4×C29C2211yescharacteristic
23C29×#484—21no—
24C29×#483—21no—
25C29×#481—21no—
26C29×#481—21no—
27C29×#481—21no—
28C29×#481—21no—
29C29×#481—21no—
30C29×#480—21no—
31C29×#469—21no—
32C29×#468—21no—
33C29×#466—21no—
34C29×#465—21no—
35C29×#436—21no—
36C29×#435—21no—
37C29×#435—21no—
38C8×D4×C29—21no—
39C2×C29×#108C2211yescharacteristic
40C2×C29×#108C2211yescharacteristic
41C29×#428C2211yescharacteristic
42C29×#428C2211yescharacteristic
43C29×#428C2211yescharacteristic
44C2×C29×#106C2211yescharacteristic
45C2×C29×#106C2211yescharacteristic
46C29×#424C2211yescharacteristic
47C29×#418C2211yescharacteristic
48C29×#417C2211yescharacteristic
49C29×#417C2211yescharacteristic
50C29×#417C2211yescharacteristic
51C2×C29×#102C2211yescharacteristic
52C2×C29×#102C2211yescharacteristic
53C2×C29×#100C2211yescharacteristic
54C2×C29×#100C2211yescharacteristic
55C29×#408C2211yescharacteristic
56C29×#407C2211yescharacteristic
57C2×C29×C22⋊C8C2211yescharacteristic
58C29×#405C2211yescharacteristic
59C29×#343C2211yescharacteristic
60C29×#343C2211yescharacteristic
61C29×#343C2211yescharacteristic
62C29×#343C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#341C2211yescharacteristic
66C29×#341C2211yescharacteristic
67C2×#41×C29C2311yescharacteristic
68C22×D4×C29—21no—
69C22×D4×C29C2311yescharacteristic
70C23×C4×C29—21no—
71C23×C4×C29C2311yescharacteristic
72C29×AGL(1,ℤ/8)—22no—
73C29×AGL(1,ℤ/8)—41no—
74C2×SD16×C29—21no—
75C2×D8×C29—21no—
76C29×#131—22no—
77C29×#131—41no—
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29—22no—
82C2×M16×C29—22no—
83C2×M16×C29—41no—
84C2×M16×C29—41no—
85C2×M16×C29C2311yescharacteristic
86C2×M16×C29C2311yescharacteristic
87C2×M16×C29C2311yescharacteristic
88C2×M16×C29C2311yescharacteristic
89C2×M16×C29C2311yescharacteristic
90C2×M16×C29C2311yescharacteristic
91C22×C8×C29—21no—
92C22×C8×C29—21no—
93C22×C8×C29—21no—
94C22×C8×C29C2311yescharacteristic
95C22×C8×C29C2311yescharacteristic
96C29×#123—21no—
97C29×C22⋊Q8D411yescharacteristic
98C29×C22⋊Q8D411yescharacteristic
99C29×#121—21no—
100C29×#121—21no—
101C29×#121—21no—
102C29×#121—21no—
103C29×#121D411yescharacteristic
104C29×#121D411yescharacteristic
105C29×#120—21no—
106C4×D4×C29—21no—
107C4×D4×C29—21no—
108C29×#117C2311yescharacteristic
109C2×C4⋊C4×C29—21no—
110C2×C4⋊C4×C29—21no—
111C2×C4⋊C4×C29—21no—
112C2×C4⋊C4×C29—21no—
113C2×C4⋊C4×C29—21no—
114C2×C4⋊C4×C29C2311yescharacteristic
115C2×C4⋊C4×C29C2311yescharacteristic
116C2×C4⋊C4×C29C2311yescharacteristic
117C2×C22⋊C4×C29—21no—
118C29×#108—22no—
119C29×#108—41no—
120C29×#107—21no—
121C29×#107—21no—
122C29×#107—21no—
123C29×#106—21no—
124C29×#106—21no—
125C29×#106—21no—
126C29×#106—21no—
127C29×#106—21no—
128C29×#106—21no—
129C29×#106—21no—
130C29×C4⋊C8—21no—
131C29×C4⋊C8—21no—
132C29×#103—21no—
133C29×#103—21no—
134C29×#103—21no—
135C29×#102—21no—
136C29×#102—21no—
137C29×#102—21no—
138C29×#102—21no—
139C29×#102—21no—
140C29×#102—21no—
141C29×#102—21no—
142C29×#102—21no—
143C29×#102—21no—
144C29×#100—22no—
145C29×#100—41no—
146C29×C22⋊C8—21no—
147C29×C22⋊C8—21no—
148C29×C22⋊C8—21no—
149C29×C22⋊C8—21no—
150C29×C22⋊C8D411yescharacteristic
151C29×C22⋊C8D411yescharacteristic
152C29×C22⋊C8D411yescharacteristic
153C29×C22⋊C8D411yescharacteristic
154C29×#97—21no—
155C4×C8×C29—21no—
156C24×C29—21no—
157C24×C29#4111yescharacteristic
158#41×C29—21no—
159#41×C29—21no—
160#41×C29—21no—
161#41×C29—21no—
162C2×Q8×C29C2×D411yescharacteristic
163C2×D4×C29—21no—
164C2×D4×C29—21no—
165C2×D4×C29—21no—
166C2×D4×C29—21no—
167C2×D4×C29—21no—
168C2×D4×C29—21no—
169C2×D4×C29—21no—
170C2×D4×C29—21no—
171C2×D4×C29—21no—
172C2×D4×C29—41no—
173C2×D4×C29—41no—
174C2×D4×C29—82no—
175C2×D4×C29C2×D411yescharacteristic
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—41no—
185C22×C4×C29—41no—
186C22×C4×C29—82no—
187C22×C4×C29C2×D411yescharacteristic
188C22×C4×C29C2×D411yescharacteristic
189C22×C4×C29C2×D411yescharacteristic
190C22×C4×C29C2×D411yescharacteristic
191C22×C4×C29#4111yescharacteristic
192C22×C4×C29C2411yescharacteristic
193SD16×C29—42no—
194D8×C29—42no—
195M16×C29—21no—
196M16×C29—21no—
197M16×C29—21no—
198M16×C29—21no—
199M16×C29—21no—
200M16×C29—21no—
201M16×C29—21no—
202M16×C29—21no—
203M16×C29—21no—
204M16×C29—21no—
205M16×C29—42no—
206M16×C29—42no—
207M16×C29—42no—
208M16×C29#4112yes—
209M16×C29#4112yes—
210C2×C8×C29—21no—
211C2×C8×C29—21no—
212C2×C8×C29—21no—
213C2×C8×C29—21no—
214C2×C8×C29—21no—
215C2×C8×C29—21no—
216C2×C8×C29—21no—
217C2×C8×C29—21no—
218C2×C8×C29—21no—
219C2×C8×C29—21no—
220C2×C8×C29—42no—
221C2×C8×C29—42no—
222C2×C8×C29—42no—
223C2×C8×C29C2×D411yescharacteristic
224C2×C8×C29C2×D411yescharacteristic
225C2×C8×C29C2×D411yescharacteristic
226C2×C8×C29C2×D411yescharacteristic
227C4⋊C4×C29—21no—
228C4⋊C4×C29—21no—
229C4⋊C4×C29—21no—
230C4⋊C4×C29—21no—
231C4⋊C4×C29—21no—
232C4⋊C4×C29—21no—
233C4⋊C4×C29—21no—
234C4⋊C4×C29—21no—
235C4⋊C4×C29—41no—
236C4⋊C4×C29—41no—
237C4⋊C4×C29C2×D411yescharacteristic
238C4⋊C4×C29C2×D411yescharacteristic
239C22⋊C4×C29—21no—
240C22⋊C4×C29—21no—
241C22⋊C4×C29—21no—
242C22⋊C4×C29—21no—
243C22⋊C4×C29—21no—
244C22⋊C4×C29—41no—
245C22⋊C4×C29—41no—
246C42×C29—21no—
247#25270C2911yesmaximal, characteristic, direct product factor, Sylow
248C23×C29—21no—
249C23×C29—21no—
250C23×C29—22no—
251C23×C29—21no—
252C23×C29—41no—
253C23×C29—41no—
254C23×C29—41no—
255C23×C29—41no—
256C23×C29—81no—
257C23×C29—81no—
258C23×C29#12111yescharacteristic
259C23×C29#12111yescharacteristic
260C23×C29C2×#4111yescharacteristic
261Q8×C29—21no—
262Q8×C29—21no—
263D4×C29—21no—
264D4×C29—21no—
265D4×C29—41no—
266D4×C29—41no—
267D4×C29—42no—
268D4×C29—41no—
269D4×C29—41no—
270D4×C29—41no—
271D4×C29—41no—
272D4×C29—81no—
273D4×C29—82no—
274D4×C29—82no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—21no—
283C2×C4×C29—21no—
284C2×C4×C29—21no—
285C2×C4×C29—21no—
286C2×C4×C29—21no—
287C2×C4×C29—21no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—82no—
294C2×C4×C29—82no—
295C2×C4×C29—81no—
296C2×C4×C29—81no—
297C2×C4×C29—81no—
298C2×C4×C29#12111yescharacteristic
299C2×C4×C29#12111yescharacteristic
300C2×C4×C29C22×D411yescharacteristic
301C2×C4×C29C22×D411yescharacteristic
302C2×C4×C29C2×#4111yescharacteristic
303C2×C4×C29C2×#4111yescharacteristic
304C2×C4×C29H(5,𝔽2)11yescharacteristic
305C2×C4×C292−1+411yescharacteristic
306C8×C29—21no—
307C8×C29—21no—
308C8×C29—22no—
309C8×C29—22no—
310C8×C29—21no—
311C8×C29—21no—
312C8×C29—41no—
313C8×C29—41no—
314C8×C29—41no—
315C8×C29—41no—
316#3092C2×C2911yescharacteristic, complemented
317C2×#481C2×C2911yescharacteristic, complemented
318#3055C2×C2911yescharacteristic
319#2933C2×C2911yescharacteristic, complemented
320#2090C2×C2911yescharacteristic, complemented
321#2079C2×C2911yescharacteristic, complemented
322#2063C2×C2911yescharacteristic, complemented
323#2051C2×C2911yescharacteristic, complemented
324#1951C2×C2911yescharacteristic, complemented
325#1931C2×C2911yescharacteristic, complemented
326#1907C2×C2911yescharacteristic, complemented
327#1900C2×C2911yescharacteristic, complemented
328#1855C2×C2911yescharacteristic, complemented
329#1815C2×C2911yescharacteristic, complemented
330C2×#343C2×C2911yescharacteristic, complemented
331C22×C29—21no—
332C22×C29—21no—
333C22×C29—21no—
334C22×C29—21no—
335C22×C29—21no—
336C22×C29—21no—
337C22×C29—21no—
338C22×C29—42no—
339C22×C29—42no—
340C22×C29—41no—
341C22×C29—41no—
342C22×C29—41no—
343C22×C29—81no—
344C22×C29—81no—
345C22×C29—81no—
346C22×C29—161no—
347C22×C29—161no—
348C22×C29#47112yes—
349C22×C29C2×#12111yescharacteristic
350C22×C29#52911yescharacteristic
351C22×C29#53911yescharacteristic
352C4×C29—21no—
353C4×C29—21no—
354C4×C29—41no—
355C4×C29—41no—
356C4×C29—41no—
357C4×C29—81no—
358C4×C29—81no—
359C4×C29—81no—
360C4×C29#54611yescharacteristic
361C4×C29#54611yescharacteristic
362C4×C29#54711yescharacteristic
363C4×C29#54711yescharacteristic
364C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
365C2×#131C22×C2911yescharacteristic
366C22×M16C22×C2911yescharacteristic
367C22×M16C22×C2911yescharacteristic
368#525C22×C2911yescharacteristic
369C2×#121C22×C2911yescharacteristic
370C22×C4⋊C4C22×C2911yescharacteristic
371#484—21no—
372#483—21no—
373#481—21no—
374#481—21no—
375#481—21no—
376#481—21no—
377#481—21no—
378#480—21no—
379#469—21no—
380#468—21no—
381#466—21no—
382#465—21no—
383#436—21no—
384#435—21no—
385#435—21no—
386C8×D4—21no—
387C2×#108C22×C2911yescharacteristic
388C2×#108C22×C2911yescharacteristic
389#428C22×C2911yescharacteristic
390#428C22×C2911yescharacteristic
391#428C22×C2911yescharacteristic
392C2×#106C22×C2911yescharacteristic
393C2×#106C22×C2911yescharacteristic
394#424C22×C2911yescharacteristic
395#418C22×C2911yescharacteristic
396#417C22×C2911yescharacteristic
397#417C22×C2911yescharacteristic
398#417C22×C2911yescharacteristic
399C2×#102C22×C2911yescharacteristic
400C2×#102C22×C2911yescharacteristic
401C2×#100C22×C2911yescharacteristic
402C2×#100C22×C2911yescharacteristic
403#408C22×C2911yescharacteristic
404#407C22×C2911yescharacteristic
405C2×C22⋊C8C22×C2911yescharacteristic
406#405C22×C2911yescharacteristic
407#343C22×C2911yescharacteristic
408#343C22×C2911yescharacteristic
409#343C22×C2911yescharacteristic
410#343C22×C2911yescharacteristic
411#343C22×C2911yescharacteristic
412#343C22×C2911yescharacteristic
413#341C22×C2911yescharacteristic
414#341C22×C2911yescharacteristic
415C2×C29—21no—
416C2×C29—21no—
417C2×C29—22no—
418C2×C29—41no—
419C2×C29—81no—
420C2×C29—161no—
421C2×C29#242511yescharacteristic
422C2×C29C2×#47111yescharacteristic
423C2×C29#306811yescharacteristic
424C2×#41C23×C2911yescharacteristic
425C22×D4—21no—
426C22×D4C23×C2911yescharacteristic
427C23×C4—21no—
428C23×C4C23×C2911yescharacteristic
429AGL(1,ℤ/8)—22no—
430AGL(1,ℤ/8)—41no—
431C2×SD16—21no—
432C2×D8—21no—
433#131—22no—
434#131—41no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—22no—
439C2×M16—22no—
440C2×M16—41no—
441C2×M16—41no—
442C2×M16C23×C2911yescharacteristic
443C2×M16C23×C2911yescharacteristic
444C2×M16C23×C2911yescharacteristic
445C2×M16C23×C2911yescharacteristic
446C2×M16C23×C2911yescharacteristic
447C2×M16C23×C2911yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—21no—
451C22×C8C23×C2911yescharacteristic
452C22×C8C23×C2911yescharacteristic
453#123—21no—
454C22⋊Q8D4×C2911yescharacteristic
455C22⋊Q8D4×C2911yescharacteristic
456#121—21no—
457#121—21no—
458#121—21no—
459#121—21no—
460#121D4×C2911yescharacteristic
461#121D4×C2911yescharacteristic
462#120—21no—
463C4×D4—21no—
464C4×D4—21no—
465#117C23×C2911yescharacteristic
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4C23×C2911yescharacteristic
472C2×C4⋊C4C23×C2911yescharacteristic
473C2×C4⋊C4C23×C2911yescharacteristic
474C2×C22⋊C4—21no—
475#108—22no—
476#108—41no—
477#107—21no—
478#107—21no—
479#107—21no—
480#106—21no—
481#106—21no—
482#106—21no—
483#106—21no—
484#106—21no—
485#106—21no—
486#106—21no—
487C4⋊C8—21no—
488C4⋊C8—21no—
489#103—21no—
490#103—21no—
491#103—21no—
492#102—21no—
493#102—21no—
494#102—21no—
495#102—21no—
496#102—21no—
497#102—21no—
498#102—21no—
499#102—21no—
500#102—21no—
501#100—22no—
502#100—41no—
503C22⋊C8—21no—
504C22⋊C8—21no—
505C22⋊C8—21no—
506C22⋊C8—21no—
507C22⋊C8D4×C2911yescharacteristic
508C22⋊C8D4×C2911yescharacteristic
509C22⋊C8D4×C2911yescharacteristic
510C22⋊C8D4×C2911yescharacteristic
511#97—21no—
512C4×C8—21no—
513C29#2527011yescharacteristic, direct product factor, Sylow
514C24—21no—
515C24#41×C2911yescharacteristic
516#41—21no—
517#41—21no—
518#41—21no—
519#41—21no—
520C2×Q8C2×D4×C2911yescharacteristic
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—82no—
533C2×D4C2×D4×C2911yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—82no—
545C22×C4C2×D4×C2911yescharacteristic
546C22×C4C2×D4×C2911yescharacteristic
547C22×C4C2×D4×C2911yescharacteristic
548C22×C4C2×D4×C2911yescharacteristic
549C22×C4#41×C2911yescharacteristic
550C22×C4C24×C2911yescharacteristic
551SD16—42no—
552D8—42no—
553M16—21no—
554M16—21no—
555M16—21no—
556M16—21no—
557M16—21no—
558M16—21no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—42no—
564M16—42no—
565M16—42no—
566M16#41×C2912yes—
567M16#41×C2912yes—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—42no—
579C2×C8—42no—
580C2×C8—42no—
581C2×C8C2×D4×C2911yescharacteristic
582C2×C8C2×D4×C2911yescharacteristic
583C2×C8C2×D4×C2911yescharacteristic
584C2×C8C2×D4×C2911yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4C2×D4×C2911yescharacteristic
596C4⋊C4C2×D4×C2911yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C42—21no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—81no—
614C23—81no—
615C23C29×#12111yescharacteristic
616C23C29×#12111yescharacteristic
617C23C2×#41×C2911yescharacteristic
618Q8—21no—
619Q8—21no—
620D4—21no—
621D4—21no—
622D4—42no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—81no—
630D4—82no—
631D4—82no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4C29×#12111yescharacteristic
656C2×C4C29×#12111yescharacteristic
657C2×C4C22×D4×C2911yescharacteristic
658C2×C4C22×D4×C2911yescharacteristic
659C2×C4C2×#41×C2911yescharacteristic
660C2×C4C2×#41×C2911yescharacteristic
661C2×C4C29×H(5,𝔽2)11yescharacteristic
662C2×C4C29×2−1+411yescharacteristic
663C8—21no—
664C8—21no—
665C8—22no—
666C8—22no—
667C8—21no—
668C8—21no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—42no—
681C22—42no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—161no—
689C22—161no—
690C22C29×#47112yes—
691C22C2×C29×#12111yescharacteristic
692C22C29×#52911yescharacteristic
693C22C29×#53911yescharacteristic
694C4—21no—
695C4—21no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C29×#54611yescharacteristic
703C4C29×#54611yescharacteristic
704C4C29×#54711yescharacteristic
705C4C29×#54711yescharacteristic
706C2—21no—
707C2—21no—
708C2—22no—
709C2—41no—
710C2—81no—
711C2—161no—
712C2C29×#242511yescharacteristic
713C2C2×C29×#47111yescharacteristic
714C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3055C2
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
1. C29×#3092C2semidirect
2. C2×C29×#481C2semidirect
4. C29×#2933C2semidirect
5. C29×#2090C2semidirect
6. C29×#2079C2semidirect
7. C29×#2063C2semidirect
8. C29×#2051C2semidirect
9. C29×#1951C2semidirect
10. C29×#1931C2semidirect
11. C29×#1907C2semidirect
12. C29×#1900C2semidirect
13. C29×#1855C2semidirect
14. C29×#1815C2semidirect
15. C2×C29×#343C2semidirect
247. #25270C29direct (N × H)
316. #3092C2×C29semidirect
317. C2×#481C2×C29semidirect
319. #2933C2×C29semidirect
320. #2090C2×C29semidirect
321. #2079C2×C29semidirect
322. #2063C2×C29semidirect
323. #2051C2×C29semidirect
324. #1951C2×C29semidirect
325. #1931C2×C29semidirect
326. #1907C2×C29semidirect
327. #1900C2×C29semidirect
328. #1855C2×C29semidirect
329. #1815C2×C29semidirect
330. C2×#343C2×C29semidirect
513. C29#25270direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30922
C2×C29×#4812
C29×#30552
C29×#29332
C29×#20902
C29×#20792
C29×#20632
C29×#20512
C29×#19512
C29×#19312
C29×#19072
C29×#19002
C29×#18552
C29×#18152
C2×C29×#3432
#2527029