Finite Group Databasebeta

← #14324440

Subgroups — #14324440

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
3C4×#6719C211yesmaximal, characteristic
4C2×#91115C211yesmaximal, characteristic
5#11751051C211yesmaximal, characteristic
6#11751047C211yesmaximal, characteristic
7#11751043C211yesmaximal, characteristic
8#11751034C211yesmaximal, characteristic, complemented
9#11751034C211yesmaximal, characteristic, complemented
10#11751030C211yesmaximal, characteristic, complemented
11#11751029C211yesmaximal, characteristic, complemented
12#11750756C211yesmaximal, characteristic, complemented
13#11750755C211yesmaximal, characteristic, complemented
14#11750748C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10605178—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38#91767C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#73447—51nomaximal, Hall
54C2×#4024—31no—
55C4×C5×C22⋊C4D311yescharacteristic
56C4×C22⋊Dic5—31no—
57C2×#3963—31no—
58#65239—31no—
59#65235—31no—
60#65231—31no—
61#65222—31no—
62#65222—31no—
63#65218—31no—
64#65217—31no—
65#64944—31no—
66#64943—31no—
67#64936—31no—
68#64935—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5—41no—
71C22×C3×C4×C5—41no—
72C22×C3×C4×C5Q814yescomplemented
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—22no—
80C22×Dic15—41no—
81C22×Dic15—41no—
82C22×Dic15—41no—
83C22×Dic15—41no—
84C22×Dic15C2×C414yes—
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×Dic30—41no—
94C2×Dic30—41no—
95C2×Dic30C2×C414yescomplemented
96C3×C5×C22⋊C4—22no—
97C3×C5×C22⋊C4C2×C414yes—
98C3×C42×C5—41no—
99C3×C42×C5—41no—
100#6719—22no—
101#6719C2×C414yes—
102C4⋊Dic15—41no—
103C4⋊Dic15—41no—
104C4⋊Dic15C2×C414yescomplemented
105#6712—41no—
106#6712—41no—
107#6712—41no—
108#6712—41no—
109#6712C2×C414yescomplemented
110#6712C2×C414yescomplemented
111C4×Dic15—41no—
112C4×Dic15—41no—
113C2×#878—51no—
114C3×C4×C22⋊C4D511yescharacteristic
115C4×#217—51no—
116C2×C3⋊#95—51no—
117#4950—51no—
118#4946—51no—
119#4942—51no—
120#4933—51no—
121#4933—51no—
122#4929—51no—
123#4928—51no—
124#4655—51no—
125#4654—51no—
126#4647—51no—
127#4646—51no—
128C23×C4×C5C2×D311yescharacteristic
129C23×Dic5—31no—
130C23×Dic5—31no—
131C22×Dic10—31no—
132C2×C5×C22⋊C4C2×D311yescharacteristic
133C2×C5×C22⋊C4C2×D311yescharacteristic
134C2×C42×C5C2×D311yescharacteristic
135C2×C42×C5C2×D311yescharacteristic
136C2×C22⋊Dic5—31no—
137C2×C22⋊Dic5—31no—
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×#683—31no—
142C2×#683—31no—
143C2×#683—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×#683—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149#4024—38no—
150C5×#95C2×D311yescharacteristic
151C5×#95C2×D311yescharacteristic
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#2329—151noSylow
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5C22×C412yes—
170C23×C3×C5C2×Q812yes—
171C23×C3×C5#4112yes—
172C23×C3×C5C2411yescharacteristic
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—44no—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
190C2×C3×C4×C5C2×Q812yes—
191C2×C3×C4×C5C2×Q812yes—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—44no—
213C2×Dic15—44no—
214C2×Dic15C22×C412yes—
215C2×Dic15C22×C412yes—
216C2×Dic15C22×C412yes—
217C2×Dic15C22×C412yes—
218Dic30—44no—
219C23×C3×C4C2×D511yescharacteristic
220C23×Dic3—51no—
221C23×Dic3—51no—
222C22×Dic6—51no—
223C2×C3×C22⋊C4C2×D511yescharacteristic
224C2×C3×C22⋊C4C2×D511yescharacteristic
225C2×C3×C42C2×D511yescharacteristic
226C2×C3×C42C2×D511yescharacteristic
227C2×#217—51no—
228C2×#217—51no—
229C2×C4⋊Dic3—51no—
230C2×C4⋊Dic3—51no—
231C2×C4⋊Dic3—51no—
232C2×Dic3⋊C4—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4—51no—
237C2×Dic3⋊C4—51no—
238C2×C4×Dic3—51no—
239C2×C4×Dic3—51no—
240#878—58no—
241C3×#95C2×D511yescharacteristic
242C3×#95C2×D511yescharacteristic
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95—51no—
247C3⋊#95—51no—
248C3⋊#95—51no—
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C24×C5C22×D311yescharacteristic
256C22×C4×C5—41no—
257C22×C4×C5—41no—
258C22×C4×C5Dic614yescomplemented
259C22×C4×C5C22×D311yescharacteristic
260C22×C4×C5C22×D311yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C22×C4×C5C22×D311yescharacteristic
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×Dic5—31no—
266C22×Dic5—31no—
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5—34no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—62no—
275C22×Dic5—121no—
276C22×Dic5—121no—
277C22×Dic5—121no—
278C22×Dic5—121no—
279C2×Dic10—34no—
280C2×Dic10—121no—
281C2×Dic10—121no—
282C5×C22⋊C4—22no—
283C5×C22⋊C4C4×D314yes—
284C42×C5—41no—
285C42×C5—41no—
286C22⋊Dic5—34no—
287C22⋊Dic5—62no—
288C4⋊Dic5—34no—
289C4⋊Dic5—121no—
290C4⋊Dic5—121no—
291#683—34no—
292#683—34no—
293#683—121no—
294#683—121no—
295#683—121no—
296#683—121no—
297C4×Dic5—121no—
298C4×Dic5—121no—
299C2×C22⋊Q8—151no—
300#391—151no—
301#391—151no—
302#389—151no—
303#389—151no—
304#387—151no—
305#387—151no—
306#387—151no—
307#387—151no—
308#385—151no—
309#385—151no—
310#380—151no—
311C4×C22⋊C4—151no—
312C4×C22⋊C4D1511yescharacteristic
313C2×#95—151no—
314C22×C3×C5—22no—
315C22×C3×C5—22no—
316C22×C3×C5—22no—
317C22×C3×C5—22no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5C4×Q814yes—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5C22×Q811yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5H(5,𝔽2)11yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C52−1+411yescharacteristic
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330C3×C4×C5—22no—
331C3×C4×C5—22no—
332C3×C4×C5—41no—
333C3×C4×C5—41no—
334Dic15—22no—
335Dic15—22no—
336Dic15—22no—
337Dic15—22no—
338Dic15—41no—
339Dic15—41no—
340Dic15—41no—
341Dic15—41no—
342C24×C3C22×D511yescharacteristic
343C22×C3×C4—41no—
344C22×C3×C4—41no—
345C22×C3×C4Dic1014yescomplemented
346C22×C3×C4C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×Dic3—51no—
353C22×Dic3—51no—
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3—54no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3—51no—
360C22×Dic3—51no—
361C22×Dic3—102no—
362C22×Dic3—201no—
363C22×Dic3—201no—
364C22×Dic3—201no—
365C22×Dic3—201no—
366C2×Dic6—54no—
367C2×Dic6—201no—
368C2×Dic6—201no—
369C3×C22⋊C4—22no—
370C3×C22⋊C4C4×D514yes—
371C3×C42—41no—
372C3×C42—41no—
373#217—54no—
374#217—102no—
375C4⋊Dic3—54no—
376C4⋊Dic3—201no—
377C4⋊Dic3—201no—
378Dic3⋊C4—54no—
379Dic3⋊C4—54no—
380Dic3⋊C4—201no—
381Dic3⋊C4—201no—
382Dic3⋊C4—201no—
383Dic3⋊C4—201no—
384C4×Dic3—201no—
385C4×Dic3—201no—
386C23×C5—21no—
387C23×C5—21no—
388C23×C5—21no—
389C23×C5—21no—
390C23×C5C2×Dic612yes—
391C23×C5C2×C4×D312yes—
392C23×C5#23512yes—
393C23×C5C23×D311yescharacteristic
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—44no—
409C2×C4×C5C2×Dic612yes—
410C2×C4×C5C2×Dic612yes—
411C2×C4×C5C2×C4×D312yes—
412C2×C4×C5C2×C4×D312yes—
413C2×Dic5—32no—
414C2×Dic5—32no—
415C2×Dic5—32no—
416C2×Dic5—32no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423C2×Dic5—61no—
424C2×Dic5—61no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—124no—
438C2×Dic5—124no—
439Dic10—124no—
440C22×Q8—151no—
441C23×C4—151no—
442C23×C4—151no—
443C23×C4C2×D1511yescharacteristic
444C22⋊Q8—158no—
445C2×C4⋊C4—151no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—151no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C22⋊C4C2×D1511yescharacteristic
457C2×C22⋊C4C2×D1511yescharacteristic
458C2×C42—151no—
459C2×C42—151no—
460C2×C42C2×D1511yescharacteristic
461C2×C42C2×D1511yescharacteristic
462#95—151no—
463#95—151no—
464#95—151no—
465#95—151no—
466#95—151no—
467#95—151no—
468#95—151no—
469#95—151no—
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474#95C2×D1511yescharacteristic
475#95C2×D1511yescharacteristic
476C2×C3×C5—24no—
477C2×C3×C5C2×C4×Q811yescharacteristic
478C2×C3×C5#51811yescharacteristic
479C2×C3×C5#52011yescharacteristic
480C2×C3×C5#53811yescharacteristic
481C2×C3×C5#53911yescharacteristic
482C2×C3×C5#54311yescharacteristic
483C2×C3×C5#54411yescharacteristic
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3C2×Dic1012yes—
489C23×C3C2×C4×D512yes—
490C23×C3#70912yes—
491C23×C3C23×D511yescharacteristic
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—44no—
507C2×C3×C4C2×Dic1012yes—
508C2×C3×C4C2×Dic1012yes—
509C2×C3×C4C2×C4×D512yes—
510C2×C3×C4C2×C4×D512yes—
511C2×Dic3—52no—
512C2×Dic3—52no—
513C2×Dic3—52no—
514C2×Dic3—52no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C2×Dic3—101no—
521C2×Dic3—101no—
522C2×Dic3—101no—
523C2×Dic3—101no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—204no—
536C2×Dic3—204no—
537Dic6—204no—
538C22×C5—22no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5C4×Dic614yes—
545C22×C5C22×Dic611yescharacteristic
546C22×C5C22×C4×D311yescharacteristic
547C22×C5C2×#23511yescharacteristic
548C22×C5#100411yescharacteristic
549C22×C5#100411yescharacteristic
550C22×C5#100911yescharacteristic
551C22×C5#101011yescharacteristic
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—41no—
557C4×C5—41no—
558Dic5—62no—
559Dic5—62no—
560Dic5—62no—
561Dic5—62no—
562Dic5—121no—
563Dic5—121no—
564Dic5—121no—
565Dic5—121no—
566C24C22×D1511yescharacteristic
567C2×Q8—154no—
568C2×Q8—601no—
569C2×Q8—601no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—151no—
573C22×C4—151no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—154no—
577C22×C4—151no—
578C22×C4—151no—
579C22×C4—151no—
580C22×C4—151no—
581C22×C4—302no—
582C22×C4—601no—
583C22×C4—601no—
584C22×C4—601no—
585C22×C4—601no—
586C22×C4Dic3014yescomplemented
587C22×C4C22×D1511yescharacteristic
588C22×C4C22×D1511yescharacteristic
589C22×C4C22×D1511yescharacteristic
590C22×C4C22×D1511yescharacteristic
591C22×C4C22×D1511yescharacteristic
592C22×C4C22×D1511yescharacteristic
593C4⋊C4—154no—
594C4⋊C4—154no—
595C4⋊C4—154no—
596C4⋊C4—601no—
597C4⋊C4—601no—
598C4⋊C4—601no—
599C4⋊C4—601no—
600C4⋊C4—601no—
601C4⋊C4—601no—
602C22⋊C4—22no—
603C22⋊C4—154no—
604C22⋊C4—302no—
605C22⋊C4C4×D1514yes—
606C42—41no—
607C42—41no—
608C42—601no—
609C42—601no—
610C3×C5#232911yescharacteristic, complemented, Hall
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3C4×Dic1014yes—
618C22×C3C22×Dic1011yescharacteristic
619C22×C3C22×C4×D511yescharacteristic
620C22×C3C2×#70911yescharacteristic
621C22×C3#414411yescharacteristic
622C22×C3#414411yescharacteristic
623C22×C3#414911yescharacteristic
624C22×C3#415011yescharacteristic
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—41no—
630C3×C4—41no—
631Dic3—102no—
632Dic3—102no—
633Dic3—102no—
634Dic3—102no—
635Dic3—201no—
636Dic3—201no—
637Dic3—201no—
638Dic3—201no—
639C2×C5—24no—
640C2×C5C2×C4×Dic611yescharacteristic
641C2×C5#548311yescharacteristic
642C2×C5#551911yescharacteristic
643C2×C5#554511yescharacteristic
644C2×C5#554611yescharacteristic
645C2×C5#556011yescharacteristic
646C2×C5#556411yescharacteristic
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23C2×Dic3012yes—
652C23C2×C4×D1512yes—
653C23#681712yes—
654C23C23×D1511yescharacteristic
655Q8—604no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—44no—
671C2×C4—152no—
672C2×C4—152no—
673C2×C4—152no—
674C2×C4—152no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—301no—
678C2×C4—301no—
679C2×C4—301no—
680C2×C4—301no—
681C2×C4—301no—
682C2×C4—301no—
683C2×C4—301no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4—301no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—604no—
696C2×C4—604no—
697C2×C4C2×Dic3012yes—
698C2×C4C2×Dic3012yes—
699C2×C4C2×C4×D1512yes—
700C2×C4C2×C4×D1512yes—
701C2×C3—24no—
702C2×C3C2×C4×Dic1011yescharacteristic
703C2×C3#6581711yescharacteristic
704C2×C3#6585311yescharacteristic
705C2×C3#6587911yescharacteristic
706C2×C3#6588011yescharacteristic
707C2×C3#6589411yescharacteristic
708C2×C3#6589811yescharacteristic
709C5#7344711yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22C4×Dic3014yes—
717C22C22×Dic3011yescharacteristic
718C22C22×C4×D1511yescharacteristic
719C22C2×#681711yescharacteristic
720C22#9209511yescharacteristic
721C22#9209511yescharacteristic
722C22#9210011yescharacteristic
723C22#9210111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—302no—
731C4—302no—
732C4—302no—
733C4—302no—
734C4—601no—
735C4—601no—
736C4—601no—
737C4—601no—
738C3#1060517811yescharacteristic, complemented, Sylow
739C2—24no—
740C2C2×C4×Dic3011yescharacteristic
741C2#1175624211yescharacteristic
742C2#1175627811yescharacteristic
743C2#1175630411yescharacteristic
744C2#1175630511yescharacteristic
745C2#1175631911yescharacteristic
746C2#1175632311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C4×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#2329
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #11751034C2semidirect
9. #11751034C2semidirect
10. #11751030C2semidirect
11. #11751029C2semidirect
12. #11750756C2semidirect
13. #11750755C2semidirect
14. #11750748C2semidirect
15. #11750747C2semidirect
38. #91767C4semidirect
72. C22×C3×C4×C5Q8semidirect
95. C2×Dic30C2×C4semidirect
104. C4⋊Dic15C2×C4semidirect
109. #6712C2×C4semidirect
110. #6712C2×C4semidirect
258. C22×C4×C5Dic6semidirect
345. C22×C3×C4Dic10semidirect
586. C22×C4Dic30semidirect
610. C3×C5#2329semidirect
709. C5#73447semidirect
738. C3#10605178semidirect

Maximal subgroups

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

subgroupindex
C2×#917672
C3×C4×C5×C22⋊C42
C4×#67192
C2×#911152
#117510512
#117510472
#117510432
#117510342
#117510302
#117510292
#117507562
#117507552
#117507482
#117507472
#106051783
#734475