Finite Group Databasebeta

← C5×#32729 #11955449

Subgroups — C5×#32729 #11955449

Order 1280.

776 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2855C211yesmaximal, characteristic, complemented
2C5×#2850C211yesmaximal, characteristic
3C5×#2101C211yesmaximal, characteristic, complemented
4C5×#2097C211yesmaximal, characteristic, complemented
5C5×#2067C211yesmaximal, characteristic, complemented
6C5×#2066C211yesmaximal, characteristic, complemented
7C5×#2056C211yesmaximal, characteristic, complemented
8C5×#2055C211yesmaximal, characteristic, complemented
9C5×#2042C211yesmaximal, characteristic, complemented
10C5×#2036C211yesmaximal, characteristic, complemented
11C5×#2034C211yesmaximal, characteristic
12C5×#2015C211yesmaximal, characteristic, complemented
13C5×#2001C211yesmaximal, characteristic, complemented
14C5×#2000C211yesmaximal, characteristic
15C5×#1797C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C2×C5×#124C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#391C2211yescharacteristic
38C5×#391C2211yescharacteristic
39C5×#391C2211yescharacteristic
40C5×#390C2211yescharacteristic
41C5×#389C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#388—21no—
44C5×#388—21no—
45C5×#387—21no—
46C5×#387—21no—
47C5×#386—21no—
48C5×#386—21no—
49C5×#385—21no—
50C5×#382C2211yescharacteristic
51C5×#381—21no—
52C5×#380C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#32729C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×Q8C2311yescharacteristic
62C22×C5×D4—21no—
63C22×C5×D4C2311yescharacteristic
64C23×C4×C5D411yescharacteristic
65C23×C4×C5D411yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C2×C5×Q16—41no—
68C2×C5×Q16—41no—
69C2×C5×Q16—41no—
70C2×C5×SD16—41no—
71C2×C5×SD16—41no—
72C2×C5×SD16—41no—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×#124—41no—
78C5×#124—41no—
79C5×C22⋊Q8—41no—
80C5×C22⋊Q8—41no—
81C5×C22⋊Q8—41no—
82C5×C22⋊Q8—41no—
83C5×#121—41no—
84C5×#121—41no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C22⋊C4—21no—
95C2×C5×C22⋊C4—21no—
96C2×C5×C22⋊C4—21no—
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C42×C5—41no—
103C2×C42×C5—41no—
104C2×C42×C5D411yescharacteristic
105C2×C42×C5D411yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C2×C42×C5C2311yescharacteristic
108C5×#107—41no—
109C5×#106—41no—
110C5×C4⋊C8—41no—
111C5×C4⋊C8—41no—
112C5×#103—41no—
113C5×#103—41no—
114C5×#103—41no—
115C5×#103—41no—
116C5×#103—41no—
117C5×#102—41no—
118C5×#102—41no—
119C5×#102—41no—
120C5×C22⋊C8—41no—
121C5×C22⋊C8—41no—
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133#2855C2×C511yescharacteristic, complemented
134#2850C2×C511yescharacteristic
135#2101C2×C511yescharacteristic, complemented
136#2097C2×C511yescharacteristic, complemented
137#2067C2×C511yescharacteristic, complemented
138#2066C2×C511yescharacteristic, complemented
139#2056C2×C511yescharacteristic, complemented
140#2055C2×C511yescharacteristic, complemented
141#2042C2×C511yescharacteristic, complemented
142#2036C2×C511yescharacteristic, complemented
143#2034C2×C511yescharacteristic
144#2015C2×C511yescharacteristic, complemented
145#2001C2×C511yescharacteristic, complemented
146#2000C2×C511yescharacteristic
147#1797C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5C2×D411yescharacteristic
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—42no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—41no—
187C22×C4×C5—41no—
188C22×C4×C5—41no—
189C22×C4×C5—41no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2411yescharacteristic
196C5×Q16—44no—
197C5×SD16—44no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C42×C5—21no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—41no—
237C42×C5—41no—
238C22×Q16C22×C511yescharacteristic
239C22×SD16C22×C511yescharacteristic
240C2×#124C22×C511yescharacteristic
241C2×C22⋊Q8C22×C511yescharacteristic
242C2×C22⋊Q8C22×C511yescharacteristic
243C2×#121C22×C511yescharacteristic
244C22×C42C22×C511yescharacteristic
245C2×#107C22×C511yescharacteristic
246C2×#106C22×C511yescharacteristic
247C2×C4⋊C8C22×C511yescharacteristic
248C2×C4⋊C8C22×C511yescharacteristic
249C2×#103C22×C511yescharacteristic
250C2×#103C22×C511yescharacteristic
251C2×#103C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×C22⋊C8C22×C511yescharacteristic
258C2×C22⋊C8C22×C511yescharacteristic
259#391C22×C511yescharacteristic
260#391C22×C511yescharacteristic
261#391C22×C511yescharacteristic
262#390C22×C511yescharacteristic
263#389C22×C511yescharacteristic
264#389C22×C511yescharacteristic
265#388—21no—
266#388—21no—
267#387—21no—
268#387—21no—
269#386—21no—
270#386—21no—
271#385—21no—
272#382C22×C511yescharacteristic
273#381—21no—
274#380C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#336C22×C511yescharacteristic
280#336C22×C511yescharacteristic
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—41no—
288C23×C5—41no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5#13712yes—
295C23×C5C22×D411yescharacteristic
296C5×Q8—41no—
297C5×Q8—41no—
298C5×Q8—41no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—41no—
302C5×Q8—41no—
303C5×Q8—41no—
304C5×D4—41no—
305C5×D4—41no—
306C5×D4—41no—
307C5×D4—41no—
308C5×D4—84no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—44no—
324C2×C4×C5—44no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5#13512yes—
351C2×C4×C5H(5,𝔽2)11yescharacteristic
352C2×C4×C5H(5,𝔽2)11yescharacteristic
353C2×C4×C5H(5,𝔽2)11yescharacteristic
354C2×C4×C5H(5,𝔽2)11yescharacteristic
355C2×C4×C5H(5,𝔽2)11yescharacteristic
356C2×C4×C52−1+411yescharacteristic
357C5×C8—41no—
358C5×C8—41no—
359C5×C8—41no—
360C5×C8—41no—
361C22×Q8C23×C511yescharacteristic
362C22×Q8C23×C511yescharacteristic
363C22×D4—21no—
364C22×D4C23×C511yescharacteristic
365C23×C4C5×D411yescharacteristic
366C23×C4C5×D411yescharacteristic
367C23×C4C23×C511yescharacteristic
368C2×Q16—41no—
369C2×Q16—41no—
370C2×Q16—41no—
371C2×SD16—41no—
372C2×SD16—41no—
373C2×SD16—41no—
374C22×C8C23×C511yescharacteristic
375C22×C8C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378#124—41no—
379#124—41no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384#121—41no—
385#121—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—41no—
404C2×C42—41no—
405C2×C42C5×D411yescharacteristic
406C2×C42C5×D411yescharacteristic
407C2×C42C23×C511yescharacteristic
408C2×C42C23×C511yescharacteristic
409#107—41no—
410#106—41no—
411C4⋊C8—41no—
412C4⋊C8—41no—
413#103—41no—
414#103—41no—
415#103—41no—
416#103—41no—
417#103—41no—
418#102—41no—
419#102—41no—
420#102—41no—
421C22⋊C8—41no—
422C22⋊C8—41no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5—81no—
446C22×C5—81no—
447C22×C5—81no—
448C22×C5#53411yescharacteristic
449C22×C5#53511yescharacteristic
450C22×C5#53711yescharacteristic
451C22×C5C2×#13511yescharacteristic
452C22×C5C2×#13711yescharacteristic
453C22×C5#57511yescharacteristic
454C22×C5#57511yescharacteristic
455C4×C5—22no—
456C4×C5—41no—
457C4×C5—41no—
458C4×C5—41no—
459C4×C5—41no—
460C4×C5—81no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5—81no—
467C4×C5#56011yescharacteristic
468C4×C5#56011yescharacteristic
469C4×C5#56211yescharacteristic
470C4×C5#56211yescharacteristic
471C24—21no—
472C24C2×C5×D411yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D411yescharacteristic
516C22×C4C2×C5×D411yescharacteristic
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C24×C511yescharacteristic
519Q16—44no—
520SD16—44no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—41no—
560C42—41no—
561C2×C5—42no—
562C2×C5—161no—
563C2×C5#281311yescharacteristic
564C2×C5#319111yescharacteristic
565C2×C5#319611yescharacteristic
566C2×C5#321211yescharacteristic
567C2×C5#321511yescharacteristic
568C2×C5#324811yescharacteristic
569C2×C5#325611yescharacteristic
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C5×#13712yes—
584C23C22×C5×D411yescharacteristic
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—84no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
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×C4C5×#13512yes—
640C2×C4C5×H(5,𝔽2)11yescharacteristic
641C2×C4C5×H(5,𝔽2)11yescharacteristic
642C2×C4C5×H(5,𝔽2)11yescharacteristic
643C2×C4C5×H(5,𝔽2)11yescharacteristic
644C2×C4C5×H(5,𝔽2)11yescharacteristic
645C2×C4C5×2−1+411yescharacteristic
646C8—41no—
647C8—41no—
648C8—41no—
649C8—41no—
650C5#3272911yescharacteristic, direct product factor, Sylow
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22C5×#53411yescharacteristic
666C22C5×#53511yescharacteristic
667C22C5×#53711yescharacteristic
668C22C2×C5×#13511yescharacteristic
669C22C2×C5×#13711yescharacteristic
670C22C5×#57511yescharacteristic
671C22C5×#57511yescharacteristic
672C4—22no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4C5×#56011yescharacteristic
685C4C5×#56011yescharacteristic
686C4C5×#56211yescharacteristic
687C4C5×#56211yescharacteristic
688C2—42no—
689C2—161no—
690C2C5×#281311yescharacteristic
691C2C5×#319111yescharacteristic
692C2C5×#319611yescharacteristic
693C2C5×#321211yescharacteristic
694C2C5×#321511yescharacteristic
695C2C5×#324811yescharacteristic
696C2C5×#325611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2855C2semidirect
3. C5×#2101C2semidirect
4. C5×#2097C2semidirect
5. C5×#2067C2semidirect
6. C5×#2066C2semidirect
7. C5×#2056C2semidirect
8. C5×#2055C2semidirect
9. C5×#2042C2semidirect
10. C5×#2036C2semidirect
12. C5×#2015C2semidirect
13. C5×#2001C2semidirect
15. C5×#1797C2semidirect
59. #32729C5direct (N × H)
133. #2855C2×C5semidirect
135. #2101C2×C5semidirect
136. #2097C2×C5semidirect
137. #2067C2×C5semidirect
138. #2066C2×C5semidirect
139. #2056C2×C5semidirect
140. #2055C2×C5semidirect
141. #2042C2×C5semidirect
142. #2036C2×C5semidirect
144. #2015C2×C5semidirect
145. #2001C2×C5semidirect
147. #1797C2×C5semidirect
650. C5#32729direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28552
C5×#28502
C5×#21012
C5×#20972
C5×#20672
C5×#20662
C5×#20562
C5×#20552
C5×#20422
C5×#20362
C5×#20342
C5×#20152
C5×#20012
C5×#20002
C5×#17972
#327295