Finite Group Databasebeta

← C29×#15101 #20310001

Subgroups — C29×#15101 #20310001

Order 7424.

1226 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#387C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C29C211yesmaximal, characteristic
3C29×#1444C211yesmaximal, characteristic
4C29×#1444C211yesmaximal, characteristic
5C29×#1442C212yesmaximal
6C29×#1441C211yesmaximal, characteristic
7C29×#1441C211yesmaximal, characteristic
8C29×#1441C212yesmaximal
9C29×#1436C212yesmaximal
10C29×#1436C212yesmaximal
11C29×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C29C2211yescharacteristic
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C4⋊C4×C29C2211yescharacteristic
16C22×C4⋊C4×C29C2212yes—
17C22×C4⋊C4×C29C2212yes—
18C22×C42×C29C2211yescharacteristic
19C22×C42×C29C2212yes—
20C29×#387—24no—
21C4×C4⋊C4×C29—24no—
22C2×C29×#95C2211yescharacteristic
23C2×C29×#95C2211yescharacteristic
24C2×C29×#95C2211yescharacteristic
25C2×C29×#95C2211yescharacteristic
26C2×C29×#95C2212yes—
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2211yescharacteristic
31C2×C29×#95C2211yescharacteristic
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2212yes—
36C2×C29×#95C2212yes—
37C23×C4×C29C2311yescharacteristic
38C23×C4×C29C2311yescharacteristic
39C23×C4×C29C2311yescharacteristic
40C23×C4×C29C2312yes—
41C23×C4×C29C2312yes—
42C23×C4×C29C2312yes—
43C23×C4×C29C2312yes—
44C23×C4×C29C2311yescharacteristic
45C23×C4×C29C2311yescharacteristic
46C23×C4×C29C2311yescharacteristic
47C23×C4×C29C2311yescharacteristic
48C2×C4⋊C4×C29—22no—
49C2×C4⋊C4×C29—22no—
50C2×C4⋊C4×C29—22no—
51C2×C4⋊C4×C29—24no—
52C2×C4⋊C4×C29—24no—
53C2×C4⋊C4×C29—22no—
54C2×C4⋊C4×C29—22no—
55C2×C4⋊C4×C29—22no—
56C2×C4⋊C4×C29—24no—
57C2×C4⋊C4×C29—24no—
58C2×C4⋊C4×C29—24no—
59C2×C4⋊C4×C29—22no—
60C2×C4⋊C4×C29—22no—
61C2×C4⋊C4×C29—42no—
62C2×C4⋊C4×C29—42no—
63C2×C4⋊C4×C29—42no—
64C2×C42×C29—22no—
65C2×C42×C29—22no—
66C2×C42×C29—24no—
67C2×C42×C29—42no—
68C2×C42×C29—42no—
69C2×C42×C29D414yes—
70C29×#95—24no—
71C29×#95—22no—
72C29×#95—22no—
73C29×#95—22no—
74C29×#95—22no—
75C29×#95—24no—
76C29×#95—22no—
77C29×#95—22no—
78C29×#95—24no—
79C29×#95—24no—
80C29×#95—42no—
81C29×#95—42no—
82C29×#95—42no—
83C29×#95—42no—
84C29×#95Q818yes—
85C24×C29C2411yescharacteristic
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—22no—
89C22×C4×C29—22no—
90C22×C4×C29—22no—
91C22×C4×C29—22no—
92C22×C4×C29—22no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—22no—
100C22×C4×C29—22no—
101C22×C4×C29—21no—
102C22×C4×C29—21no—
103C22×C4×C29—22no—
104C22×C4×C29—22no—
105C22×C4×C29—22no—
106C22×C4×C29—22no—
107C22×C4×C29—21no—
108C22×C4×C29—21no—
109C22×C4×C29—22no—
110C22×C4×C29—22no—
111C22×C4×C29—22no—
112C22×C4×C29—22no—
113C22×C4×C29—22no—
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—22no—
120C22×C4×C29—22no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—22no—
124C22×C4×C29—22no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—22no—
128C22×C4×C29—21no—
129C22×C4×C29—22no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—21no—
139C22×C4×C29—22no—
140C22×C4×C29—21no—
141C22×C4×C29C2×D412yes—
142C22×C4×C29C2×D412yes—
143C22×C4×C29C2×D412yes—
144C22×C4×C29C2×Q814yes—
145C22×C4×C29C2×Q814yes—
146C22×C4×C29C2×Q814yes—
147C22×C4×C29#4112yes—
148C22×C4×C29#4114yes—
149C22×C4×C29#4114yes—
150C22×C4×C29#4112yes—
151C22×C4×C29#4112yes—
152C22×C4×C29#4112yes—
153C4⋊C4×C29—28no—
154C4⋊C4×C29—28no—
155C4⋊C4×C29—28no—
156C4⋊C4×C29—48no—
157C4⋊C4×C29—48no—
158C4⋊C4×C29—44no—
159C42×C29—28no—
160C42×C29—48no—
161#15101C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29C22×D411yescharacteristic
163C23×C29C22×Q812yes—
164C23×C29C2×#4111yescharacteristic
165C23×C29C2×#4111yescharacteristic
166C23×C29C2×#4112yes—
167C23×C29C2×#4112yes—
168C23×C29C2×#4111yescharacteristic
169C23×C29C2×#4111yescharacteristic
170C23×C29H(5,𝔽2)12yes—
171C23×C29H(5,𝔽2)11yescharacteristic
172C23×C292−1+411yescharacteristic
173C2×C4×C29—22no—
174C2×C4×C29—22no—
175C2×C4×C29—22no—
176C2×C4×C29—24no—
177C2×C4×C29—24no—
178C2×C4×C29—22no—
179C2×C4×C29—24no—
180C2×C4×C29—24no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—24no—
184C2×C4×C29—22no—
185C2×C4×C29—24no—
186C2×C4×C29—22no—
187C2×C4×C29—24no—
188C2×C4×C29—24no—
189C2×C4×C29—22no—
190C2×C4×C29—24no—
191C2×C4×C29—24no—
192C2×C4×C29—24no—
193C2×C4×C29—24no—
194C2×C4×C29—22no—
195C2×C4×C29—24no—
196C2×C4×C29—22no—
197C2×C4×C29—24no—
198C2×C4×C29—24no—
199C2×C4×C29—24no—
200C2×C4×C29—24no—
201C2×C4×C29—41no—
202C2×C4×C29—41no—
203C2×C4×C29—42no—
204C2×C4×C29—42no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—42no—
208C2×C4×C29—41no—
209C2×C4×C29—42no—
210C2×C4×C29—41no—
211C2×C4×C29—42no—
212C2×C4×C29—42no—
213C2×C4×C29—42no—
214C2×C4×C29—42no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—41no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—42no—
222C2×C4×C29—41no—
223C2×C4×C29—42no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29#12314yes—
239C2×C4×C29C4⋊Q814yes—
240C2×#387C2×C2911yescharacteristic
241C2×C4×C4⋊C4C2×C2911yescharacteristic
242#1444C2×C2911yescharacteristic
243#1444C2×C2911yescharacteristic
244#1442C2×C2912yes—
245#1441C2×C2911yescharacteristic
246#1441C2×C2911yescharacteristic
247#1441C2×C2912yes—
248#1436C2×C2912yes—
249#1436C2×C2912yes—
250#1434C2×C2911yescharacteristic
251C22×C29C2×#12311yescharacteristic
252C22×C29#52511yescharacteristic
253C22×C29#52511yescharacteristic
254C22×C29#52511yescharacteristic
255C22×C29#52912yes—
256C22×C29#52912yes—
257C22×C29C2×C4⋊Q811yescharacteristic
258C22×C29#53312yes—
259C22×C29#53312yes—
260C22×C29#53511yescharacteristic
261C22×C29#53711yescharacteristic
262C22×C29#53812yes—
263C22×C29#53912yes—
264C22×C29#55112yes—
265C22×C29#55211yescharacteristic
266C22×C29#55312yes—
267C22×C29#55311yescharacteristic
268C22×C29#55412yes—
269C22×C29#55412yes—
270C22×C29#55412yes—
271C22×C29#55511yescharacteristic
272C22×C29#55611yescharacteristic
273C22×C29#55712yes—
274C4×C29—24no—
275C4×C29—24no—
276C4×C29—44no—
277C4×C29—44no—
278C4×C29—42no—
279C4×C29—44no—
280C4×C29—44no—
281C4×C29—42no—
282C4×C29—42no—
283C4×C29—81no—
284C4×C29—81no—
285C22×C4⋊C4C22×C2911yescharacteristic
286C22×C4⋊C4C22×C2911yescharacteristic
287C22×C4⋊C4C22×C2911yescharacteristic
288C22×C4⋊C4C22×C2911yescharacteristic
289C22×C4⋊C4C22×C2912yes—
290C22×C4⋊C4C22×C2912yes—
291C22×C42C22×C2911yescharacteristic
292C22×C42C22×C2912yes—
293#387—24no—
294C4×C4⋊C4—24no—
295C2×#95C22×C2911yescharacteristic
296C2×#95C22×C2911yescharacteristic
297C2×#95C22×C2911yescharacteristic
298C2×#95C22×C2911yescharacteristic
299C2×#95C22×C2912yes—
300C2×#95C22×C2912yes—
301C2×#95C22×C2912yes—
302C2×#95C22×C2912yes—
303C2×#95C22×C2911yescharacteristic
304C2×#95C22×C2911yescharacteristic
305C2×#95C22×C2912yes—
306C2×#95C22×C2912yes—
307C2×#95C22×C2912yes—
308C2×#95C22×C2912yes—
309C2×#95C22×C2912yes—
310C2×C29#239911yescharacteristic
311C2×C29#248511yescharacteristic
312C2×C29#250211yescharacteristic
313C2×C29#257412yes—
314C2×C29#258411yescharacteristic
315C2×C29#258512yes—
316C2×C29#258712yes—
317C2×C29#258812yes—
318C2×C29#259811yescharacteristic
319C2×C29#263611yescharacteristic
320C2×C29#285311yescharacteristic
321C23×C4C23×C2911yescharacteristic
322C23×C4C23×C2911yescharacteristic
323C23×C4C23×C2911yescharacteristic
324C23×C4C23×C2912yes—
325C23×C4C23×C2912yes—
326C23×C4C23×C2911yescharacteristic
327C23×C4C23×C2911yescharacteristic
328C23×C4C23×C2912yes—
329C23×C4C23×C2912yes—
330C23×C4C23×C2911yescharacteristic
331C23×C4C23×C2911yescharacteristic
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42D4×C2914yes—
354#95—24no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—22no—
361#95—22no—
362#95—24no—
363#95—24no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95Q8×C2918yes—
369C29#1510111yescharacteristic, direct product factor, Sylow
370C24C24×C2911yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4C2×D4×C2912yes—
427C22×C4C2×D4×C2912yes—
428C22×C4C2×D4×C2912yes—
429C22×C4C2×Q8×C2914yes—
430C22×C4C2×Q8×C2914yes—
431C22×C4C2×Q8×C2914yes—
432C22×C4#41×C2912yes—
433C22×C4#41×C2914yes—
434C22×C4#41×C2914yes—
435C22×C4#41×C2912yes—
436C22×C4#41×C2912yes—
437C22×C4#41×C2912yes—
438C4⋊C4—28no—
439C4⋊C4—28no—
440C4⋊C4—28no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C4⋊C4—44no—
444C42—28no—
445C42—48no—
446C23C22×D4×C2911yescharacteristic
447C23C22×Q8×C2912yes—
448C23C2×#41×C2911yescharacteristic
449C23C2×#41×C2911yescharacteristic
450C23C2×#41×C2912yes—
451C23C2×#41×C2912yes—
452C23C2×#41×C2911yescharacteristic
453C23C2×#41×C2911yescharacteristic
454C23C29×H(5,𝔽2)12yes—
455C23C29×H(5,𝔽2)11yescharacteristic
456C23C29×2−1+411yescharacteristic
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4C29×#12314yes—
523C2×C4C29×C4⋊Q814yes—
524C22C2×C29×#12311yescharacteristic
525C22C29×#52511yescharacteristic
526C22C29×#52511yescharacteristic
527C22C29×#52511yescharacteristic
528C22C29×#52912yes—
529C22C29×#52912yes—
530C22C2×C29×C4⋊Q811yescharacteristic
531C22C29×#53312yes—
532C22C29×#53312yes—
533C22C29×#53511yescharacteristic
534C22C29×#53711yescharacteristic
535C22C29×#53812yes—
536C22C29×#53912yes—
537C22C29×#55112yes—
538C22C29×#55211yescharacteristic
539C22C29×#55311yescharacteristic
540C22C29×#55312yes—
541C22C29×#55412yes—
542C22C29×#55412yes—
543C22C29×#55412yes—
544C22C29×#55511yescharacteristic
545C22C29×#55611yescharacteristic
546C22C29×#55712yes—
547C4—24no—
548C4—24no—
549C4—42no—
550C4—42no—
551C4—44no—
552C4—44no—
553C4—42no—
554C4—44no—
555C4—44no—
556C4—81no—
557C4—81no—
558C2C29×#239911yescharacteristic
559C2C29×#248511yescharacteristic
560C2C29×#250211yescharacteristic
561C2C29×#257412yes—
562C2C29×#258411yescharacteristic
563C2C29×#258512yes—
564C2C29×#258712yes—
565C2C29×#258812yes—
566C2C29×#259811yescharacteristic
567C2C29×#263611yescharacteristic
568C2C29×#285311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C29C24
commutator, Frattini, cosocleC24C24×C29
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
161. #15101C29direct (N × H)
369. C29#15101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3872
C2×C4×C4⋊C4×C292
C29×#14442
C29×#14422
C29×#14412
C29×#14362
C29×#14342
#1510129