Finite Group Databasebeta

← C5×#25955 #11948675

Subgroups — C5×#25955 #11948675

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#475C211yesmaximal, characteristic, complemented
2C22×C5×#103C211yesmaximal, characteristic
3C5×#2440C211yesmaximal, characteristic
4C5×Q8×C22⋊C4C211yesmaximal, characteristic
5C5×#2096C211yesmaximal, characteristic, complemented
6C5×#2066C211yesmaximal, characteristic, complemented
7C5×#2066C211yesmaximal, characteristic, complemented
8C5×#2024C211yesmaximal, characteristic, complemented
9C5×#1865C211yesmaximal, characteristic, complemented
10C5×#1865C211yesmaximal, characteristic, complemented
11C5×#1853C211yesmaximal, characteristic
12C5×#1850C211yesmaximal, characteristic
13C5×#1807C211yesmaximal, characteristic
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1787C211yesmaximal, characteristic
16C23×C5×Q8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8—21no—
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#475—24no—
24C2×C5×#106C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103—24no—
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#103C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C5×#398—21no—
41C5×#395—21no—
42C5×#391—21no—
43C5×#391—21no—
44C5×#391C2211yescharacteristic
45C5×#391C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#385—21no—
49C5×#384C2211yescharacteristic
50C5×#380—21no—
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C4×C5×C22⋊C4—21no—
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25955C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8—21no—
63C22×C5×Q8—21no—
64C22×C5×Q8—22no—
65C22×C5×Q8—22no—
66C22×C5×Q8—22no—
67C22×C5×Q8—41no—
68C22×C5×Q8—41no—
69C22×C5×Q8Q814yescomplemented
70C22×C5×Q8C2311yescharacteristic
71C22×C5×Q8C2311yescharacteristic
72C23×C4×C5—21no—
73C23×C4×C5—21no—
74C23×C4×C5C2311yescharacteristic
75C22×C5×C8—22no—
76C22×C5×C8—22no—
77C22×C5×C8—41no—
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C5×C4⋊Q8—22no—
83C5×C4⋊Q8—41no—
84C5×C22⋊Q8—44no—
85C4×C5×Q8—22no—
86C4×C5×Q8—22no—
87C4×C5×Q8—41no—
88C4×C5×Q8—41no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—41no—
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C5×C22⋊C4D411yescharacteristic
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C5×#106—22no—
114C5×#106—22no—
115C5×#106—41no—
116C5×#106—41no—
117C5×C4⋊C8—22no—
118C5×C4⋊C8—41no—
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—22no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#103—41no—
125C5×#103—41no—
126C5×#103D414yes—
127C5×C22⋊C8—22no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95D411yescharacteristic
137C5×#95D411yescharacteristic
138C2×#475C2×C511yescharacteristic, complemented
139C22×#103C2×C511yescharacteristic
140#2440C2×C511yescharacteristic
141Q8×C22⋊C4C2×C511yescharacteristic
142#2096C2×C511yescharacteristic, complemented
143#2066C2×C511yescharacteristic, complemented
144#2066C2×C511yescharacteristic, complemented
145#2024C2×C511yescharacteristic, complemented
146#1865C2×C511yescharacteristic, complemented
147#1865C2×C511yescharacteristic, complemented
148#1853C2×C511yescharacteristic
149#1850C2×C511yescharacteristic
150#1807C2×C511yescharacteristic
151#1803C2×C511yescharacteristic, complemented
152#1787C2×C511yescharacteristic
153C24×C5C2×D411yescharacteristic
154C2×C5×Q8—24no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—28no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—42no—
165C2×C5×Q8—42no—
166C2×C5×Q8—42no—
167C2×C5×Q8—44no—
168C2×C5×Q8—44no—
169C2×C5×Q8—44no—
170C2×C5×Q8—42no—
171C2×C5×Q8—81no—
172C2×C5×Q8C2×D412yes—
173C2×C5×Q8C2×Q812yes—
174C2×C5×Q8C2×Q812yes—
175C2×C5×Q8#4112yes—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
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—42no—
190C22×C4×C5—42no—
191C22×C4×C5—42no—
192C22×C4×C5—42no—
193C22×C4×C5—81no—
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×Q812yes—
200C22×C4×C5#4112yes—
201C22×C4×C5C2411yescharacteristic
202C2×C5×C8—21no—
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—44no—
214C2×C5×C8C2×D412yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—42no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—42no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4—42no—
231C5×C4⋊C4—42no—
232C5×C4⋊C4—42no—
233C5×C4⋊C4—81no—
234C5×C4⋊C4C2×D412yes—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4SD1614yes—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—42no—
244C42×C5—42no—
245C23×Q8C22×C511yescharacteristic
246C23×C8C22×C511yescharacteristic
247C2×C4⋊Q8C22×C511yescharacteristic
248C2×C22⋊Q8—21no—
249C2×C4×Q8C22×C511yescharacteristic
250C2×C4×Q8C22×C511yescharacteristic
251C22×C4⋊C4C22×C511yescharacteristic
252#475—24no—
253C2×#106C22×C511yescharacteristic
254C2×#106C22×C511yescharacteristic
255C2×#106C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×C4⋊C8C22×C511yescharacteristic
258C2×C4⋊C8C22×C511yescharacteristic
259C2×#103—24no—
260C2×#103C22×C511yescharacteristic
261C2×#103C22×C511yescharacteristic
262C2×#103C22×C511yescharacteristic
263C2×#103C22×C511yescharacteristic
264C2×#103C22×C511yescharacteristic
265C2×#103C22×C511yescharacteristic
266C2×#103C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×C22⋊C8C22×C511yescharacteristic
269#398—21no—
270#395—21no—
271#391—21no—
272#391—21no—
273#391C22×C511yescharacteristic
274#391C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#389C22×C511yescharacteristic
277#385—21no—
278#384C22×C511yescharacteristic
279#380—21no—
280#380C22×C511yescharacteristic
281#380C22×C511yescharacteristic
282C4×C22⋊C4—21no—
283C4×C22⋊C4C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#336C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5C22⋊Q812yes—
295C23×C5C2×SD1612yes—
296C23×C5#13712yes—
297C23×C5C22×D411yescharacteristic
298C5×Q8—22no—
299C5×Q8—22no—
300C5×Q8—22no—
301C5×Q8—22no—
302C5×Q8—22no—
303C5×Q8—48no—
304C5×Q8—41no—
305C5×Q8—41no—
306C5×Q8—84no—
307C5×Q8C22⋊Q814yescomplemented
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—22no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—48no—
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—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—84no—
350C2×C4×C5C22⋊Q812yes—
351C2×C4×C5C2×SD1612yes—
352C2×C4×C5C2×SD1612yes—
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C5C22×Q811yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5C2×#4111yescharacteristic
357C2×C4×C5H(5,𝔽2)11yescharacteristic
358C2×C4×C5H(5,𝔽2)11yescharacteristic
359C5×C8—22no—
360C5×C8—41no—
361C5×C8—41no—
362C5×C8—41no—
363C22×Q8—21no—
364C22×Q8—21no—
365C22×Q8—22no—
366C22×Q8—22no—
367C22×Q8—22no—
368C22×Q8—41no—
369C22×Q8—41no—
370C22×Q8C5×Q814yescomplemented
371C22×Q8C23×C511yescharacteristic
372C22×Q8C23×C511yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4C23×C511yescharacteristic
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—41no—
379C22×C8C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C4⋊Q8—22no—
384C4⋊Q8—41no—
385C22⋊Q8—44no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—41no—
389C4×Q8—41no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4C5×D411yescharacteristic
409C2×C22⋊C4C5×D411yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C511yescharacteristic
413C2×C42C23×C511yescharacteristic
414#106—22no—
415#106—22no—
416#106—41no—
417#106—41no—
418C4⋊C8—22no—
419C4⋊C8—41no—
420#103—22no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—22no—
425#103—41no—
426#103—41no—
427#103C5×D414yes—
428C22⋊C8—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95C5×D411yescharacteristic
438#95C5×D411yescharacteristic
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5#47514yescomplemented
446C22×C5C2×C22⋊Q811yescharacteristic
447C22×C5D4211yescharacteristic
448C22×C5#54611yescharacteristic
449C22×C5C22×SD1611yescharacteristic
450C22×C5C2×#13711yescharacteristic
451C22×C5#57711yescharacteristic
452C22×C5#57811yescharacteristic
453C4×C5—22no—
454C4×C5—24no—
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—41no—
461C4×C5—81no—
462C4×C5—81no—
463C4×C5—81no—
464C4×C5—81no—
465C4×C5—81no—
466C4×C5C2×C22⋊Q811yescharacteristic
467C4×C5#54311yescharacteristic
468C4×C5#54611yescharacteristic
469C4×C5#55111yescharacteristic
470C24C2×C5×D411yescharacteristic
471C2×Q8—24no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—28no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—42no—
488C2×Q8—81no—
489C2×Q8C2×C5×D412yes—
490C2×Q8C2×C5×Q812yes—
491C2×Q8C2×C5×Q812yes—
492C2×Q8C5×#4112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—81no—
511C22×C4C2×C5×D411yescharacteristic
512C22×C4C2×C5×D411yescharacteristic
513C22×C4C2×C5×D411yescharacteristic
514C22×C4C2×C5×D411yescharacteristic
515C22×C4C2×C5×D411yescharacteristic
516C22×C4C2×C5×Q812yes—
517C22×C4C5×#4112yes—
518C22×C4C24×C511yescharacteristic
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—44no—
531C2×C8C2×C5×D412yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4C2×C5×D412yes—
552C22⋊C4—22no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4C5×SD1614yes—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—42no—
561C42—42no—
562C2×C5—24no—
563C2×C5#243711yescharacteristic
564C2×C5C2×#47511yescharacteristic
565C2×C5#308211yescharacteristic
566C2×C5#327011yescharacteristic
567C2×C5D4×SD1611yescharacteristic
568C2×C5#329811yescharacteristic
569C2×C5#331611yescharacteristic
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23C5×C22⋊Q812yes—
575C23C2×C5×SD1612yes—
576C23C5×#13712yes—
577C23C22×C5×D411yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—48no—
584Q8—41no—
585Q8—41no—
586Q8—84no—
587Q8C5×C22⋊Q814yescomplemented
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—48no—
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—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4C5×C22⋊Q812yes—
631C2×C4C2×C5×SD1612yes—
632C2×C4C2×C5×SD1612yes—
633C2×C4C22×C5×D411yescharacteristic
634C2×C4C22×C5×Q811yescharacteristic
635C2×C4C2×C5×#4111yescharacteristic
636C2×C4C2×C5×#4111yescharacteristic
637C2×C4C5×H(5,𝔽2)11yescharacteristic
638C2×C4C5×H(5,𝔽2)11yescharacteristic
639C8—22no—
640C8—41no—
641C8—41no—
642C8—41no—
643C5#2595511yescharacteristic, direct product factor, Sylow
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22C5×#47514yescomplemented
651C22C2×C5×C22⋊Q811yescharacteristic
652C22C5×D4211yescharacteristic
653C22C5×#54611yescharacteristic
654C22C22×C5×SD1611yescharacteristic
655C22C2×C5×#13711yescharacteristic
656C22C5×#57711yescharacteristic
657C22C5×#57811yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—24no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C2×C5×C22⋊Q811yescharacteristic
672C4C5×#54311yescharacteristic
673C4C5×#54611yescharacteristic
674C4C5×#55111yescharacteristic
675C2—24no—
676C2C5×#243711yescharacteristic
677C2C2×C5×#47511yescharacteristic
678C2C5×#308211yescharacteristic
679C2C5×#327011yescharacteristic
680C2C5×D4×SD1611yescharacteristic
681C2C5×#329811yescharacteristic
682C2C5×#331611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#475C2semidirect
5. C5×#2096C2semidirect
6. C5×#2066C2semidirect
7. C5×#2066C2semidirect
8. C5×#2024C2semidirect
9. C5×#1865C2semidirect
10. C5×#1865C2semidirect
14. C5×#1803C2semidirect
61. #25955C5direct (N × H)
69. C22×C5×Q8Q8semidirect
138. C2×#475C2×C5semidirect
142. #2096C2×C5semidirect
143. #2066C2×C5semidirect
144. #2066C2×C5semidirect
145. #2024C2×C5semidirect
146. #1865C2×C5semidirect
147. #1865C2×C5semidirect
151. #1803C2×C5semidirect
307. C5×Q8C22⋊Q8semidirect
370. C22×Q8C5×Q8semidirect
445. C22×C5#475semidirect
587. Q8C5×C22⋊Q8semidirect
643. C5#25955direct (N × H)
650. C22C5×#475semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4752
C22×C5×#1032
C5×#24402
C5×Q8×C22⋊C42
C5×#20962
C5×#20662
C5×#20242
C5×#18652
C5×#18532
C5×#18502
C5×#18072
C5×#18032
C5×#17872
#259555