Finite Group Databasebeta

← C29×#24562 #20319462

Subgroups — C29×#24562 #20319462

Order 7424.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#480C211yesmaximal, characteristic, complemented
2C2×C29×#408C211yesmaximal, characteristic, complemented
3C29×#2615C211yesmaximal, characteristic
4C29×#2311C211yesmaximal, characteristic, complemented
5C29×#2076C211yesmaximal, characteristic, complemented
6C29×#2075C211yesmaximal, characteristic, complemented
7C29×#2034C211yesmaximal, characteristic, complemented
8C29×#2033C211yesmaximal, characteristic, complemented
9C29×#1895C211yesmaximal, characteristic, complemented
10C29×#1893C211yesmaximal, characteristic, complemented
11C29×#1875C211yesmaximal, characteristic, complemented
12C29×#1854C211yesmaximal, characteristic, complemented
13C29×#1824C211yesmaximal, characteristic, complemented
14C29×#1809C211yesmaximal, characteristic, complemented
15C29×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C23×C8×C29C2211yescharacteristic
19C2×C29×#121C2211yescharacteristic
20C2×C29×#121C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C22×C4⋊C4×C29C2211yescharacteristic
24C29×#480—24no—
25C2×C29×#107C2211yescharacteristic
26C2×C29×#107C2211yescharacteristic
27C2×C29×#107C2211yescharacteristic
28C2×C29×#106C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C29×#408—24no—
34C2×C29×C22⋊C8C2211yescharacteristic
35C2×C29×C22⋊C8C2211yescharacteristic
36C2×C29×C22⋊C8C2211yescharacteristic
37C2×C29×C22⋊C8C2211yescharacteristic
38C29×#393—21no—
39C29×#392—21no—
40C29×#392—21no—
41C29×#392—21no—
42C29×#391—21no—
43C29×#390—21no—
44C29×#386—21no—
45C29×#386—21no—
46C29×#380C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#380C2211yescharacteristic
49C29×#380C2211yescharacteristic
50C29×#380C2211yescharacteristic
51C29×#380C2211yescharacteristic
52C29×#380C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#340C2211yescharacteristic
60C29×#340C2211yescharacteristic
61C2×#41×C29—22no—
62C2×#41×C29—22no—
63C2×#41×C29—22no—
64C2×#41×C29—22no—
65C2×#41×C29—41no—
66C2×#41×C29—41no—
67C22×Q8×C29D411yescharacteristic
68C22×D4×C29—21no—
69C22×D4×C29—21no—
70C22×D4×C29—21no—
71C22×D4×C29D411yescharacteristic
72C22×D4×C29D411yescharacteristic
73C22×D4×C29D411yescharacteristic
74C22×D4×C29C2311yescharacteristic
75C23×C4×C29—21no—
76C23×C4×C29C2311yescharacteristic
77C23×C4×C29C2311yescharacteristic
78C23×C4×C29C2311yescharacteristic
79C2×M16×C29—22no—
80C2×M16×C29—22no—
81C2×M16×C29—41no—
82C22×C8×C29—22no—
83C22×C8×C29—22no—
84C22×C8×C29—41no—
85C22×C8×C29C2311yescharacteristic
86C22×C8×C29C2311yescharacteristic
87C22×C8×C29C2311yescharacteristic
88C22×C8×C29C2311yescharacteristic
89C29×#121—22no—
90C29×#121—22no—
91C29×#121—22no—
92C29×#121—22no—
93C29×#121—41no—
94C29×#121—41no—
95C29×#117—41no—
96C29×#117—41no—
97C2×C4⋊C4×C29—22no—
98C2×C4⋊C4×C29—22no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C4⋊C4×C29C2311yescharacteristic
102C2×C4⋊C4×C29C2311yescharacteristic
103C2×C4⋊C4×C29C2311yescharacteristic
104C2×C4⋊C4×C29C2311yescharacteristic
105C2×C4⋊C4×C29C2311yescharacteristic
106C2×C4⋊C4×C29C2311yescharacteristic
107C2×C22⋊C4×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29—21no—
111C2×C22⋊C4×C29—21no—
112C2×C22⋊C4×C29—21no—
113C2×C22⋊C4×C29—21no—
114C2×C22⋊C4×C29—21no—
115C2×C22⋊C4×C29—21no—
116C2×C22⋊C4×C29—21no—
117C2×C22⋊C4×C29—21no—
118C2×C42×C29—21no—
119C29×#107—22no—
120C29×#107—22no—
121C29×#107—41no—
122C29×#106—41no—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—41no—
126C29×#102—41no—
127C29×C22⋊C8—22no—
128C29×C22⋊C8—22no—
129C29×C22⋊C8—22no—
130C29×C22⋊C8D414yescomplemented
131C29×#95—21no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—21no—
137C29×#95—21no—
138C24×C29—21no—
139C24×C29C2×D411yescharacteristic
140C24×C29C2×D411yescharacteristic
141C24×C29C2×D411yescharacteristic
142#41×C29—44no—
143#41×C29—44no—
144#41×C29—44no—
145#41×C29—44no—
146C2×Q8×C29—22no—
147C2×Q8×C29—22no—
148C2×Q8×C29—41no—
149C2×D4×C29—22no—
150C2×D4×C29—22no—
151C2×D4×C29—22no—
152C2×D4×C29—22no—
153C2×D4×C29—22no—
154C2×D4×C29—22no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—41no—
162C2×D4×C29—41no—
163C2×D4×C29—41no—
164C2×D4×C29—42no—
165C2×D4×C29—42no—
166C2×D4×C29—42no—
167C2×D4×C29—81no—
168C2×D4×C29—81no—
169C2×D4×C29—81no—
170C2×D4×C29—81no—
171C2×D4×C29—81no—
172C2×D4×C29—81no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—21no—
182C22×C4×C29—21no—
183C22×C4×C29—21no—
184C22×C4×C29—21no—
185C22×C4×C29—21no—
186C22×C4×C29—21no—
187C22×C4×C29—21no—
188C22×C4×C29—21no—
189C22×C4×C29—21no—
190C22×C4×C29—21no—
191C22×C4×C29—21no—
192C22×C4×C29—21no—
193C22×C4×C29—21no—
194C22×C4×C29—42no—
195C22×C4×C29—81no—
196C22×C4×C29—81no—
197C22×C4×C29C2×D411yescharacteristic
198C22×C4×C29C2×D411yescharacteristic
199C22×C4×C29C2×D412yes—
200C22×C4×C29C2×D411yescharacteristic
201C22×C4×C29#4112yes—
202C22×C4×C29#4112yes—
203C22×C4×C29#4112yes—
204C22×C4×C29C2411yescharacteristic
205M16×C29—44no—
206C2×C8×C29—21no—
207C2×C8×C29—21no—
208C2×C8×C29—21no—
209C2×C8×C29—21no—
210C2×C8×C29—21no—
211C2×C8×C29—21no—
212C2×C8×C29—21no—
213C2×C8×C29—21no—
214C2×C8×C29—21no—
215C2×C8×C29—21no—
216C2×C8×C29—44no—
217C2×C8×C29C2×D412yes—
218C2×C8×C29C2×D412yes—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—21no—
223C4⋊C4×C29—21no—
224C4⋊C4×C29—21no—
225C4⋊C4×C29—21no—
226C4⋊C4×C29—21no—
227C4⋊C4×C29—21no—
228C4⋊C4×C29—21no—
229C4⋊C4×C29—21no—
230C4⋊C4×C29—21no—
231C4⋊C4×C29—21no—
232C4⋊C4×C29—21no—
233C4⋊C4×C29—42no—
234C22⋊C4×C29—42no—
235C22⋊C4×C29—42no—
236C22⋊C4×C29—42no—
237C22⋊C4×C29—42no—
238C22⋊C4×C29—81no—
239C22⋊C4×C29—81no—
240C22⋊C4×C29—81no—
241C22⋊C4×C29—81no—
242C22⋊C4×C29—81no—
243C22⋊C4×C29—81no—
244C22⋊C4×C29—81no—
245C42×C29—42no—
246#24562C2911yesmaximal, characteristic, direct product factor, Sylow
247C23×C29—21no—
248C23×C29—21no—
249C23×C29—21no—
250C23×C29—21no—
251C23×C29—21no—
252C23×C29—21no—
253C23×C29—21no—
254C23×C29—21no—
255C23×C29—21no—
256C23×C29—21no—
257C23×C29—21no—
258C23×C29—21no—
259C23×C29—21no—
260C23×C29—21no—
261C23×C29—21no—
262C23×C29—21no—
263C23×C29—21no—
264C23×C29—21no—
265C23×C29—21no—
266C23×C29—41no—
267C23×C29—41no—
268C23×C29—41no—
269C23×C29—41no—
270C23×C29—41no—
271C23×C29—41no—
272C23×C29—41no—
273C23×C29#12112yes—
274C23×C29#12312yes—
275C23×C29C22×D411yescharacteristic
276Q8×C29—44no—
277D4×C29—44no—
278D4×C29—44no—
279D4×C29—44no—
280D4×C29—41no—
281D4×C29—41no—
282D4×C29—41no—
283D4×C29—41no—
284D4×C29—84no—
285D4×C29—84no—
286D4×C29—84no—
287C2×C4×C29—21no—
288C2×C4×C29—21no—
289C2×C4×C29—21no—
290C2×C4×C29—21no—
291C2×C4×C29—22no—
292C2×C4×C29—22no—
293C2×C4×C29—22no—
294C2×C4×C29—22no—
295C2×C4×C29—22no—
296C2×C4×C29—22no—
297C2×C4×C29—22no—
298C2×C4×C29—22no—
299C2×C4×C29—21no—
300C2×C4×C29—21no—
301C2×C4×C29—21no—
302C2×C4×C29—41no—
303C2×C4×C29—41no—
304C2×C4×C29—41no—
305C2×C4×C29—41no—
306C2×C4×C29—41no—
307C2×C4×C29—41no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—41no—
314C2×C4×C29—41no—
315C2×C4×C29—41no—
316C2×C4×C29—41no—
317C2×C4×C29—41no—
318C2×C4×C29—41no—
319C2×C4×C29—41no—
320C2×C4×C29—41no—
321C2×C4×C29—41no—
322C2×C4×C29—41no—
323C2×C4×C29—41no—
324C2×C4×C29—41no—
325C2×C4×C29—41no—
326C2×C4×C29—41no—
327C2×C4×C29—84no—
328C2×C4×C29#12112yes—
329C2×C4×C29#12312yes—
330C2×C4×C29C22×D411yescharacteristic
331C2×C4×C29C2×#4111yescharacteristic
332C2×C4×C29C2×#4111yescharacteristic
333C2×C4×C29C2×#4111yescharacteristic
334C2×C4×C29H(5,𝔽2)11yescharacteristic
335C2×C4×C29H(5,𝔽2)11yescharacteristic
336C8×C29—22no—
337C8×C29—22no—
338C8×C29—41no—
339C8×C29—41no—
340C2×#480C2×C2911yescharacteristic, complemented
341C2×#408C2×C2911yescharacteristic, complemented
342#2615C2×C2911yescharacteristic
343#2311C2×C2911yescharacteristic, complemented
344#2076C2×C2911yescharacteristic, complemented
345#2075C2×C2911yescharacteristic, complemented
346#2034C2×C2911yescharacteristic, complemented
347#2033C2×C2911yescharacteristic, complemented
348#1895C2×C2911yescharacteristic, complemented
349#1893C2×C2911yescharacteristic, complemented
350#1875C2×C2911yescharacteristic, complemented
351#1854C2×C2911yescharacteristic, complemented
352#1824C2×C2911yescharacteristic, complemented
353#1809C2×C2911yescharacteristic, complemented
354#1808C2×C2911yescharacteristic, complemented
355C22×C29—22no—
356C22×C29—22no—
357C22×C29—22no—
358C22×C29—22no—
359C22×C29—22no—
360C22×C29—22no—
361C22×C29—41no—
362C22×C29—41no—
363C22×C29—41no—
364C22×C29—41no—
365C22×C29—41no—
366C22×C29—41no—
367C22×C29—41no—
368C22×C29—41no—
369C22×C29—41no—
370C22×C29—41no—
371C22×C29—41no—
372C22×C29—41no—
373C22×C29—41no—
374C22×C29—41no—
375C22×C29—41no—
376C22×C29—81no—
377C22×C29—81no—
378C22×C29—81no—
379C22×C29—81no—
380C22×C29—81no—
381C22×C29—81no—
382C22×C29—81no—
383C22×C29C2×#12111yescharacteristic
384C22×C29C2×#12311yescharacteristic
385C22×C29#53411yescharacteristic
386C22×C29#57611yescharacteristic
387C22×C29#57611yescharacteristic
388C22×C29#57711yescharacteristic
389C22×C29#57811yescharacteristic
390C4×C29—22no—
391C4×C29—22no—
392C4×C29—41no—
393C4×C29—81no—
394C4×C29—81no—
395C4×C29—81no—
396C4×C29—81no—
397C4×C29—81no—
398C4×C29—81no—
399C4×C29—81no—
400C4×C29#54611yescharacteristic
401C4×C29#54611yescharacteristic
402C4×C29#55111yescharacteristic
403C4×C29#55111yescharacteristic
404C22×#41C22×C2911yescharacteristic
405C22×M16C22×C2911yescharacteristic
406C23×C8C22×C2911yescharacteristic
407C2×#121C22×C2911yescharacteristic
408C2×#121C22×C2911yescharacteristic
409C2×#121C22×C2911yescharacteristic
410C2×#117C22×C2911yescharacteristic
411C22×C4⋊C4C22×C2911yescharacteristic
412#480—24no—
413C2×#107C22×C2911yescharacteristic
414C2×#107C22×C2911yescharacteristic
415C2×#107C22×C2911yescharacteristic
416C2×#106C22×C2911yescharacteristic
417C2×#102C22×C2911yescharacteristic
418C2×#102C22×C2911yescharacteristic
419C2×#102C22×C2911yescharacteristic
420C2×#102C22×C2911yescharacteristic
421#408—24no—
422C2×C22⋊C8C22×C2911yescharacteristic
423C2×C22⋊C8C22×C2911yescharacteristic
424C2×C22⋊C8C22×C2911yescharacteristic
425C2×C22⋊C8C22×C2911yescharacteristic
426#393—21no—
427#392—21no—
428#392—21no—
429#392—21no—
430#391—21no—
431#390—21no—
432#386—21no—
433#386—21no—
434#380C22×C2911yescharacteristic
435#380C22×C2911yescharacteristic
436#380C22×C2911yescharacteristic
437#380C22×C2911yescharacteristic
438#380C22×C2911yescharacteristic
439#380C22×C2911yescharacteristic
440#380C22×C2911yescharacteristic
441#340C22×C2911yescharacteristic
442#340C22×C2911yescharacteristic
443#340C22×C2911yescharacteristic
444#340C22×C2911yescharacteristic
445#340C22×C2911yescharacteristic
446#340C22×C2911yescharacteristic
447#340C22×C2911yescharacteristic
448#340C22×C2911yescharacteristic
449C2×C29—42no—
450C2×C29—42no—
451C2×C29—81no—
452C2×C29—161no—
453C2×C29#241211yescharacteristic
454C2×C29#305811yescharacteristic
455C2×C29#306311yescharacteristic
456C2×C29#309611yescharacteristic
457C2×C29#309811yescharacteristic
458C2×C29#319811yescharacteristic
459C2×C29#320311yescharacteristic
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C22×Q8D4×C2911yescharacteristic
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4D4×C2911yescharacteristic
471C22×D4D4×C2911yescharacteristic
472C22×D4D4×C2911yescharacteristic
473C22×D4C23×C2911yescharacteristic
474C23×C4—21no—
475C23×C4C23×C2911yescharacteristic
476C23×C4C23×C2911yescharacteristic
477C23×C4C23×C2911yescharacteristic
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—41no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C23×C2911yescharacteristic
485C22×C8C23×C2911yescharacteristic
486C22×C8C23×C2911yescharacteristic
487C22×C8C23×C2911yescharacteristic
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#117—41no—
495#117—41no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4C23×C2911yescharacteristic
500C2×C4⋊C4C23×C2911yescharacteristic
501C2×C4⋊C4C23×C2911yescharacteristic
502C2×C4⋊C4C23×C2911yescharacteristic
503C2×C4⋊C4C23×C2911yescharacteristic
504C2×C4⋊C4C23×C2911yescharacteristic
505C2×C4⋊C4C23×C2911yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C42—21no—
518#107—22no—
519#107—22no—
520#107—41no—
521#106—41no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8D4×C2914yescomplemented
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537C29#2456211yescharacteristic, direct product factor, Sylow
538C24—21no—
539C24C2×D4×C2911yescharacteristic
540C24C2×D4×C2911yescharacteristic
541C24C2×D4×C2911yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C2911yescharacteristic
598C22×C4C2×D4×C2911yescharacteristic
599C22×C4C2×D4×C2912yes—
600C22×C4C2×D4×C2911yescharacteristic
601C22×C4#41×C2912yes—
602C22×C4#41×C2912yes—
603C22×C4#41×C2912yes—
604C22×C4C24×C2911yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C2912yes—
618C2×C8C2×D4×C2912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23C29×#12112yes—
673C23C29×#12312yes—
674C23C22×D4×C2911yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4C29×#12112yes—
728C2×C4C29×#12312yes—
729C2×C4C22×D4×C2911yescharacteristic
730C2×C4C2×#41×C2911yescharacteristic
731C2×C4C2×#41×C2911yescharacteristic
732C2×C4C2×#41×C2911yescharacteristic
733C2×C4C29×H(5,𝔽2)11yescharacteristic
734C2×C4C29×H(5,𝔽2)11yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×C29×#12111yescharacteristic
768C22C2×C29×#12311yescharacteristic
769C22C29×#53411yescharacteristic
770C22C29×#57611yescharacteristic
771C22C29×#57611yescharacteristic
772C22C29×#57711yescharacteristic
773C22C29×#57811yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C29×#54611yescharacteristic
785C4C29×#54611yescharacteristic
786C4C29×#55111yescharacteristic
787C4C29×#55111yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2C29×#241211yescharacteristic
793C2C29×#305811yescharacteristic
794C2C29×#306311yescharacteristic
795C2C29×#309611yescharacteristic
796C2C29×#309811yescharacteristic
797C2C29×#319811yescharacteristic
798C2C29×#320311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#480C2semidirect
2. C2×C29×#408C2semidirect
4. C29×#2311C2semidirect
5. C29×#2076C2semidirect
6. C29×#2075C2semidirect
7. C29×#2034C2semidirect
8. C29×#2033C2semidirect
9. C29×#1895C2semidirect
10. C29×#1893C2semidirect
11. C29×#1875C2semidirect
12. C29×#1854C2semidirect
13. C29×#1824C2semidirect
14. C29×#1809C2semidirect
15. C29×#1808C2semidirect
130. C29×C22⋊C8D4semidirect
246. #24562C29direct (N × H)
340. C2×#480C2×C29semidirect
341. C2×#408C2×C29semidirect
343. #2311C2×C29semidirect
344. #2076C2×C29semidirect
345. #2075C2×C29semidirect
346. #2034C2×C29semidirect
347. #2033C2×C29semidirect
348. #1895C2×C29semidirect
349. #1893C2×C29semidirect
350. #1875C2×C29semidirect
351. #1854C2×C29semidirect
352. #1824C2×C29semidirect
353. #1809C2×C29semidirect
354. #1808C2×C29semidirect
529. C22⋊C8D4×C29semidirect
537. C29#24562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4802
C2×C29×#4082
C29×#26152
C29×#23112
C29×#20762
C29×#20752
C29×#20342
C29×#20332
C29×#18952
C29×#18932
C29×#18752
C29×#18542
C29×#18242
C29×#18092
C29×#18082
#2456229