Finite Group Databasebeta

← C29×#25147 #20320047

Subgroups — C29×#25147 #20320047

Order 7424.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#471C211yesmaximal, characteristic, complemented
2C29×#3055C211yesmaximal, characteristic, complemented
3C29×#3005C211yesmaximal, characteristic, complemented
4C2×C29×#449C211yesmaximal, characteristic, complemented
5C29×#2933C211yesmaximal, characteristic, complemented
6C2×C29×#413C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic, complemented
8C29×#2052C211yesmaximal, characteristic, complemented
9C29×#2046C211yesmaximal, characteristic, complemented
10C29×#2018C211yesmaximal, characteristic, complemented
11C29×#1978C211yesmaximal, characteristic, complemented
12C29×#1930C211yesmaximal, characteristic, complemented
13C29×#1907C211yesmaximal, characteristic, complemented
14C29×#1900C211yesmaximal, characteristic, complemented
15C29×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C2×C29×#137C2211yescharacteristic
18C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C22×SD16×C29C2211yescharacteristic
21C22×D8×C29C2211yescharacteristic
22C2×C29×#131C2211yescharacteristic
23C22×M16×C29C2211yescharacteristic
24C22×M16×C29C2211yescharacteristic
25C29×#525C2211yescharacteristic
26C2×C29×#121C2211yescharacteristic
27C29×#471—24no—
28C29×#469—21no—
29C29×#468—21no—
30C29×#466—21no—
31C29×#465—21no—
32C29×#452—21no—
33C29×#452—21no—
34C29×#449—21no—
35C29×#449—21no—
36C29×#449—21no—
37C29×#449—21no—
38C29×#449—21no—
39C29×#449—21no—
40C29×#436—21no—
41C29×#435—21no—
42C29×#435—21no—
43C8×D4×C29—21no—
44C2×C29×#108C2211yescharacteristic
45C2×C29×#108C2211yescharacteristic
46C29×#428C2211yescharacteristic
47C29×#424C2211yescharacteristic
48C29×#419C2211yescharacteristic
49C29×#418C2211yescharacteristic
50C29×#418C2211yescharacteristic
51C29×#417C2211yescharacteristic
52C2×C29×#103C2211yescharacteristic
53C2×C29×#102C2211yescharacteristic
54C29×#413—24no—
55C2×C29×#101C2211yescharacteristic
56C2×C29×#101C2211yescharacteristic
57C2×C29×#100C2211yescharacteristic
58C2×C29×#100C2211yescharacteristic
59C2×C29×#100C2211yescharacteristic
60C2×C29×#100C2211yescharacteristic
61C29×#408C2211yescharacteristic
62C29×#407C2211yescharacteristic
63C2×C29×C22⋊C8C2211yescharacteristic
64C29×#405C2211yescharacteristic
65C29×#343C2211yescharacteristic
66C29×#343C2211yescharacteristic
67C29×#341C2211yescharacteristic
68C29×#341C2211yescharacteristic
69C2×#41×C29—22no—
70C2×#41×C29—22no—
71C2×#41×C29—21no—
72C2×#41×C29—21no—
73C2×#41×C29—21no—
74C2×#41×C29—21no—
75C2×#41×C29—41no—
76C2×#41×C29—41no—
77C2×#41×C29C2311yescharacteristic
78C22×Q8×C29C2311yescharacteristic
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29C2311yescharacteristic
82C22×D4×C29C2311yescharacteristic
83C23×C4×C29—21no—
84C23×C4×C29C2311yescharacteristic
85C29×#137—22no—
86C29×#137—41no—
87C29×AGL(1,ℤ/8)—22no—
88C29×AGL(1,ℤ/8)—22no—
89C29×AGL(1,ℤ/8)—41no—
90C29×AGL(1,ℤ/8)—41no—
91C2×Q16×C29—21no—
92C2×SD16×C29—21no—
93C2×SD16×C29—21no—
94C2×SD16×C29—22no—
95C2×SD16×C29—21no—
96C2×SD16×C29—21no—
97C2×SD16×C29—21no—
98C2×SD16×C29—41no—
99C2×D8×C29—21no—
100C2×D8×C29—21no—
101C2×D8×C29—22no—
102C2×D8×C29—21no—
103C2×D8×C29—21no—
104C2×D8×C29—41no—
105C29×#131—22no—
106C29×#131—41no—
107C2×M16×C29—21no—
108C2×M16×C29—21no—
109C2×M16×C29—21no—
110C2×M16×C29—22no—
111C2×M16×C29—22no—
112C2×M16×C29—41no—
113C2×M16×C29—41no—
114C2×M16×C29C2311yescharacteristic
115C2×M16×C29C2311yescharacteristic
116C2×M16×C29C2311yescharacteristic
117C2×M16×C29C2311yescharacteristic
118C2×M16×C29C2311yescharacteristic
119C2×M16×C29C2311yescharacteristic
120C22×C8×C29—21no—
121C22×C8×C29—21no—
122C22×C8×C29—21no—
123C22×C8×C29C2311yescharacteristic
124C22×C8×C29C2311yescharacteristic
125C29×#123—21no—
126C29×C22⋊Q8D411yescharacteristic
127C29×C22⋊Q8D411yescharacteristic
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121D411yescharacteristic
133C29×#121D411yescharacteristic
134C29×#120—21no—
135C4×D4×C29—21no—
136C4×D4×C29—21no—
137C29×#117C2311yescharacteristic
138C2×C4⋊C4×C29C2311yescharacteristic
139C2×C22⋊C4×C29—21no—
140C29×#108—22no—
141C29×#108—41no—
142C29×#107—21no—
143C29×#106—21no—
144C29×C4⋊C8—21no—
145C29×C4⋊C8—21no—
146C29×#103—21no—
147C29×#103—21no—
148C29×#103—21no—
149C29×#103—21no—
150C29×#103—21no—
151C29×#102—21no—
152C29×#102—21no—
153C29×#102—21no—
154C29×#102—21no—
155C29×#102—21no—
156C29×#102—21no—
157C29×#102—21no—
158C29×#101—22no—
159C29×#101D414yescomplemented
160C29×#100—22no—
161C29×#100—22no—
162C29×#100—22no—
163C29×#100—41no—
164C29×C22⋊C8—21no—
165C29×C22⋊C8—21no—
166C29×C22⋊C8—21no—
167C29×C22⋊C8—21no—
168C29×C22⋊C8D411yescharacteristic
169C29×C22⋊C8D411yescharacteristic
170C29×C22⋊C8D411yescharacteristic
171C29×C22⋊C8D411yescharacteristic
172C29×#97—21no—
173C4×C8×C29—21no—
174C24×C29—21no—
175C24×C29—21no—
176C24×C29#4111yescharacteristic
177#41×C29—21no—
178#41×C29—21no—
179#41×C29—21no—
180#41×C29—21no—
181#41×C29—42no—
182#41×C29—42no—
183#41×C29—42no—
184#41×C29—42no—
185#41×C29—42no—
186#41×C29—42no—
187#41×C29—42no—
188#41×C29—42no—
189C2×Q8×C29—21no—
190C2×Q8×C29—21no—
191C2×Q8×C29—21no—
192C2×Q8×C29—21no—
193C2×Q8×C29—21no—
194C2×Q8×C29C2×D411yescharacteristic
195C2×Q8×C29C2×D412yes—
196C2×D4×C29—24no—
197C2×D4×C29—21no—
198C2×D4×C29—21no—
199C2×D4×C29—21no—
200C2×D4×C29—21no—
201C2×D4×C29—21no—
202C2×D4×C29—21no—
203C2×D4×C29—21no—
204C2×D4×C29—21no—
205C2×D4×C29—21no—
206C2×D4×C29—21no—
207C2×D4×C29—21no—
208C2×D4×C29—21no—
209C2×D4×C29—21no—
210C2×D4×C29—21no—
211C2×D4×C29—42no—
212C2×D4×C29—41no—
213C2×D4×C29—41no—
214C2×D4×C29—41no—
215C2×D4×C29—41no—
216C2×D4×C29—82no—
217C2×D4×C29C2×D411yescharacteristic
218C2×D4×C29#4112yes—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—24no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—21no—
227C22×C4×C29—42no—
228C22×C4×C29—41no—
229C22×C4×C29—41no—
230C22×C4×C29C2×D411yescharacteristic
231C22×C4×C29C2×D411yescharacteristic
232C22×C4×C29C2×D411yescharacteristic
233C22×C4×C29C2×D411yescharacteristic
234C22×C4×C29#4111yescharacteristic
235C22×C4×C29C2411yescharacteristic
236Q16×C29—42no—
237SD16×C29—42no—
238SD16×C29—42no—
239SD16×C29—42no—
240SD16×C29—42no—
241SD16×C29—42no—
242D8×C29—42no—
243D8×C29—42no—
244D8×C29—42no—
245D8×C29—42no—
246M16×C29—21no—
247M16×C29—21no—
248M16×C29—21no—
249M16×C29—21no—
250M16×C29—21no—
251M16×C29—21no—
252M16×C29—21no—
253M16×C29—21no—
254M16×C29—21no—
255M16×C29—21no—
256M16×C29—42no—
257M16×C29—42no—
258M16×C29—42no—
259M16×C29C2×D412yes—
260M16×C29C2×D412yes—
261C2×C8×C29—21no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—21no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—21no—
270C2×C8×C29—21no—
271C2×C8×C29—42no—
272C2×C8×C29—42no—
273C2×C8×C29—42no—
274C2×C8×C29C2×D411yescharacteristic
275C2×C8×C29C2×D411yescharacteristic
276C2×C8×C29C2×D411yescharacteristic
277C2×C8×C29C2×D411yescharacteristic
278C4⋊C4×C29—21no—
279C4⋊C4×C29—21no—
280C4⋊C4×C29—21no—
281C4⋊C4×C29—21no—
282C4⋊C4×C29C2×D411yescharacteristic
283C4⋊C4×C29C2×D411yescharacteristic
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—41no—
290C22⋊C4×C29—41no—
291C42×C29—21no—
292#25147C2911yesmaximal, characteristic, direct product factor, Sylow
293C23×C29—21no—
294C23×C29—21no—
295C23×C29—21no—
296C23×C29—22no—
297C23×C29—41no—
298C23×C29—41no—
299C23×C29—41no—
300C23×C29—41no—
301C23×C29—41no—
302C23×C29—41no—
303C23×C29—41no—
304C23×C29—81no—
305C23×C29—81no—
306C23×C29—81no—
307C23×C29—81no—
308C23×C29#12111yescharacteristic
309C23×C29#12111yescharacteristic
310C23×C29C2×#4111yescharacteristic
311Q8×C29—21no—
312Q8×C29—22no—
313Q8×C29—22no—
314Q8×C29—21no—
315Q8×C29—41no—
316Q8×C29—41no—
317D4×C29—21no—
318D4×C29—22no—
319D4×C29—21no—
320D4×C29—22no—
321D4×C29—42no—
322D4×C29—44no—
323D4×C29—44no—
324D4×C29—41no—
325D4×C29—41no—
326D4×C29—41no—
327D4×C29—41no—
328D4×C29—41no—
329D4×C29—41no—
330D4×C29—41no—
331D4×C29—41no—
332D4×C29—81no—
333D4×C29—82no—
334D4×C29—82no—
335C2×C4×C29—21no—
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—21no—
347C2×C4×C29—21no—
348C2×C4×C29—22no—
349C2×C4×C29—44no—
350C2×C4×C29—44no—
351C2×C4×C29—41no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—41no—
355C2×C4×C29—41no—
356C2×C4×C29—81no—
357C2×C4×C29#12111yescharacteristic
358C2×C4×C29#12111yescharacteristic
359C2×C4×C29C22×D411yescharacteristic
360C2×C4×C29C22×D411yescharacteristic
361C2×C4×C29C22×D411yescharacteristic
362C2×C4×C29C2×#4111yescharacteristic
363C2×C4×C29H(5,𝔽2)11yescharacteristic
364C2×C4×C29H(5,𝔽2)11yescharacteristic
365C8×C29—21no—
366C8×C29—21no—
367C8×C29—22no—
368C8×C29—22no—
369C8×C29—21no—
370C8×C29—21no—
371C8×C29—41no—
372C8×C29—41no—
373C8×C29—41no—
374C8×C29—41no—
375C2×#471C2×C2911yescharacteristic, complemented
376#3055C2×C2911yescharacteristic, complemented
377#3005C2×C2911yescharacteristic, complemented
378C2×#449C2×C2911yescharacteristic, complemented
379#2933C2×C2911yescharacteristic, complemented
380C2×#413C2×C2911yescharacteristic, complemented
381#2063C2×C2911yescharacteristic, complemented
382#2052C2×C2911yescharacteristic, complemented
383#2046C2×C2911yescharacteristic, complemented
384#2018C2×C2911yescharacteristic, complemented
385#1978C2×C2911yescharacteristic, complemented
386#1930C2×C2911yescharacteristic, complemented
387#1907C2×C2911yescharacteristic, complemented
388#1900C2×C2911yescharacteristic, complemented
389#1855C2×C2911yescharacteristic, complemented
390C22×C29—21no—
391C22×C29—21no—
392C22×C29—21no—
393C22×C29—21no—
394C22×C29—21no—
395C22×C29—21no—
396C22×C29—21no—
397C22×C29—21no—
398C22×C29—42no—
399C22×C29—41no—
400C22×C29—41no—
401C22×C29—41no—
402C22×C29—81no—
403C22×C29—81no—
404C22×C29—82no—
405C22×C29—82no—
406C22×C29—81no—
407C22×C29—81no—
408C22×C29—81no—
409C22×C29—81no—
410C22×C29—81no—
411C22×C29—161no—
412C22×C29—161no—
413C22×C29C2×#12111yescharacteristic
414C22×C29#52511yescharacteristic
415C22×C29#53811yescharacteristic
416C4×C29—21no—
417C4×C29—21no—
418C4×C29—42no—
419C4×C29—41no—
420C4×C29—41no—
421C4×C29—41no—
422C4×C29—81no—
423C4×C29D4211yescharacteristic
424C4×C29D4211yescharacteristic
425C4×C29#54611yescharacteristic
426C4×C29#54611yescharacteristic
427C22×#41C22×C2911yescharacteristic
428C2×#137C22×C2911yescharacteristic
429C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
430C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
431C22×SD16C22×C2911yescharacteristic
432C22×D8C22×C2911yescharacteristic
433C2×#131C22×C2911yescharacteristic
434C22×M16C22×C2911yescharacteristic
435C22×M16C22×C2911yescharacteristic
436#525C22×C2911yescharacteristic
437C2×#121C22×C2911yescharacteristic
438#471—24no—
439#469—21no—
440#468—21no—
441#466—21no—
442#465—21no—
443#452—21no—
444#452—21no—
445#449—21no—
446#449—21no—
447#449—21no—
448#449—21no—
449#449—21no—
450#449—21no—
451#436—21no—
452#435—21no—
453#435—21no—
454C8×D4—21no—
455C2×#108C22×C2911yescharacteristic
456C2×#108C22×C2911yescharacteristic
457#428C22×C2911yescharacteristic
458#424C22×C2911yescharacteristic
459#419C22×C2911yescharacteristic
460#418C22×C2911yescharacteristic
461#418C22×C2911yescharacteristic
462#417C22×C2911yescharacteristic
463C2×#103C22×C2911yescharacteristic
464C2×#102C22×C2911yescharacteristic
465#413—24no—
466C2×#101C22×C2911yescharacteristic
467C2×#101C22×C2911yescharacteristic
468C2×#100C22×C2911yescharacteristic
469C2×#100C22×C2911yescharacteristic
470C2×#100C22×C2911yescharacteristic
471C2×#100C22×C2911yescharacteristic
472#408C22×C2911yescharacteristic
473#407C22×C2911yescharacteristic
474C2×C22⋊C8C22×C2911yescharacteristic
475#405C22×C2911yescharacteristic
476#343C22×C2911yescharacteristic
477#343C22×C2911yescharacteristic
478#341C22×C2911yescharacteristic
479#341C22×C2911yescharacteristic
480C2×C29—21no—
481C2×C29—21no—
482C2×C29—41no—
483C2×C29—41no—
484C2×C29—81no—
485C2×C29—82no—
486C2×C29—161no—
487C2×C29#242411yescharacteristic
488C2×C29#306711yescharacteristic
489C2×C29#306811yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41C23×C2911yescharacteristic
499C22×Q8C23×C2911yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C23×C2911yescharacteristic
503C22×D4C23×C2911yescharacteristic
504C23×C4—21no—
505C23×C4C23×C2911yescharacteristic
506#137—22no—
507#137—41no—
508AGL(1,ℤ/8)—22no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—41no—
511AGL(1,ℤ/8)—41no—
512C2×Q16—21no—
513C2×SD16—22no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—41no—
520C2×D8—21no—
521C2×D8—21no—
522C2×D8—22no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—41no—
526#131—22no—
527#131—41no—
528C2×M16—21no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16C23×C2911yescharacteristic
536C2×M16C23×C2911yescharacteristic
537C2×M16C23×C2911yescharacteristic
538C2×M16C23×C2911yescharacteristic
539C2×M16C23×C2911yescharacteristic
540C2×M16C23×C2911yescharacteristic
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—21no—
544C22×C8C23×C2911yescharacteristic
545C22×C8C23×C2911yescharacteristic
546#123—21no—
547C22⋊Q8D4×C2911yescharacteristic
548C22⋊Q8D4×C2911yescharacteristic
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121D4×C2911yescharacteristic
554#121D4×C2911yescharacteristic
555#120—21no—
556C4×D4—21no—
557C4×D4—21no—
558#117C23×C2911yescharacteristic
559C2×C4⋊C4C23×C2911yescharacteristic
560C2×C22⋊C4—21no—
561#108—22no—
562#108—41no—
563#107—21no—
564#106—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567#103—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#101—22no—
580#101D4×C2914yescomplemented
581#100—22no—
582#100—22no—
583#100—22no—
584#100—41no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8D4×C2911yescharacteristic
590C22⋊C8D4×C2911yescharacteristic
591C22⋊C8D4×C2911yescharacteristic
592C22⋊C8D4×C2911yescharacteristic
593#97—21no—
594C4×C8—21no—
595C29#2514711yescharacteristic, direct product factor, Sylow
596C24—21no—
597C24—21no—
598C24#41×C2911yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C2912yes—
617C2×Q8C2×D4×C2911yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C2911yescharacteristic
640C2×D4#41×C2912yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C2911yescharacteristic
653C22×C4C2×D4×C2911yescharacteristic
654C22×C4C2×D4×C2911yescharacteristic
655C22×C4C2×D4×C2911yescharacteristic
656C22×C4#41×C2911yescharacteristic
657C22×C4C24×C2911yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C2912yes—
682M16C2×D4×C2912yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C2911yescharacteristic
697C2×C8C2×D4×C2911yescharacteristic
698C2×C8C2×D4×C2911yescharacteristic
699C2×C8C2×D4×C2911yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C2911yescharacteristic
705C4⋊C4C2×D4×C2911yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23C29×#12111yescharacteristic
730C23C29×#12111yescharacteristic
731C23C2×#41×C2911yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4C29×#12111yescharacteristic
779C2×C4C29×#12111yescharacteristic
780C2×C4C22×D4×C2911yescharacteristic
781C2×C4C22×D4×C2911yescharacteristic
782C2×C4C22×D4×C2911yescharacteristic
783C2×C4C2×#41×C2911yescharacteristic
784C2×C4C29×H(5,𝔽2)11yescharacteristic
785C2×C4C29×H(5,𝔽2)11yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—42no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×C29×#12111yescharacteristic
820C22C29×#52511yescharacteristic
821C22C29×#53811yescharacteristic
822C4—21no—
823C4—21no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—81no—
829C4D42×C2911yescharacteristic
830C4D42×C2911yescharacteristic
831C4C29×#54611yescharacteristic
832C4C29×#54611yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C29×#242411yescharacteristic
841C2C29×#306711yescharacteristic
842C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
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. C2×C29×#471C2semidirect
2. C29×#3055C2semidirect
3. C29×#3005C2semidirect
4. C2×C29×#449C2semidirect
5. C29×#2933C2semidirect
6. C2×C29×#413C2semidirect
7. C29×#2063C2semidirect
8. C29×#2052C2semidirect
9. C29×#2046C2semidirect
10. C29×#2018C2semidirect
11. C29×#1978C2semidirect
12. C29×#1930C2semidirect
13. C29×#1907C2semidirect
14. C29×#1900C2semidirect
15. C29×#1855C2semidirect
159. C29×#101D4semidirect
292. #25147C29direct (N × H)
375. C2×#471C2×C29semidirect
376. #3055C2×C29semidirect
377. #3005C2×C29semidirect
378. C2×#449C2×C29semidirect
379. #2933C2×C29semidirect
380. C2×#413C2×C29semidirect
381. #2063C2×C29semidirect
382. #2052C2×C29semidirect
383. #2046C2×C29semidirect
384. #2018C2×C29semidirect
385. #1978C2×C29semidirect
386. #1930C2×C29semidirect
387. #1907C2×C29semidirect
388. #1900C2×C29semidirect
389. #1855C2×C29semidirect
580. #101D4×C29semidirect
595. C29#25147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4712
C29×#30552
C29×#30052
C2×C29×#4492
C29×#29332
C2×C29×#4132
C29×#20632
C29×#20522
C29×#20462
C29×#20182
C29×#19782
C29×#19302
C29×#19072
C29×#19002
C29×#18552
#2514729