Finite Group Databasebeta

← C5×#24165 #11946885

Subgroups — C5×#24165 #11946885

Order 1280.

1022 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C5×#462C211yesmaximal, characteristic, complemented
4C5×#2323C211yesmaximal, characteristic
5C5×#2036C211yesmaximal, characteristic
6C5×#2035C211yesmaximal, characteristic
7C5×#2001C211yesmaximal, characteristic
8C5×#2001C211yesmaximal, characteristic
9C5×#1989C211yesmaximal, characteristic, complemented
10C5×#1981C211yesmaximal, characteristic, complemented
11C5×#1878C211yesmaximal, characteristic, complemented
12C5×#1878C211yesmaximal, characteristic, complemented
13C5×#1865C211yesmaximal, characteristic, complemented
14C5×#1863C211yesmaximal, characteristic, complemented
15C5×#1798C211yesmaximal, characteristic
16C22×C5×Q16C2211yescharacteristic
17C22×C5×Q16C2211yescharacteristic
18C5×#541—24no—
19C5×#541—24no—
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#126—21no—
22C2×C5×#126—21no—
23C2×C5×#125—21no—
24C2×C5×#125—21no—
25C2×C5×#125C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C5×C22⋊Q8C2211yescharacteristic
29C2×C4×C5×Q8C2211yescharacteristic
30C2×C4×C5×Q8C2211yescharacteristic
31C2×C4×C5×Q8C2211yescharacteristic
32C2×C5×#117C2211yescharacteristic
33C5×#479—24no—
34C5×#462—24no—
35C2×C5×#107C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#103C2211yescharacteristic
43C2×C5×#103C2211yescharacteristic
44C2×C5×#103C2211yescharacteristic
45C2×C5×#103C2211yescharacteristic
46C2×C5×#103C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C5×#391C2211yescharacteristic
50C5×#389—21no—
51C5×#389C2211yescharacteristic
52C5×#388—21no—
53C5×#388—21no—
54C5×#387—21no—
55C5×#380C2211yescharacteristic
56C4×C5×C4⋊C4C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24165C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8C2311yescharacteristic
65C22×C5×Q8C2311yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C2×C5×Q16—22no—
69C2×C5×Q16—22no—
70C2×C5×Q16—22no—
71C2×C5×Q16—22no—
72C2×C5×Q16—41no—
73C2×C5×Q16—41no—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×C4⋊Q8—22no—
79C5×C4⋊Q8D414yes—
80C5×#126—28no—
81C5×#126—28no—
82C5×#125—28no—
83C5×#125—28no—
84C5×#125—22no—
85C5×#125D414yes—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C4×C5×Q8—22no—
93C4×C5×Q8—22no—
94C4×C5×Q8—22no—
95C4×C5×Q8—22no—
96C4×C5×Q8—22no—
97C4×C5×Q8—22no—
98C5×#117—22no—
99C5×#117—22no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4D411yescharacteristic
123C2×C5×C22⋊C4D411yescharacteristic
124C2×C42×C5—21no—
125C2×C42×C5—21no—
126C2×C42×C5—21no—
127C2×C42×C5—21no—
128C2×C42×C5C2311yescharacteristic
129C2×C42×C5C2311yescharacteristic
130C5×#107—22no—
131C5×#106—22no—
132C5×C4⋊C8—22no—
133C5×C4⋊C8—22no—
134C5×#103—22no—
135C5×#103—22no—
136C5×#103—22no—
137C5×#103—22no—
138C5×#103—22no—
139C5×#103—22no—
140C5×#103—41no—
141C5×#103—41no—
142C5×C22⋊C8—41no—
143C5×C22⋊C8—41no—
144C5×#95—21no—
145C5×#95—21no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C2×#541C2×C511yescharacteristic
150C2×#479C2×C511yescharacteristic, complemented
151C2×#462C2×C511yescharacteristic, complemented
152#2323C2×C511yescharacteristic
153#2036C2×C511yescharacteristic
154#2035C2×C511yescharacteristic
155#2001C2×C511yescharacteristic
156#2001C2×C511yescharacteristic
157#1989C2×C511yescharacteristic, complemented
158#1981C2×C511yescharacteristic, complemented
159#1878C2×C511yescharacteristic, complemented
160#1878C2×C511yescharacteristic, complemented
161#1865C2×C511yescharacteristic, complemented
162#1863C2×C511yescharacteristic, complemented
163#1798C2×C511yescharacteristic
164C24×C5C2×D411yescharacteristic
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—21no—
180C2×C5×Q8C2×D412yes—
181C2×C5×Q8C2×D412yes—
182C2×C5×Q8#4112yes—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2411yescharacteristic
203C5×Q16—44no—
204C5×Q16—44no—
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—
215C2×C5×C8—21no—
216C2×C5×C8—21no—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—24no—
221C5×C4⋊C4—24no—
222C5×C4⋊C4—24no—
223C5×C4⋊C4—24no—
224C5×C4⋊C4—24no—
225C5×C4⋊C4—24no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—22no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—42no—
236C5×C4⋊C4—81no—
237C5×C4⋊C4C2×D412yes—
238C5×C4⋊C4C2×D412yes—
239C5×C4⋊C4#4112yes—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—24no—
242C5×C22⋊C4—24no—
243C5×C22⋊C4—22no—
244C5×C22⋊C4—22no—
245C5×C22⋊C4—81no—
246C42×C5—24no—
247C42×C5—24no—
248C42×C5—21no—
249C42×C5—21no—
250C42×C5—42no—
251C42×C5—81no—
252C42×C5C2×D412yes—
253C42×C5C2×D412yes—
254C22×Q16C22×C511yescharacteristic
255C22×Q16C22×C511yescharacteristic
256#541—24no—
257#541—24no—
258C2×C4⋊Q8C22×C511yescharacteristic
259C2×#126—21no—
260C2×#126—21no—
261C2×#125—21no—
262C2×#125—21no—
263C2×#125C22×C511yescharacteristic
264C2×C22⋊Q8C22×C511yescharacteristic
265C2×C22⋊Q8C22×C511yescharacteristic
266C2×C22⋊Q8C22×C511yescharacteristic
267C2×C4×Q8C22×C511yescharacteristic
268C2×C4×Q8C22×C511yescharacteristic
269C2×C4×Q8C22×C511yescharacteristic
270C2×#117C22×C511yescharacteristic
271#479—24no—
272#462—24no—
273C2×#107C22×C511yescharacteristic
274C2×#106C22×C511yescharacteristic
275C2×C4⋊C8C22×C511yescharacteristic
276C2×C4⋊C8C22×C511yescharacteristic
277C2×#103C22×C511yescharacteristic
278C2×#103C22×C511yescharacteristic
279C2×#103C22×C511yescharacteristic
280C2×#103C22×C511yescharacteristic
281C2×#103C22×C511yescharacteristic
282C2×#103C22×C511yescharacteristic
283C2×#103C22×C511yescharacteristic
284C2×#103C22×C511yescharacteristic
285C2×C22⋊C8C22×C511yescharacteristic
286C2×C22⋊C8C22×C511yescharacteristic
287#391C22×C511yescharacteristic
288#389—21no—
289#389C22×C511yescharacteristic
290#388—21no—
291#388—21no—
292#387—21no—
293#380C22×C511yescharacteristic
294C4×C4⋊C4C22×C511yescharacteristic
295#340C22×C511yescharacteristic
296#340C22×C511yescharacteristic
297#340C22×C511yescharacteristic
298#340C22×C511yescharacteristic
299#336C22×C511yescharacteristic
300#336C22×C511yescharacteristic
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—21no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5C22×D411yescharacteristic
309C5×Q8—22no—
310C5×Q8—22no—
311C5×Q8—22no—
312C5×Q8—22no—
313C5×Q8—22no—
314C5×Q8—22no—
315C5×Q8—41no—
316C5×Q8—41no—
317C5×Q8—41no—
318C5×Q8—41no—
319C5×Q8—41no—
320C5×Q8—41no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
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#12012yes—
363C2×C4×C5#12012yes—
364C2×C4×C5C22×D411yescharacteristic
365C2×C4×C5C22×D411yescharacteristic
366C2×C4×C5C2×#4111yescharacteristic
367C2×C4×C5C2×#4111yescharacteristic
368C2×C4×C5H(5,𝔽2)11yescharacteristic
369C2×C4×C52−1+411yescharacteristic
370C5×C8—41no—
371C5×C8—41no—
372C5×C8—41no—
373C5×C8—41no—
374C22×Q8C23×C511yescharacteristic
375C22×Q8C23×C511yescharacteristic
376C22×Q8C23×C511yescharacteristic
377C23×C4C23×C511yescharacteristic
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16—22no—
381C2×Q16—22no—
382C2×Q16—41no—
383C2×Q16—41no—
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386C22×C8C23×C511yescharacteristic
387C22×C8C23×C511yescharacteristic
388C4⋊Q8—22no—
389C4⋊Q8C5×D414yes—
390#126—28no—
391#126—28no—
392#125—28no—
393#125—28no—
394#125—22no—
395#125C5×D414yes—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—22no—
408#117—22no—
409#117—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4C5×D411yescharacteristic
422C2×C4⋊C4C5×D411yescharacteristic
423C2×C4⋊C4C23×C511yescharacteristic
424C2×C4⋊C4C23×C511yescharacteristic
425C2×C4⋊C4C23×C511yescharacteristic
426C2×C4⋊C4C23×C511yescharacteristic
427C2×C4⋊C4C23×C511yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4C5×D411yescharacteristic
433C2×C22⋊C4C5×D411yescharacteristic
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C511yescharacteristic
439C2×C42C23×C511yescharacteristic
440#107—22no—
441#106—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444#103—22no—
445#103—22no—
446#103—22no—
447#103—22no—
448#103—22no—
449#103—22no—
450#103—41no—
451#103—41no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—41no—
462C22×C5—41no—
463C22×C5—41no—
464C22×C5—41no—
465C22×C5—41no—
466C22×C5C2×#12011yescharacteristic
467C22×C5#52511yescharacteristic
468C22×C5#53711yescharacteristic
469C22×C5#57711yescharacteristic
470C22×C5#57811yescharacteristic
471C22×C5#57811yescharacteristic
472C22×C5#57811yescharacteristic
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—42no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—42no—
479C4×C5—42no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—41no—
483C4×C5—42no—
484C4×C5—81no—
485C4×C5—81no—
486C4×C5#54611yescharacteristic
487C4×C5#54711yescharacteristic
488C4×C5#54811yescharacteristic
489C4×C5#55011yescharacteristic
490C24C2×C5×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×C5×D412yes—
507C2×Q8C2×C5×D412yes—
508C2×Q8C5×#4112yes—
509C22×C4—21no—
510C22×C4—21no—
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—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C24×C511yescharacteristic
529Q16—44no—
530Q16—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—24no—
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—42no—
562C4⋊C4—81no—
563C4⋊C4C2×C5×D412yes—
564C4⋊C4C2×C5×D412yes—
565C4⋊C4C5×#4112yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—81no—
572C42—24no—
573C42—24no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—81no—
578C42C2×C5×D412yes—
579C42C2×C5×D412yes—
580C2×C5—81no—
581C2×C5#240711yescharacteristic
582C2×C5#301111yescharacteristic
583C2×C5#301311yescharacteristic
584C2×C5#312011yescharacteristic
585C2×C5#312711yescharacteristic
586C2×C5#325811yescharacteristic
587C2×C5#326111yescharacteristic
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23C22×C5×D411yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
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×C4C5×#12012yes—
650C2×C4C5×#12012yes—
651C2×C4C22×C5×D411yescharacteristic
652C2×C4C22×C5×D411yescharacteristic
653C2×C4C2×C5×#4111yescharacteristic
654C2×C4C2×C5×#4111yescharacteristic
655C2×C4C5×H(5,𝔽2)11yescharacteristic
656C2×C4C5×2−1+411yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C5#2416511yescharacteristic, direct product factor, Sylow
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×C5×#12011yescharacteristic
670C22C5×#52511yescharacteristic
671C22C5×#53711yescharacteristic
672C22C5×#57711yescharacteristic
673C22C5×#57811yescharacteristic
674C22C5×#57811yescharacteristic
675C22C5×#57811yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—42no—
680C4—41no—
681C4—42no—
682C4—42no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4C5×#54611yescharacteristic
690C4C5×#54711yescharacteristic
691C4C5×#54811yescharacteristic
692C4C5×#55011yescharacteristic
693C2—81no—
694C2C5×#240711yescharacteristic
695C2C5×#301111yescharacteristic
696C2C5×#301311yescharacteristic
697C2C5×#312011yescharacteristic
698C2C5×#312711yescharacteristic
699C2C5×#325811yescharacteristic
700C2C5×#326111yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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×#479C2semidirect
3. C2×C5×#462C2semidirect
9. C5×#1989C2semidirect
10. C5×#1981C2semidirect
11. C5×#1878C2semidirect
12. C5×#1878C2semidirect
13. C5×#1865C2semidirect
14. C5×#1863C2semidirect
63. #24165C5direct (N × H)
150. C2×#479C2×C5semidirect
151. C2×#462C2×C5semidirect
157. #1989C2×C5semidirect
158. #1981C2×C5semidirect
159. #1878C2×C5semidirect
160. #1878C2×C5semidirect
161. #1865C2×C5semidirect
162. #1863C2×C5semidirect
661. C5#24165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5412
C2×C5×#4792
C2×C5×#4622
C5×#23232
C5×#20362
C5×#20352
C5×#20012
C5×#19892
C5×#19812
C5×#18782
C5×#18652
C5×#18632
C5×#17982
#241655