Finite Group Databasebeta

← #14326238

Subgroups — #14326238

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×#91781C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D15C211yesmaximal, characteristic
3C2×C22⋊C4×D15C211yesmaximal, characteristic
4C3×C5×#388C211yesmaximal, characteristic, complemented
5#11751090C211yesmaximal, characteristic, complemented
6#11751056C211yesmaximal, characteristic
7#11751052C211yesmaximal, characteristic, complemented
8#11751046C211yesmaximal, characteristic, complemented
9#11751045C211yesmaximal, characteristic, complemented
10C4×#6714C211yesmaximal, characteristic, complemented
11C4×#6714C211yesmaximal, characteristic, complemented
12#11750769C211yesmaximal, characteristic, complemented
13#11750768C211yesmaximal, characteristic, complemented
14#11750767C211yesmaximal, characteristic, complemented
15#11750765C211yesmaximal, characteristic, complemented
16#10607564—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×#6719C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic, complemented
39C2×#6712C2211yescharacteristic, complemented
40C2×#6712C2211yescharacteristic, complemented
41C2×C4×Dic15C2211yescharacteristic, complemented
42C2×C4×Dic15C2211yescharacteristic, complemented
43C2×C4×Dic15C2211yescharacteristic, complemented
44#91781—24no—
45C22⋊C4×D15—24no—
46C22⋊C4×D15C418yescomplemented
47C3×C5×#95C2211yescharacteristic, complemented
48C3×C5×#95C2211yescharacteristic, complemented
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#75833—51nomaximal, Hall
56C2×#4038—31no—
57C2×D5×C22⋊C4—31no—
58C2×D5×C22⋊C4—31no—
59C5×#388D311yescharacteristic, complemented
60#65278—31no—
61#65244—31no—
62#65240—31no—
63#65234—31no—
64#65233—31no—
65C4×#685—31no—
66C4×#685—31no—
67#64957—31no—
68#64956—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15—22no—
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15C2×C414yes—
79C23×D15C2311yescharacteristic
80C23×D15C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×C4×D15—22no—
94C2×C4×D15—22no—
95C2×C4×D15—22no—
96C2×C4×D15—22no—
97C2×C4×D15—22no—
98C2×C4×D15—22no—
99C2×C4×D15—41no—
100C2×C4×D15—41no—
101C2×C4×D15—41no—
102C2×C4×D15—41no—
103C2×C4×D15C2×C414yescomplemented
104C2×C4×D15C2×C414yescomplemented
105C3×C5×C4⋊C4—22no—
106C3×C5×C22⋊C4—22no—
107C3×C5×C22⋊C4—41no—
108C3×C5×C22⋊C4C2×C414yescomplemented
109C3×C42×C5—41no—
110#6719—22no—
111#6719—41no—
112#6719C2×C414yescomplemented
113#6714—22no—
114#6714—22no—
115#6714—22no—
116#6714—22no—
117#6714—22no—
118#6714C2×C414yes—
119#6714C2×C414yes—
120#6714D414yes—
121C4⋊Dic15—22no—
122#6712—41no—
123#6712—41no—
124C4×Dic15—22no—
125C4×Dic15—22no—
126C4×Dic15—41no—
127C2×#892—51no—
128C2×D3×C22⋊C4—51no—
129C2×D3×C22⋊C4—51no—
130C3×#388D511yescharacteristic, complemented
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—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
148C2×C5×C22⋊C4C2×D311yescharacteristic
149C2×C5×C22⋊C4C2×D311yescharacteristic
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5C2×D311yescharacteristic, complemented
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×C4⋊Dic5—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169#4038—64no—
170D5×C22⋊C4—38no—
171D5×C22⋊C4—64no—
172C5×#95C2×D311yescharacteristic, complemented
173C5×#95C2×D311yescharacteristic, complemented
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2342—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—28no—
198C22×D15—28no—
199C22×D15—44no—
200C22×D15—44no—
201C22×D15—44no—
202C22×D15—44no—
203C22×D15—44no—
204C22×D15C22×C412yes—
205C22×D15C22×C412yes—
206C22×D15C2×D412yes—
207C22×D15#4112yes—
208C22×D15#4112yes—
209C22×D15#4112yes—
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×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C22×C412yes—
226C2×C3×C4×C5C22×C412yes—
227C2×C3×C4×C5C2×D412yes—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15C22×C412yes—
244C2×Dic15C22×C412yes—
245C2×Dic15C2×D412yes—
246C4×D15—28no—
247C4×D15—44no—
248C4×D15—44no—
249C4×D15—44no—
250C24×D3—51no—
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
256C2×C3×C22⋊C4C2×D511yescharacteristic
257C2×C3×C22⋊C4C2×D511yescharacteristic
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42C2×D511yescharacteristic, complemented
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)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277#892—104no—
278D3×C22⋊C4—58no—
279D3×C22⋊C4—104no—
280C3×#95C2×D511yescharacteristic, complemented
281C3×#95C2×D511yescharacteristic, complemented
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5C22×D311yescharacteristic
289C23×D5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—62no—
296C23×D5—121no—
297C23×D5—121no—
298C22×C4×C5C22×D311yescharacteristic
299C22×C4×C5C22×D311yescharacteristic
300C22×C4×C5C22×D311yescharacteristic
301C22×C4×C5C22×D311yescharacteristic
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C2×C4×D5—34no—
311C2×C4×D5—34no—
312C2×C4×D5—62no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—22no—
323C5×C22⋊C4—22no—
324C5×C22⋊C4—41no—
325C5×C22⋊C4C4×D314yescomplemented
326C42×C5—41no—
327C22⋊Dic5—34no—
328C22⋊Dic5—62no—
329C22⋊Dic5—121no—
330#685—34no—
331#685—34no—
332#685—34no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685—62no—
337#685—62no—
338C4⋊Dic5—62no—
339#683—121no—
340#683—121no—
341C4×Dic5—62no—
342C4×Dic5—62no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—151no—
348#388—151no—
349#388—151no—
350#388D1511yescharacteristic, complemented
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×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×D15—22no—
374C2×D15—22no—
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—416no—
386C2×D15#11714yescomplemented
387C2×D15C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390C3×C4×C5—22no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5—41no—
394Dic15—22no—
395Dic15—22no—
396Dic15—22no—
397Dic15—41no—
398Dic15—41no—
399Dic15—41no—
400C24×C3C22×D511yescharacteristic
401C23×D3—51no—
402C23×D3—51no—
403C23×D3—54no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—102no—
408C23×D3—201no—
409C23×D3—201no—
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3—51no—
422C2×C4×D3—54no—
423C2×C4×D3—54no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C4⋊C4—22no—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—41no—
437C3×C22⋊C4C4×D514yescomplemented
438C3×C42—41no—
439#217—54no—
440#217—102no—
441#217—201no—
442(C2×D3)⋊C4—54no—
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)⋊C4—102no—
450C4⋊Dic3—102no—
451Dic3⋊C4—201no—
452Dic3⋊C4—201no—
453C4×Dic3—102no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C2×C4×D312yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—32no—
465C22×D5—32no—
466C22×D5—32no—
467C22×D5—32no—
468C22×D5—32no—
469C22×D5—32no—
470C22×D5—68no—
471C22×D5—68no—
472C22×D5—61no—
473C22×D5—61no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—61no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5—124no—
483C22×D5—124no—
484C22×D5—124no—
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—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5C2×C4×D312yes—
501C2×C4×C5C2×C4×D312yes—
502C2×C4×C5D3×D412yes—
503C2×Dic5—32no—
504C2×Dic5—32no—
505C2×Dic5—32no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—61no—
521C4×D5—68no—
522C4×D5—124no—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—151no—
527C23×C4—151no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4C2×D1511yescharacteristic, complemented
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—158no—
540C2×C22⋊C4—151no—
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—304no—
548C2×C22⋊C4C2×D1511yescharacteristic
549C2×C22⋊C4C2×D1511yescharacteristic
550C2×C22⋊C4C2×D1511yescharacteristic
551C2×C42—151no—
552C2×C42—151no—
553C2×C42—151no—
554C2×C42C2×D1511yescharacteristic, complemented
555#95—151no—
556#95—151no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95C2×D1511yescharacteristic, complemented
562#95C2×D1511yescharacteristic, complemented
563C2×C3×C5—42no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571D15—24no—
572D15—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3C2×C4×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—52no—
583C22×D3—52no—
584C22×D3—52no—
585C22×D3—52no—
586C22×D3—52no—
587C22×D3—108no—
588C22×D3—108no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—101no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3—204no—
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—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4C2×C4×D512yes—
618C2×C3×C4C2×C4×D512yes—
619C2×C3×C4D4×D512yes—
620C2×Dic3—52no—
621C2×Dic3—52no—
622C2×Dic3—52no—
623C2×Dic3—101no—
624C2×Dic3—101no—
625C2×Dic3—101no—
626C2×Dic3—101no—
627C2×Dic3—101no—
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×Dic3—101no—
637C2×Dic3—101no—
638C4×D3—108no—
639C4×D3—204no—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
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—34no—
657C2×D5—34no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—62no—
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—22no—
674C4×C5—41no—
675C4×C5—41no—
676C4×C5—41no—
677Dic5—62no—
678Dic5—62no—
679Dic5—62no—
680Dic5—121no—
681Dic5—121no—
682Dic5—121no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—302no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—601no—
691C24—601no—
692C24C22×D1511yescharacteristic
693C22×C4—151no—
694C22×C4—151no—
695C22×C4—151no—
696C22×C4—154no—
697C22×C4—154no—
698C22×C4—151no—
699C22×C4—151no—
700C22×C4—151no—
701C22×C4—302no—
702C22×C4—302no—
703C22×C4—302no—
704C22×C4—302no—
705C22×C4—302no—
706C22×C4—302no—
707C22×C4—601no—
708C22×C4—601no—
709C22×C4—601no—
710C22×C4—601no—
711C22×C4C22×D1511yescharacteristic
712C22×C4C22×D1511yescharacteristic
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
715C22×C4C22×D1511yescharacteristic
716C22×C4C22×D1511yescharacteristic
717C4⋊C4—22no—
718C4⋊C4—302no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—22no—
722C22⋊C4—41no—
723C22⋊C4—154no—
724C22⋊C4—154no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—302no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—601no—
734C22⋊C4C4×D1514yescomplemented
735C42—41no—
736C42—302no—
737C42—302no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3C22×C4×D511yescharacteristic
748C22×C3C2×D4×D511yescharacteristic
749C22×C3#414411yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3D5×#4111yescharacteristic
752C22×C3D5×#4111yescharacteristic
753C22×C3#414911yescharacteristic
754C2×D3—54no—
755C2×D3—54no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—102no—
768C2×D3—2016no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775Dic3—102no—
776Dic3—102no—
777Dic3—102no—
778Dic3—201no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—42no—
782C2×C5D3×#11711yescharacteristic
783C2×C5C4×D3×D411yescharacteristic
784C2×C5#554511yescharacteristic
785C2×C5#561011yescharacteristic
786C2×C5#565911yescharacteristic
787C2×C5#567611yescharacteristic
788C2×C5#570511yescharacteristic
789D5—64no—
790D5—64no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—152no—
798C23—152no—
799C23—152no—
800C23—152no—
801C23—152no—
802C23—152no—
803C23—308no—
804C23—308no—
805C23—301no—
806C23—301no—
807C23—301no—
808C23—301no—
809C23—301no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—604no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23C2×C4×D1512yes—
819C23C23×D1511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—152no—
836C2×C4—152no—
837C2×C4—152no—
838C2×C4—308no—
839C2×C4—301no—
840C2×C4—301no—
841C2×C4—301no—
842C2×C4—301no—
843C2×C4—301no—
844C2×C4—301no—
845C2×C4—301no—
846C2×C4—301no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—604no—
855C2×C4—604no—
856C2×C4—604no—
857C2×C4C2×C4×D1512yes—
858C2×C4C2×C4×D1512yes—
859C2×C4D4×D1512yes—
860C2×C3—42no—
861C2×C3D5×#11711yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6594411yescharacteristic
865C2×C3#6599311yescharacteristic
866C2×C3#6601011yescharacteristic
867C2×C3#6603911yescharacteristic
868D3—104no—
869D3—104no—
870C5#7583311yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—154no—
879C22—154no—
880C22—302no—
881C22—302no—
882C22—302no—
883C22—302no—
884C22—302no—
885C22—302no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22C22×C4×D1511yescharacteristic
894C22C2×D4×D1511yescharacteristic
895C22#9209511yescharacteristic
896C22#41×D1511yescharacteristic
897C22#41×D1511yescharacteristic
898C22#41×D1511yescharacteristic
899C22#9210011yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—41no—
904C4—41no—
905C4—41no—
906C4—302no—
907C4—302no—
908C4—302no—
909C4—601no—
910C4—601no—
911C4—601no—
912C3#1060756411yescharacteristic, complemented, Sylow
913C2—42no—
914C2—304no—
915C2—304no—
916C2D15×#11711yescharacteristic
917C2C4×D4×D1511yescharacteristic
918C2#1175630411yescharacteristic
919C2#1175636911yescharacteristic
920C2#1175641811yescharacteristic
921C2#1175643511yescharacteristic
922C2#1175646411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenter#388D15
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91781C2semidirect
4. C3×C5×#388C2semidirect
5. #11751090C2semidirect
7. #11751052C2semidirect
8. #11751046C2semidirect
9. #11751045C2semidirect
10. C4×#6714C2semidirect
11. C4×#6714C2semidirect
12. #11750769C2semidirect
13. #11750768C2semidirect
14. #11750767C2semidirect
15. #11750765C2semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C3×C42×C5C22semidirect
38. C2×C4⋊Dic15C22semidirect
39. C2×#6712C22semidirect
40. C2×#6712C22semidirect
41. C2×C4×Dic15C22semidirect
42. C2×C4×Dic15C22semidirect
43. C2×C4×Dic15C22semidirect
46. C22⋊C4×D15C4semidirect
47. C3×C5×#95C22semidirect
48. C3×C5×#95C22semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
59. C5×#388D3semidirect
103. C2×C4×D15C2×C4semidirect
104. C2×C4×D15C2×C4semidirect
108. C3×C5×C22⋊C4C2×C4semidirect
112. #6719C2×C4semidirect
130. C3×#388D5semidirect
147. C2×C5×C4⋊C4C2×D3semidirect
151. C2×C42×C5C2×D3semidirect
172. C5×#95C2×D3semidirect
173. C5×#95C2×D3semidirect
255. C2×C3×C4⋊C4C2×D5semidirect
259. C2×C3×C42C2×D5semidirect
280. C3×#95C2×D5semidirect
281. C3×#95C2×D5semidirect
325. C5×C22⋊C4C4×D3semidirect
350. #388D15semidirect
386. C2×D15#117semidirect
437. C3×C22⋊C4C4×D5semidirect
534. C2×C4⋊C4C2×D15semidirect
554. C2×C42C2×D15semidirect
561. #95C2×D15semidirect
562. #95C2×D15semidirect
734. C22⋊C4C4×D15semidirect
739. C3×C5#2342semidirect
870. C5#75833semidirect
912. C3#10607564semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C22⋊C4×D152
C3×C5×#3882
#117510902
#117510562
#117510522
#117510462
#117510452
C4×#67142
#117507692
#117507682
#117507672
#117507652
#106075643
#758335