Finite Group Databasebeta

← C29×#25195 #20320095

Subgroups — C29×#25195 #20320095

Order 7424.

1014 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3063C211yesmaximal, characteristic, complemented
2C29×#3046C211yesmaximal, characteristic, complemented
3C2×C29×#455C211yesmaximal, characteristic, complemented
4C29×#3012C211yesmaximal, characteristic
5C2×C29×#444C211yesmaximal, characteristic, complemented
6C29×#2897C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic, complemented
8C29×#2052C211yesmaximal, characteristic, complemented
9C29×#2039C211yesmaximal, characteristic, complemented
10C29×#2003C211yesmaximal, characteristic, complemented
11C29×#1959C211yesmaximal, characteristic, complemented
12C29×#1938C211yesmaximal, characteristic, complemented
13C29×#1908C211yesmaximal, characteristic, complemented
14C29×#1907C211yesmaximal, characteristic, complemented
15C29×#1859C211yesmaximal, characteristic, complemented
16C2×C29×H(5,𝔽2)C2211yescharacteristic
17C2×C29×#137C2211yescharacteristic
18C2×C29×#137C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C29×#135C2211yescharacteristic
21C2×C29×#131C2211yescharacteristic
22C2×C29×#131C2211yescharacteristic, complemented
23C29×#537C2211yescharacteristic
24C29×#536C2211yescharacteristic, complemented
25C2×C29×#124C2211yescharacteristic
26C29×#520C2211yescharacteristic
27C29×#470—21no—
28C29×#468—21no—
29C29×#467—21no—
30C29×#465—21no—
31C29×#464—21no—
32C29×#463—21no—
33C29×#462—21no—
34C29×#461—21no—
35C29×#455—24no—
36C29×#452—21no—
37C29×#450—21no—
38C29×#449—21no—
39C29×#447—21no—
40C29×#444—24no—
41C2×C29×#108C2211yescharacteristic, complemented
42C29×#428C2211yescharacteristic, complemented
43C29×#424C2211yescharacteristic, complemented
44C2×C29×#104C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic
46C2×C29×#104C2211yescharacteristic, complemented
47C29×#418—21no—
48C29×#418C2211yescharacteristic
49C29×#417—21no—
50C29×#417C2211yescharacteristic
51C29×#417C2211yescharacteristic
52C29×#417C2211yescharacteristic, complemented
53C29×#416—21no—
54C29×#416C2211yescharacteristic
55C2×C29×#103C2211yescharacteristic, complemented
56C2×C29×#103C2211yescharacteristic, complemented
57C2×C29×#102—21no—
58C2×C29×#102C2211yescharacteristic
59C2×C29×#102C2211yescharacteristic
60C2×C29×#101C2211yescharacteristic, complemented
61C2×C29×#100C2211yescharacteristic
62C29×#408C2211yescharacteristic
63C2×C29×#97C2211yescharacteristic, complemented
64C29×#384C2211yescharacteristic, complemented
65C29×#343C2211yescharacteristic, complemented
66C29×#343C2211yescharacteristic, complemented
67C29×#341C2211yescharacteristic, complemented
68C29×#339C2211yescharacteristic, complemented
69C29×H(5,𝔽2)—22no—
70C29×H(5,𝔽2)—22no—
71C29×H(5,𝔽2)—22no—
72C29×H(5,𝔽2)—41no—
73C2×#41×C29—21no—
74C2×#41×C29—21no—
75C2×#41×C29C2311yescharacteristic
76C2×#41×C29C2311yescharacteristic
77C2×#41×C29C2311yescharacteristic
78C22×Q8×C29C2311yescharacteristic
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29—41no—
82C22×D4×C29C2311yescharacteristic
83C29×#137—22no—
84C29×#137—22no—
85C29×#137—22no—
86C29×#137—41no—
87C29×AGL(1,ℤ/8)—22no—
88C29×AGL(1,ℤ/8)—41no—
89C29×#135—22no—
90C29×#135—22no—
91C2×Q16×C29—21no—
92C2×Q16×C29—21no—
93C2×Q16×C29D411yescharacteristic
94C2×SD16×C29—21no—
95C2×SD16×C29—21no—
96C2×SD16×C29—21no—
97C2×SD16×C29D411yescharacteristic
98C2×SD16×C29D411yescharacteristic
99C2×D8×C29—21no—
100C2×D8×C29D411yescharacteristic
101C29×#131—22no—
102C29×#131—22no—
103C29×#131—41no—
104C29×#131—41no—
105C2×M16×C29—21no—
106C2×M16×C29—21no—
107C2×M16×C29C2311yescharacteristic
108C2×M16×C29C2311yescharacteristic
109C2×M16×C29C2311yescharacteristic
110C2×M16×C29C2311yescharacteristic
111C22×C8×C29—21no—
112C22×C8×C29—21no—
113C22×C8×C29C2311yescharacteristic
114C22×C8×C29C2311yescharacteristic
115C29×C4⋊Q8—21no—
116C29×#124—21no—
117C29×#124—22no—
118C29×#124—22no—
119C29×#123—41no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8—21no—
122C29×C22⋊Q8—21no—
123C29×C22⋊Q8—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—41no—
127C4×Q8×C29—21no—
128C4×D4×C29—21no—
129C4×D4×C29—41no—
130C29×#117—21no—
131C29×#117C2311yescharacteristic
132C2×C4⋊C4×C29—21no—
133C2×C4⋊C4×C29—41no—
134C2×C4⋊C4×C29C2311yescharacteristic
135C2×C4⋊C4×C29C2311yescharacteristic
136C2×C22⋊C4×C29—41no—
137C2×C42×C29C2311yescharacteristic
138C29×#108—22no—
139C29×#107—21no—
140C29×#106—21no—
141C29×C4⋊C8—21no—
142C29×C4⋊C8—21no—
143C29×#104—22no—
144C29×#104—22no—
145C29×#104D414yescomplemented
146C29×#103—21no—
147C29×#103—21no—
148C29×#103—21no—
149C29×#103—21no—
150C29×#103—21no—
151C29×#103—21no—
152C29×#103—21no—
153C29×#103D411yescharacteristic
154C29×#103D411yescharacteristic
155C29×#102—21no—
156C29×#102—21no—
157C29×#102—21no—
158C29×#102—21no—
159C29×#102—21no—
160C29×#102—21no—
161C29×#102—21no—
162C29×#102—21no—
163C29×#102—21no—
164C29×#102D411yescharacteristic
165C29×#102D411yescharacteristic
166C29×#101—41no—
167C29×#100—22no—
168C29×C22⋊C8—21no—
169C29×C22⋊C8—21no—
170C29×#97—22no—
171C24×C29—21no—
172C24×C29—41no—
173#41×C29—21no—
174#41×C29—21no—
175#41×C29—24no—
176#41×C29—21no—
177#41×C29—21no—
178#41×C29—21no—
179#41×C29—21no—
180#41×C29—21no—
181#41×C29—21no—
182#41×C29—21no—
183#41×C29—21no—
184#41×C29—42no—
185#41×C29—42no—
186#41×C29—42no—
187#41×C29C2×D412yes—
188#41×C29#4112yes—
189C2×Q8×C29—21no—
190C2×Q8×C29—21no—
191C2×Q8×C29—21no—
192C2×Q8×C29—21no—
193C2×Q8×C29—21no—
194C2×Q8×C29—21no—
195C2×Q8×C29C2×D411yescharacteristic
196C2×Q8×C29C2×D411yescharacteristic
197C2×Q8×C29C2×D411yescharacteristic
198C2×D4×C29—21no—
199C2×D4×C29—24no—
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—42no—
208C2×D4×C29—41no—
209C2×D4×C29—41no—
210C2×D4×C29—42no—
211C2×D4×C29—44no—
212C2×D4×C29—44no—
213C2×D4×C29—42no—
214C2×D4×C29—41no—
215C2×D4×C29C2×D411yescharacteristic
216C2×D4×C29C2×D411yescharacteristic
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—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29—41no—
227C22×C4×C29—41no—
228C22×C4×C29C2411yescharacteristic
229Q16×C29—22no—
230Q16×C29—42no—
231Q16×C29—42no—
232SD16×C29—22no—
233SD16×C29—22no—
234SD16×C29—42no—
235SD16×C29—42no—
236SD16×C29—42no—
237D8×C29—22no—
238D8×C29—42no—
239M16×C29—21no—
240M16×C29—21no—
241M16×C29—21no—
242M16×C29—21no—
243M16×C29—21no—
244M16×C29—21no—
245M16×C29—21no—
246M16×C29—42no—
247M16×C29—42no—
248M16×C29C2×D412yes—
249C2×C8×C29—21no—
250C2×C8×C29—21no—
251C2×C8×C29—21no—
252C2×C8×C29—21no—
253C2×C8×C29—21no—
254C2×C8×C29—21no—
255C2×C8×C29—21no—
256C2×C8×C29—21no—
257C2×C8×C29—42no—
258C2×C8×C29—42no—
259C2×C8×C29C2×D411yescharacteristic
260C2×C8×C29C2×D411yescharacteristic
261C2×C8×C29C2×D411yescharacteristic
262C2×C8×C29C2×D411yescharacteristic
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—41no—
268C4⋊C4×C29—41no—
269C4⋊C4×C29—41no—
270C4⋊C4×C29—41no—
271C4⋊C4×C29—82no—
272C4⋊C4×C29C2×D411yescharacteristic
273C4⋊C4×C29C2×D411yescharacteristic
274C22⋊C4×C29—21no—
275C22⋊C4×C29—44no—
276C22⋊C4×C29—41no—
277C22⋊C4×C29—41no—
278C22⋊C4×C29—41no—
279C22⋊C4×C29—41no—
280C22⋊C4×C29—41no—
281C42×C29—21no—
282C42×C29—21no—
283C42×C29—41no—
284C42×C29C2×D412yes—
285#25195C2911yesmaximal, characteristic, direct product factor, Sylow
286C23×C29—21no—
287C23×C29—21no—
288C23×C29—21no—
289C23×C29—22no—
290C23×C29—44no—
291C23×C29—41no—
292C23×C29—41no—
293C23×C29—81no—
294C23×C29—81no—
295C23×C29—161no—
296C23×C29—161no—
297C23×C29H(5,𝔽2)11yescharacteristic
298Q8×C29—21no—
299Q8×C29—21no—
300Q8×C29—21no—
301Q8×C29—21no—
302Q8×C29—21no—
303Q8×C29—41no—
304Q8×C29—41no—
305Q8×C29—41no—
306Q8×C29—41no—
307Q8×C29#12112yes—
308D4×C29—22no—
309D4×C29—22no—
310D4×C29—21no—
311D4×C29—21no—
312D4×C29—22no—
313D4×C29—21no—
314D4×C29—21no—
315D4×C29—21no—
316D4×C29—22no—
317D4×C29—44no—
318D4×C29—44no—
319D4×C29—41no—
320D4×C29—41no—
321D4×C29—41no—
322D4×C29—41no—
323D4×C29—41no—
324D4×C29—41no—
325D4×C29—161no—
326D4×C29#12112yes—
327C2×C4×C29—21no—
328C2×C4×C29—22no—
329C2×C4×C29—22no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—21no—
333C2×C4×C29—21no—
334C2×C4×C29—22no—
335C2×C4×C29—44no—
336C2×C4×C29—41no—
337C2×C4×C29—41no—
338C2×C4×C29—41no—
339C2×C4×C29—41no—
340C2×C4×C29—41no—
341C2×C4×C29—41no—
342C2×C4×C29—41no—
343C2×C4×C29—41no—
344C2×C4×C29—41no—
345C2×C4×C29—41no—
346C2×C4×C29—41no—
347C2×C4×C29—81no—
348C2×C4×C29—81no—
349C2×C4×C29—161no—
350C2×C4×C29C22×D411yescharacteristic
351C2×C4×C29C22×D411yescharacteristic
352C2×C4×C29C22×D411yescharacteristic
353C2×C4×C29C2×#4111yescharacteristic
354C2×C4×C29C2×#4111yescharacteristic
355C2×C4×C29H(5,𝔽2)11yescharacteristic
356C8×C29—21no—
357C8×C29—21no—
358C8×C29—21no—
359C8×C29—21no—
360C8×C29—22no—
361C8×C29—41no—
362C8×C29—41no—
363C8×C29—41no—
364#3063C2×C2911yescharacteristic, complemented
365#3046C2×C2911yescharacteristic, complemented
366C2×#455C2×C2911yescharacteristic, complemented
367#3012C2×C2911yescharacteristic
368C2×#444C2×C2911yescharacteristic, complemented
369#2897C2×C2911yescharacteristic, complemented
370#2063C2×C2911yescharacteristic, complemented
371#2052C2×C2911yescharacteristic, complemented
372#2039C2×C2911yescharacteristic, complemented
373#2003C2×C2911yescharacteristic, complemented
374#1959C2×C2911yescharacteristic, complemented
375#1938C2×C2911yescharacteristic, complemented
376#1908C2×C2911yescharacteristic, complemented
377#1907C2×C2911yescharacteristic, complemented
378#1859C2×C2911yescharacteristic, complemented
379C22×C29—21no—
380C22×C29—21no—
381C22×C29—22no—
382C22×C29—41no—
383C22×C29—41no—
384C22×C29—41no—
385C22×C29—42no—
386C22×C29—41no—
387C22×C29—41no—
388C22×C29—41no—
389C22×C29—41no—
390C22×C29—41no—
391C22×C29—82no—
392C22×C29—81no—
393C22×C29—81no—
394C22×C29—161no—
395C22×C29—164no—
396C22×C29#53811yescharacteristic
397C22×C29D4211yescharacteristic
398C22×C29#54611yescharacteristic
399C4×C29—22no—
400C4×C29—42no—
401C4×C29—41no—
402C4×C29—41no—
403C4×C29—41no—
404C4×C29—41no—
405C4×C29—81no—
406C4×C29—81no—
407C4×C29—81no—
408C4×C29C2×#12111yescharacteristic
409C4×C29#52511yescharacteristic
410C4×C29D4211yescharacteristic
411C4×C29#54611yescharacteristic
412C2×H(5,𝔽2)C22×C2911yescharacteristic
413C2×#137C22×C2911yescharacteristic
414C2×#137C22×C2911yescharacteristic
415C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
416C2×#135C22×C2911yescharacteristic
417C2×#131C22×C2911yescharacteristic
418C2×#131C22×C2911yescharacteristic, complemented
419#537C22×C2911yescharacteristic
420#536C22×C2911yescharacteristic, complemented
421C2×#124C22×C2911yescharacteristic
422#520C22×C2911yescharacteristic
423#470—21no—
424#468—21no—
425#467—21no—
426#465—21no—
427#464—21no—
428#463—21no—
429#462—21no—
430#461—21no—
431#455—24no—
432#452—21no—
433#450—21no—
434#449—21no—
435#447—21no—
436#444—24no—
437C2×#108C22×C2911yescharacteristic, complemented
438#428C22×C2911yescharacteristic, complemented
439#424C22×C2911yescharacteristic, complemented
440C2×#104C22×C2911yescharacteristic
441C2×#104C22×C2911yescharacteristic
442C2×#104C22×C2911yescharacteristic, complemented
443#418—21no—
444#418C22×C2911yescharacteristic
445#417—21no—
446#417C22×C2911yescharacteristic
447#417C22×C2911yescharacteristic
448#417C22×C2911yescharacteristic, complemented
449#416—21no—
450#416C22×C2911yescharacteristic
451C2×#103C22×C2911yescharacteristic, complemented
452C2×#103C22×C2911yescharacteristic, complemented
453C2×#102—21no—
454C2×#102C22×C2911yescharacteristic
455C2×#102C22×C2911yescharacteristic
456C2×#101C22×C2911yescharacteristic, complemented
457C2×#100C22×C2911yescharacteristic
458#408C22×C2911yescharacteristic
459C2×#97C22×C2911yescharacteristic, complemented
460#384C22×C2911yescharacteristic, complemented
461#343C22×C2911yescharacteristic, complemented
462#343C22×C2911yescharacteristic, complemented
463#341C22×C2911yescharacteristic, complemented
464#339C22×C2911yescharacteristic, complemented
465C2×C29—21no—
466C2×C29—21no—
467C2×C29—42no—
468C2×C29—81no—
469C2×C29—81no—
470C2×C29—82no—
471C2×C29#242411yescharacteristic
472C2×C29#328811yescharacteristic
473C2×C29#328911yescharacteristic
474H(5,𝔽2)—22no—
475H(5,𝔽2)—22no—
476H(5,𝔽2)—22no—
477H(5,𝔽2)—41no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41C23×C2911yescharacteristic
481C2×#41C23×C2911yescharacteristic
482C2×#41C23×C2911yescharacteristic
483C22×Q8C23×C2911yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—41no—
487C22×D4C23×C2911yescharacteristic
488#137—22no—
489#137—22no—
490#137—22no—
491#137—41no—
492AGL(1,ℤ/8)—22no—
493AGL(1,ℤ/8)—41no—
494#135—22no—
495#135—22no—
496C2×Q16—21no—
497C2×Q16—21no—
498C2×Q16D4×C2911yescharacteristic
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—21no—
502C2×SD16D4×C2911yescharacteristic
503C2×SD16D4×C2911yescharacteristic
504C2×D8—21no—
505C2×D8D4×C2911yescharacteristic
506#131—22no—
507#131—22no—
508#131—41no—
509#131—41no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16C23×C2911yescharacteristic
513C2×M16C23×C2911yescharacteristic
514C2×M16C23×C2911yescharacteristic
515C2×M16C23×C2911yescharacteristic
516C22×C8—21no—
517C22×C8—21no—
518C22×C8C23×C2911yescharacteristic
519C22×C8C23×C2911yescharacteristic
520C4⋊Q8—21no—
521#124—21no—
522#124—22no—
523#124—22no—
524#123—41no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532C4×Q8—21no—
533C4×D4—21no—
534C4×D4—41no—
535#117—21no—
536#117C23×C2911yescharacteristic
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4C23×C2911yescharacteristic
540C2×C4⋊C4C23×C2911yescharacteristic
541C2×C22⋊C4—41no—
542C2×C42C23×C2911yescharacteristic
543#108—22no—
544#107—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548#104—22no—
549#104—22no—
550#104D4×C2914yescomplemented
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#103D4×C2911yescharacteristic
559#103D4×C2911yescharacteristic
560#102—21no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102D4×C2911yescharacteristic
570#102D4×C2911yescharacteristic
571#101—41no—
572#100—22no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575#97—22no—
576C29#2519511yescharacteristic, direct product factor, Sylow
577C24—21no—
578C24—41no—
579#41—21no—
580#41—21no—
581#41—24no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—21no—
586#41—21no—
587#41—21no—
588#41—21no—
589#41—21no—
590#41—42no—
591#41—42no—
592#41—42no—
593#41C2×D4×C2912yes—
594#41#41×C2912yes—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C2911yescharacteristic
602C2×Q8C2×D4×C2911yescharacteristic
603C2×Q8C2×D4×C2911yescharacteristic
604C2×D4—21no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—42no—
620C2×D4—41no—
621C2×D4C2×D4×C2911yescharacteristic
622C2×D4C2×D4×C2911yescharacteristic
623C2×D4C2×D4×C2911yescharacteristic
624C2×D4#41×C2912yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4C24×C2911yescharacteristic
635Q16—22no—
636Q16—42no—
637Q16—42no—
638SD16—22no—
639SD16—22no—
640SD16—42no—
641SD16—42no—
642SD16—42no—
643D8—22no—
644D8—42no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—42no—
653M16—42no—
654M16C2×D4×C2912yes—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8C2×D4×C2911yescharacteristic
666C2×C8C2×D4×C2911yescharacteristic
667C2×C8C2×D4×C2911yescharacteristic
668C2×C8C2×D4×C2911yescharacteristic
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—82no—
678C4⋊C4C2×D4×C2911yescharacteristic
679C4⋊C4C2×D4×C2911yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—44no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C42—21no—
688C42—21no—
689C42—41no—
690C42C2×D4×C2912yes—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—41no—
698C23—81no—
699C23—81no—
700C23—161no—
701C23—161no—
702C23C29×H(5,𝔽2)11yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—21no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8C29×#12112yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—21no—
717D4—22no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—22no—
722D4—44no—
723D4—44no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—161no—
731D4C29×#12112yes—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—161no—
755C2×C4C22×D4×C2911yescharacteristic
756C2×C4C22×D4×C2911yescharacteristic
757C2×C4C22×D4×C2911yescharacteristic
758C2×C4C2×#41×C2911yescharacteristic
759C2×C4C2×#41×C2911yescharacteristic
760C2×C4C29×H(5,𝔽2)11yescharacteristic
761C8—21no—
762C8—21no—
763C8—21no—
764C8—21no—
765C8—22no—
766C8—41no—
767C8—41no—
768C8—41no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—82no—
782C22—81no—
783C22—81no—
784C22—161no—
785C22—164no—
786C22C29×#53811yescharacteristic
787C22D42×C2911yescharacteristic
788C22C29×#54611yescharacteristic
789C4—22no—
790C4—42no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4C2×C29×#12111yescharacteristic
799C4C29×#52511yescharacteristic
800C4D42×C2911yescharacteristic
801C4C29×#54611yescharacteristic
802C2—21no—
803C2—21no—
804C2—42no—
805C2—81no—
806C2—81no—
807C2—82no—
808C2C29×#242411yescharacteristic
809C2C29×#328811yescharacteristic
810C2C29×#328911yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3012C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3063C2semidirect
2. C29×#3046C2semidirect
3. C2×C29×#455C2semidirect
5. C2×C29×#444C2semidirect
6. C29×#2897C2semidirect
7. C29×#2063C2semidirect
8. C29×#2052C2semidirect
9. C29×#2039C2semidirect
10. C29×#2003C2semidirect
11. C29×#1959C2semidirect
12. C29×#1938C2semidirect
13. C29×#1908C2semidirect
14. C29×#1907C2semidirect
15. C29×#1859C2semidirect
22. C2×C29×#131C22semidirect
24. C29×#536C22semidirect
41. C2×C29×#108C22semidirect
42. C29×#428C22semidirect
43. C29×#424C22semidirect
46. C2×C29×#104C22semidirect
52. C29×#417C22semidirect
55. C2×C29×#103C22semidirect
56. C2×C29×#103C22semidirect
60. C2×C29×#101C22semidirect
63. C2×C29×#97C22semidirect
64. C29×#384C22semidirect
65. C29×#343C22semidirect
66. C29×#343C22semidirect
67. C29×#341C22semidirect
68. C29×#339C22semidirect
145. C29×#104D4semidirect
285. #25195C29direct (N × H)
364. #3063C2×C29semidirect
365. #3046C2×C29semidirect
366. C2×#455C2×C29semidirect
368. C2×#444C2×C29semidirect
369. #2897C2×C29semidirect
370. #2063C2×C29semidirect
371. #2052C2×C29semidirect
372. #2039C2×C29semidirect
373. #2003C2×C29semidirect
374. #1959C2×C29semidirect
375. #1938C2×C29semidirect
376. #1908C2×C29semidirect
377. #1907C2×C29semidirect
378. #1859C2×C29semidirect
418. C2×#131C22×C29semidirect
420. #536C22×C29semidirect
437. C2×#108C22×C29semidirect
438. #428C22×C29semidirect
439. #424C22×C29semidirect
442. C2×#104C22×C29semidirect
448. #417C22×C29semidirect
451. C2×#103C22×C29semidirect
452. C2×#103C22×C29semidirect
456. C2×#101C22×C29semidirect
459. C2×#97C22×C29semidirect
460. #384C22×C29semidirect
461. #343C22×C29semidirect
462. #343C22×C29semidirect
463. #341C22×C29semidirect
464. #339C22×C29semidirect
550. #104D4×C29semidirect
576. C29#25195direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30632
C29×#30462
C2×C29×#4552
C29×#30122
C2×C29×#4442
C29×#28972
C29×#20632
C29×#20522
C29×#20392
C29×#20032
C29×#19592
C29×#19382
C29×#19082
C29×#19072
C29×#18592
#2519529