Finite Group Databasebeta

← #14326332

Subgroups — #14326332

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#892C211yesmaximal, characteristic, complemented
2C2×#91473C211yesmaximal, characteristic
3C2×D3×#685C211yesmaximal, characteristic
4#11751090C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic
7#11748902C211yesmaximal, characteristic, complemented
8#11748887C211yesmaximal, characteristic, complemented
9#11748881C211yesmaximal, characteristic, complemented
10Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11748777C211yesmaximal, characteristic, complemented
12#11748771C211yesmaximal, characteristic, complemented
13C4×#6667C211yesmaximal, characteristic, complemented
14#11748706C211yesmaximal, characteristic, complemented
15#11748705C211yesmaximal, characteristic, complemented
16#10614002—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6712C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
29C2×C4×C5×Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C5×#892—24no—
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45#91473—24no—
46D3×#685C418yescomplemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75833—51nomaximal, Hall
56C2×C5×#117—31no—
57C22×#685—31no—
58C2×D5×C22⋊C4—31no—
59#65500—31no—
60#65279—31no—
61#65279D311yescharacteristic, complemented
62#65278—31no—
63#65278—31no—
64#65244—31no—
65#65231—31no—
66C22⋊C4×Dic5—31no—
67#65229—31no—
68#65229—31no—
69C4×#685—31no—
70C4×#685—31no—
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×D3×D5—22no—
75C22×D3×D5—22no—
76C22×D3×D5—22no—
77C22×D3×D5—22no—
78C22×D3×D5—41no—
79C22×D3×D5—41no—
80C22×D3×D5C2×C414yes—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C4×D15—22no—
88C2×C4×D15—22no—
89C2×C4×D15—41no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—22no—
95C2×C4×C5×D3C2×C414yescomplemented
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—41no—
102C2×D3×Dic5—41no—
103C2×D3×Dic5—41no—
104C2×D3×Dic5C2×C414yescomplemented
105C3×C5×C4⋊C4—22no—
106#6714—22no—
107#6714C2×C414yes—
108#6712—41no—
109C5×(C2×D3)⋊C4—22no—
110C5×(C2×D3)⋊C4D414yes—
111C5×C4⋊Dic3—22no—
112C4×C5×Dic3—22no—
113C4×C5×Dic3—22no—
114C3×#685—22no—
115C3×#685—41no—
116C3×#685C2×C414yescomplemented
117C3×C4×Dic5—41no—
118#6669—41no—
119#6667—22no—
120#6667C2×C414yes—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—22no—
123#6665—22no—
124#6665—41no—
125#6665C2×C414yescomplemented
126Dic3×Dic5—41no—
127C2×#892D511yescharacteristic, complemented
128C2×D3×C22⋊C4—51no—
129C2×D3×C22⋊C4—51no—
130C3×#388—51no—
131#4989—51no—
132#4955—51no—
133#4951—51no—
134#4945—51no—
135#4944—51no—
136C4×(C2×D3)⋊C4—51no—
137C4×(C2×D3)⋊C4—51no—
138#4668—51no—
139#4667—51no—
140#4666—51no—
141#4664—51no—
142C24×D5—31no—
143C23×C4×C5—31no—
144C23×Dic5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C5×#117—64no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C42×C5—31no—
153C2×C42×C5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—38no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×#683—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5C2×D311yescharacteristic, complemented
171D5×C22⋊C4—64no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic, complemented
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×D15#4112yes—
188C22×D15#4112yes—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3C22×C412yes—
194C22×C5×D3C2×D412yes—
195C22×C5×D3#4112yes—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5C22×C412yes—
203C2×D3×D5—28no—
204C2×D3×D5—28no—
205C2×D3×D5—44no—
206C2×D3×D5—44no—
207C2×D3×D5—44no—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5C22×C412yes—
218C2×C3×C4×C5C2×D412yes—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C4×D15—44no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3C22×C412yes—
237C2×C5×Dic3C2×D412yes—
238C4×C5×D3—28no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C22×C412yes—
248#1200—44no—
249D3×Dic5—44no—
250C24×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3C2×D511yescharacteristic
255C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C42—51no—
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4C2×D511yescharacteristic
270C2×(C2×D3)⋊C4C2×D511yescharacteristic
271C2×C4⋊Dic3C2×D511yescharacteristic, complemented
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3C2×D511yescharacteristic, complemented
276C2×C4×Dic3C2×D511yescharacteristic, complemented
277#892—24no—
278D3×C22⋊C4—58no—
279D3×C22⋊C4—104no—
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C23×D5—31no—
290C23×D5—34no—
291C23×D5—62no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—34no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—31no—
308C22×Dic5—34no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—121no—
312C22×Dic5—121no—
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—22no—
323C5×C4⋊C4—62no—
324C5×C22⋊C4—34no—
325C5×C22⋊C4—62no—
326C42×C5—62no—
327C42×C5—62no—
328C22⋊Dic5—62no—
329C22⋊Dic5—62no—
330#685—22no—
331#685—34no—
332#685—34no—
333#685—34no—
334#685—41no—
335#685—62no—
336#685—62no—
337#685—62no—
338#685—121no—
339#685C4×D314yescomplemented
340#683—121no—
341#683—121no—
342C4×Dic5—41no—
343C4×Dic5—121no—
344C2×#117—31no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—51no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5C23×C411yescharacteristic
360C22×C3×C5C22×D411yescharacteristic
361C22×C3×C5C2×#4111yescharacteristic
362C22×C3×C5C2×#4111yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C2×D15—22no—
367C2×D15—22no—
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15#11714yescomplemented
373C2×C5×D3—22no—
374C2×C5×D3—22no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3C4×D414yes—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387D3×D5—416no—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390C3×C4×C5—41no—
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3—51no—
401C23×D3—51no—
402C23×D3—54no—
403C23×D3—102no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—201no—
408C23×D3—201no—
409C23×D3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—54no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—201no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3C4×D514yescomplemented
434C3×C4⋊C4—22no—
435C3×C22⋊C4—54no—
436C3×C22⋊C4—102no—
437C3×C22⋊C4—201no—
438C3×C42—201no—
439#217—54no—
440#217—102no—
441#217—201no—
442(C2×D3)⋊C4—22no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—54no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—102no—
448(C2×D3)⋊C4—102no—
449(C2×D3)⋊C4C22⋊D514yes—
450C4⋊Dic3—22no—
451Dic3⋊C4—201no—
452Dic3⋊C4—201no—
453C4×Dic3—22no—
454C4×Dic3—22no—
455C4×Dic3—201no—
456C23×C5—32no—
457C23×C5—32no—
458C23×C5—32no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—61no—
462C23×C5—61no—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—32no—
471C22×D5—32no—
472C22×D5—32no—
473C22×D5—68no—
474C22×D5—68no—
475C22×D5—61no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—124no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5—124no—
483C22×D5—124no—
484C22×D5C2×C4×D312yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
494C2×C4×C5—68no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5C2×C4×D312yes—
503C2×C4×C5D3×D412yes—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—32no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—124no—
522C2×Dic5C2×C4×D312yes—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—31no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—64no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4D3×D511yescharacteristic, complemented
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—158no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—151no—
550C2×C22⋊C4—304no—
551C2×C42—31no—
552C2×C42—31no—
553C2×C42—51no—
554C2×C42—151no—
555#95—51no—
556#95—51no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5C2×#11711yescharacteristic
564C2×C3×C5C2×C4×D411yescharacteristic
565C2×C3×C5#51811yescharacteristic
566C2×C3×C5#54611yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#55111yescharacteristic
569C2×C3×C5#55111yescharacteristic
570D15—24no—
571C3×D5—42no—
572C5×D3—24no—
573C23×C3—52no—
574C23×C3—101no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3C23×D511yescharacteristic
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—52no—
586C22×D3—52no—
587C22×D3—52no—
588C22×D3—108no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—108no—
594C22×D3—204no—
595C22×D3—204no—
596C22×D3—204no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3C2×C4×D512yes—
600C22×D3#70912yes—
601C22×D3C2×C22⋊D512yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—52no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4C2×C4×D512yes—
619C2×C3×C4C2×C22⋊D512yes—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—52no—
628C2×Dic3—101no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3C2×C4×D512yes—
637C2×Dic3C2×C22⋊D512yes—
638C4×D3—28no—
639C4×D3—204no—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—34no—
643C22×C5—62no—
644C22×C5—62no—
645C22×C5—62no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×D3×D411yescharacteristic
651C22×C5#100411yescharacteristic
652C22×C5D3×#4111yescharacteristic
653C22×C5D3×#4111yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—34no—
660C2×D5—41no—
661C2×D5—41no—
662C2×D5—41no—
663C2×D5—41no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—62no—
670C2×D5—1216no—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—41no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—41no—
679Dic5—41no—
680Dic5—62no—
681Dic5—121no—
682Dic5—121no—
683C24—31no—
684C24—51no—
685C24—154no—
686C24—151no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—302no—
691C24—601no—
692C24—601no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—154no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—302no—
707C22×C4—302no—
708C22×C4—302no—
709C22×C4—302no—
710C22×C4—601no—
711C22×C4—601no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—22no—
718C4⋊C4—62no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—54no—
723C22⋊C4—62no—
724C22⋊C4—102no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—201no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—302no—
734C22⋊C4—601no—
735C42—62no—
736C42—62no—
737C42—201no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—102no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—201no—
744C22×C3—201no—
745C22×C3—201no—
746C22×C3—201no—
747C22×C3C22×C4×D511yescharacteristic
748C22×C3C2×#70911yescharacteristic
749C22×C3D5×#4111yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3#414911yescharacteristic
752C22×C3#414911yescharacteristic
753C22×C3C22×C22⋊D511yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—54no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—2016no—
768C2×D3C4×C22⋊D514yes—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—41no—
772C3×C4—102no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—41no—
778Dic3—102no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—64no—
782C2×C5D3×#11711yescharacteristic
783C2×C5C4×D3×D411yescharacteristic
784C2×C5#554511yescharacteristic
785C2×C5#561011yescharacteristic
786C2×C5#565911yescharacteristic
787C2×C5#567611yescharacteristic
788C2×C5#570511yescharacteristic
789D5—42no—
790D5—64no—
791C23—32no—
792C23—32no—
793C23—32no—
794C23—52no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—101no—
800C23—101no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—152no—
806C23—152no—
807C23—152no—
808C23—308no—
809C23—308no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—301no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23—604no—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—52no—
830C2×C4—68no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—152no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—604no—
856C2×C4—604no—
857C2×C4—604no—
858C2×C4C4×D3×D512yes—
859C2×C4D3×C22⋊D512yes—
860C2×C3—202no—
861C2×C3D5×#11711yescharacteristic
862C2×C3#6585511yescharacteristic
863C2×C3#6586111yescharacteristic
864C2×C3#6586111yescharacteristic
865C2×C3C2×C4×C22⋊D511yescharacteristic
866C2×C3#6616311yescharacteristic
867C2×C3#6616311yescharacteristic
868D3—24no—
869D3—104no—
870C5#7583311yescharacteristic, complemented, Sylow
871C22—34no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—154no—
882C22—201no—
883C22—201no—
884C22—201no—
885C22—201no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22C2×C4×D3×D511yescharacteristic
894C22D3×#70911yescharacteristic
895C22#9202411yescharacteristic
896C22#9202611yescharacteristic
897C22#9203411yescharacteristic
898C22#9203511yescharacteristic
899C22C2×D3×C22⋊D511yescharacteristic
900C4—22no—
901C4—22no—
902C4—41no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—121no—
907C4—201no—
908C4—201no—
909C4—302no—
910C4—601no—
911C4—601no—
912C3#1061400211yescharacteristic, complemented, Sylow
913C2—64no—
914C2—202no—
915C2—304no—
916C2#1175383511yescharacteristic
917C2#1175383911yescharacteristic
918C2#1175391911yescharacteristic
919C2#1175392111yescharacteristic
920C2C4×D3×C22⋊D511yescharacteristic
921C2#1175506911yescharacteristic
922C2#1175528011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#892C2semidirect
4. #11751090C2semidirect
5. C3×#65279C2semidirect
7. #11748902C2semidirect
8. #11748887C2semidirect
9. #11748881C2semidirect
10. Dic5×(C2×D3)⋊C4C2semidirect
11. #11748777C2semidirect
12. #11748771C2semidirect
13. C4×#6667C2semidirect
14. #11748706C2semidirect
15. #11748705C2semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
25. C2×#6712C22semidirect
28. C2×C5×C4⋊Dic3C22semidirect
29. C2×C4×C5×Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C2×#6669C22semidirect
44. C2×Dic3×Dic5C22semidirect
46. D3×#685C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
61. #65279D3semidirect
95. C2×C4×C5×D3C2×C4semidirect
104. C2×D3×Dic5C2×C4semidirect
116. C3×#685C2×C4semidirect
125. #6665C2×C4semidirect
127. C2×#892D5semidirect
149. C2×C5×C4⋊C4C2×D3semidirect
170. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
255. C2×C3×C4⋊C4C2×D5semidirect
271. C2×C4⋊Dic3C2×D5semidirect
275. C2×C4×Dic3C2×D5semidirect
276. C2×C4×Dic3C2×D5semidirect
339. #685C4×D3semidirect
372. C2×D15#117semidirect
433. C2×C4×D3C4×D5semidirect
534. C2×C4⋊C4D3×D5semidirect
739. C3×C5#2342semidirect
870. C5#75833semidirect
912. C3#10614002semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8922
C2×#914732
C2×D3×#6852
#117510902
C3×#652792
#117489402
#117489022
#117488872
#117488812
Dic5×(C2×D3)⋊C42
#117487772
#117487712
C4×#66672
#117487062
#117487052
#106140023
#758335