Finite Group Databasebeta

← C29×#25182 #20320082

Subgroups — C29×#25182 #20320082

Order 7424.

992 conjugacy classes of subgroups.

The subgroup lattice has 790 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×#454C211yesmaximal, characteristic
4C29×#3011C211yesmaximal, characteristic, complemented
5C29×#2946C211yesmaximal, characteristic, complemented
6C29×#2898C211yesmaximal, characteristic, complemented
7C29×#2064C211yesmaximal, characteristic, complemented
8C29×#2051C211yesmaximal, characteristic, complemented
9C29×#2038C211yesmaximal, characteristic, complemented
10C29×#2015C211yesmaximal, characteristic, complemented
11C29×#1979C211yesmaximal, characteristic, complemented
12C29×#1929C211yesmaximal, characteristic, complemented
13C29×#1885C211yesmaximal, characteristic, complemented
14C29×#1882C211yesmaximal, characteristic, complemented
15C29×#1866C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×#137C2211yescharacteristic
18C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C22×Q16×C29C2211yescharacteristic
21C22×SD16×C29C2211yescharacteristic
22C2×C29×#131C2211yescharacteristic
23C29×#536C2211yescharacteristic
24C2×C29×#124C2211yescharacteristic
25C29×#520C2211yescharacteristic
26C29×#518C2211yescharacteristic
27C29×#471—24no—
28C29×#463—21no—
29C29×#463—21no—
30C29×#461—21no—
31C29×#461—21no—
32C29×#454—24no—
33C29×#452—21no—
34C29×#452—21no—
35C29×#451—21no—
36C29×#451—21no—
37C29×#442—21no—
38C29×#440—21no—
39C4×SD16×C29—21no—
40C4×D8×C29—21no—
41C2×C29×#108C2211yescharacteristic
42C2×C29×#108C2211yescharacteristic
43C29×#428C2211yescharacteristic
44C29×#424C2211yescharacteristic
45C2×C29×#104C2211yescharacteristic
46C2×C29×#104C2211yescharacteristic
47C29×#419—21no—
48C29×#419C2211yescharacteristic
49C29×#419C2211yescharacteristic
50C29×#419C2211yescharacteristic
51C29×#417—21no—
52C29×#417C2211yescharacteristic
53C29×#416—21no—
54C29×#416C2211yescharacteristic
55C29×#416C2211yescharacteristic
56C2×C29×#103—21no—
57C2×C29×#103C2211yescharacteristic
58C2×C29×#102C2211yescharacteristic
59C2×C29×#101C2211yescharacteristic
60C2×C29×#101C2211yescharacteristic
61C2×C29×#100C2211yescharacteristic
62C29×#408C2211yescharacteristic
63C29×#405C2211yescharacteristic
64C29×#391C2211yescharacteristic
65C29×#343C2211yescharacteristic
66C29×#339C2211yescharacteristic
67C29×#339C2211yescharacteristic
68C29×#336C2211yescharacteristic
69C29×2−1+4—22no—
70C29×2−1+4—22no—
71C29×2−1+4—22no—
72C29×2−1+4—41no—
73C2×#41×C29—21no—
74C2×#41×C29—21no—
75C2×#41×C29—41no—
76C2×#41×C29C2311yescharacteristic
77C2×#41×C29C2311yescharacteristic
78C22×Q8×C29—21no—
79C22×Q8×C29—21no—
80C22×Q8×C29C2311yescharacteristic
81C22×Q8×C29C2311yescharacteristic
82C22×D4×C29C2311yescharacteristic
83C29×#137—22no—
84C29×#137—22no—
85C29×AGL(1,ℤ/8)—22no—
86C29×AGL(1,ℤ/8)—22no—
87C29×AGL(1,ℤ/8)—41no—
88C29×AGL(1,ℤ/8)D414yes—
89C2×Q16×C29—21no—
90C2×Q16×C29—22no—
91C2×Q16×C29—21no—
92C2×Q16×C29—21no—
93C2×Q16×C29—41no—
94C2×SD16×C29—21no—
95C2×SD16×C29—21no—
96C2×SD16×C29—21no—
97C2×SD16×C29—22no—
98C2×SD16×C29—21no—
99C2×SD16×C29—21no—
100C2×SD16×C29—41no—
101C2×D8×C29—21no—
102C2×D8×C29—21no—
103C29×#131—22no—
104C29×#131—41no—
105C2×M16×C29—21no—
106C2×M16×C29C2311yescharacteristic
107C2×M16×C29C2311yescharacteristic
108C2×M16×C29C2311yescharacteristic
109C2×M16×C29C2311yescharacteristic
110C22×C8×C29—21no—
111C22×C8×C29C2311yescharacteristic
112C22×C8×C29C2311yescharacteristic
113C29×C4⋊Q8—21no—
114C29×#124—22no—
115C29×#124—22no—
116C29×#124—21no—
117C29×#123—41no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C4×Q8×C29—21no—
121C4×D4×C29—21no—
122C4×D4×C29—21no—
123C4×D4×C29—21no—
124C4×D4×C29—21no—
125C4×D4×C29—21no—
126C4×D4×C29—41no—
127C29×#117—21no—
128C29×#117C2311yescharacteristic
129C29×#117C2311yescharacteristic
130C2×C4⋊C4×C29—21no—
131C2×C4⋊C4×C29C2311yescharacteristic
132C2×C22⋊C4×C29—41no—
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×#103—21no—
147C29×#103—21no—
148C29×#103—21no—
149C29×#103—21no—
150C29×#103—21no—
151C29×#103—21no—
152C29×#103D411yescharacteristic
153C29×#103D411yescharacteristic
154C29×#103D411yescharacteristic
155C29×#103D411yescharacteristic
156C29×#102—21no—
157C29×#102—21no—
158C29×#102—21no—
159C29×#102D411yescharacteristic
160C29×#102D411yescharacteristic
161C29×#102D411yescharacteristic
162C29×#102D411yescharacteristic
163C29×#101—22no—
164C29×#101—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—
172#41×C29—21no—
173#41×C29—21no—
174#41×C29—24no—
175#41×C29—21no—
176#41×C29—21no—
177#41×C29—21no—
178#41×C29—21no—
179#41×C29—42no—
180#41×C29—44no—
181#41×C29—42no—
182#41×C29—44no—
183#41×C29—42no—
184#41×C29C2×D412yes—
185#41×C29#4112yes—
186C2×Q8×C29—21no—
187C2×Q8×C29—24no—
188C2×Q8×C29—21no—
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×C29—21no—
196C2×Q8×C29—21no—
197C2×Q8×C29—21no—
198C2×Q8×C29—41no—
199C2×Q8×C29—42no—
200C2×Q8×C29—42no—
201C2×Q8×C29—42no—
202C2×Q8×C29C2×D411yescharacteristic
203C2×Q8×C29C2×D411yescharacteristic
204C2×Q8×C29#4112yes—
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—21no—
212C2×D4×C29—41no—
213C2×D4×C29C2×D411yescharacteristic
214C2×D4×C29C2×D412yes—
215C2×D4×C29C2×D411yescharacteristic
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—41no—
223C22×C4×C29—41no—
224C22×C4×C29—41no—
225C22×C4×C29—41no—
226C22×C4×C29—41no—
227C22×C4×C29C2411yescharacteristic
228Q16×C29—42no—
229Q16×C29—42no—
230Q16×C29—42no—
231SD16×C29—24no—
232SD16×C29—42no—
233SD16×C29—42no—
234SD16×C29—42no—
235SD16×C29—42no—
236D8×C29—24no—
237D8×C29—42no—
238M16×C29—21no—
239M16×C29—21no—
240M16×C29—21no—
241M16×C29—21no—
242M16×C29—21no—
243M16×C29—21no—
244M16×C29—21no—
245M16×C29—42no—
246M16×C29C2×D412yes—
247C2×C8×C29—21no—
248C2×C8×C29—21no—
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—42no—
256C2×C8×C29C2×D411yescharacteristic
257C2×C8×C29C2×D411yescharacteristic
258C2×C8×C29C2×D411yescharacteristic
259C2×C8×C29C2×D411yescharacteristic
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—41no—
263C4⋊C4×C29—41no—
264C4⋊C4×C29—41no—
265C4⋊C4×C29C2×D411yescharacteristic
266C4⋊C4×C29C2×D411yescharacteristic
267C4⋊C4×C29C2×D411yescharacteristic
268C4⋊C4×C29C2×D411yescharacteristic
269C22⋊C4×C29—21no—
270C22⋊C4×C29—21no—
271C22⋊C4×C29—41no—
272C22⋊C4×C29—41no—
273C22⋊C4×C29—44no—
274C22⋊C4×C29—41no—
275C22⋊C4×C29—41no—
276C22⋊C4×C29—41no—
277C42×C29—21no—
278C42×C29—21no—
279C42×C29—21no—
280C42×C29—21no—
281C42×C29—41no—
282#25182C2911yesmaximal, characteristic, direct product factor, Sylow
283C23×C29—21no—
284C23×C29—21no—
285C23×C29—22no—
286C23×C29—41no—
287C23×C29—41no—
288C23×C29—81no—
289C23×C29—81no—
290C23×C29H(5,𝔽2)11yescharacteristic
291Q8×C29—21no—
292Q8×C29—21no—
293Q8×C29—22no—
294Q8×C29—21no—
295Q8×C29—22no—
296Q8×C29—44no—
297Q8×C29—41no—
298Q8×C29—41no—
299Q8×C29—41no—
300Q8×C29—41no—
301Q8×C29—41no—
302Q8×C29—41no—
303Q8×C29#12112yes—
304D4×C29—22no—
305D4×C29—22no—
306D4×C29—22no—
307D4×C29—21no—
308D4×C29—21no—
309D4×C29—22no—
310D4×C29—21no—
311D4×C29—44no—
312D4×C29—41no—
313D4×C29—41no—
314D4×C29—41no—
315D4×C29—41no—
316D4×C29#12112yes—
317C2×C4×C29—21no—
318C2×C4×C29—22no—
319C2×C4×C29—22no—
320C2×C4×C29—21no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—21no—
324C2×C4×C29—21no—
325C2×C4×C29—22no—
326C2×C4×C29—44no—
327C2×C4×C29—44no—
328C2×C4×C29—41no—
329C2×C4×C29—41no—
330C2×C4×C29—41no—
331C2×C4×C29—41no—
332C2×C4×C29—41no—
333C2×C4×C29—41no—
334C2×C4×C29—41no—
335C2×C4×C29—41no—
336C2×C4×C29—41no—
337C2×C4×C29—41no—
338C2×C4×C29—41no—
339C2×C4×C29—81no—
340C2×C4×C29—161no—
341C2×C4×C29—161no—
342C2×C4×C29—161no—
343C2×C4×C29C22×D411yescharacteristic
344C2×C4×C29C22×D411yescharacteristic
345C2×C4×C29C22×D411yescharacteristic
346C2×C4×C29C2×#4111yescharacteristic
347C2×C4×C29C2×#4111yescharacteristic
348C2×C4×C29H(5,𝔽2)11yescharacteristic
349C8×C29—22no—
350C8×C29—21no—
351C8×C29—21no—
352C8×C29—21no—
353C8×C29—21no—
354C8×C29—41no—
355C8×C29—41no—
356C8×C29—41no—
357C2×#471C2×C2911yescharacteristic, complemented
358#3042C2×C2911yescharacteristic, complemented
359C2×#454C2×C2911yescharacteristic
360#3011C2×C2911yescharacteristic, complemented
361#2946C2×C2911yescharacteristic, complemented
362#2898C2×C2911yescharacteristic, complemented
363#2064C2×C2911yescharacteristic, complemented
364#2051C2×C2911yescharacteristic, complemented
365#2038C2×C2911yescharacteristic, complemented
366#2015C2×C2911yescharacteristic, complemented
367#1979C2×C2911yescharacteristic, complemented
368#1929C2×C2911yescharacteristic, complemented
369#1885C2×C2911yescharacteristic, complemented
370#1882C2×C2911yescharacteristic, complemented
371#1866C2×C2911yescharacteristic, complemented
372C22×C29—21no—
373C22×C29—21no—
374C22×C29—22no—
375C22×C29—41no—
376C22×C29—41no—
377C22×C29—41no—
378C22×C29—42no—
379C22×C29—41no—
380C22×C29—41no—
381C22×C29—82no—
382C22×C29—81no—
383C22×C29—81no—
384C22×C29—161no—
385C22×C29#53811yescharacteristic
386C22×C29D4211yescharacteristic
387C22×C29#54611yescharacteristic
388C4×C29—22no—
389C4×C29—41no—
390C4×C29—42no—
391C4×C29—41no—
392C4×C29—41no—
393C4×C29—41no—
394C4×C29—41no—
395C4×C29—81no—
396C4×C29—81no—
397C4×C29—81no—
398C4×C29C2×#12111yescharacteristic
399C4×C29#52511yescharacteristic
400C4×C29D4211yescharacteristic
401C4×C29#54611yescharacteristic
402C2×2−1+4C22×C2911yescharacteristic
403C2×#137C22×C2911yescharacteristic
404C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
405C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
406C22×Q16C22×C2911yescharacteristic
407C22×SD16C22×C2911yescharacteristic
408C2×#131C22×C2911yescharacteristic
409#536C22×C2911yescharacteristic
410C2×#124C22×C2911yescharacteristic
411#520C22×C2911yescharacteristic
412#518C22×C2911yescharacteristic
413#471—24no—
414#463—21no—
415#463—21no—
416#461—21no—
417#461—21no—
418#454—24no—
419#452—21no—
420#452—21no—
421#451—21no—
422#451—21no—
423#442—21no—
424#440—21no—
425C4×SD16—21no—
426C4×D8—21no—
427C2×#108C22×C2911yescharacteristic
428C2×#108C22×C2911yescharacteristic
429#428C22×C2911yescharacteristic
430#424C22×C2911yescharacteristic
431C2×#104C22×C2911yescharacteristic
432C2×#104C22×C2911yescharacteristic
433#419—21no—
434#419C22×C2911yescharacteristic
435#419C22×C2911yescharacteristic
436#419C22×C2911yescharacteristic
437#417—21no—
438#417C22×C2911yescharacteristic
439#416—21no—
440#416C22×C2911yescharacteristic
441#416C22×C2911yescharacteristic
442C2×#103—21no—
443C2×#103C22×C2911yescharacteristic
444C2×#102C22×C2911yescharacteristic
445C2×#101C22×C2911yescharacteristic
446C2×#101C22×C2911yescharacteristic
447C2×#100C22×C2911yescharacteristic
448#408C22×C2911yescharacteristic
449#405C22×C2911yescharacteristic
450#391C22×C2911yescharacteristic
451#343C22×C2911yescharacteristic
452#339C22×C2911yescharacteristic
453#339C22×C2911yescharacteristic
454#336C22×C2911yescharacteristic
455C2×C29—21no—
456C2×C29—21no—
457C2×C29—42no—
458C2×C29—81no—
459C2×C29—82no—
460C2×C29#242411yescharacteristic
461C2×C29#328911yescharacteristic
462C2×C29#329011yescharacteristic
4632−1+4—22no—
4642−1+4—22no—
4652−1+4—22no—
4662−1+4—41no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—41no—
470C2×#41C23×C2911yescharacteristic
471C2×#41C23×C2911yescharacteristic
472C22×Q8—21no—
473C22×Q8—21no—
474C22×Q8C23×C2911yescharacteristic
475C22×Q8C23×C2911yescharacteristic
476C22×D4C23×C2911yescharacteristic
477#137—22no—
478#137—22no—
479AGL(1,ℤ/8)—22no—
480AGL(1,ℤ/8)—22no—
481AGL(1,ℤ/8)—41no—
482AGL(1,ℤ/8)D4×C2914yes—
483C2×Q16—21no—
484C2×Q16—22no—
485C2×Q16—21no—
486C2×Q16—21no—
487C2×Q16—41no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—41no—
495C2×D8—21no—
496C2×D8—21no—
497#131—22no—
498#131—41no—
499C2×M16—21no—
500C2×M16C23×C2911yescharacteristic
501C2×M16C23×C2911yescharacteristic
502C2×M16C23×C2911yescharacteristic
503C2×M16C23×C2911yescharacteristic
504C22×C8—21no—
505C22×C8C23×C2911yescharacteristic
506C22×C8C23×C2911yescharacteristic
507C4⋊Q8—21no—
508#124—22no—
509#124—22no—
510#124—21no—
511#123—41no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C4×Q8—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—41no—
521#117—21no—
522#117C23×C2911yescharacteristic
523#117C23×C2911yescharacteristic
524C2×C4⋊C4—21no—
525C2×C4⋊C4C23×C2911yescharacteristic
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C42C23×C2911yescharacteristic
529#108—22no—
530#108—41no—
531#107—21no—
532#106—21no—
533C4⋊C8—21no—
534C4⋊C8—21no—
535#104—22no—
536#104—22no—
537#103—21no—
538#103—21no—
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#103—21no—
546#103D4×C2911yescharacteristic
547#103D4×C2911yescharacteristic
548#103D4×C2911yescharacteristic
549#103D4×C2911yescharacteristic
550#102—21no—
551#102—21no—
552#102—21no—
553#102D4×C2911yescharacteristic
554#102D4×C2911yescharacteristic
555#102D4×C2911yescharacteristic
556#102D4×C2911yescharacteristic
557#101—22no—
558#101—22no—
559#100—22no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562#97—21no—
563C4×C8—21no—
564#95—41no—
565C29#2518211yescharacteristic, direct product factor, Sylow
566C24—21no—
567#41—21no—
568#41—21no—
569#41—24no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—42no—
575#41—44no—
576#41—42no—
577#41—44no—
578#41—42no—
579#41C2×D4×C2912yes—
580#41#41×C2912yes—
581C2×Q8—21no—
582C2×Q8—24no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—41no—
594C2×Q8—42no—
595C2×Q8—42no—
596C2×Q8—42no—
597C2×Q8C2×D4×C2911yescharacteristic
598C2×Q8C2×D4×C2911yescharacteristic
599C2×Q8#41×C2912yes—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4C2×D4×C2912yes—
609C2×D4C2×D4×C2911yescharacteristic
610C2×D4C2×D4×C2911yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4C24×C2911yescharacteristic
623Q16—42no—
624Q16—42no—
625Q16—42no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—24no—
632D8—42no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—42no—
641M16C2×D4×C2912yes—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—42no—
651C2×C8C2×D4×C2911yescharacteristic
652C2×C8C2×D4×C2911yescharacteristic
653C2×C8C2×D4×C2911yescharacteristic
654C2×C8C2×D4×C2911yescharacteristic
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4C2×D4×C2911yescharacteristic
661C4⋊C4C2×D4×C2911yescharacteristic
662C4⋊C4C2×D4×C2911yescharacteristic
663C4⋊C4C2×D4×C2911yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—44no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—41no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23C29×H(5,𝔽2)11yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—22no—
688Q8—21no—
689Q8—22no—
690Q8—44no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8C29×#12112yes—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—21no—
702D4—21no—
703D4—22no—
704D4—21no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4C29×#12112yes—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—81no—
734C2×C4—161no—
735C2×C4—161no—
736C2×C4—161no—
737C2×C4C22×D4×C2911yescharacteristic
738C2×C4C22×D4×C2911yescharacteristic
739C2×C4C22×D4×C2911yescharacteristic
740C2×C4C2×#41×C2911yescharacteristic
741C2×C4C2×#41×C2911yescharacteristic
742C2×C4C29×H(5,𝔽2)11yescharacteristic
743C8—22no—
744C8—21no—
745C8—21no—
746C8—21no—
747C8—21no—
748C8—41no—
749C8—41no—
750C8—41no—
751C22—21no—
752C22—21no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—82no—
761C22—81no—
762C22—81no—
763C22—161no—
764C22C29×#53811yescharacteristic
765C22D42×C2911yescharacteristic
766C22C29×#54611yescharacteristic
767C4—22no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4C2×C29×#12111yescharacteristic
778C4C29×#52511yescharacteristic
779C4D42×C2911yescharacteristic
780C4C29×#54611yescharacteristic
781C2—21no—
782C2—21no—
783C2—42no—
784C2—81no—
785C2—82no—
786C2C29×#242411yescharacteristic
787C2C29×#328911yescharacteristic
788C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#454C2
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×#3011C2semidirect
5. C29×#2946C2semidirect
6. C29×#2898C2semidirect
7. C29×#2064C2semidirect
8. C29×#2051C2semidirect
9. C29×#2038C2semidirect
10. C29×#2015C2semidirect
11. C29×#1979C2semidirect
12. C29×#1929C2semidirect
13. C29×#1885C2semidirect
14. C29×#1882C2semidirect
15. C29×#1866C2semidirect
282. #25182C29direct (N × H)
357. C2×#471C2×C29semidirect
358. #3042C2×C29semidirect
360. #3011C2×C29semidirect
361. #2946C2×C29semidirect
362. #2898C2×C29semidirect
363. #2064C2×C29semidirect
364. #2051C2×C29semidirect
365. #2038C2×C29semidirect
366. #2015C2×C29semidirect
367. #1979C2×C29semidirect
368. #1929C2×C29semidirect
369. #1885C2×C29semidirect
370. #1882C2×C29semidirect
371. #1866C2×C29semidirect
565. C29#25182direct (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×#4542
C29×#30112
C29×#29462
C29×#28982
C29×#20642
C29×#20512
C29×#20382
C29×#20152
C29×#19792
C29×#19292
C29×#18852
C29×#18822
C29×#18662
#2518229