Finite Group Databasebeta

← C5×#29693 #11952413

Subgroups — C5×#29693 #11952413

Order 1280.

1056 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#529C211yesmaximal, characteristic
2C2×C5×#479C211yesmaximal, characteristic, complemented
3C2×C5×#478C211yesmaximal, characteristic, complemented
4C5×#2851C211yesmaximal, characteristic, complemented
5C5×#2059C211yesmaximal, characteristic, complemented
6C5×#2059C211yesmaximal, characteristic, complemented
7C5×#2042C211yesmaximal, characteristic, complemented
8C5×#2042C211yesmaximal, characteristic, complemented
9C5×#2036C211yesmaximal, characteristic, complemented
10C5×#2035C211yesmaximal, characteristic, complemented
11C5×#2034C211yesmaximal, characteristic
12C5×#2033C211yesmaximal, characteristic
13C5×#1805C211yesmaximal, characteristic, complemented
14C5×#1804C211yesmaximal, characteristic, complemented
15C5×#1797C211yesmaximal, characteristic, complemented
16C5×#529—24no—
17C5×#529—24no—
18C2×C5×#126—21no—
19C2×C5×#125C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic
21C2×C5×#124C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4—21no—
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117—21no—
29C22×C42×C5C2211yescharacteristic
30C5×#479—24no—
31C5×#478—24no—
32C2×C5×#107C2211yescharacteristic
33C2×C5×#107C2211yescharacteristic
34C2×C5×#106C2211yescharacteristic
35C2×C5×#106C2211yescharacteristic
36C2×C5×C4⋊C8C2211yescharacteristic
37C2×C5×C4⋊C8C2211yescharacteristic
38C2×C5×#103C2211yescharacteristic
39C2×C5×#103C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#102C2211yescharacteristic
43C2×C5×#102C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×#102C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#387—21no—
51C5×#387—21no—
52C5×#385—21no—
53C5×#385—21no—
54C5×#382C2211yescharacteristic
55C5×#380C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#29693C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8C2311yescharacteristic
65C22×C5×D4—21no—
66C22×C5×D4C2311yescharacteristic
67C23×C4×C5—21no—
68C23×C4×C5D411yescharacteristic
69C23×C4×C5D411yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C5×#126—28no—
76C5×#125—22no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#124—22no—
81C5×#124—22no—
82C5×#123—28no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×#121—22no—
86C5×#121—22no—
87C4×C5×Q8—22no—
88C4×C5×Q8D414yes—
89C4×C5×D4—28no—
90C4×C5×D4—22no—
91C4×C5×D4D414yes—
92C5×#117—28no—
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—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C22⋊C4—21no—
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×C42×C5—21no—
115C2×C42×C5—22no—
116C2×C42×C5—22no—
117C2×C42×C5D411yescharacteristic
118C2×C42×C5D411yescharacteristic
119C2×C42×C5C2311yescharacteristic
120C2×C42×C5C2311yescharacteristic
121C5×#107—22no—
122C5×#107—22no—
123C5×#106—22no—
124C5×#106—22no—
125C5×C4⋊C8—22no—
126C5×C4⋊C8—22no—
127C5×#103—22no—
128C5×#103—22no—
129C5×#103—41no—
130C5×#103—41no—
131C5×#102—22no—
132C5×#102—22no—
133C5×#102—41no—
134C5×#102—41no—
135C5×C22⋊C8—41no—
136C5×C22⋊C8—41no—
137C5×#95—21no—
138C5×#95—21no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C2×#529C2×C511yescharacteristic
144C2×#479C2×C511yescharacteristic, complemented
145C2×#478C2×C511yescharacteristic, complemented
146#2851C2×C511yescharacteristic, complemented
147#2059C2×C511yescharacteristic, complemented
148#2059C2×C511yescharacteristic, complemented
149#2042C2×C511yescharacteristic, complemented
150#2042C2×C511yescharacteristic, complemented
151#2036C2×C511yescharacteristic, complemented
152#2035C2×C511yescharacteristic, complemented
153#2034C2×C511yescharacteristic
154#2033C2×C511yescharacteristic
155#1805C2×C511yescharacteristic, complemented
156#1804C2×C511yescharacteristic, complemented
157#1797C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C24×C5C2×D411yescharacteristic
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8C2×D412yes—
166C2×C5×D4—24no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—42no—
173C2×C5×D4—42no—
174C2×C5×D4C2×D412yes—
175C22×C4×C5—22no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
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—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—41no—
193C22×C4×C5—41no—
194C22×C4×C5—41no—
195C22×C4×C5—42no—
196C22×C4×C5—42no—
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2411yescharacteristic
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—21no—
214C2×C5×C8—21no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
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—21no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4—42no—
231C5×C4⋊C4—42no—
232C5×C4⋊C4—42no—
233C5×C4⋊C4C2×D412yes—
234C5×C4⋊C4C2×D412yes—
235C5×C22⋊C4—24no—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—42no—
242C42×C5—22no—
243C42×C5—22no—
244C42×C5—24no—
245C42×C5—21no—
246C42×C5—21no—
247C42×C5C2×D412yes—
248C42×C5C2×D412yes—
249#529—24no—
250#529—24no—
251C2×#126—21no—
252C2×#125C22×C511yescharacteristic
253C2×#125C22×C511yescharacteristic
254C2×#124C22×C511yescharacteristic
255C2×#123—21no—
256C2×C22⋊Q8C22×C511yescharacteristic
257C2×#121C22×C511yescharacteristic
258C2×C4×Q8C22×C511yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4C22×C511yescharacteristic
261C2×#117—21no—
262C22×C42C22×C511yescharacteristic
263#479—24no—
264#478—24no—
265C2×#107C22×C511yescharacteristic
266C2×#107C22×C511yescharacteristic
267C2×#106C22×C511yescharacteristic
268C2×#106C22×C511yescharacteristic
269C2×C4⋊C8C22×C511yescharacteristic
270C2×C4⋊C8C22×C511yescharacteristic
271C2×#103C22×C511yescharacteristic
272C2×#103C22×C511yescharacteristic
273C2×#103C22×C511yescharacteristic
274C2×#103C22×C511yescharacteristic
275C2×#102C22×C511yescharacteristic
276C2×#102C22×C511yescharacteristic
277C2×#102C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×C22⋊C8C22×C511yescharacteristic
280C2×C22⋊C8C22×C511yescharacteristic
281#389C22×C511yescharacteristic
282#389C22×C511yescharacteristic
283#387—21no—
284#387—21no—
285#385—21no—
286#385—21no—
287#382C22×C511yescharacteristic
288#380C22×C511yescharacteristic
289#380C22×C511yescharacteristic
290#340C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#340C22×C511yescharacteristic
293#340C22×C511yescharacteristic
294#336C22×C511yescharacteristic
295#336C22×C511yescharacteristic
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—22no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5#13512yes—
310C23×C5C22×D411yescharacteristic
311C5×Q8—22no—
312C5×Q8—22no—
313C5×Q8—41no—
314C5×Q8—41no—
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—48no—
318C5×D4—41no—
319C5×D4—41no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—44no—
337C2×C4×C5—44no—
338C2×C4×C5—48no—
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—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#12012yes—
362C2×C4×C5#12012yes—
363C2×C4×C5C22×D411yescharacteristic
364C2×C4×C5C22×D411yescharacteristic
365C2×C4×C5H(5,𝔽2)11yescharacteristic
366C2×C4×C52−1+411yescharacteristic
367C2×C4×C52−1+411yescharacteristic
368C2×C4×C52−1+411yescharacteristic
369C5×C8—41no—
370C5×C8—41no—
371C5×C8—41no—
372C5×C8—41no—
373C22×Q8C23×C511yescharacteristic
374C22×D4—21no—
375C22×D4C23×C511yescharacteristic
376C23×C4—21no—
377C23×C4C5×D411yescharacteristic
378C23×C4C5×D411yescharacteristic
379C23×C4C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384#126—28no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—22no—
389#124—22no—
390#124—22no—
391#123—28no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394#121—22no—
395#121—22no—
396C4×Q8—22no—
397C4×Q8C5×D414yes—
398C4×D4—28no—
399C4×D4—22no—
400C4×D4C5×D414yes—
401#117—28no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C4⋊C4C23×C511yescharacteristic
412C2×C4⋊C4C23×C511yescharacteristic
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42C5×D411yescharacteristic
427C2×C42C5×D411yescharacteristic
428C2×C42C23×C511yescharacteristic
429C2×C42C23×C511yescharacteristic
430#107—22no—
431#107—22no—
432#106—22no—
433#106—22no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436#103—22no—
437#103—22no—
438#103—41no—
439#103—41no—
440#102—22no—
441#102—22no—
442#102—41no—
443#102—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5—42no—
461C22×C5—42no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5C2×#12011yescharacteristic
467C22×C5#53611yescharacteristic
468C22×C5#53711yescharacteristic
469C22×C5C2×#13511yescharacteristic
470C22×C5#57511yescharacteristic
471C22×C5#57511yescharacteristic
472C22×C5#57511yescharacteristic
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—41no—
476C4×C5—42no—
477C4×C5—41no—
478C4×C5—42no—
479C4×C5—41no—
480C4×C5—42no—
481C4×C5—81no—
482C4×C5—81no—
483C4×C5—81no—
484C4×C5—81no—
485C4×C5#53611yescharacteristic
486C4×C5#53611yescharacteristic
487C4×C5#53711yescharacteristic
488C4×C5#53711yescharacteristic
489C24—21no—
490C24C2×C5×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8C2×C5×D412yes—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×C5×D412yes—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C24×C511yescharacteristic
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×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—21no—
551C4⋊C4—21no—
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—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4C2×C5×D412yes—
565C4⋊C4C2×C5×D412yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C42—22no—
574C42—22no—
575C42—24no—
576C42—21no—
577C42—21no—
578C42C2×C5×D412yes—
579C42C2×C5×D412yes—
580C2×C5—42no—
581C2×C5—82no—
582C2×C5#261611yescharacteristic
583C2×C5#300211yescharacteristic
584C2×C5#300511yescharacteristic
585C2×C5#323211yescharacteristic
586C2×C5#324011yescharacteristic
587C2×C5#325011yescharacteristic
588C2×C5#325611yescharacteristic
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23C5×#13512yes—
603C23C22×C5×D411yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—22no—
609D4—22no—
610D4—48no—
611D4—41no—
612D4—41no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—44no—
630C2×C4—44no—
631C2×C4—48no—
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—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4C5×#12012yes—
655C2×C4C5×#12012yes—
656C2×C4C22×C5×D411yescharacteristic
657C2×C4C22×C5×D411yescharacteristic
658C2×C4C5×H(5,𝔽2)11yescharacteristic
659C2×C4C5×2−1+411yescharacteristic
660C2×C4C5×2−1+411yescharacteristic
661C2×C4C5×2−1+411yescharacteristic
662C8—41no—
663C8—41no—
664C8—41no—
665C8—41no—
666C5#2969311yescharacteristic, direct product factor, Sylow
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C5×#12011yescharacteristic
682C22C5×#53611yescharacteristic
683C22C5×#53711yescharacteristic
684C22C2×C5×#13511yescharacteristic
685C22C5×#57511yescharacteristic
686C22C5×#57511yescharacteristic
687C22C5×#57511yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—42no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C5×#53611yescharacteristic
701C4C5×#53611yescharacteristic
702C4C5×#53711yescharacteristic
703C4C5×#53711yescharacteristic
704C2—42no—
705C2—82no—
706C2C5×#261611yescharacteristic
707C2C5×#300211yescharacteristic
708C2C5×#300511yescharacteristic
709C2C5×#323211yescharacteristic
710C2C5×#324011yescharacteristic
711C2C5×#325011yescharacteristic
712C2C5×#325611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#479C2semidirect
3. C2×C5×#478C2semidirect
4. C5×#2851C2semidirect
5. C5×#2059C2semidirect
6. C5×#2059C2semidirect
7. C5×#2042C2semidirect
8. C5×#2042C2semidirect
9. C5×#2036C2semidirect
10. C5×#2035C2semidirect
13. C5×#1805C2semidirect
14. C5×#1804C2semidirect
15. C5×#1797C2semidirect
63. #29693C5direct (N × H)
144. C2×#479C2×C5semidirect
145. C2×#478C2×C5semidirect
146. #2851C2×C5semidirect
147. #2059C2×C5semidirect
148. #2059C2×C5semidirect
149. #2042C2×C5semidirect
150. #2042C2×C5semidirect
151. #2036C2×C5semidirect
152. #2035C2×C5semidirect
155. #1805C2×C5semidirect
156. #1804C2×C5semidirect
157. #1797C2×C5semidirect
666. C5#29693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5292
C2×C5×#4792
C2×C5×#4782
C5×#28512
C5×#20592
C5×#20422
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#18052
C5×#18042
C5×#17972
#296935