Finite Group Databasebeta

← #14330999

Subgroups — #14330999

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic
3#11751079C211yesmaximal, characteristic, complemented
4#11751073C211yesmaximal, characteristic, complemented
5#11751052C211yesmaximal, characteristic
6#11751046C211yesmaximal, characteristic
7#11751046C211yesmaximal, characteristic
8#11751044C211yesmaximal, characteristic
9#11751043C211yesmaximal, characteristic
10#11751034C211yesmaximal, characteristic, complemented
11#11751030C211yesmaximal, characteristic, complemented
12#11750754C211yesmaximal, characteristic, complemented
13#11750753C211yesmaximal, characteristic, complemented
14#11750748C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10607223—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38#91767C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#75492—51nomaximal, Hall
54C2×#4024—31no—
55C5×#388D311yescharacteristic
56#65267—31no—
57#65262—31no—
58#65240—31no—
59#65234—31no—
60#65234—31no—
61#65232—31no—
62#65231—31no—
63#65222—31no—
64#65218—31no—
65#64942—31no—
66#64941—31no—
67#64936—31no—
68#64935—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15—41no—
77C22×Dic15—41no—
78C22×Dic15C2×C414yes—
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×Dic30—41no—
88C2×Dic30—41no—
89C2×Dic30C2×C414yes—
90C3×C5×C4⋊C4—41no—
91C3×C5×C22⋊C4—41no—
92C3×C5×C22⋊C4—41no—
93C3×C5×C22⋊C4C2×C414yes—
94C3×C42×C5—41no—
95#6719—41no—
96#6719—41no—
97#6719C2×C414yes—
98C4⋊Dic15—41no—
99C4⋊Dic15C2×C414yes—
100#6712—41no—
101#6712—41no—
102#6712—41no—
103#6712—41no—
104#6712C2×C414yes—
105#6712C2×C414yes—
106C4×Dic15—41no—
107C4×Dic15—41no—
108C4×Dic15—41no—
109C2×#878—51no—
110C3×#388D511yescharacteristic
111#4978—51no—
112#4972—51no—
113#4951—51no—
114#4945—51no—
115#4945—51no—
116#4943—51no—
117#4942—51no—
118#4933—51no—
119#4929—51no—
120#4653—51no—
121#4652—51no—
122#4647—51no—
123#4646—51no—
124C23×Dic5—31no—
125C22×Dic10—31no—
126C2×C5×C4⋊C4C2×D311yescharacteristic
127C2×C5×C22⋊C4C2×D311yescharacteristic
128C2×C5×C22⋊C4C2×D311yescharacteristic
129C2×C5×C22⋊C4C2×D311yescharacteristic
130C2×C42×C5C2×D311yescharacteristic
131C2×C22⋊Dic5—31no—
132C2×C22⋊Dic5—31no—
133C2×C22⋊Dic5—31no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145#4024—38no—
146C5×#95C2×D311yescharacteristic
147C5×#95C2×D311yescharacteristic
148#3963—31no—
149#3963—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#2378—151noSylow
161C23×C3×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5C22×C412yes—
168C23×C3×C5C2411yescharacteristic
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C22×C412yes—
186C2×C3×C4×C5C22×C412yes—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—44no—
208C2×Dic15C22×C412yes—
209C2×Dic15C22×C412yes—
210C2×Dic15C22×C412yes—
211C2×Dic15C22×C412yes—
212Dic30—44no—
213C23×Dic3—51no—
214C22×Dic6—51no—
215C2×C3×C4⋊C4C2×D511yescharacteristic
216C2×C3×C22⋊C4C2×D511yescharacteristic
217C2×C3×C22⋊C4C2×D511yescharacteristic
218C2×C3×C22⋊C4C2×D511yescharacteristic
219C2×C3×C42C2×D511yescharacteristic
220C2×#217—51no—
221C2×#217—51no—
222C2×#217—51no—
223C2×C4⋊Dic3—51no—
224C2×C4⋊Dic3—51no—
225C2×Dic3⋊C4—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234#878—58no—
235C3×#95C2×D511yescharacteristic
236C3×#95C2×D511yescharacteristic
237C3⋊#95—51no—
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95—51no—
246C3⋊#95—51no—
247C3⋊#95—51no—
248C3⋊#95—51no—
249C24×C5C22×D311yescharacteristic
250C22×C4×C5C22×D311yescharacteristic
251C22×C4×C5C22×D311yescharacteristic
252C22×C4×C5C22×D311yescharacteristic
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×Dic5—31no—
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—34no—
261C22×Dic5—31no—
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C22×Dic5—121no—
266C22×Dic5—121no—
267C2×Dic10—34no—
268C2×Dic10—121no—
269C2×Dic10—121no—
270C5×C4⋊C4—41no—
271C5×C22⋊C4—41no—
272C5×C22⋊C4—41no—
273C5×C22⋊C4C4×D314yes—
274C42×C5—41no—
275C22⋊Dic5—34no—
276C22⋊Dic5—121no—
277C22⋊Dic5—121no—
278C4⋊Dic5—34no—
279C4⋊Dic5—121no—
280#683—34no—
281#683—34no—
282#683—121no—
283#683—121no—
284#683—121no—
285#683—121no—
286C4×Dic5—121no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C2×C22⋊Q8—151no—
290#391—151no—
291#391—151no—
292#389—151no—
293#389—151no—
294#388—151no—
295#388—151no—
296#388—151no—
297#388D1511yescharacteristic
298#387—151no—
299#387—151no—
300#387—151no—
301#387—151no—
302#381—151no—
303#380—151no—
304C22×C3×C5—22no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—41no—
308C22×C3×C5—41no—
309C22×C3×C5—41no—
310C22×C3×C5—41no—
311C22×C3×C5C23×C411yescharacteristic
312C22×C3×C5H(5,𝔽2)11yescharacteristic
313C22×C3×C5H(5,𝔽2)11yescharacteristic
314C22×C3×C5H(5,𝔽2)11yescharacteristic
315C22×C3×C52−1+411yescharacteristic
316C22×C3×C52−1+411yescharacteristic
317C22×C3×C52−1+411yescharacteristic
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—41no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324Dic15—22no—
325Dic15—22no—
326Dic15—22no—
327Dic15—22no—
328Dic15—41no—
329Dic15—41no—
330Dic15—41no—
331Dic15—41no—
332C24×C3C22×D511yescharacteristic
333C22×C3×C4C22×D511yescharacteristic
334C22×C3×C4C22×D511yescharacteristic
335C22×C3×C4C22×D511yescharacteristic
336C22×C3×C4C22×D511yescharacteristic
337C22×C3×C4C22×D511yescharacteristic
338C22×C3×C4C22×D511yescharacteristic
339C22×Dic3—51no—
340C22×Dic3—51no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—54no—
344C22×Dic3—51no—
345C22×Dic3—51no—
346C22×Dic3—51no—
347C22×Dic3—51no—
348C22×Dic3—201no—
349C22×Dic3—201no—
350C2×Dic6—54no—
351C2×Dic6—201no—
352C2×Dic6—201no—
353C3×C4⋊C4—41no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4C4×D514yes—
357C3×C42—41no—
358#217—54no—
359#217—201no—
360#217—201no—
361C4⋊Dic3—54no—
362C4⋊Dic3—201no—
363Dic3⋊C4—54no—
364Dic3⋊C4—54no—
365Dic3⋊C4—201no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368Dic3⋊C4—201no—
369C4×Dic3—201no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C23×C5—21no—
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5—21no—
378C23×C5C2×C4×D312yes—
379C23×C5C23×D311yescharacteristic
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5C2×C4×D312yes—
397C2×C4×C5C2×C4×D312yes—
398C2×Dic5—32no—
399C2×Dic5—32no—
400C2×Dic5—32no—
401C2×Dic5—32no—
402C2×Dic5—61no—
403C2×Dic5—61no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5—124no—
423Dic10—124no—
424C22×Q8—151no—
425C23×C4—151no—
426C22⋊Q8—158no—
427C2×C4⋊C4—151no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4C2×D1511yescharacteristic
436C2×C22⋊C4—151no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4C2×D1511yescharacteristic
440C2×C22⋊C4C2×D1511yescharacteristic
441C2×C22⋊C4C2×D1511yescharacteristic
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42C2×D1511yescharacteristic
446#95—151no—
447#95—151no—
448#95—151no—
449#95—151no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95C2×D1511yescharacteristic
459#95C2×D1511yescharacteristic
460C2×C3×C5—42no—
461C2×C3×C5#51811yescharacteristic
462C2×C3×C5#51911yescharacteristic
463C2×C3×C5#52011yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56211yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C2×C3×C5#56311yescharacteristic
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3C2×C4×D512yes—
475C23×C3C23×D511yescharacteristic
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4C2×C4×D512yes—
493C2×C3×C4C2×C4×D512yes—
494C2×Dic3—52no—
495C2×Dic3—52no—
496C2×Dic3—52no—
497C2×Dic3—52no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—101no—
504C2×Dic3—101no—
505C2×Dic3—101no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3—204no—
519Dic6—204no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5C22×C4×D311yescharacteristic
528C22×C5#100411yescharacteristic
529C22×C5#100411yescharacteristic
530C22×C5#100911yescharacteristic
531C22×C5#101011yescharacteristic
532C22×C5#101011yescharacteristic
533C22×C5#101011yescharacteristic
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—41no—
537C4×C5—41no—
538C4×C5—41no—
539C4×C5—41no—
540Dic5—62no—
541Dic5—62no—
542Dic5—62no—
543Dic5—62no—
544Dic5—121no—
545Dic5—121no—
546Dic5—121no—
547Dic5—121no—
548C24C22×D1511yescharacteristic
549C2×Q8—154no—
550C2×Q8—601no—
551C2×Q8—601no—
552C22×C4—151no—
553C22×C4—151no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—154no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—601no—
562C22×C4—601no—
563C22×C4C22×D1511yescharacteristic
564C22×C4C22×D1511yescharacteristic
565C22×C4C22×D1511yescharacteristic
566C22×C4C22×D1511yescharacteristic
567C22×C4C22×D1511yescharacteristic
568C22×C4C22×D1511yescharacteristic
569C4⋊C4—41no—
570C4⋊C4—154no—
571C4⋊C4—154no—
572C4⋊C4—154no—
573C4⋊C4—601no—
574C4⋊C4—601no—
575C4⋊C4—601no—
576C4⋊C4—601no—
577C4⋊C4—601no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—154no—
581C22⋊C4—601no—
582C22⋊C4—601no—
583C22⋊C4C4×D1514yes—
584C42—41no—
585C42—601no—
586C42—601no—
587C42—601no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3C22×C4×D511yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414411yescharacteristic
599C22×C3#414911yescharacteristic
600C22×C3#415011yescharacteristic
601C22×C3#415011yescharacteristic
602C22×C3#415011yescharacteristic
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609Dic3—102no—
610Dic3—102no—
611Dic3—102no—
612Dic3—102no—
613Dic3—201no—
614Dic3—201no—
615Dic3—201no—
616Dic3—201no—
617C2×C5—42no—
618C2×C5#551611yescharacteristic
619C2×C5#554511yescharacteristic
620C2×C5#554611yescharacteristic
621C2×C5#562111yescharacteristic
622C2×C5#565111yescharacteristic
623C2×C5#568411yescharacteristic
624C2×C5#571211yescharacteristic
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23C2×C4×D1512yes—
632C23C23×D1511yescharacteristic
633Q8—604no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—152no—
651C2×C4—152no—
652C2×C4—152no—
653C2×C4—152no—
654C2×C4—301no—
655C2×C4—301no—
656C2×C4—301no—
657C2×C4—301no—
658C2×C4—301no—
659C2×C4—301no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—301no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—604no—
675C2×C4C2×C4×D1512yes—
676C2×C4C2×C4×D1512yes—
677C2×C3—42no—
678C2×C3#6585011yescharacteristic
679C2×C3#6587911yescharacteristic
680C2×C3#6588011yescharacteristic
681C2×C3#6595511yescharacteristic
682C2×C3#6598511yescharacteristic
683C2×C3#6601811yescharacteristic
684C2×C3#6604611yescharacteristic
685C5#7549211yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22C22×C4×D1511yescharacteristic
694C22#9209511yescharacteristic
695C22#9209511yescharacteristic
696C22#9210011yescharacteristic
697C22#9210111yescharacteristic
698C22#9210111yescharacteristic
699C22#9210111yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—302no—
707C4—302no—
708C4—302no—
709C4—302no—
710C4—601no—
711C4—601no—
712C4—601no—
713C4—601no—
714C3#1060722311yescharacteristic, complemented, Sylow
715C2—42no—
716C2#1175627511yescharacteristic
717C2#1175630411yescharacteristic
718C2#1175630511yescharacteristic
719C2#1175638011yescharacteristic
720C2#1175641011yescharacteristic
721C2#1175644311yescharacteristic
722C2#1175647111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenter#388D15
hypocenterC3×C5#2378
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #11751079C2semidirect
4. #11751073C2semidirect
10. #11751034C2semidirect
11. #11751030C2semidirect
12. #11750754C2semidirect
13. #11750753C2semidirect
14. #11750748C2semidirect
15. #11750747C2semidirect
38. #91767C4semidirect
588. C3×C5#2378semidirect
685. C5#75492semidirect
714. C3#10607223semidirect

Maximal subgroups

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

subgroupindex
C2×#917672
C3×C5×#3882
#117510792
#117510732
#117510522
#117510462
#117510442
#117510432
#117510342
#117510302
#117507542
#117507532
#117507482
#117507472
#106072233
#754925