Finite Group Databasebeta

← C5×#24309 #11947029

Subgroups — C5×#24309 #11947029

Order 1280.

1068 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#544C211yesmaximal, characteristic, complemented
2C2×C5×#478C211yesmaximal, characteristic, complemented
3C2×C5×#476C211yesmaximal, characteristic, complemented
4C5×#2324C211yesmaximal, characteristic
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2058C211yesmaximal, characteristic, complemented
7C5×#2025C211yesmaximal, characteristic, complemented
8C5×#2023C211yesmaximal, characteristic, complemented
9C5×#1989C211yesmaximal, characteristic, complemented
10C5×#1988C211yesmaximal, characteristic, complemented
11C5×#1875C211yesmaximal, characteristic
12C5×#1874C211yesmaximal, characteristic
13C5×#1854C211yesmaximal, characteristic, complemented
14C5×#1853C211yesmaximal, characteristic, complemented
15C5×#1798C211yesmaximal, characteristic, complemented
16C5×#544—24no—
17C5×#544—24no—
18C2×C5×C4⋊Q8—21no—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#125—21no—
22C2×C5×#125C2211yescharacteristic
23C2×C5×#125C2211yescharacteristic
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#478—24no—
32C5×#476—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#106C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×#106C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×C22⋊C8C2211yescharacteristic
44C2×C5×C22⋊C8C2211yescharacteristic
45C5×#390—21no—
46C5×#390C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#388—21no—
49C5×#386—21no—
50C5×#385—21no—
51C5×#380C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24309C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8—21no—
66C22×C5×D4—21no—
67C22×C5×D4C2311yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×C4⋊Q8—28no—
76C5×C4⋊Q8—22no—
77C5×C4⋊Q8—22no—
78C5×C4⋊Q8—22no—
79C5×C4⋊Q8D414yescomplemented
80C5×#125—28no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#125—22no—
84C5×#125D414yescomplemented
85C5×C22⋊Q8—28no—
86C5×C22⋊Q8—28no—
87C5×#121—22no—
88C5×#121Q814yescomplemented
89C4×C5×D4—22no—
90C4×C5×D4—22no—
91C5×#117—22no—
92C5×#117—22no—
93C5×#117—22no—
94C5×#117—22no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—22no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C4⋊C4D411yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C42×C5—21no—
123C2×C42×C5—21no—
124C2×C42×C5C2311yescharacteristic
125C2×C42×C5C2311yescharacteristic
126C5×#107—22no—
127C5×#106—22no—
128C5×#106—22no—
129C5×#106—22no—
130C5×C4⋊C8—22no—
131C5×C4⋊C8—22no—
132C5×#102—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C5×C22⋊C8—22no—
137C5×C22⋊C8—22no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C2×#544C2×C511yescharacteristic, complemented
142C2×#478C2×C511yescharacteristic, complemented
143C2×#476C2×C511yescharacteristic, complemented
144#2324C2×C511yescharacteristic
145#2059C2×C511yescharacteristic, complemented
146#2058C2×C511yescharacteristic, complemented
147#2025C2×C511yescharacteristic, complemented
148#2023C2×C511yescharacteristic, complemented
149#1989C2×C511yescharacteristic, complemented
150#1988C2×C511yescharacteristic, complemented
151#1875C2×C511yescharacteristic
152#1874C2×C511yescharacteristic
153#1854C2×C511yescharacteristic, complemented
154#1853C2×C511yescharacteristic, complemented
155#1798C2×C511yescharacteristic, complemented
156C24×C5—21no—
157C24×C5C2×D411yescharacteristic
158C2×C5×Q8—24no—
159C2×C5×Q8—24no—
160C2×C5×Q8—81no—
161C2×C5×Q8—81no—
162C2×C5×Q8—81no—
163C2×C5×Q8—81no—
164C2×C5×D4—24no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—81no—
171C2×C5×D4—81no—
172C2×C5×D4C2×Q812yes—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—24no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—42no—
186C22×C4×C5—81no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×Q812yes—
196C22×C4×C5#4112yes—
197C22×C4×C5C2411yescharacteristic
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
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—
210C5×C4⋊C4—24no—
211C5×C4⋊C4—24no—
212C5×C4⋊C4—24no—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—22no—
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—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—81no—
229C5×C4⋊C4C2×D412yes—
230C5×C4⋊C4C2×D412yes—
231C5×C4⋊C4C2×D412yes—
232C5×C4⋊C4C2×D412yes—
233C5×C4⋊C4C2×Q812yes—
234C5×C22⋊C4—24no—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—22no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—42no—
239C5×C22⋊C4—81no—
240C5×C22⋊C4—81no—
241C5×C22⋊C4—81no—
242C42×C5—24no—
243C42×C5—21no—
244C42×C5—21no—
245C42×C5—81no—
246C42×C5C2×D412yes—
247C42×C5C2×D412yes—
248#544—24no—
249#544—24no—
250C2×C4⋊Q8—21no—
251C2×C4⋊Q8C22×C511yescharacteristic
252C2×C4⋊Q8C22×C511yescharacteristic
253C2×#125—21no—
254C2×#125C22×C511yescharacteristic
255C2×#125C22×C511yescharacteristic
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×#121C22×C511yescharacteristic
259C2×C4×D4C22×C511yescharacteristic
260C2×#117C22×C511yescharacteristic
261C2×#117C22×C511yescharacteristic
262C22×C4⋊C4C22×C511yescharacteristic
263#478—24no—
264#476—24no—
265C2×#107C22×C511yescharacteristic
266C2×#106C22×C511yescharacteristic
267C2×#106C22×C511yescharacteristic
268C2×#106C22×C511yescharacteristic
269C2×C4⋊C8C22×C511yescharacteristic
270C2×C4⋊C8C22×C511yescharacteristic
271C2×#102C22×C511yescharacteristic
272C2×#102C22×C511yescharacteristic
273C2×#102C22×C511yescharacteristic
274C2×#102C22×C511yescharacteristic
275C2×C22⋊C8C22×C511yescharacteristic
276C2×C22⋊C8C22×C511yescharacteristic
277#390—21no—
278#390C22×C511yescharacteristic
279#389C22×C511yescharacteristic
280#388—21no—
281#386—21no—
282#385—21no—
283#380C22×C511yescharacteristic
284C4×C4⋊C4C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#340C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#340C22×C511yescharacteristic
293#336C22×C511yescharacteristic
294#336C22×C511yescharacteristic
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5C22⋊Q812yes—
309C23×C5C22×D411yescharacteristic
310C5×Q8—84no—
311C5×Q8—84no—
312C5×D4—22no—
313C5×D4—22no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—84no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
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—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—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—84no—
355C2×C4×C5—84no—
356C2×C4×C5#12012yes—
357C2×C4×C5#12012yes—
358C2×C4×C5C22⋊Q812yes—
359C2×C4×C5C22×D411yescharacteristic
360C2×C4×C5C22×D411yescharacteristic
361C2×C4×C5C22×Q811yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C52−1+411yescharacteristic
364C2×C4×C52−1+411yescharacteristic
365C5×C8—41no—
366C5×C8—41no—
367C5×C8—41no—
368C5×C8—41no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×D4—21no—
372C22×D4C23×C511yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4C23×C511yescharacteristic
376C22×C8C23×C511yescharacteristic
377C22×C8C23×C511yescharacteristic
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380C4⋊Q8—28no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8C5×D414yescomplemented
385#125—28no—
386#125—22no—
387#125—22no—
388#125—22no—
389#125C5×D414yescomplemented
390C22⋊Q8—28no—
391C22⋊Q8—28no—
392#121—22no—
393#121C5×Q814yescomplemented
394C4×D4—22no—
395C4×D4—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C5×D411yescharacteristic
411C2×C4⋊C4C5×D411yescharacteristic
412C2×C4⋊C4C23×C511yescharacteristic
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C4⋊C4C23×C511yescharacteristic
417C2×C4⋊C4C23×C511yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4C5×D411yescharacteristic
426C2×C22⋊C4C5×D411yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42C23×C511yescharacteristic
430C2×C42C23×C511yescharacteristic
431#107—22no—
432#106—22no—
433#106—22no—
434#106—22no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437#102—22no—
438#102—22no—
439#102—22no—
440#102—22no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443#95—21no—
444#95—21no—
445#95—21no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5C2×#12011yescharacteristic
461C22×C5C2×C22⋊Q811yescharacteristic
462C22×C5#53611yescharacteristic
463C22×C5#57611yescharacteristic
464C22×C5#57711yescharacteristic
465C22×C5#57711yescharacteristic
466C22×C5#57711yescharacteristic
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—22no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—41no—
474C4×C5—42no—
475C4×C5—42no—
476C4×C5—42no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5#54811yescharacteristic
480C4×C5#54811yescharacteristic
481C4×C5D4×Q811yescharacteristic
482C4×C5D4×Q811yescharacteristic
483C24—21no—
484C24C2×C5×D411yescharacteristic
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—81no—
488C2×Q8—81no—
489C2×Q8—81no—
490C2×Q8—81no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C2×C5×Q812yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C2×C5×D411yescharacteristic
518C22×C4C2×C5×D411yescharacteristic
519C22×C4C2×C5×D411yescharacteristic
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×Q812yes—
523C22×C4C5×#4112yes—
524C22×C4C24×C511yescharacteristic
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—81no—
556C4⋊C4C2×C5×D412yes—
557C4⋊C4C2×C5×D412yes—
558C4⋊C4C2×C5×D412yes—
559C4⋊C4C2×C5×D412yes—
560C4⋊C4C2×C5×Q812yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—24no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C42—24no—
570C42—21no—
571C42—21no—
572C42—81no—
573C42C2×C5×D412yes—
574C42C2×C5×D412yes—
575C2×C5—42no—
576C2×C5—82no—
577C2×C5#240911yescharacteristic
578C2×C5#301011yescharacteristic
579C2×C5#301211yescharacteristic
580C2×C5#308111yescharacteristic
581C2×C5#308411yescharacteristic
582C2×C5#324111yescharacteristic
583C2×C5#324411yescharacteristic
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C5×C22⋊Q812yes—
598C23C22×C5×D411yescharacteristic
599Q8—84no—
600Q8—84no—
601D4—22no—
602D4—22no—
603D4—41no—
604D4—41no—
605D4—84no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
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—84no—
644C2×C4—84no—
645C2×C4C5×#12012yes—
646C2×C4C5×#12012yes—
647C2×C4C5×C22⋊Q812yes—
648C2×C4C22×C5×D411yescharacteristic
649C2×C4C22×C5×D411yescharacteristic
650C2×C4C22×C5×Q811yescharacteristic
651C2×C4C2×C5×#4111yescharacteristic
652C2×C4C5×2−1+411yescharacteristic
653C2×C4C5×2−1+411yescharacteristic
654C8—41no—
655C8—41no—
656C8—41no—
657C8—41no—
658C5#2430911yescharacteristic, direct product factor, Sylow
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×C5×#12011yescharacteristic
674C22C2×C5×C22⋊Q811yescharacteristic
675C22C5×#53611yescharacteristic
676C22C5×#57611yescharacteristic
677C22C5×#57711yescharacteristic
678C22C5×#57711yescharacteristic
679C22C5×#57711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C5×#54811yescharacteristic
693C4C5×#54811yescharacteristic
694C4C5×D4×Q811yescharacteristic
695C4C5×D4×Q811yescharacteristic
696C2—42no—
697C2—82no—
698C2C5×#240911yescharacteristic
699C2C5×#301011yescharacteristic
700C2C5×#301211yescharacteristic
701C2C5×#308111yescharacteristic
702C2C5×#308411yescharacteristic
703C2C5×#324111yescharacteristic
704C2C5×#324411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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
1. C2×C5×#544C2semidirect
2. C2×C5×#478C2semidirect
3. C2×C5×#476C2semidirect
5. C5×#2059C2semidirect
6. C5×#2058C2semidirect
7. C5×#2025C2semidirect
8. C5×#2023C2semidirect
9. C5×#1989C2semidirect
10. C5×#1988C2semidirect
13. C5×#1854C2semidirect
14. C5×#1853C2semidirect
15. C5×#1798C2semidirect
63. #24309C5direct (N × H)
79. C5×C4⋊Q8D4semidirect
84. C5×#125D4semidirect
88. C5×#121Q8semidirect
141. C2×#544C2×C5semidirect
142. C2×#478C2×C5semidirect
143. C2×#476C2×C5semidirect
145. #2059C2×C5semidirect
146. #2058C2×C5semidirect
147. #2025C2×C5semidirect
148. #2023C2×C5semidirect
149. #1989C2×C5semidirect
150. #1988C2×C5semidirect
153. #1854C2×C5semidirect
154. #1853C2×C5semidirect
155. #1798C2×C5semidirect
384. C4⋊Q8C5×D4semidirect
389. #125C5×D4semidirect
393. #121C5×Q8semidirect
658. C5#24309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
C2×C5×#4782
C2×C5×#4762
C5×#23242
C5×#20592
C5×#20582
C5×#20252
C5×#20232
C5×#19892
C5×#19882
C5×#18752
C5×#18742
C5×#18542
C5×#18532
C5×#17982
#243095