Finite Group Databasebeta

← #14321811

Subgroups — #14321811

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91575C211yesmaximal, characteristic
2C22×Dic3×Dic5C211yesmaximal, characteristic
3C2×#91323C211yesmaximal, characteristic, complemented
4#11751047C211yesmaximal, characteristic
5C5×#4942C211yesmaximal, characteristic
6C3×C22⋊C4×Dic5C211yesmaximal, characteristic
7#11749515C211yesmaximal, characteristic
8Dic5×#217C211yesmaximal, characteristic
9#11748650C211yesmaximal, characteristic, complemented
10#11748649C211yesmaximal, characteristic, complemented
11#11748640C211yesmaximal, characteristic, complemented
12Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#11748638C211yesmaximal, characteristic, complemented
14#11748631C211yesmaximal, characteristic, complemented
15#11748630C211yesmaximal, characteristic, complemented
16#10605597—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31#91575C418yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×Dic3×Dic5—24no—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91323—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55C4×#878—51nomaximal, Hall
56C2×#4070—31no—
57C22×C4×Dic5—31no—
58C2×#4033—31no—
59C5×#380—31no—
60C4⋊C4×Dic5—31no—
61#65263—31no—
62#65262—31no—
63#65235—31no—
64#65235—31no—
65C22⋊C4×Dic5—31no—
66C22⋊C4×Dic5D311yescharacteristic
67#64941—31no—
68#64941—31no—
69#64938—31no—
70#64938—31no—
71C24×C3×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15—22no—
75C22×Dic15—22no—
76C22×Dic15—22no—
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×C5×Dic3—22no—
82C22×C5×Dic3—22no—
83C22×C5×Dic3C2×C414yes—
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5Q814yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×#1204—22no—
96C2×#1204—22no—
97C2×#1204C2×C414yescomplemented
98C3×C5×C22⋊C4—22no—
99#6719C2×C414yes—
100#6712—22no—
101#6712—22no—
102C5×#217—22no—
103C5×Dic3⋊C4—22no—
104C5×Dic3⋊C4—22no—
105C3×C22⋊Dic5C2×C414yes—
106C3×C4×Dic5—22no—
107C3×C4×Dic5—22no—
108Dic3⋊Dic5C2×C414yescomplemented
109#6669C2×C414yescomplemented
110#6668—22no—
111#6668—22no—
112#6668C2×C414yescomplemented
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115Dic3×Dic5—22no—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5D414yes—
119C22×C4×Dic3—51no—
120C2×#878—51no—
121C2×C4×Dic6—51no—
122C3×C4×C22⋊C4—51no—
123C4×#217—51no—
124#4950—51no—
125#4946—51no—
126#4942D511yescharacteristic
127C4×C4⋊Dic3—51no—
128C4×Dic3⋊C4—51no—
129C4×Dic3⋊C4—51no—
130#4655—51no—
131#4654—51no—
132#4647—51no—
133#4646—51no—
134C23×C4×C5—31no—
135C23×Dic5—31no—
136C23×Dic5C2×D311yescharacteristic
137C22×Dic10—31no—
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4C2×D311yescharacteristic
142C2×C22⋊Dic5—31no—
143C2×C22⋊Dic5C2×D311yescharacteristic
144C2×C4⋊Dic5—31no—
145#4070—38no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×#683—31no—
151C2×#683—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—64no—
159C2×C4×Dic5C2×D311yescharacteristic
160C2×C4×Dic5C2×D311yescharacteristic
161#4033—64no—
162C5×#95—31no—
163C5×#95—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963C2×D311yescharacteristic
171#3963C2×D311yescharacteristic
172C4×C22⋊Q8—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5C22×C412yes—
178C23×C3×C5C2×Q812yes—
179C23×C3×C5#4112yes—
180C23×C3×C5C2411yescharacteristic
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×Dic15—28no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C22×C412yes—
197C2×Dic15C22×C412yes—
198C2×Dic15C2×D412yes—
199C2×Dic15#4112yes—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—28no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C5×Dic3C2×D412yes—
212C2×C5×Dic3#4112yes—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—28no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C2×D412yes—
223C2×C3×Dic5C2×Q812yes—
224C2×C3×Dic5C2×Q812yes—
225C2×C3×Dic5#4112yes—
226#1204—28no—
227C23×C3×C4—51no—
228C23×Dic3—51no—
229C23×Dic3C2×D511yescharacteristic
230C22×Dic6—51no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4C2×D511yescharacteristic
233C2×C3×C42—51no—
234C2×C3×C42—51no—
235C2×#217—51no—
236C2×#217C2×D511yescharacteristic
237C2×C4⋊Dic3—51no—
238C2×C4⋊Dic3—51no—
239C2×C4⋊Dic3—51no—
240C2×Dic3⋊C4—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4C2×D511yescharacteristic
245C2×Dic3⋊C4C2×D511yescharacteristic
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249C2×C4×Dic3—51no—
250C2×C4×Dic3—51no—
251C2×C4×Dic3—51no—
252C2×C4×Dic3—104no—
253#878—58no—
254C4×Dic6—104no—
255C3×#95—51no—
256C3×#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95—51no—
263C3⋊#95C2×D511yescharacteristic
264C3⋊#95C2×D511yescharacteristic
265C24×C5C22×D311yescharacteristic
266C22×C4×C5—31no—
267C22×C4×C5—34no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—62no—
272C22×C4×C5—62no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×Dic5—22no—
276C22×Dic5—22no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—31no—
281C22×Dic5—62no—
282C22×Dic5—62no—
283C22×Dic5—62no—
284C22×Dic5Dic614yescomplemented
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C2×Dic10—34no—
290C2×Dic10—62no—
291C2×Dic10—62no—
292C5×C4⋊C4—62no—
293C5×C4⋊C4—62no—
294C5×C22⋊C4—22no—
295C5×C22⋊C4—62no—
296C22⋊Dic5—34no—
297C22⋊Dic5C4×D314yes—
298C4⋊Dic5—34no—
299#683—34no—
300#683—34no—
301#683—62no—
302#683—62no—
303#683—62no—
304#683—62no—
305C4×Dic5—22no—
306C4×Dic5—22no—
307C4×Dic5—34no—
308C4×Dic5—62no—
309C4×Dic5—62no—
310C4×Dic5—62no—
311C4×Dic5—62no—
312C4×Dic5—62no—
313C2×C22⋊Q8—151no—
314C2×C4×Q8—151no—
315C22×C42—151no—
316#391—151no—
317#389—151no—
318#387—151no—
319#387—151no—
320#385—151no—
321#385—151no—
322#380—31no—
323C4×C4⋊C4—151no—
324C4×C4⋊C4—151no—
325C4×C4⋊C4—151no—
326C4×C22⋊C4—51no—
327C4×C22⋊C4—151no—
328C22×C3×C5—22no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—22no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5C4×Q814yescomplemented
335C22×C3×C5C23×C411yescharacteristic
336C22×C3×C5C22×D411yescharacteristic
337C22×C3×C5C22×Q811yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C3×C4×C5—41no—
343C3×C4×C5—41no—
344Dic15—22no—
345Dic15—22no—
346Dic15—22no—
347Dic15—22no—
348C3×Dic5—22no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5C22⋊Q814yescomplemented
352C5×Dic3—22no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C5×Dic3C4×D414yes—
356C24×C3C22×D511yescharacteristic
357C22×C3×C4—51no—
358C22×C3×C4—54no—
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—102no—
363C22×C3×C4—102no—
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×Dic3—22no—
367C22×Dic3—22no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—51no—
372C22×Dic3—102no—
373C22×Dic3—102no—
374C22×Dic3—102no—
375C22×Dic3C4×D514yes—
376C22×Dic3C22×D511yescharacteristic
377C22×Dic3C22×D511yescharacteristic
378C22×Dic3C22×D511yescharacteristic
379C22×Dic3C22×D511yescharacteristic
380C2×Dic6—54no—
381C2×Dic6—102no—
382C2×Dic6—102no—
383C3×C22⋊C4—22no—
384C3×C22⋊C4—54no—
385C3×C42—102no—
386C3×C42—102no—
387#217—22no—
388#217—54no—
389C4⋊Dic3—54no—
390C4⋊Dic3—102no—
391C4⋊Dic3—102no—
392Dic3⋊C4—22no—
393Dic3⋊C4—22no—
394Dic3⋊C4—54no—
395Dic3⋊C4—54no—
396Dic3⋊C4—102no—
397Dic3⋊C4—102no—
398C4×Dic3—54no—
399C4×Dic3—102no—
400C4×Dic3—102no—
401C4×Dic3—102no—
402C4×Dic3—102no—
403C4×Dic3—102no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5C2×Dic612yes—
409C23×C5C2×C4×D312yes—
410C23×C5#23512yes—
411C23×C5C23×D311yescharacteristic
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—32no—
419C2×C4×C5—32no—
420C2×C4×C5—32no—
421C2×C4×C5—32no—
422C2×C4×C5—68no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—28no—
438C2×Dic5—32no—
439C2×Dic5—32no—
440C2×Dic5—32no—
441C2×Dic5—32no—
442C2×Dic5—68no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5C2×Dic612yes—
452C2×Dic5C2×Dic612yes—
453C2×Dic5C2×C4×D312yes—
454C2×Dic5C2×C4×D312yes—
455C2×Dic5D3×D412yes—
456C2×Dic5#23712yes—
457Dic10—68no—
458C22×Q8—151no—
459C23×C4—31no—
460C23×C4—51no—
461C23×C4—151no—
462C22⋊Q8—158no—
463C4×Q8—304no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—151no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4D3×D511yescharacteristic
477C2×C42—51no—
478C2×C42—51no—
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484C2×C42—151no—
485C2×C42—304no—
486#95—31no—
487#95—31no—
488#95—51no—
489#95—51no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5—24no—
497C2×C3×C5C2×C4×D411yescharacteristic
498C2×C3×C5C2×C4×Q811yescharacteristic
499C2×C3×C5C4×#4111yescharacteristic
500C2×C3×C5C2×C22⋊Q811yescharacteristic
501C2×C3×C5#52511yescharacteristic
502C2×C3×C5#52911yescharacteristic
503C2×C3×C5#53311yescharacteristic
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3C2×C4×D512yes—
509C23×C3#71112yes—
510C23×C3Q8×D512yes—
511C23×C3C23×D511yescharacteristic
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—52no—
521C2×C3×C4—52no—
522C2×C3×C4—52no—
523C2×C3×C4—52no—
524C2×C3×C4—108no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—28no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—52no—
541C2×Dic3—52no—
542C2×Dic3—52no—
543C2×Dic3—52no—
544C2×Dic3—108no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3C2×C4×D512yes—
554C2×Dic3C2×C4×D512yes—
555C2×Dic3D4×D512yes—
556C2×Dic3#71112yes—
557Dic6—108no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5C4×Dic614yescomplemented
565C22×C5C22×Dic611yescharacteristic
566C22×C5C22×C4×D311yescharacteristic
567C22×C5C2×#23511yescharacteristic
568C22×C5C2×D3×D411yescharacteristic
569C22×C5C2×#23711yescharacteristic
570C22×C5D3×#4111yescharacteristic
571C22×C5D3×#4111yescharacteristic
572C4×C5—34no—
573C4×C5—41no—
574C4×C5—41no—
575C4×C5—62no—
576C4×C5—121no—
577C4×C5—121no—
578Dic5—22no—
579Dic5—22no—
580Dic5—22no—
581Dic5—62no—
582Dic5—62no—
583Dic5—62no—
584Dic5—62no—
585Dic5#87814yescomplemented
586C24C2×D3×D511yescharacteristic
587C2×Q8—154no—
588C2×Q8—302no—
589C2×Q8—302no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—51no—
596C22×C4—54no—
597C22×C4—51no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—151no—
605C22×C4—151no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—302no—
609C22×C4—302no—
610C22×C4—302no—
611C22×C4C2×D3×D511yescharacteristic
612C22×C4C2×D3×D511yescharacteristic
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—154no—
616C4⋊C4—154no—
617C4⋊C4—154no—
618C4⋊C4—302no—
619C4⋊C4—302no—
620C4⋊C4—302no—
621C4⋊C4—302no—
622C22⋊C4—22no—
623C22⋊C4—54no—
624C22⋊C4—62no—
625C22⋊C4—154no—
626C42—102no—
627C42—102no—
628C42—154no—
629C42—302no—
630C42—302no—
631C42—302no—
632C42—302no—
633C42—302no—
634C3×C5C4×C22⋊Q811yescharacteristic, complemented, Hall
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3#403314yescomplemented
642C22×C3C22×C4×D511yescharacteristic
643C22×C3C2×D4×D511yescharacteristic
644C22×C3C2×#71111yescharacteristic
645C22×C3C2×#71111yescharacteristic
646C22×C3C2×Q8×D511yescharacteristic
647C22×C3D5×#4111yescharacteristic
648C22×C3D5×#4111yescharacteristic
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—54no—
652C3×C4—102no—
653C3×C4—102no—
654C3×C4—102no—
655Dic3—22no—
656Dic3—41no—
657Dic3—41no—
658Dic3—102no—
659Dic3—102no—
660Dic3—102no—
661Dic3—102no—
662Dic3#402714yes—
663C2×C5—24no—
664C2×C5C2×C4×Dic611yescharacteristic
665C2×C5C2×#87811yescharacteristic
666C2×C5#551711yescharacteristic
667C2×C5C4×#23711yescharacteristic
668C2×C5#553811yescharacteristic
669C2×C5C4×D3×D411yescharacteristic
670C2×C5#554711yescharacteristic
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23D5×Dic612yes—
676C23C4×D3×D512yes—
677C23#678212yes—
678C23C22×D3×D511yescharacteristic
679Q8—308no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—68no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—108no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—152no—
713C2×C4—152no—
714C2×C4—152no—
715C2×C4—152no—
716C2×C4—308no—
717C2×C4—301no—
718C2×C4—301no—
719C2×C4—301no—
720C2×C4—301no—
721C2×C4—301no—
722C2×C4—301no—
723C2×C4—301no—
724C2×C4—301no—
725C2×C3—24no—
726C2×C3C2×#402711yescharacteristic
727C2×C3C2×#403311yescharacteristic
728C2×C3#6585611yescharacteristic
729C2×C3#6593411yescharacteristic
730C2×C3#6594011yescharacteristic
731C2×C3#6595611yescharacteristic
732C2×C3D5×C22⋊Q811yescharacteristic
733C5C4×#87811yescharacteristic, complemented, Sylow
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22#9132314yescomplemented
741C22C2×D5×Dic611yescharacteristic
742C22C2×C4×D3×D511yescharacteristic
743C22D3×D4×D511yescharacteristic
744C22D5×#23711yescharacteristic
745C22D3×#71111yescharacteristic
746C22#9202411yescharacteristic
747C22C2×#678211yescharacteristic
748C4—34no—
749C4—41no—
750C4—41no—
751C4—54no—
752C4—62no—
753C4—102no—
754C4—102no—
755C4—102no—
756C4—121no—
757C4—121no—
758C4—302no—
759C4—302no—
760C4—302no—
761C4—302no—
762C3#1060559711yescharacteristic, complemented, Sylow
763C2—24no—
764C2#1175278911yescharacteristic
765C2#1175281811yescharacteristic
766C2D5×#87811yescharacteristic
767C2D3×#402711yescharacteristic
768C2C2×#9132311yescharacteristic
769C2#1175477311yescharacteristic
770C2#1175484911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#91323C2semidirect
9. #11748650C2semidirect
10. #11748649C2semidirect
11. #11748640C2semidirect
12. Dic5×Dic3⋊C4C2semidirect
13. #11748638C2semidirect
14. #11748631C2semidirect
15. #11748630C2semidirect
31. #91575C4semidirect
90. C22×C3×Dic5Q8semidirect
97. C2×#1204C2×C4semidirect
108. Dic3⋊Dic5C2×C4semidirect
109. #6669C2×C4semidirect
112. #6668C2×C4semidirect
284. C22×Dic5Dic6semidirect
334. C22×C3×C5C4×Q8semidirect
351. C3×Dic5C22⋊Q8semidirect
564. C22×C5C4×Dic6semidirect
585. Dic5#878semidirect
634. C3×C5C4×C22⋊Q8semidirect
641. C22×C3#4033semidirect
733. C5C4×#878semidirect
740. C22#91323semidirect
762. C3#10605597semidirect

Maximal subgroups

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

subgroupindex
C2×#915752
C22×Dic3×Dic52
C2×#913232
#117510472
C5×#49422
C3×C22⋊C4×Dic52
#117495152
Dic5×#2172
#117486502
#117486492
#117486402
Dic5×Dic3⋊C42
#117486382
#117486312
#117486302
#106055973
C4×#8785