Finite Group Databasebeta

← C5×#32709 #11955429

Subgroups — C5×#32709 #11955429

Order 1280.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2848C211yesmaximal, characteristic, complemented
2C5×#2847C211yesmaximal, characteristic
3C5×#2077C211yesmaximal, characteristic, complemented
4C5×#2076C211yesmaximal, characteristic, complemented
5C5×#2075C211yesmaximal, characteristic, complemented
6C5×#2036C211yesmaximal, characteristic, complemented
7C5×#2036C211yesmaximal, characteristic, complemented
8C5×#2035C211yesmaximal, characteristic, complemented
9C5×#2034C211yesmaximal, characteristic, complemented
10C5×#2033C211yesmaximal, characteristic, complemented
11C5×#2033C211yesmaximal, characteristic, complemented
12C5×#2000C211yesmaximal, characteristic, complemented
13C5×#2000C211yesmaximal, characteristic, complemented
14C5×#2000C211yesmaximal, characteristic, complemented
15C5×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic, complemented
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic
23C2×C5×#121C2211yescharacteristic
24C2×C5×#120—21no—
25C2×C5×#107C2211yescharacteristic, complemented
26C2×C5×#107C2211yescharacteristic, complemented
27C2×C5×#106C2211yescharacteristic, complemented
28C2×C5×#103C2211yescharacteristic, complemented
29C2×C5×#103C2211yescharacteristic, complemented
30C2×C5×#103C2211yescharacteristic, complemented
31C2×C5×#102C2211yescharacteristic, complemented
32C2×C5×#102C2211yescharacteristic, complemented
33C2×C5×#102C2211yescharacteristic, complemented
34C2×C5×C22⋊C8C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C5×#386—21no—
41C5×#386—21no—
42C5×#386—21no—
43C5×#385—21no—
44C5×#385—21no—
45C5×#385—21no—
46C5×#380C2211yescharacteristic
47C5×#380C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#379—21no—
53C5×#340C2211yescharacteristic, complemented
54C5×#340C2211yescharacteristic, complemented
55C5×#340C2211yescharacteristic, complemented
56C5×#340C2211yescharacteristic, complemented
57C5×#340C2211yescharacteristic, complemented
58C5×#340C2211yescharacteristic, complemented
59#32709C511yesmaximal, characteristic, direct product factor, Sylow
60C25×C5D411yescharacteristic
61C22×C5×Q8C2311yescharacteristic
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5—41no—
70C23×C4×C5—41no—
71C23×C4×C5—41no—
72C23×C4×C5D411yescharacteristic
73C23×C4×C5D411yescharacteristic
74C23×C4×C5D411yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C2×C5×SD16—41no—
79C2×C5×SD16—41no—
80C2×C5×SD16—41no—
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C5×C22⋊Q8—41no—
86C5×C22⋊Q8—41no—
87C5×C22⋊Q8—41no—
88C5×C22⋊Q8—41no—
89C5×C22⋊Q8—41no—
90C5×C22⋊Q8—41no—
91C5×#121—41no—
92C5×#121—41no—
93C5×#121—41no—
94C5×#121—41no—
95C5×#121—41no—
96C5×#121—41no—
97C5×#120—44no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C5×#107—41no—
120C5×#107—41no—
121C5×#106—41no—
122C5×#103—41no—
123C5×#103—41no—
124C5×#103—41no—
125C5×#102—41no—
126C5×#102—41no—
127C5×#102—41no—
128C5×C22⋊C8—41no—
129C5×C22⋊C8—41no—
130C5×C22⋊C8—41no—
131C5×C22⋊C8—41no—
132C5×C22⋊C8—41no—
133C5×C22⋊C8—41no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140#2848C2×C511yescharacteristic, complemented
141#2847C2×C511yescharacteristic
142#2077C2×C511yescharacteristic, complemented
143#2076C2×C511yescharacteristic, complemented
144#2075C2×C511yescharacteristic, complemented
145#2036C2×C511yescharacteristic, complemented
146#2036C2×C511yescharacteristic, complemented
147#2035C2×C511yescharacteristic, complemented
148#2034C2×C511yescharacteristic, complemented
149#2033C2×C511yescharacteristic, complemented
150#2033C2×C511yescharacteristic, complemented
151#2000C2×C511yescharacteristic, complemented
152#2000C2×C511yescharacteristic, complemented
153#2000C2×C511yescharacteristic, complemented
154#1779C2×C511yescharacteristic, complemented
155C24×C5—22no—
156C24×C5—22no—
157C24×C5—22no—
158C24×C5—21no—
159C24×C5—41no—
160C24×C5—41no—
161C24×C5—41no—
162C24×C5—41no—
163C24×C5C2×D411yescharacteristic
164C24×C5C2×D411yescharacteristic
165C24×C5C2×D411yescharacteristic
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—42no—
179C2×C5×D4—42no—
180C2×C5×D4—42no—
181C2×C5×D4—42no—
182C2×C5×D4—42no—
183C2×C5×D4—42no—
184C2×C5×D4—42no—
185C2×C5×D4—42no—
186C2×C5×D4—42no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—41no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5—41no—
216C22×C4×C5—41no—
217C22×C4×C5—41no—
218C22×C4×C5—41no—
219C22×C4×C5—41no—
220C22×C4×C5—41no—
221C22×C4×C5—44no—
222C22×C4×C5—44no—
223C22×C4×C5—44no—
224C22×C4×C5—44no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2411yescharacteristic
229C5×SD16—44no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C2×C5×C8—21no—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—42no—
255C5×C4⋊C4—42no—
256C5×C4⋊C4—42no—
257C5×C22⋊C4—42no—
258C5×C22⋊C4—42no—
259C5×C22⋊C4—42no—
260C5×C22⋊C4—42no—
261C5×C22⋊C4—42no—
262C5×C22⋊C4—42no—
263C5×C22⋊C4—42no—
264C5×C22⋊C4—42no—
265C5×C22⋊C4—42no—
266C5×C22⋊C4—42no—
267C5×C22⋊C4—42no—
268C5×C22⋊C4—42no—
269C24×C4C22×C511yescharacteristic
270C22×SD16C22×C511yescharacteristic, complemented
271C2×C22⋊Q8C22×C511yescharacteristic
272C2×C22⋊Q8C22×C511yescharacteristic
273C2×C22⋊Q8C22×C511yescharacteristic
274C2×#121C22×C511yescharacteristic
275C2×#121C22×C511yescharacteristic
276C2×#121C22×C511yescharacteristic
277C2×#120—21no—
278C2×#107C22×C511yescharacteristic, complemented
279C2×#107C22×C511yescharacteristic, complemented
280C2×#106C22×C511yescharacteristic, complemented
281C2×#103C22×C511yescharacteristic, complemented
282C2×#103C22×C511yescharacteristic, complemented
283C2×#103C22×C511yescharacteristic, complemented
284C2×#102C22×C511yescharacteristic, complemented
285C2×#102C22×C511yescharacteristic, complemented
286C2×#102C22×C511yescharacteristic, complemented
287C2×C22⋊C8C22×C511yescharacteristic
288C2×C22⋊C8C22×C511yescharacteristic
289C2×C22⋊C8C22×C511yescharacteristic
290C2×C22⋊C8C22×C511yescharacteristic
291C2×C22⋊C8C22×C511yescharacteristic
292C2×C22⋊C8C22×C511yescharacteristic
293#386—21no—
294#386—21no—
295#386—21no—
296#385—21no—
297#385—21no—
298#385—21no—
299#380C22×C511yescharacteristic
300#380C22×C511yescharacteristic
301#380C22×C511yescharacteristic
302#380C22×C511yescharacteristic
303#380C22×C511yescharacteristic
304#380C22×C511yescharacteristic
305#379—21no—
306#340C22×C511yescharacteristic, complemented
307#340C22×C511yescharacteristic, complemented
308#340C22×C511yescharacteristic, complemented
309#340C22×C511yescharacteristic, complemented
310#340C22×C511yescharacteristic, complemented
311#340C22×C511yescharacteristic, complemented
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5#13512yes—
345C23×C5AGL(1,ℤ/8)12yes—
346C23×C5#13712yes—
347C23×C5C22×D411yescharacteristic
348C5×Q8—41no—
349C5×Q8—41no—
350C5×Q8—41no—
351C5×Q8—41no—
352C5×D4—41no—
353C5×D4—41no—
354C5×D4—41no—
355C5×D4—41no—
356C5×D4—84no—
357C5×D4—84no—
358C5×D4—84no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5H(5,𝔽2)11yescharacteristic
405C2×C4×C5H(5,𝔽2)11yescharacteristic
406C2×C4×C5H(5,𝔽2)11yescharacteristic
407C2×C4×C5H(5,𝔽2)11yescharacteristic
408C2×C4×C5H(5,𝔽2)11yescharacteristic
409C2×C4×C5H(5,𝔽2)11yescharacteristic
410C5×C8—41no—
411C5×C8—41no—
412C5×C8—41no—
413C5×C8—41no—
414C25C5×D411yescharacteristic
415C22×Q8C23×C511yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C511yescharacteristic
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4C5×D411yescharacteristic
427C23×C4C5×D411yescharacteristic
428C23×C4C5×D411yescharacteristic
429C23×C4C23×C511yescharacteristic
430C23×C4C23×C511yescharacteristic
431C23×C4C23×C511yescharacteristic
432C2×SD16—41no—
433C2×SD16—41no—
434C2×SD16—41no—
435C22×C8C23×C511yescharacteristic
436C22×C8C23×C511yescharacteristic
437C22×C8C23×C511yescharacteristic
438C22×C8C23×C511yescharacteristic
439C22⋊Q8—41no—
440C22⋊Q8—41no—
441C22⋊Q8—41no—
442C22⋊Q8—41no—
443C22⋊Q8—41no—
444C22⋊Q8—41no—
445#121—41no—
446#121—41no—
447#121—41no—
448#121—41no—
449#121—41no—
450#121—41no—
451#120—44no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4C23×C511yescharacteristic
456C2×C4⋊C4C23×C511yescharacteristic
457C2×C4⋊C4C23×C511yescharacteristic
458C2×C4⋊C4C23×C511yescharacteristic
459C2×C4⋊C4C23×C511yescharacteristic
460C2×C4⋊C4C23×C511yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473#107—41no—
474#107—41no—
475#106—41no—
476#103—41no—
477#103—41no—
478#103—41no—
479#102—41no—
480#102—41no—
481#102—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494C22×C5—22no—
495C22×C5—22no—
496C22×C5—22no—
497C22×C5—22no—
498C22×C5—22no—
499C22×C5—22no—
500C22×C5—22no—
501C22×C5—22no—
502C22×C5—22no—
503C22×C5—416no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5—81no—
517C22×C5—81no—
518C22×C5—81no—
519C22×C5—81no—
520C22×C5—81no—
521C22×C5—81no—
522C22×C5—81no—
523C22×C5#53411yescharacteristic
524C22×C5#53411yescharacteristic
525C22×C5#53411yescharacteristic
526C22×C5C2×#13511yescharacteristic
527C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
528C22×C5C2×#13711yescharacteristic
529C22×C5#57511yescharacteristic
530C4×C5—41no—
531C4×C5—41no—
532C4×C5—41no—
533C4×C5—81no—
534C4×C5—81no—
535C4×C5—81no—
536C4×C5—81no—
537C4×C5—81no—
538C4×C5—81no—
539C4×C5—81no—
540C4×C5#56011yescharacteristic
541C4×C5#56011yescharacteristic
542C4×C5#56011yescharacteristic
543C4×C5H(3,𝔽4)11yescharacteristic
544C24—22no—
545C24—22no—
546C24—22no—
547C24—21no—
548C24—41no—
549C24—41no—
550C24—41no—
551C24—41no—
552C24C2×C5×D411yescharacteristic
553C24C2×C5×D411yescharacteristic
554C24C2×C5×D411yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4C2×C5×D411yescharacteristic
615C22×C4C2×C5×D411yescharacteristic
616C22×C4C2×C5×D411yescharacteristic
617C22×C4C24×C511yescharacteristic
618SD16—44no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C2×C5—42no—
659C2×C5—42no—
660C2×C5—42no—
661C2×C5—161no—
662C2×C5#281211yescharacteristic
663C2×C5#318811yescharacteristic
664C2×C5#319011yescharacteristic
665C2×C5#319111yescharacteristic
666C2×C5#319311yescharacteristic
667C2×C5#319411yescharacteristic
668C2×C5#319611yescharacteristic
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23C5×#13512yes—
702C23C5×AGL(1,ℤ/8)12yes—
703C23C5×#13712yes—
704C23C22×C5×D411yescharacteristic
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—84no—
714D4—84no—
715D4—84no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4C5×H(5,𝔽2)11yescharacteristic
762C2×C4C5×H(5,𝔽2)11yescharacteristic
763C2×C4C5×H(5,𝔽2)11yescharacteristic
764C2×C4C5×H(5,𝔽2)11yescharacteristic
765C2×C4C5×H(5,𝔽2)11yescharacteristic
766C2×C4C5×H(5,𝔽2)11yescharacteristic
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C5#3270911yescharacteristic, direct product factor, Sylow
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C5×#53411yescharacteristic
802C22C5×#53411yescharacteristic
803C22C5×#53411yescharacteristic
804C22C2×C5×#13511yescharacteristic
805C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
806C22C2×C5×#13711yescharacteristic
807C22C5×#57511yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C5×#56011yescharacteristic
819C4C5×#56011yescharacteristic
820C4C5×#56011yescharacteristic
821C4C5×H(3,𝔽4)11yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C5×#281211yescharacteristic
827C2C5×#318811yescharacteristic
828C2C5×#319011yescharacteristic
829C2C5×#319111yescharacteristic
830C2C5×#319311yescharacteristic
831C2C5×#319411yescharacteristic
832C2C5×#319611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2848C2semidirect
3. C5×#2077C2semidirect
4. C5×#2076C2semidirect
5. C5×#2075C2semidirect
6. C5×#2036C2semidirect
7. C5×#2036C2semidirect
8. C5×#2035C2semidirect
9. C5×#2034C2semidirect
10. C5×#2033C2semidirect
11. C5×#2033C2semidirect
12. C5×#2000C2semidirect
13. C5×#2000C2semidirect
14. C5×#2000C2semidirect
15. C5×#1779C2semidirect
17. C22×C5×SD16C22semidirect
25. C2×C5×#107C22semidirect
26. C2×C5×#107C22semidirect
27. C2×C5×#106C22semidirect
28. C2×C5×#103C22semidirect
29. C2×C5×#103C22semidirect
30. C2×C5×#103C22semidirect
31. C2×C5×#102C22semidirect
32. C2×C5×#102C22semidirect
33. C2×C5×#102C22semidirect
53. C5×#340C22semidirect
54. C5×#340C22semidirect
55. C5×#340C22semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. C5×#340C22semidirect
59. #32709C5direct (N × H)
140. #2848C2×C5semidirect
142. #2077C2×C5semidirect
143. #2076C2×C5semidirect
144. #2075C2×C5semidirect
145. #2036C2×C5semidirect
146. #2036C2×C5semidirect
147. #2035C2×C5semidirect
148. #2034C2×C5semidirect
149. #2033C2×C5semidirect
150. #2033C2×C5semidirect
151. #2000C2×C5semidirect
152. #2000C2×C5semidirect
153. #2000C2×C5semidirect
154. #1779C2×C5semidirect
270. C22×SD16C22×C5semidirect
278. C2×#107C22×C5semidirect
279. C2×#107C22×C5semidirect
280. C2×#106C22×C5semidirect
281. C2×#103C22×C5semidirect
282. C2×#103C22×C5semidirect
283. C2×#103C22×C5semidirect
284. C2×#102C22×C5semidirect
285. C2×#102C22×C5semidirect
286. C2×#102C22×C5semidirect
306. #340C22×C5semidirect
307. #340C22×C5semidirect
308. #340C22×C5semidirect
309. #340C22×C5semidirect
310. #340C22×C5semidirect
311. #340C22×C5semidirect
771. C5#32709direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28482
C5×#28472
C5×#20772
C5×#20762
C5×#20752
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#20002
C5×#17792
#327095