Finite Group Databasebeta

← #14320583

Subgroups — #14320583

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D20C211yesmaximal, characteristic
2C2×#91393C211yesmaximal, characteristic, complemented
3C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
4#11750754C211yesmaximal, characteristic, complemented
5C5×#4648C211yesmaximal, characteristic, complemented
6C3×#64954C211yesmaximal, characteristic
7#11748896C211yesmaximal, characteristic
8#11748890C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10Dic3×#685C211yesmaximal, characteristic, complemented
11#11748712C211yesmaximal, characteristic, complemented
12#11748710C211yesmaximal, characteristic, complemented
13#11748704C211yesmaximal, characteristic, complemented
14#11748688C211yesmaximal, characteristic, complemented
15#11748667C211yesmaximal, characteristic, complemented
16#10605145—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42Dic3×D20C418yescomplemented
43#91393—24no—
44C4×D5×Dic3—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74657—51nomaximal, Hall
56C2×C4×D20—31no—
57C2×#4018—31no—
58C2×C42×D5—31no—
59C5×#376—31no—
60C4×#685—31no—
61C4×#685—31no—
62C4×C4⋊Dic5—31no—
63#64959—31no—
64#64959—31no—
65#64957—31no—
66#64957—31no—
67#64954—31no—
68#64954D311yescharacteristic
69#64942—31no—
70#64942—31no—
71C23×C3×D5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×D20—22no—
87C2×C3×D20—22no—
88C2×C3×D20C2×C414yes—
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—22no—
92C2×D5×Dic3—22no—
93C2×D5×Dic3—22no—
94C2×D5×Dic3—22no—
95C2×D5×Dic3—22no—
96C2×D5×Dic3—22no—
97C2×D5×Dic3—22no—
98C2×D5×Dic3—22no—
99C2×D5×Dic3C2×C414yes—
100C2×D5×Dic3C2×C414yescomplemented
101C4⋊Dic15C2×C414yescomplemented
102#6712—22no—
103C4×Dic15—22no—
104C4×C5×Dic3—22no—
105C4×C5×Dic3C2×C414yescomplemented
106C4×C5×Dic3D414yescomplemented
107C3×#685—22no—
108C3×#685—22no—
109C3×#685—22no—
110Dic3⋊Dic5—22no—
111Dic3⋊Dic5—22no—
112#6669—22no—
113#6665—22no—
114#6665—22no—
115#6665—22no—
116#6665C2×C414yes—
117#6665C2×C414yescomplemented
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5—22no—
121C2×D4×Dic3—51no—
122C22×C4×Dic3—51no—
123C2×#877—51no—
124C3×#386—51no—
125#5220—51no—
126#5210—51no—
127#4946—51no—
128#4945—51no—
129#4944—51no—
130Dic3×C22⋊C4—51no—
131Dic3×C22⋊C4—51no—
132#4654—51no—
133#4653—51no—
134#4649—51no—
135#4648D511yescharacteristic, complemented
136C22×D20C2×D311yescharacteristic
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C22×C4×D5—31no—
140C22×C4×D5C2×D311yescharacteristic
141C2×C42×C5—31no—
142C2×C42×C5—31no—
143C2×C42×C5—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685C2×D311yescharacteristic
150C2×#685C2×D311yescharacteristic
151C2×#685C2×D311yescharacteristic
152C2×C4⋊Dic5—31no—
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5—31no—
155C2×#683—31no—
156C2×#683—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C4×D20—38no—
162#4018—64no—
163C42×D5—64no—
164C5×#95—31no—
165C5×#95—31no—
166C5×#95—31no—
167C5×#95C2×D311yescharacteristic
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963C2×D311yescharacteristic
174#2290—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5—21no—
182C22×C3×D5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5C22×C412yes—
187C22×C3×D5C22×C412yes—
188C22×C3×D5#4112yes—
189C22×C3×D5#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5C2×D412yes—
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×Dic15C22×C412yes—
209C2×Dic15C22×C412yes—
210C2×Dic15#4112yes—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3C22×C412yes—
219C2×C5×Dic3C22×C412yes—
220C2×C5×Dic3C2×D412yes—
221C2×C5×Dic3C2×D412yes—
222C2×C5×Dic3#4112yes—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5#4112yes—
229C3×D20—28no—
230C3×C4×D5—28no—
231D5×Dic3—28no—
232D5×Dic3—28no—
233D5×Dic3—28no—
234C22×C3×D4—51no—
235C23×C3×C4—51no—
236C23×Dic3—51no—
237C23×Dic3—51no—
238C23×Dic3—51no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×#217—51no—
243C2×#217—51no—
244C2×#217—51no—
245C2×#217—51no—
246C2×#217—51no—
247D4×Dic3—58no—
248C2×C4⋊Dic3—51no—
249C2×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×C4×Dic3—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—104no—
258C2×C4×Dic3C2×D511yescharacteristic
259C2×C4×Dic3C2×D511yescharacteristic
260C2×C4×Dic3C2×D511yescharacteristic
261#877—104no—
262C3×#95—51no—
263C3×#95C2×D511yescharacteristic
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95C2×D511yescharacteristic
270C3⋊#95C2×D511yescharacteristic
271C3⋊#95C2×D511yescharacteristic
272C23×D5C22×D311yescharacteristic
273C23×D5C22×D311yescharacteristic
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×Dic5—31no—
282C22×Dic5—31no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C2×D20—22no—
288C2×D20—22no—
289C2×D20C4×D314yes—
290C2×C4×D5—22no—
291C2×C4×D5—22no—
292C2×C4×D5—22no—
293C2×C4×D5—34no—
294C2×C4×D5—34no—
295C2×C4×D5—62no—
296C2×C4×D5—62no—
297C2×C4×D5—62no—
298C2×C4×D5—62no—
299C2×C4×D5—62no—
300C2×C4×D5—62no—
301C2×C4×D5—62no—
302C42×C5—34no—
303C42×C5—34no—
304C42×C5—62no—
305#685—22no—
306#685—22no—
307#685—22no—
308#685—34no—
309#685—34no—
310#685—62no—
311#685—62no—
312#685—62no—
313C4⋊Dic5—34no—
314C4⋊Dic5—62no—
315C4⋊Dic5—62no—
316#683—62no—
317#683—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C4×Dic5—62no—
322C2×C4×D4—151no—
323C2×#117—151no—
324C22×C42—151no—
325#388—151no—
326#388—151no—
327#387—151no—
328#387—151no—
329#386—51no—
330#386—151no—
331#385—151no—
332#385—151no—
333C4×C4⋊C4—151no—
334C4×C22⋊C4—151no—
335C4×C22⋊C4—151no—
336#376—31no—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C22×D411yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5C2×#4111yescharacteristic
343C22×C3×C5C2×#4111yescharacteristic
344C2×C3×D5—22no—
345C2×C3×D5—22no—
346C2×C3×D5—22no—
347C2×C3×D5—22no—
348C2×C3×D5—22no—
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5#11714yescomplemented
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—41no—
361Dic15—22no—
362Dic15—22no—
363Dic15—22no—
364Dic15—41no—
365C3×Dic5—22no—
366C3×Dic5—41no—
367C5×Dic3—22no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3C4×D414yes—
371C24×C3—51no—
372C24×C3—51no—
373C2×C3×D4—54no—
374C2×C3×D4—102no—
375C2×C3×D4—102no—
376C22×C3×C4—51no—
377C22×C3×C4—51no—
378C22×C3×C4—102no—
379C22×C3×C4—102no—
380C22×C3×C4—102no—
381C22×C3×C4C22×D511yescharacteristic
382C22×C3×C4C22×D511yescharacteristic
383C22×C3×C4C22×D511yescharacteristic
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—54no—
388C22×Dic3—54no—
389C22×Dic3—51no—
390C22×Dic3—102no—
391C22×Dic3—102no—
392C22×Dic3—102no—
393C22×Dic3—102no—
394C22×Dic3—102no—
395C22×Dic3—102no—
396C22×Dic3—102no—
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C22×Dic3C22×D511yescharacteristic
400C22×Dic3C22×D511yescharacteristic
401C3×C22⋊C4—102no—
402C3×C22⋊C4—102no—
403C3×C22⋊C4—102no—
404#217—54no—
405#217—54no—
406#217—102no—
407#217—102no—
408#217—102no—
409C4⋊Dic3—54no—
410Dic3⋊C4—102no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413Dic3⋊C4—102no—
414C4×Dic3—22no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3C4×D514yescomplemented
420C4×Dic3D2014yescomplemented
421C23×C5C23×D311yescharacteristic
422C22×D5—21no—
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—21no—
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5C2×C4×D312yes—
433C22×D5C2×C4×D312yes—
434C22×D5#23712yes—
435C22×D5#23712yes—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—32no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5—61no—
454C2×C4×C5—61no—
455C2×C4×C5C2×C4×D312yes—
456C2×C4×C5D3×D412yes—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—32no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5#23712yes—
475D20—28no—
476C4×D5—28no—
477C4×D5—68no—
478C4×D5—68no—
479C4×D5—68no—
480C22×D4—51no—
481C23×C4—51no—
482C23×C4—151no—
483C23×C4—151no—
484C23×C4—151no—
485C4×D4—158no—
486#117—304no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—151no—
500C2×C42—31no—
501C2×C42—31no—
502C2×C42—31no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—304no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95D3×D511yescharacteristic
518C2×C3×C5C2×#11711yescharacteristic
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5C4×#4111yescharacteristic
521C2×C3×C5#52511yescharacteristic
522C2×C3×C5#52511yescharacteristic
523C2×C3×C5#52911yescharacteristic
524C2×C3×C5#52911yescharacteristic
525C3×D5—24no—
526C3×D5—42no—
527C23×C3—52no—
528C23×C3—52no—
529C23×C3—52no—
530C23×C3—52no—
531C23×C3—101no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3—101no—
539C23×C3—101no—
540C23×C3—101no—
541C23×C3C23×D511yescharacteristic
542C3×D4—108no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—52no—
551C2×C3×C4—108no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4C2×C4×D512yes—
558C2×C3×C4C2×D2012yes—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—52no—
567C2×Dic3—52no—
568C2×Dic3—52no—
569C2×Dic3—108no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—108no—
577C2×Dic3—108no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3C2×C4×D512yes—
582C2×Dic3C2×C4×D512yes—
583C2×Dic3C2×D2012yes—
584C2×Dic3C2×D2012yes—
585C2×Dic3#70912yes—
586C22×C5C22×C4×D311yescharacteristic
587C22×C5C2×D3×D411yescharacteristic
588C22×C5C2×#23711yescharacteristic
589C22×C5C2×#23711yescharacteristic
590C22×C5C2×#23711yescharacteristic
591C22×C5D3×#4111yescharacteristic
592C22×C5D3×#4111yescharacteristic
593C2×D5—22no—
594C2×D5—22no—
595C2×D5—22no—
596C2×D5—22no—
597C2×D5—22no—
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—41no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5#87714yescomplemented
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—34no—
610C4×C5—41no—
611C4×C5—62no—
612C4×C5—62no—
613C4×C5—121no—
614Dic5—22no—
615Dic5—41no—
616Dic5—62no—
617Dic5—62no—
618Dic5—62no—
619Dic5—121no—
620C24—51no—
621C24—51no—
622C2×D4—54no—
623C2×D4—102no—
624C2×D4—102no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—102no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—154no—
635C22×C4—154no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—151no—
639C22×C4—151no—
640C22×C4—302no—
641C22×C4—302no—
642C22×C4—302no—
643C22×C4—302no—
644C22×C4—302no—
645C22×C4—302no—
646C22×C4—302no—
647C22×C4C2×D3×D511yescharacteristic
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—154no—
651C4⋊C4—302no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C4⋊C4—302no—
655C22⋊C4—102no—
656C22⋊C4—102no—
657C22⋊C4—102no—
658C22⋊C4—154no—
659C22⋊C4—154no—
660C22⋊C4—302no—
661C22⋊C4—302no—
662C22⋊C4—302no—
663C42—34no—
664C42—34no—
665C42—62no—
666C42—302no—
667C42—302no—
668C42—302no—
669C42—302no—
670C3×C5#229011yescharacteristic, complemented, Hall
671C22×C3—54no—
672C22×C3—102no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—102no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3—102no—
680C22×C3—102no—
681C22×C3—201no—
682C22×C3—201no—
683C22×C3—201no—
684C22×C3—201no—
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C22×D2011yescharacteristic
687C22×C3C2×#70911yescharacteristic
688C22×C3D5×#4111yescharacteristic
689C22×C3D5×#4111yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3D5×#4111yescharacteristic
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—41no—
695C3×C4—102no—
696C3×C4—201no—
697Dic3—22no—
698Dic3—22no—
699Dic3—41no—
700Dic3—102no—
701Dic3—102no—
702Dic3—102no—
703Dic3—201no—
704Dic3C4×D2014yes—
705C2×C5C2×#87711yescharacteristic
706C2×C5C4×#23711yescharacteristic
707C2×C5C4×D3×D411yescharacteristic
708C2×C5#558611yescharacteristic
709C2×C5#560011yescharacteristic
710C2×C5#560611yescharacteristic
711C2×C5#564911yescharacteristic
712D5—24no—
713D5—42no—
714C23—52no—
715C23—52no—
716C23—52no—
717C23—52no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23—101no—
726C23—101no—
727C23—101no—
728C23C22×D3×D511yescharacteristic
729D4—108no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—32no—
742C2×C4—52no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—108no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—152no—
757C2×C4—152no—
758C2×C4—152no—
759C2×C4—308no—
760C2×C4—308no—
761C2×C4—308no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—301no—
771C2×C4C4×D3×D512yes—
772C2×C4D3×D2012yes—
773C2×C3—104no—
774C2×C3—202no—
775C2×C3C2×C4×D2011yescharacteristic
776C2×C3D5×#11711yescharacteristic
777C2×C3#6585611yescharacteristic
778C2×C3#6585811yescharacteristic
779C2×C3#6585811yescharacteristic
780C2×C3#6586211yescharacteristic
781C2×C3#6586211yescharacteristic
782C5#7465711yescharacteristic, complemented, Sylow
783C22—54no—
784C22—102no—
785C22—102no—
786C22—102no—
787C22—102no—
788C22—102no—
789C22—102no—
790C22—102no—
791C22—102no—
792C22—102no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—201no—
797C22C2×C4×D3×D511yescharacteristic
798C22C2×D3×D2011yescharacteristic
799C22D3×#70911yescharacteristic
800C22D5×#23711yescharacteristic
801C22D5×#23711yescharacteristic
802C22D5×#23711yescharacteristic
803C22#9203411yescharacteristic
804C4—22no—
805C4—22no—
806C4—34no—
807C4—41no—
808C4—62no—
809C4—62no—
810C4—102no—
811C4—121no—
812C4—201no—
813C4—302no—
814C4—302no—
815C4—302no—
816C4—601no—
817C3#1060514511yescharacteristic, complemented, Sylow
818C2—104no—
819C2—202no—
820C2C4×D3×D2011yescharacteristic
821C2D5×#87711yescharacteristic
822C2#1175287511yescharacteristic
823C2#1175291111yescharacteristic
824C2#1175339811yescharacteristic
825C2#1175350711yescharacteristic
826C2#1175387911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenter#95D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91393C2semidirect
3. C2×C4×D5×Dic3C2semidirect
4. #11750754C2semidirect
5. C5×#4648C2semidirect
8. #11748890C2semidirect
9. Dic3×#685C2semidirect
10. Dic3×#685C2semidirect
11. #11748712C2semidirect
12. #11748710C2semidirect
13. #11748704C2semidirect
14. #11748688C2semidirect
15. #11748667C2semidirect
42. Dic3×D20C4semidirect
100. C2×D5×Dic3C2×C4semidirect
101. C4⋊Dic15C2×C4semidirect
105. C4×C5×Dic3C2×C4semidirect
106. C4×C5×Dic3D4semidirect
117. #6665C2×C4semidirect
135. #4648D5semidirect
357. C2×C3×D5#117semidirect
419. C4×Dic3C4×D5semidirect
420. C4×Dic3D20semidirect
606. C2×D5#877semidirect
670. C3×C5#2290semidirect
782. C5#74657semidirect
817. C3#10605145semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D202
C2×#913932
C2×C4×D5×Dic32
#117507542
C5×#46482
C3×#649542
#117488962
#117488902
Dic3×#6852
#117487122
#117487102
#117487042
#117486882
#117486672
#106051453
#746575