Finite Group Databasebeta

← C5×#29677 #11952397

Subgroups — C5×#29677 #11952397

Order 1280.

1138 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic, complemented
2C2×C5×#464C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic, complemented
4C5×#2620C211yesmaximal, characteristic, complemented
5C5×#2024C211yesmaximal, characteristic, complemented
6C5×#2023C211yesmaximal, characteristic, complemented
7C5×#2015C211yesmaximal, characteristic, complemented
8C5×#2012C211yesmaximal, characteristic, complemented
9C5×#2001C211yesmaximal, characteristic, complemented
10C5×#2000C211yesmaximal, characteristic, complemented
11C5×#2000C211yesmaximal, characteristic, complemented
12C5×#1999C211yesmaximal, characteristic
13C5×#1803C211yesmaximal, characteristic, complemented
14C5×#1802C211yesmaximal, characteristic, complemented
15C5×#1798C211yesmaximal, characteristic, complemented
16C22×C5×Q16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C22×C5×D8C2211yescharacteristic
20C5×#542—24no—
21C5×#542—24no—
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×#126—21no—
24C2×C5×#124—21no—
25C2×C5×#124C2211yescharacteristic
26C2×C5×#124C2211yescharacteristic
27C2×C5×#123—21no—
28C2×C5×C22⋊Q8—21no—
29C2×C5×C22⋊Q8C2211yescharacteristic
30C2×C5×C22⋊Q8C2211yescharacteristic
31C2×C5×#121C2211yescharacteristic
32C2×C5×#121C2211yescharacteristic
33C2×C4×C5×Q8C2211yescharacteristic
34C2×C4×C5×D4C2211yescharacteristic
35C2×C5×#117C2211yescharacteristic
36C5×#464—24no—
37C5×#463—24no—
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2211yescharacteristic
41C2×C5×#103C2211yescharacteristic
42C2×C5×#103C2211yescharacteristic
43C2×C5×#103C2211yescharacteristic
44C2×C5×#102C2211yescharacteristic
45C2×C5×#102C2211yescharacteristic
46C2×C5×#102C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C5×#396—21no—
51C5×#396—21no—
52C5×#394—21no—
53C5×#394—21no—
54C5×#391C2211yescharacteristic
55C5×#390C2211yescharacteristic
56C5×#384C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61C5×#336C2211yescharacteristic
62C5×#336C2211yescharacteristic
63#29677C511yesmaximal, characteristic, direct product factor, Sylow
64C22×C5×Q8—21no—
65C22×C5×Q8C2311yescharacteristic
66C22×C5×Q8C2311yescharacteristic
67C22×C5×D4—21no—
68C22×C5×D4—21no—
69C22×C5×D4C2311yescharacteristic
70C22×C5×D4C2311yescharacteristic
71C23×C4×C5—21no—
72C23×C4×C5C2311yescharacteristic
73C2×C5×Q16—22no—
74C2×C5×Q16—41no—
75C2×C5×Q16—41no—
76C2×C5×SD16—22no—
77C2×C5×SD16—22no—
78C2×C5×SD16—41no—
79C2×C5×SD16—41no—
80C2×C5×SD16—41no—
81C2×C5×SD16—41no—
82C2×C5×D8—22no—
83C2×C5×D8—41no—
84C2×C5×D8—41no—
85C22×C5×C8C2311yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C22×C5×C8C2311yescharacteristic
89C5×C4⋊Q8—22no—
90C5×C4⋊Q8—22no—
91C5×#126—28no—
92C5×#124—28no—
93C5×#124—22no—
94C5×#124—22no—
95C5×#124—22no—
96C5×#124—22no—
97C5×#123—28no—
98C5×C22⋊Q8—28no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8—41no—
102C5×C22⋊Q8—41no—
103C5×#121—22no—
104C5×#121—22no—
105C5×#121—41no—
106C5×#121—41no—
107C4×C5×Q8—22no—
108C4×C5×Q8D414yescomplemented
109C4×C5×D4—22no—
110C4×C5×D4D414yescomplemented
111C5×#117—22no—
112C5×#117—22no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4D411yescharacteristic
120C2×C5×C4⋊C4D411yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C4⋊C4C2311yescharacteristic
123C2×C5×C4⋊C4C2311yescharacteristic
124C2×C5×C4⋊C4C2311yescharacteristic
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4—21no—
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—21no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C5×C22⋊C4—21no—
135C2×C5×C22⋊C4—21no—
136C2×C5×C22⋊C4D411yescharacteristic
137C2×C5×C22⋊C4D411yescharacteristic
138C2×C42×C5—21no—
139C2×C42×C5C2311yescharacteristic
140C2×C42×C5C2311yescharacteristic
141C5×C4⋊C8—22no—
142C5×C4⋊C8—22no—
143C5×#103—22no—
144C5×#103—22no—
145C5×#103—41no—
146C5×#103—41no—
147C5×#102—22no—
148C5×#102—22no—
149C5×#102—41no—
150C5×#102—41no—
151C5×C22⋊C8—41no—
152C5×C22⋊C8—41no—
153C5×#95—21no—
154C5×#95—21no—
155C2×#542C2×C511yescharacteristic, complemented
156C2×#464C2×C511yescharacteristic, complemented
157C2×#463C2×C511yescharacteristic, complemented
158#2620C2×C511yescharacteristic, complemented
159#2024C2×C511yescharacteristic, complemented
160#2023C2×C511yescharacteristic, complemented
161#2015C2×C511yescharacteristic, complemented
162#2012C2×C511yescharacteristic, complemented
163#2001C2×C511yescharacteristic, complemented
164#2000C2×C511yescharacteristic, complemented
165#2000C2×C511yescharacteristic, complemented
166#1999C2×C511yescharacteristic
167#1803C2×C511yescharacteristic, complemented
168#1802C2×C511yescharacteristic, complemented
169#1798C2×C511yescharacteristic, complemented
170C24×C5—21no—
171C24×C5—21no—
172C24×C5C2×D411yescharacteristic
173C2×C5×Q8—24no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—21no—
180C2×C5×Q8—21no—
181C2×C5×Q8—21no—
182C2×C5×Q8—21no—
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8—81no—
186C2×C5×Q8—81no—
187C2×C5×Q8C2×D412yes—
188C2×C5×D4—24no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4—21no—
200C2×C5×D4—42no—
201C2×C5×D4—81no—
202C2×C5×D4—81no—
203C2×C5×D4—81no—
204C2×C5×D4—81no—
205C2×C5×D4C2×D412yes—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—24no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—81no—
220C22×C4×C5—81no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2411yescharacteristic
227C5×Q16—44no—
228C5×SD16—44no—
229C5×SD16—44no—
230C5×D8—44no—
231C2×C5×C8—21no—
232C2×C5×C8—21no—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—21no—
243C5×C4⋊C4—24no—
244C5×C4⋊C4—24no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—22no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—42no—
255C5×C4⋊C4—81no—
256C5×C4⋊C4—81no—
257C5×C4⋊C4C2×D412yes—
258C5×C4⋊C4C2×D412yes—
259C5×C22⋊C4—24no—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—22no—
265C5×C22⋊C4—22no—
266C5×C22⋊C4—42no—
267C5×C22⋊C4—42no—
268C5×C22⋊C4—42no—
269C5×C22⋊C4—42no—
270C5×C22⋊C4—81no—
271C5×C22⋊C4—81no—
272C42×C5—24no—
273C42×C5—21no—
274C42×C5—21no—
275C42×C5C2×D412yes—
276C42×C5C2×D412yes—
277C22×Q16C22×C511yescharacteristic
278C22×SD16C22×C511yescharacteristic
279C22×SD16C22×C511yescharacteristic
280C22×D8C22×C511yescharacteristic
281#542—24no—
282#542—24no—
283C2×C4⋊Q8C22×C511yescharacteristic
284C2×#126—21no—
285C2×#124—21no—
286C2×#124C22×C511yescharacteristic
287C2×#124C22×C511yescharacteristic
288C2×#123—21no—
289C2×C22⋊Q8—21no—
290C2×C22⋊Q8C22×C511yescharacteristic
291C2×C22⋊Q8C22×C511yescharacteristic
292C2×#121C22×C511yescharacteristic
293C2×#121C22×C511yescharacteristic
294C2×C4×Q8C22×C511yescharacteristic
295C2×C4×D4C22×C511yescharacteristic
296C2×#117C22×C511yescharacteristic
297#464—24no—
298#463—24no—
299C2×C4⋊C8C22×C511yescharacteristic
300C2×C4⋊C8C22×C511yescharacteristic
301C2×#103C22×C511yescharacteristic
302C2×#103C22×C511yescharacteristic
303C2×#103C22×C511yescharacteristic
304C2×#103C22×C511yescharacteristic
305C2×#102C22×C511yescharacteristic
306C2×#102C22×C511yescharacteristic
307C2×#102C22×C511yescharacteristic
308C2×#102C22×C511yescharacteristic
309C2×C22⋊C8C22×C511yescharacteristic
310C2×C22⋊C8C22×C511yescharacteristic
311#396—21no—
312#396—21no—
313#394—21no—
314#394—21no—
315#391C22×C511yescharacteristic
316#390C22×C511yescharacteristic
317#384C22×C511yescharacteristic
318#340C22×C511yescharacteristic
319#340C22×C511yescharacteristic
320#340C22×C511yescharacteristic
321#340C22×C511yescharacteristic
322#336C22×C511yescharacteristic
323#336C22×C511yescharacteristic
324C23×C5—21no—
325C23×C5—22no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5C22×D411yescharacteristic
346C5×Q8—22no—
347C5×Q8—22no—
348C5×Q8—41no—
349C5×Q8—41no—
350C5×Q8—41no—
351C5×Q8—41no—
352C5×Q8—41no—
353C5×Q8—41no—
354C5×Q8—84no—
355C5×D4—22no—
356C5×D4—22no—
357C5×D4—41no—
358C5×D4—41no—
359C5×D4—41no—
360C5×D4—41no—
361C5×D4—41no—
362C5×D4—41no—
363C5×D4—84no—
364C5×D4—84no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—22no—
371C2×C4×C5—21no—
372C2×C4×C5—22no—
373C2×C4×C5—21no—
374C2×C4×C5—22no—
375C2×C4×C5—21no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—84no—
401C2×C4×C5#12012yes—
402C2×C4×C5#12012yes—
403C2×C4×C5C22×D411yescharacteristic
404C2×C4×C5C22×D411yescharacteristic
405C2×C4×C5H(5,𝔽2)11yescharacteristic
406C2×C4×C5H(5,𝔽2)11yescharacteristic
407C2×C4×C5H(5,𝔽2)11yescharacteristic
408C2×C4×C52−1+411yescharacteristic
409C5×C8—41no—
410C5×C8—41no—
411C5×C8—41no—
412C5×C8—41no—
413C22×Q8—21no—
414C22×Q8C23×C511yescharacteristic
415C22×Q8C23×C511yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C511yescharacteristic
419C22×D4C23×C511yescharacteristic
420C23×C4—21no—
421C23×C4C23×C511yescharacteristic
422C2×Q16—22no—
423C2×Q16—41no—
424C2×Q16—41no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—41no—
428C2×SD16—41no—
429C2×SD16—41no—
430C2×SD16—41no—
431C2×D8—22no—
432C2×D8—41no—
433C2×D8—41no—
434C22×C8C23×C511yescharacteristic
435C22×C8C23×C511yescharacteristic
436C22×C8C23×C511yescharacteristic
437C22×C8C23×C511yescharacteristic
438C4⋊Q8—22no—
439C4⋊Q8—22no—
440#126—28no—
441#124—28no—
442#124—22no—
443#124—22no—
444#124—22no—
445#124—22no—
446#123—28no—
447C22⋊Q8—28no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—41no—
451C22⋊Q8—41no—
452#121—22no—
453#121—22no—
454#121—41no—
455#121—41no—
456C4×Q8—22no—
457C4×Q8C5×D414yescomplemented
458C4×D4—22no—
459C4×D4C5×D414yescomplemented
460#117—22no—
461#117—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4C5×D411yescharacteristic
469C2×C4⋊C4C5×D411yescharacteristic
470C2×C4⋊C4C23×C511yescharacteristic
471C2×C4⋊C4C23×C511yescharacteristic
472C2×C4⋊C4C23×C511yescharacteristic
473C2×C4⋊C4C23×C511yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4C5×D411yescharacteristic
486C2×C22⋊C4C5×D411yescharacteristic
487C2×C42—21no—
488C2×C42C23×C511yescharacteristic
489C2×C42C23×C511yescharacteristic
490C4⋊C8—22no—
491C4⋊C8—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#103—41no—
496#102—22no—
497#102—22no—
498#102—41no—
499#102—41no—
500C22⋊C8—41no—
501C22⋊C8—41no—
502#95—21no—
503#95—21no—
504C22×C5—41no—
505C22×C5—42no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—42no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—42no—
514C22×C5—81no—
515C22×C5—81no—
516C22×C5—81no—
517C22×C5—81no—
518C22×C5—81no—
519C22×C5—81no—
520C22×C5—81no—
521C22×C5—81no—
522C22×C5—81no—
523C22×C5—81no—
524C22×C5—81no—
525C22×C5C2×#12011yescharacteristic
526C22×C5#53511yescharacteristic
527C22×C5#53711yescharacteristic
528C22×C5#57611yescharacteristic
529C22×C5#57711yescharacteristic
530C22×C5#57711yescharacteristic
531C22×C5#57811yescharacteristic
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—41no—
535C4×C5—42no—
536C4×C5—41no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—41no—
540C4×C5—81no—
541C4×C5—81no—
542C4×C5—81no—
543C4×C5#53511yescharacteristic
544C4×C5#53511yescharacteristic
545C4×C5#53711yescharacteristic
546C4×C5#53711yescharacteristic
547C24—21no—
548C24—21no—
549C24C2×C5×D411yescharacteristic
550C2×Q8—24no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—81no—
563C2×Q8—81no—
564C2×Q8C2×C5×D412yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×C5×D412yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C2×C5×D411yescharacteristic
601C22×C4C2×C5×D411yescharacteristic
602C22×C4C2×C5×D411yescharacteristic
603C22×C4C24×C511yescharacteristic
604Q16—44no—
605SD16—44no—
606SD16—44no—
607D8—44no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4—81no—
634C4⋊C4C2×C5×D412yes—
635C4⋊C4C2×C5×D412yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—24no—
650C42—21no—
651C42—21no—
652C42C2×C5×D412yes—
653C42C2×C5×D412yes—
654C2×C5—81no—
655C2×C5—82no—
656C2×C5—161no—
657C2×C5#261511yescharacteristic
658C2×C5#301211yescharacteristic
659C2×C5#301311yescharacteristic
660C2×C5#322411yescharacteristic
661C2×C5#322511yescharacteristic
662C2×C5#326211yescharacteristic
663C2×C5#326311yescharacteristic
664C23—21no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23C22×C5×D411yescharacteristic
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—84no—
695D4—22no—
696D4—22no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4C5×#12012yes—
742C2×C4C5×#12012yes—
743C2×C4C22×C5×D411yescharacteristic
744C2×C4C22×C5×D411yescharacteristic
745C2×C4C5×H(5,𝔽2)11yescharacteristic
746C2×C4C5×H(5,𝔽2)11yescharacteristic
747C2×C4C5×H(5,𝔽2)11yescharacteristic
748C2×C4C5×2−1+411yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C5#2967711yescharacteristic, direct product factor, Sylow
754C22—41no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22C2×C5×#12011yescharacteristic
776C22C5×#53511yescharacteristic
777C22C5×#53711yescharacteristic
778C22C5×#57611yescharacteristic
779C22C5×#57711yescharacteristic
780C22C5×#57711yescharacteristic
781C22C5×#57811yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4C5×#53511yescharacteristic
794C4C5×#53511yescharacteristic
795C4C5×#53711yescharacteristic
796C4C5×#53711yescharacteristic
797C2—81no—
798C2—82no—
799C2—161no—
800C2C5×#261511yescharacteristic
801C2C5×#301211yescharacteristic
802C2C5×#301311yescharacteristic
803C2C5×#322411yescharacteristic
804C2C5×#322511yescharacteristic
805C2C5×#326211yescharacteristic
806C2C5×#326311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1999C2
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×#542C2semidirect
2. C2×C5×#464C2semidirect
3. C2×C5×#463C2semidirect
4. C5×#2620C2semidirect
5. C5×#2024C2semidirect
6. C5×#2023C2semidirect
7. C5×#2015C2semidirect
8. C5×#2012C2semidirect
9. C5×#2001C2semidirect
10. C5×#2000C2semidirect
11. C5×#2000C2semidirect
13. C5×#1803C2semidirect
14. C5×#1802C2semidirect
15. C5×#1798C2semidirect
63. #29677C5direct (N × H)
108. C4×C5×Q8D4semidirect
110. C4×C5×D4D4semidirect
155. C2×#542C2×C5semidirect
156. C2×#464C2×C5semidirect
157. C2×#463C2×C5semidirect
158. #2620C2×C5semidirect
159. #2024C2×C5semidirect
160. #2023C2×C5semidirect
161. #2015C2×C5semidirect
162. #2012C2×C5semidirect
163. #2001C2×C5semidirect
164. #2000C2×C5semidirect
165. #2000C2×C5semidirect
167. #1803C2×C5semidirect
168. #1802C2×C5semidirect
169. #1798C2×C5semidirect
457. C4×Q8C5×D4semidirect
459. C4×D4C5×D4semidirect
753. C5#29677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×C5×#4642
C2×C5×#4632
C5×#26202
C5×#20242
C5×#20232
C5×#20152
C5×#20122
C5×#20012
C5×#20002
C5×#19992
C5×#18032
C5×#18022
C5×#17982
#296775