Finite Group Databasebeta

← C5×#24075 #11946795

Subgroups — C5×#24075 #11946795

Order 1280.

1066 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic
2C2×C5×#485C211yesmaximal, characteristic, complemented
3C2×C5×#482C211yesmaximal, characteristic
4C5×#2316C211yesmaximal, characteristic, complemented
5C5×#2058C211yesmaximal, characteristic, complemented
6C5×#2057C211yesmaximal, characteristic, complemented
7C5×#2042C211yesmaximal, characteristic, complemented
8C5×#2042C211yesmaximal, characteristic, complemented
9C5×#1874C211yesmaximal, characteristic
10C5×#1872C211yesmaximal, characteristic, complemented
11C5×#1865C211yesmaximal, characteristic, complemented
12C5×#1864C211yesmaximal, characteristic, complemented
13C5×#1863C211yesmaximal, characteristic, complemented
14C5×#1862C211yesmaximal, characteristic, complemented
15C5×#1818C211yesmaximal, characteristic, complemented
16C5×#542—24no—
17C5×#542—24no—
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×#126—21no—
20C2×C5×#124—21no—
21C2×C5×#124C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#485—24no—
32C5×#482—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#107C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C5×#389—21no—
48C5×#389—21no—
49C5×#389C2211yescharacteristic
50C5×#389C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#389C2211yescharacteristic
53C5×#380—21no—
54C5×#380—21no—
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24075C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8C2311yescharacteristic
66C22×C5×D4—21no—
67C22×C5×D4C2311yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×C4⋊Q8—22no—
76C5×C4⋊Q8—22no—
77C5×#126—28no—
78C5×#124—28no—
79C5×#124—22no—
80C5×#124—22no—
81C5×#123—28no—
82C5×C22⋊Q8—28no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8D414yes—
85C5×#121—22no—
86C5×#121D414yes—
87C4×C5×Q8—22no—
88C4×C5×Q8—22no—
89C4×C5×D4—22no—
90C4×C5×D4—22no—
91C5×#117—22no—
92C5×#117—22no—
93C5×#117—22no—
94C5×#117—22no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C4⋊C4D411yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
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—
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C42×C5—21no—
122C2×C42×C5—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C5×#107—22no—
126C5×#107—22no—
127C5×#106—22no—
128C5×#106—22no—
129C5×#103—22no—
130C5×#103—22no—
131C5×#103—22no—
132C5×#103—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×#102—22no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#542C2×C511yescharacteristic
144C2×#485C2×C511yescharacteristic, complemented
145C2×#482C2×C511yescharacteristic
146#2316C2×C511yescharacteristic, complemented
147#2058C2×C511yescharacteristic, complemented
148#2057C2×C511yescharacteristic, complemented
149#2042C2×C511yescharacteristic, complemented
150#2042C2×C511yescharacteristic, complemented
151#1874C2×C511yescharacteristic
152#1872C2×C511yescharacteristic, complemented
153#1865C2×C511yescharacteristic, complemented
154#1864C2×C511yescharacteristic, complemented
155#1863C2×C511yescharacteristic, complemented
156#1862C2×C511yescharacteristic, complemented
157#1818C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C24×C5C2×D411yescharacteristic
160C2×C5×Q8—24no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—81no—
167C2×C5×Q8—81no—
168C2×C5×Q8C2×D412yes—
169C2×C5×D4—24no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—81no—
176C2×C5×D4—81no—
177C2×C5×D4C2×D412yes—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—24no—
188C22×C4×C5—24no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—81no—
192C22×C4×C5—81no—
193C22×C4×C5—81no—
194C22×C4×C5—81no—
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D412yes—
201C22×C4×C5C2×D412yes—
202C22×C4×C5C2411yescharacteristic
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8—21no—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—81no—
230C5×C4⋊C4—81no—
231C5×C4⋊C4—81no—
232C5×C4⋊C4—81no—
233C5×C4⋊C4C2×D412yes—
234C5×C4⋊C4C2×D412yes—
235C5×C4⋊C4#4112yes—
236C5×C4⋊C4#4112yes—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—22no—
242C5×C22⋊C4—22no—
243C5×C22⋊C4—24no—
244C5×C22⋊C4—42no—
245C42×C5—24no—
246C42×C5—21no—
247C42×C5—21no—
248C42×C5—21no—
249C42×C5—21no—
250C42×C5—42no—
251#542—24no—
252#542—24no—
253C2×C4⋊Q8C22×C511yescharacteristic
254C2×#126—21no—
255C2×#124—21no—
256C2×#124C22×C511yescharacteristic
257C2×#123—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C22×C511yescharacteristic
260C2×#121C22×C511yescharacteristic
261C2×C4×Q8C22×C511yescharacteristic
262C2×C4×D4C22×C511yescharacteristic
263C2×#117C22×C511yescharacteristic
264C2×#117C22×C511yescharacteristic
265C22×C4⋊C4C22×C511yescharacteristic
266#485—24no—
267#482—24no—
268C2×#107C22×C511yescharacteristic
269C2×#107C22×C511yescharacteristic
270C2×#106C22×C511yescharacteristic
271C2×#106C22×C511yescharacteristic
272C2×#103C22×C511yescharacteristic
273C2×#103C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#103C22×C511yescharacteristic
276C2×#102C22×C511yescharacteristic
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×#102C22×C511yescharacteristic
280C2×C22⋊C8C22×C511yescharacteristic
281C2×C22⋊C8C22×C511yescharacteristic
282#389—21no—
283#389—21no—
284#389C22×C511yescharacteristic
285#389C22×C511yescharacteristic
286#389C22×C511yescharacteristic
287#389C22×C511yescharacteristic
288#380—21no—
289#380—21no—
290#340C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#340C22×C511yescharacteristic
293#340C22×C511yescharacteristic
294#336C22×C511yescharacteristic
295#336C22×C511yescharacteristic
296#336C22×C511yescharacteristic
297#336C22×C511yescharacteristic
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—22no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5#12012yes—
312C23×C5C22×D411yescharacteristic
313C5×Q8—22no—
314C5×Q8—22no—
315C5×Q8—41no—
316C5×Q8—41no—
317C5×Q8—84no—
318C5×D4—22no—
319C5×D4—22no—
320C5×D4—41no—
321C5×D4—41no—
322C5×D4—84no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—22no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—84no—
363C2×C4×C5—84no—
364C2×C4×C5#12012yes—
365C2×C4×C5C22×D411yescharacteristic
366C2×C4×C5C22×D411yescharacteristic
367C2×C4×C5C2×#4111yescharacteristic
368C2×C4×C5C2×#4111yescharacteristic
369C2×C4×C52−1+411yescharacteristic
370C2×C4×C52−1+411yescharacteristic
371C5×C8—41no—
372C5×C8—41no—
373C5×C8—41no—
374C5×C8—41no—
375C22×Q8—21no—
376C22×Q8C23×C511yescharacteristic
377C22×D4—21no—
378C22×D4C23×C511yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386C4⋊Q8—22no—
387C4⋊Q8—22no—
388#126—28no—
389#124—28no—
390#124—22no—
391#124—22no—
392#123—28no—
393C22⋊Q8—28no—
394C22⋊Q8—22no—
395C22⋊Q8C5×D414yes—
396#121—22no—
397#121C5×D414yes—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×D4—22no—
401C4×D4—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C5×D411yescharacteristic
417C2×C4⋊C4C5×D411yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C4⋊C4C23×C511yescharacteristic
420C2×C4⋊C4C23×C511yescharacteristic
421C2×C4⋊C4C23×C511yescharacteristic
422C2×C4⋊C4C23×C511yescharacteristic
423C2×C4⋊C4C23×C511yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4C5×D411yescharacteristic
431C2×C22⋊C4C5×D411yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C23×C511yescharacteristic
435C2×C42C23×C511yescharacteristic
436#107—22no—
437#107—22no—
438#106—22no—
439#106—22no—
440#103—22no—
441#103—22no—
442#103—22no—
443#103—22no—
444#102—22no—
445#102—22no—
446#102—22no—
447#102—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454C22×C5—22no—
455C22×C5—22no—
456C22×C5—22no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—42no—
462C22×C5—42no—
463C22×C5—42no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5—81no—
467C22×C5—81no—
468C22×C5C2×#12011yescharacteristic
469C22×C5#52511yescharacteristic
470C22×C5#53611yescharacteristic
471C22×C5#57611yescharacteristic
472C22×C5#57711yescharacteristic
473C22×C5#57711yescharacteristic
474C22×C5#57811yescharacteristic
475C4×C5—22no—
476C4×C5—42no—
477C4×C5—42no—
478C4×C5—42no—
479C4×C5—41no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—42no—
483C4×C5—41no—
484C4×C5—41no—
485C4×C5—81no—
486C4×C5—81no—
487C4×C5#54711yescharacteristic
488C4×C5#54711yescharacteristic
489C4×C5#54711yescharacteristic
490C4×C5#54711yescharacteristic
491C24—21no—
492C24C2×C5×D411yescharacteristic
493C2×Q8—24no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8C2×C5×D412yes—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4C2×C5×D412yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D412yes—
534C22×C4C2×C5×D412yes—
535C22×C4C24×C511yescharacteristic
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4C2×C5×D412yes—
567C4⋊C4C2×C5×D412yes—
568C4⋊C4C5×#4112yes—
569C4⋊C4C5×#4112yes—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—24no—
577C22⋊C4—42no—
578C42—24no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—42no—
584C2×C5—42no—
585C2×C5—82no—
586C2×C5#240611yescharacteristic
587C2×C5#301211yescharacteristic
588C2×C5#301311yescharacteristic
589C2×C5#311811yescharacteristic
590C2×C5#312111yescharacteristic
591C2×C5#324311yescharacteristic
592C2×C5#324411yescharacteristic
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C5×#12012yes—
607C23C22×C5×D411yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—84no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4C5×#12012yes—
660C2×C4C22×C5×D411yescharacteristic
661C2×C4C22×C5×D411yescharacteristic
662C2×C4C2×C5×#4111yescharacteristic
663C2×C4C2×C5×#4111yescharacteristic
664C2×C4C5×2−1+411yescharacteristic
665C2×C4C5×2−1+411yescharacteristic
666C8—41no—
667C8—41no—
668C8—41no—
669C8—41no—
670C5#2407511yescharacteristic, direct product factor, Sylow
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C5×#12011yescharacteristic
686C22C5×#52511yescharacteristic
687C22C5×#53611yescharacteristic
688C22C5×#57611yescharacteristic
689C22C5×#57711yescharacteristic
690C22C5×#57711yescharacteristic
691C22C5×#57811yescharacteristic
692C4—22no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4C5×#54711yescharacteristic
705C4C5×#54711yescharacteristic
706C4C5×#54711yescharacteristic
707C4C5×#54711yescharacteristic
708C2—42no—
709C2—82no—
710C2C5×#240611yescharacteristic
711C2C5×#301211yescharacteristic
712C2C5×#301311yescharacteristic
713C2C5×#311811yescharacteristic
714C2C5×#312111yescharacteristic
715C2C5×#324311yescharacteristic
716C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#485C2semidirect
4. C5×#2316C2semidirect
5. C5×#2058C2semidirect
6. C5×#2057C2semidirect
7. C5×#2042C2semidirect
8. C5×#2042C2semidirect
10. C5×#1872C2semidirect
11. C5×#1865C2semidirect
12. C5×#1864C2semidirect
13. C5×#1863C2semidirect
14. C5×#1862C2semidirect
15. C5×#1818C2semidirect
63. #24075C5direct (N × H)
144. C2×#485C2×C5semidirect
146. #2316C2×C5semidirect
147. #2058C2×C5semidirect
148. #2057C2×C5semidirect
149. #2042C2×C5semidirect
150. #2042C2×C5semidirect
152. #1872C2×C5semidirect
153. #1865C2×C5semidirect
154. #1864C2×C5semidirect
155. #1863C2×C5semidirect
156. #1862C2×C5semidirect
157. #1818C2×C5semidirect
670. C5#24075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×C5×#4852
C2×C5×#4822
C5×#23162
C5×#20582
C5×#20572
C5×#20422
C5×#18742
C5×#18722
C5×#18652
C5×#18642
C5×#18632
C5×#18622
C5×#18182
#240755