Finite Group Databasebeta

← C29×#25525 #20320425

Subgroups — C29×#25525 #20320425

Order 7424.

1072 conjugacy classes of subgroups.

The subgroup lattice has 854 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×#2857C211yesmaximal, characteristic, complemented
5C29×#2060C211yesmaximal, characteristic, complemented
6C29×#2038C211yesmaximal, characteristic, complemented
7C29×#2028C211yesmaximal, characteristic, complemented
8C29×#2005C211yesmaximal, characteristic, complemented
9C29×#1901C211yesmaximal, characteristic, complemented
10C29×#1896C211yesmaximal, characteristic
11C29×#1886C211yesmaximal, characteristic, complemented
12C29×#1882C211yesmaximal, characteristic, complemented
13C29×#1859C211yesmaximal, characteristic, complemented
14C29×#1857C211yesmaximal, characteristic, complemented
15C2×C29×#339C211yesmaximal, 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
37C22×C42×C29C2211yescharacteristic
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×#391C2211yescharacteristic
59C29×#391C2211yescharacteristic
60C29×#389—22no—
61C29×#384C2211yescharacteristic
62C29×#380—22no—
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×C29—21no—
75C23×C4×C29C2311yescharacteristic
76C29×#137—22no—
77C29×#137—41no—
78C2×Q16×C29—21no—
79C2×SD16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29—22no—
82C2×M16×C29—41no—
83C2×M16×C29C2311yescharacteristic
84C2×M16×C29C2311yescharacteristic
85C2×M16×C29C2311yescharacteristic
86C2×M16×C29C2311yescharacteristic
87C22×C8×C29—21no—
88C29×C4⋊Q8—21no—
89C29×C4⋊Q8—21no—
90C29×C4⋊Q8—21no—
91C29×C4⋊Q8—22no—
92C29×C4⋊Q8—41no—
93C29×#126—22no—
94C29×#126—22no—
95C29×#126—22no—
96C29×#126—22no—
97C29×#125—22no—
98C29×#125—22no—
99C29×#125—22no—
100C29×#125—21no—
101C29×#125—21no—
102C29×#124—22no—
103C29×#124—21no—
104C29×#123—22no—
105C29×#123—22no—
106C29×#123—21no—
107C29×#123—22no—
108C29×C22⋊Q8—22no—
109C29×C22⋊Q8—22no—
110C29×C22⋊Q8—21no—
111C29×C22⋊Q8—21no—
112C29×C22⋊Q8—21no—
113C29×C22⋊Q8—21no—
114C29×C22⋊Q8—22no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8—21no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8D411yescharacteristic
122C29×C22⋊Q8D411yescharacteristic
123C29×#121D411yescharacteristic
124C29×#121D411yescharacteristic
125C29×#120—21no—
126C4×Q8×C29—22no—
127C4×Q8×C29—21no—
128C4×Q8×C29—21no—
129C4×Q8×C29—21no—
130C4×Q8×C29—21no—
131C4×Q8×C29—21no—
132C4×D4×C29—22no—
133C4×D4×C29—21no—
134C4×D4×C29—22no—
135C4×D4×C29—21no—
136C4×D4×C29—21no—
137C29×#117—22no—
138C29×#117—22no—
139C29×#117—21no—
140C29×#117—21no—
141C29×#117—22no—
142C29×#117—21no—
143C29×#117D411yescharacteristic
144C29×#117D411yescharacteristic
145C29×#117C2311yescharacteristic
146C29×#117C2311yescharacteristic
147C29×#117C2311yescharacteristic
148C2×C4⋊C4×C29—21no—
149C2×C4⋊C4×C29—21no—
150C2×C4⋊C4×C29—22no—
151C2×C4⋊C4×C29—22no—
152C2×C4⋊C4×C29D412yes—
153C2×C4⋊C4×C29D411yescharacteristic
154C2×C4⋊C4×C29D411yescharacteristic
155C2×C4⋊C4×C29C2311yescharacteristic
156C2×C4⋊C4×C29C2311yescharacteristic
157C2×C22⋊C4×C29—21no—
158C2×C22⋊C4×C29—21no—
159C2×C22⋊C4×C29D412yes—
160C2×C42×C29—21no—
161C2×C42×C29—22no—
162C2×C42×C29—21no—
163C2×C42×C29—41no—
164C2×C42×C29C2311yescharacteristic
165C2×C42×C29C2311yescharacteristic
166C29×#107—21no—
167C29×#107—21no—
168C29×#107—21no—
169C29×#106—21no—
170C29×#106—21no—
171C29×#106—21no—
172C29×#104—22no—
173C29×#104—41no—
174C29×#103—21no—
175C29×#103—21no—
176C29×#103—21no—
177C29×#103—21no—
178C29×#103—21no—
179C29×#103—21no—
180C29×#103—21no—
181C29×#102—21no—
182C29×#101—22no—
183C29×#101—41no—
184C29×C22⋊C8—21no—
185C29×C22⋊C8—21no—
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—24no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—22no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—42no—
225C22×C4×C29—42no—
226C22×C4×C29C2×D412yes—
227C22×C4×C29C2×D411yescharacteristic
228C22×C4×C29C2×D411yescharacteristic
229C22×C4×C29C2×D411yescharacteristic
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D412yes—
233C22×C4×C29C2411yescharacteristic
234Q16×C29—42no—
235SD16×C29—42no—
236M16×C29—21no—
237M16×C29—21no—
238M16×C29—21no—
239M16×C29—21no—
240M16×C29—21no—
241M16×C29—21no—
242M16×C29—21no—
243M16×C29—42no—
244M16×C29#4112yes—
245C2×C8×C29—21no—
246C2×C8×C29—21no—
247C2×C8×C29—21no—
248C2×C8×C29—21no—
249C2×C8×C29—42no—
250C4⋊C4×C29—22no—
251C4⋊C4×C29—22no—
252C4⋊C4×C29—22no—
253C4⋊C4×C29—22no—
254C4⋊C4×C29—22no—
255C4⋊C4×C29—22no—
256C4⋊C4×C29—22no—
257C4⋊C4×C29—22no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—22no—
261C4⋊C4×C29—22no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—44no—
269C4⋊C4×C29—44no—
270C4⋊C4×C29—41no—
271C4⋊C4×C29—41no—
272C4⋊C4×C29C2×D411yescharacteristic
273C4⋊C4×C29C2×D411yescharacteristic
274C4⋊C4×C29C2×D411yescharacteristic
275C4⋊C4×C29C2×D411yescharacteristic
276C4⋊C4×C29C2×D411yescharacteristic
277C4⋊C4×C29C2×D411yescharacteristic
278C22⋊C4×C29—22no—
279C22⋊C4×C29—22no—
280C22⋊C4×C29—22no—
281C22⋊C4×C29—21no—
282C22⋊C4×C29—21no—
283C22⋊C4×C29—22no—
284C22⋊C4×C29—22no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—41no—
293C22⋊C4×C29—41no—
294C42×C29—22no—
295C42×C29—22no—
296C42×C29—22no—
297C42×C29—21no—
298C42×C29—21no—
299C42×C29—21no—
300C42×C29—21no—
301C42×C29—21no—
302C42×C29—21no—
303C42×C29—21no—
304C42×C29—21no—
305C42×C29—42no—
306C42×C29#4112yes—
307#25525C2911yesmaximal, characteristic, direct product factor, Sylow
308C23×C29—21no—
309C23×C29—21no—
310C23×C29—22no—
311C23×C29—21no—
312C23×C29—41no—
313C23×C29#12011yescharacteristic
314C23×C29#12011yescharacteristic
315C23×C29C22×D411yescharacteristic
316Q8×C29—21no—
317Q8×C29—21no—
318Q8×C29—41no—
319Q8×C29—41no—
320Q8×C29—41no—
321Q8×C29—41no—
322Q8×C29—41no—
323Q8×C29—41no—
324Q8×C29—41no—
325Q8×C29—41no—
326Q8×C29—82no—
327D4×C29—21no—
328D4×C29—21no—
329D4×C29—41no—
330D4×C29—41no—
331D4×C29—42no—
332D4×C29—81no—
333C2×C4×C29—22no—
334C2×C4×C29—22no—
335C2×C4×C29—22no—
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—21no—
346C2×C4×C29—22no—
347C2×C4×C29—21no—
348C2×C4×C29—21no—
349C2×C4×C29—21no—
350C2×C4×C29—21no—
351C2×C4×C29—21no—
352C2×C4×C29—22no—
353C2×C4×C29—21no—
354C2×C4×C29—21no—
355C2×C4×C29—22no—
356C2×C4×C29—22no—
357C2×C4×C29—22no—
358C2×C4×C29—48no—
359C2×C4×C29—41no—
360C2×C4×C29—41no—
361C2×C4×C29—42no—
362C2×C4×C29—41no—
363C2×C4×C29—41no—
364C2×C4×C29—42no—
365C2×C4×C29—42no—
366C2×C4×C29—41no—
367C2×C4×C29—41no—
368C2×C4×C29—41no—
369C2×C4×C29—41no—
370C2×C4×C29—81no—
371C2×C4×C29—82no—
372C2×C4×C29#12011yescharacteristic
373C2×C4×C29#12011yescharacteristic
374C2×C4×C29C22×D411yescharacteristic
375C2×C4×C29C22×D411yescharacteristic
376C2×C4×C29C2×#4111yescharacteristic
377C2×C4×C29C2×#4111yescharacteristic
378C2×C4×C29H(5,𝔽2)11yescharacteristic
379C2×C4×C292−1+411yescharacteristic
380C8×C29—22no—
381C8×C29—41no—
382C8×C29—41no—
383C8×C29—41no—
384#3495C2×C2911yescharacteristic
385#3095C2×C2911yescharacteristic, complemented
386#3056C2×C2911yescharacteristic
387#2857C2×C2911yescharacteristic, complemented
388#2060C2×C2911yescharacteristic, complemented
389#2038C2×C2911yescharacteristic, complemented
390#2028C2×C2911yescharacteristic, complemented
391#2005C2×C2911yescharacteristic, complemented
392#1901C2×C2911yescharacteristic, complemented
393#1896C2×C2911yescharacteristic
394#1886C2×C2911yescharacteristic, complemented
395#1882C2×C2911yescharacteristic, complemented
396#1859C2×C2911yescharacteristic, complemented
397#1857C2×C2911yescharacteristic, complemented
398C2×#339C2×C2911yescharacteristic, complemented
399C22×C29—21no—
400C22×C29—21no—
401C22×C29—21no—
402C22×C29—21no—
403C22×C29—21no—
404C22×C29—21no—
405C22×C29—21no—
406C22×C29—42no—
407C22×C29—42no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29#45612yes—
412C22×C29C2×#12011yescharacteristic
413C22×C29#54611yescharacteristic
414C22×C29#54711yescharacteristic
415C4×C29—24no—
416C4×C29—21no—
417C4×C29—21no—
418C4×C29—42no—
419C4×C29—42no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—41no—
423C4×C29—41no—
424C4×C29—42no—
425C4×C29—41no—
426C4×C29—41no—
427C4×C29—41no—
428C4×C29—81no—
429C4×C29—81no—
430C4×C29#53211yescharacteristic
431C4×C29#53711yescharacteristic
432C4×C29#54611yescharacteristic
433C4×C29#54711yescharacteristic
434C2×#137C22×C2911yescharacteristic
435C22×M16C22×C2911yescharacteristic
436#556—21no—
437#554—21no—
438#552—21no—
439#552—22no—
440#552—21no—
441#551—22no—
442#544C22×C2911yescharacteristic
443#542—21no—
444#541—21no—
445#536C22×C2911yescharacteristic
446#533—21no—
447C2×C4⋊Q8C22×C2911yescharacteristic
448#529—21no—
449#525C22×C2911yescharacteristic
450C2×C22⋊Q8C22×C2911yescharacteristic
451C2×C22⋊Q8C22×C2911yescharacteristic
452#520C22×C2911yescharacteristic
453#519C22×C2911yescharacteristic
454C2×#117C22×C2911yescharacteristic
455C22×C42C22×C2911yescharacteristic
456#485—21no—
457#485—21no—
458#484—21no—
459#483—21no—
460#470—21no—
461#468—21no—
462#467—21no—
463#465—21no—
464#428C22×C2911yescharacteristic
465#428C22×C2911yescharacteristic
466#428C22×C2911yescharacteristic
467C2×#104C22×C2911yescharacteristic
468C2×#104C22×C2911yescharacteristic
469#419C22×C2911yescharacteristic
470#419C22×C2911yescharacteristic
471#419C22×C2911yescharacteristic
472#417C22×C2911yescharacteristic
473C2×#101C22×C2911yescharacteristic
474C2×#101C22×C2911yescharacteristic
475#407C22×C2911yescharacteristic
476#391C22×C2911yescharacteristic
477#391C22×C2911yescharacteristic
478#389—22no—
479#384C22×C2911yescharacteristic
480#380—22no—
481#343C22×C2911yescharacteristic
482#343C22×C2911yescharacteristic
483#339C22×C2911yescharacteristic
484#339C22×C2911yescharacteristic
485#339C22×C2911yescharacteristic
486#339C22×C2911yescharacteristic
487#339C22×C2911yescharacteristic
488#339C22×C2911yescharacteristic
489C2×C29—21no—
490C2×C29—21no—
491C2×C29—22no—
492C2×C29—41no—
493C2×C29—81no—
494C2×C29#243011yescharacteristic
495C2×C29C2×#45611yescharacteristic
496C2×C29#301811yescharacteristic
497C2×#41C23×C2911yescharacteristic
498C22×Q8C23×C2911yescharacteristic
499C22×Q8C23×C2911yescharacteristic
500C23×C4—21no—
501C23×C4C23×C2911yescharacteristic
502#137—22no—
503#137—41no—
504C2×Q16—21no—
505C2×SD16—21no—
506C2×M16—21no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16C23×C2911yescharacteristic
510C2×M16C23×C2911yescharacteristic
511C2×M16C23×C2911yescharacteristic
512C2×M16C23×C2911yescharacteristic
513C22×C8—21no—
514C4⋊Q8—21no—
515C4⋊Q8—21no—
516C4⋊Q8—21no—
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519#126—22no—
520#126—22no—
521#126—22no—
522#126—22no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—21no—
527#125—21no—
528#124—22no—
529#124—21no—
530#123—22no—
531#123—22no—
532#123—21no—
533#123—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—22no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8D4×C2911yescharacteristic
548C22⋊Q8D4×C2911yescharacteristic
549#121D4×C2911yescharacteristic
550#121D4×C2911yescharacteristic
551#120—21no—
552C4×Q8—22no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×D4—22no—
559C4×D4—21no—
560C4×D4—22no—
561C4×D4—21no—
562C4×D4—21no—
563#117—22no—
564#117—22no—
565#117—21no—
566#117—21no—
567#117—22no—
568#117—21no—
569#117D4×C2911yescharacteristic
570#117D4×C2911yescharacteristic
571#117C23×C2911yescharacteristic
572#117C23×C2911yescharacteristic
573#117C23×C2911yescharacteristic
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4D4×C2912yes—
579C2×C4⋊C4D4×C2911yescharacteristic
580C2×C4⋊C4D4×C2911yescharacteristic
581C2×C4⋊C4C23×C2911yescharacteristic
582C2×C4⋊C4C23×C2911yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4D4×C2912yes—
586C2×C42—21no—
587C2×C42—22no—
588C2×C42—21no—
589C2×C42—41no—
590C2×C42C23×C2911yescharacteristic
591C2×C42C23×C2911yescharacteristic
592#107—21no—
593#107—21no—
594#107—21no—
595#106—21no—
596#106—21no—
597#106—21no—
598#104—22no—
599#104—41no—
600#103—21no—
601#103—21no—
602#103—21no—
603#103—21no—
604#103—21no—
605#103—21no—
606#103—21no—
607#102—21no—
608#101—22no—
609#101—41no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612#95—22no—
613#95—22no—
614C29#2552511yescharacteristic, direct product factor, Sylow
615C24C2×D4×C2911yescharacteristic
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620C2×Q8—22no—
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×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8C2×D4×C2911yescharacteristic
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4C2×D4×C2911yescharacteristic
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4C2×D4×C2912yes—
654C22×C4C2×D4×C2911yescharacteristic
655C22×C4C2×D4×C2911yescharacteristic
656C22×C4C2×D4×C2911yescharacteristic
657C22×C4C2×D4×C2911yescharacteristic
658C22×C4C2×D4×C2911yescharacteristic
659C22×C4C2×D4×C2912yes—
660C22×C4C24×C2911yescharacteristic
661Q16—42no—
662SD16—42no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—42no—
671M16#41×C2912yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4C2×D4×C2911yescharacteristic
700C4⋊C4C2×D4×C2911yescharacteristic
701C4⋊C4C2×D4×C2911yescharacteristic
702C4⋊C4C2×D4×C2911yescharacteristic
703C4⋊C4C2×D4×C2911yescharacteristic
704C4⋊C4C2×D4×C2911yescharacteristic
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—42no—
733C42#41×C2912yes—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23C29×#12011yescharacteristic
740C23C29×#12011yescharacteristic
741C23C22×D4×C2911yescharacteristic
742Q8—21no—
743Q8—21no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—82no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—81no—
797C2×C4—82no—
798C2×C4C29×#12011yescharacteristic
799C2×C4C29×#12011yescharacteristic
800C2×C4C22×D4×C2911yescharacteristic
801C2×C4C22×D4×C2911yescharacteristic
802C2×C4C2×#41×C2911yescharacteristic
803C2×C4C2×#41×C2911yescharacteristic
804C2×C4C29×H(5,𝔽2)11yescharacteristic
805C2×C4C29×2−1+411yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22C29×#45612yes—
823C22C2×C29×#12011yescharacteristic
824C22C29×#54611yescharacteristic
825C22C29×#54711yescharacteristic
826C4—24no—
827C4—21no—
828C4—21no—
829C4—42no—
830C4—42no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4C29×#53211yescharacteristic
842C4C29×#53711yescharacteristic
843C4C29×#54611yescharacteristic
844C4C29×#54711yescharacteristic
845C2—21no—
846C2—22no—
847C2—21no—
848C2—41no—
849C2—81no—
850C2C29×#243011yescharacteristic
851C2C2×C29×#45611yescharacteristic
852C2C29×#301811yescharacteristic
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×#2857C2semidirect
5. C29×#2060C2semidirect
6. C29×#2038C2semidirect
7. C29×#2028C2semidirect
8. C29×#2005C2semidirect
9. C29×#1901C2semidirect
11. C29×#1886C2semidirect
12. C29×#1882C2semidirect
13. C29×#1859C2semidirect
14. C29×#1857C2semidirect
15. C2×C29×#339C2semidirect
307. #25525C29direct (N × H)
385. #3095C2×C29semidirect
387. #2857C2×C29semidirect
388. #2060C2×C29semidirect
389. #2038C2×C29semidirect
390. #2028C2×C29semidirect
391. #2005C2×C29semidirect
392. #1901C2×C29semidirect
394. #1886C2×C29semidirect
395. #1882C2×C29semidirect
396. #1859C2×C29semidirect
397. #1857C2×C29semidirect
398. C2×#339C2×C29semidirect
614. C29#25525direct (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×#28572
C29×#20602
C29×#20382
C29×#20282
C29×#20052
C29×#19012
C29×#18962
C29×#18862
C29×#18822
C29×#18592
C29×#18572
C2×C29×#3392
#2552529