Finite Group Databasebeta

← C29×#25187 #20320087

Subgroups — C29×#25187 #20320087

Order 7424.

1050 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#471C211yesmaximal, characteristic, complemented
2C29×#3042C211yesmaximal, characteristic, complemented
3C2×C29×#453C211yesmaximal, characteristic
4C29×#3009C211yesmaximal, characteristic, complemented
5C29×#2946C211yesmaximal, characteristic, complemented
6C29×#2897C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic, complemented
8C29×#2051C211yesmaximal, characteristic, complemented
9C29×#2038C211yesmaximal, characteristic, complemented
10C29×#2014C211yesmaximal, characteristic, complemented
11C29×#1977C211yesmaximal, characteristic, complemented
12C29×#1929C211yesmaximal, characteristic, complemented
13C29×#1887C211yesmaximal, characteristic, complemented
14C29×#1882C211yesmaximal, characteristic, complemented
15C29×#1866C211yesmaximal, characteristic, complemented
16C2×C29×H(5,𝔽2)C2211yescharacteristic
17C2×C29×#137C2211yescharacteristic
18C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C22×SD16×C29C2211yescharacteristic
21C22×SD16×C29C2211yescharacteristic, complemented
22C2×C29×#131C2211yescharacteristic
23C29×#536C2211yescharacteristic
24C2×C29×#127C2211yescharacteristic
25C29×#520C2211yescharacteristic
26C29×#518C2211yescharacteristic, complemented
27C29×#471—24no—
28C29×#463—21no—
29C29×#463—21no—
30C29×#461—21no—
31C29×#461—21no—
32C29×#453—24no—
33C29×#452—21no—
34C29×#452—21no—
35C29×#450—21no—
36C29×#450—21no—
37C29×#442—21no—
38C29×#440—21no—
39C4×SD16×C29—21no—
40C4×D8×C29—21no—
41C2×C29×#108C2211yescharacteristic, complemented
42C2×C29×#108C2211yescharacteristic, complemented
43C29×#428C2211yescharacteristic, complemented
44C29×#424C2211yescharacteristic, complemented
45C2×C29×#104C2211yescharacteristic
46C2×C29×#104C2211yescharacteristic
47C29×#419C2211yescharacteristic, complemented
48C29×#418—21no—
49C29×#418C2211yescharacteristic
50C29×#418C2211yescharacteristic
51C29×#417—21no—
52C29×#417C2211yescharacteristic
53C29×#416—21no—
54C29×#416C2211yescharacteristic
55C29×#416C2211yescharacteristic
56C2×C29×#102—21no—
57C2×C29×#102C2211yescharacteristic
58C2×C29×#102C2211yescharacteristic, complemented
59C2×C29×#101C2211yescharacteristic, complemented
60C2×C29×#100C2211yescharacteristic
61C2×C29×#100C2211yescharacteristic, complemented
62C29×#408C2211yescharacteristic
63C29×#405C2211yescharacteristic, complemented
64C29×#391C2211yescharacteristic, complemented
65C29×#343C2211yescharacteristic, complemented
66C29×#339C2211yescharacteristic, complemented
67C29×#339C2211yescharacteristic, complemented
68C29×#336C2211yescharacteristic, 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
77C22×Q8×C29C2311yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29—41no—
81C22×D4×C29—41no—
82C22×D4×C29C2311yescharacteristic
83C22×D4×C29C2311yescharacteristic
84C29×#137—22no—
85C29×#137—22no—
86C29×AGL(1,ℤ/8)—22no—
87C29×AGL(1,ℤ/8)—22no—
88C29×AGL(1,ℤ/8)—41no—
89C29×AGL(1,ℤ/8)D414yes—
90C2×Q16×C29—21no—
91C2×SD16×C29—21no—
92C2×SD16×C29—21no—
93C2×SD16×C29—21no—
94C2×SD16×C29—22no—
95C2×SD16×C29—22no—
96C2×SD16×C29—21no—
97C2×SD16×C29—21no—
98C2×SD16×C29—21no—
99C2×SD16×C29—21no—
100C2×SD16×C29—41no—
101C2×SD16×C29—41no—
102C2×D8×C29—21no—
103C2×D8×C29—21no—
104C29×#131—22no—
105C29×#131—41no—
106C2×M16×C29—21no—
107C2×M16×C29C2311yescharacteristic
108C2×M16×C29C2311yescharacteristic
109C2×M16×C29C2311yescharacteristic
110C2×M16×C29C2311yescharacteristic
111C22×C8×C29—21no—
112C22×C8×C29C2311yescharacteristic
113C22×C8×C29C2311yescharacteristic
114C29×C4⋊Q8—21no—
115C29×#127—22no—
116C29×#127—22no—
117C29×#124—21no—
118C29×#123—41no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C4×Q8×C29—21no—
122C4×D4×C29—21no—
123C4×D4×C29—21no—
124C4×D4×C29—21no—
125C4×D4×C29—21no—
126C4×D4×C29—21no—
127C4×D4×C29—41no—
128C29×#117—21no—
129C29×#117C2311yescharacteristic
130C29×#117C2311yescharacteristic
131C2×C4⋊C4×C29—21no—
132C2×C4⋊C4×C29C2311yescharacteristic
133C2×C22⋊C4×C29—41no—
134C2×C42×C29C2311yescharacteristic
135C29×#108—22no—
136C29×#108—41no—
137C29×#107—21no—
138C29×#106—21no—
139C29×C4⋊C8—21no—
140C29×C4⋊C8—21no—
141C29×#104—22no—
142C29×#104—22no—
143C29×#103—21no—
144C29×#103—21no—
145C29×#103—21no—
146C29×#103D411yescharacteristic, complemented
147C29×#103D411yescharacteristic, complemented
148C29×#103D411yescharacteristic, complemented
149C29×#103D411yescharacteristic, complemented
150C29×#102—21no—
151C29×#102—21no—
152C29×#102—21no—
153C29×#102—21no—
154C29×#102—21no—
155C29×#102—21no—
156C29×#102—21no—
157C29×#102—21no—
158C29×#102—21no—
159C29×#102D411yescharacteristic, complemented
160C29×#102D411yescharacteristic, complemented
161C29×#102D411yescharacteristic, complemented
162C29×#102D411yescharacteristic, complemented
163C29×#101—22no—
164C29×#100—22no—
165C29×#100—22no—
166C29×C22⋊C8—21no—
167C29×C22⋊C8—21no—
168C29×#97—21no—
169C4×C8×C29—21no—
170C29×#95—41no—
171C24×C29—21no—
172C24×C29—21no—
173C24×C29—41no—
174#41×C29—21no—
175#41×C29—21no—
176#41×C29—24no—
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×C29C2×D412yes—
185#41×C29#4112yes—
186C2×Q8×C29—21no—
187C2×Q8×C29—21no—
188C2×Q8×C29—21no—
189C2×Q8×C29—21no—
190C2×Q8×C29—21no—
191C2×Q8×C29—21no—
192C2×Q8×C29C2×D411yescharacteristic
193C2×Q8×C29C2×D411yescharacteristic
194C2×D4×C29—21no—
195C2×D4×C29—24no—
196C2×D4×C29—21no—
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—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—44no—
215C2×D4×C29—82no—
216C2×D4×C29—82no—
217C2×D4×C29C2×D411yescharacteristic
218C2×D4×C29C2×D412yes—
219C2×D4×C29C2×D411yescharacteristic
220C2×D4×C29#4112yes—
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×C29—41no—
229C22×C4×C29—41no—
230C22×C4×C29C2411yescharacteristic
231Q16×C29—42no—
232SD16×C29—24no—
233SD16×C29—42no—
234SD16×C29—42no—
235SD16×C29—42no—
236SD16×C29—42no—
237SD16×C29—42no—
238SD16×C29—42no—
239D8×C29—24no—
240D8×C29—42no—
241M16×C29—21no—
242M16×C29—21no—
243M16×C29—21no—
244M16×C29—21no—
245M16×C29—21no—
246M16×C29—21no—
247M16×C29—21no—
248M16×C29—42no—
249M16×C29C2×D412yes—
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—21no—
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—41no—
266C4⋊C4×C29—41no—
267C4⋊C4×C29—41no—
268C4⋊C4×C29C2×D411yescharacteristic
269C4⋊C4×C29C2×D411yescharacteristic
270C4⋊C4×C29C2×D411yescharacteristic
271C4⋊C4×C29C2×D411yescharacteristic
272C22⋊C4×C29—21no—
273C22⋊C4×C29—21no—
274C22⋊C4×C29—41no—
275C22⋊C4×C29—41no—
276C22⋊C4×C29—41no—
277C22⋊C4×C29—41no—
278C22⋊C4×C29—41no—
279C42×C29—21no—
280C42×C29—21no—
281C42×C29—21no—
282C42×C29—21no—
283C42×C29—41no—
284#25187C2911yesmaximal, characteristic, direct product factor, Sylow
285C23×C29—21no—
286C23×C29—21no—
287C23×C29—22no—
288C23×C29—22no—
289C23×C29—44no—
290C23×C29—41no—
291C23×C29—41no—
292C23×C29—41no—
293C23×C29—41no—
294C23×C29—81no—
295C23×C29—81no—
296C23×C29—81no—
297C23×C29—81no—
298C23×C29—161no—
299C23×C29—161no—
300C23×C29H(5,𝔽2)11yescharacteristic
301Q8×C29—21no—
302Q8×C29—21no—
303Q8×C29—21no—
304Q8×C29—41no—
305Q8×C29—41no—
306Q8×C29—41no—
307Q8×C29—41no—
308Q8×C29#12112yes—
309D4×C29—22no—
310D4×C29—22no—
311D4×C29—22no—
312D4×C29—21no—
313D4×C29—22no—
314D4×C29—21no—
315D4×C29—22no—
316D4×C29—21no—
317D4×C29—22no—
318D4×C29—44no—
319D4×C29—44no—
320D4×C29—41no—
321D4×C29—41no—
322D4×C29—41no—
323D4×C29—41no—
324D4×C29—41no—
325D4×C29—41no—
326D4×C29—88no—
327D4×C29#12112yes—
328C2×C4×C29—21no—
329C2×C4×C29—22no—
330C2×C4×C29—22no—
331C2×C4×C29—22no—
332C2×C4×C29—21no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—21no—
336C2×C4×C29—21no—
337C2×C4×C29—44no—
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—81no—
347C2×C4×C29—161no—
348C2×C4×C29—161no—
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—22no—
357C8×C29—21no—
358C8×C29—21no—
359C8×C29—21no—
360C8×C29—21no—
361C8×C29—41no—
362C8×C29—41no—
363C8×C29—41no—
364C2×#471C2×C2911yescharacteristic, complemented
365#3042C2×C2911yescharacteristic, complemented
366C2×#453C2×C2911yescharacteristic
367#3009C2×C2911yescharacteristic, complemented
368#2946C2×C2911yescharacteristic, complemented
369#2897C2×C2911yescharacteristic, complemented
370#2063C2×C2911yescharacteristic, complemented
371#2051C2×C2911yescharacteristic, complemented
372#2038C2×C2911yescharacteristic, complemented
373#2014C2×C2911yescharacteristic, complemented
374#1977C2×C2911yescharacteristic, complemented
375#1929C2×C2911yescharacteristic, complemented
376#1887C2×C2911yescharacteristic, complemented
377#1882C2×C2911yescharacteristic, complemented
378#1866C2×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—42no—
387C22×C29—41no—
388C22×C29—41no—
389C22×C29—82no—
390C22×C29—82no—
391C22×C29—81no—
392C22×C29—81no—
393C22×C29—81no—
394C22×C29—81no—
395C22×C29—161no—
396C22×C29—161no—
397C22×C29—164no—
398C22×C29#53811yescharacteristic
399C22×C29D4211yescharacteristic
400C22×C29#54611yescharacteristic
401C4×C29—22no—
402C4×C29—42no—
403C4×C29—41no—
404C4×C29—41no—
405C4×C29—41no—
406C4×C29—41no—
407C4×C29—41no—
408C4×C29—81no—
409C4×C29—81no—
410C4×C29C2×#12111yescharacteristic
411C4×C29#52511yescharacteristic
412C4×C29D4211yescharacteristic
413C4×C29#54611yescharacteristic
414C2×H(5,𝔽2)C22×C2911yescharacteristic
415C2×#137C22×C2911yescharacteristic
416C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
417C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
418C22×SD16C22×C2911yescharacteristic
419C22×SD16C22×C2911yescharacteristic, complemented
420C2×#131C22×C2911yescharacteristic
421#536C22×C2911yescharacteristic
422C2×#127C22×C2911yescharacteristic
423#520C22×C2911yescharacteristic
424#518C22×C2911yescharacteristic, complemented
425#471—24no—
426#463—21no—
427#463—21no—
428#461—21no—
429#461—21no—
430#453—24no—
431#452—21no—
432#452—21no—
433#450—21no—
434#450—21no—
435#442—21no—
436#440—21no—
437C4×SD16—21no—
438C4×D8—21no—
439C2×#108C22×C2911yescharacteristic, complemented
440C2×#108C22×C2911yescharacteristic, complemented
441#428C22×C2911yescharacteristic, complemented
442#424C22×C2911yescharacteristic, complemented
443C2×#104C22×C2911yescharacteristic
444C2×#104C22×C2911yescharacteristic
445#419C22×C2911yescharacteristic, complemented
446#418—21no—
447#418C22×C2911yescharacteristic
448#418C22×C2911yescharacteristic
449#417—21no—
450#417C22×C2911yescharacteristic
451#416—21no—
452#416C22×C2911yescharacteristic
453#416C22×C2911yescharacteristic
454C2×#102—21no—
455C2×#102C22×C2911yescharacteristic
456C2×#102C22×C2911yescharacteristic, complemented
457C2×#101C22×C2911yescharacteristic, complemented
458C2×#100C22×C2911yescharacteristic
459C2×#100C22×C2911yescharacteristic, complemented
460#408C22×C2911yescharacteristic
461#405C22×C2911yescharacteristic, complemented
462#391C22×C2911yescharacteristic, complemented
463#343C22×C2911yescharacteristic, complemented
464#339C22×C2911yescharacteristic, complemented
465#339C22×C2911yescharacteristic, complemented
466#336C22×C2911yescharacteristic, complemented
467C2×C29—21no—
468C2×C29—21no—
469C2×C29—42no—
470C2×C29—81no—
471C2×C29—82no—
472C2×C29—82no—
473C2×C29#242411yescharacteristic
474C2×C29#328811yescharacteristic
475C2×C29#329111yescharacteristic
476H(5,𝔽2)—22no—
477H(5,𝔽2)—22no—
478H(5,𝔽2)—22no—
479H(5,𝔽2)—41no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41C23×C2911yescharacteristic
483C2×#41C23×C2911yescharacteristic
484C22×Q8C23×C2911yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4C23×C2911yescharacteristic
490C22×D4C23×C2911yescharacteristic
491#137—22no—
492#137—22no—
493AGL(1,ℤ/8)—22no—
494AGL(1,ℤ/8)—22no—
495AGL(1,ℤ/8)—41no—
496AGL(1,ℤ/8)D4×C2914yes—
497C2×Q16—21no—
498C2×SD16—21no—
499C2×SD16—21no—
500C2×SD16—22no—
501C2×SD16—21no—
502C2×SD16—22no—
503C2×SD16—21no—
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—21no—
510C2×D8—21no—
511#131—22no—
512#131—41no—
513C2×M16—21no—
514C2×M16C23×C2911yescharacteristic
515C2×M16C23×C2911yescharacteristic
516C2×M16C23×C2911yescharacteristic
517C2×M16C23×C2911yescharacteristic
518C22×C8—21no—
519C22×C8C23×C2911yescharacteristic
520C22×C8C23×C2911yescharacteristic
521C4⋊Q8—21no—
522#127—22no—
523#127—22no—
524#124—21no—
525#123—41no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C4×Q8—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—41no—
535#117—21no—
536#117C23×C2911yescharacteristic
537#117C23×C2911yescharacteristic
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C2911yescharacteristic
540C2×C22⋊C4—41no—
541C2×C42C23×C2911yescharacteristic
542#108—22no—
543#108—41no—
544#107—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548#104—22no—
549#104—22no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C2911yescharacteristic, complemented
554#103D4×C2911yescharacteristic, complemented
555#103D4×C2911yescharacteristic, complemented
556#103D4×C2911yescharacteristic, complemented
557#102—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102D4×C2911yescharacteristic, complemented
567#102D4×C2911yescharacteristic, complemented
568#102D4×C2911yescharacteristic, complemented
569#102D4×C2911yescharacteristic, complemented
570#101—22no—
571#100—22no—
572#100—22no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577#95—41no—
578C29#2518711yescharacteristic, direct product factor, Sylow
579C24—21no—
580C24—21no—
581C24—41no—
582#41—21no—
583#41—21no—
584#41—24no—
585#41—21no—
586#41—21no—
587#41—21no—
588#41—21no—
589#41—42no—
590#41—42no—
591#41—42no—
592#41C2×D4×C2912yes—
593#41#41×C2912yes—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8C2×D4×C2911yescharacteristic
601C2×Q8C2×D4×C2911yescharacteristic
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—42no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—44no—
623C2×D4—82no—
624C2×D4—82no—
625C2×D4C2×D4×C2912yes—
626C2×D4C2×D4×C2911yescharacteristic
627C2×D4C2×D4×C2911yescharacteristic
628C2×D4#41×C2912yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4C24×C2911yescharacteristic
639Q16—42no—
640SD16—24no—
641SD16—42no—
642SD16—42no—
643SD16—42no—
644SD16—42no—
645SD16—42no—
646SD16—42no—
647D8—24no—
648D8—42no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16—42no—
657M16C2×D4×C2912yes—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—42no—
667C2×C8C2×D4×C2911yescharacteristic
668C2×C8C2×D4×C2911yescharacteristic
669C2×C8C2×D4×C2911yescharacteristic
670C2×C8C2×D4×C2911yescharacteristic
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4C2×D4×C2911yescharacteristic
677C4⋊C4C2×D4×C2911yescharacteristic
678C4⋊C4C2×D4×C2911yescharacteristic
679C4⋊C4C2×D4×C2911yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—41no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—22no—
696C23—44no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23—81no—
705C23—161no—
706C23—161no—
707C23C29×H(5,𝔽2)11yescharacteristic
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8C29×#12112yes—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—21no—
720D4—22no—
721D4—21no—
722D4—22no—
723D4—21no—
724D4—22no—
725D4—44no—
726D4—44no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—88no—
734D4C29×#12112yes—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—44no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—81no—
754C2×C4—161no—
755C2×C4—161no—
756C2×C4—161no—
757C2×C4C22×D4×C2911yescharacteristic
758C2×C4C22×D4×C2911yescharacteristic
759C2×C4C22×D4×C2911yescharacteristic
760C2×C4C2×#41×C2911yescharacteristic
761C2×C4C2×#41×C2911yescharacteristic
762C2×C4C29×H(5,𝔽2)11yescharacteristic
763C8—22no—
764C8—21no—
765C8—21no—
766C8—21no—
767C8—21no—
768C8—41no—
769C8—41no—
770C8—41no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—82no—
782C22—82no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—161no—
788C22—161no—
789C22—164no—
790C22C29×#53811yescharacteristic
791C22D42×C2911yescharacteristic
792C22C29×#54611yescharacteristic
793C4—22no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—81no—
801C4—81no—
802C4C2×C29×#12111yescharacteristic
803C4C29×#52511yescharacteristic
804C4D42×C2911yescharacteristic
805C4C29×#54611yescharacteristic
806C2—21no—
807C2—21no—
808C2—42no—
809C2—81no—
810C2—82no—
811C2—82no—
812C2C29×#242411yescharacteristic
813C2C29×#328811yescharacteristic
814C2C29×#329111yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#453C2
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. C2×C29×#471C2semidirect
2. C29×#3042C2semidirect
4. C29×#3009C2semidirect
5. C29×#2946C2semidirect
6. C29×#2897C2semidirect
7. C29×#2063C2semidirect
8. C29×#2051C2semidirect
9. C29×#2038C2semidirect
10. C29×#2014C2semidirect
11. C29×#1977C2semidirect
12. C29×#1929C2semidirect
13. C29×#1887C2semidirect
14. C29×#1882C2semidirect
15. C29×#1866C2semidirect
21. C22×SD16×C29C22semidirect
26. C29×#518C22semidirect
41. C2×C29×#108C22semidirect
42. C2×C29×#108C22semidirect
43. C29×#428C22semidirect
44. C29×#424C22semidirect
47. C29×#419C22semidirect
58. C2×C29×#102C22semidirect
59. C2×C29×#101C22semidirect
61. C2×C29×#100C22semidirect
63. C29×#405C22semidirect
64. C29×#391C22semidirect
65. C29×#343C22semidirect
66. C29×#339C22semidirect
67. C29×#339C22semidirect
68. C29×#336C22semidirect
146. C29×#103D4semidirect
147. C29×#103D4semidirect
148. C29×#103D4semidirect
149. C29×#103D4semidirect
159. C29×#102D4semidirect
160. C29×#102D4semidirect
161. C29×#102D4semidirect
162. C29×#102D4semidirect
284. #25187C29direct (N × H)
364. C2×#471C2×C29semidirect
365. #3042C2×C29semidirect
367. #3009C2×C29semidirect
368. #2946C2×C29semidirect
369. #2897C2×C29semidirect
370. #2063C2×C29semidirect
371. #2051C2×C29semidirect
372. #2038C2×C29semidirect
373. #2014C2×C29semidirect
374. #1977C2×C29semidirect
375. #1929C2×C29semidirect
376. #1887C2×C29semidirect
377. #1882C2×C29semidirect
378. #1866C2×C29semidirect
419. C22×SD16C22×C29semidirect
424. #518C22×C29semidirect
439. C2×#108C22×C29semidirect
440. C2×#108C22×C29semidirect
441. #428C22×C29semidirect
442. #424C22×C29semidirect
445. #419C22×C29semidirect
456. C2×#102C22×C29semidirect
457. C2×#101C22×C29semidirect
459. C2×#100C22×C29semidirect
461. #405C22×C29semidirect
462. #391C22×C29semidirect
463. #343C22×C29semidirect
464. #339C22×C29semidirect
465. #339C22×C29semidirect
466. #336C22×C29semidirect
553. #103D4×C29semidirect
554. #103D4×C29semidirect
555. #103D4×C29semidirect
556. #103D4×C29semidirect
566. #102D4×C29semidirect
567. #102D4×C29semidirect
568. #102D4×C29semidirect
569. #102D4×C29semidirect
578. C29#25187direct (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×#30422
C2×C29×#4532
C29×#30092
C29×#29462
C29×#28972
C29×#20632
C29×#20512
C29×#20382
C29×#20142
C29×#19772
C29×#19292
C29×#18872
C29×#18822
C29×#18662
#2518729