Finite Group Databasebeta

← #14330833

Subgroups — #14330833

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91828C211yesmaximal, characteristic
2C3×C5×#390C211yesmaximal, characteristic, complemented
3#11751321C211yesmaximal, characteristic, complemented
4#11751090C211yesmaximal, characteristic, complemented
5#11751079C211yesmaximal, characteristic, complemented
6#11751059C211yesmaximal, characteristic, complemented
7#11751058C211yesmaximal, characteristic, complemented
8#11751057C211yesmaximal, characteristic, complemented
9#11751057C211yesmaximal, characteristic, complemented
10#11751047C211yesmaximal, characteristic, complemented
11#11751046C211yesmaximal, characteristic, complemented
12#11751044C211yesmaximal, characteristic, complemented
13#11751043C211yesmaximal, characteristic, complemented
14#11751041C211yesmaximal, characteristic, complemented
15#11751034C211yesmaximal, characteristic, complemented
16#10608041—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33#91828C418yescomplemented
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6712C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#76310—51nomaximal, Hall
54C2×#4085—31no—
55C5×#390D311yescharacteristic, complemented
56#65509—31no—
57#65278—31no—
58#65267—31no—
59#65247—31no—
60#65246—31no—
61#65245—31no—
62#65245—31no—
63#65235—31no—
64#65234—31no—
65#65232—31no—
66#65231—31no—
67#65229—31no—
68#65222—31no—
69C24×C3×C5C2311yescharacteristic
70C24×C3×C5C2311yescharacteristic
71C23×D15C2311yescharacteristic
72C2×C3×C5×D4—41no—
73C2×C3×C5×D4—41no—
74C2×C3×C5×D4C2×C414yescomplemented
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—41no—
81C2×#1220—41no—
82C2×#1220—41no—
83C2×#1220—41no—
84C2×#1220C2×C414yes—
85C2×#1220C2×C414yescomplemented
86C22×Dic15—41no—
87C22×Dic15—41no—
88C22×Dic15—41no—
89C22×Dic15—41no—
90C22×Dic15—41no—
91C22×Dic15C2×C414yescomplemented
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C2×C4×D15—41no—
100C2×C4×D15—41no—
101C2×C4×D15—41no—
102C3×C5×C4⋊C4—41no—
103C3×C5×C22⋊C4—41no—
104C3×C5×C22⋊C4—41no—
105C3×C5×C22⋊C4—41no—
106C3×C5×C22⋊C4—41no—
107C3×C42×C5—41no—
108#6719—41no—
109#6719—41no—
110#6719—41no—
111#6719C2×C414yescomplemented
112#6714—41no—
113#6714—41no—
114#6714—41no—
115#6714C2×C414yescomplemented
116#6712—41no—
117#6712—41no—
118#6712—41no—
119#6712C2×C414yescomplemented
120C4×Dic15—41no—
121C2×#939—51no—
122C3×#390D511yescharacteristic, complemented
123#5220—51no—
124#4989—51no—
125#4978—51no—
126#4958—51no—
127#4957—51no—
128#4956—51no—
129#4956—51no—
130#4946—51no—
131#4945—51no—
132#4943—51no—
133#4942—51no—
134#4940—51no—
135#4933—51no—
136C22×C5×D4C2×D311yescharacteristic
137C22×C22⋊D5—31no—
138C22×C22⋊D5—31no—
139C23×Dic5—31no—
140C23×Dic5—31no—
141C22×C4×D5—31no—
142C2×C5×C4⋊C4C2×D311yescharacteristic
143C2×C5×C22⋊C4C2×D311yescharacteristic
144C2×C5×C22⋊C4C2×D311yescharacteristic
145C2×C5×C22⋊C4C2×D311yescharacteristic
146C2×C5×C22⋊C4C2×D311yescharacteristic
147C2×C42×C5C2×D311yescharacteristic
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—31no—
152#4085—38no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#683—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×#683—31no—
161C2×C4×Dic5—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#2377—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C22×C412yes—
187C23×C3×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15C22×C412yes—
195C3×C5×D4—44no—
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—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5C22×C412yes—
211#1220—44no—
212#1220—44no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
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—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—44no—
232C2×Dic15—44no—
233C2×Dic15C22×C412yes—
234C2×Dic15C22×C412yes—
235C2×Dic15C22×C412yes—
236C4×D15—44no—
237C22×C3×D4C2×D511yescharacteristic
238C22×#67—51no—
239C22×#67—51no—
240C23×Dic3—51no—
241C23×Dic3—51no—
242C22×C4×D3—51no—
243C2×C3×C4⋊C4C2×D511yescharacteristic
244C2×C3×C22⋊C4C2×D511yescharacteristic
245C2×C3×C22⋊C4C2×D511yescharacteristic
246C2×C3×C22⋊C4C2×D511yescharacteristic
247C2×C3×C22⋊C4C2×D511yescharacteristic
248C2×C3×C42C2×D511yescharacteristic
249C2×#217—51no—
250C2×#217—51no—
251C2×#217—51no—
252C2×#217—51no—
253#939—58no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×(C2×D3)⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×C4×Dic3—51no—
263C3⋊#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C24×C5C22×D311yescharacteristic
274C24×C5C22×D311yescharacteristic
275C23×D5—31no—
276C2×C5×D4—41no—
277C2×C5×D4—41no—
278C2×C5×D4C4×D314yescomplemented
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C22×C4×C5C22×D311yescharacteristic
284C2×C22⋊D5—34no—
285C2×C22⋊D5—34no—
286C2×C22⋊D5—121no—
287C2×C22⋊D5—121no—
288C2×C22⋊D5—121no—
289C2×C22⋊D5—121no—
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—34no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5—31no—
297C22×Dic5—31no—
298C22×Dic5—121no—
299C22×Dic5—121no—
300C22×Dic5—121no—
301C22×Dic5—121no—
302C22×Dic5—121no—
303C2×C4×D5—121no—
304C2×C4×D5—121no—
305C2×C4×D5—121no—
306C5×C4⋊C4—41no—
307C5×C22⋊C4—41no—
308C5×C22⋊C4—41no—
309C5×C22⋊C4—41no—
310C5×C22⋊C4—41no—
311C42×C5—41no—
312C22⋊Dic5—34no—
313C22⋊Dic5—121no—
314C22⋊Dic5—121no—
315C22⋊Dic5—121no—
316#685—34no—
317#685—121no—
318#685—121no—
319#685—121no—
320#683—34no—
321#683—121no—
322#683—121no—
323#683—121no—
324C4×Dic5—121no—
325C2×#121—151no—
326#390—151no—
327#390D1511yescharacteristic, complemented
328#388—151no—
329#388—151no—
330#387—151no—
331#387—151no—
332#386—151no—
333#386—151no—
334#386—151no—
335#386—151no—
336#385—151no—
337#385—151no—
338#381—151no—
339#380—151no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—41no—
353C22×C3×C5—41no—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5H(5,𝔽2)11yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C22×C3×C5H(5,𝔽2)11yescharacteristic
358C22×C3×C5H(5,𝔽2)11yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C52−1+411yescharacteristic
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—41no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C3×C4×C5—22no—
369C3×C4×C5—41no—
370C3×C4×C5—41no—
371C3×C4×C5—41no—
372C3×C4×C5—41no—
373Dic15—22no—
374Dic15—22no—
375Dic15—22no—
376Dic15—41no—
377Dic15—41no—
378Dic15—41no—
379Dic15—41no—
380C24×C3C22×D511yescharacteristic
381C24×C3C22×D511yescharacteristic
382C23×D3—51no—
383C2×C3×D4—41no—
384C2×C3×D4—41no—
385C2×C3×D4C4×D514yescomplemented
386C22×C3×C4C22×D511yescharacteristic
387C22×C3×C4C22×D511yescharacteristic
388C22×C3×C4C22×D511yescharacteristic
389C22×C3×C4C22×D511yescharacteristic
390C22×C3×C4C22×D511yescharacteristic
391C2×#67—54no—
392C2×#67—54no—
393C2×#67—201no—
394C2×#67—201no—
395C2×#67—201no—
396C2×#67—201no—
397C22×Dic3—51no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—54no—
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—201no—
406C22×Dic3—201no—
407C22×Dic3—201no—
408C22×Dic3—201no—
409C22×Dic3—201no—
410C2×C4×D3—201no—
411C2×C4×D3—201no—
412C2×C4×D3—201no—
413C3×C4⋊C4—41no—
414C3×C22⋊C4—41no—
415C3×C22⋊C4—41no—
416C3×C22⋊C4—41no—
417C3×C22⋊C4—41no—
418C3×C42—41no—
419#217—54no—
420#217—201no—
421#217—201no—
422#217—201no—
423(C2×D3)⋊C4—54no—
424(C2×D3)⋊C4—201no—
425(C2×D3)⋊C4—201no—
426(C2×D3)⋊C4—201no—
427Dic3⋊C4—54no—
428Dic3⋊C4—201no—
429Dic3⋊C4—201no—
430Dic3⋊C4—201no—
431C4×Dic3—201no—
432C23×C5—21no—
433C23×C5—21no—
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5—21no—
443C23×C5—21no—
444C23×C5C2×C4×D312yes—
445C23×C5C2×C4×D312yes—
446C23×C5C23×D311yescharacteristic
447C22×D5—32no—
448C22×D5—61no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5—61no—
454C5×D4—44no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—21no—
464C2×C4×C5—21no—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5C2×C4×D312yes—
470C22⋊D5—124no—
471C22⋊D5—124no—
472C2×Dic5—32no—
473C2×Dic5—32no—
474C2×Dic5—32no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—124no—
494C2×Dic5—124no—
495C4×D5—124no—
496C22×D4—151no—
497C22×D4—151no—
498C22×D4C2×D1511yescharacteristic
499C23×C4—151no—
500C23×C4—151no—
501C23×C4—151no—
502#121—158no—
503C2×C4⋊C4—151no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—151no—
506C2×C4⋊C4—151no—
507C2×C4⋊C4C2×D1511yescharacteristic
508C2×C22⋊C4—151no—
509C2×C22⋊C4—151no—
510C2×C22⋊C4—151no—
511C2×C22⋊C4—151no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4—151no—
515C2×C22⋊C4—151no—
516C2×C22⋊C4C2×D1511yescharacteristic
517C2×C22⋊C4C2×D1511yescharacteristic
518C2×C22⋊C4C2×D1511yescharacteristic
519C2×C22⋊C4C2×D1511yescharacteristic
520C2×C42—151no—
521C2×C42C2×D1511yescharacteristic
522#95—151no—
523#95—151no—
524#95—151no—
525#95—151no—
526#95—151no—
527#95—151no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532C2×C3×C5—42no—
533C2×C3×C5—42no—
534C2×C3×C5#51811yescharacteristic
535C2×C3×C5#51811yescharacteristic
536C2×C3×C5#52011yescharacteristic
537C2×C3×C5#56011yescharacteristic
538C2×C3×C5#56011yescharacteristic
539C2×C3×C5#56211yescharacteristic
540C2×C3×C5#56211yescharacteristic
541D15—42no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3C2×C4×D512yes—
555C23×C3C2×C4×D512yes—
556C23×C3C23×D511yescharacteristic
557C22×D3—52no—
558C22×D3—101no—
559C22×D3—101no—
560C22×D3—101no—
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—101no—
564C3×D4—44no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4C2×C4×D512yes—
580#67—204no—
581#67—204no—
582C2×Dic3—52no—
583C2×Dic3—52no—
584C2×Dic3—52no—
585C2×Dic3—101no—
586C2×Dic3—101no—
587C2×Dic3—101no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—101no—
602C2×Dic3—101no—
603C2×Dic3—204no—
604C2×Dic3—204no—
605C4×D3—204no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5—22no—
611C22×C5—22no—
612C22×C5—41no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5C22×C4×D311yescharacteristic
621C22×C5#100411yescharacteristic
622C22×C5#100411yescharacteristic
623C22×C5#100411yescharacteristic
624C22×C5#100411yescharacteristic
625C22×C5#100911yescharacteristic
626C22×C5#101011yescharacteristic
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—62no—
630C2×D5—121no—
631C2×D5—121no—
632C2×D5—121no—
633C2×D5—121no—
634C4×C5—22no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639Dic5—62no—
640Dic5—62no—
641Dic5—62no—
642Dic5—121no—
643Dic5—121no—
644Dic5—121no—
645Dic5—121no—
646C24—151no—
647C24C22×D1511yescharacteristic
648C24C22×D1511yescharacteristic
649C2×D4—41no—
650C2×D4—41no—
651C2×D4—154no—
652C2×D4—154no—
653C2×D4—601no—
654C2×D4—601no—
655C2×D4—601no—
656C2×D4—601no—
657C2×D4C4×D1514yescomplemented
658C22×C4—151no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—154no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—601no—
667C22×C4—601no—
668C22×C4—601no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4—601no—
673C22×C4—601no—
674C22×C4C22×D1511yescharacteristic
675C22×C4C22×D1511yescharacteristic
676C22×C4C22×D1511yescharacteristic
677C22×C4C22×D1511yescharacteristic
678C22×C4C22×D1511yescharacteristic
679C4⋊C4—41no—
680C4⋊C4—154no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C4⋊C4—601no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—154no—
689C22⋊C4—154no—
690C22⋊C4—601no—
691C22⋊C4—601no—
692C22⋊C4—601no—
693C22⋊C4—601no—
694C22⋊C4—601no—
695C22⋊C4—601no—
696C42—41no—
697C42—601no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3C22×C4×D511yescharacteristic
714C22×C3#414411yescharacteristic
715C22×C3#414411yescharacteristic
716C22×C3#414411yescharacteristic
717C22×C3#414411yescharacteristic
718C22×C3#414911yescharacteristic
719C22×C3#415011yescharacteristic
720C2×D3—102no—
721C2×D3—102no—
722C2×D3—102no—
723C2×D3—201no—
724C2×D3—201no—
725C2×D3—201no—
726C2×D3—201no—
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732Dic3—102no—
733Dic3—102no—
734Dic3—102no—
735Dic3—201no—
736Dic3—201no—
737Dic3—201no—
738Dic3—201no—
739C2×C5—42no—
740C2×C5—42no—
741C2×C5#548611yescharacteristic
742C2×C5#554511yescharacteristic
743C2×C5#554611yescharacteristic
744C2×C5#562011yescharacteristic
745C2×C5#562111yescharacteristic
746C2×C5#568411yescharacteristic
747C2×C5#572011yescharacteristic
748D5—122no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—152no—
762C23—301no—
763C23—301no—
764C23—301no—
765C23—301no—
766C23—301no—
767C23—301no—
768C23C2×C4×D1512yes—
769C23C2×C4×D1512yes—
770C23C23×D1511yescharacteristic
771D4—44no—
772D4—604no—
773D4—604no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—152no—
789C2×C4—152no—
790C2×C4—152no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—301no—
794C2×C4—301no—
795C2×C4—301no—
796C2×C4—301no—
797C2×C4—301no—
798C2×C4—301no—
799C2×C4—301no—
800C2×C4—301no—
801C2×C4—301no—
802C2×C4—301no—
803C2×C4—301no—
804C2×C4—301no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—301no—
808C2×C4—301no—
809C2×C4—604no—
810C2×C4—604no—
811C2×C4—604no—
812C2×C4C2×C4×D1512yes—
813C2×C3—42no—
814C2×C3—42no—
815C2×C3#6582011yescharacteristic
816C2×C3#6587911yescharacteristic
817C2×C3#6588011yescharacteristic
818C2×C3#6595411yescharacteristic
819C2×C3#6595511yescharacteristic
820C2×C3#6601811yescharacteristic
821C2×C3#6605411yescharacteristic
822D3—202no—
823C5#7631011yescharacteristic, complemented, Sylow
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—302no—
839C22—302no—
840C22—302no—
841C22—601no—
842C22—601no—
843C22—601no—
844C22—601no—
845C22C22×C4×D1511yescharacteristic
846C22#9209511yescharacteristic
847C22#9209511yescharacteristic
848C22#9209511yescharacteristic
849C22#9209511yescharacteristic
850C22#9210011yescharacteristic
851C22#9210111yescharacteristic
852C4—22no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—302no—
858C4—302no—
859C4—302no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4—601no—
864C3#1060804111yescharacteristic, complemented, Sylow
865C2—42no—
866C2—42no—
867C2—602no—
868C2#1175624511yescharacteristic
869C2#1175630411yescharacteristic
870C2#1175630511yescharacteristic
871C2#1175637911yescharacteristic
872C2#1175638011yescharacteristic
873C2#1175644311yescharacteristic
874C2#1175647911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#390C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91828C2
hypercenter#390D15
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C3×C5×#390C2semidirect
3. #11751321C2semidirect
4. #11751090C2semidirect
5. #11751079C2semidirect
6. #11751059C2semidirect
7. #11751058C2semidirect
8. #11751057C2semidirect
9. #11751057C2semidirect
10. #11751047C2semidirect
11. #11751046C2semidirect
12. #11751044C2semidirect
13. #11751043C2semidirect
14. #11751041C2semidirect
15. #11751034C2semidirect
33. #91828C4semidirect
55. C5×#390D3semidirect
74. C2×C3×C5×D4C2×C4semidirect
85. C2×#1220C2×C4semidirect
91. C22×Dic15C2×C4semidirect
111. #6719C2×C4semidirect
115. #6714C2×C4semidirect
119. #6712C2×C4semidirect
122. C3×#390D5semidirect
278. C2×C5×D4C4×D3semidirect
327. #390D15semidirect
385. C2×C3×D4C4×D5semidirect
657. C2×D4C4×D15semidirect
698. C3×C5#2377semidirect
823. C5#76310semidirect
864. C3#10608041semidirect

Maximal subgroups

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

subgroupindex
C2×#918282
C3×C5×#3902
#117513212
#117510902
#117510792
#117510592
#117510582
#117510572
#117510472
#117510462
#117510442
#117510432
#117510412
#117510342
#106080413
#763105