Finite Group Databasebeta

← C5×#36725 #11959445

Subgroups — C5×#36725 #11959445

Order 1280.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2846C212yesmaximal, complemented
2C5×#2736C211yesmaximal, characteristic, complemented
3C5×#2735C211yesmaximal, characteristic, complemented
4C5×#2735C212yesmaximal, complemented
5C5×#2697C212yesmaximal, complemented
6C5×#2685C212yesmaximal, complemented
7C5×#2685C212yesmaximal, complemented
8C5×#2684C212yesmaximal, complemented
9C5×#2678C212yesmaximal, complemented
10C5×#2670C211yesmaximal, characteristic, complemented
11C5×#2668C211yesmaximal, characteristic, complemented
12C5×#2626C211yesmaximal, characteristic, complemented
13C5×#2617C211yesmaximal, characteristic, complemented
14C5×#2480C212yesmaximal, complemented
15C5×#2472C212yesmaximal, complemented
16C5×#2424C212yesmaximal, complemented
17C5×#2418C212yesmaximal, complemented
18C5×#2321C212yesmaximal, complemented
19C2×C5×#379C211yesmaximal, characteristic, complemented
20C26×C5C2211yescharacteristic
21C2×C5×#126C2212yescomplemented
22C2×C5×#124C2212yescomplemented
23C2×C5×#123C2212yescomplemented
24C2×C5×C22⋊Q8C2211yescharacteristic, complemented
25C2×C5×#121C2212yescomplemented
26C2×C5×#121C2211yescharacteristic, complemented
27C2×C5×#120C2212yes—
28C2×C5×#120C2212yes—
29C2×C5×#120C2212yes—
30C2×C5×#120C2212yes—
31C2×C5×#120C2212yes—
32C2×C5×#120C2212yes—
33C2×C5×#120C2212yes—
34C2×C4×C5×D4C2212yescomplemented
35C22×C5×C22⋊C4C2212yes—
36C22×C5×C22⋊C4C2212yes—
37C22×C5×C22⋊C4C2211yescharacteristic
38C22×C5×C22⋊C4C2211yescharacteristic
39C5×#399C2211yescharacteristic, complemented
40C5×#399C2212yescomplemented
41C5×#399C2211yescharacteristic, complemented
42C5×#397C2212yescomplemented
43C5×#397C2211yescharacteristic, complemented
44C5×#397C2212yescomplemented
45C5×#397C2211yescharacteristic, complemented
46C5×#397C2212yescomplemented
47C5×#397C2212yescomplemented
48C5×#397C2212yescomplemented
49C5×#396C2212yescomplemented
50C5×#396C2212yescomplemented
51C5×#396C2212yescomplemented
52C5×#396C2212yescomplemented
53C5×#394C2212yescomplemented
54C5×#394C2212yescomplemented
55C5×#394C2212yescomplemented
56C5×#394C2212yescomplemented
57C5×#394C2212yescomplemented
58C5×#394C2212yescomplemented
59C5×#394C2212yescomplemented
60C5×#394C2212yescomplemented
61C5×#393C2212yescomplemented
62C5×#393C2211yescharacteristic, complemented
63C5×#393C2211yescharacteristic, complemented
64C5×#392C2211yescharacteristic, complemented
65C5×#392C2211yescharacteristic, complemented
66C5×#392C2212yescomplemented
67C5×#390C2212yescomplemented
68C5×#390C2212yescomplemented
69C5×#390C2212yescomplemented
70C5×#390C2212yescomplemented
71C5×#388C2212yescomplemented
72C5×#388C2212yescomplemented
73C5×#388C2212yescomplemented
74C5×#388C2212yescomplemented
75C5×#388C2212yescomplemented
76C5×#388C2212yescomplemented
77C5×#388C2212yescomplemented
78C5×#388C2212yescomplemented
79C5×#388C2212yescomplemented
80C5×#388C2212yescomplemented
81C5×#388C2212yescomplemented
82C5×#388C2212yescomplemented
83C5×#386C2212yescomplemented
84C5×#386C2212yescomplemented
85C5×#386C2212yescomplemented
86C5×#386C2212yescomplemented
87C5×#386C2212yescomplemented
88C5×#386C2212yescomplemented
89C5×#385C2212yescomplemented
90C5×#385C2212yescomplemented
91C5×#380C2211yescharacteristic, complemented
92C5×#380C2211yescharacteristic, complemented
93C5×#379C2212yes—
94C5×#379C2211yescharacteristic
95C5×#379C2212yes—
96C5×#379C2212yes—
97C5×#379C2212yes—
98C5×#379C2212yes—
99C5×#379C2212yes—
100C5×#379C2211yescharacteristic
101C5×#379C2212yes—
102C5×#379C2212yes—
103C5×#379C2211yescharacteristic
104C5×#379C2211yescharacteristic
105C5×#379C2212yes—
106C4×C5×C22⋊C4C2212yescomplemented
107#36725C511yesmaximal, characteristic, direct product factor, Sylow
108C25×C5—24no—
109C25×C5—44no—
110C25×C5—44no—
111C25×C5—42no—
112C25×C5—42no—
113C25×C5C2312yes—
114C25×C5C2311yescharacteristic
115C25×C5C2312yes—
116C25×C5C2311yescharacteristic
117C25×C5C2311yescharacteristic
118C22×C5×Q8C2311yescharacteristic, complemented
119C22×C5×D4C2312yes—
120C22×C5×D4C2312yes—
121C22×C5×D4C2312yes—
122C22×C5×D4C2312yes—
123C22×C5×D4C2312yes—
124C22×C5×D4C2312yes—
125C22×C5×D4C2312yes—
126C22×C5×D4C2311yescharacteristic, complemented
127C23×C4×C5C2312yes—
128C23×C4×C5C2311yescharacteristic
129C23×C4×C5C2311yescharacteristic
130C23×C4×C5C2312yescomplemented
131C5×#126—44no—
132C5×#124—44no—
133C5×#123—44no—
134C5×C22⋊Q8—42no—
135C5×#121—44no—
136C5×#121—42no—
137C5×#120—28no—
138C5×#120—44no—
139C5×#120—44no—
140C5×#120—44no—
141C5×#120—44no—
142C5×#120—44no—
143C5×#120—44no—
144C4×C5×D4—44no—
145C2×C5×C4⋊C4C2312yescomplemented
146C2×C5×C4⋊C4C2312yescomplemented
147C2×C5×C4⋊C4C2312yescomplemented
148C2×C5×C4⋊C4C2312yescomplemented
149C2×C5×C4⋊C4C2312yescomplemented
150C2×C5×C4⋊C4C2312yescomplemented
151C2×C5×C4⋊C4C2311yescharacteristic, complemented
152C2×C5×C4⋊C4C2312yescomplemented
153C2×C5×C4⋊C4C2311yescharacteristic, complemented
154C2×C5×C4⋊C4C2312yescomplemented
155C2×C5×C22⋊C4—44no—
156C2×C5×C22⋊C4—44no—
157C2×C5×C22⋊C4—42no—
158C2×C5×C22⋊C4—42no—
159C2×C5×C22⋊C4C2312yes—
160C2×C5×C22⋊C4C2312yes—
161C2×C5×C22⋊C4C2312yes—
162C2×C5×C22⋊C4C2312yes—
163C2×C5×C22⋊C4C2312yes—
164C2×C5×C22⋊C4C2312yes—
165C2×C5×C22⋊C4C2312yes—
166C2×C5×C22⋊C4C2312yes—
167C2×C5×C22⋊C4C2312yes—
168C2×C5×C22⋊C4C2312yes—
169C2×C5×C22⋊C4C2312yes—
170C2×C5×C22⋊C4C2312yes—
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2311yescharacteristic
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2312yes—
175C2×C5×C22⋊C4C2312yes—
176C2×C5×C22⋊C4C2312yes—
177C2×C5×C22⋊C4C2312yes—
178C2×C5×C22⋊C4C2312yes—
179C2×C5×C22⋊C4C2312yes—
180C2×C5×C22⋊C4C2311yescharacteristic
181C2×C5×C22⋊C4C2312yes—
182C2×C5×C22⋊C4C2312yes—
183C2×C5×C22⋊C4C2312yes—
184C2×C5×C22⋊C4C2312yes—
185C2×C5×C22⋊C4C2312yes—
186C2×C5×C22⋊C4C2312yes—
187C2×C5×C22⋊C4C2312yes—
188C2×C5×C22⋊C4C2312yes—
189C2×C5×C22⋊C4C2312yes—
190C2×C5×C22⋊C4C2312yes—
191C2×C5×C22⋊C4C2311yescharacteristic
192C2×C5×C22⋊C4C2311yescharacteristic
193C2×C5×C22⋊C4C2311yescharacteristic
194C2×C5×C22⋊C4C2311yescharacteristic
195C2×C5×C22⋊C4C2312yescomplemented
196C2×C5×C22⋊C4C2312yescomplemented
197C2×C5×C22⋊C4C2312yescomplemented
198C2×C5×C22⋊C4C2312yescomplemented
199C2×C5×C22⋊C4C2312yescomplemented
200C2×C5×C22⋊C4C2312yescomplemented
201C2×C42×C5C2312yescomplemented
202C2×C42×C5C2312yescomplemented
203C2×C42×C5C2312yescomplemented
204C5×#95C2312yescomplemented
205C5×#95C2312yescomplemented
206C5×#95C2311yescharacteristic, complemented
207C5×#95C2311yescharacteristic, complemented
208C5×#95C2311yescharacteristic, complemented
209C5×#95C2311yescharacteristic, complemented
210C5×#95C2312yescomplemented
211C5×#95C2312yescomplemented
212C5×#95C2312yescomplemented
213C5×#95C2312yescomplemented
214C5×#95C2312yescomplemented
215C5×#95C2312yescomplemented
216C5×#95C2312yescomplemented
217C5×#95C2312yescomplemented
218#2846C2×C512yescomplemented
219#2736C2×C511yescharacteristic, complemented
220#2735C2×C512yescomplemented
221#2735C2×C511yescharacteristic, complemented
222#2697C2×C512yescomplemented
223#2685C2×C512yescomplemented
224#2685C2×C512yescomplemented
225#2684C2×C512yescomplemented
226#2678C2×C512yescomplemented
227#2670C2×C511yescharacteristic, complemented
228#2668C2×C511yescharacteristic, complemented
229#2626C2×C511yescharacteristic, complemented
230#2617C2×C511yescharacteristic, complemented
231#2480C2×C512yescomplemented
232#2472C2×C512yescomplemented
233#2424C2×C512yescomplemented
234#2418C2×C512yescomplemented
235#2321C2×C512yescomplemented
236C2×#379C2×C511yescharacteristic, complemented
237C24×C5—24no—
238C24×C5—24no—
239C24×C5—24no—
240C24×C5—22no—
241C24×C5—22no—
242C24×C5—22no—
243C24×C5—24no—
244C24×C5—22no—
245C24×C5—24no—
246C24×C5—24no—
247C24×C5—24no—
248C24×C5—24no—
249C24×C5—24no—
250C24×C5—24no—
251C24×C5—42no—
252C24×C5—42no—
253C24×C5—42no—
254C24×C5—42no—
255C24×C5—41no—
256C24×C5—42no—
257C24×C5—41no—
258C24×C5—42no—
259C24×C5—42no—
260C24×C5—42no—
261C24×C5—42no—
262C24×C5—41no—
263C24×C5—42no—
264C24×C5—41no—
265C24×C5—432no—
266C24×C5—416no—
267C24×C5—432no—
268C24×C5—416no—
269C24×C5—416no—
270C24×C5#4114yes—
271C24×C5C2412yes—
272C24×C5C2411yescharacteristic
273C24×C5C2411yescharacteristic
274C24×C5C2412yes—
275C24×C5C2412yes—
276C24×C5C2411yescharacteristic
277C2×C5×Q8—41no—
278C2×C5×Q8—42no—
279C2×C5×D4—24no—
280C2×C5×D4—24no—
281C2×C5×D4—24no—
282C2×C5×D4—24no—
283C2×C5×D4—24no—
284C2×C5×D4—24no—
285C2×C5×D4—24no—
286C2×C5×D4—24no—
287C2×C5×D4—24no—
288C2×C5×D4—42no—
289C2×C5×D4—42no—
290C2×C5×D4—42no—
291C2×C5×D4—42no—
292C2×C5×D4—42no—
293C2×C5×D4—42no—
294C2×C5×D4—42no—
295C2×C5×D4—42no—
296C2×C5×D4—42no—
297C2×C5×D4—42no—
298C2×C5×D4—42no—
299C2×C5×D4—42no—
300C2×C5×D4—42no—
301C2×C5×D4—41no—
302C22×C4×C5—24no—
303C22×C4×C5—22no—
304C22×C4×C5—22no—
305C22×C4×C5—42no—
306C22×C4×C5—42no—
307C22×C4×C5—42no—
308C22×C4×C5—42no—
309C22×C4×C5—42no—
310C22×C4×C5—42no—
311C22×C4×C5—42no—
312C22×C4×C5C2412yes—
313C22×C4×C5C2412yes—
314C22×C4×C5C2412yes—
315C22×C4×C5C2412yes—
316C22×C4×C5C2412yes—
317C22×C4×C5C2412yes—
318C22×C4×C5C2412yes—
319C22×C4×C5C2412yes—
320C22×C4×C5C2411yescharacteristic
321C22×C4×C5C2411yescharacteristic
322C22×C4×C5C2411yescharacteristic
323C22×C4×C5C2411yescharacteristic
324C22×C4×C5C2412yes—
325C5×C4⋊C4—42no—
326C5×C4⋊C4—42no—
327C5×C4⋊C4—41no—
328C5×C4⋊C4—41no—
329C5×C4⋊C4—42no—
330C5×C4⋊C4—42no—
331C5×C4⋊C4—42no—
332C5×C4⋊C4—42no—
333C5×C4⋊C4—42no—
334C5×C4⋊C4—42no—
335C5×C22⋊C4—24no—
336C5×C22⋊C4—24no—
337C5×C22⋊C4—24no—
338C5×C22⋊C4—24no—
339C5×C22⋊C4—24no—
340C5×C22⋊C4—24no—
341C5×C22⋊C4—24no—
342C5×C22⋊C4—24no—
343C5×C22⋊C4—24no—
344C5×C22⋊C4—24no—
345C5×C22⋊C4—24no—
346C5×C22⋊C4—24no—
347C5×C22⋊C4—24no—
348C5×C22⋊C4—42no—
349C5×C22⋊C4—42no—
350C5×C22⋊C4—41no—
351C5×C22⋊C4—42no—
352C5×C22⋊C4—42no—
353C5×C22⋊C4—42no—
354C5×C22⋊C4—41no—
355C5×C22⋊C4—41no—
356C5×C22⋊C4—41no—
357C5×C22⋊C4—41no—
358C5×C22⋊C4—41no—
359C5×C22⋊C4—42no—
360C5×C22⋊C4—42no—
361C5×C22⋊C4—42no—
362C5×C22⋊C4—42no—
363C5×C22⋊C4—42no—
364C5×C22⋊C4—42no—
365C5×C22⋊C4—42no—
366C5×C22⋊C4—42no—
367C5×C22⋊C4—42no—
368C5×C22⋊C4—42no—
369C5×C22⋊C4—42no—
370C5×C22⋊C4—42no—
371C5×C22⋊C4—42no—
372C5×C22⋊C4—42no—
373C5×C22⋊C4—42no—
374C5×C22⋊C4—42no—
375C5×C22⋊C4—42no—
376C5×C22⋊C4—42no—
377C42×C5—42no—
378C42×C5—42no—
379C42×C5—42no—
380C26C22×C511yescharacteristic
381C2×#126C22×C512yescomplemented
382C2×#124C22×C512yescomplemented
383C2×#123C22×C512yescomplemented
384C2×C22⋊Q8C22×C511yescharacteristic, complemented
385C2×#121C22×C512yescomplemented
386C2×#121C22×C511yescharacteristic, complemented
387C2×#120C22×C512yes—
388C2×#120C22×C512yes—
389C2×#120C22×C512yes—
390C2×#120C22×C512yes—
391C2×#120C22×C512yes—
392C2×#120C22×C512yes—
393C2×#120C22×C512yes—
394C2×C4×D4C22×C512yescomplemented
395C22×C22⋊C4C22×C511yescharacteristic
396C22×C22⋊C4C22×C511yescharacteristic
397C22×C22⋊C4C22×C512yes—
398C22×C22⋊C4C22×C512yes—
399#399C22×C511yescharacteristic, complemented
400#399C22×C511yescharacteristic, complemented
401#399C22×C512yescomplemented
402#397C22×C511yescharacteristic, complemented
403#397C22×C511yescharacteristic, complemented
404#397C22×C512yescomplemented
405#397C22×C512yescomplemented
406#397C22×C512yescomplemented
407#397C22×C512yescomplemented
408#397C22×C512yescomplemented
409#396C22×C512yescomplemented
410#396C22×C512yescomplemented
411#396C22×C512yescomplemented
412#396C22×C512yescomplemented
413#394C22×C512yescomplemented
414#394C22×C512yescomplemented
415#394C22×C512yescomplemented
416#394C22×C512yescomplemented
417#394C22×C512yescomplemented
418#394C22×C512yescomplemented
419#394C22×C512yescomplemented
420#394C22×C512yescomplemented
421#393C22×C511yescharacteristic, complemented
422#393C22×C511yescharacteristic, complemented
423#393C22×C512yescomplemented
424#392C22×C511yescharacteristic, complemented
425#392C22×C511yescharacteristic, complemented
426#392C22×C512yescomplemented
427#390C22×C512yescomplemented
428#390C22×C512yescomplemented
429#390C22×C512yescomplemented
430#390C22×C512yescomplemented
431#388C22×C512yescomplemented
432#388C22×C512yescomplemented
433#388C22×C512yescomplemented
434#388C22×C512yescomplemented
435#388C22×C512yescomplemented
436#388C22×C512yescomplemented
437#388C22×C512yescomplemented
438#388C22×C512yescomplemented
439#388C22×C512yescomplemented
440#388C22×C512yescomplemented
441#388C22×C512yescomplemented
442#388C22×C512yescomplemented
443#386C22×C512yescomplemented
444#386C22×C512yescomplemented
445#386C22×C512yescomplemented
446#386C22×C512yescomplemented
447#386C22×C512yescomplemented
448#386C22×C512yescomplemented
449#385C22×C512yescomplemented
450#385C22×C512yescomplemented
451#380C22×C511yescharacteristic, complemented
452#380C22×C511yescharacteristic, complemented
453#379C22×C512yes—
454#379C22×C512yes—
455#379C22×C512yes—
456#379C22×C512yes—
457#379C22×C512yes—
458#379C22×C512yes—
459#379C22×C512yes—
460#379C22×C511yescharacteristic
461#379C22×C511yescharacteristic
462#379C22×C512yes—
463#379C22×C512yes—
464#379C22×C511yescharacteristic
465#379C22×C511yescharacteristic
466C4×C22⋊C4C22×C512yescomplemented
467C23×C5—22no—
468C23×C5—22no—
469C23×C5—216no—
470C23×C5—28no—
471C23×C5—22no—
472C23×C5—22no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—21no—
477C23×C5—22no—
478C23×C5—22no—
479C23×C5—22no—
480C23×C5—22no—
481C23×C5—22no—
482C23×C5—22no—
483C23×C5—22no—
484C23×C5—22no—
485C23×C5—22no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5—22no—
494C23×C5—22no—
495C23×C5—22no—
496C23×C5—22no—
497C23×C5—22no—
498C23×C5—48no—
499C23×C5—48no—
500C23×C5—48no—
501C23×C5—48no—
502C23×C5—48no—
503C23×C5—48no—
504C23×C5—48no—
505C23×C5—48no—
506C23×C5—48no—
507C23×C5—48no—
508C23×C5—44no—
509C23×C5—44no—
510C23×C5—48no—
511C23×C5—48no—
512C23×C5—44no—
513C23×C5—44no—
514C23×C5—44no—
515C23×C5—48no—
516C23×C5—44no—
517C23×C5—48no—
518C23×C5—48no—
519C23×C5—48no—
520C23×C5—48no—
521C23×C5—4128no—
522C23×C5—48no—
523C23×C5—44no—
524C23×C5—44no—
525C23×C5—48no—
526C23×C5C2×#4112yes—
527C23×C5C2×#4112yes—
528C23×C5C2×#4112yes—
529C23×C5H(5,𝔽2)14yes—
530C23×C5H(5,𝔽2)14yes—
531C23×C5H(5,𝔽2)12yes—
532C23×C5H(5,𝔽2)12yes—
533C23×C5C2511yescharacteristic
534C5×Q8—82no—
535C5×D4—48no—
536C5×D4—84no—
537C5×D4—84no—
538C5×D4—84no—
539C5×D4—84no—
540C5×D4—84no—
541C5×D4—84no—
542C5×D4—82no—
543C2×C4×C5—22no—
544C2×C4×C5—22no—
545C2×C4×C5—22no—
546C2×C4×C5—22no—
547C2×C4×C5—22no—
548C2×C4×C5—22no—
549C2×C4×C5—22no—
550C2×C4×C5—22no—
551C2×C4×C5—22no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—22no—
558C2×C4×C5—22no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—22no—
563C2×C4×C5—22no—
564C2×C4×C5—22no—
565C2×C4×C5—22no—
566C2×C4×C5—22no—
567C2×C4×C5—22no—
568C2×C4×C5—22no—
569C2×C4×C5—21no—
570C2×C4×C5—22no—
571C2×C4×C5—22no—
572C2×C4×C5—22no—
573C2×C4×C5—21no—
574C2×C4×C5—22no—
575C2×C4×C5—21no—
576C2×C4×C5—21no—
577C2×C4×C5—22no—
578C2×C4×C5—84no—
579C2×C4×C5—82no—
580C2×C4×C5—82no—
581C2×C4×C5—84no—
582C25—24no—
583C25—44no—
584C25—44no—
585C25—42no—
586C25—42no—
587C25C23×C512yes—
588C25C23×C511yescharacteristic
589C25C23×C511yescharacteristic
590C25C23×C512yes—
591C25C23×C511yescharacteristic
592C22×Q8C23×C511yescharacteristic, complemented
593C22×D4C23×C512yes—
594C22×D4C23×C512yes—
595C22×D4C23×C512yes—
596C22×D4C23×C512yes—
597C22×D4C23×C512yes—
598C22×D4C23×C512yes—
599C22×D4C23×C512yes—
600C22×D4C23×C511yescharacteristic, complemented
601C23×C4C23×C512yes—
602C23×C4C23×C511yescharacteristic
603C23×C4C23×C511yescharacteristic
604C23×C4C23×C512yescomplemented
605#126—44no—
606#124—44no—
607#123—44no—
608C22⋊Q8—42no—
609#121—44no—
610#121—42no—
611#120—28no—
612#120—44no—
613#120—44no—
614#120—44no—
615#120—44no—
616#120—44no—
617#120—44no—
618C4×D4—44no—
619C2×C4⋊C4C23×C512yescomplemented
620C2×C4⋊C4C23×C512yescomplemented
621C2×C4⋊C4C23×C511yescharacteristic, complemented
622C2×C4⋊C4C23×C511yescharacteristic, complemented
623C2×C4⋊C4C23×C512yescomplemented
624C2×C4⋊C4C23×C512yescomplemented
625C2×C4⋊C4C23×C512yescomplemented
626C2×C4⋊C4C23×C512yescomplemented
627C2×C4⋊C4C23×C512yescomplemented
628C2×C4⋊C4C23×C512yescomplemented
629C2×C22⋊C4—44no—
630C2×C22⋊C4—44no—
631C2×C22⋊C4—42no—
632C2×C22⋊C4—42no—
633C2×C22⋊C4C23×C512yes—
634C2×C22⋊C4C23×C512yes—
635C2×C22⋊C4C23×C512yes—
636C2×C22⋊C4C23×C512yes—
637C2×C22⋊C4C23×C512yes—
638C2×C22⋊C4C23×C512yes—
639C2×C22⋊C4C23×C512yes—
640C2×C22⋊C4C23×C512yes—
641C2×C22⋊C4C23×C512yes—
642C2×C22⋊C4C23×C512yes—
643C2×C22⋊C4C23×C512yes—
644C2×C22⋊C4C23×C512yes—
645C2×C22⋊C4C23×C512yes—
646C2×C22⋊C4C23×C511yescharacteristic
647C2×C22⋊C4C23×C512yes—
648C2×C22⋊C4C23×C512yes—
649C2×C22⋊C4C23×C512yes—
650C2×C22⋊C4C23×C511yescharacteristic
651C2×C22⋊C4C23×C512yes—
652C2×C22⋊C4C23×C512yes—
653C2×C22⋊C4C23×C511yescharacteristic
654C2×C22⋊C4C23×C511yescharacteristic
655C2×C22⋊C4C23×C511yescharacteristic
656C2×C22⋊C4C23×C511yescharacteristic
657C2×C22⋊C4C23×C512yes—
658C2×C22⋊C4C23×C512yes—
659C2×C22⋊C4C23×C512yes—
660C2×C22⋊C4C23×C512yes—
661C2×C22⋊C4C23×C512yes—
662C2×C22⋊C4C23×C512yes—
663C2×C22⋊C4C23×C512yes—
664C2×C22⋊C4C23×C512yes—
665C2×C22⋊C4C23×C512yes—
666C2×C22⋊C4C23×C512yes—
667C2×C22⋊C4C23×C512yes—
668C2×C22⋊C4C23×C512yes—
669C2×C22⋊C4C23×C512yescomplemented
670C2×C22⋊C4C23×C512yescomplemented
671C2×C22⋊C4C23×C512yescomplemented
672C2×C22⋊C4C23×C512yescomplemented
673C2×C22⋊C4C23×C512yescomplemented
674C2×C22⋊C4C23×C512yescomplemented
675C2×C42C23×C512yescomplemented
676C2×C42C23×C512yescomplemented
677C2×C42C23×C512yescomplemented
678#95C23×C512yescomplemented
679#95C23×C512yescomplemented
680#95C23×C511yescharacteristic, complemented
681#95C23×C511yescharacteristic, complemented
682#95C23×C511yescharacteristic, complemented
683#95C23×C511yescharacteristic, complemented
684#95C23×C512yescomplemented
685#95C23×C512yescomplemented
686#95C23×C512yescomplemented
687#95C23×C512yescomplemented
688#95C23×C512yescomplemented
689#95C23×C512yescomplemented
690#95C23×C512yescomplemented
691#95C23×C512yescomplemented
692C22×C5—24no—
693C22×C5—24no—
694C22×C5—22no—
695C22×C5—22no—
696C22×C5—22no—
697C22×C5—22no—
698C22×C5—24no—
699C22×C5—24no—
700C22×C5—24no—
701C22×C5—24no—
702C22×C5—24no—
703C22×C5—24no—
704C22×C5—24no—
705C22×C5—24no—
706C22×C5—432no—
707C22×C5—416no—
708C22×C5—432no—
709C22×C5—416no—
710C22×C5—416no—
711C22×C5—42no—
712C22×C5—42no—
713C22×C5—42no—
714C22×C5—42no—
715C22×C5—42no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5—42no—
719C22×C5—42no—
720C22×C5—42no—
721C22×C5—42no—
722C22×C5—42no—
723C22×C5—41no—
724C22×C5—41no—
725C22×C5—42no—
726C22×C5—42no—
727C22×C5—42no—
728C22×C5—42no—
729C22×C5—42no—
730C22×C5—42no—
731C22×C5—42no—
732C22×C5#53814yes—
733C22×C5C22×#4111yescharacteristic
734C22×C5C2×H(5,𝔽2)11yescharacteristic
735C22×C5C2×H(5,𝔽2)11yescharacteristic
736C22×C5C2×H(5,𝔽2)12yes—
737C22×C5C2×H(5,𝔽2)12yes—
738C4×C5—42no—
739C4×C5—42no—
740C4×C5—42no—
741C4×C5—42no—
742C4×C5—41no—
743C4×C5—41no—
744C4×C5—42no—
745C4×C5—41no—
746C4×C5—42no—
747C4×C5—41no—
748C4×C5—42no—
749C4×C5—42no—
750C4×C5—42no—
751C24—24no—
752C24—24no—
753C24—24no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—22no—
758C24—24no—
759C24—24no—
760C24—24no—
761C24—24no—
762C24—24no—
763C24—24no—
764C24—24no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24—42no—
769C24—41no—
770C24—41no—
771C24—42no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—42no—
776C24—41no—
777C24—41no—
778C24—42no—
779C24—432no—
780C24—416no—
781C24—432no—
782C24—416no—
783C24—416no—
784C24C5×#4114yes—
785C24C24×C512yes—
786C24C24×C511yescharacteristic
787C24C24×C511yescharacteristic
788C24C24×C512yes—
789C24C24×C512yes—
790C24C24×C511yescharacteristic
791C2×Q8—41no—
792C2×Q8—42no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—41no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4C24×C512yes—
827C22×C4C24×C512yes—
828C22×C4C24×C512yes—
829C22×C4C24×C512yes—
830C22×C4C24×C512yes—
831C22×C4C24×C511yescharacteristic
832C22×C4C24×C511yescharacteristic
833C22×C4C24×C512yes—
834C22×C4C24×C512yes—
835C22×C4C24×C512yes—
836C22×C4C24×C512yes—
837C22×C4C24×C511yescharacteristic
838C22×C4C24×C511yescharacteristic
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—42no—
863C22⋊C4—42no—
864C22⋊C4—41no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—41no—
869C22⋊C4—41no—
870C22⋊C4—41no—
871C22⋊C4—41no—
872C22⋊C4—41no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—42no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C2×C5—24no—
895C2×C5—42no—
896C2×C5—42no—
897C2×C5—44no—
898C2×C5—44no—
899C2×C5—82no—
900C2×C5C2×#53811yescharacteristic
901C2×C5#349012yes—
902C2×C5#353212yes—
903C2×C5#353211yescharacteristic
904C2×C5#353211yescharacteristic
905C23—22no—
906C23—22no—
907C23—216no—
908C23—28no—
909C23—22no—
910C23—22no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—48no—
937C23—48no—
938C23—48no—
939C23—48no—
940C23—48no—
941C23—48no—
942C23—48no—
943C23—48no—
944C23—48no—
945C23—48no—
946C23—44no—
947C23—44no—
948C23—48no—
949C23—48no—
950C23—44no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—48no—
955C23—48no—
956C23—48no—
957C23—48no—
958C23—48no—
959C23—4128no—
960C23—48no—
961C23—44no—
962C23—44no—
963C23—48no—
964C23C2×C5×#4112yes—
965C23C2×C5×#4112yes—
966C23C2×C5×#4112yes—
967C23C5×H(5,𝔽2)14yes—
968C23C5×H(5,𝔽2)14yes—
969C23C5×H(5,𝔽2)12yes—
970C23C5×H(5,𝔽2)12yes—
971C23C25×C511yescharacteristic
972Q8—82no—
973D4—48no—
974D4—84no—
975D4—84no—
976D4—84no—
977D4—84no—
978D4—84no—
979D4—84no—
980D4—82no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—84no—
1017C2×C4—82no—
1018C2×C4—82no—
1019C2×C4—84no—
1020C5#3672511yescharacteristic, direct product factor, Sylow
1021C22—24no—
1022C22—24no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—432no—
1036C22—416no—
1037C22—432no—
1038C22—416no—
1039C22—416no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22C5×#53814yes—
1062C22C22×C5×#4111yescharacteristic
1063C22C2×C5×H(5,𝔽2)11yescharacteristic
1064C22C2×C5×H(5,𝔽2)11yescharacteristic
1065C22C2×C5×H(5,𝔽2)12yes—
1066C22C2×C5×H(5,𝔽2)12yes—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—41no—
1072C4—42no—
1073C4—41no—
1074C4—42no—
1075C4—41no—
1076C4—41no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C2—24no—
1081C2—42no—
1082C2—42no—
1083C2—44no—
1084C2—44no—
1085C2—82no—
1086C2C2×C5×#53811yescharacteristic
1087C2C5×#349012yes—
1088C2C5×#353212yes—
1089C2C5×#353211yescharacteristic
1090C2C5×#353211yescharacteristic
subgroupG/H
center, socleC23×C5C25
commutator, Frattini, cosocleC23C25×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2846C2semidirect
2. C5×#2736C2semidirect
3. C5×#2735C2semidirect
4. C5×#2735C2semidirect
5. C5×#2697C2semidirect
6. C5×#2685C2semidirect
7. C5×#2685C2semidirect
8. C5×#2684C2semidirect
9. C5×#2678C2semidirect
10. C5×#2670C2semidirect
11. C5×#2668C2semidirect
12. C5×#2626C2semidirect
13. C5×#2617C2semidirect
14. C5×#2480C2semidirect
15. C5×#2472C2semidirect
16. C5×#2424C2semidirect
17. C5×#2418C2semidirect
18. C5×#2321C2semidirect
19. C2×C5×#379C2semidirect
21. C2×C5×#126C22semidirect
22. C2×C5×#124C22semidirect
23. C2×C5×#123C22semidirect
24. C2×C5×C22⋊Q8C22semidirect
25. C2×C5×#121C22semidirect
26. C2×C5×#121C22semidirect
34. C2×C4×C5×D4C22semidirect
39. C5×#399C22semidirect
40. C5×#399C22semidirect
41. C5×#399C22semidirect
42. C5×#397C22semidirect
43. C5×#397C22semidirect
44. C5×#397C22semidirect
45. C5×#397C22semidirect
46. C5×#397C22semidirect
47. C5×#397C22semidirect
48. C5×#397C22semidirect
49. C5×#396C22semidirect
50. C5×#396C22semidirect
51. C5×#396C22semidirect
52. C5×#396C22semidirect
53. C5×#394C22semidirect
54. C5×#394C22semidirect
55. C5×#394C22semidirect
56. C5×#394C22semidirect
57. C5×#394C22semidirect
58. C5×#394C22semidirect
59. C5×#394C22semidirect
60. C5×#394C22semidirect
61. C5×#393C22semidirect
62. C5×#393C22semidirect
63. C5×#393C22semidirect
64. C5×#392C22semidirect
65. C5×#392C22semidirect
66. C5×#392C22semidirect
67. C5×#390C22semidirect
68. C5×#390C22semidirect
69. C5×#390C22semidirect
70. C5×#390C22semidirect
71. C5×#388C22semidirect
72. C5×#388C22semidirect
73. C5×#388C22semidirect
74. C5×#388C22semidirect
75. C5×#388C22semidirect
76. C5×#388C22semidirect
77. C5×#388C22semidirect
78. C5×#388C22semidirect
79. C5×#388C22semidirect
80. C5×#388C22semidirect
81. C5×#388C22semidirect
82. C5×#388C22semidirect
83. C5×#386C22semidirect
84. C5×#386C22semidirect
85. C5×#386C22semidirect
86. C5×#386C22semidirect
87. C5×#386C22semidirect
88. C5×#386C22semidirect
89. C5×#385C22semidirect
90. C5×#385C22semidirect
91. C5×#380C22semidirect
92. C5×#380C22semidirect
106. C4×C5×C22⋊C4C22semidirect
107. #36725C5direct (N × H)
118. C22×C5×Q8C23semidirect
126. C22×C5×D4C23semidirect
130. C23×C4×C5C23semidirect
145. C2×C5×C4⋊C4C23semidirect
146. C2×C5×C4⋊C4C23semidirect
147. C2×C5×C4⋊C4C23semidirect
148. C2×C5×C4⋊C4C23semidirect
149. C2×C5×C4⋊C4C23semidirect
150. C2×C5×C4⋊C4C23semidirect
151. C2×C5×C4⋊C4C23semidirect
152. C2×C5×C4⋊C4C23semidirect
153. C2×C5×C4⋊C4C23semidirect
154. C2×C5×C4⋊C4C23semidirect
195. C2×C5×C22⋊C4C23semidirect
196. C2×C5×C22⋊C4C23semidirect
197. C2×C5×C22⋊C4C23semidirect
198. C2×C5×C22⋊C4C23semidirect
199. C2×C5×C22⋊C4C23semidirect
200. C2×C5×C22⋊C4C23semidirect
201. C2×C42×C5C23semidirect
202. C2×C42×C5C23semidirect
203. C2×C42×C5C23semidirect
204. C5×#95C23semidirect
205. C5×#95C23semidirect
206. C5×#95C23semidirect
207. C5×#95C23semidirect
208. C5×#95C23semidirect
209. C5×#95C23semidirect
210. C5×#95C23semidirect
211. C5×#95C23semidirect
212. C5×#95C23semidirect
213. C5×#95C23semidirect
214. C5×#95C23semidirect
215. C5×#95C23semidirect
216. C5×#95C23semidirect
217. C5×#95C23semidirect
218. #2846C2×C5semidirect
219. #2736C2×C5semidirect
220. #2735C2×C5semidirect
221. #2735C2×C5semidirect
222. #2697C2×C5semidirect
223. #2685C2×C5semidirect
224. #2685C2×C5semidirect
225. #2684C2×C5semidirect
226. #2678C2×C5semidirect
227. #2670C2×C5semidirect
228. #2668C2×C5semidirect
229. #2626C2×C5semidirect
230. #2617C2×C5semidirect
231. #2480C2×C5semidirect
232. #2472C2×C5semidirect
233. #2424C2×C5semidirect
234. #2418C2×C5semidirect
235. #2321C2×C5semidirect
236. C2×#379C2×C5semidirect
381. C2×#126C22×C5semidirect
382. C2×#124C22×C5semidirect
383. C2×#123C22×C5semidirect
384. C2×C22⋊Q8C22×C5semidirect
385. C2×#121C22×C5semidirect
386. C2×#121C22×C5semidirect
394. C2×C4×D4C22×C5semidirect
399. #399C22×C5semidirect
400. #399C22×C5semidirect
401. #399C22×C5semidirect
402. #397C22×C5semidirect
403. #397C22×C5semidirect
404. #397C22×C5semidirect
405. #397C22×C5semidirect
406. #397C22×C5semidirect
407. #397C22×C5semidirect
408. #397C22×C5semidirect
409. #396C22×C5semidirect
410. #396C22×C5semidirect
411. #396C22×C5semidirect
412. #396C22×C5semidirect
413. #394C22×C5semidirect
414. #394C22×C5semidirect
415. #394C22×C5semidirect
416. #394C22×C5semidirect
417. #394C22×C5semidirect
418. #394C22×C5semidirect
419. #394C22×C5semidirect
420. #394C22×C5semidirect
421. #393C22×C5semidirect
422. #393C22×C5semidirect
423. #393C22×C5semidirect
424. #392C22×C5semidirect
425. #392C22×C5semidirect
426. #392C22×C5semidirect
427. #390C22×C5semidirect
428. #390C22×C5semidirect
429. #390C22×C5semidirect
430. #390C22×C5semidirect
431. #388C22×C5semidirect
432. #388C22×C5semidirect
433. #388C22×C5semidirect
434. #388C22×C5semidirect
435. #388C22×C5semidirect
436. #388C22×C5semidirect
437. #388C22×C5semidirect
438. #388C22×C5semidirect
439. #388C22×C5semidirect
440. #388C22×C5semidirect
441. #388C22×C5semidirect
442. #388C22×C5semidirect
443. #386C22×C5semidirect
444. #386C22×C5semidirect
445. #386C22×C5semidirect
446. #386C22×C5semidirect
447. #386C22×C5semidirect
448. #386C22×C5semidirect
449. #385C22×C5semidirect
450. #385C22×C5semidirect
451. #380C22×C5semidirect
452. #380C22×C5semidirect
466. C4×C22⋊C4C22×C5semidirect
592. C22×Q8C23×C5semidirect
600. C22×D4C23×C5semidirect
604. C23×C4C23×C5semidirect
619. C2×C4⋊C4C23×C5semidirect
620. C2×C4⋊C4C23×C5semidirect
621. C2×C4⋊C4C23×C5semidirect
622. C2×C4⋊C4C23×C5semidirect
623. C2×C4⋊C4C23×C5semidirect
624. C2×C4⋊C4C23×C5semidirect
625. C2×C4⋊C4C23×C5semidirect
626. C2×C4⋊C4C23×C5semidirect
627. C2×C4⋊C4C23×C5semidirect
628. C2×C4⋊C4C23×C5semidirect
669. C2×C22⋊C4C23×C5semidirect
670. C2×C22⋊C4C23×C5semidirect
671. C2×C22⋊C4C23×C5semidirect
672. C2×C22⋊C4C23×C5semidirect
673. C2×C22⋊C4C23×C5semidirect
674. C2×C22⋊C4C23×C5semidirect
675. C2×C42C23×C5semidirect
676. C2×C42C23×C5semidirect
677. C2×C42C23×C5semidirect
678. #95C23×C5semidirect
679. #95C23×C5semidirect
680. #95C23×C5semidirect
681. #95C23×C5semidirect
682. #95C23×C5semidirect
683. #95C23×C5semidirect
684. #95C23×C5semidirect
685. #95C23×C5semidirect
686. #95C23×C5semidirect
687. #95C23×C5semidirect
688. #95C23×C5semidirect
689. #95C23×C5semidirect
690. #95C23×C5semidirect
691. #95C23×C5semidirect
1020. C5#36725direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28462
C5×#27362
C5×#27352
C5×#26972
C5×#26852
C5×#26842
C5×#26782
C5×#26702
C5×#26682
C5×#26262
C5×#26172
C5×#24802
C5×#24722
C5×#24242
C5×#24182
C5×#23212
C2×C5×#3792
#367255