Finite Group Databasebeta

← #14330839

Subgroups — #14330839

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×#91773C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3#11751090C211yesmaximal, characteristic, complemented
4#11751088C211yesmaximal, characteristic, complemented
5#11751059C211yesmaximal, characteristic, complemented
6#11751059C211yesmaximal, characteristic, complemented
7#11751058C211yesmaximal, characteristic, complemented
8#11751057C211yesmaximal, characteristic, complemented
9#11751051C211yesmaximal, characteristic, complemented
10#11751040C211yesmaximal, characteristic, complemented
11#11751034C211yesmaximal, characteristic, complemented
12#11750771C211yesmaximal, characteristic, complemented
13#11750766C211yesmaximal, characteristic, complemented
14#11750765C211yesmaximal, characteristic, complemented
15#11750756C211yesmaximal, characteristic, complemented
16#10607221—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
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×C42×C5C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91773C418yescomplemented
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#75490—51nomaximal, Hall
54C2×#4030—31no—
55C5×#388D311yescharacteristic, complemented
56#65278—31no—
57#65276—31no—
58#65247—31no—
59#65247—31no—
60#65246—31no—
61#65245—31no—
62#65239—31no—
63#65228—31no—
64#65222—31no—
65#64959—31no—
66#64954—31no—
67#64953—31no—
68#64944—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C23×D15C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—41no—
79C2×#1220—41no—
80C2×#1220—41no—
81C2×#1220—41no—
82C2×#1220C2×C414yes—
83C2×#1220C2×C414yescomplemented
84C22×Dic15—41no—
85C22×Dic15—41no—
86C22×Dic15—41no—
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×D60—41no—
94C2×D60—41no—
95C2×D60C2×C414yescomplemented
96C2×C4×D15—41no—
97C2×C4×D15—41no—
98C2×C4×D15—41no—
99C2×C4×D15—41no—
100C2×C4×D15—41no—
101C2×C4×D15C2×C414yescomplemented
102C3×C5×C4⋊C4—41no—
103C3×C5×C22⋊C4—41no—
104C3×C5×C22⋊C4—41no—
105C3×C5×C22⋊C4C2×C414yescomplemented
106C3×C42×C5—41no—
107#6719—41no—
108#6714—41no—
109#6714—41no—
110#6714—41no—
111#6714—41no—
112#6714—41no—
113#6714—41no—
114#6714—41no—
115#6714C2×C414yescomplemented
116C4⋊Dic15—41no—
117C4⋊Dic15—41no—
118#6712—41no—
119#6712C2×C414yescomplemented
120C4×Dic15—41no—
121C2×#884—51no—
122C3×#388D511yescharacteristic, complemented
123#4989—51no—
124#4987—51no—
125#4958—51no—
126#4958—51no—
127#4957—51no—
128#4956—51no—
129#4950—51no—
130#4939—51no—
131#4933—51no—
132#4670—51no—
133#4665—51no—
134#4664—51no—
135#4655—51no—
136C22×C22⋊D5—31no—
137C22×C22⋊D5—31no—
138C23×Dic5—31no—
139C22×D20—31no—
140C22×C4×D5—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×C42×C5C2×D311yescharacteristic
147C2×C22⋊Dic5—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161#4030—38no—
162C5×#95C2×D311yescharacteristic
163C5×#95C2×D311yescharacteristic
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×C5C22×C412yes—
180C23×C3×C5C2411yescharacteristic
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15C22×C412yes—
194C22×D15C22×C412yes—
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—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C22×C412yes—
212C2×C3×C4×C5C22×C412yes—
213#1220—44no—
214#1220—44no—
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×Dic15C22×C412yes—
233C2×Dic15C22×C412yes—
234D60—44no—
235C4×D15—44no—
236C4×D15—44no—
237C22×#67—51no—
238C22×#67—51no—
239C23×Dic3—51no—
240C22×D12—51no—
241C22×C4×D3—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×C42C2×D511yescharacteristic
248C2×#217—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4—51no—
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×C4×Dic3—51no—
262#884—58no—
263C3×#95C2×D511yescharacteristic
264C3×#95C2×D511yescharacteristic
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
274C23×D5—31no—
275C23×D5—31no—
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C2×C22⋊D5—34no—
283C2×C22⋊D5—34no—
284C2×C22⋊D5—121no—
285C2×C22⋊D5—121no—
286C2×C22⋊D5—121no—
287C2×C22⋊D5—121no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—121no—
295C22×Dic5—121no—
296C22×Dic5—121no—
297C2×D20—34no—
298C2×D20—121no—
299C2×D20—121no—
300C2×C4×D5—34no—
301C2×C4×D5—121no—
302C2×C4×D5—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⋊C4C4×D314yescomplemented
310C42×C5—41no—
311C22⋊Dic5—121no—
312#685—34no—
313#685—121no—
314#685—121no—
315#685—121no—
316#685—121no—
317#685—121no—
318#685—121no—
319#685—121no—
320C4⋊Dic5—121no—
321C4⋊Dic5—121no—
322#683—34no—
323#683—121no—
324C4×Dic5—121no—
325C2×#121—151no—
326#390—151no—
327#390—151no—
328#388—151no—
329#388D1511yescharacteristic, complemented
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—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C23×C411yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C22×C3×C5H(5,𝔽2)11yescharacteristic
351C22×C3×C5H(5,𝔽2)11yescharacteristic
352C22×C3×C5H(5,𝔽2)11yescharacteristic
353C22×C3×C52−1+411yescharacteristic
354C2×D15—22no—
355C2×D15—22no—
356C2×D15—22no—
357C2×D15—22no—
358C2×D15—22no—
359C2×D15—22no—
360C2×D15—41no—
361C2×D15—41no—
362C2×D15—41no—
363C2×D15—41no—
364C2×D15—41no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—41no—
371C3×C4×C5—41no—
372C3×C4×C5—41no—
373C3×C4×C5—41no—
374Dic15—22no—
375Dic15—22no—
376Dic15—41no—
377Dic15—41no—
378Dic15—41no—
379Dic15—41no—
380C24×C3C22×D511yescharacteristic
381C23×D3—51no—
382C23×D3—51no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C22×C3×C4C22×D511yescharacteristic
386C22×C3×C4C22×D511yescharacteristic
387C22×C3×C4C22×D511yescharacteristic
388C22×C3×C4C22×D511yescharacteristic
389C2×#67—54no—
390C2×#67—54no—
391C2×#67—201no—
392C2×#67—201no—
393C2×#67—201no—
394C2×#67—201no—
395C22×Dic3—51no—
396C22×Dic3—51no—
397C22×Dic3—51no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—201no—
402C22×Dic3—201no—
403C22×Dic3—201no—
404C2×D12—54no—
405C2×D12—201no—
406C2×D12—201no—
407C2×C4×D3—54no—
408C2×C4×D3—201no—
409C2×C4×D3—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⋊C4C4×D514yescomplemented
417C3×C42—41no—
418#217—201no—
419(C2×D3)⋊C4—54no—
420(C2×D3)⋊C4—201no—
421(C2×D3)⋊C4—201no—
422(C2×D3)⋊C4—201no—
423(C2×D3)⋊C4—201no—
424(C2×D3)⋊C4—201no—
425(C2×D3)⋊C4—201no—
426(C2×D3)⋊C4—201no—
427C4⋊Dic3—201no—
428C4⋊Dic3—201no—
429Dic3⋊C4—54no—
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×C5C2×C4×D312yes—
439C23×C5C23×D311yescharacteristic
440C22×D5—32no—
441C22×D5—32no—
442C22×D5—61no—
443C22×D5—61no—
444C22×D5—61no—
445C22×D5—61no—
446C22×D5—61no—
447C22×D5—61no—
448C22×D5—61no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5—61no—
454C2×C4×C5—21no—
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×C5—21no—
470C2×C4×C5C2×C4×D312yes—
471C2×C4×C5C2×C4×D312yes—
472C22⋊D5—124no—
473C22⋊D5—124no—
474C2×Dic5—32no—
475C2×Dic5—32no—
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—124no—
493D20—124no—
494C4×D5—124no—
495C4×D5—124no—
496C22×D4—151no—
497C22×D4—151no—
498C22×D4—151no—
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⋊C4—151no—
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#95C2×D1511yescharacteristic
531#95C2×D1511yescharacteristic
532C2×C3×C5—42no—
533C2×C3×C5#51811yescharacteristic
534C2×C3×C5#51811yescharacteristic
535C2×C3×C5#52011yescharacteristic
536C2×C3×C5#56011yescharacteristic
537C2×C3×C5#56011yescharacteristic
538C2×C3×C5#56211yescharacteristic
539C2×C3×C5#56211yescharacteristic
540D15—42no—
541D15—42no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3C2×C4×D512yes—
549C23×C3C23×D511yescharacteristic
550C22×D3—52no—
551C22×D3—52no—
552C22×D3—101no—
553C22×D3—101no—
554C22×D3—101no—
555C22×D3—101no—
556C22×D3—101no—
557C22×D3—101no—
558C22×D3—101no—
559C22×D3—101no—
560C22×D3—101no—
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—101no—
564C2×C3×C4—21no—
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×C4—21no—
580C2×C3×C4C2×C4×D512yes—
581C2×C3×C4C2×C4×D512yes—
582#67—204no—
583#67—204no—
584C2×Dic3—52no—
585C2×Dic3—52no—
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—204no—
603D12—204no—
604C4×D3—204no—
605C4×D3—204no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—41no—
610C22×C5—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5C22×C4×D311yescharacteristic
614C22×C5#100411yescharacteristic
615C22×C5#100411yescharacteristic
616C22×C5#100911yescharacteristic
617C22×C5#100911yescharacteristic
618C22×C5#100911yescharacteristic
619C22×C5#101011yescharacteristic
620C2×D5—62no—
621C2×D5—62no—
622C2×D5—62no—
623C2×D5—62no—
624C2×D5—62no—
625C2×D5—62no—
626C2×D5—121no—
627C2×D5—121no—
628C2×D5—121no—
629C2×D5—121no—
630C2×D5—121no—
631C2×D5—121no—
632C2×D5—121no—
633C2×D5—121no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639C4×C5—41no—
640Dic5—62no—
641Dic5—62no—
642Dic5—121no—
643Dic5—121no—
644Dic5—121no—
645Dic5—121no—
646C24—151no—
647C24—151no—
648C24C22×D1511yescharacteristic
649C2×D4—154no—
650C2×D4—154no—
651C2×D4—154no—
652C2×D4—601no—
653C2×D4—601no—
654C2×D4—601no—
655C2×D4—601no—
656C2×D4—601no—
657C2×D4—601no—
658C22×C4—151no—
659C22×C4—151no—
660C22×C4—154no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—601no—
666C22×C4—601no—
667C22×C4—601no—
668C22×C4—601no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4—601no—
673C22×C4C22×D1511yescharacteristic
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—154no—
687C22⋊C4—601no—
688C22⋊C4—601no—
689C22⋊C4—601no—
690C22⋊C4—601no—
691C22⋊C4—601no—
692C22⋊C4—601no—
693C22⋊C4—601no—
694C22⋊C4—601no—
695C22⋊C4C4×D1514yescomplemented
696C42—41no—
697C42—601no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3C22×C4×D511yescharacteristic
707C22×C3#414411yescharacteristic
708C22×C3#414411yescharacteristic
709C22×C3#414911yescharacteristic
710C22×C3#414911yescharacteristic
711C22×C3#414911yescharacteristic
712C22×C3#415011yescharacteristic
713C2×D3—102no—
714C2×D3—102no—
715C2×D3—102no—
716C2×D3—102no—
717C2×D3—102no—
718C2×D3—102no—
719C2×D3—201no—
720C2×D3—201no—
721C2×D3—201no—
722C2×D3—201no—
723C2×D3—201no—
724C2×D3—201no—
725C2×D3—201no—
726C2×D3—201no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733Dic3—102no—
734Dic3—102no—
735Dic3—201no—
736Dic3—201no—
737Dic3—201no—
738Dic3—201no—
739C2×C5—42no—
740C2×C5#552311yescharacteristic
741C2×C5#554511yescharacteristic
742C2×C5#554511yescharacteristic
743C2×C5#562011yescharacteristic
744C2×C5#566711yescharacteristic
745C2×C5#568411yescharacteristic
746C2×C5#571111yescharacteristic
747D5—122no—
748D5—122no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—152no—
756C23—152no—
757C23—301no—
758C23—301no—
759C23—301no—
760C23—301no—
761C23—301no—
762C23—301no—
763C23—301no—
764C23—301no—
765C23—301no—
766C23—301no—
767C23—301no—
768C23—301no—
769C23C2×C4×D1512yes—
770C23C23×D1511yescharacteristic
771D4—604no—
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—21no—
789C2×C4—21no—
790C2×C4—152no—
791C2×C4—152no—
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—604no—
809C2×C4—604no—
810C2×C4—604no—
811C2×C4C2×C4×D1512yes—
812C2×C4C2×C4×D1512yes—
813C2×C3—42no—
814C2×C3#6585711yescharacteristic
815C2×C3#6587911yescharacteristic
816C2×C3#6587911yescharacteristic
817C2×C3#6595411yescharacteristic
818C2×C3#6600111yescharacteristic
819C2×C3#6601811yescharacteristic
820C2×C3#6604511yescharacteristic
821D3—202no—
822D3—202no—
823C5#7549011yescharacteristic, complemented, Sylow
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—302no—
832C22—302no—
833C22—302no—
834C22—302no—
835C22—302no—
836C22—302no—
837C22—601no—
838C22—601no—
839C22—601no—
840C22—601no—
841C22—601no—
842C22—601no—
843C22—601no—
844C22—601no—
845C22C22×C4×D1511yescharacteristic
846C22#9209511yescharacteristic
847C22#9209511yescharacteristic
848C22#9210011yescharacteristic
849C22#9210011yescharacteristic
850C22#9210011yescharacteristic
851C22#9210111yescharacteristic
852C4—22no—
853C4—22no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—302no—
859C4—302no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4—601no—
864C3#1060722111yescharacteristic, complemented, Sylow
865C2—42no—
866C2—602no—
867C2—602no—
868C2#1175628211yescharacteristic
869C2#1175630411yescharacteristic
870C2#1175630411yescharacteristic
871C2#1175637911yescharacteristic
872C2#1175642611yescharacteristic
873C2#1175644311yescharacteristic
874C2#1175647011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91773C2
hypercenter#388D15
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. #11751090C2semidirect
4. #11751088C2semidirect
5. #11751059C2semidirect
6. #11751059C2semidirect
7. #11751058C2semidirect
8. #11751057C2semidirect
9. #11751051C2semidirect
10. #11751040C2semidirect
11. #11751034C2semidirect
12. #11750771C2semidirect
13. #11750766C2semidirect
14. #11750765C2semidirect
15. #11750756C2semidirect
42. #91773C4semidirect
55. C5×#388D3semidirect
83. C2×#1220C2×C4semidirect
95. C2×D60C2×C4semidirect
101. C2×C4×D15C2×C4semidirect
105. C3×C5×C22⋊C4C2×C4semidirect
115. #6714C2×C4semidirect
119. #6712C2×C4semidirect
122. C3×#388D5semidirect
309. C5×C22⋊C4C4×D3semidirect
329. #388D15semidirect
416. C3×C22⋊C4C4×D5semidirect
695. C22⋊C4C4×D15semidirect
698. C3×C5#2377semidirect
823. C5#75490semidirect
864. C3#10607221semidirect

Maximal subgroups

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

subgroupindex
C2×#917732
C3×C5×#3882
#117510902
#117510882
#117510592
#117510582
#117510572
#117510512
#117510402
#117510342
#117507712
#117507662
#117507652
#117507562
#106072213
#754905