Finite Group Databasebeta

← C5×#14015 #11936735

Subgroups — C5×#14015 #11936735

Order 1280.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic
2C23×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#386C211yesmaximal, characteristic
5C2×C5×#385C212yesmaximal, complemented
6C2×C5×#385C211yesmaximal, characteristic, complemented
7C5×#1444C212yesmaximal, complemented
8C5×#1439C212yesmaximal, complemented
9C5×#1436C212yesmaximal, complemented
10C5×C22⋊#95C211yesmaximal, characteristic, complemented
11C5×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C24×C4×C5C2211yescharacteristic
16C24×C4×C5C2211yescharacteristic
17C2×C4×C5×D4—24no—
18C2×C4×C5×D4—24no—
19C2×C4×C5×D4—24no—
20C22×C5×C4⋊C4—24no—
21C22×C5×C4⋊C4—28no—
22C22×C5×C4⋊C4C2212yes—
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2212yes—
25C22×C5×C4⋊C4C2212yes—
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2212yes—
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2212yes—
31C22×C5×C22⋊C4C2211yescharacteristic
32C22×C42×C5C2211yescharacteristic
33C5×#386—24no—
34C5×#386C418yescomplemented
35C5×#385—28no—
36C5×#385—24no—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40C2×C5×#95C2212yes—
41C2×C5×#95C2212yes—
42C2×C5×#95C2212yes—
43C2×C5×#95C2212yes—
44#14015C511yesmaximal, characteristic, direct product factor, Sylow
45C25×C5C2311yescharacteristic
46C25×C5C2311yescharacteristic
47C22×C5×D4—22no—
48C22×C5×D4—22no—
49C22×C5×D4—22no—
50C22×C5×D4—22no—
51C22×C5×D4C2×C414yes—
52C22×C5×D4D414yes—
53C22×C5×D4Q814yes—
54C23×C4×C5—22no—
55C23×C4×C5—22no—
56C23×C4×C5—24no—
57C23×C4×C5—24no—
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—24no—
63C23×C4×C5—24no—
64C23×C4×C5—22no—
65C23×C4×C5—22no—
66C23×C4×C5—22no—
67C23×C4×C5—22no—
68C23×C4×C5—24no—
69C23×C4×C5—42no—
70C23×C4×C5—42no—
71C23×C4×C5—42no—
72C23×C4×C5C2×C414yescomplemented
73C23×C4×C5D414yes—
74C23×C4×C5C2312yes—
75C23×C4×C5C2312yes—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2312yes—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2312yes—
82C23×C4×C5C2311yescharacteristic
83C4×C5×D4—232no—
84C2×C5×C4⋊C4—232no—
85C2×C5×C4⋊C4—24no—
86C2×C5×C4⋊C4—24no—
87C2×C5×C4⋊C4—24no—
88C2×C5×C4⋊C4—24no—
89C2×C5×C4⋊C4—24no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—42no—
96C2×C5×C4⋊C4D418yescomplemented
97C2×C5×C22⋊C4—22no—
98C2×C5×C22⋊C4—22no—
99C2×C5×C22⋊C4—22no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—22no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4—22no—
104C2×C5×C22⋊C4—22no—
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—22no—
108C2×C5×C22⋊C4—22no—
109C2×C5×C22⋊C4—22no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—42no—
112C2×C5×C22⋊C4C2×C414yescomplemented
113C2×C5×C22⋊C4C2×C418yescomplemented
114C2×C5×C22⋊C4D414yes—
115C2×C42×C5—22no—
116C2×C42×C5—22no—
117C2×C42×C5—22no—
118C5×#95—24no—
119C5×#95—24no—
120C5×#95—24no—
121C5×#95—24no—
122C5×#95—24no—
123C5×#95—42no—
124C5×#95C2×C418yescomplemented
125C22×C4×D4C2×C511yescharacteristic
126C23×C4⋊C4C2×C511yescharacteristic, complemented
127C2×#386C2×C511yescharacteristic
128C2×#386C2×C511yescharacteristic
129C2×#385C2×C512yescomplemented
130C2×#385C2×C511yescharacteristic, complemented
131#1444C2×C512yescomplemented
132#1439C2×C512yescomplemented
133#1436C2×C512yescomplemented
134C22⋊#95C2×C511yescharacteristic, complemented
135C22⋊#95C2×C511yescharacteristic, complemented
136C24×C5—22no—
137C24×C5—22no—
138C24×C5—22no—
139C24×C5—22no—
140C24×C5—22no—
141C24×C5—21no—
142C24×C5—21no—
143C24×C5—22no—
144C24×C5—21no—
145C24×C5—21no—
146C24×C5—22no—
147C24×C5—22no—
148C24×C5C22×C412yes—
149C24×C5C22×C412yes—
150C24×C5C2×D412yes—
151C24×C5C2×D412yes—
152C24×C5C2×D412yes—
153C24×C5C2×D412yes—
154C24×C5C2×Q812yes—
155C24×C5C2×Q812yes—
156C24×C5#4112yes—
157C24×C5#4112yes—
158C24×C5C2411yescharacteristic
159C2×C5×D4—28no—
160C2×C5×D4—28no—
161C2×C5×D4—28no—
162C2×C5×D4—28no—
163C2×C5×D4—28no—
164C2×C5×D4—28no—
165C2×C5×D4C4⋊C4116yescomplemented
166C22×C4×C5—28no—
167C22×C4×C5—216no—
168C22×C4×C5—28no—
169C22×C4×C5—28no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—22no—
181C22×C4×C5—216no—
182C22×C4×C5—28no—
183C22×C4×C5—28no—
184C22×C4×C5—28no—
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—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—28no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—44no—
218C22×C4×C5—48no—
219C22×C4×C5—48no—
220C22×C4×C5—48no—
221C22×C4×C5—48no—
222C22×C4×C5—48no—
223C22×C4×C5—48no—
224C22×C4×C5—44no—
225C22×C4×C5—44no—
226C22×C4×C5—44no—
227C22×C4×C5—44no—
228C22×C4×C5C22×C414yes—
229C22×C4×C5C22×C412yes—
230C22×C4×C5C22×C414yes—
231C22×C4×C5C2×D412yes—
232C22×C4×C5C2×D412yes—
233C22×C4×C5C2×D414yes—
234C22×C4×C5C2×D412yes—
235C22×C4×C5C2×D412yes—
236C22×C4×C5C2×D414yes—
237C22×C4×C5C2×D412yes—
238C22×C4×C5C2×D414yes—
239C22×C4×C5C2×Q812yes—
240C22×C4×C5#4114yes—
241C5×C4⋊C4—216no—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—216no—
244C5×C4⋊C4—48no—
245C5×C22⋊C4—28no—
246C5×C22⋊C4—28no—
247C5×C22⋊C4—28no—
248C5×C22⋊C4—216no—
249C5×C22⋊C4—48no—
250C5×C22⋊C4—44no—
251C42×C5—28no—
252C23×D4C22×C511yescharacteristic
253C24×C4C22×C511yescharacteristic
254C24×C4C22×C511yescharacteristic
255C24×C4C22×C511yescharacteristic
256C24×C4C22×C511yescharacteristic
257C2×C4×D4—24no—
258C2×C4×D4—24no—
259C2×C4×D4—24no—
260C22×C4⋊C4—24no—
261C22×C4⋊C4—28no—
262C22×C4⋊C4C22×C512yes—
263C22×C4⋊C4C22×C511yescharacteristic
264C22×C4⋊C4C22×C512yes—
265C22×C4⋊C4C22×C512yes—
266C22×C22⋊C4C22×C511yescharacteristic
267C22×C22⋊C4C22×C511yescharacteristic
268C22×C22⋊C4C22×C512yes—
269C22×C22⋊C4C22×C511yescharacteristic
270C22×C22⋊C4C22×C512yes—
271C22×C22⋊C4C22×C511yescharacteristic
272C22×C42C22×C511yescharacteristic
273#386—24no—
274#386C4×C518yescomplemented
275#385—28no—
276#385—24no—
277C2×#95C22×C512yes—
278C2×#95C22×C512yes—
279C2×#95C22×C512yes—
280C2×#95C22×C512yes—
281C2×#95C22×C512yes—
282C2×#95C22×C512yes—
283C2×#95C22×C512yes—
284C23×C5—24no—
285C23×C5—24no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—24no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—24no—
294C23×C5—24no—
295C23×C5—24no—
296C23×C5—24no—
297C23×C5—24no—
298C23×C5—24no—
299C23×C5—24no—
300C23×C5—24no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5—24no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—24no—
309C23×C5—24no—
310C23×C5—24no—
311C23×C5—24no—
312C23×C5—41no—
313C23×C5—41no—
314C23×C5—42no—
315C23×C5—41no—
316C23×C5—41no—
317C23×C5—42no—
318C23×C5—42no—
319C23×C5—42no—
320C23×C5—42no—
321C23×C5—42no—
322C23×C5C2×C4⋊C414yes—
323C23×C5C2×C4⋊C414yescomplemented
324C23×C5C4×D414yes—
325C23×C5C4×D414yes—
326C23×C5#12014yes—
327C23×C5C22⋊Q814yes—
328C23×C5C22⋊Q814yes—
329C23×C5#12314yes—
330C23×C5C23×C411yescharacteristic
331C23×C5C22×D411yescharacteristic
332C23×C5C22×D411yescharacteristic
333C23×C5C22×D411yescharacteristic
334C23×C5C22×D412yes—
335C23×C5C22×Q811yescharacteristic
336C23×C5C2×#4111yescharacteristic
337C23×C5C2×#4111yescharacteristic
338C23×C5C2×#4112yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C52−1+412yes—
341C5×D4—232no—
342C2×C4×C5—232no—
343C2×C4×C5—24no—
344C2×C4×C5—24no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—24no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—24no—
354C2×C4×C5—24no—
355C2×C4×C5—24no—
356C2×C4×C5—22no—
357C2×C4×C5—24no—
358C2×C4×C5—24no—
359C2×C4×C5—24no—
360C2×C4×C5—24no—
361C2×C4×C5—24no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—24no—
367C2×C4×C5—22no—
368C2×C4×C5—24no—
369C2×C4×C5—24no—
370C2×C4×C5—24no—
371C2×C4×C5—24no—
372C2×C4×C5—416no—
373C2×C4×C5—416no—
374C2×C4×C5—416no—
375C2×C4×C5—42no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—42no—
380C2×C4×C5—41no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5—42no—
397C2×C4×C5—42no—
398C2×C4×C5C2×C4⋊C414yescomplemented
399C2×C4×C5C4×D418yescomplemented
400C2×C4×C5#12014yes—
401C25C23×C511yescharacteristic
402C25C23×C511yescharacteristic
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4C2×C4×C514yes—
408C22×D4C5×D414yes—
409C22×D4C5×Q814yes—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4C2×C4×C514yescomplemented
429C23×C4C5×D414yes—
430C23×C4C23×C512yes—
431C23×C4C23×C512yes—
432C23×C4C23×C511yescharacteristic
433C23×C4C23×C512yes—
434C23×C4C23×C511yescharacteristic
435C23×C4C23×C511yescharacteristic
436C23×C4C23×C511yescharacteristic
437C23×C4C23×C512yes—
438C23×C4C23×C511yescharacteristic
439C4×D4—232no—
440C2×C4⋊C4—232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4C5×D418yescomplemented
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4C2×C4×C514yescomplemented
469C2×C22⋊C4C2×C4×C518yescomplemented
470C2×C22⋊C4C5×D414yes—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
478#95—24no—
479#95—42no—
480#95C2×C4×C518yescomplemented
481C22×C5—24no—
482C22×C5—24no—
483C22×C5—28no—
484C22×C5—28no—
485C22×C5—24no—
486C22×C5—24no—
487C22×C5—24no—
488C22×C5—28no—
489C22×C5—28no—
490C22×C5—24no—
491C22×C5—28no—
492C22×C5—24no—
493C22×C5—42no—
494C22×C5—42no—
495C22×C5—44no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—44no—
500C22×C5—44no—
501C22×C5—42no—
502C22×C5#38518yescomplemented
503C22×C5C22×C4⋊C411yescharacteristic
504C22×C5C2×C4×D411yescharacteristic
505C22×C5C2×C4×D412yes—
506C22×C5C2×C4×D411yescharacteristic
507C22×C5#52012yes—
508C22×C5C2×#12011yescharacteristic
509C22×C5C2×#12011yescharacteristic
510C22×C5C2×C22⋊Q811yescharacteristic
511C22×C5C2×C22⋊Q811yescharacteristic
512C22×C5C2×#12311yescharacteristic
513C22×C5#52511yescharacteristic
514C22×C5#52512yes—
515C22×C5#53411yescharacteristic
516C22×C5#53611yescharacteristic
517C22×C5#53912yes—
518C22×C5D4212yes—
519C22×C5D4212yes—
520C22×C5#54712yes—
521C22×C5#54712yes—
522C22×C5#54812yes—
523C22×C5D4×Q812yes—
524C22×C5#55312yes—
525C22×C5#55412yes—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—28no—
529C4×C5—44no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—44no—
533C4×C5—42no—
534C4×C5—82no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—21no—
544C24—21no—
545C24—22no—
546C24—22no—
547C24C22×C4×C512yes—
548C24C22×C4×C512yes—
549C24C2×C5×D412yes—
550C24C2×C5×D412yes—
551C24C2×C5×D412yes—
552C24C2×C5×D412yes—
553C24C2×C5×Q812yes—
554C24C2×C5×Q812yes—
555C24C5×#4112yes—
556C24C5×#4112yes—
557C24C24×C511yescharacteristic
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4C5×C4⋊C4116yescomplemented
565C22×C4—28no—
566C22×C4—216no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22×C4×C514yes—
628C22×C4C22×C4×C512yes—
629C22×C4C22×C4×C514yes—
630C22×C4C2×C5×D412yes—
631C22×C4C2×C5×D412yes—
632C22×C4C2×C5×D414yes—
633C22×C4C2×C5×D412yes—
634C22×C4C2×C5×D412yes—
635C22×C4C2×C5×D414yes—
636C22×C4C2×C5×D414yes—
637C22×C4C2×C5×D412yes—
638C22×C4C2×C5×Q812yes—
639C22×C4C5×#4114yes—
640C4⋊C4—216no—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—48no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C42—28no—
651C2×C5—28no—
652C2×C5—44no—
653C2×C5C2×#38511yescharacteristic
654C2×C5C4×#12011yescharacteristic
655C2×C5#232211yescharacteristic
656C2×C5D4×C4⋊C412yes—
657C2×C5#236112yes—
658C2×C5#240311yescharacteristic
659C2×C5#240611yescharacteristic
660C2×C5#240911yescharacteristic
661C2×C5#244312yes—
662C2×C5#244912yes—
663C2×C5#257911yescharacteristic
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23C2×C5×C4⋊C414yes—
703C23C2×C5×C4⋊C414yescomplemented
704C23C4×C5×D414yes—
705C23C4×C5×D414yes—
706C23C5×#12014yes—
707C23C5×C22⋊Q814yes—
708C23C5×C22⋊Q814yes—
709C23C5×#12314yes—
710C23C23×C4×C511yescharacteristic
711C23C22×C5×D411yescharacteristic
712C23C22×C5×D411yescharacteristic
713C23C22×C5×D411yescharacteristic
714C23C22×C5×D412yes—
715C23C22×C5×Q811yescharacteristic
716C23C2×C5×#4111yescharacteristic
717C23C2×C5×#4111yescharacteristic
718C23C2×C5×#4112yes—
719C23C5×H(5,𝔽2)12yes—
720C23C5×2−1+412yes—
721D4—232no—
722C2×C4—232no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4C2×C5×C4⋊C414yescomplemented
779C2×C4C4×C5×D418yescomplemented
780C2×C4C5×#12014yes—
781C5#1401511yescharacteristic, direct product factor, Sylow
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—24no—
793C22—28no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—44no—
803C22C5×#38518yescomplemented
804C22C22×C5×C4⋊C411yescharacteristic
805C22C2×C4×C5×D411yescharacteristic
806C22C2×C4×C5×D411yescharacteristic
807C22C2×C4×C5×D412yes—
808C22C5×#52012yes—
809C22C2×C5×#12011yescharacteristic
810C22C2×C5×#12011yescharacteristic
811C22C2×C5×C22⋊Q811yescharacteristic
812C22C2×C5×C22⋊Q811yescharacteristic
813C22C2×C5×#12311yescharacteristic
814C22C5×#52511yescharacteristic
815C22C5×#52512yes—
816C22C5×#53411yescharacteristic
817C22C5×#53611yescharacteristic
818C22C5×#53912yes—
819C22C5×D4212yes—
820C22C5×D4212yes—
821C22C5×#54712yes—
822C22C5×#54712yes—
823C22C5×#54812yes—
824C22C5×D4×Q812yes—
825C22C5×#55312yes—
826C22C5×#55412yes—
827C4—24no—
828C4—28no—
829C4—24no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—42no—
835C4—82no—
836C2—28no—
837C2—44no—
838C2C2×C5×#38511yescharacteristic
839C2C4×C5×#12011yescharacteristic
840C2C5×#232211yescharacteristic
841C2C5×D4×C4⋊C412yes—
842C2C5×#236112yes—
843C2C5×#240311yescharacteristic
844C2C5×#240611yescharacteristic
845C2C5×#240911yescharacteristic
846C2C5×#244312yes—
847C2C5×#244912yes—
848C2C5×#257911yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C5×C4⋊C4C2semidirect
5. C2×C5×#385C2semidirect
6. C2×C5×#385C2semidirect
7. C5×#1444C2semidirect
8. C5×#1439C2semidirect
9. C5×#1436C2semidirect
10. C5×C22⋊#95C2semidirect
11. C5×C22⋊#95C2semidirect
34. C5×#386C4semidirect
44. #14015C5direct (N × H)
72. C23×C4×C5C2×C4semidirect
96. C2×C5×C4⋊C4D4semidirect
112. C2×C5×C22⋊C4C2×C4semidirect
113. C2×C5×C22⋊C4C2×C4semidirect
124. C5×#95C2×C4semidirect
126. C23×C4⋊C4C2×C5semidirect
129. C2×#385C2×C5semidirect
130. C2×#385C2×C5semidirect
131. #1444C2×C5semidirect
132. #1439C2×C5semidirect
133. #1436C2×C5semidirect
134. C22⋊#95C2×C5semidirect
135. C22⋊#95C2×C5semidirect
165. C2×C5×D4C4⋊C4semidirect
274. #386C4×C5semidirect
323. C23×C5C2×C4⋊C4semidirect
398. C2×C4×C5C2×C4⋊C4semidirect
399. C2×C4×C5C4×D4semidirect
428. C23×C4C2×C4×C5semidirect
452. C2×C4⋊C4C5×D4semidirect
468. C2×C22⋊C4C2×C4×C5semidirect
469. C2×C22⋊C4C2×C4×C5semidirect
480. #95C2×C4×C5semidirect
502. C22×C5#385semidirect
564. C2×D4C5×C4⋊C4semidirect
703. C23C2×C5×C4⋊C4semidirect
778. C2×C4C2×C5×C4⋊C4semidirect
779. C2×C4C4×C5×D4semidirect
781. C5#14015direct (N × H)
803. C22C5×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C23×C5×C4⋊C42
C2×C5×#3862
C2×C5×#3852
C5×#14442
C5×#14392
C5×#14362
C5×C22⋊#952
#140155