Finite Group Databasebeta

← C5×#24127 #11946847

Subgroups — C5×#24127 #11946847

Order 1280.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C4×C5×Q16C211yesmaximal, characteristic, complemented
4C5×#2536C211yesmaximal, characteristic
5C5×#2036C211yesmaximal, characteristic, complemented
6C5×#2035C211yesmaximal, characteristic, complemented
7C5×#2001C211yesmaximal, characteristic, complemented
8C5×#2001C211yesmaximal, characteristic, complemented
9C5×#1991C211yesmaximal, characteristic, complemented
10C5×#1954C211yesmaximal, characteristic
11C5×#1873C211yesmaximal, characteristic, complemented
12C5×#1872C211yesmaximal, characteristic, complemented
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1852C211yesmaximal, characteristic, complemented
15C5×#1805C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C5×#552—24no—
18C5×#552—24no—
19C2×C5×#126—21no—
20C2×C5×#125—21no—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C5×#117—21no—
31C2×C5×#117C2211yescharacteristic
32C22×C5×C4⋊C4C2211yescharacteristic
33C5×#479—24no—
34C4×C5×Q16—24no—
35C2×C5×#107C2211yescharacteristic
36C2×C5×#107C2211yescharacteristic
37C2×C5×#106C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#103C2211yescharacteristic
43C2×C5×#103C2211yescharacteristic
44C2×C5×#103C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C4×C5×C8C2211yescharacteristic
50C5×#398—21no—
51C5×#394—21no—
52C5×#388—21no—
53C5×#388—21no—
54C5×#382C2211yescharacteristic
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62C5×#340C2211yescharacteristic
63#24127C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8C2311yescharacteristic
65C22×C5×Q8C2311yescharacteristic
66C22×C5×D4D411yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C2×C5×Q16—22no—
71C2×C5×Q16—22no—
72C2×C5×Q16—22no—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×#126—28no—
78C5×#125—28no—
79C5×#125—22no—
80C5×#125D414yes—
81C5×#123—28no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—41no—
89C5×C22⋊Q8—41no—
90C4×C5×Q8—22no—
91C4×C5×Q8—22no—
92C4×C5×Q8—22no—
93C4×C5×Q8D414yes—
94C4×C5×D4—22no—
95C4×C5×D4—22no—
96C5×#117—28no—
97C5×#117—22no—
98C5×#117—22no—
99C2×C5×C4⋊C4—21no—
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—22no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C5×C22⋊C4D411yescharacteristic
126C2×C42×C5—21no—
127C2×C42×C5—21no—
128C2×C42×C5—21no—
129C2×C42×C5C2311yescharacteristic
130C5×#107—22no—
131C5×#107—22no—
132C5×#106—22no—
133C5×C4⋊C8—22no—
134C5×#103—22no—
135C5×#103—22no—
136C5×#103—22no—
137C5×#103—22no—
138C5×#103—41no—
139C5×#103—41no—
140C5×C22⋊C8—22no—
141C5×C22⋊C8—22no—
142C5×C22⋊C8—41no—
143C5×C22⋊C8—41no—
144C4×C5×C8—22no—
145C5×#95—21no—
146C5×#95—21no—
147C5×#95—21no—
148C5×#95—21no—
149C2×#552C2×C511yescharacteristic
150C2×#479C2×C511yescharacteristic, complemented
151C2×C4×Q16C2×C511yescharacteristic, complemented
152#2536C2×C511yescharacteristic
153#2036C2×C511yescharacteristic, complemented
154#2035C2×C511yescharacteristic, complemented
155#2001C2×C511yescharacteristic, complemented
156#2001C2×C511yescharacteristic, complemented
157#1991C2×C511yescharacteristic, complemented
158#1954C2×C511yescharacteristic
159#1873C2×C511yescharacteristic, complemented
160#1872C2×C511yescharacteristic, complemented
161#1854C2×C511yescharacteristic, complemented
162#1852C2×C511yescharacteristic, complemented
163#1805C2×C511yescharacteristic, complemented
164C24×C5C2×D411yescharacteristic
165C24×C5C2×D411yescharacteristic
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×Q8C2×D412yes—
177C2×C5×Q8#4112yes—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—41no—
181C22×C4×C5—24no—
182C22×C4×C5—21no—
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×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—42no—
203C22×C4×C5—42no—
204C22×C4×C5C2×D411yescharacteristic
205C22×C4×C5C2×D411yescharacteristic
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2411yescharacteristic
209C5×Q16—28no—
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—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
219C2×C5×C8—21no—
220C2×C5×C8—21no—
221C2×C5×C8#4112yes—
222C5×C4⋊C4—24no—
223C5×C4⋊C4—24no—
224C5×C4⋊C4—24no—
225C5×C4⋊C4—24no—
226C5×C4⋊C4—24no—
227C5×C4⋊C4—24no—
228C5×C4⋊C4—22no—
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—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—42no—
239C5×C4⋊C4—42no—
240C5×C4⋊C4—42no—
241C5×C4⋊C4C2×D412yes—
242C5×C4⋊C4C2×D412yes—
243C5×C4⋊C4C2×D412yes—
244C5×C22⋊C4—24no—
245C5×C22⋊C4—24no—
246C5×C22⋊C4—24no—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—42no—
250C5×C22⋊C4—42no—
251C5×C22⋊C4—42no—
252C5×C22⋊C4—42no—
253C42×C5—24no—
254C42×C5—24no—
255C42×C5—42no—
256C42×C5C2×D412yes—
257C42×C5C2×D412yes—
258C22×Q16C22×C511yescharacteristic
259#552—24no—
260#552—24no—
261C2×#126—21no—
262C2×#125—21no—
263C2×#125C22×C511yescharacteristic
264C2×#123—21no—
265C2×C22⋊Q8C22×C511yescharacteristic
266C2×C22⋊Q8C22×C511yescharacteristic
267C2×C22⋊Q8C22×C511yescharacteristic
268C2×C22⋊Q8C22×C511yescharacteristic
269C2×C4×Q8C22×C511yescharacteristic
270C2×C4×Q8C22×C511yescharacteristic
271C2×C4×D4C22×C511yescharacteristic
272C2×#117—21no—
273C2×#117C22×C511yescharacteristic
274C22×C4⋊C4C22×C511yescharacteristic
275#479—24no—
276C4×Q16—24no—
277C2×#107C22×C511yescharacteristic
278C2×#107C22×C511yescharacteristic
279C2×#106C22×C511yescharacteristic
280C2×C4⋊C8C22×C511yescharacteristic
281C2×#103C22×C511yescharacteristic
282C2×#103C22×C511yescharacteristic
283C2×#103C22×C511yescharacteristic
284C2×#103C22×C511yescharacteristic
285C2×#103C22×C511yescharacteristic
286C2×#103C22×C511yescharacteristic
287C2×C22⋊C8C22×C511yescharacteristic
288C2×C22⋊C8C22×C511yescharacteristic
289C2×C22⋊C8C22×C511yescharacteristic
290C2×C22⋊C8C22×C511yescharacteristic
291C2×C4×C8C22×C511yescharacteristic
292#398—21no—
293#394—21no—
294#388—21no—
295#388—21no—
296#382C22×C511yescharacteristic
297#380C22×C511yescharacteristic
298#380C22×C511yescharacteristic
299#340C22×C511yescharacteristic
300#340C22×C511yescharacteristic
301#340C22×C511yescharacteristic
302#340C22×C511yescharacteristic
303#340C22×C511yescharacteristic
304#340C22×C511yescharacteristic
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5#13512yes—
319C23×C5C22×D411yescharacteristic
320C5×Q8—22no—
321C5×Q8—22no—
322C5×Q8—22no—
323C5×Q8—22no—
324C5×Q8—41no—
325C5×Q8—41no—
326C5×Q8—41no—
327C5×Q8—41no—
328C5×D4—44no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—21no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—48no—
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—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5#12012yes—
373C2×C4×C5#12012yes—
374C2×C4×C5C22×D411yescharacteristic
375C2×C4×C5C22×D411yescharacteristic
376C2×C4×C5C2×#4111yescharacteristic
377C2×C4×C5C2×#4111yescharacteristic
378C2×C4×C5H(5,𝔽2)11yescharacteristic
379C2×C4×C52−1+411yescharacteristic
380C5×C8—22no—
381C5×C8—41no—
382C5×C8—41no—
383C5×C8—41no—
384C22×Q8C23×C511yescharacteristic
385C22×Q8C23×C511yescharacteristic
386C22×D4C5×D411yescharacteristic
387C23×C4—21no—
388C23×C4C23×C511yescharacteristic
389C23×C4C23×C511yescharacteristic
390C2×Q16—22no—
391C2×Q16—22no—
392C2×Q16—22no—
393C22×C8C23×C511yescharacteristic
394C22×C8C23×C511yescharacteristic
395C22×C8C23×C511yescharacteristic
396C22×C8C23×C511yescharacteristic
397#126—28no—
398#125—28no—
399#125—22no—
400#125C5×D414yes—
401#123—28no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—41no—
409C22⋊Q8—41no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8C5×D414yes—
414C4×D4—22no—
415C4×D4—22no—
416#117—28no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C5×D411yescharacteristic
431C2×C4⋊C4C23×C511yescharacteristic
432C2×C4⋊C4C23×C511yescharacteristic
433C2×C4⋊C4C23×C511yescharacteristic
434C2×C4⋊C4C23×C511yescharacteristic
435C2×C4⋊C4C23×C511yescharacteristic
436C2×C4⋊C4C23×C511yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4C5×D411yescharacteristic
445C2×C22⋊C4C5×D411yescharacteristic
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C511yescharacteristic
450#107—22no—
451#107—22no—
452#106—22no—
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103—41no—
459#103—41no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—41no—
463C22⋊C8—41no—
464C4×C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—41no—
473C22×C5—41no—
474C22×C5—41no—
475C22×C5—41no—
476C22×C5—41no—
477C22×C5—41no—
478C22×C5—41no—
479C22×C5—41no—
480C22×C5—41no—
481C22×C5—41no—
482C22×C5—41no—
483C22×C5C2×#12011yescharacteristic
484C22×C5#54611yescharacteristic
485C22×C5#54711yescharacteristic
486C22×C5C2×#13511yescharacteristic
487C22×C5#57511yescharacteristic
488C22×C5#57811yescharacteristic
489C22×C5#57811yescharacteristic
490C4×C5—22no—
491C4×C5—22no—
492C4×C5—41no—
493C4×C5—41no—
494C4×C5—42no—
495C4×C5—42no—
496C4×C5—42no—
497C4×C5—42no—
498C4×C5—42no—
499C4×C5—81no—
500C4×C5—81no—
501C4×C5—81no—
502C4×C5#52511yescharacteristic
503C4×C5#53711yescharacteristic
504C4×C5#54811yescharacteristic
505C4×C5#55011yescharacteristic
506C24C2×C5×D411yescharacteristic
507C24C2×C5×D411yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C2×C5×D412yes—
519C2×Q8C5×#4112yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4C2×C5×D411yescharacteristic
547C22×C4C2×C5×D411yescharacteristic
548C22×C4C2×C5×D411yescharacteristic
549C22×C4C2×C5×D411yescharacteristic
550C22×C4C24×C511yescharacteristic
551Q16—28no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8C5×#4112yes—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4C2×C5×D412yes—
584C4⋊C4C2×C5×D412yes—
585C4⋊C4C2×C5×D412yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C42—24no—
596C42—24no—
597C42—42no—
598C42C2×C5×D412yes—
599C42C2×C5×D412yes—
600C2×C5—42no—
601C2×C5—81no—
602C2×C5#240711yescharacteristic
603C2×C5#300211yescharacteristic
604C2×C5#301111yescharacteristic
605C2×C5#330011yescharacteristic
606C2×C5#332711yescharacteristic
607C2×C5#333611yescharacteristic
608C2×C5#335211yescharacteristic
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23C5×#13512yes—
623C23C22×C5×D411yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
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—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4C5×#12012yes—
677C2×C4C5×#12012yes—
678C2×C4C22×C5×D411yescharacteristic
679C2×C4C22×C5×D411yescharacteristic
680C2×C4C2×C5×#4111yescharacteristic
681C2×C4C2×C5×#4111yescharacteristic
682C2×C4C5×H(5,𝔽2)11yescharacteristic
683C2×C4C5×2−1+411yescharacteristic
684C8—22no—
685C8—41no—
686C8—41no—
687C8—41no—
688C5#2412711yescharacteristic, direct product factor, Sylow
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×C5×#12011yescharacteristic
704C22C5×#54611yescharacteristic
705C22C5×#54711yescharacteristic
706C22C2×C5×#13511yescharacteristic
707C22C5×#57511yescharacteristic
708C22C5×#57811yescharacteristic
709C22C5×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C5×#52511yescharacteristic
723C4C5×#53711yescharacteristic
724C4C5×#54811yescharacteristic
725C4C5×#55011yescharacteristic
726C2—42no—
727C2—81no—
728C2C5×#240711yescharacteristic
729C2C5×#300211yescharacteristic
730C2C5×#301111yescharacteristic
731C2C5×#330011yescharacteristic
732C2C5×#332711yescharacteristic
733C2C5×#333611yescharacteristic
734C2C5×#335211yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#479C2semidirect
3. C2×C4×C5×Q16C2semidirect
5. C5×#2036C2semidirect
6. C5×#2035C2semidirect
7. C5×#2001C2semidirect
8. C5×#2001C2semidirect
9. C5×#1991C2semidirect
11. C5×#1873C2semidirect
12. C5×#1872C2semidirect
13. C5×#1854C2semidirect
14. C5×#1852C2semidirect
15. C5×#1805C2semidirect
63. #24127C5direct (N × H)
150. C2×#479C2×C5semidirect
151. C2×C4×Q16C2×C5semidirect
153. #2036C2×C5semidirect
154. #2035C2×C5semidirect
155. #2001C2×C5semidirect
156. #2001C2×C5semidirect
157. #1991C2×C5semidirect
159. #1873C2×C5semidirect
160. #1872C2×C5semidirect
161. #1854C2×C5semidirect
162. #1852C2×C5semidirect
163. #1805C2×C5semidirect
688. C5#24127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×C5×#4792
C2×C4×C5×Q162
C5×#25362
C5×#20362
C5×#20352
C5×#20012
C5×#19912
C5×#19542
C5×#18732
C5×#18722
C5×#18542
C5×#18522
C5×#18052
#241275