Finite Group Databasebeta

← #14327402

Subgroups — #14327402

Order 1920.

1320 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
1C22×#6712C211yesmaximal, characteristic, complemented
2C2×#91559C211yesmaximal, characteristic
3C2×#91393C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic
6#11749516C211yesmaximal, characteristic, complemented
7#11749500C211yesmaximal, characteristic
8#11749487C211yesmaximal, characteristic, complemented
9#11748885C211yesmaximal, characteristic, complemented
10#11748806C211yesmaximal, characteristic, complemented
11#11748707C211yesmaximal, characteristic, complemented
12#11748706C211yesmaximal, characteristic, complemented
13#11748650C211yesmaximal, characteristic, complemented
14#11748645C211yesmaximal, characteristic, complemented
15#11748644C211yesmaximal, characteristic, complemented
16#10605192—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×#6712—24no—
23C2×#6712C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34#91559C418yescomplemented
35C2×#6669C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91393—24no—
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74673—51nomaximal, Hall
56C22×#683—31no—
57C2×#4027—31no—
58C2×#4018—31no—
59C4×C5×C22⋊C4—31no—
60#65502D311yescharacteristic
61#65247—31no—
62#65231—31no—
63C22⋊C4×Dic5—31no—
64#65229—31no—
65#65222—31no—
66C4×#683—31no—
67#64958—31no—
68#64956—31no—
69#64941—31no—
70#64939—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—22no—
79C22×Dic15—22no—
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15—41no—
83C22×Dic15C2×C414yes—
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C3×C22⋊D5—22no—
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5C2×C414yes—
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×D5×Dic3—22no—
99C2×D5×Dic3—22no—
100C2×D5×Dic3C2×C414yescomplemented
101#6712—22no—
102#6712—22no—
103#6712—22no—
104#6712D414yescomplemented
105C5×#217—22no—
106C5×#217C2×C414yes—
107C4×C5×Dic3—22no—
108C4×C5×Dic3—41no—
109C3×C22⋊Dic5—22no—
110C3×#685—22no—
111C3×#685—41no—
112#6669—22no—
113#6669—22no—
114#6668C2×C414yescomplemented
115#6665—22no—
116#6665—41no—
117#6665C2×C414yescomplemented
118Dic3×Dic5—22no—
119Dic3×Dic5—41no—
120Dic3×Dic5C2×C414yescomplemented
121C2×D4×Dic3—51no—
122C22×Dic3⋊C4—51no—
123C2×#877—51no—
124C3×#386—51no—
125#5220—51no—
126C4×#217D511yescharacteristic, complemented
127#4945—51no—
128#4944—51no—
129#4942—51no—
130#4942—51no—
131Dic3×C22⋊C4—51no—
132#4654—51no—
133#4653—51no—
134#4650—51no—
135#4649—51no—
136C23×C4×C5C2×D311yescharacteristic
137C22×C22⋊D5C2×D311yescharacteristic
138C23×Dic5—31no—
139C23×Dic5—31no—
140C22×C4×D5—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C42×C5—31no—
144C2×C42×C5—31no—
145C2×C22⋊Dic5C2×D311yescharacteristic
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685C2×D311yescharacteristic
150C2×#685C2×D311yescharacteristic
151C2×#683—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683—31no—
157C2×#683—31no—
158C2×#683—64no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162#4027—38no—
163#4018—64no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174#2352—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5#4112yes—
181C23×C3×C5#4112yes—
182C23×C3×C5C2411yescharacteristic
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
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—44no—
196C2×C3×C4×C5C2×D412yes—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—28no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—44no—
206C2×Dic15C22×C412yes—
207C2×Dic15C22×C412yes—
208C2×Dic15C2×D412yes—
209C2×Dic15C2×D412yes—
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×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C22×C412yes—
222C2×C5×Dic3C22×C412yes—
223C3×C22⋊D5—28no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5C22×C412yes—
233D5×Dic3—28no—
234C22×C3×D4—51no—
235C23×C3×C4C2×D511yescharacteristic
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×#217C2×D511yescharacteristic
246C2×#217C2×D511yescharacteristic
247D4×Dic3—58no—
248C2×C4⋊Dic3—51no—
249C2×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4—104no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3C2×D511yescharacteristic
260C2×C4×Dic3C2×D511yescharacteristic
261#877—104no—
262C3×#95—51no—
263C3×#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95C2×D511yescharacteristic
271C3⋊#95C2×D511yescharacteristic
272C24×C5C22×D311yescharacteristic
273C23×D5C22×D311yescharacteristic
274C22×C4×C5—22no—
275C22×C4×C5—22no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5—41no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—22no—
284C2×C22⋊D5—22no—
285C2×C22⋊D5C4×D314yes—
286C22×Dic5—31no—
287C22×Dic5—34no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—62no—
292C22×Dic5—62no—
293C22×Dic5—62no—
294C22×Dic5—62no—
295C22×Dic5—121no—
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C22×Dic5C22×D311yescharacteristic
299C2×C4×D5—34no—
300C2×C4×D5—62no—
301C2×C4×D5—62no—
302C5×C22⋊C4—34no—
303C5×C22⋊C4—62no—
304C42×C5—62no—
305C42×C5—121no—
306C22⋊Dic5—22no—
307#685—22no—
308#685—34no—
309#685—41no—
310#685—62no—
311#685—121no—
312#683—34no—
313#683—34no—
314#683—62no—
315#683—62no—
316#683—62no—
317#683—62no—
318#683—62no—
319C4×Dic5—34no—
320C4×Dic5—62no—
321C4×Dic5—121no—
322C2×C4×D4—151no—
323C2×#117—151no—
324C22×C4⋊C4—151no—
325#388—151no—
326#388—151no—
327#387—151no—
328#387—151no—
329#386—51no—
330#386—151no—
331#382—151no—
332#380—151no—
333#380—151no—
334C4×C4⋊C4—151no—
335C4×C22⋊C4—31no—
336C4×C22⋊C4—151no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5#11714yescomplemented
344C22×C3×C5C23×C411yescharacteristic
345C22×C3×C5C22×D411yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5C2×#4111yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C22×C3×C52−1+411yescharacteristic
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—22no—
359C3×C4×C5—41no—
360Dic15—22no—
361Dic15—22no—
362Dic15—41no—
363Dic15C4×D414yes—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C5×Dic3—22no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3—41no—
371C24×C3—51no—
372C24×C3C22×D511yescharacteristic
373C2×C3×D4—54no—
374C2×C3×D4—102no—
375C2×C3×D4—102no—
376C22×C3×C4—22no—
377C22×C3×C4—22no—
378C22×C3×C4—41no—
379C22×C3×C4—51no—
380C22×C3×C4—51no—
381C22×C3×C4—51no—
382C22×C3×C4C22×D511yescharacteristic
383C22×C3×C4C22×D511yescharacteristic
384C22×Dic3—51no—
385C22×Dic3—54no—
386C22×Dic3—51no—
387C22×Dic3—51no—
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—201no—
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C22×Dic3C22×D511yescharacteristic
400C22×Dic3C22×D511yescharacteristic
401C3×C22⋊C4—102no—
402C3×C22⋊C4—102no—
403C3×C22⋊C4—201no—
404#217—22no—
405#217—54no—
406#217—102no—
407#217—201no—
408#217C4×D514yes—
409C4⋊Dic3—54no—
410Dic3⋊C4—54no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413Dic3⋊C4—102no—
414Dic3⋊C4—102no—
415Dic3⋊C4—102no—
416C4×Dic3—22no—
417C4×Dic3—41no—
418C4×Dic3—54no—
419C4×Dic3—102no—
420C4×Dic3—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5C2×C4×D312yes—
426C23×C5#23712yes—
427C23×C5#23712yes—
428C23×C5C23×D311yescharacteristic
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—21no—
434C22×D5—21no—
435C22×D5C2×C4×D312yes—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—32no—
442C2×C4×C5—32no—
443C2×C4×C5—44no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
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×C5D3×D412yes—
455C22⋊D5—28no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—32no—
465C2×Dic5—32no—
466C2×Dic5—32no—
467C2×Dic5—32no—
468C2×Dic5—32no—
469C2×Dic5—68no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—124no—
478C2×Dic5C2×C4×D312yes—
479C4×D5—68no—
480C22×D4—51no—
481C23×C4—151no—
482C23×C4—151no—
483C23×C4—151no—
484C23×C4D3×D511yescharacteristic
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×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—304no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4—151no—
502C2×C22⋊C4—151no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—31no—
509#95—31no—
510#95—51no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95—151no—
518C2×C3×C5—24no—
519C2×C3×C5C2×#11711yescharacteristic
520C2×C3×C5C2×C4×D411yescharacteristic
521C2×C3×C5#52011yescharacteristic
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5#54811yescharacteristic
524C2×C3×C5#55211yescharacteristic
525C2×C3×C5#55311yescharacteristic
526C3×D5—42no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—52no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3C2×C4×D512yes—
539C23×C3#70912yes—
540C23×C3#70912yes—
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—44no—
549C2×C3×C4—52no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4D4×D512yes—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—52no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—52no—
574C2×Dic3—108no—
575C2×Dic3—108no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—204no—
584C2×Dic3C2×C4×D512yes—
585C2×Dic3C2×C4×D512yes—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5#87714yescomplemented
593C22×C5C22×C4×D311yescharacteristic
594C22×C5C2×D3×D411yescharacteristic
595C22×C5C2×#23711yescharacteristic
596C22×C5C2×#23711yescharacteristic
597C22×C5#100411yescharacteristic
598C22×C5D3×#4111yescharacteristic
599C22×C5#101011yescharacteristic
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—22no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C4×C5—22no—
608C4×C5—41no—
609C4×C5—62no—
610C4×C5—62no—
611C4×C5—121no—
612C4×C5—121no—
613Dic5—22no—
614Dic5—34no—
615Dic5—41no—
616Dic5—41no—
617Dic5—62no—
618Dic5—62no—
619Dic5—121no—
620C24—51no—
621C24C2×D3×D511yescharacteristic
622C2×D4—54no—
623C2×D4—102no—
624C2×D4—102no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—41no—
632C22×C4—51no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—154no—
636C22×C4—151no—
637C22×C4—154no—
638C22×C4—151no—
639C22×C4—151no—
640C22×C4—151no—
641C22×C4—302no—
642C22×C4—302no—
643C22×C4—302no—
644C22×C4—302no—
645C22×C4—302no—
646C22×C4—302no—
647C22×C4—601no—
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C22⋊C4—34no—
658C22⋊C4—62no—
659C22⋊C4—102no—
660C22⋊C4—102no—
661C22⋊C4—154no—
662C22⋊C4—201no—
663C22⋊C4—302no—
664C22⋊C4—601no—
665C42—62no—
666C42—121no—
667C42—154no—
668C42—302no—
669C42—601no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3—102no—
680C22×C3—201no—
681C22×C3—201no—
682C22×C3—201no—
683C22×C3—201no—
684C22×C3#401814yescomplemented
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C2×#70911yescharacteristic
687C22×C3C2×#70911yescharacteristic
688C22×C3C2×D4×D511yescharacteristic
689C22×C3#414411yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3#415011yescharacteristic
692C3×C4—22no—
693C3×C4—41no—
694C3×C4—102no—
695C3×C4—201no—
696C3×C4—201no—
697Dic3—22no—
698Dic3—22no—
699Dic3—41no—
700Dic3—41no—
701Dic3—54no—
702Dic3—102no—
703Dic3—102no—
704Dic3—201no—
705C2×C5—24no—
706C2×C5C2×#87711yescharacteristic
707C2×C5C4×D3×D411yescharacteristic
708C2×C5#554611yescharacteristic
709C2×C5#559111yescharacteristic
710C2×C5#559811yescharacteristic
711C2×C5#560111yescharacteristic
712C2×C5#565011yescharacteristic
713D5—42no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—52no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23#676512yes—
726C23C4×D3×D512yes—
727C23#677912yes—
728C23C22×D3×D511yescharacteristic
729D4—108no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—44no—
738C2×C4—52no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—152no—
758C2×C4—152no—
759C2×C4—152no—
760C2×C4—152no—
761C2×C4—152no—
762C2×C4—308no—
763C2×C4—308no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—301no—
771C2×C4—604no—
772C2×C4#679012yes—
773C2×C3—24no—
774C2×C3—202no—
775C2×C3C2×#401811yescharacteristic
776C2×C3#6582411yescharacteristic
777C2×C3#6586511yescharacteristic
778C2×C3#6587411yescharacteristic
779C2×C3C4×D4×D511yescharacteristic
780C2×C3#6588011yescharacteristic
781C2×C3#6588611yescharacteristic
782C5#7467311yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—102no—
790C22—102no—
791C22—102no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22#9139314yescomplemented
797C22C2×#676511yescharacteristic
798C22#9200111yescharacteristic
799C22C2×C4×D3×D511yescharacteristic
800C22#9201611yescharacteristic
801C22C2×#677911yescharacteristic
802C22C2×#679011yescharacteristic
803C22#9204911yescharacteristic
804C4—22no—
805C4—41no—
806C4—62no—
807C4—62no—
808C4—102no—
809C4—121no—
810C4—121no—
811C4—154no—
812C4—201no—
813C4—201no—
814C4—302no—
815C4—302no—
816C4—601no—
817C3#1060519211yescharacteristic, complemented, Sylow
818C2—24no—
819C2—202no—
820C2C2×#9139311yescharacteristic
821C2#1175428611yescharacteristic
822C2#1175436911yescharacteristic
823C2#1175444611yescharacteristic
824C2#1175444811yescharacteristic
825C2C4×#679011yescharacteristic
826C2#1175539811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6712C2semidirect
3. C2×#91393C2semidirect
4. C4×C5×#217C2semidirect
6. #11749516C2semidirect
8. #11749487C2semidirect
9. #11748885C2semidirect
10. #11748806C2semidirect
11. #11748707C2semidirect
12. #11748706C2semidirect
13. #11748650C2semidirect
14. #11748645C2semidirect
15. #11748644C2semidirect
34. #91559C4semidirect
100. C2×D5×Dic3C2×C4semidirect
104. #6712D4semidirect
114. #6668C2×C4semidirect
117. #6665C2×C4semidirect
120. Dic3×Dic5C2×C4semidirect
126. C4×#217D5semidirect
343. C22×C3×C5#117semidirect
592. C22×C5#877semidirect
670. C3×C5#2352semidirect
684. C22×C3#4018semidirect
782. C5#74673semidirect
796. C22#91393semidirect
817. C3#10605192semidirect

Maximal subgroups

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

subgroupindex
C22×#67122
C2×#915592
C2×#913932
C4×C5×#2172
C3×#655022
#117495162
#117495002
#117494872
#117488852
#117488062
#117487072
#117487062
#117486502
#117486452
#117486442
#106051923
#746735