Finite Group Databasebeta

← C5×#22661 #11945381

Subgroups — C5×#22661 #11945381

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#435C211yesmaximal, characteristic
2C2×C5×#428C211yesmaximal, characteristic, complemented
3C22×C5×#107C211yesmaximal, characteristic, complemented
4C5×#2352C211yesmaximal, characteristic
5C5×D4×C4⋊C4C211yesmaximal, characteristic
6C5×#1949C211yesmaximal, characteristic, complemented
7C5×#1947C211yesmaximal, characteristic, complemented
8C5×#1854C211yesmaximal, characteristic, complemented
9C5×#1853C211yesmaximal, characteristic, complemented
10C5×#1852C211yesmaximal, characteristic, complemented
11C5×#1852C211yesmaximal, characteristic, complemented
12C5×#1847C211yesmaximal, characteristic, complemented
13C5×#1809C211yesmaximal, characteristic, complemented
14C5×#1807C211yesmaximal, characteristic, complemented
15C5×#1776C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C4×C5×D4—21no—
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#435C418yescomplemented
25C5×#428—24no—
26C2×C5×#107—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×#107C2211yescharacteristic
31C2×C5×#107C2211yescharacteristic
32C2×C5×#107C2211yescharacteristic
33C2×C5×#106C2211yescharacteristic
34C2×C5×#106C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×#97C2211yescharacteristic
41C5×#389—21no—
42C5×#388—21no—
43C5×#387—21no—
44C5×#386—21no—
45C5×#385—21no—
46C5×#385—21no—
47C5×#384C2211yescharacteristic
48C5×#382C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C4⋊C4C2211yescharacteristic
55C4×C5×C22⋊C4—21no—
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#340C2211yescharacteristic
62#22661C511yesmaximal, characteristic, direct product factor, Sylow
63C22×C5×D4D411yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C2×C5×M16—22no—
70C2×C5×M16—22no—
71C2×C5×M16C2×C414yescomplemented
72C22×C5×C8—22no—
73C22×C5×C8—22no—
74C22×C5×C8C2×C414yescomplemented
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C4×C5×D4—44no—
80C4×C5×D4C2×C414yes—
81C4×C5×D4Q814yes—
82C5×#117—22no—
83C5×#117—41no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4D411yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C42×C5—21no—
112C2×C42×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C5×#107—22no—
116C5×#107—22no—
117C5×#107—22no—
118C5×#107—22no—
119C5×#107—41no—
120C5×#107D414yescomplemented
121C5×#106—22no—
122C5×#106—22no—
123C5×#106—22no—
124C5×#106—41no—
125C5×C4⋊C8C2×C414yescomplemented
126C5×C22⋊C8C2×C414yescomplemented
127C5×C22⋊C8C2×C414yescomplemented
128C5×#97C2×C414yescomplemented
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C2×#435C2×C511yescharacteristic
138C2×#428C2×C511yescharacteristic, complemented
139C22×#107C2×C511yescharacteristic, complemented
140#2352C2×C511yescharacteristic
141D4×C4⋊C4C2×C511yescharacteristic
142#1949C2×C511yescharacteristic, complemented
143#1947C2×C511yescharacteristic, complemented
144#1854C2×C511yescharacteristic, complemented
145#1853C2×C511yescharacteristic, complemented
146#1852C2×C511yescharacteristic, complemented
147#1852C2×C511yescharacteristic, complemented
148#1847C2×C511yescharacteristic, complemented
149#1809C2×C511yescharacteristic, complemented
150#1807C2×C511yescharacteristic, complemented
151#1776C2×C511yescharacteristic, complemented
152C24×C5C2×D411yescharacteristic
153C24×C5C2×D411yescharacteristic
154C2×C5×D4—22no—
155C2×C5×D4—22no—
156C2×C5×D4C4⋊C414yes—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—42no—
174C22×C4×C5—42no—
175C22×C4×C5—42no—
176C22×C4×C5—42no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—81no—
180C22×C4×C5—81no—
181C22×C4×C5—81no—
182C22×C4×C5C22×C412yes—
183C22×C4×C5C22×C412yes—
184C22×C4×C5C2×D411yescharacteristic
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×Q812yes—
189C22×C4×C5C2×Q812yes—
190C22×C4×C5C2411yescharacteristic
191C5×M16—28no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—28no—
199C2×C5×C8C22×C412yes—
200C2×C5×C8C22×C412yes—
201C2×C5×C8C22×C412yes—
202C2×C5×C8C22×C412yes—
203C2×C5×C8C2×D412yes—
204C2×C5×C8#4112yes—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4C4⋊C414yes—
225C5×C4⋊C4C2×D412yes—
226C5×C4⋊C4C2×D412yes—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—81no—
232C5×C22⋊C4C4⋊C414yes—
233C5×C22⋊C4C4⋊C414yes—
234C42×C5—42no—
235C42×C5—42no—
236C42×C5—81no—
237C42×C5C22×C412yes—
238C42×C5C2×Q812yes—
239C22×M16C22×C511yescharacteristic
240C23×C8C22×C511yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C22×C511yescharacteristic
243C2×#117C22×C511yescharacteristic
244C22×C4⋊C4C22×C511yescharacteristic
245C22×C4⋊C4C22×C511yescharacteristic
246C22×C4⋊C4C22×C511yescharacteristic
247#435C4×C518yescomplemented
248#428—24no—
249C2×#107—24no—
250C2×#107C22×C511yescharacteristic
251C2×#107C22×C511yescharacteristic
252C2×#107C22×C511yescharacteristic
253C2×#107C22×C511yescharacteristic
254C2×#107C22×C511yescharacteristic
255C2×#107C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×#106C22×C511yescharacteristic
258C2×#106C22×C511yescharacteristic
259C2×#106C22×C511yescharacteristic
260C2×C4⋊C8C22×C511yescharacteristic
261C2×C22⋊C8C22×C511yescharacteristic
262C2×C22⋊C8C22×C511yescharacteristic
263C2×#97C22×C511yescharacteristic
264#389—21no—
265#388—21no—
266#387—21no—
267#386—21no—
268#385—21no—
269#385—21no—
270#384C22×C511yescharacteristic
271#382C22×C511yescharacteristic
272#380C22×C511yescharacteristic
273#380C22×C511yescharacteristic
274#380C22×C511yescharacteristic
275#380C22×C511yescharacteristic
276C4×C4⋊C4C22×C511yescharacteristic
277C4×C4⋊C4C22×C511yescharacteristic
278C4×C22⋊C4—21no—
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5C2×C4⋊C412yes—
296C23×C5C2×C4⋊C412yes—
297C23×C5AGL(1,ℤ/8)12yes—
298C23×C5#13712yes—
299C23×C5C22×D411yescharacteristic
300C5×D4—28no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—84no—
342C2×C4×C5—84no—
343C2×C4×C5—84no—
344C2×C4×C5C2×C4⋊C412yes—
345C2×C4×C5C2×C4⋊C412yes—
346C2×C4×C5C2×C4⋊C412yes—
347C2×C4×C5C2×C4⋊C412yes—
348C2×C4×C5C23×C411yescharacteristic
349C2×C4×C5C22×D411yescharacteristic
350C2×C4×C5C22×Q811yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5H(5,𝔽2)11yescharacteristic
353C2×C4×C52−1+411yescharacteristic
354C5×C8—22no—
355C5×C8—22no—
356C5×C8—22no—
357C5×C8C4×D414yescomplemented
358C22×D4C5×D411yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C23×C511yescharacteristic
363C23×C4C23×C511yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16C2×C4×C514yescomplemented
367C22×C8—22no—
368C22×C8—22no—
369C22×C8C2×C4×C514yescomplemented
370C22×C8C23×C511yescharacteristic
371C22×C8C23×C511yescharacteristic
372C22×C8C23×C511yescharacteristic
373C22×C8C23×C511yescharacteristic
374C4×D4—44no—
375C4×D4C2×C4×C514yes—
376C4×D4C5×Q814yes—
377#117—22no—
378#117—41no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4C5×D411yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C4⋊C4C23×C511yescharacteristic
394C2×C4⋊C4C23×C511yescharacteristic
395C2×C4⋊C4C23×C511yescharacteristic
396C2×C4⋊C4C23×C511yescharacteristic
397C2×C4⋊C4C23×C511yescharacteristic
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4C5×D411yescharacteristic
405C2×C22⋊C4C5×D411yescharacteristic
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C23×C511yescharacteristic
410#107—22no—
411#107—22no—
412#107—22no—
413#107—22no—
414#107—41no—
415#107C5×D414yescomplemented
416#106—22no—
417#106—22no—
418#106—22no—
419#106—41no—
420C4⋊C8C2×C4×C514yescomplemented
421C22⋊C8C2×C4×C514yescomplemented
422C22⋊C8C2×C4×C514yescomplemented
423#97C2×C4×C514yescomplemented
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5#42814yescomplemented
446C22×C5C22×C4⋊C411yescharacteristic
447C22×C5D4211yescharacteristic
448C22×C5#54711yescharacteristic
449C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C5C2×#13711yescharacteristic
451C22×C5#57611yescharacteristic
452C22×C5#57811yescharacteristic
453C4×C5—22no—
454C4×C5—22no—
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—42no—
458C4×C5—42no—
459C4×C5—81no—
460C4×C5—81no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5C2×C4×D411yescharacteristic
466C4×C5#52011yescharacteristic
467C4×C5D4×Q811yescharacteristic
468C4×C5#55411yescharacteristic
469C24C2×C5×D411yescharacteristic
470C24C2×C5×D411yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4C5×C4⋊C414yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4C22×C4×C512yes—
500C22×C4C22×C4×C512yes—
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C2×C5×D411yescharacteristic
504C22×C4C2×C5×D411yescharacteristic
505C22×C4C2×C5×Q812yes—
506C22×C4C2×C5×Q812yes—
507C22×C4C24×C511yescharacteristic
508M16—28no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—28no—
516C2×C8C22×C4×C512yes—
517C2×C8C22×C4×C512yes—
518C2×C8C22×C4×C512yes—
519C2×C8C22×C4×C512yes—
520C2×C8C2×C5×D412yes—
521C2×C8C5×#4112yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4C5×C4⋊C414yes—
542C4⋊C4C2×C5×D412yes—
543C4⋊C4C2×C5×D412yes—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4C5×C4⋊C414yes—
550C22⋊C4C5×C4⋊C414yes—
551C42—42no—
552C42—42no—
553C42—81no—
554C42C22×C4×C512yes—
555C42C2×C5×Q812yes—
556C2×C5—24no—
557C2×C5—42no—
558C2×C5D4×C4⋊C411yescharacteristic
559C2×C5C2×#42811yescharacteristic
560C2×C5#291311yescharacteristic
561C2×C5#326411yescharacteristic
562C2×C5#327011yescharacteristic
563C2×C5#334311yescharacteristic
564C2×C5#334611yescharacteristic
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C2×C5×C4⋊C412yes—
576C23C2×C5×C4⋊C412yes—
577C23C5×AGL(1,ℤ/8)12yes—
578C23C5×#13712yes—
579C23C22×C5×D411yescharacteristic
580D4—28no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4C2×C5×C4⋊C412yes—
625C2×C4C2×C5×C4⋊C412yes—
626C2×C4C2×C5×C4⋊C412yes—
627C2×C4C2×C5×C4⋊C412yes—
628C2×C4C23×C4×C511yescharacteristic
629C2×C4C22×C5×D411yescharacteristic
630C2×C4C22×C5×Q811yescharacteristic
631C2×C4C2×C5×#4111yescharacteristic
632C2×C4C5×H(5,𝔽2)11yescharacteristic
633C2×C4C5×2−1+411yescharacteristic
634C8—22no—
635C8—22no—
636C8—22no—
637C8C4×C5×D414yescomplemented
638C5#2266111yescharacteristic, direct product factor, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22C5×#42814yescomplemented
653C22C22×C5×C4⋊C411yescharacteristic
654C22C5×D4211yescharacteristic
655C22C5×#54711yescharacteristic
656C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
657C22C2×C5×#13711yescharacteristic
658C22C5×#57611yescharacteristic
659C22C5×#57811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C2×C4×C5×D411yescharacteristic
673C4C5×#52011yescharacteristic
674C4C5×D4×Q811yescharacteristic
675C4C5×#55411yescharacteristic
676C2—24no—
677C2—42no—
678C2C5×D4×C4⋊C411yescharacteristic
679C2C2×C5×#42811yescharacteristic
680C2C5×#291311yescharacteristic
681C2C5×#326411yescharacteristic
682C2C5×#327011yescharacteristic
683C2C5×#334311yescharacteristic
684C2C5×#334611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×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×#428C2semidirect
3. C22×C5×#107C2semidirect
6. C5×#1949C2semidirect
7. C5×#1947C2semidirect
8. C5×#1854C2semidirect
9. C5×#1853C2semidirect
10. C5×#1852C2semidirect
11. C5×#1852C2semidirect
12. C5×#1847C2semidirect
13. C5×#1809C2semidirect
14. C5×#1807C2semidirect
15. C5×#1776C2semidirect
24. C5×#435C4semidirect
62. #22661C5direct (N × H)
71. C2×C5×M16C2×C4semidirect
74. C22×C5×C8C2×C4semidirect
120. C5×#107D4semidirect
125. C5×C4⋊C8C2×C4semidirect
126. C5×C22⋊C8C2×C4semidirect
127. C5×C22⋊C8C2×C4semidirect
128. C5×#97C2×C4semidirect
138. C2×#428C2×C5semidirect
139. C22×#107C2×C5semidirect
142. #1949C2×C5semidirect
143. #1947C2×C5semidirect
144. #1854C2×C5semidirect
145. #1853C2×C5semidirect
146. #1852C2×C5semidirect
147. #1852C2×C5semidirect
148. #1847C2×C5semidirect
149. #1809C2×C5semidirect
150. #1807C2×C5semidirect
151. #1776C2×C5semidirect
247. #435C4×C5semidirect
357. C5×C8C4×D4semidirect
366. C2×M16C2×C4×C5semidirect
369. C22×C8C2×C4×C5semidirect
415. #107C5×D4semidirect
420. C4⋊C8C2×C4×C5semidirect
421. C22⋊C8C2×C4×C5semidirect
422. C22⋊C8C2×C4×C5semidirect
423. #97C2×C4×C5semidirect
445. C22×C5#428semidirect
637. C8C4×C5×D4semidirect
638. C5#22661direct (N × H)
652. C22C5×#428semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4352
C2×C5×#4282
C22×C5×#1072
C5×#23522
C5×D4×C4⋊C42
C5×#19492
C5×#19472
C5×#18542
C5×#18532
C5×#18522
C5×#18472
C5×#18092
C5×#18072
C5×#17762
#226615