Finite Group Databasebeta

← C5×#14017 #11936737

Subgroups — C5×#14017 #11936737

Order 1280.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Q8C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic
3C2×C5×#391C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic
5C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
6C5×#1444C212yesmaximal
7C5×#1442C212yesmaximal
8C5×#1436C212yesmaximal
9C5×#1436C212yesmaximal
10C5×C4⋊#95C211yesmaximal, characteristic
11C5×C4⋊#95C211yesmaximal, characteristic
12C23×C5×Q8C2211yescharacteristic
13C2×C4×C5×Q8—24no—
14C2×C4×C5×Q8—24no—
15C2×C4×C5×Q8—24no—
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2212yes—
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2212yes—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2212yes—
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C5×#391—24no—
28C5×#391C418yescomplemented
29C5×#389—24no—
30C4×C5×C4⋊C4—24no—
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2212yes—
42#14017C511yesmaximal, characteristic, direct product factor, Sylow
43C22×C5×Q8—22no—
44C22×C5×Q8—22no—
45C22×C5×Q8—22no—
46C22×C5×Q8—22no—
47C22×C5×Q8C2×C414yes—
48C22×C5×Q8D414yes—
49C22×C5×Q8Q814yes—
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2312yes—
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2312yes—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2312yes—
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C4×C5×Q8—232no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4—24no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—24no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—42no—
80C2×C5×C4⋊C4C2×C414yes—
81C2×C5×C4⋊C4D414yes—
82C2×C5×C4⋊C4Q814yescomplemented
83C2×C42×C5—22no—
84C2×C42×C5—24no—
85C2×C42×C5—24no—
86C2×C42×C5—24no—
87C2×C42×C5—22no—
88C2×C42×C5—22no—
89C2×C42×C5—22no—
90C2×C42×C5—22no—
91C2×C42×C5—22no—
92C2×C42×C5—22no—
93C2×C42×C5C2×C414yes—
94C2×C42×C5D414yes—
95C5×#95—22no—
96C5×#95—22no—
97C5×#95—24no—
98C5×#95—24no—
99C5×#95—24no—
100C5×#95—24no—
101C5×#95—24no—
102C5×#95—42no—
103C5×#95—42no—
104C5×#95C2×C418yes—
105C5×#95C2×C418yes—
106C22×C4×Q8C2×C511yescharacteristic
107C2×#391C2×C511yescharacteristic
108C2×#391C2×C511yescharacteristic
109C2×#389C2×C511yescharacteristic
110C2×C4×C4⋊C4C2×C511yescharacteristic
111#1444C2×C512yes—
112#1442C2×C512yes—
113#1436C2×C512yes—
114#1436C2×C512yes—
115C4⋊#95C2×C511yescharacteristic
116C4⋊#95C2×C511yescharacteristic
117C24×C5C2411yescharacteristic
118C2×C5×Q8—28no—
119C2×C5×Q8—28no—
120C2×C5×Q8—28no—
121C2×C5×Q8—28no—
122C2×C5×Q8—28no—
123C2×C5×Q8—28no—
124C2×C5×Q8C4⋊C4116yescomplemented
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—22no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5C22×C412yes—
181C22×C4×C5C22×C414yes—
182C22×C4×C5C22×C414yes—
183C22×C4×C5C22×C412yes—
184C22×C4×C5C22×C412yes—
185C22×C4×C5C2×D414yes—
186C22×C4×C5C2×D412yes—
187C22×C4×C5C2×D414yes—
188C22×C4×C5C2×D412yes—
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2×D412yes—
192C22×C4×C5C2×Q812yes—
193C22×C4×C5C2×Q814yes—
194C22×C4×C5C2×Q812yes—
195C22×C4×C5C2×Q812yes—
196C22×C4×C5C2×Q812yes—
197C22×C4×C5#4112yes—
198C22×C4×C5#4112yes—
199C22×C4×C5#4112yes—
200C22×C4×C5#4112yes—
201C22×C4×C5#4112yes—
202C5×C4⋊C4—28no—
203C5×C4⋊C4—216no—
204C5×C4⋊C4—28no—
205C5×C4⋊C4—28no—
206C5×C4⋊C4—28no—
207C5×C4⋊C4—48no—
208C5×C4⋊C4—44no—
209C42×C5—216no—
210C42×C5—28no—
211C42×C5—28no—
212C42×C5—44no—
213C23×Q8C22×C511yescharacteristic
214C2×C4×Q8—24no—
215C2×C4×Q8—24no—
216C2×C4×Q8—24no—
217C22×C4⋊C4C22×C512yes—
218C22×C4⋊C4C22×C511yescharacteristic
219C22×C4⋊C4C22×C511yescharacteristic
220C22×C4⋊C4C22×C512yes—
221C22×C4⋊C4C22×C511yescharacteristic
222C22×C4⋊C4C22×C511yescharacteristic
223C22×C4⋊C4C22×C511yescharacteristic
224C22×C42C22×C512yes—
225C22×C42C22×C511yescharacteristic
226C22×C42C22×C511yescharacteristic
227C22×C42C22×C511yescharacteristic
228#391—24no—
229#391C4×C518yescomplemented
230#389—24no—
231C4×C4⋊C4—24no—
232C2×#95C22×C512yes—
233C2×#95C22×C512yes—
234C2×#95C22×C511yescharacteristic
235C2×#95C22×C512yes—
236C2×#95C22×C512yes—
237C2×#95C22×C512yes—
238C2×#95C22×C511yescharacteristic
239C2×#95C22×C512yes—
240C2×#95C22×C512yes—
241C2×#95C22×C512yes—
242C2×#95C22×C512yes—
243C23×C5C23×C411yescharacteristic
244C23×C5C22×D411yescharacteristic
245C23×C5C22×D411yescharacteristic
246C23×C5C22×D411yescharacteristic
247C23×C5C22×Q811yescharacteristic
248C23×C5C22×Q811yescharacteristic
249C23×C5C2×#4111yescharacteristic
250C23×C5C2×#4111yescharacteristic
251C23×C5C2×#4111yescharacteristic
252C23×C5C2×#4111yescharacteristic
253C23×C5C2×#4111yescharacteristic
254C23×C5H(5,𝔽2)11yescharacteristic
255C23×C52−1+411yescharacteristic
256C23×C52−1+411yescharacteristic
257C23×C52−1+411yescharacteristic
258C5×Q8—232no—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—22no—
266C2×C4×C5—24no—
267C2×C4×C5—24no—
268C2×C4×C5—24no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—24no—
283C2×C4×C5—24no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—42no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—42no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—42no—
310C2×C4×C5—41no—
311C2×C4×C5—42no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—42no—
316C2×C4×C5—41no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5C2×C4⋊C418yes—
327C2×C4×C5C2×C4⋊C414yes—
328C2×C4×C5C4×D414yes—
329C2×C4×C5C4×D414yes—
330C2×C4×C5C4×Q814yescomplemented
331C2×C4×C5#12014yes—
332C2×C4×C5C22⋊Q814yes—
333C2×C4×C5C22⋊Q814yes—
334C2×C4×C5C22⋊Q814yes—
335C2×C4×C5#12314yes—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8C2×C4×C514yes—
341C22×Q8C5×D414yes—
342C22×Q8C5×Q814yes—
343C23×C4C23×C512yes—
344C23×C4C23×C512yes—
345C23×C4C23×C511yescharacteristic
346C23×C4C23×C512yes—
347C23×C4C23×C511yescharacteristic
348C23×C4C23×C511yescharacteristic
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C512yes—
351C23×C4C23×C511yescharacteristic
352C23×C4C23×C511yescharacteristic
353C23×C4C23×C511yescharacteristic
354C4×Q8—232no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C2×C4×C514yes—
374C2×C4⋊C4C5×D414yes—
375C2×C4⋊C4C5×Q814yescomplemented
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42C2×C4×C514yes—
387C2×C42C5×D414yes—
388#95—22no—
389#95—22no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—42no—
396#95—42no—
397#95C2×C4×C518yes—
398#95C2×C4×C518yes—
399C22×C5C22×C4⋊C411yescharacteristic
400C22×C5C2×C4×D411yescharacteristic
401C22×C5C2×C4×D411yescharacteristic
402C22×C5C2×C4×Q811yescharacteristic
403C22×C5C4×#4111yescharacteristic
404C22×C5#51911yescharacteristic
405C22×C5#52011yescharacteristic
406C22×C5C2×#12011yescharacteristic
407C22×C5C2×C22⋊Q811yescharacteristic
408C22×C5C2×C22⋊Q811yescharacteristic
409C22×C5C2×C22⋊Q811yescharacteristic
410C22×C5C2×#12311yescharacteristic
411C22×C5#52511yescharacteristic
412C22×C5#52911yescharacteristic
413C22×C5#53311yescharacteristic
414C22×C5#53611yescharacteristic
415C22×C5#53711yescharacteristic
416C22×C5#54111yescharacteristic
417C22×C5#54211yescharacteristic
418C22×C5#54611yescharacteristic
419C22×C5#54711yescharacteristic
420C22×C5#54811yescharacteristic
421C22×C5#54811yescharacteristic
422C22×C5#54811yescharacteristic
423C22×C5D4×Q811yescharacteristic
424C22×C5D4×Q811yescharacteristic
425C22×C5#55011yescharacteristic
426C22×C5#55611yescharacteristic
427C22×C5#55611yescharacteristic
428C22×C5#55711yescharacteristic
429C22×C5#55711yescharacteristic
430C22×C5#55711yescharacteristic
431C22×C5#55711yescharacteristic
432C22×C5Q8211yescharacteristic
433C22×C5#55911yescharacteristic
434C4×C5—24no—
435C4×C5—28no—
436C4×C5—24no—
437C4×C5—42no—
438C4×C5—44no—
439C4×C5—42no—
440C4×C5—44no—
441C4×C5—42no—
442C4×C5—42no—
443C4×C5—82no—
444C4×C5#38518yes—
445C24C24×C511yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8C5×C4⋊C4116yescomplemented
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4C22×C4×C512yes—
509C22×C4C22×C4×C514yes—
510C22×C4C22×C4×C514yes—
511C22×C4C22×C4×C512yes—
512C22×C4C22×C4×C512yes—
513C22×C4C2×C5×D414yes—
514C22×C4C2×C5×D412yes—
515C22×C4C2×C5×D414yes—
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D412yes—
518C22×C4C2×C5×D412yes—
519C22×C4C2×C5×D412yes—
520C22×C4C2×C5×Q812yes—
521C22×C4C2×C5×Q814yes—
522C22×C4C2×C5×Q812yes—
523C22×C4C2×C5×Q812yes—
524C22×C4C2×C5×Q812yes—
525C22×C4C5×#4112yes—
526C22×C4C5×#4112yes—
527C22×C4C5×#4112yes—
528C22×C4C5×#4112yes—
529C22×C4C5×#4112yes—
530C4⋊C4—216no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—48no—
536C4⋊C4—44no—
537C42—216no—
538C42—28no—
539C42—28no—
540C42—44no—
541C2×C5C2×#38511yescharacteristic
542C2×C5C4×C22⋊Q811yescharacteristic
543C2×C5#232311yescharacteristic
544C2×C5Q8×C4⋊C411yescharacteristic
545C2×C5#235111yescharacteristic
546C2×C5#236511yescharacteristic
547C2×C5#236711yescharacteristic
548C2×C5#240711yescharacteristic
549C2×C5#240911yescharacteristic
550C2×C5#244611yescharacteristic
551C2×C5#244811yescharacteristic
552C2×C5#245111yescharacteristic
553C2×C5#245311yescharacteristic
554C2×C5#258111yescharacteristic
555C2×C5#258211yescharacteristic
556C23C23×C4×C511yescharacteristic
557C23C22×C5×D411yescharacteristic
558C23C22×C5×D411yescharacteristic
559C23C22×C5×D411yescharacteristic
560C23C22×C5×Q811yescharacteristic
561C23C22×C5×Q811yescharacteristic
562C23C2×C5×#4111yescharacteristic
563C23C2×C5×#4111yescharacteristic
564C23C2×C5×#4111yescharacteristic
565C23C2×C5×#4111yescharacteristic
566C23C2×C5×#4111yescharacteristic
567C23C5×H(5,𝔽2)11yescharacteristic
568C23C5×2−1+411yescharacteristic
569C23C5×2−1+411yescharacteristic
570C23C5×2−1+411yescharacteristic
571Q8—232no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4C2×C5×C4⋊C418yes—
640C2×C4C2×C5×C4⋊C414yes—
641C2×C4C4×C5×D414yes—
642C2×C4C4×C5×D414yes—
643C2×C4C4×C5×Q814yescomplemented
644C2×C4C5×#12014yes—
645C2×C4C5×C22⋊Q814yes—
646C2×C4C5×C22⋊Q814yes—
647C2×C4C5×C22⋊Q814yes—
648C2×C4C5×#12314yes—
649C5#1401711yescharacteristic, direct product factor, Sylow
650C22C22×C5×C4⋊C411yescharacteristic
651C22C2×C4×C5×D411yescharacteristic
652C22C2×C4×C5×D411yescharacteristic
653C22C2×C4×C5×Q811yescharacteristic
654C22C4×C5×#4111yescharacteristic
655C22C5×#51911yescharacteristic
656C22C5×#52011yescharacteristic
657C22C2×C5×#12011yescharacteristic
658C22C2×C5×C22⋊Q811yescharacteristic
659C22C2×C5×C22⋊Q811yescharacteristic
660C22C2×C5×C22⋊Q811yescharacteristic
661C22C2×C5×#12311yescharacteristic
662C22C5×#52511yescharacteristic
663C22C5×#52911yescharacteristic
664C22C5×#53311yescharacteristic
665C22C5×#53611yescharacteristic
666C22C5×#53711yescharacteristic
667C22C5×#54111yescharacteristic
668C22C5×#54211yescharacteristic
669C22C5×#54611yescharacteristic
670C22C5×#54711yescharacteristic
671C22C5×#54811yescharacteristic
672C22C5×#54811yescharacteristic
673C22C5×#54811yescharacteristic
674C22C5×D4×Q811yescharacteristic
675C22C5×D4×Q811yescharacteristic
676C22C5×#55011yescharacteristic
677C22C5×#55611yescharacteristic
678C22C5×#55611yescharacteristic
679C22C5×#55711yescharacteristic
680C22C5×#55711yescharacteristic
681C22C5×#55711yescharacteristic
682C22C5×#55711yescharacteristic
683C22C5×Q8211yescharacteristic
684C22C5×#55911yescharacteristic
685C4—28no—
686C4—24no—
687C4—24no—
688C4—42no—
689C4—44no—
690C4—42no—
691C4—44no—
692C4—42no—
693C4—42no—
694C4—82no—
695C4C5×#38518yes—
696C2C2×C5×#38511yescharacteristic
697C2C4×C5×C22⋊Q811yescharacteristic
698C2C5×#232311yescharacteristic
699C2C5×Q8×C4⋊C411yescharacteristic
700C2C5×#235111yescharacteristic
701C2C5×#236511yescharacteristic
702C2C5×#236711yescharacteristic
703C2C5×#240711yescharacteristic
704C2C5×#240911yescharacteristic
705C2C5×#244611yescharacteristic
706C2C5×#244811yescharacteristic
707C2C5×#245111yescharacteristic
708C2C5×#245311yescharacteristic
709C2C5×#258111yescharacteristic
710C2C5×#258211yescharacteristic
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×#391C4semidirect
42. #14017C5direct (N × H)
82. C2×C5×C4⋊C4Q8semidirect
124. C2×C5×Q8C4⋊C4semidirect
229. #391C4×C5semidirect
330. C2×C4×C5C4×Q8semidirect
375. C2×C4⋊C4C5×Q8semidirect
452. C2×Q8C5×C4⋊C4semidirect
643. C2×C4C4×C5×Q8semidirect
649. C5#14017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×Q82
C2×C5×#3912
C2×C5×#3892
C2×C4×C5×C4⋊C42
C5×#14442
C5×#14422
C5×#14362
C5×C4⋊#952
#140175