Finite Group Databasebeta

← C5×#71550 #14280026

Subgroups — C5×#71550 #14280026

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×#67C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C5×#217C211yesmaximal, characteristic, complemented
4C22×C5×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×C5×C3⋊#95C212yesmaximal, complemented
6C5×#1438—31nomaximal, Hall
7C25×C3×C5C2211yescharacteristic
8C24×C5×D3C2211yescharacteristic
9C23×C3×C4×C5C2212yes—
10C22×C5×#67—22no—
11C22×C5×#67—22no—
12C22×C5×#67—24no—
13C22×C5×#67—24no—
14C22×C5×#67C414yescomplemented
15C23×C5×Dic3C2212yes—
16C23×C5×Dic3C2211yescharacteristic
17C2×C3×C5×C22⋊C4—22no—
18C2×C3×C5×C22⋊C4—24no—
19C2×C5×#217—22no—
20C2×C5×#217—24no—
21C2×C5×(C2×D3)⋊C4—24no—
22C2×C5×(C2×D3)⋊C4—24no—
23C2×C5×(C2×D3)⋊C4—24no—
24C5×C3⋊#95—24no—
25#71550C511yesmaximal, characteristic, direct product factor, Hall
26C23×C5×D4—31no—
27C22×C5×C22⋊C4—31no—
28C22×C5×C22⋊C4—32no—
29C22×C5×C22⋊C4D311yescharacteristic, complemented
30C2×C5×#95—32no—
31C24×C3×C5—22no—
32C24×C3×C5—22no—
33C24×C3×C5—22no—
34C24×C3×C5—22no—
35C24×C3×C5—22no—
36C24×C3×C5—22no—
37C24×C3×C5C2×C412yes—
38C24×C3×C5D412yes—
39C24×C3×C5D412yes—
40C24×C3×C5C2311yescharacteristic
41C23×C5×D3—22no—
42C23×C5×D3—22no—
43C23×C5×D3—21no—
44C23×C5×D3—22no—
45C23×C5×D3—21no—
46C23×C5×D3—22no—
47C23×C5×D3—22no—
48C23×C5×D3C2×C412yes—
49C23×C5×D3D414yes—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5D414yescomplemented
57C2×C5×#67—216no—
58C2×C5×#67—216no—
59C2×C5×#67—28no—
60C2×C5×#67—28no—
61C2×C5×#67—28no—
62C22×C5×Dic3—21no—
63C22×C5×Dic3—22no—
64C22×C5×Dic3—21no—
65C22×C5×Dic3—22no—
66C22×C5×Dic3—22no—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—22no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3C2×C412yes—
72C22×C5×Dic3D414yes—
73C22×C5×Dic3D414yescomplemented
74C3×C5×C22⋊C4—28no—
75C5×#217—28no—
76C5×(C2×D3)⋊C4—216no—
77C23×#67C2×C511yescharacteristic
78C22×C3×C22⋊C4C2×C511yescharacteristic, complemented
79C22×#217C2×C511yescharacteristic, complemented
80C22×(C2×D3)⋊C4C2×C512yescomplemented
81C2×C3⋊#95C2×C512yescomplemented
82C25×C5—31no—
83C25×C5C2×D311yescharacteristic
84C22×C5×D4—34no—
85C22×C5×D4—64no—
86C22×C5×D4—64no—
87C22×C5×D4—62no—
88C22×C5×D4—62no—
89C23×C4×C5—31no—
90C23×C4×C5—32no—
91C23×C4×C5C2×D312yes—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—64no—
95C2×C5×C22⋊C4—64no—
96C2×C5×C22⋊C4—64no—
97C2×C5×C22⋊C4—62no—
98C2×C5×C22⋊C4—64no—
99C5×#95—64no—
100#1438—31noSylow
101C23×C3×C5—22no—
102C23×C3×C5—22no—
103C23×C3×C5—24no—
104C23×C3×C5—24no—
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5—24no—
108C23×C3×C5—24no—
109C23×C3×C5—24no—
110C23×C3×C5—24no—
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—42no—
114C23×C3×C5—42no—
115C23×C3×C5—42no—
116C23×C3×C5—42no—
117C23×C3×C5—42no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C22⋊C414yescomplemented
122C23×C3×C5C22×C411yescharacteristic
123C23×C3×C5C2×D411yescharacteristic
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D411yescharacteristic
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×D412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5#4112yes—
131C22×C5×D3—22no—
132C22×C5×D3—22no—
133C22×C5×D3—24no—
134C22×C5×D3—24no—
135C22×C5×D3—24no—
136C22×C5×D3—24no—
137C22×C5×D3—24no—
138C22×C5×D3—24no—
139C22×C5×D3—24no—
140C22×C5×D3—24no—
141C22×C5×D3—41no—
142C22×C5×D3—41no—
143C22×C5×D3—42no—
144C22×C5×D3—42no—
145C22×C5×D3—42no—
146C22×C5×D3—42no—
147C22×C5×D3—41no—
148C22×C5×D3—41no—
149C22×C5×D3—42no—
150C22×C5×D3—42no—
151C22×C5×D3C22⋊C414yescomplemented
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5—42no—
159C5×#67—232no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—24no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3—24no—
165C2×C5×Dic3—24no—
166C2×C5×Dic3—24no—
167C2×C5×Dic3—42no—
168C2×C5×Dic3—42no—
169C2×C5×Dic3—42no—
170C2×C5×Dic3—42no—
171C2×C5×Dic3C22⋊C414yescomplemented
172C25×C3C22×C511yescharacteristic
173C24×D3C22×C511yescharacteristic
174C23×C3×C4C22×C512yes—
175C22×#67—22no—
176C22×#67—22no—
177C22×#67—24no—
178C22×#67—24no—
179C22×#67C4×C514yescomplemented
180C23×Dic3C22×C512yes—
181C23×Dic3C22×C511yescharacteristic
182C2×C3×C22⋊C4—22no—
183C2×C3×C22⋊C4—24no—
184C2×#217—22no—
185C2×#217—24no—
186C2×(C2×D3)⋊C4—24no—
187C2×(C2×D3)⋊C4—24no—
188C2×(C2×D3)⋊C4—24no—
189C3⋊#95—24no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5—22no—
196C24×C5—32no—
197C24×C5—34no—
198C24×C5—61no—
199C24×C5—62no—
200C24×C5—62no—
201C24×C5—62no—
202C24×C5—62no—
203C24×C5—62no—
204C24×C5—61no—
205C24×C5C4×D312yes—
206C24×C5D1212yes—
207C24×C5#6712yes—
208C24×C5C22×D311yescharacteristic
209C2×C5×D4—68no—
210C2×C5×D4—68no—
211C2×C5×D4—616no—
212C2×C5×D4—616no—
213C2×C5×D4—68no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—32no—
221C22×C4×C5—34no—
222C22×C4×C5—34no—
223C22×C4×C5—61no—
224C22×C4×C5—62no—
225C22×C4×C5—61no—
226C22×C4×C5—62no—
227C22×C4×C5—62no—
228C22×C4×C5—62no—
229C22×C4×C5—62no—
230C22×C4×C5—62no—
231C22×C4×C5—62no—
232C22×C4×C5#6714yescomplemented
233C5×C22⋊C4—28no—
234C5×C22⋊C4—616no—
235C5×C22⋊C4—68no—
236C23×D4—31no—
237C22×C22⋊C4—31no—
238C22×C22⋊C4—32no—
239C22×C22⋊C4C5×D311yescharacteristic, complemented
240C2×#95—32no—
241C22×C3×C5—24no—
242C22×C3×C5—24no—
243C22×C3×C5—24no—
244C22×C3×C5—44no—
245C22×C3×C5—44no—
246C22×C3×C5—44no—
247C22×C3×C5—44no—
248C22×C3×C5—44no—
249C22×C3×C5—44no—
250C22×C3×C5C2×C22⋊C411yescharacteristic
251C22×C3×C5C2×C22⋊C411yescharacteristic
252C22×C3×C5C2×C22⋊C411yescharacteristic
253C22×C3×C5C4×D412yes—
254C22×C3×C5C4×D412yes—
255C22×C3×C5#12012yes—
256C22×C3×C5#12011yescharacteristic
257C22×C3×C5#12012yes—
258C22×C3×C5#12012yes—
259C22×C3×C5#12011yescharacteristic
260C22×C3×C5#12112yes—
261C22×C3×C5#12112yes—
262C22×C3×C5#12112yes—
263C22×C3×C5#12112yes—
264C22×C3×C5#12112yes—
265C22×C3×C5#12112yes—
266C22×C3×C5#12312yes—
267C22×C3×C5#12311yescharacteristic
268C22×C3×C5#12311yescharacteristic
269C22×C3×C5#12412yes—
270C22×C3×C5#12712yes—
271C2×C5×D3—24no—
272C2×C5×D3—28no—
273C2×C5×D3—42no—
274C2×C5×D3—42no—
275C2×C5×D3—44no—
276C2×C5×D3—44no—
277C2×C5×D3—44no—
278C2×C5×D3—44no—
279C2×C5×D3—44no—
280C3×C4×C5—44no—
281C5×Dic3—24no—
282C5×Dic3—44no—
283C24×C3—22no—
284C24×C3—22no—
285C24×C3—22no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3C2×C4×C512yes—
290C24×C3C5×D412yes—
291C24×C3C5×D412yes—
292C24×C3C23×C511yescharacteristic
293C23×D3—22no—
294C23×D3—22no—
295C23×D3—21no—
296C23×D3—22no—
297C23×D3—21no—
298C23×D3—22no—
299C23×D3—22no—
300C23×D3C2×C4×C512yes—
301C23×D3C5×D414yes—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4C5×D414yescomplemented
309C2×#67—216no—
310C2×#67—216no—
311C2×#67—28no—
312C2×#67—28no—
313C2×#67—28no—
314C22×Dic3—21no—
315C22×Dic3—22no—
316C22×Dic3—21no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3C2×C4×C512yes—
324C22×Dic3C5×D414yes—
325C22×Dic3C5×D414yescomplemented
326C3×C22⋊C4—28no—
327#217—28no—
328(C2×D3)⋊C4—216no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—24no—
332C23×C5—22no—
333C23×C5—24no—
334C23×C5—22no—
335C23×C5—24no—
336C23×C5—22no—
337C23×C5—24no—
338C23×C5—24no—
339C23×C5—24no—
340C23×C5—22no—
341C23×C5—34no—
342C23×C5—42no—
343C23×C5—42no—
344C23×C5—42no—
345C23×C5—42no—
346C23×C5—42no—
347C23×C5—42no—
348C23×C5—42no—
349C23×C5—42no—
350C23×C5—62no—
351C23×C5—64no—
352C23×C5—64no—
353C23×C5—64no—
354C23×C5—64no—
355C23×C5—62no—
356C23×C5—64no—
357C23×C5—64no—
358C23×C5—64no—
359C23×C5—64no—
360C23×C5—121no—
361C23×C5—122no—
362C23×C5—122no—
363C23×C5—121no—
364C23×C5—121no—
365C23×C5—122no—
366C23×C5—122no—
367C23×C5—122no—
368C23×C5—122no—
369C23×C5—121no—
370C23×C5(C2×D3)⋊C414yescomplemented
371C23×C5C2×C4×D311yescharacteristic
372C23×C5C2×D1211yescharacteristic
373C23×C5#23512yes—
374C23×C5D3×D412yes—
375C23×C5D3×D412yes—
376C23×C5D3×D412yes—
377C23×C5#23712yes—
378C23×C5C2×#6711yescharacteristic
379C23×C5C2×#6712yes—
380C5×D4—632no—
381C2×C4×C5—24no—
382C2×C4×C5—24no—
383C2×C4×C5—24no—
384C2×C4×C5—34no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—62no—
390C2×C4×C5—64no—
391C2×C4×C5—62no—
392C2×C4×C5—64no—
393C2×C4×C5—64no—
394C2×C4×C5—64no—
395C2×C4×C5—64no—
396C2×C4×C5—122no—
397C2×C4×C5—122no—
398C2×C4×C5—122no—
399C2×C4×C5—122no—
400C25—31no—
401C25C2×C5×D311yescharacteristic
402C22×D4—34no—
403C22×D4—64no—
404C22×D4—64no—
405C22×D4—62no—
406C22×D4—62no—
407C23×C4—31no—
408C23×C4—32no—
409C23×C4C2×C5×D312yes—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—64no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—64no—
417#95—64no—
418C2×C3×C5—44no—
419C2×C3×C5#37911yescharacteristic
420C2×C3×C5#38612yes—
421C2×C3×C5#38611yescharacteristic
422C2×C3×C5#38611yescharacteristic
423C2×C3×C5#39012yes—
424C2×C3×C5#39212yes—
425C2×C3×C5#39212yes—
426C2×C3×C5#39412yes—
427C2×C3×C5#39412yes—
428C5×D3—44no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3C5×C22⋊C414yescomplemented
450C23×C3C22×C4×C511yescharacteristic
451C23×C3C2×C5×D411yescharacteristic
452C23×C3C2×C5×D412yes—
453C23×C3C2×C5×D412yes—
454C23×C3C2×C5×D412yes—
455C23×C3C2×C5×D411yescharacteristic
456C23×C3C2×C5×D412yes—
457C23×C3C5×#4112yes—
458C23×C3C5×#4112yes—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—24no—
466C22×D3—24no—
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3—42no—
474C22×D3—42no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3C5×C22⋊C414yescomplemented
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487#67—232no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3C5×C22⋊C414yescomplemented
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—44no—
504C22×C5—44no—
505C22×C5—44no—
506C22×C5—44no—
507C22×C5—44no—
508C22×C5—44no—
509C22×C5—64no—
510C22×C5—68no—
511C22×C5—124no—
512C22×C5—122no—
513C22×C5—122no—
514C22×C5—124no—
515C22×C5—124no—
516C22×C5—124no—
517C22×C5—124no—
518C22×C5D3×C22⋊C411yescharacteristic
519C22×C5D3×C22⋊C411yescharacteristic
520C22×C5#67⋊C412yes—
521C22×C5#88212yes—
522C22×C5#88211yescharacteristic
523C22×C5#88312yes—
524C22×C5#88412yes—
525C22×C5#88412yes—
526C22×C5#88512yes—
527C22×C5#88611yescharacteristic
528C22×C5C2×(C2×D3)⋊C411yescharacteristic
529C22×C5C4×#6712yes—
530C22×C5#92911yescharacteristic
531C22×C5#93012yes—
532C22×C5#93712yes—
533C22×C5#93712yes—
534C22×C5#93812yes—
535C22×C5#93912yes—
536C22×C5#93912yes—
537C22×C5#94012yes—
538C22×C5#95311yescharacteristic
539C4×C5—44no—
540C4×C5—64no—
541C4×C5—124no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—32no—
549C24—34no—
550C24—61no—
551C24—62no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—62no—
556C24—61no—
557C24C4×C5×D312yes—
558C24C5×D1212yes—
559C24C5×#6712yes—
560C24C22×C5×D311yescharacteristic
561C2×D4—68no—
562C2×D4—68no—
563C2×D4—616no—
564C2×D4—616no—
565C2×D4—68no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—32no—
573C22×C4—34no—
574C22×C4—34no—
575C22×C4—61no—
576C22×C4—62no—
577C22×C4—61no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4C5×#6714yescomplemented
585C22⋊C4—28no—
586C22⋊C4—616no—
587C22⋊C4—68no—
588C3×C5#143811yescharacteristic, complemented, Hall
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3C2×C5×C22⋊C411yescharacteristic
599C22×C3C2×C5×C22⋊C411yescharacteristic
600C22×C3C2×C5×C22⋊C411yescharacteristic
601C22×C3C4×C5×D412yes—
602C22×C3C4×C5×D412yes—
603C22×C3C5×#12012yes—
604C22×C3C5×#12011yescharacteristic
605C22×C3C5×#12012yes—
606C22×C3C5×#12012yes—
607C22×C3C5×#12011yescharacteristic
608C22×C3C5×#12112yes—
609C22×C3C5×#12112yes—
610C22×C3C5×#12112yes—
611C22×C3C5×#12112yes—
612C22×C3C5×#12112yes—
613C22×C3C5×#12112yes—
614C22×C3C5×#12312yes—
615C22×C3C5×#12311yescharacteristic
616C22×C3C5×#12311yescharacteristic
617C22×C3C5×#12412yes—
618C22×C3C5×#12712yes—
619C2×D3—24no—
620C2×D3—28no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C3×C4—44no—
629Dic3—24no—
630Dic3—44no—
631C2×C5—44no—
632C2×C5—124no—
633C2×C5#495511yescharacteristic
634C2×C5#495612yes—
635C2×C5#495712yes—
636C2×C5#495811yescharacteristic
637C2×C5#495912yes—
638C2×C5#496012yes—
639C2×C5#496112yes—
640C2×C5#521311yescharacteristic
641C2×C5#522312yes—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—34no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—62no—
664C23—64no—
665C23—64no—
666C23—64no—
667C23—64no—
668C23—62no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—64no—
673C23—121no—
674C23—122no—
675C23—122no—
676C23—121no—
677C23—121no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—121no—
683C23C5×(C2×D3)⋊C414yescomplemented
684C23C2×C4×C5×D311yescharacteristic
685C23C2×C5×D1211yescharacteristic
686C23C5×#23512yes—
687C23C5×D3×D412yes—
688C23C5×D3×D412yes—
689C23C5×D3×D412yes—
690C23C5×#23712yes—
691C23C2×C5×#6711yescharacteristic
692C23C2×C5×#6712yes—
693D4—632no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—34no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—62no—
703C2×C4—64no—
704C2×C4—62no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C3—44no—
714C2×C3C5×#37911yescharacteristic
715C2×C3C5×#38612yes—
716C2×C3C5×#38611yescharacteristic
717C2×C3C5×#38611yescharacteristic
718C2×C3C5×#39012yes—
719C2×C3C5×#39212yes—
720C2×C3C5×#39212yes—
721C2×C3C5×#39412yes—
722C2×C3C5×#39412yes—
723D3—44no—
724C5#7155011yescharacteristic, direct product factor, Sylow
725C22—24no—
726C22—24no—
727C22—24no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—64no—
735C22—68no—
736C22—124no—
737C22—122no—
738C22—122no—
739C22—124no—
740C22—124no—
741C22—124no—
742C22—124no—
743C22C5×D3×C22⋊C411yescharacteristic
744C22C5×D3×C22⋊C411yescharacteristic
745C22C5×#67⋊C412yes—
746C22C5×#88212yes—
747C22C5×#88211yescharacteristic
748C22C5×#88312yes—
749C22C5×#88412yes—
750C22C5×#88412yes—
751C22C5×#88512yes—
752C22C5×#88611yescharacteristic
753C22C2×C5×(C2×D3)⋊C411yescharacteristic
754C22C4×C5×#6712yes—
755C22C5×#92911yescharacteristic
756C22C5×#93012yes—
757C22C5×#93712yes—
758C22C5×#93712yes—
759C22C5×#93812yes—
760C22C5×#93912yes—
761C22C5×#93912yes—
762C22C5×#94012yes—
763C22C5×#95311yescharacteristic
764C4—44no—
765C4—64no—
766C4—124no—
767C3C5×#143811yescharacteristic, complemented, Sylow
768C2—44no—
769C2—124no—
770C2C5×#495511yescharacteristic
771C2C5×#495612yes—
772C2C5×#495712yes—
773C2C5×#495811yescharacteristic
774C2C5×#495912yes—
775C2C5×#496012yes—
776C2C5×#496112yes—
777C2C5×#521311yescharacteristic
778C2C5×#522312yes—
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C5×#67C2
cosocleC24×C3C23×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C5×#1438
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C5×#217C2semidirect
4. C22×C5×(C2×D3)⋊C4C2semidirect
5. C2×C5×C3⋊#95C2semidirect
14. C22×C5×#67C4semidirect
25. #71550C5direct (N × H)
29. C22×C5×C22⋊C4D3semidirect
56. C22×C3×C4×C5D4semidirect
73. C22×C5×Dic3D4semidirect
78. C22×C3×C22⋊C4C2×C5semidirect
79. C22×#217C2×C5semidirect
80. C22×(C2×D3)⋊C4C2×C5semidirect
81. C2×C3⋊#95C2×C5semidirect
121. C23×C3×C5C22⋊C4semidirect
151. C22×C5×D3C22⋊C4semidirect
171. C2×C5×Dic3C22⋊C4semidirect
179. C22×#67C4×C5semidirect
232. C22×C4×C5#67semidirect
239. C22×C22⋊C4C5×D3semidirect
308. C22×C3×C4C5×D4semidirect
325. C22×Dic3C5×D4semidirect
370. C23×C5(C2×D3)⋊C4semidirect
449. C23×C3C5×C22⋊C4semidirect
479. C22×D3C5×C22⋊C4semidirect
499. C2×Dic3C5×C22⋊C4semidirect
584. C22×C4C5×#67semidirect
588. C3×C5#1438semidirect
683. C23C5×(C2×D3)⋊C4semidirect
724. C5#71550direct (N × H)
767. C3C5×#1438semidirect

Maximal subgroups

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

subgroupindex
C23×C5×#672
C22×C3×C5×C22⋊C42
C22×C5×#2172
C22×C5×(C2×D3)⋊C42
C2×C5×C3⋊#952
C5×#14383
#715505