Finite Group Databasebeta

← #14327323

Subgroups — #14327323

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×#91770C211yesmaximal, characteristic
3C2×#91761C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5#11751314C211yesmaximal, characteristic
6#11751059C211yesmaximal, characteristic
7#11751043C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
9#11751041C211yesmaximal, characteristic, complemented
10#11751034C211yesmaximal, characteristic, complemented
11C4×#6712C211yesmaximal, characteristic, complemented
12#11750770C211yesmaximal, characteristic, complemented
13#11750768C211yesmaximal, characteristic, complemented
14#11750753C211yesmaximal, characteristic, complemented
15#11750751C211yesmaximal, characteristic, complemented
16#10605192—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6712—24no—
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×#6712C2211yescharacteristic
38C2×#6712C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43#91770C418yescomplemented
44#91761—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#73461—51nomaximal, Hall
56C22×#683—31no—
57C2×#4027—31no—
58C2×#4018—31no—
59C4×C5×C22⋊C4D311yescharacteristic, complemented
60#65502—31no—
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×D15C2311yescharacteristic
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220C2×C414yes—
85C22×Dic15—22no—
86C22×Dic15—22no—
87C22×Dic15—22no—
88C22×Dic15—22no—
89C22×Dic15—41no—
90C22×Dic15C2×C414yes—
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×C4×D15—22no—
99C2×C4×D15—22no—
100C2×C4×D15C2×C414yescomplemented
101C3×C5×C22⋊C4—22no—
102C3×C5×C22⋊C4C2×C414yes—
103C3×C42×C5—22no—
104C3×C42×C5—41no—
105#6719—22no—
106#6714—22no—
107#6714—22no—
108#6714—41no—
109#6714—41no—
110#6714C2×C414yescomplemented
111#6712—22no—
112#6712—22no—
113#6712—22no—
114#6712—22no—
115#6712—22no—
116#6712C2×C414yescomplemented
117#6712D414yescomplemented
118C4×Dic15—22no—
119C4×Dic15—41no—
120C4×Dic15C2×C414yescomplemented
121C22×Dic3⋊C4—51no—
122C2×#67⋊C4—51no—
123C2×#872—51no—
124C3×C4×C22⋊C4D511yescharacteristic, complemented
125#5213—51no—
126#4958—51no—
127#4942—51no—
128Dic3×C22⋊C4—51no—
129#4940—51no—
130#4933—51no—
131C4×Dic3⋊C4—51no—
132#4669—51no—
133#4667—51no—
134#4652—51no—
135#4650—51no—
136C23×C4×C5C2×D311yescharacteristic
137C22×C22⋊D5—31no—
138C23×Dic5—31no—
139C23×Dic5—31no—
140C22×C4×D5—31no—
141C2×C5×C22⋊C4C2×D311yescharacteristic
142C2×C5×C22⋊C4C2×D311yescharacteristic
143C2×C42×C5C2×D311yescharacteristic
144C2×C42×C5C2×D311yescharacteristic
145C2×C22⋊Dic5—31no—
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
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×#95C2×D311yescharacteristic
165C5×#95C2×D311yescharacteristic
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
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×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15C22×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—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—44no—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C22×C412yes—
208C2×C3×C4×C5C2×D412yes—
209#1220—28no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—28no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—44no—
227C2×Dic15C22×C412yes—
228C2×Dic15C22×C412yes—
229C2×Dic15C22×C412yes—
230C2×Dic15C2×D412yes—
231C2×Dic15C2×D412yes—
232C2×Dic15#4112yes—
233C4×D15—28no—
234C23×C3×C4C2×D511yescharacteristic
235C22×#67—51no—
236C23×Dic3—51no—
237C23×Dic3—51no—
238C22×C4×D3—51no—
239C2×C3×C22⋊C4C2×D511yescharacteristic
240C2×C3×C22⋊C4C2×D511yescharacteristic
241C2×C3×C42C2×D511yescharacteristic
242C2×C3×C42C2×D511yescharacteristic
243C2×#217—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—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—51no—
256C2×Dic3⋊C4—104no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260#67⋊C4—58no—
261#872—104no—
262C3×#95C2×D511yescharacteristic
263C3×#95C2×D511yescharacteristic
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C24×C5C22×D311yescharacteristic
273C23×D5—31no—
274C22×C4×C5—22no—
275C22×C4×C5—22no—
276C22×C4×C5—41no—
277C22×C4×C5C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—34no—
284C2×C22⋊D5—62no—
285C2×C22⋊D5—62no—
286C22×Dic5—31no—
287C22×Dic5—34no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—62no—
295C22×Dic5—62no—
296C22×Dic5—62no—
297C22×Dic5—62no—
298C22×Dic5—121no—
299C2×C4×D5—34no—
300C2×C4×D5—62no—
301C2×C4×D5—62no—
302C5×C22⋊C4—22no—
303C5×C22⋊C4C4×D314yes—
304C42×C5—22no—
305C42×C5—41no—
306C22⋊Dic5—62no—
307#685—34no—
308#685—62no—
309#685—62no—
310#685—121no—
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—151no—
330#386—151no—
331#382—151no—
332#380—151no—
333#380—151no—
334C4×C4⋊C4—151no—
335C4×C22⋊C4—151no—
336C4×C22⋊C4D1511yescharacteristic, complemented
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×D15—22no—
352C2×D15—22no—
353C2×D15—22no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—41no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—22no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364Dic15—22no—
365Dic15—22no—
366Dic15—22no—
367Dic15—41no—
368Dic15—41no—
369Dic15—41no—
370Dic15C4×D414yes—
371C24×C3C22×D511yescharacteristic
372C23×D3—51no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—41no—
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—54no—
383C2×#67—102no—
384C2×#67—102no—
385C22×Dic3—51no—
386C22×Dic3—54no—
387C22×Dic3—51no—
388C22×Dic3—51no—
389C22×Dic3—51no—
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—51no—
393C22×Dic3—102no—
394C22×Dic3—102no—
395C22×Dic3—102no—
396C22×Dic3—102no—
397C22×Dic3—201no—
398C2×C4×D3—54no—
399C2×C4×D3—102no—
400C2×C4×D3—102no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4C4×D514yes—
403C3×C42—22no—
404C3×C42—41no—
405#217—102no—
406(C2×D3)⋊C4—54no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4—102no—
409(C2×D3)⋊C4—201no—
410(C2×D3)⋊C4—201no—
411Dic3⋊C4—54no—
412Dic3⋊C4—54no—
413Dic3⋊C4—102no—
414Dic3⋊C4—102no—
415Dic3⋊C4—102no—
416Dic3⋊C4—102no—
417Dic3⋊C4—102no—
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#23512yes—
427C23×C5#23512yes—
428C23×C5C23×D311yescharacteristic
429C22×D5—32no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
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—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—44no—
452C2×C4×C5C2×C4×D312yes—
453C2×C4×C5C2×C4×D312yes—
454C2×C4×C5D3×D412yes—
455C22⋊D5—68no—
456C2×Dic5—32no—
457C2×Dic5—32no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—68no—
463C2×Dic5—61no—
464C2×Dic5—61no—
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—61no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—124no—
479C4×D5—68no—
480C22×D4—151no—
481C23×C4—151no—
482C23×C4—151no—
483C23×C4—151no—
484C23×C4C2×D1511yescharacteristic
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—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—151no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4C2×D1511yescharacteristic
502C2×C22⋊C4C2×D1511yescharacteristic
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42C2×D1511yescharacteristic
507C2×C42C2×D1511yescharacteristic
508#95—151no—
509#95—151no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95C2×D1511yescharacteristic
517#95C2×D1511yescharacteristic
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
526D15—42no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3C2×C4×D512yes—
532C23×C3#70912yes—
533C23×C3#70912yes—
534C23×C3C23×D511yescharacteristic
535C22×D3—52no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C22×D3—101no—
541C22×D3—101no—
542C2×C3×C4—21no—
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—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—44no—
558C2×C3×C4C2×C4×D512yes—
559C2×C3×C4C2×C4×D512yes—
560C2×C3×C4D4×D512yes—
561#67—108no—
562C2×Dic3—52no—
563C2×Dic3—52no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—52no—
567C2×Dic3—52no—
568C2×Dic3—108no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—101no—
584C2×Dic3—204no—
585C4×D3—108no—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5#87214yescomplemented
593C22×C5C22×C4×D311yescharacteristic
594C22×C5C2×#23511yescharacteristic
595C22×C5C2×#23511yescharacteristic
596C22×C5C2×D3×D411yescharacteristic
597C22×C5#100411yescharacteristic
598C22×C5D3×#4111yescharacteristic
599C22×C5#101011yescharacteristic
600C2×D5—62no—
601C2×D5—62no—
602C2×D5—62no—
603C2×D5—121no—
604C2×D5—121no—
605C2×D5—121no—
606C2×D5—121no—
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—22no—
610C4×C5—41no—
611C4×C5—41no—
612C4×C5—41no—
613Dic5—34no—
614Dic5—62no—
615Dic5—62no—
616Dic5—62no—
617Dic5—121no—
618Dic5—121no—
619Dic5—121no—
620C24—151no—
621C24C22×D1511yescharacteristic
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—151no—
629C22×C4—154no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—154no—
634C22×C4—151no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—302no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4—302no—
642C22×C4—302no—
643C22×C4—601no—
644C22×C4C22×D1511yescharacteristic
645C22×C4C22×D1511yescharacteristic
646C22×C4C22×D1511yescharacteristic
647C22×C4C22×D1511yescharacteristic
648C22×C4C22×D1511yescharacteristic
649C22×C4C22×D1511yescharacteristic
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C22⋊C4—22no—
658C22⋊C4—154no—
659C22⋊C4—302no—
660C22⋊C4—302no—
661C22⋊C4—302no—
662C22⋊C4—601no—
663C22⋊C4—601no—
664C22⋊C4C4×D1514yes—
665C42—22no—
666C42—41no—
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#401814yescomplemented
678C22×C3C22×C4×D511yescharacteristic
679C22×C3C2×#70911yescharacteristic
680C22×C3C2×#70911yescharacteristic
681C22×C3C2×D4×D511yescharacteristic
682C22×C3#414411yescharacteristic
683C22×C3D5×#4111yescharacteristic
684C22×C3#415011yescharacteristic
685C2×D3—102no—
686C2×D3—102no—
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—201no—
691C2×D3—201no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698Dic3—54no—
699Dic3—102no—
700Dic3—102no—
701Dic3—102no—
702Dic3—201no—
703Dic3—201no—
704Dic3—201no—
705C2×C5—24no—
706C2×C5C2×#87211yescharacteristic
707C2×C5#549011yescharacteristic
708C2×C5#553111yescharacteristic
709C2×C5#554011yescharacteristic
710C2×C5C4×D3×D411yescharacteristic
711C2×C5#554611yescharacteristic
712C2×C5#555211yescharacteristic
713D5—122no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—152no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23—301no—
725C23C2×C4×D1512yes—
726C23#681712yes—
727C23#681712yes—
728C23C23×D1511yescharacteristic
729D4—308no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—152no—
747C2×C4—152no—
748C2×C4—152no—
749C2×C4—152no—
750C2×C4—152no—
751C2×C4—152no—
752C2×C4—308no—
753C2×C4—308no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—604no—
770C2×C4C2×C4×D1512yes—
771C2×C4C2×C4×D1512yes—
772C2×C4D4×D1512yes—
773C2×C3—24no—
774C2×C3C2×#401811yescharacteristic
775C2×C3#6582411yescharacteristic
776C2×C3#6586511yescharacteristic
777C2×C3#6587411yescharacteristic
778C2×C3C4×D4×D511yescharacteristic
779C2×C3#6588011yescharacteristic
780C2×C3#6588611yescharacteristic
781D3—202no—
782C5#7346111yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—302no—
790C22—302no—
791C22—302no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22#9176114yescomplemented
797C22C22×C4×D1511yescharacteristic
798C22C2×#681711yescharacteristic
799C22C2×#681711yescharacteristic
800C22C2×D4×D1511yescharacteristic
801C22#9209511yescharacteristic
802C22#41×D1511yescharacteristic
803C22#9210111yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—154no—
811C4—302no—
812C4—302no—
813C4—302no—
814C4—601no—
815C4—601no—
816C4—601no—
817C3#1060519211yescharacteristic, complemented, Sylow
818C2—24no—
819C2—602no—
820C2C2×#9176111yescharacteristic
821C2#1175624911yescharacteristic
822C2#1175629011yescharacteristic
823C2#1175629911yescharacteristic
824C2C4×D4×D1511yescharacteristic
825C2#1175630511yescharacteristic
826C2#1175631111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C4×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#2352
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
1. C22×#6712C2semidirect
3. C2×#91761C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
7. #11751043C2semidirect
8. C22⋊C4×Dic15C2semidirect
9. #11751041C2semidirect
10. #11751034C2semidirect
11. C4×#6712C2semidirect
12. #11750770C2semidirect
13. #11750768C2semidirect
14. #11750753C2semidirect
15. #11750751C2semidirect
43. #91770C4semidirect
59. C4×C5×C22⋊C4D3semidirect
100. C2×C4×D15C2×C4semidirect
110. #6714C2×C4semidirect
116. #6712C2×C4semidirect
117. #6712D4semidirect
120. C4×Dic15C2×C4semidirect
124. C3×C4×C22⋊C4D5semidirect
336. C4×C22⋊C4D15semidirect
343. C22×C3×C5#117semidirect
592. C22×C5#872semidirect
670. C3×C5#2352semidirect
677. C22×C3#4018semidirect
782. C5#73461semidirect
796. C22#91761semidirect
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×#917702
C2×#917612
C3×C4×C5×C22⋊C42
#117513142
#117510592
#117510432
C22⋊C4×Dic152
#117510412
#117510342
C4×#67122
#117507702
#117507682
#117507532
#117507512
#106051923
#734615