Finite Group Databasebeta

← #14322643

Subgroups — #14322643

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic, complemented
3#11751088C211yesmaximal, characteristic
4#11751081C211yesmaximal, characteristic, complemented
5#11751079C211yesmaximal, characteristic, complemented
6C4×#6714C211yesmaximal, characteristic
7#11751034C211yesmaximal, characteristic, complemented
8#11750768C211yesmaximal, characteristic
9#11750767C211yesmaximal, characteristic
10#11750765C211yesmaximal, characteristic
11#11750765C211yesmaximal, characteristic
12#11750756C211yesmaximal, characteristic, complemented
13#11750755C211yesmaximal, characteristic, complemented
14#11750754C211yesmaximal, characteristic, complemented
15#11750753C211yesmaximal, characteristic, complemented
16#10607027—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C4⋊C4×D15C418yescomplemented
37C3×C5×#95C2211yescharacteristic
38C3×C5×#95C2211yescharacteristic
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#75296—51nomaximal, Hall
54C2×D5×C4⋊C4—31no—
55C5×#387D311yescharacteristic, complemented
56#65276—31no—
57#65270—31no—
58#65267—31no—
59C4×#685—31no—
60#65222—31no—
61#64956—31no—
62#64955—31no—
63#64953—31no—
64#64953—31no—
65#64944—31no—
66#64943—31no—
67#64942—31no—
68#64941—31no—
69C23×D15C2311yescharacteristic
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×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15—41no—
87C2×C4×D15—41no—
88C2×C4×D15—41no—
89C2×C4×D15—41no—
90C2×C4×D15C2×C414yes—
91C2×C4×D15C2×C414yes—
92C2×C4×D15C2×C414yes—
93C3×C5×C4⋊C4—41no—
94C3×C5×C4⋊C4C2×C414yes—
95C3×C42×C5—41no—
96#6714—22no—
97#6714—22no—
98#6714—22no—
99#6714—22no—
100C4⋊Dic15—41no—
101C4⋊Dic15C2×C414yes—
102#6712—41no—
103#6712—41no—
104#6712C2×C414yes—
105#6712C2×C414yes—
106C4×Dic15—41no—
107C4×Dic15—41no—
108C4×Dic15—41no—
109C2×D3×C4⋊C4—51no—
110C3×#387D511yescharacteristic, complemented
111#4987—51no—
112#4980—51no—
113#4978—51no—
114C4×(C2×D3)⋊C4—51no—
115#4933—51no—
116#4667—51no—
117#4666—51no—
118#4664—51no—
119#4664—51no—
120#4655—51no—
121#4654—51no—
122#4653—51no—
123#4652—51no—
124C22×C4×D5—31no—
125C22×C4×D5—31no—
126C22×C4×D5—31no—
127C2×C5×C4⋊C4C2×D311yescharacteristic
128C2×C5×C4⋊C4C2×D311yescharacteristic
129C2×C42×C5C2×D311yescharacteristic
130C2×#685—31no—
131C2×#685—31no—
132C2×#685—31no—
133C2×#685—31no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143D5×C4⋊C4—38no—
144C5×#95C2×D311yescharacteristic
145C5×#95C2×D311yescharacteristic
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#2313—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×D15—21no—
163C22×D15—21no—
164C22×D15—21no—
165C22×D15—21no—
166C22×D15C22×C412yes—
167C22×D15#4112yes—
168C22×D15#4112yes—
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×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C22×C412yes—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
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—21no—
208C2×Dic15C22×C412yes—
209C2×Dic15C22×C412yes—
210C2×Dic15C22×C412yes—
211C4×D15—28no—
212C4×D15—44no—
213C4×D15—44no—
214C22×C4×D3—51no—
215C22×C4×D3—51no—
216C22×C4×D3—51no—
217C2×C3×C4⋊C4C2×D511yescharacteristic
218C2×C3×C4⋊C4C2×D511yescharacteristic
219C2×C3×C42C2×D511yescharacteristic
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—51no—
223C2×(C2×D3)⋊C4—51no—
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233D3×C4⋊C4—58no—
234C3×#95C2×D511yescharacteristic
235C3×#95C2×D511yescharacteristic
236C3×#95C2×D511yescharacteristic
237C3×#95C2×D511yescharacteristic
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—
249C3⋊#95—51no—
250C23×D5—31no—
251C22×C4×C5C22×D311yescharacteristic
252C22×C4×C5C22×D311yescharacteristic
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×C4×C5C22×D311yescharacteristic
257C22×C4×C5C22×D311yescharacteristic
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—31no—
261C22×Dic5—31no—
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5—31no—
265C2×C4×D5—34no—
266C2×C4×D5—34no—
267C2×C4×D5—34no—
268C2×C4×D5—62no—
269C2×C4×D5—62no—
270C2×C4×D5—121no—
271C2×C4×D5—121no—
272C2×C4×D5—121no—
273C2×C4×D5—121no—
274C5×C4⋊C4—41no—
275C5×C4⋊C4C4×D314yes—
276C42×C5—41no—
277#685—62no—
278#685—62no—
279#685—62no—
280#685—62no—
281C4⋊Dic5—34no—
282C4⋊Dic5—121no—
283#683—34no—
284#683—34no—
285#683—121no—
286#683—121no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C4×Dic5—121no—
290C22×C4⋊C4—151no—
291#387—151no—
292#387—151no—
293#387—151no—
294#387—151no—
295#387—151no—
296#387—151no—
297#387—151no—
298#387D1511yescharacteristic, complemented
299#381—151no—
300#381—151no—
301#380—151no—
302#380—151no—
303C4×C22⋊C4—151no—
304C4×C22⋊C4—151no—
305C22×C3×C5C23×C411yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5H(5,𝔽2)11yescharacteristic
309C22×C3×C5H(5,𝔽2)11yescharacteristic
310C22×C3×C52−1+411yescharacteristic
311C22×C3×C52−1+411yescharacteristic
312C2×D15—22no—
313C2×D15—22no—
314C2×D15—22no—
315C2×D15—22no—
316C2×D15—22no—
317C2×D15—22no—
318C2×D15#11714yes—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321C3×C4×C5—22no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5—41no—
326Dic15—22no—
327Dic15—22no—
328Dic15—22no—
329Dic15—41no—
330Dic15—41no—
331Dic15—41no—
332Dic15—41no—
333C23×D3—51no—
334C22×C3×C4C22×D511yescharacteristic
335C22×C3×C4C22×D511yescharacteristic
336C22×C3×C4C22×D511yescharacteristic
337C22×C3×C4C22×D511yescharacteristic
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D511yescharacteristic
340C22×C3×C4C22×D511yescharacteristic
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—51no—
345C22×Dic3—51no—
346C22×Dic3—51no—
347C22×Dic3—51no—
348C2×C4×D3—54no—
349C2×C4×D3—54no—
350C2×C4×D3—54no—
351C2×C4×D3—102no—
352C2×C4×D3—102no—
353C2×C4×D3—201no—
354C2×C4×D3—201no—
355C2×C4×D3—201no—
356C2×C4×D3—201no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4C4×D514yes—
359C3×C42—41no—
360(C2×D3)⋊C4—102no—
361(C2×D3)⋊C4—102no—
362(C2×D3)⋊C4—102no—
363(C2×D3)⋊C4—102no—
364C4⋊Dic3—54no—
365C4⋊Dic3—201no—
366Dic3⋊C4—54no—
367Dic3⋊C4—54no—
368Dic3⋊C4—201no—
369Dic3⋊C4—201no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C4×Dic3—201no—
373C23×C5C23×D311yescharacteristic
374C22×D5—32no—
375C22×D5—32no—
376C22×D5—32no—
377C22×D5—61no—
378C22×D5—61no—
379C22×D5—61no—
380C22×D5—61no—
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×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5C2×C4×D312yes—
400C2×C4×C5C2×C4×D312yes—
401C2×C4×C5C2×C4×D312yes—
402C2×Dic5—32no—
403C2×Dic5—32no—
404C2×Dic5—32no—
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—61no—
423C4×D5—68no—
424C4×D5—124no—
425C4×D5—124no—
426C23×C4—151no—
427C23×C4—151no—
428C23×C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—158no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—151no—
436C2×C4⋊C4C2×D1511yescharacteristic
437C2×C4⋊C4C2×D1511yescharacteristic
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
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
460#95C2×D1511yescharacteristic
461#95C2×D1511yescharacteristic
462C2×C3×C5C2×#11711yescharacteristic
463C2×C3×C5#51811yescharacteristic
464C2×C3×C5#51911yescharacteristic
465C2×C3×C5#53911yescharacteristic
466C2×C3×C5#53911yescharacteristic
467C2×C3×C5#53911yescharacteristic
468C2×C3×C5#53911yescharacteristic
469D15—24no—
470C23×C3C23×D511yescharacteristic
471C22×D3—52no—
472C22×D3—52no—
473C22×D3—52no—
474C22×D3—101no—
475C22×D3—101no—
476C22×D3—101no—
477C22×D3—101no—
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×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4C2×C4×D512yes—
497C2×C3×C4C2×C4×D512yes—
498C2×C3×C4C2×C4×D512yes—
499C2×Dic3—52no—
500C2×Dic3—52no—
501C2×Dic3—52no—
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—101no—
519C2×Dic3—101no—
520C4×D3—108no—
521C4×D3—204no—
522C4×D3—204no—
523C22×C5C22×C4×D311yescharacteristic
524C22×C5#100411yescharacteristic
525C22×C5#100711yescharacteristic
526C22×C5D3×#4111yescharacteristic
527C22×C5D3×#4111yescharacteristic
528C22×C5#100911yescharacteristic
529C22×C5#101011yescharacteristic
530C2×D5—34no—
531C2×D5—62no—
532C2×D5—62no—
533C2×D5—62no—
534C2×D5—62no—
535C2×D5—62no—
536C2×D5—62no—
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—41no—
541C4×C5—41no—
542C4×C5—41no—
543C4×C5—41no—
544Dic5—62no—
545Dic5—62no—
546Dic5—62no—
547Dic5—121no—
548Dic5—121no—
549Dic5—121no—
550Dic5—121no—
551C24—151no—
552C22×C4—151no—
553C22×C4—151no—
554C22×C4—151no—
555C22×C4—154no—
556C22×C4—154no—
557C22×C4—154no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—302no—
563C22×C4—302no—
564C22×C4—601no—
565C22×C4—601no—
566C22×C4—601no—
567C22×C4—601no—
568C22×C4C22×D1511yescharacteristic
569C22×C4C22×D1511yescharacteristic
570C22×C4C22×D1511yescharacteristic
571C22×C4C22×D1511yescharacteristic
572C22×C4C22×D1511yescharacteristic
573C22×C4C22×D1511yescharacteristic
574C22×C4C22×D1511yescharacteristic
575C4⋊C4—41no—
576C4⋊C4—154no—
577C4⋊C4—154no—
578C4⋊C4—154no—
579C4⋊C4—601no—
580C4⋊C4—601no—
581C4⋊C4—601no—
582C4⋊C4C4×D1514yes—
583C22⋊C4—302no—
584C22⋊C4—302no—
585C22⋊C4—302no—
586C22⋊C4—302no—
587C42—41no—
588C42—601no—
589C42—601no—
590C42—601no—
591C3×C5#231311yescharacteristic, complemented, Hall
592C22×C3C22×C4×D511yescharacteristic
593C22×C3#414411yescharacteristic
594C22×C3#414711yescharacteristic
595C22×C3D5×#4111yescharacteristic
596C22×C3D5×#4111yescharacteristic
597C22×C3#414911yescharacteristic
598C22×C3#415011yescharacteristic
599C2×D3—54no—
600C2×D3—102no—
601C2×D3—102no—
602C2×D3—102no—
603C2×D3—102no—
604C2×D3—102no—
605C2×D3—102no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613Dic3—102no—
614Dic3—102no—
615Dic3—102no—
616Dic3—201no—
617Dic3—201no—
618Dic3—201no—
619Dic3—201no—
620C2×C5D3×#11711yescharacteristic
621C2×C5#554511yescharacteristic
622C2×C5#557211yescharacteristic
623C2×C5#563811yescharacteristic
624C2×C5#566011yescharacteristic
625C2×C5#569211yescharacteristic
626C2×C5#570711yescharacteristic
627D5—64no—
628C23—152no—
629C23—152no—
630C23—152no—
631C23—301no—
632C23—301no—
633C23—301no—
634C23—301no—
635C23C23×D1511yescharacteristic
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—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—152no—
655C2×C4—152no—
656C2×C4—152no—
657C2×C4—308no—
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—301no—
675C2×C4—301no—
676C2×C4—604no—
677C2×C4—604no—
678C2×C4C2×C4×D1512yes—
679C2×C4C2×C4×D1512yes—
680C2×C4C2×C4×D1512yes—
681C2×C3D5×#11711yescharacteristic
682C2×C3#6587911yescharacteristic
683C2×C3#6590611yescharacteristic
684C2×C3#6597211yescharacteristic
685C2×C3#6599411yescharacteristic
686C2×C3#6602611yescharacteristic
687C2×C3#6604111yescharacteristic
688D3—104no—
689C5#7529611yescharacteristic, complemented, Sylow
690C22—154no—
691C22—302no—
692C22—302no—
693C22—302no—
694C22—302no—
695C22—302no—
696C22—302no—
697C22C22×C4×D1511yescharacteristic
698C22#9209511yescharacteristic
699C22#9209811yescharacteristic
700C22#41×D1511yescharacteristic
701C22#41×D1511yescharacteristic
702C22#9210011yescharacteristic
703C22#9210111yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—302no—
712C4—302no—
713C4—302no—
714C4—601no—
715C4—601no—
716C4—601no—
717C4—601no—
718C3#1060702711yescharacteristic, complemented, Sylow
719C2—304no—
720C2D15×#11711yescharacteristic
721C2#1175630411yescharacteristic
722C2#1175633111yescharacteristic
723C2#1175639711yescharacteristic
724C2#1175641911yescharacteristic
725C2#1175645111yescharacteristic
726C2#1175646611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#387C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#387D15
hypocenterC3×C5#2313
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C3×C5×#387C2semidirect
4. #11751081C2semidirect
5. #11751079C2semidirect
7. #11751034C2semidirect
12. #11750756C2semidirect
13. #11750755C2semidirect
14. #11750754C2semidirect
15. #11750753C2semidirect
36. C4⋊C4×D15C4semidirect
55. C5×#387D3semidirect
110. C3×#387D5semidirect
298. #387D15semidirect
591. C3×C5#2313semidirect
689. C5#75296semidirect
718. C3#10607027semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C3×C5×#3872
#117510882
#117510812
#117510792
C4×#67142
#117510342
#117507682
#117507672
#117507652
#117507562
#117507552
#117507542
#117507532
#106070273
#752965