Finite Group Databasebeta

← C5×#24883 #11947603

Subgroups — C5×#24883 #11947603

Order 1280.

1064 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#484C211yesmaximal, characteristic, complemented
2C2×C5×#417C211yesmaximal, characteristic, complemented
3C5×#2407C211yesmaximal, characteristic
4C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#2093C211yesmaximal, characteristic, complemented
6C5×#2072C211yesmaximal, characteristic, complemented
7C5×#2036C211yesmaximal, characteristic, complemented
8C5×#2034C211yesmaximal, characteristic, complemented
9C5×#1927C211yesmaximal, characteristic, complemented
10C5×#1925C211yesmaximal, characteristic, complemented
11C5×#1874C211yesmaximal, characteristic, complemented
12C5×#1870C211yesmaximal, characteristic, complemented
13C5×#1852C211yesmaximal, characteristic, complemented
14C5×#1809C211yesmaximal, characteristic, complemented
15C5×#1788C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#484—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C5×#417—24no—
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C5×#394—21no—
42C5×#392—21no—
43C5×#391C2211yescharacteristic
44C5×#390C2211yescharacteristic
45C5×#389—21no—
46C5×#386—21no—
47C5×#385—21no—
48C5×#385—21no—
49C5×#385—21no—
50C5×#384C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#380C2211yescharacteristic
54C4×C5×C4⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#24883C511yesmaximal, characteristic, direct product factor, Sylow
62C2×C5×#41—22no—
63C2×C5×#41—22no—
64C2×C5×#41—22no—
65C2×C5×#41—22no—
66C2×C5×#41—41no—
67C2×C5×#41—41no—
68C22×C5×Q8C2311yescharacteristic
69C22×C5×D4—21no—
70C22×C5×D4—21no—
71C22×C5×D4D411yescharacteristic
72C22×C5×D4C2311yescharacteristic
73C23×C4×C5—21no—
74C23×C4×C5—21no—
75C23×C4×C5—21no—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C2×C5×M16—22no—
79C2×C5×M16—22no—
80C2×C5×M16—41no—
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—41no—
87C5×#121—22no—
88C5×#121—41no—
89C4×C5×D4—22no—
90C4×C5×D4—22no—
91C4×C5×D4—44no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—41no—
100C2×C5×C4⋊C4—41no—
101C2×C5×C4⋊C4D411yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4D411yescharacteristic
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C42×C5—21no—
118C2×C42×C5C2311yescharacteristic
119C5×#107—22no—
120C5×#107—22no—
121C5×#107—41no—
122C5×#106—41no—
123C5×#103—22no—
124C5×#103—22no—
125C5×#103—41no—
126C5×#103D414yescomplemented
127C5×#102—22no—
128C5×#102—22no—
129C5×#102—22no—
130C5×#102—41no—
131C5×C22⋊C8—22no—
132C5×C22⋊C8—22no—
133C5×C22⋊C8—41no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C2×#484C2×C511yescharacteristic, complemented
141C2×#417C2×C511yescharacteristic, complemented
142#2407C2×C511yescharacteristic
143D4×C4⋊C4C2×C511yescharacteristic, complemented
144#2093C2×C511yescharacteristic, complemented
145#2072C2×C511yescharacteristic, complemented
146#2036C2×C511yescharacteristic, complemented
147#2034C2×C511yescharacteristic, complemented
148#1927C2×C511yescharacteristic, complemented
149#1925C2×C511yescharacteristic, complemented
150#1874C2×C511yescharacteristic, complemented
151#1870C2×C511yescharacteristic, complemented
152#1852C2×C511yescharacteristic, complemented
153#1809C2×C511yescharacteristic, complemented
154#1788C2×C511yescharacteristic, complemented
155C24×C5—21no—
156C24×C5C2×D411yescharacteristic
157C24×C5C2×D411yescharacteristic
158C5×#41—28no—
159C5×#41—44no—
160C5×#41—44no—
161C5×#41—44no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8C2×D412yes—
168C2×C5×D4—22no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—42no—
177C2×C5×D4—42no—
178C2×C5×D4—42no—
179C2×C5×D4—42no—
180C2×C5×D4—42no—
181C2×C5×D4—81no—
182C2×C5×D4#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×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—42no—
201C22×C4×C5—42no—
202C22×C4×C5—42no—
203C22×C4×C5—42no—
204C22×C4×C5—42no—
205C22×C4×C5—42no—
206C22×C4×C5—42no—
207C22×C4×C5—81no—
208C22×C4×C5—81no—
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5#4112yes—
214C22×C4×C5#4112yes—
215C22×C4×C5C2411yescharacteristic
216C5×M16—44no—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
219C2×C5×C8—21no—
220C2×C5×C8—21no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8C2×D412yes—
229C5×C4⋊C4—22no—
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—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—42no—
242C5×C4⋊C4—42no—
243C5×C4⋊C4—42no—
244C5×C4⋊C4—42no—
245C5×C4⋊C4—81no—
246C5×C4⋊C4C2×D412yes—
247C5×C22⋊C4—22no—
248C5×C22⋊C4—22no—
249C5×C22⋊C4—42no—
250C5×C22⋊C4—42no—
251C5×C22⋊C4—42no—
252C5×C22⋊C4—42no—
253C5×C22⋊C4—42no—
254C5×C22⋊C4—81no—
255C5×C22⋊C4—81no—
256C42×C5—21no—
257C42×C5—21no—
258C42×C5—42no—
259C22×#41C22×C511yescharacteristic
260C22×M16C22×C511yescharacteristic
261C2×C22⋊Q8C22×C511yescharacteristic
262C2×#121C22×C511yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C22×C511yescharacteristic
265C22×C4⋊C4C22×C511yescharacteristic
266C22×C4⋊C4C22×C511yescharacteristic
267#484—24no—
268C2×#107C22×C511yescharacteristic
269C2×#107C22×C511yescharacteristic
270C2×#107C22×C511yescharacteristic
271C2×#106C22×C511yescharacteristic
272#417—24no—
273C2×#103C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#103C22×C511yescharacteristic
276C2×#103C22×C511yescharacteristic
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×#102C22×C511yescharacteristic
280C2×#102C22×C511yescharacteristic
281C2×C22⋊C8C22×C511yescharacteristic
282C2×C22⋊C8C22×C511yescharacteristic
283C2×C22⋊C8C22×C511yescharacteristic
284#394—21no—
285#392—21no—
286#391C22×C511yescharacteristic
287#390C22×C511yescharacteristic
288#389—21no—
289#386—21no—
290#385—21no—
291#385—21no—
292#385—21no—
293#384C22×C511yescharacteristic
294#380C22×C511yescharacteristic
295#380C22×C511yescharacteristic
296#380C22×C511yescharacteristic
297C4×C4⋊C4C22×C511yescharacteristic
298#340C22×C511yescharacteristic
299#340C22×C511yescharacteristic
300#340C22×C511yescharacteristic
301#340C22×C511yescharacteristic
302#336C22×C511yescharacteristic
303#336C22×C511yescharacteristic
304C23×C5—21no—
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—22no—
317C23×C5—41no—
318C23×C5—41no—
319C23×C5—41no—
320C23×C5—41no—
321C23×C5—41no—
322C23×C5—41no—
323C23×C5#12312yes—
324C23×C5#13712yes—
325C23×C5C22×D411yescharacteristic
326C5×Q8—22no—
327C5×Q8—22no—
328C5×Q8—41no—
329C5×Q8—41no—
330C5×D4—28no—
331C5×D4—22no—
332C5×D4—22no—
333C5×D4—48no—
334C5×D4—41no—
335C5×D4—41no—
336C5×D4—84no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—48no—
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—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—84no—
378C2×C4×C5—84no—
379C2×C4×C5#12312yes—
380C2×C4×C5AGL(1,ℤ/8)12yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C2×#4111yescharacteristic
383C2×C4×C5C2×#4111yescharacteristic
384C2×C4×C5C2×#4111yescharacteristic
385C2×C4×C5H(5,𝔽2)11yescharacteristic
386C2×C4×C5H(5,𝔽2)11yescharacteristic
387C5×C8—22no—
388C5×C8—41no—
389C5×C8—41no—
390C5×C8—41no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41—41no—
396C2×#41—41no—
397C22×Q8C23×C511yescharacteristic
398C22×D4—21no—
399C22×D4—21no—
400C22×D4C5×D411yescharacteristic
401C22×D4C23×C511yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4C23×C511yescharacteristic
406C23×C4C23×C511yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8C23×C511yescharacteristic
411C22×C8C23×C511yescharacteristic
412C22×C8C23×C511yescharacteristic
413C22×C8C23×C511yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8—41no—
416#121—22no—
417#121—41no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—44no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
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×C42C23×C511yescharacteristic
448#107—22no—
449#107—22no—
450#107—41no—
451#106—41no—
452#103—22no—
453#103—22no—
454#103—41no—
455#103C5×D414yescomplemented
456#102—22no—
457#102—22no—
458#102—22no—
459#102—41no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—41no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5—22no—
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×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—81no—
487C22×C5—81no—
488C22×C5—81no—
489C22×C5—81no—
490C22×C5C2×#12311yescharacteristic
491C22×C5D4211yescharacteristic
492C22×C5#54611yescharacteristic
493C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
494C22×C5C2×#13711yescharacteristic
495C22×C5#57611yescharacteristic
496C22×C5#57811yescharacteristic
497C4×C5—22no—
498C4×C5—22no—
499C4×C5—41no—
500C4×C5—41no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5—81no—
504C4×C5—81no—
505C4×C5—81no—
506C4×C5—81no—
507C4×C5—81no—
508C4×C5#52511yescharacteristic
509C4×C5#53811yescharacteristic
510C4×C5#54611yescharacteristic
511C4×C5#55111yescharacteristic
512C24—21no—
513C24C2×C5×D411yescharacteristic
514C24C2×C5×D411yescharacteristic
515#41—28no—
516#41—44no—
517#41—44no—
518#41—44no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8C2×C5×D412yes—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4C5×#4112yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4C2×C5×D411yescharacteristic
567C22×C4C2×C5×D411yescharacteristic
568C22×C4C2×C5×D411yescharacteristic
569C22×C4C2×C5×D411yescharacteristic
570C22×C4C5×#4112yes—
571C22×C4C5×#4112yes—
572C22×C4C24×C511yescharacteristic
573M16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8C2×C5×D412yes—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—81no—
603C4⋊C4C2×C5×D412yes—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—42no—
616C2×C5—42no—
617C2×C5—42no—
618C2×C5—82no—
619C2×C5#241811yescharacteristic
620C2×C5#309211yescharacteristic
621C2×C5#309811yescharacteristic
622C2×C5#327011yescharacteristic
623C2×C5#327411yescharacteristic
624C2×C5#331411yescharacteristic
625C2×C5#333011yescharacteristic
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C5×#12312yes—
646C23C5×#13712yes—
647C23C22×C5×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—41no—
651Q8—41no—
652D4—28no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—41no—
657D4—41no—
658D4—84no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4C5×#12312yes—
702C2×C4C5×AGL(1,ℤ/8)12yes—
703C2×C4C22×C5×D411yescharacteristic
704C2×C4C2×C5×#4111yescharacteristic
705C2×C4C2×C5×#4111yescharacteristic
706C2×C4C2×C5×#4111yescharacteristic
707C2×C4C5×H(5,𝔽2)11yescharacteristic
708C2×C4C5×H(5,𝔽2)11yescharacteristic
709C8—22no—
710C8—41no—
711C8—41no—
712C8—41no—
713C5#2488311yescharacteristic, direct product factor, Sylow
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C2×C5×#12311yescharacteristic
736C22C5×D4211yescharacteristic
737C22C5×#54611yescharacteristic
738C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
739C22C2×C5×#13711yescharacteristic
740C22C5×#57611yescharacteristic
741C22C5×#57811yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4C5×#52511yescharacteristic
754C4C5×#53811yescharacteristic
755C4C5×#54611yescharacteristic
756C4C5×#55111yescharacteristic
757C2—42no—
758C2—42no—
759C2—82no—
760C2C5×#241811yescharacteristic
761C2C5×#309211yescharacteristic
762C2C5×#309811yescharacteristic
763C2C5×#327011yescharacteristic
764C2C5×#327411yescharacteristic
765C2C5×#331411yescharacteristic
766C2C5×#333011yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2407C2
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
1. C2×C5×#484C2semidirect
2. C2×C5×#417C2semidirect
4. C5×D4×C4⋊C4C2semidirect
5. C5×#2093C2semidirect
6. C5×#2072C2semidirect
7. C5×#2036C2semidirect
8. C5×#2034C2semidirect
9. C5×#1927C2semidirect
10. C5×#1925C2semidirect
11. C5×#1874C2semidirect
12. C5×#1870C2semidirect
13. C5×#1852C2semidirect
14. C5×#1809C2semidirect
15. C5×#1788C2semidirect
61. #24883C5direct (N × H)
126. C5×#103D4semidirect
140. C2×#484C2×C5semidirect
141. C2×#417C2×C5semidirect
143. D4×C4⋊C4C2×C5semidirect
144. #2093C2×C5semidirect
145. #2072C2×C5semidirect
146. #2036C2×C5semidirect
147. #2034C2×C5semidirect
148. #1927C2×C5semidirect
149. #1925C2×C5semidirect
150. #1874C2×C5semidirect
151. #1870C2×C5semidirect
152. #1852C2×C5semidirect
153. #1809C2×C5semidirect
154. #1788C2×C5semidirect
455. #103C5×D4semidirect
713. C5#24883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C2×C5×#4172
C5×#24072
C5×D4×C4⋊C42
C5×#20932
C5×#20722
C5×#20362
C5×#20342
C5×#19272
C5×#19252
C5×#18742
C5×#18702
C5×#18522
C5×#18092
C5×#17882
#248835