Finite Group Databasebeta

← C29×#25207 #20320107

Subgroups — C29×#25207 #20320107

Order 7424.

904 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#482C211yesmaximal, characteristic, complemented
2C2×C29×#466C211yesmaximal, characteristic
3C29×#2500C211yesmaximal, characteristic, complemented
4C29×#2363C211yesmaximal, characteristic, complemented
5C29×#2083C211yesmaximal, characteristic, complemented
6C29×#2073C211yesmaximal, characteristic, complemented
7C29×#2065C211yesmaximal, characteristic, complemented
8C29×#2054C211yesmaximal, characteristic, complemented
9C29×#1949C211yesmaximal, characteristic, complemented
10C29×#1925C211yesmaximal, characteristic, complemented
11C29×#1879C211yesmaximal, characteristic, complemented
12C29×#1875C211yesmaximal, characteristic, complemented
13C29×#1850C211yesmaximal, characteristic, complemented
14C29×#1802C211yesmaximal, characteristic, complemented
15C29×#1735C211yesmaximal, characteristic, complemented
16C22×D8×C29C2211yescharacteristic
17C23×C8×C29C2211yescharacteristic
18C2×C29×#121C2211yescharacteristic
19C2×C29×#121C2211yescharacteristic
20C2×C4×D4×C29C2211yescharacteristic
21C2×C29×#117C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C29×#482—24no—
24C29×#466—24no—
25C2×C29×#107C2211yescharacteristic
26C2×C29×#107C2211yescharacteristic
27C2×C29×#106C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#102C2211yescharacteristic
36C2×C29×C22⋊C8C2211yescharacteristic
37C29×#394—21no—
38C29×#394—21no—
39C29×#390—21no—
40C29×#390C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#388—21no—
45C29×#388—21no—
46C29×#388—21no—
47C29×#386—21no—
48C29×#384C2211yescharacteristic
49C29×#382C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C22⋊C4×C29—21no—
52C4×C22⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×D4×C29—21no—
62C22×D4×C29—21no—
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C23×C4×C29C2311yescharacteristic
67C2×D8×C29—22no—
68C2×D8×C29—22no—
69C2×D8×C29—41no—
70C22×C8×C29—22no—
71C22×C8×C29—22no—
72C22×C8×C29—41no—
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C29×#121—22no—
78C29×#121—22no—
79C29×#121—22no—
80C29×#121D414yes—
81C4×D4×C29—22no—
82C4×D4×C29—41no—
83C29×#117—22no—
84C29×#117—22no—
85C29×#117—22no—
86C29×#117—41no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
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×C29—21no—
112C2×C42×C29C2311yescharacteristic
113C2×C42×C29C2311yescharacteristic
114C29×#107—22no—
115C29×#107—22no—
116C29×#106—22no—
117C29×C4⋊C8—22no—
118C29×C4⋊C8—41no—
119C29×#102—22no—
120C29×#102—22no—
121C29×#102—22no—
122C29×#102—22no—
123C29×#102—22no—
124C29×#102—41no—
125C29×C22⋊C8—22no—
126C29×#95—21no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95D411yescharacteristic
131C29×#95D411yescharacteristic
132C24×C29—21no—
133C24×C29—21no—
134C24×C29C2×D411yescharacteristic
135C2×D4×C29—24no—
136C2×D4×C29—21no—
137C2×D4×C29—21no—
138C2×D4×C29—21no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—42no—
148C2×D4×C29—81no—
149C2×D4×C29—81no—
150C2×D4×C29—81no—
151C2×D4×C29—81no—
152C2×D4×C29C2×D412yes—
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
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—42no—
164C22×C4×C29—42no—
165C22×C4×C29—81no—
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D412yes—
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29#4112yes—
173C22×C4×C29C2411yescharacteristic
174D8×C29—44no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—44no—
187C2×C8×C29#4112yes—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—81no—
199C4⋊C4×C29—81no—
200C4⋊C4×C29—81no—
201C4⋊C4×C29C2×D412yes—
202C4⋊C4×C29#4112yes—
203C22⋊C4×C29—24no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—42no—
207C22⋊C4×C29—42no—
208C22⋊C4×C29—42no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—81no—
214C22⋊C4×C29—81no—
215C22⋊C4×C29—81no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—21no—
219C42×C29—21no—
220C42×C29—42no—
221C42×C29—42no—
222C42×C29—81no—
223#25207C2911yesmaximal, characteristic, direct product factor, Sylow
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—22no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29—41no—
243C23×C29—41no—
244C23×C29#12112yes—
245C23×C29C22×D411yescharacteristic
246D4×C29—22no—
247D4×C29—22no—
248D4×C29—41no—
249D4×C29—41no—
250D4×C29—41no—
251D4×C29—41no—
252D4×C29—41no—
253D4×C29—41no—
254D4×C29—84no—
255D4×C29—84no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—22no—
261C2×C4×C29—22no—
262C2×C4×C29—22no—
263C2×C4×C29—22no—
264C2×C4×C29—22no—
265C2×C4×C29—21no—
266C2×C4×C29—22no—
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—41no—
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—84no—
292C2×C4×C29#12112yes—
293C2×C4×C29#13512yes—
294C2×C4×C29C22×D411yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29C2×#4111yescharacteristic
297C2×C4×C29C2×#4111yescharacteristic
298C2×C4×C29H(5,𝔽2)11yescharacteristic
299C2×C4×C292−1+411yescharacteristic
300C8×C29—22no—
301C8×C29—41no—
302C8×C29—41no—
303C8×C29—41no—
304C2×#482C2×C2911yescharacteristic, complemented
305C2×#466C2×C2911yescharacteristic
306#2500C2×C2911yescharacteristic, complemented
307#2363C2×C2911yescharacteristic, complemented
308#2083C2×C2911yescharacteristic, complemented
309#2073C2×C2911yescharacteristic, complemented
310#2065C2×C2911yescharacteristic, complemented
311#2054C2×C2911yescharacteristic, complemented
312#1949C2×C2911yescharacteristic, complemented
313#1925C2×C2911yescharacteristic, complemented
314#1879C2×C2911yescharacteristic, complemented
315#1875C2×C2911yescharacteristic, complemented
316#1850C2×C2911yescharacteristic, complemented
317#1802C2×C2911yescharacteristic, complemented
318#1735C2×C2911yescharacteristic, complemented
319C22×C29—22no—
320C22×C29—22no—
321C22×C29—22no—
322C22×C29—41no—
323C22×C29—41no—
324C22×C29—41no—
325C22×C29—41no—
326C22×C29—42no—
327C22×C29—42no—
328C22×C29—42no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29—81no—
340C22×C29C2×#12111yescharacteristic
341C22×C29#54611yescharacteristic
342C22×C29#54711yescharacteristic
343C22×C29C2×#13511yescharacteristic
344C22×C29#57511yescharacteristic
345C22×C29#57611yescharacteristic
346C22×C29#57611yescharacteristic
347C4×C29—22no—
348C4×C29—22no—
349C4×C29—41no—
350C4×C29—41no—
351C4×C29—42no—
352C4×C29—42no—
353C4×C29—41no—
354C4×C29—81no—
355C4×C29—81no—
356C4×C29—81no—
357C4×C29—81no—
358C4×C29#52911yescharacteristic
359C4×C29#53911yescharacteristic
360C4×C29#54611yescharacteristic
361C4×C29#54711yescharacteristic
362C22×D8C22×C2911yescharacteristic
363C23×C8C22×C2911yescharacteristic
364C2×#121C22×C2911yescharacteristic
365C2×#121C22×C2911yescharacteristic
366C2×C4×D4C22×C2911yescharacteristic
367C2×#117C22×C2911yescharacteristic
368C2×#117C22×C2911yescharacteristic
369#482—24no—
370#466—24no—
371C2×#107C22×C2911yescharacteristic
372C2×#107C22×C2911yescharacteristic
373C2×#106C22×C2911yescharacteristic
374C2×C4⋊C8C22×C2911yescharacteristic
375C2×C4⋊C8C22×C2911yescharacteristic
376C2×#102C22×C2911yescharacteristic
377C2×#102C22×C2911yescharacteristic
378C2×#102C22×C2911yescharacteristic
379C2×#102C22×C2911yescharacteristic
380C2×#102C22×C2911yescharacteristic
381C2×#102C22×C2911yescharacteristic
382C2×C22⋊C8C22×C2911yescharacteristic
383#394—21no—
384#394—21no—
385#390—21no—
386#390C22×C2911yescharacteristic
387#390C22×C2911yescharacteristic
388#390C22×C2911yescharacteristic
389#389C22×C2911yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#386—21no—
394#384C22×C2911yescharacteristic
395#382C22×C2911yescharacteristic
396C4×C4⋊C4C22×C2911yescharacteristic
397C4×C22⋊C4—21no—
398C4×C22⋊C4C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#340C22×C2911yescharacteristic
402#340C22×C2911yescharacteristic
403#340C22×C2911yescharacteristic
404#340C22×C2911yescharacteristic
405#336C22×C2911yescharacteristic
406#336C22×C2911yescharacteristic
407C2×C29—42no—
408C2×C29—82no—
409C2×C29—161no—
410C2×C29#242511yescharacteristic
411C2×C29#303511yescharacteristic
412C2×C29#304111yescharacteristic
413C2×C29#329711yescharacteristic
414C2×C29#330911yescharacteristic
415C2×C29#334111yescharacteristic
416C2×C29#334711yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C2911yescharacteristic
420C22×D4C23×C2911yescharacteristic
421C23×C4—21no—
422C23×C4C23×C2911yescharacteristic
423C2×D8—22no—
424C2×D8—22no—
425C2×D8—41no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8C23×C2911yescharacteristic
430C22×C8C23×C2911yescharacteristic
431C22×C8C23×C2911yescharacteristic
432C22×C8C23×C2911yescharacteristic
433#121—22no—
434#121—22no—
435#121—22no—
436#121D4×C2914yes—
437C4×D4—22no—
438C4×D4—41no—
439#117—22no—
440#117—22no—
441#117—22no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C4⋊C4C23×C2911yescharacteristic
451C2×C4⋊C4C23×C2911yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C2911yescharacteristic
464C2×C22⋊C4D4×C2911yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C2911yescharacteristic
469C2×C42C23×C2911yescharacteristic
470#107—22no—
471#107—22no—
472#106—22no—
473C4⋊C8—22no—
474C4⋊C8—41no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—41no—
481C22⋊C8—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C2911yescharacteristic
487#95D4×C2911yescharacteristic
488C29#2520711yescharacteristic, direct product factor, Sylow
489C24—21no—
490C24—21no—
491C24C2×D4×C2911yescharacteristic
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C2×D4×C2912yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4C2×D4×C2911yescharacteristic
524C22×C4C2×D4×C2911yescharacteristic
525C22×C4C2×D4×C2911yescharacteristic
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2912yes—
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4#41×C2912yes—
530C22×C4C24×C2911yescharacteristic
531D8—44no—
532C2×C8—21no—
533C2×C8—21no—
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—44no—
544C2×C8#41×C2912yes—
545C4⋊C4—21no—
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—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4C2×D4×C2912yes—
559C4⋊C4#41×C2912yes—
560C22⋊C4—24no—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
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—
579C42—81no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C29×#12112yes—
601C23C22×D4×C2911yescharacteristic
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—84no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
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—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4C29×#12112yes—
649C2×C4C29×#13512yes—
650C2×C4C22×D4×C2911yescharacteristic
651C2×C4C2×#41×C2911yescharacteristic
652C2×C4C2×#41×C2911yescharacteristic
653C2×C4C2×#41×C2911yescharacteristic
654C2×C4C29×H(5,𝔽2)11yescharacteristic
655C2×C4C29×2−1+411yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C29×#12111yescharacteristic
682C22C29×#54611yescharacteristic
683C22C29×#54711yescharacteristic
684C22C2×C29×#13511yescharacteristic
685C22C29×#57511yescharacteristic
686C22C29×#57611yescharacteristic
687C22C29×#57611yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C29×#52911yescharacteristic
700C4C29×#53911yescharacteristic
701C4C29×#54611yescharacteristic
702C4C29×#54711yescharacteristic
703C2—42no—
704C2—82no—
705C2—161no—
706C2C29×#242511yescharacteristic
707C2C29×#303511yescharacteristic
708C2C29×#304111yescharacteristic
709C2C29×#329711yescharacteristic
710C2C29×#330911yescharacteristic
711C2C29×#334111yescharacteristic
712C2C29×#334711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#466C2
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×#482C2semidirect
3. C29×#2500C2semidirect
4. C29×#2363C2semidirect
5. C29×#2083C2semidirect
6. C29×#2073C2semidirect
7. C29×#2065C2semidirect
8. C29×#2054C2semidirect
9. C29×#1949C2semidirect
10. C29×#1925C2semidirect
11. C29×#1879C2semidirect
12. C29×#1875C2semidirect
13. C29×#1850C2semidirect
14. C29×#1802C2semidirect
15. C29×#1735C2semidirect
223. #25207C29direct (N × H)
304. C2×#482C2×C29semidirect
306. #2500C2×C29semidirect
307. #2363C2×C29semidirect
308. #2083C2×C29semidirect
309. #2073C2×C29semidirect
310. #2065C2×C29semidirect
311. #2054C2×C29semidirect
312. #1949C2×C29semidirect
313. #1925C2×C29semidirect
314. #1879C2×C29semidirect
315. #1875C2×C29semidirect
316. #1850C2×C29semidirect
317. #1802C2×C29semidirect
318. #1735C2×C29semidirect
488. C29#25207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4822
C2×C29×#4662
C29×#25002
C29×#23632
C29×#20832
C29×#20732
C29×#20652
C29×#20542
C29×#19492
C29×#19252
C29×#18792
C29×#18752
C29×#18502
C29×#18022
C29×#17352
#2520729