Finite Group Databasebeta

← C5×#14005 #11936725

Subgroups — C5×#14005 #11936725

Order 1280.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C212yesmaximal
2C2×C5×#389C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic
5C2×C5×#384C211yesmaximal, characteristic
6C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
7C5×#1444C212yesmaximal
8C5×#1441C212yesmaximal
9C5×#1436C212yesmaximal
10C5×C4⋊#95C211yesmaximal, characteristic
11C4×C5×#95C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C5×C4⋊C4C2212yes—
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C4⋊C4C2212yes—
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×C42×C5C2212yes—
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C5×#389—28no—
26C5×#389—24no—
27C5×#389—24no—
28C5×#389C418yescomplemented
29C5×#384—24no—
30C4×C5×C4⋊C4—24no—
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41#14005C511yesmaximal, characteristic, direct product factor, Sylow
42C23×C4×C5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—24no—
55C2×C5×C4⋊C4—22no—
56C2×C5×C4⋊C4—24no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—24no—
60C2×C5×C4⋊C4—24no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—24no—
63C2×C5×C4⋊C4—24no—
64C2×C5×C4⋊C4—24no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4—22no—
68C2×C5×C4⋊C4—24no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—42no—
71C2×C5×C4⋊C4—42no—
72C2×C5×C4⋊C4—42no—
73C2×C5×C4⋊C4—42no—
74C2×C5×C4⋊C4C2×C414yes—
75C2×C5×C4⋊C4C2×C418yes—
76C2×C5×C4⋊C4C2×C414yes—
77C2×C5×C4⋊C4D414yes—
78C2×C5×C4⋊C4D414yes—
79C2×C5×C4⋊C4Q814yes—
80C2×C42×C5—22no—
81C2×C42×C5—22no—
82C2×C42×C5—22no—
83C2×C42×C5—22no—
84C2×C42×C5—24no—
85C2×C42×C5—24no—
86C2×C42×C5—22no—
87C2×C42×C5—22no—
88C2×C42×C5—22no—
89C2×C42×C5—42no—
90C2×C42×C5C2×C414yes—
91C2×C42×C5Q814yes—
92C5×#95—24no—
93C5×#95—24no—
94C5×#95—24no—
95C5×#95—24no—
96C5×#95—22no—
97C5×#95—22no—
98C5×#95—42no—
99C5×#95C2×C418yes—
100C5×#95D414yes—
101C5×#95Q814yes—
102C2×#389C2×C511yescharacteristic
103C2×#389C2×C512yes—
104C2×#389C2×C511yescharacteristic
105C2×#389C2×C511yescharacteristic
106C2×#384C2×C511yescharacteristic
107C2×C4×C4⋊C4C2×C511yescharacteristic
108#1444C2×C512yes—
109#1441C2×C512yes—
110#1436C2×C512yes—
111C4⋊#95C2×C511yescharacteristic
112C4×#95C2×C511yescharacteristic
113C24×C5C2411yescharacteristic
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5C22×C414yes—
168C22×C4×C5C22×C414yes—
169C22×C4×C5C22×C412yes—
170C22×C4×C5C22×C412yes—
171C22×C4×C5C22×C412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D414yes—
174C22×C4×C5C2×D414yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×D412yes—
178C22×C4×C5C2×D412yes—
179C22×C4×C5C2×Q812yes—
180C22×C4×C5C2×Q812yes—
181C22×C4×C5C2×Q814yes—
182C22×C4×C5C2×Q812yes—
183C22×C4×C5C2×Q812yes—
184C22×C4×C5C2×Q812yes—
185C22×C4×C5C2×Q812yes—
186C22×C4×C5C2×Q812yes—
187C22×C4×C5#4112yes—
188C22×C4×C5#4112yes—
189C22×C4×C5#4112yes—
190C22×C4×C5#4112yes—
191C5×C4⋊C4—216no—
192C5×C4⋊C4—28no—
193C5×C4⋊C4—28no—
194C5×C4⋊C4—48no—
195C5×C4⋊C4—48no—
196C5×C4⋊C4—48no—
197C5×C4⋊C4—48no—
198C5×C4⋊C4—44no—
199C5×C4⋊C4C4⋊C4116yescomplemented
200C42×C5—28no—
201C42×C5—28no—
202C42×C5—48no—
203C42×C5—44no—
204C22×C4⋊C4C22×C511yescharacteristic
205C22×C4⋊C4C22×C512yes—
206C22×C4⋊C4C22×C512yes—
207C22×C4⋊C4C22×C512yes—
208C22×C4⋊C4C22×C512yes—
209C22×C4⋊C4C22×C511yescharacteristic
210C22×C4⋊C4C22×C512yes—
211C22×C4⋊C4C22×C511yescharacteristic
212C22×C4⋊C4C22×C511yescharacteristic
213C22×C42C22×C511yescharacteristic
214C22×C42C22×C512yes—
215C22×C42C22×C511yescharacteristic
216C22×C42C22×C511yescharacteristic
217#389—24no—
218#389—24no—
219#389—28no—
220#389C4×C518yescomplemented
221#384—24no—
222C4×C4⋊C4—24no—
223C2×#95C22×C511yescharacteristic
224C2×#95C22×C511yescharacteristic
225C2×#95C22×C512yes—
226C2×#95C22×C512yes—
227C2×#95C22×C512yes—
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C512yes—
231C2×#95C22×C511yescharacteristic
232C2×#95C22×C511yescharacteristic
233C23×C5C23×C411yescharacteristic
234C23×C5C22×D411yescharacteristic
235C23×C5C22×D411yescharacteristic
236C23×C5C22×D411yescharacteristic
237C23×C5C22×Q811yescharacteristic
238C23×C5C22×Q811yescharacteristic
239C23×C5C22×Q811yescharacteristic
240C23×C5C2×#4111yescharacteristic
241C23×C5C2×#4111yescharacteristic
242C23×C5C2×#4111yescharacteristic
243C23×C5C2×#4111yescharacteristic
244C23×C5H(5,𝔽2)11yescharacteristic
245C23×C5H(5,𝔽2)11yescharacteristic
246C23×C52−1+411yescharacteristic
247C23×C52−1+411yescharacteristic
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—24no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—24no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—24no—
284C2×C4×C5—24no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—42no—
290C2×C4×C5—41no—
291C2×C4×C5—42no—
292C2×C4×C5—41no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—41no—
296C2×C4×C5—42no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—42no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—42no—
306C2×C4×C5—41no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5C2×C4⋊C418yes—
315C2×C4×C5C2×C4⋊C414yes—
316C2×C4×C5C4×D414yes—
317C2×C4×C5C4×D414yes—
318C2×C4×C5C4×Q814yes—
319C2×C4×C5C4×Q814yes—
320C2×C4×C5#12114yes—
321C2×C4×C5C22⋊Q814yes—
322C2×C4×C5#12514yes—
323C2×C4×C5C4⋊Q814yes—
324C2×C4×C5C4⋊Q814yes—
325C23×C4C23×C512yes—
326C23×C4C23×C512yes—
327C23×C4C23×C512yes—
328C23×C4C23×C511yescharacteristic
329C23×C4C23×C511yescharacteristic
330C23×C4C23×C511yescharacteristic
331C23×C4C23×C512yes—
332C23×C4C23×C511yescharacteristic
333C23×C4C23×C511yescharacteristic
334C23×C4C23×C511yescharacteristic
335C23×C4C23×C511yescharacteristic
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4C2×C4×C514yes—
358C2×C4⋊C4C2×C4×C518yes—
359C2×C4⋊C4C2×C4×C514yes—
360C2×C4⋊C4C5×D414yes—
361C2×C4⋊C4C5×D414yes—
362C2×C4⋊C4C5×Q814yes—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—42no—
373C2×C42C2×C4×C514yes—
374C2×C42C5×Q814yes—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—22no—
380#95—22no—
381#95—42no—
382#95C2×C4×C518yes—
383#95C5×D414yes—
384#95C5×Q814yes—
385C22×C5C22×C4⋊C411yescharacteristic
386C22×C5C2×C4×D411yescharacteristic
387C22×C5C2×C4×D411yescharacteristic
388C22×C5C2×C4×Q811yescharacteristic
389C22×C5C2×C4×Q811yescharacteristic
390C22×C5#52011yescharacteristic
391C22×C5#52011yescharacteristic
392C22×C5C2×#12111yescharacteristic
393C22×C5C2×C22⋊Q811yescharacteristic
394C22×C5C2×#12511yescharacteristic
395C22×C5C2×C4⋊Q811yescharacteristic
396C22×C5C2×C4⋊Q811yescharacteristic
397C22×C5#53211yescharacteristic
398C22×C5#53311yescharacteristic
399C22×C5#53311yescharacteristic
400C22×C5#54011yescharacteristic
401C22×C5#54111yescharacteristic
402C22×C5#54411yescharacteristic
403C22×C5#54411yescharacteristic
404C22×C5D4211yescharacteristic
405C22×C5D4211yescharacteristic
406C22×C5#54611yescharacteristic
407C22×C5#54711yescharacteristic
408C22×C5#54711yescharacteristic
409C22×C5#54811yescharacteristic
410C22×C5D4×Q811yescharacteristic
411C22×C5D4×Q811yescharacteristic
412C22×C5D4×Q811yescharacteristic
413C22×C5#55011yescharacteristic
414C22×C5#55211yescharacteristic
415C22×C5#55311yescharacteristic
416C22×C5#55411yescharacteristic
417C22×C5#55411yescharacteristic
418C22×C5#55711yescharacteristic
419C22×C5Q8211yescharacteristic
420C4×C5—28no—
421C4×C5—24no—
422C4×C5—24no—
423C4×C5—24no—
424C4×C5—44no—
425C4×C5—44no—
426C4×C5—42no—
427C4×C5—42no—
428C4×C5—42no—
429C4×C5—82no—
430C4×C5#38918yescomplemented
431C24C24×C511yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C22×C4×C514yes—
486C22×C4C22×C4×C514yes—
487C22×C4C22×C4×C512yes—
488C22×C4C22×C4×C512yes—
489C22×C4C22×C4×C512yes—
490C22×C4C2×C5×D414yes—
491C22×C4C2×C5×D412yes—
492C22×C4C2×C5×D414yes—
493C22×C4C2×C5×D412yes—
494C22×C4C2×C5×D412yes—
495C22×C4C2×C5×D412yes—
496C22×C4C2×C5×D412yes—
497C22×C4C2×C5×Q812yes—
498C22×C4C2×C5×Q812yes—
499C22×C4C2×C5×Q814yes—
500C22×C4C2×C5×Q812yes—
501C22×C4C2×C5×Q812yes—
502C22×C4C2×C5×Q812yes—
503C22×C4C2×C5×Q812yes—
504C22×C4C2×C5×Q812yes—
505C22×C4C5×#4112yes—
506C22×C4C5×#4112yes—
507C22×C4C5×#4112yes—
508C22×C4C5×#4112yes—
509C4⋊C4—216no—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—48no—
513C4⋊C4—48no—
514C4⋊C4—48no—
515C4⋊C4—48no—
516C4⋊C4—44no—
517C4⋊C4C5×C4⋊C4116yescomplemented
518C42—28no—
519C42—28no—
520C42—48no—
521C42—44no—
522C2×C5C2×#38911yescharacteristic
523C2×C5C4×C4⋊Q811yescharacteristic
524C2×C5#233011yescharacteristic
525C2×C5D4×C4⋊C411yescharacteristic
526C2×C5Q8×C4⋊C411yescharacteristic
527C2×C5#236011yescharacteristic
528C2×C5#236111yescharacteristic
529C2×C5#242811yescharacteristic
530C2×C5#242911yescharacteristic
531C2×C5#244011yescharacteristic
532C2×C5#244111yescharacteristic
533C2×C5#250611yescharacteristic
534C2×C5#250711yescharacteristic
535C2×C5#255011yescharacteristic
536C2×C5#255111yescharacteristic
537C23C23×C4×C511yescharacteristic
538C23C22×C5×D411yescharacteristic
539C23C22×C5×D411yescharacteristic
540C23C22×C5×D411yescharacteristic
541C23C22×C5×Q811yescharacteristic
542C23C22×C5×Q811yescharacteristic
543C23C22×C5×Q811yescharacteristic
544C23C2×C5×#4111yescharacteristic
545C23C2×C5×#4111yescharacteristic
546C23C2×C5×#4111yescharacteristic
547C23C2×C5×#4111yescharacteristic
548C23C5×H(5,𝔽2)11yescharacteristic
549C23C5×H(5,𝔽2)11yescharacteristic
550C23C5×2−1+411yescharacteristic
551C23C5×2−1+411yescharacteristic
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×C5×C4⋊C418yes—
619C2×C4C2×C5×C4⋊C414yes—
620C2×C4C4×C5×D414yes—
621C2×C4C4×C5×D414yes—
622C2×C4C4×C5×Q814yes—
623C2×C4C4×C5×Q814yes—
624C2×C4C5×#12114yes—
625C2×C4C5×C22⋊Q814yes—
626C2×C4C5×#12514yes—
627C2×C4C5×C4⋊Q814yes—
628C2×C4C5×C4⋊Q814yes—
629C5#1400511yescharacteristic, direct product factor, Sylow
630C22C22×C5×C4⋊C411yescharacteristic
631C22C2×C4×C5×D411yescharacteristic
632C22C2×C4×C5×D411yescharacteristic
633C22C2×C4×C5×Q811yescharacteristic
634C22C2×C4×C5×Q811yescharacteristic
635C22C5×#52011yescharacteristic
636C22C5×#52011yescharacteristic
637C22C2×C5×#12111yescharacteristic
638C22C2×C5×C22⋊Q811yescharacteristic
639C22C2×C5×#12511yescharacteristic
640C22C2×C5×C4⋊Q811yescharacteristic
641C22C2×C5×C4⋊Q811yescharacteristic
642C22C5×#53211yescharacteristic
643C22C5×#53311yescharacteristic
644C22C5×#53311yescharacteristic
645C22C5×#54011yescharacteristic
646C22C5×#54111yescharacteristic
647C22C5×#54411yescharacteristic
648C22C5×#54411yescharacteristic
649C22C5×D4211yescharacteristic
650C22C5×D4211yescharacteristic
651C22C5×#54611yescharacteristic
652C22C5×#54711yescharacteristic
653C22C5×#54711yescharacteristic
654C22C5×#54811yescharacteristic
655C22C5×D4×Q811yescharacteristic
656C22C5×D4×Q811yescharacteristic
657C22C5×D4×Q811yescharacteristic
658C22C5×#55011yescharacteristic
659C22C5×#55211yescharacteristic
660C22C5×#55311yescharacteristic
661C22C5×#55411yescharacteristic
662C22C5×#55411yescharacteristic
663C22C5×#55711yescharacteristic
664C22C5×Q8211yescharacteristic
665C4—28no—
666C4—24no—
667C4—24no—
668C4—24no—
669C4—44no—
670C4—44no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—82no—
675C4C5×#38918yescomplemented
676C2C2×C5×#38911yescharacteristic
677C2C4×C5×C4⋊Q811yescharacteristic
678C2C5×#233011yescharacteristic
679C2C5×D4×C4⋊C411yescharacteristic
680C2C5×Q8×C4⋊C411yescharacteristic
681C2C5×#236011yescharacteristic
682C2C5×#236111yescharacteristic
683C2C5×#242811yescharacteristic
684C2C5×#242911yescharacteristic
685C2C5×#244011yescharacteristic
686C2C5×#244111yescharacteristic
687C2C5×#250611yescharacteristic
688C2C5×#250711yescharacteristic
689C2C5×#255011yescharacteristic
690C2C5×#255111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
28. C5×#389C4semidirect
41. #14005C5direct (N × H)
199. C5×C4⋊C4C4⋊C4semidirect
220. #389C4×C5semidirect
430. C4×C5#389semidirect
517. C4⋊C4C5×C4⋊C4semidirect
629. C5#14005direct (N × H)
675. C4C5×#389semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C2×C5×#3842
C2×C4×C5×C4⋊C42
C5×#14442
C5×#14412
C5×#14362
C5×C4⋊#952
C4×C5×#952
#140055