Finite Group Databasebeta

← C29×#25969 #20320869

Subgroups — C29×#25969 #20320869

Order 7424.

960 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#479C211yesmaximal, characteristic, complemented
2C2×C29×#417C211yesmaximal, characteristic
3C29×#2442C211yesmaximal, characteristic, complemented
4C29×#2341C211yesmaximal, characteristic
5C29×#2092C211yesmaximal, characteristic, complemented
6C29×#2067C211yesmaximal, characteristic, complemented
7C29×#2067C211yesmaximal, characteristic, complemented
8C29×#2025C211yesmaximal, characteristic, complemented
9C29×#1863C211yesmaximal, characteristic, complemented
10C29×#1863C211yesmaximal, characteristic, complemented
11C29×#1852C211yesmaximal, characteristic, complemented
12C29×#1851C211yesmaximal, characteristic, complemented
13C29×#1809C211yesmaximal, characteristic, complemented
14C29×#1805C211yesmaximal, characteristic, complemented
15C29×#1788C211yesmaximal, characteristic
16C22×#41×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C2×C29×#125C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C29×#479—24no—
23C2×C29×#107C2211yescharacteristic
24C2×C29×#107C2211yescharacteristic
25C2×C29×#107C2211yescharacteristic
26C2×C29×#106C2211yescharacteristic
27C2×C29×C4⋊C8C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C29×#417—24no—
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C29×#400—21no—
40C29×#398—21no—
41C29×#390—21no—
42C29×#390—21no—
43C29×#390C2211yescharacteristic
44C29×#390C2211yescharacteristic
45C29×#389C2211yescharacteristic
46C29×#389C2211yescharacteristic
47C29×#385—21no—
48C29×#382C2211yescharacteristic
49C29×#380—21no—
50C29×#380—21no—
51C29×#380C2211yescharacteristic
52C29×#380C2211yescharacteristic
53C4×C22⋊C4×C29—21no—
54C4×C22⋊C4×C29C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C2×#41×C29—22no—
62C2×#41×C29—22no—
63C2×#41×C29—22no—
64C2×#41×C29—41no—
65C2×#41×C29—41no—
66C2×#41×C29Q814yes—
67C22×Q8×C29C2311yescharacteristic
68C22×D4×C29—21no—
69C22×D4×C29C2311yescharacteristic
70C23×C4×C29—21no—
71C23×C4×C29—21no—
72C23×C4×C29C2311yescharacteristic
73C2×M16×C29—22no—
74C2×M16×C29—22no—
75C2×M16×C29—41no—
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C22×C8×C29C2311yescharacteristic
79C22×C8×C29C2311yescharacteristic
80C29×#125—22no—
81C29×#125—41no—
82C4×Q8×C29—22no—
83C4×Q8×C29—22no—
84C4×Q8×C29—41no—
85C4×Q8×C29—41no—
86C2×C4⋊C4×C29—22no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—41no—
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C22⋊C4×C29—21no—
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—21no—
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29D411yescharacteristic
108C2×C22⋊C4×C29D411yescharacteristic
109C2×C42×C29—21no—
110C2×C42×C29—21no—
111C2×C42×C29C2311yescharacteristic
112C2×C42×C29C2311yescharacteristic
113C29×#107—22no—
114C29×#107—41no—
115C29×#107—41no—
116C29×#106—22no—
117C29×C4⋊C8—22no—
118C29×C4⋊C8—41no—
119C29×#103—22no—
120C29×#103—22no—
121C29×#103—22no—
122C29×#103D414yes—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—41no—
126C29×#102—41no—
127C29×C22⋊C8—22no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95D411yescharacteristic
135C29×#95D411yescharacteristic
136C24×C29—21no—
137C24×C29C2×D411yescharacteristic
138#41×C29—28no—
139#41×C29—44no—
140#41×C29—44no—
141#41×C29—44no—
142C2×Q8×C29—21no—
143C2×Q8×C29—21no—
144C2×Q8×C29—21no—
145C2×Q8×C29C2×D412yes—
146C2×Q8×C29C2×Q812yes—
147C2×Q8×C29#4112yes—
148C2×D4×C29—24no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—42no—
155C2×D4×C29—42no—
156C2×D4×C29C2×Q812yes—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—24no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—42no—
170C22×C4×C29—42no—
171C22×C4×C29—42no—
172C22×C4×C29—42no—
173C22×C4×C29—81no—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2×Q812yes—
180C22×C4×C29#4112yes—
181C22×C4×C29C2411yescharacteristic
182M16×C29—44no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29C2×D412yes—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—42no—
209C4⋊C4×C29—42no—
210C4⋊C4×C29—42no—
211C4⋊C4×C29—81no—
212C4⋊C4×C29—81no—
213C4⋊C4×C29C2×D412yes—
214C22⋊C4×C29—41no—
215C22⋊C4×C29—41no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—42no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—81no—
220C22⋊C4×C29—81no—
221C22⋊C4×C29—81no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—21no—
226C42×C29—42no—
227C42×C29—42no—
228#25969C2911yesmaximal, characteristic, direct product factor, Sylow
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—22no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29C22⋊Q812yes—
243C23×C29C22×D411yescharacteristic
244Q8×C29—22no—
245Q8×C29—22no—
246Q8×C29—22no—
247Q8×C29C22⋊Q814yes—
248D4×C29—22no—
249D4×C29—22no—
250D4×C29—48no—
251D4×C29—41no—
252D4×C29—41no—
253C2×C4×C29—22no—
254C2×C4×C29—22no—
255C2×C4×C29—21no—
256C2×C4×C29—22no—
257C2×C4×C29—21no—
258C2×C4×C29—22no—
259C2×C4×C29—22no—
260C2×C4×C29—22no—
261C2×C4×C29—22no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—22no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—21no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—21no—
274C2×C4×C29—21no—
275C2×C4×C29—48no—
276C2×C4×C29—41no—
277C2×C4×C29—41no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
280C2×C4×C29—41no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—41no—
290C2×C4×C29—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—84no—
294C2×C4×C29C22⋊Q812yes—
295C2×C4×C29C22×D411yescharacteristic
296C2×C4×C29C22×Q811yescharacteristic
297C2×C4×C29C2×#4111yescharacteristic
298C2×C4×C29C2×#4111yescharacteristic
299C2×C4×C29H(5,𝔽2)11yescharacteristic
300C2×C4×C29H(5,𝔽2)11yescharacteristic
301C8×C29—22no—
302C8×C29—41no—
303C8×C29—41no—
304C8×C29—41no—
305C2×#479C2×C2911yescharacteristic, complemented
306C2×#417C2×C2911yescharacteristic
307#2442C2×C2911yescharacteristic, complemented
308#2341C2×C2911yescharacteristic
309#2092C2×C2911yescharacteristic, complemented
310#2067C2×C2911yescharacteristic, complemented
311#2067C2×C2911yescharacteristic, complemented
312#2025C2×C2911yescharacteristic, complemented
313#1863C2×C2911yescharacteristic, complemented
314#1863C2×C2911yescharacteristic, complemented
315#1852C2×C2911yescharacteristic, complemented
316#1851C2×C2911yescharacteristic, complemented
317#1809C2×C2911yescharacteristic, complemented
318#1805C2×C2911yescharacteristic, complemented
319#1788C2×C2911yescharacteristic
320C22×C29—22no—
321C22×C29—22no—
322C22×C29—22no—
323C22×C29—41no—
324C22×C29—41no—
325C22×C29—41no—
326C22×C29—41no—
327C22×C29—42no—
328C22×C29—42no—
329C22×C29—42no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29C2×C22⋊Q811yescharacteristic
335C22×C29D4211yescharacteristic
336C22×C29#54611yescharacteristic
337C22×C29#57511yescharacteristic
338C22×C29#57511yescharacteristic
339C22×C29#57611yescharacteristic
340C22×C29#57811yescharacteristic
341C4×C29—22no—
342C4×C29—24no—
343C4×C29—41no—
344C4×C29—42no—
345C4×C29—41no—
346C4×C29—41no—
347C4×C29—41no—
348C4×C29—81no—
349C4×C29—81no—
350C4×C29—81no—
351C4×C29—81no—
352C4×C29—81no—
353C4×C29C2×C22⋊Q811yescharacteristic
354C4×C29#54311yescharacteristic
355C4×C29#54611yescharacteristic
356C4×C29#55111yescharacteristic
357C22×#41C22×C2911yescharacteristic
358C22×M16C22×C2911yescharacteristic
359C2×#125C22×C2911yescharacteristic
360C2×C4×Q8C22×C2911yescharacteristic
361C2×C4×Q8C22×C2911yescharacteristic
362C22×C4⋊C4C22×C2911yescharacteristic
363#479—24no—
364C2×#107C22×C2911yescharacteristic
365C2×#107C22×C2911yescharacteristic
366C2×#107C22×C2911yescharacteristic
367C2×#106C22×C2911yescharacteristic
368C2×C4⋊C8C22×C2911yescharacteristic
369C2×C4⋊C8C22×C2911yescharacteristic
370#417—24no—
371C2×#103C22×C2911yescharacteristic
372C2×#103C22×C2911yescharacteristic
373C2×#103C22×C2911yescharacteristic
374C2×#103C22×C2911yescharacteristic
375C2×#102C22×C2911yescharacteristic
376C2×#102C22×C2911yescharacteristic
377C2×#102C22×C2911yescharacteristic
378C2×#102C22×C2911yescharacteristic
379C2×C22⋊C8C22×C2911yescharacteristic
380#400—21no—
381#398—21no—
382#390—21no—
383#390—21no—
384#390C22×C2911yescharacteristic
385#390C22×C2911yescharacteristic
386#389C22×C2911yescharacteristic
387#389C22×C2911yescharacteristic
388#385—21no—
389#382C22×C2911yescharacteristic
390#380—21no—
391#380—21no—
392#380C22×C2911yescharacteristic
393#380C22×C2911yescharacteristic
394C4×C22⋊C4—21no—
395C4×C22⋊C4C22×C2911yescharacteristic
396#340C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#340C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#336C22×C2911yescharacteristic
401#336C22×C2911yescharacteristic
402C2×C29—42no—
403C2×C29—82no—
404C2×C29#243711yescharacteristic
405C2×C29#308011yescharacteristic
406C2×C29#308311yescharacteristic
407C2×C29#326811yescharacteristic
408C2×C29#327711yescharacteristic
409C2×C29#330911yescharacteristic
410C2×C29#332711yescharacteristic
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—41no—
415C2×#41—41no—
416C2×#41Q8×C2914yes—
417C22×Q8C23×C2911yescharacteristic
418C22×D4—21no—
419C22×D4C23×C2911yescharacteristic
420C23×C4—21no—
421C23×C4—21no—
422C23×C4C23×C2911yescharacteristic
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—41no—
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428C22×C8C23×C2911yescharacteristic
429C22×C8C23×C2911yescharacteristic
430#125—22no—
431#125—41no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—41no—
435C4×Q8—41no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4C23×C2911yescharacteristic
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C4⋊C4C23×C2911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C2911yescharacteristic
458C2×C22⋊C4D4×C2911yescharacteristic
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C2911yescharacteristic
462C2×C42C23×C2911yescharacteristic
463#107—22no—
464#107—41no—
465#107—41no—
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103D4×C2914yes—
473#102—22no—
474#102—22no—
475#102—41no—
476#102—41no—
477C22⋊C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C2911yescharacteristic
485#95D4×C2911yescharacteristic
486C29#2596911yescharacteristic, direct product factor, Sylow
487C24—21no—
488C24C2×D4×C2911yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8C2×D4×C2912yes—
497C2×Q8C2×Q8×C2912yes—
498C2×Q8#41×C2912yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×Q8×C2912yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C2911yescharacteristic
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4C2×D4×C2911yescharacteristic
530C22×C4C2×Q8×C2912yes—
531C22×C4#41×C2912yes—
532C22×C4C24×C2911yescharacteristic
533M16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C2×D4×C2912yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4C2×D4×C2912yes—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—42no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C29×C22⋊Q812yes—
593C23C22×D4×C2911yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8C29×C22⋊Q814yes—
598D4—22no—
599D4—22no—
600D4—48no—
601D4—41no—
602D4—41no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4C29×C22⋊Q812yes—
645C2×C4C22×D4×C2911yescharacteristic
646C2×C4C22×Q8×C2911yescharacteristic
647C2×C4C2×#41×C2911yescharacteristic
648C2×C4C2×#41×C2911yescharacteristic
649C2×C4C29×H(5,𝔽2)11yescharacteristic
650C2×C4C29×H(5,𝔽2)11yescharacteristic
651C8—22no—
652C8—41no—
653C8—41no—
654C8—41no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×C29×C22⋊Q811yescharacteristic
670C22D42×C2911yescharacteristic
671C22C29×#54611yescharacteristic
672C22C29×#57511yescharacteristic
673C22C29×#57511yescharacteristic
674C22C29×#57611yescharacteristic
675C22C29×#57811yescharacteristic
676C4—22no—
677C4—24no—
678C4—41no—
679C4—42no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4C2×C29×C22⋊Q811yescharacteristic
689C4C29×#54311yescharacteristic
690C4C29×#54611yescharacteristic
691C4C29×#55111yescharacteristic
692C2—42no—
693C2—82no—
694C2C29×#243711yescharacteristic
695C2C29×#308011yescharacteristic
696C2C29×#308311yescharacteristic
697C2C29×#326811yescharacteristic
698C2C29×#327711yescharacteristic
699C2C29×#330911yescharacteristic
700C2C29×#332711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#479C2semidirect
3. C29×#2442C2semidirect
5. C29×#2092C2semidirect
6. C29×#2067C2semidirect
7. C29×#2067C2semidirect
8. C29×#2025C2semidirect
9. C29×#1863C2semidirect
10. C29×#1863C2semidirect
11. C29×#1852C2semidirect
12. C29×#1851C2semidirect
13. C29×#1809C2semidirect
14. C29×#1805C2semidirect
228. #25969C29direct (N × H)
305. C2×#479C2×C29semidirect
307. #2442C2×C29semidirect
309. #2092C2×C29semidirect
310. #2067C2×C29semidirect
311. #2067C2×C29semidirect
312. #2025C2×C29semidirect
313. #1863C2×C29semidirect
314. #1863C2×C29semidirect
315. #1852C2×C29semidirect
316. #1851C2×C29semidirect
317. #1809C2×C29semidirect
318. #1805C2×C29semidirect
486. C29#25969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4792
C2×C29×#4172
C29×#24422
C29×#23412
C29×#20922
C29×#20672
C29×#20252
C29×#18632
C29×#18522
C29×#18512
C29×#18092
C29×#18052
C29×#17882
#2596929