Finite Group Databasebeta

← C5×#14021 #11936741

Subgroups — C5×#14021 #11936741

Order 1280.

1506 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#391C211yesmaximal, characteristic
2C2×C5×#391C211yesmaximal, characteristic
3C2×C5×#391C211yesmaximal, characteristic
4C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
5C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
6C5×#1443C212yesmaximal
7C5×#1442C212yesmaximal
8C5×#1436C212yesmaximal
9C5×C4⋊#95C211yesmaximal, characteristic
10C5×C4⋊#95C211yesmaximal, characteristic
11C5×#1434C212yesmaximal
12C23×C5×Q8C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×C42×C5C2212yes—
20C22×C42×C5C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C5×#391—24no—
23C5×#391—24no—
24C5×#391C418yescomplemented
25C4×C5×C4⋊C4—24no—
26C4×C5×C4⋊C4—24no—
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2212yes—
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2212yes—
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40#14021C511yesmaximal, characteristic, direct product factor, Sylow
41C22×C5×Q8—22no—
42C22×C5×Q8—22no—
43C22×C5×Q8—22no—
44C22×C5×Q8—22no—
45C22×C5×Q8—22no—
46C22×C5×Q8—22no—
47C22×C5×Q8C2×C414yes—
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2312yes—
51C23×C4×C5C2312yes—
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2312yes—
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—22no—
66C2×C5×C4⋊C4—22no—
67C2×C5×C4⋊C4—22no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4C2×C414yes—
72C2×C5×C4⋊C4D414yes—
73C2×C5×C4⋊C4Q814yescomplemented
74C2×C42×C5—22no—
75C2×C42×C5—22no—
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×C42×C5—24no—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×C42×C5—24no—
82C2×C42×C5—22no—
83C2×C42×C5—42no—
84C2×C42×C5C2×C414yes—
85C2×C42×C5D414yes—
86C5×#95—24no—
87C5×#95—22no—
88C5×#95—22no—
89C5×#95—24no—
90C5×#95—24no—
91C5×#95—24no—
92C5×#95—24no—
93C5×#95—24no—
94C5×#95—24no—
95C5×#95—42no—
96C5×#95—42no—
97C5×#95C2×C418yes—
98C5×#95C2×C418yes—
99C2×#391C2×C511yescharacteristic
100C2×#391C2×C511yescharacteristic
101C2×#391C2×C511yescharacteristic
102C2×C4×C4⋊C4C2×C511yescharacteristic
103C2×C4×C4⋊C4C2×C511yescharacteristic
104#1443C2×C512yes—
105#1442C2×C512yes—
106#1436C2×C512yes—
107C4⋊#95C2×C511yescharacteristic
108C4⋊#95C2×C511yescharacteristic
109#1434C2×C512yes—
110C24×C5C2411yescharacteristic
111C2×C5×Q8—28no—
112C2×C5×Q8—28no—
113C2×C5×Q8—28no—
114C2×C5×Q8—44no—
115C2×C5×Q8—44no—
116C2×C5×Q8—44no—
117C2×C5×Q8—44no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—22no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
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—22no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—22no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5C22×C412yes—
176C22×C4×C5C22×C414yes—
177C22×C4×C5C22×C414yes—
178C22×C4×C5C22×C412yes—
179C22×C4×C5C22×C412yes—
180C22×C4×C5C2×D414yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×Q812yes—
186C22×C4×C5C2×Q812yes—
187C22×C4×C5C2×Q812yes—
188C22×C4×C5#4112yes—
189C22×C4×C5#4112yes—
190C22×C4×C5#4112yes—
191C22×C4×C5#4112yes—
192C22×C4×C5#4112yes—
193C22×C4×C5#4112yes—
194C22×C4×C5#4112yes—
195C5×C4⋊C4—28no—
196C5×C4⋊C4—28no—
197C5×C4⋊C4—28no—
198C5×C4⋊C4—28no—
199C5×C4⋊C4—44no—
200C42×C5—28no—
201C42×C5—28no—
202C42×C5—48no—
203C42×C5—44no—
204C23×Q8C22×C511yescharacteristic
205C22×C4⋊C4C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C511yescharacteristic
208C22×C4⋊C4C22×C511yescharacteristic
209C22×C4⋊C4C22×C511yescharacteristic
210C22×C42C22×C511yescharacteristic
211C22×C42C22×C512yes—
212C22×C42C22×C511yescharacteristic
213C22×C42C22×C511yescharacteristic
214#391—24no—
215#391—24no—
216#391C4×C518yescomplemented
217C4×C4⋊C4—24no—
218C4×C4⋊C4—24no—
219C2×#95C22×C511yescharacteristic
220C2×#95C22×C512yes—
221C2×#95C22×C512yes—
222C2×#95C22×C512yes—
223C2×#95C22×C512yes—
224C2×#95C22×C512yes—
225C2×#95C22×C512yes—
226C2×#95C22×C512yes—
227C2×#95C22×C511yescharacteristic
228C2×#95C22×C512yes—
229C2×#95C22×C512yes—
230C2×#95C22×C512yes—
231C2×#95C22×C512yes—
232C23×C5C23×C411yescharacteristic
233C23×C5C22×D411yescharacteristic
234C23×C5C22×D411yescharacteristic
235C23×C5C22×Q811yescharacteristic
236C23×C5C2×#4111yescharacteristic
237C23×C5C2×#4111yescharacteristic
238C23×C5C2×#4111yescharacteristic
239C23×C5C2×#4111yescharacteristic
240C23×C5C2×#4111yescharacteristic
241C23×C5C2×#4111yescharacteristic
242C23×C5C2×#4111yescharacteristic
243C23×C5H(5,𝔽2)11yescharacteristic
244C23×C52−1+411yescharacteristic
245C23×C52−1+411yescharacteristic
246C23×C52−1+411yescharacteristic
247C5×Q8—416no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—22no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—24no—
265C2×C4×C5—24no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—24no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—24no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—22no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—42no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
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×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5#11714yes—
317C2×C4×C5C4×D414yes—
318C2×C4×C5C4×D414yes—
319C2×C4×C5C4×Q814yes—
320C2×C4×C5#12114yes—
321C2×C4×C5C22⋊Q814yes—
322C2×C4×C5#12314yes—
323C2×C4×C5#12414yes—
324C2×C4×C5#12614yes—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8C2×C4×C514yes—
332C23×C4C23×C512yes—
333C23×C4C23×C512yes—
334C23×C4C23×C512yes—
335C23×C4C23×C511yescharacteristic
336C23×C4C23×C511yescharacteristic
337C23×C4C23×C512yes—
338C23×C4C23×C511yescharacteristic
339C23×C4C23×C511yescharacteristic
340C23×C4C23×C511yescharacteristic
341C23×C4C23×C511yescharacteristic
342C23×C4C23×C511yescharacteristic
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4C2×C4×C514yes—
356C2×C4⋊C4C5×D414yes—
357C2×C4⋊C4C5×Q814yescomplemented
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—42no—
368C2×C42C2×C4×C514yes—
369C2×C42C5×D414yes—
370#95—24no—
371#95—22no—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95C2×C4×C518yes—
382#95C2×C4×C518yes—
383C22×C5C2×#11711yescharacteristic
384C22×C5C2×C4×D411yescharacteristic
385C22×C5C2×C4×D411yescharacteristic
386C22×C5C2×C4×Q811yescharacteristic
387C22×C5C4×#4111yescharacteristic
388C22×C5#51911yescharacteristic
389C22×C5#52011yescharacteristic
390C22×C5C2×#12111yescharacteristic
391C22×C5C2×C22⋊Q811yescharacteristic
392C22×C5C2×#12311yescharacteristic
393C22×C5#52511yescharacteristic
394C22×C5C2×#12411yescharacteristic
395C22×C5C2×#12611yescharacteristic
396C22×C5#52911yescharacteristic
397C22×C5#53311yescharacteristic
398C22×C5#53611yescharacteristic
399C22×C5#53711yescharacteristic
400C22×C5#54111yescharacteristic
401C22×C5#54211yescharacteristic
402C22×C5#54611yescharacteristic
403C22×C5#54711yescharacteristic
404C22×C5#54811yescharacteristic
405C22×C5D4×Q811yescharacteristic
406C22×C5#55211yescharacteristic
407C22×C5#55211yescharacteristic
408C22×C5#55411yescharacteristic
409C22×C5#55611yescharacteristic
410C22×C5#55611yescharacteristic
411C22×C5#55611yescharacteristic
412C22×C5#55611yescharacteristic
413C22×C5#55611yescharacteristic
414C22×C5#55711yescharacteristic
415C22×C5#55711yescharacteristic
416C22×C5#55911yescharacteristic
417C22×C5#55911yescharacteristic
418C4×C5—24no—
419C4×C5—24no—
420C4×C5—42no—
421C4×C5—44no—
422C4×C5—42no—
423C4×C5—42no—
424C4×C5—42no—
425C4×C5—44no—
426C4×C5—44no—
427C4×C5—82no—
428C4×C5#38818yes—
429C24C24×C511yescharacteristic
430C2×Q8—28no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4C22×C4×C512yes—
495C22×C4C22×C4×C514yes—
496C22×C4C22×C4×C514yes—
497C22×C4C22×C4×C512yes—
498C22×C4C22×C4×C512yes—
499C22×C4C2×C5×D414yes—
500C22×C4C2×C5×D412yes—
501C22×C4C2×C5×D412yes—
502C22×C4C2×C5×D412yes—
503C22×C4C2×C5×D412yes—
504C22×C4C2×C5×Q812yes—
505C22×C4C2×C5×Q812yes—
506C22×C4C2×C5×Q812yes—
507C22×C4C5×#4112yes—
508C22×C4C5×#4112yes—
509C22×C4C5×#4112yes—
510C22×C4C5×#4112yes—
511C22×C4C5×#4112yes—
512C22×C4C5×#4112yes—
513C22×C4C5×#4112yes—
514C4⋊C4—28no—
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—28no—
518C4⋊C4—44no—
519C42—28no—
520C42—28no—
521C42—48no—
522C42—44no—
523C2×C5C2×#38811yescharacteristic
524C2×C5C4×C22⋊Q811yescharacteristic
525C2×C5#232311yescharacteristic
526C2×C5#235511yescharacteristic
527C2×C5#235611yescharacteristic
528C2×C5#236511yescharacteristic
529C2×C5#236711yescharacteristic
530C2×C5#241511yescharacteristic
531C2×C5#241711yescharacteristic
532C2×C5#244611yescharacteristic
533C2×C5#244711yescharacteristic
534C2×C5#251111yescharacteristic
535C2×C5#251411yescharacteristic
536C2×C5#256811yescharacteristic
537C2×C5#259211yescharacteristic
538C23C23×C4×C511yescharacteristic
539C23C22×C5×D411yescharacteristic
540C23C22×C5×D411yescharacteristic
541C23C22×C5×Q811yescharacteristic
542C23C2×C5×#4111yescharacteristic
543C23C2×C5×#4111yescharacteristic
544C23C2×C5×#4111yescharacteristic
545C23C2×C5×#4111yescharacteristic
546C23C2×C5×#4111yescharacteristic
547C23C2×C5×#4111yescharacteristic
548C23C2×C5×#4111yescharacteristic
549C23C5×H(5,𝔽2)11yescharacteristic
550C23C5×2−1+411yescharacteristic
551C23C5×2−1+411yescharacteristic
552C23C5×2−1+411yescharacteristic
553Q8—416no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4C5×#11714yes—
623C2×C4C4×C5×D414yes—
624C2×C4C4×C5×D414yes—
625C2×C4C4×C5×Q814yes—
626C2×C4C5×#12114yes—
627C2×C4C5×C22⋊Q814yes—
628C2×C4C5×#12314yes—
629C2×C4C5×#12414yes—
630C2×C4C5×#12614yes—
631C5#1402111yescharacteristic, direct product factor, Sylow
632C22C2×C5×#11711yescharacteristic
633C22C2×C4×C5×D411yescharacteristic
634C22C2×C4×C5×D411yescharacteristic
635C22C2×C4×C5×Q811yescharacteristic
636C22C4×C5×#4111yescharacteristic
637C22C5×#51911yescharacteristic
638C22C5×#52011yescharacteristic
639C22C2×C5×#12111yescharacteristic
640C22C2×C5×C22⋊Q811yescharacteristic
641C22C2×C5×#12311yescharacteristic
642C22C5×#52511yescharacteristic
643C22C2×C5×#12411yescharacteristic
644C22C2×C5×#12611yescharacteristic
645C22C5×#52911yescharacteristic
646C22C5×#53311yescharacteristic
647C22C5×#53611yescharacteristic
648C22C5×#53711yescharacteristic
649C22C5×#54111yescharacteristic
650C22C5×#54211yescharacteristic
651C22C5×#54611yescharacteristic
652C22C5×#54711yescharacteristic
653C22C5×#54811yescharacteristic
654C22C5×D4×Q811yescharacteristic
655C22C5×#55211yescharacteristic
656C22C5×#55211yescharacteristic
657C22C5×#55411yescharacteristic
658C22C5×#55611yescharacteristic
659C22C5×#55611yescharacteristic
660C22C5×#55611yescharacteristic
661C22C5×#55611yescharacteristic
662C22C5×#55611yescharacteristic
663C22C5×#55711yescharacteristic
664C22C5×#55711yescharacteristic
665C22C5×#55911yescharacteristic
666C22C5×#55911yescharacteristic
667C4—24no—
668C4—24no—
669C4—44no—
670C4—42no—
671C4—44no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—44no—
676C4—82no—
677C4C5×#38818yes—
678C2C2×C5×#38811yescharacteristic
679C2C4×C5×C22⋊Q811yescharacteristic
680C2C5×#232311yescharacteristic
681C2C5×#235511yescharacteristic
682C2C5×#235611yescharacteristic
683C2C5×#236511yescharacteristic
684C2C5×#236711yescharacteristic
685C2C5×#241511yescharacteristic
686C2C5×#241711yescharacteristic
687C2C5×#244611yescharacteristic
688C2C5×#244711yescharacteristic
689C2C5×#251111yescharacteristic
690C2C5×#251411yescharacteristic
691C2C5×#256811yescharacteristic
692C2C5×#259211yescharacteristic
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
24. C5×#391C4semidirect
40. #14021C5direct (N × H)
73. C2×C5×C4⋊C4Q8semidirect
216. #391C4×C5semidirect
357. C2×C4⋊C4C5×Q8semidirect
631. C5#14021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3912
C2×C4×C5×C4⋊C42
C5×#14432
C5×#14422
C5×#14362
C5×C4⋊#952
C5×#14342
#140215