Finite Group Databasebeta

← C5×#24335 #11947055

Subgroups — C5×#24335 #11947055

Order 1280.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2C2×C5×#478C211yesmaximal, characteristic, complemented
3C2×C4×C5×D8C211yesmaximal, characteristic
4C5×#2580C211yesmaximal, characteristic, complemented
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2057C211yesmaximal, characteristic, complemented
7C5×#2025C211yesmaximal, characteristic, complemented
8C5×#2023C211yesmaximal, characteristic, complemented
9C5×#1991C211yesmaximal, characteristic, complemented
10C5×#1984C211yesmaximal, characteristic, complemented
11C5×#1879C211yesmaximal, characteristic
12C5×#1879C211yesmaximal, characteristic
13C5×#1864C211yesmaximal, characteristic, complemented
14C5×#1862C211yesmaximal, characteristic, complemented
15C5×#1804C211yesmaximal, characteristic, complemented
16C22×C5×D8C2211yescharacteristic
17C5×#554—24no—
18C5×#554—24no—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C22×C5×C4⋊C4—21no—
31C5×#478—24no—
32C4×C5×D8—24no—
33C2×C5×#107C2211yescharacteristic
34C2×C5×#107C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×C4⋊C8C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×#102C2211yescharacteristic
40C2×C5×#102C2211yescharacteristic
41C2×C5×#102C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C4×C5×C8C2211yescharacteristic
44C5×#399—21no—
45C5×#393—21no—
46C5×#390C2211yescharacteristic
47C5×#390C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#385—21no—
51C5×#385—21no—
52C5×#382C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#24335C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8D411yescharacteristic
66C22×C5×D4C2311yescharacteristic
67C22×C5×D4C2311yescharacteristic
68C23×C4×C5—21no—
69C23×C4×C5—21no—
70C23×C4×C5—21no—
71C23×C4×C5—21no—
72C2×C5×D8—22no—
73C2×C5×D8—22no—
74C2×C5×D8Q814yescomplemented
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×C4⋊Q8—22no—
80C5×C4⋊Q8—22no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#125—22no—
84C5×#125D414yes—
85C5×C22⋊Q8—28no—
86C5×C22⋊Q8—28no—
87C5×C22⋊Q8—28no—
88C4×C5×Q8—22no—
89C4×C5×Q8—22no—
90C4×C5×D4—22no—
91C4×C5×D4—22no—
92C4×C5×D4—22no—
93C4×C5×D4—22no—
94C4×C5×D4—22no—
95C4×C5×D4—22no—
96C4×C5×D4—22no—
97C4×C5×D4D414yes—
98C2×C5×C4⋊C4—28no—
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—21no—
106C2×C5×C4⋊C4D411yescharacteristic
107C2×C5×C4⋊C4D411yescharacteristic
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C2×C42×C5C2311yescharacteristic
126C5×#107—22no—
127C5×#107—22no—
128C5×#106—22no—
129C5×C4⋊C8—22no—
130C5×#102—22no—
131C5×#102—22no—
132C5×#102—22no—
133C5×#102—22no—
134C5×#102—22no—
135C5×#102—22no—
136C4×C5×C8—22no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C2×#554C2×C511yescharacteristic, complemented
142C2×#478C2×C511yescharacteristic, complemented
143C2×C4×D8C2×C511yescharacteristic
144#2580C2×C511yescharacteristic, complemented
145#2059C2×C511yescharacteristic, complemented
146#2057C2×C511yescharacteristic, complemented
147#2025C2×C511yescharacteristic, complemented
148#2023C2×C511yescharacteristic, complemented
149#1991C2×C511yescharacteristic, complemented
150#1984C2×C511yescharacteristic, complemented
151#1879C2×C511yescharacteristic
152#1879C2×C511yescharacteristic
153#1864C2×C511yescharacteristic, complemented
154#1862C2×C511yescharacteristic, complemented
155#1804C2×C511yescharacteristic, complemented
156C24×C5—21no—
157C24×C5—21no—
158C2×C5×Q8—24no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—41no—
162C2×C5×Q8—81no—
163C2×C5×Q8—81no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4C2×D412yes—
173C2×C5×D4C2×Q812yes—
174C2×C5×D4C2×Q812yes—
175C2×C5×D4#4112yes—
176C22×C4×C5—24no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—24no—
181C22×C4×C5—24no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5—81no—
191C22×C4×C5—81no—
192C22×C4×C5—81no—
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×D411yescharacteristic
200C22×C4×C5C2411yescharacteristic
201C5×D8—28no—
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×C8C2×Q812yes—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
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—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—81no—
232C5×C4⋊C4—81no—
233C5×C4⋊C4C2×D412yes—
234C5×C4⋊C4C2×D412yes—
235C5×C4⋊C4C2×D412yes—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—42no—
242C5×C22⋊C4—81no—
243C5×C22⋊C4—81no—
244C42×C5—21no—
245C42×C5—21no—
246C42×C5—21no—
247C42×C5—21no—
248C42×C5C2×D412yes—
249C42×C5C2×D412yes—
250C22×D8C22×C511yescharacteristic
251#554—24no—
252#554—24no—
253C2×C4⋊Q8C22×C511yescharacteristic
254C2×#125C22×C511yescharacteristic
255C2×#125C22×C511yescharacteristic
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C4×Q8C22×C511yescharacteristic
260C2×C4×D4C22×C511yescharacteristic
261C2×C4×D4C22×C511yescharacteristic
262C2×C4×D4C22×C511yescharacteristic
263C2×C4×D4C22×C511yescharacteristic
264C22×C4⋊C4—21no—
265#478—24no—
266C4×D8—24no—
267C2×#107C22×C511yescharacteristic
268C2×#107C22×C511yescharacteristic
269C2×#106C22×C511yescharacteristic
270C2×C4⋊C8C22×C511yescharacteristic
271C2×#102C22×C511yescharacteristic
272C2×#102C22×C511yescharacteristic
273C2×#102C22×C511yescharacteristic
274C2×#102C22×C511yescharacteristic
275C2×#102C22×C511yescharacteristic
276C2×#102C22×C511yescharacteristic
277C2×C4×C8C22×C511yescharacteristic
278#399—21no—
279#393—21no—
280#390C22×C511yescharacteristic
281#390C22×C511yescharacteristic
282#389C22×C511yescharacteristic
283#389C22×C511yescharacteristic
284#385—21no—
285#385—21no—
286#382C22×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
295#336C22×C511yescharacteristic
296#336C22×C511yescharacteristic
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5C22×D411yescharacteristic
312C5×Q8—44no—
313C5×Q8—84no—
314C5×D4—22no—
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—22no—
318C5×D4—22no—
319C5×D4—41no—
320C5×D4—41no—
321C5×D4C22⋊Q814yes—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
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—21no—
339C2×C4×C5—21no—
340C2×C4×C5—48no—
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—41no—
355C2×C4×C5—41no—
356C2×C4×C5—84no—
357C2×C4×C5—84no—
358C2×C4×C5—84no—
359C2×C4×C5#12012yes—
360C2×C4×C5#12012yes—
361C2×C4×C5#13512yes—
362C2×C4×C5C22×D411yescharacteristic
363C2×C4×C5C22×D411yescharacteristic
364C2×C4×C5C22×Q811yescharacteristic
365C2×C4×C5C2×#4111yescharacteristic
366C2×C4×C52−1+411yescharacteristic
367C2×C4×C52−1+411yescharacteristic
368C5×C8—22no—
369C5×C8—41no—
370C5×C8—41no—
371C5×C8—41no—
372C22×Q8—21no—
373C22×Q8C5×D411yescharacteristic
374C22×D4C23×C511yescharacteristic
375C22×D4C23×C511yescharacteristic
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—21no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8C5×Q814yescomplemented
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386C22×C8C23×C511yescharacteristic
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389#125—22no—
390#125—22no—
391#125—22no—
392#125C5×D414yes—
393C22⋊Q8—28no—
394C22⋊Q8—28no—
395C22⋊Q8—28no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4C5×D414yes—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4C5×D411yescharacteristic
415C2×C4⋊C4C5×D411yescharacteristic
416C2×C4⋊C4C5×D411yescharacteristic
417C2×C4⋊C4C23×C511yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C4⋊C4C23×C511yescharacteristic
420C2×C4⋊C4C23×C511yescharacteristic
421C2×C4⋊C4C23×C511yescharacteristic
422C2×C4⋊C4C23×C511yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C42C23×C511yescharacteristic
432C2×C42C23×C511yescharacteristic
433C2×C42C23×C511yescharacteristic
434#107—22no—
435#107—22no—
436#106—22no—
437C4⋊C8—22no—
438#102—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444C4×C8—22no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449C22×C5—24no—
450C22×C5—42no—
451C22×C5—42no—
452C22×C5—42no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5—81no—
463C22×C5C2×#12011yescharacteristic
464C22×C5#54811yescharacteristic
465C22×C5D4×Q811yescharacteristic
466C22×C5C2×#13511yescharacteristic
467C22×C5#57511yescharacteristic
468C22×C5#57611yescharacteristic
469C22×C5#57611yescharacteristic
470C4×C5—22no—
471C4×C5—22no—
472C4×C5—22no—
473C4×C5—41no—
474C4×C5—42no—
475C4×C5—41no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—42no—
479C4×C5—81no—
480C4×C5—81no—
481C4×C5—81no—
482C4×C5C2×C22⋊Q811yescharacteristic
483C4×C5#53611yescharacteristic
484C4×C5#54811yescharacteristic
485C4×C5D4×Q811yescharacteristic
486C24—21no—
487C24—21no—
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—41no—
492C2×Q8—81no—
493C2×Q8—81no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4C2×C5×D412yes—
503C2×D4C2×C5×Q812yes—
504C2×D4C2×C5×Q812yes—
505C2×D4C5×#4112yes—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C24×C511yescharacteristic
531D8—28no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8C2×C5×Q812yes—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4C2×C5×D412yes—
564C4⋊C4C2×C5×D412yes—
565C4⋊C4C2×C5×D412yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42C2×C5×D412yes—
579C42C2×C5×D412yes—
580C2×C5—44no—
581C2×C5—82no—
582C2×C5#240911yescharacteristic
583C2×C5#300211yescharacteristic
584C2×C5#300811yescharacteristic
585C2×C5#336111yescharacteristic
586C2×C5#337011yescharacteristic
587C2×C5#338011yescharacteristic
588C2×C5#338911yescharacteristic
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×C5×D411yescharacteristic
604Q8—44no—
605Q8—84no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—41no—
612D4—41no—
613D4C5×C22⋊Q814yes—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—48no—
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—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4C5×#12012yes—
652C2×C4C5×#12012yes—
653C2×C4C5×#13512yes—
654C2×C4C22×C5×D411yescharacteristic
655C2×C4C22×C5×D411yescharacteristic
656C2×C4C22×C5×Q811yescharacteristic
657C2×C4C2×C5×#4111yescharacteristic
658C2×C4C5×2−1+411yescharacteristic
659C2×C4C5×2−1+411yescharacteristic
660C8—22no—
661C8—41no—
662C8—41no—
663C8—41no—
664C5#2433511yescharacteristic, direct product factor, Sylow
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C5×#12011yescharacteristic
680C22C5×#54811yescharacteristic
681C22C5×D4×Q811yescharacteristic
682C22C2×C5×#13511yescharacteristic
683C22C5×#57511yescharacteristic
684C22C5×#57611yescharacteristic
685C22C5×#57611yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C2×C5×C22⋊Q811yescharacteristic
699C4C5×#53611yescharacteristic
700C4C5×#54811yescharacteristic
701C4C5×D4×Q811yescharacteristic
702C2—44no—
703C2—82no—
704C2C5×#240911yescharacteristic
705C2C5×#300211yescharacteristic
706C2C5×#300811yescharacteristic
707C2C5×#336111yescharacteristic
708C2C5×#337011yescharacteristic
709C2C5×#338011yescharacteristic
710C2C5×#338911yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. C2×C5×#478C2semidirect
4. C5×#2580C2semidirect
5. C5×#2059C2semidirect
6. C5×#2057C2semidirect
7. C5×#2025C2semidirect
8. C5×#2023C2semidirect
9. C5×#1991C2semidirect
10. C5×#1984C2semidirect
13. C5×#1864C2semidirect
14. C5×#1862C2semidirect
15. C5×#1804C2semidirect
63. #24335C5direct (N × H)
74. C2×C5×D8Q8semidirect
141. C2×#554C2×C5semidirect
142. C2×#478C2×C5semidirect
144. #2580C2×C5semidirect
145. #2059C2×C5semidirect
146. #2057C2×C5semidirect
147. #2025C2×C5semidirect
148. #2023C2×C5semidirect
149. #1991C2×C5semidirect
150. #1984C2×C5semidirect
153. #1864C2×C5semidirect
154. #1862C2×C5semidirect
155. #1804C2×C5semidirect
382. C2×D8C5×Q8semidirect
664. C5#24335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×C5×#4782
C2×C4×C5×D82
C5×#25802
C5×#20592
C5×#20572
C5×#20252
C5×#20232
C5×#19912
C5×#19842
C5×#18792
C5×#18642
C5×#18622
C5×#18042
#243355