Finite Group Databasebeta

← C5×#26933 #11949653

Subgroups — C5×#26933 #11949653

Order 1280.

898 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×#483C211yesmaximal, characteristic, complemented
2C2×C5×#464C211yesmaximal, characteristic, complemented
3C5×#2426C211yesmaximal, characteristic
4C5×#2360C211yesmaximal, characteristic, complemented
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2042C211yesmaximal, characteristic, complemented
7C5×#2001C211yesmaximal, characteristic, complemented
8C5×#2000C211yesmaximal, characteristic
9C5×#1968C211yesmaximal, characteristic, complemented
10C5×#1926C211yesmaximal, characteristic, complemented
11C5×#1923C211yesmaximal, characteristic, complemented
12C5×#1878C211yesmaximal, characteristic, complemented
13C5×#1874C211yesmaximal, characteristic
14C5×#1865C211yesmaximal, characteristic, complemented
15C4×C5×#103C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C2×C5×#124C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C5×#483—24no—
26C5×#464—24no—
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C4×C5×C8C2211yescharacteristic
41C5×#396—21no—
42C5×#394—21no—
43C5×#391C2211yescharacteristic
44C5×#390—21no—
45C5×#390C2211yescharacteristic
46C5×#389—21no—
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#388—21no—
50C5×#387—21no—
51C5×#385—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C22⋊C4—21no—
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26933C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5C2311yescharacteristic
68C2×C5×Q16—22no—
69C2×C5×Q16—22no—
70C2×C5×Q16—41no—
71C2×C5×SD16—22no—
72C2×C5×SD16—22no—
73C2×C5×SD16—41no—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×#124—22no—
79C5×#124—41no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—41no—
84C5×#121—22no—
85C5×#121—41no—
86C4×C5×Q8—22no—
87C4×C5×Q8—22no—
88C4×C5×Q8—41no—
89C4×C5×Q8—41no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—22no—
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×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⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5—21no—
116C2×C42×C5C2311yescharacteristic
117C2×C42×C5C2311yescharacteristic
118C5×#106—22no—
119C5×#106—22no—
120C5×C4⋊C8—22no—
121C5×#103—22no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#103—41no—
125C5×#103D414yescomplemented
126C5×#102—22no—
127C5×#102—22no—
128C5×#102—41no—
129C5×C22⋊C8—22no—
130C5×C22⋊C8—41no—
131C4×C5×C8—41no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95D411yescharacteristic
138C5×#95D411yescharacteristic
139C2×#483C2×C511yescharacteristic, complemented
140C2×#464C2×C511yescharacteristic, complemented
141#2426C2×C511yescharacteristic
142#2360C2×C511yescharacteristic, complemented
143#2088C2×C511yescharacteristic, complemented
144#2042C2×C511yescharacteristic, complemented
145#2001C2×C511yescharacteristic, complemented
146#2000C2×C511yescharacteristic
147#1968C2×C511yescharacteristic, complemented
148#1926C2×C511yescharacteristic, complemented
149#1923C2×C511yescharacteristic, complemented
150#1878C2×C511yescharacteristic, complemented
151#1874C2×C511yescharacteristic
152#1865C2×C511yescharacteristic, complemented
153C4×#103C2×C511yescharacteristic, complemented
154C24×C5—21no—
155C24×C5C2×D411yescharacteristic
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8C2×D412yes—
167C2×C5×Q8#4112yes—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—42no—
175C2×C5×D4—42no—
176C2×C5×D4—81no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
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—42no—
191C22×C4×C5—42no—
192C22×C4×C5—81no—
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2411yescharacteristic
199C5×Q16—44no—
200C5×SD16—44no—
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—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8C2×D412yes—
213C5×C4⋊C4—24no—
214C5×C4⋊C4—21no—
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—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—81no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4C2×D412yes—
228C5×C4⋊C4#4112yes—
229C5×C4⋊C4#4112yes—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4—81no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—42no—
244C42×C5—42no—
245C42×C5—81no—
246C22×Q16C22×C511yescharacteristic
247C22×SD16C22×C511yescharacteristic
248C2×#124C22×C511yescharacteristic
249C2×C22⋊Q8C22×C511yescharacteristic
250C2×C22⋊Q8C22×C511yescharacteristic
251C2×#121C22×C511yescharacteristic
252C2×C4×Q8C22×C511yescharacteristic
253C2×C4×Q8C22×C511yescharacteristic
254C22×C4⋊C4C22×C511yescharacteristic
255#483—24no—
256#464—24no—
257C2×#106C22×C511yescharacteristic
258C2×#106C22×C511yescharacteristic
259C2×C4⋊C8C22×C511yescharacteristic
260C2×#103C22×C511yescharacteristic
261C2×#103C22×C511yescharacteristic
262C2×#103C22×C511yescharacteristic
263C2×#103C22×C511yescharacteristic
264C2×#103C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×#102C22×C511yescharacteristic
267C2×#102C22×C511yescharacteristic
268C2×C22⋊C8C22×C511yescharacteristic
269C2×C22⋊C8C22×C511yescharacteristic
270C2×C4×C8C22×C511yescharacteristic
271#396—21no—
272#394—21no—
273#391C22×C511yescharacteristic
274#390—21no—
275#390C22×C511yescharacteristic
276#389—21no—
277#389C22×C511yescharacteristic
278#389C22×C511yescharacteristic
279#388—21no—
280#387—21no—
281#385—21no—
282C4×C4⋊C4C22×C511yescharacteristic
283C4×C22⋊C4—21no—
284C4×C22⋊C4C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#336C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5#13512yes—
305C23×C5C22×D411yescharacteristic
306C5×Q8—22no—
307C5×Q8—22no—
308C5×Q8—22no—
309C5×Q8—22no—
310C5×Q8—41no—
311C5×Q8—41no—
312C5×Q8—41no—
313C5×Q8—41no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4—84no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
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—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—84no—
359C2×C4×C5#13712yes—
360C2×C4×C5C22×D411yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C5C2×#4111yescharacteristic
364C2×C4×C5H(5,𝔽2)11yescharacteristic
365C2×C4×C5H(5,𝔽2)11yescharacteristic
366C5×C8—22no—
367C5×C8—41no—
368C5×C8—41no—
369C5×C8—41no—
370C22×Q8C23×C511yescharacteristic
371C22×Q8C23×C511yescharacteristic
372C22×D4—21no—
373C22×D4C23×C511yescharacteristic
374C23×C4—21no—
375C23×C4C23×C511yescharacteristic
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16—41no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—41no—
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386#124—22no—
387#124—41no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—41no—
392#121—22no—
393#121—41no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—41no—
397C4×Q8—41no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—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—41no—
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
411C2×C4⋊C4C23×C511yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4C5×D411yescharacteristic
420C2×C22⋊C4C5×D411yescharacteristic
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42C23×C511yescharacteristic
425C2×C42C23×C511yescharacteristic
426#106—22no—
427#106—22no—
428C4⋊C8—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—41no—
433#103C5×D414yescomplemented
434#102—22no—
435#102—22no—
436#102—41no—
437C22⋊C8—22no—
438C22⋊C8—41no—
439C4×C8—41no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C5×D411yescharacteristic
446#95C5×D411yescharacteristic
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5#52511yescharacteristic
462C22×C5D4211yescharacteristic
463C22×C5#54611yescharacteristic
464C22×C5C2×#13511yescharacteristic
465C22×C5C2×#13711yescharacteristic
466C22×C5#57711yescharacteristic
467C22×C5#57711yescharacteristic
468C4×C5—22no—
469C4×C5—42no—
470C4×C5—41no—
471C4×C5—42no—
472C4×C5—42no—
473C4×C5—41no—
474C4×C5—41no—
475C4×C5—42no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—81no—
479C4×C5—81no—
480C4×C5#53211yescharacteristic
481C4×C5#54011yescharacteristic
482C4×C5#54611yescharacteristic
483C4×C5#55311yescharacteristic
484C24—21no—
485C24C2×C5×D411yescharacteristic
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8C2×C5×D412yes—
497C2×Q8C5×#4112yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C24×C511yescharacteristic
529Q16—44no—
530SD16—44no—
531C2×C8—21no—
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×C8C2×C5×D412yes—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4C2×C5×D412yes—
558C4⋊C4C5×#4112yes—
559C4⋊C4C5×#4112yes—
560C22⋊C4—24no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—42no—
575C42—81no—
576C2×C5—42no—
577C2×C5—161no—
578C2×C5#246411yescharacteristic
579C2×C5#310811yescharacteristic
580C2×C5#312511yescharacteristic
581C2×C5#327811yescharacteristic
582C2×C5#328211yescharacteristic
583C2×C5#329611yescharacteristic
584C2×C5#331611yescharacteristic
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C5×#13512yes—
599C23C22×C5×D411yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
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—84no—
653C2×C4C5×#13712yes—
654C2×C4C22×C5×D411yescharacteristic
655C2×C4C2×C5×#4111yescharacteristic
656C2×C4C2×C5×#4111yescharacteristic
657C2×C4C2×C5×#4111yescharacteristic
658C2×C4C5×H(5,𝔽2)11yescharacteristic
659C2×C4C5×H(5,𝔽2)11yescharacteristic
660C8—22no—
661C8—41no—
662C8—41no—
663C8—41no—
664C5#2693311yescharacteristic, direct product factor, Sylow
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C5×#52511yescharacteristic
680C22C5×D4211yescharacteristic
681C22C5×#54611yescharacteristic
682C22C2×C5×#13511yescharacteristic
683C22C2×C5×#13711yescharacteristic
684C22C5×#57711yescharacteristic
685C22C5×#57711yescharacteristic
686C4—22no—
687C4—41no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—42no—
696C4—81no—
697C4—81no—
698C4C5×#53211yescharacteristic
699C4C5×#54011yescharacteristic
700C4C5×#54611yescharacteristic
701C4C5×#55311yescharacteristic
702C2—42no—
703C2—161no—
704C2C5×#246411yescharacteristic
705C2C5×#310811yescharacteristic
706C2C5×#312511yescharacteristic
707C2C5×#327811yescharacteristic
708C2C5×#328211yescharacteristic
709C2C5×#329611yescharacteristic
710C2C5×#331611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
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×#483C2semidirect
2. C2×C5×#464C2semidirect
4. C5×#2360C2semidirect
5. C5×#2088C2semidirect
6. C5×#2042C2semidirect
7. C5×#2001C2semidirect
9. C5×#1968C2semidirect
10. C5×#1926C2semidirect
11. C5×#1923C2semidirect
12. C5×#1878C2semidirect
14. C5×#1865C2semidirect
15. C4×C5×#103C2semidirect
61. #26933C5direct (N × H)
125. C5×#103D4semidirect
139. C2×#483C2×C5semidirect
140. C2×#464C2×C5semidirect
142. #2360C2×C5semidirect
143. #2088C2×C5semidirect
144. #2042C2×C5semidirect
145. #2001C2×C5semidirect
147. #1968C2×C5semidirect
148. #1926C2×C5semidirect
149. #1923C2×C5semidirect
150. #1878C2×C5semidirect
152. #1865C2×C5semidirect
153. C4×#103C2×C5semidirect
433. #103C5×D4semidirect
664. C5#26933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C2×C5×#4642
C5×#24262
C5×#23602
C5×#20882
C5×#20422
C5×#20012
C5×#20002
C5×#19682
C5×#19262
C5×#19232
C5×#18782
C5×#18742
C5×#18652
C4×C5×#1032
#269335