Finite Group Databasebeta

← #14326545

Subgroups — #14326545

Order 1920.

1064 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×#91403C211yesmaximal, characteristic
2#11751090C211yesmaximal, characteristic
3C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#65267C211yesmaximal, characteristic, complemented
5#11748902C211yesmaximal, characteristic
6#11748889C211yesmaximal, characteristic
7#11748888C211yesmaximal, characteristic
8#11748881C211yesmaximal, characteristic
9#11748807C211yesmaximal, characteristic, complemented
10#11748806C211yesmaximal, characteristic, complemented
11C4×#6667C211yesmaximal, characteristic
12#11748690C211yesmaximal, characteristic, complemented
13#11748644C211yesmaximal, characteristic, complemented
14#11748635C211yesmaximal, characteristic, complemented
15#11748618C211yesmaximal, characteristic, complemented
16#10605497—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×#6669C2211yescharacteristic
31C2×#6668C2211yescharacteristic
32C2×#6667C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×Dic3×Dic5C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36#91403C418yescomplemented
37#91115C2211yescharacteristic
38#91115C2211yescharacteristic
39C5×C3⋊#95C2211yescharacteristic
40C5×C3⋊#95C2211yescharacteristic
41C3×#3963C2211yescharacteristic
42C3×#3963C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45#90994C2211yescharacteristic
46#90994C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75303—51nomaximal, Hall
54C2×#4018—31no—
55C4×C5×C4⋊C4—31no—
56#65278—31no—
57#65278—31no—
58#65267—31no—
59#65267D311yescharacteristic, complemented
60C4×#685—31no—
61C4×#685—31no—
62#65226—31no—
63#65222—31no—
64#65222—31no—
65#64953—31no—
66D5×#95—31no—
67#64939—31no—
68#64937—31no—
69C23×D15C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C2×C4×D15—22no—
77C2×C4×D15—22no—
78C2×C4×D15—41no—
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×#1200—22no—
88C2×#1200—22no—
89C2×#1200—22no—
90C2×#1200—22no—
91C2×#1200—41no—
92C2×#1200C2×C414yes—
93C3×C5×C4⋊C4—22no—
94#6714—22no—
95#6714C2×C414yes—
96#6712—41no—
97C5×C4⋊Dic3—22no—
98C4×C5×Dic3—41no—
99C4×C5×Dic3—41no—
100C4×C5×Dic3C2×C414yescomplemented
101C3×#683C2×C414yescomplemented
102C3×C4×Dic5—22no—
103#6669—41no—
104#6668C2×C414yescomplemented
105#6667—22no—
106#6667C2×C414yes—
107Dic3×Dic5—22no—
108Dic3×Dic5C2×C414yescomplemented
109C2×#892—51no—
110C3×#387—51no—
111#4989—51no—
112#4980—51no—
113Dic3×C4⋊C4D511yescharacteristic, complemented
114C4×(C2×D3)⋊C4—51no—
115#4932—51no—
116#4668—51no—
117#4666—51no—
118#4664—51no—
119D3×#95—51no—
120#4654—51no—
121#4653—51no—
122#4651—51no—
123#4650—51no—
124C22×C4×D5—31no—
125C22×C4×D5—31no—
126C22×C4×D5—31no—
127C2×C5×C4⋊C4—31no—
128C2×C5×C4⋊C4C2×D311yescharacteristic
129C2×C42×C5—31no—
130C2×C42×C5—31no—
131C2×C42×C5—31no—
132C2×#685—31no—
133C2×#685—31no—
134C2×#685—31no—
135C2×#685—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683C2×D311yescharacteristic
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5C2×D311yescharacteristic
143#4018—38no—
144C5×#95—31no—
145C5×#95—31no—
146#3963—31no—
147#3963—31no—
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#3963C2×D311yescharacteristic
157#3963C2×D311yescharacteristic
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2343—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×C5C22×C412yes—
177C2×C3×C4×C5#4112yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15C22×C412yes—
187C4×D15—44no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3C22×C412yes—
198C2×C5×Dic3C22×C412yes—
199C2×C5×Dic3#4112yes—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5C22×C412yes—
211C2×C3×Dic5C22×C412yes—
212#1200—28no—
213#1200—44no—
214C22×C4×D3—51no—
215C22×C4×D3—51no—
216C22×C4×D3—51no—
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4C2×D511yescharacteristic
219C2×C3×C42—51no—
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⋊Dic3C2×D511yescharacteristic
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×C4×Dic3—51no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3C2×D511yescharacteristic
231C2×C4×Dic3C2×D511yescharacteristic
232C2×C4×Dic3C2×D511yescharacteristic
233#892—58no—
234C3×#95—51no—
235C3×#95—51no—
236C3×#95—51no—
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⋊#95C2×D511yescharacteristic
249C3⋊#95C2×D511yescharacteristic
250C23×D5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5—31no—
255C22×C4×C5C22×D311yescharacteristic
256C22×C4×C5C22×D311yescharacteristic
257C22×C4×C5C22×D311yescharacteristic
258C22×Dic5—31no—
259C22×Dic5—31no—
260C22×Dic5—31no—
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263C22×Dic5C22×D311yescharacteristic
264C22×Dic5C22×D311yescharacteristic
265C2×C4×D5—34no—
266C2×C4×D5—62no—
267C2×C4×D5—62no—
268C2×C4×D5—62no—
269C2×C4×D5—62no—
270C2×C4×D5—62no—
271C2×C4×D5—62no—
272C2×C4×D5—121no—
273C2×C4×D5—121no—
274C5×C4⋊C4—22no—
275C5×C4⋊C4—62no—
276C42×C5—34no—
277C42×C5—121no—
278C42×C5—121no—
279#685—34no—
280#685—34no—
281#685—62no—
282#685—62no—
283#683—34no—
284#683—121no—
285#683—121no—
286#683C4×D314yescomplemented
287C4×Dic5—22no—
288C4×Dic5—34no—
289C4×Dic5—62no—
290C2×#117—151no—
291#387—51no—
292#387—151no—
293#387—151no—
294#387—151no—
295#385—151no—
296#385—151no—
297#383—151no—
298#382—151no—
299#381—151no—
300C4×C4⋊C4—31no—
301C4×C22⋊C4—151no—
302C4×C22⋊C4—151no—
303#376—151no—
304C2×#95—151no—
305C22×C3×C5C23×C411yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5C2×#4111yescharacteristic
309C22×C3×C5C2×#4111yescharacteristic
310C22×C3×C5H(5,𝔽2)11yescharacteristic
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—41no—
322Dic15—22no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—22no—
326C3×Dic5—22no—
327C3×Dic5—41no—
328C3×Dic5—41no—
329C5×Dic3—22no—
330C5×Dic3—22no—
331C5×Dic3—22no—
332C5×Dic3—41no—
333C23×D3—51no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D511yescharacteristic
340C22×C3×C4C22×D511yescharacteristic
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3C22×D511yescharacteristic
345C22×Dic3C22×D511yescharacteristic
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C2×C4×D3—54no—
349C2×C4×D3—102no—
350C2×C4×D3—102no—
351C2×C4×D3—102no—
352C2×C4×D3—102no—
353C2×C4×D3—102no—
354C2×C4×D3—102no—
355C2×C4×D3—201no—
356C2×C4×D3—201no—
357C3×C4⋊C4—22no—
358C3×C4⋊C4—54no—
359C3×C42—102no—
360(C2×D3)⋊C4—54no—
361(C2×D3)⋊C4—54no—
362(C2×D3)⋊C4—102no—
363(C2×D3)⋊C4—102no—
364C4⋊Dic3—22no—
365C4⋊Dic3—54no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368C4×Dic3—41no—
369C4×Dic3—41no—
370C4×Dic3—54no—
371C4×Dic3—102no—
372C4×Dic3C4×D514yescomplemented
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—32no—
389C2×C4×C5—32no—
390C2×C4×C5—32no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5—61no—
399C2×C4×C5—61no—
400C2×C4×C5C2×C4×D312yes—
401C2×C4×C5#23712yes—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—32no—
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×Dic5C2×C4×D312yes—
422C2×Dic5C2×C4×D312yes—
423C4×D5—68no—
424C4×D5—124no—
425C4×D5—124no—
426C23×C4—151no—
427C23×C4—151no—
428C23×C4—151no—
429#117—158no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4D3×D511yescharacteristic
436C2×C22⋊C4—151no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—151no—
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—31no—
443C2×C42—51no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—51no—
449#95—51no—
450#95—51no—
451#95—51no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460#95—151no—
461#95—151no—
462C2×C3×C5C2×#11711yescharacteristic
463C2×C3×C5C4×#4111yescharacteristic
464C2×C3×C5#52011yescharacteristic
465C2×C3×C5#55111yescharacteristic
466C2×C3×C5#55111yescharacteristic
467C2×C3×C5#55211yescharacteristic
468C2×C3×C5#55211yescharacteristic
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—52no—
486C2×C3×C4—52no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—101no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4C2×C4×D512yes—
498C2×C3×C4#70912yes—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
518C2×Dic3C2×C4×D512yes—
519C2×Dic3#70912yes—
520C4×D3—108no—
521C4×D3—204no—
522C4×D3—204no—
523C22×C5C22×C4×D311yescharacteristic
524C22×C5C2×#23711yescharacteristic
525C22×C5#100711yescharacteristic
526C22×C5D3×#4111yescharacteristic
527C22×C5D3×#4111yescharacteristic
528C22×C5D3×#4111yescharacteristic
529C22×C5#100911yescharacteristic
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—41no—
540C4×C5—62no—
541C4×C5—62no—
542C4×C5—62no—
543C4×C5—121no—
544Dic5—22no—
545Dic5—22no—
546Dic5—41no—
547Dic5—41no—
548Dic5—62no—
549Dic5—121no—
550Dic5—121no—
551C24—151no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—154no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—601no—
571C22×C4—601no—
572C22×C4C2×D3×D511yescharacteristic
573C22×C4C2×D3×D511yescharacteristic
574C22×C4C2×D3×D511yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—54no—
577C4⋊C4—62no—
578C4⋊C4—154no—
579C4⋊C4—601no—
580C4⋊C4—601no—
581C22⋊C4—154no—
582C22⋊C4—154no—
583C22⋊C4—302no—
584C22⋊C4—302no—
585C42—34no—
586C42—102no—
587C42—121no—
588C42—121no—
589C42—154no—
590C42—302no—
591C3×C5#234311yescharacteristic, complemented, Hall
592C22×C3C22×C4×D511yescharacteristic
593C22×C3C2×#70911yescharacteristic
594C22×C3C2×#70911yescharacteristic
595C22×C3#414411yescharacteristic
596C22×C3#414711yescharacteristic
597C22×C3D5×#4111yescharacteristic
598C22×C3D5×#4111yescharacteristic
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—41no—
609C3×C4—102no—
610C3×C4—102no—
611C3×C4—201no—
612C3×C4—201no—
613Dic3—22no—
614Dic3—22no—
615Dic3—22no—
616Dic3—41no—
617Dic3—102no—
618Dic3—201no—
619Dic3—201no—
620C2×C5D3×#11711yescharacteristic
621C2×C5C4×#23711yescharacteristic
622C2×C5#557411yescharacteristic
623C2×C5#563911yescharacteristic
624C2×C5#565811yescharacteristic
625C2×C5#569311yescharacteristic
626C2×C5#570511yescharacteristic
627D5—64no—
628C23—152no—
629C23—152no—
630C23—152no—
631C23—301no—
632C23—301no—
633C23—301no—
634C23—301no—
635C23C22×D3×D511yescharacteristic
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—52no—
647C2×C4—52no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—152no—
668C2×C4—308no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—604no—
678C2×C4—604no—
679C2×C4C4×D3×D512yes—
680C2×C4#677912yes—
681C2×C3C4×#70911yescharacteristic
682C2×C3#6583811yescharacteristic
683C2×C3D5×#11711yescharacteristic
684C2×C3#6589011yescharacteristic
685C2×C3#6589011yescharacteristic
686C2×C3#6591511yescharacteristic
687C2×C3#6591511yescharacteristic
688D3—104no—
689C5#7530311yescharacteristic, complemented, Sylow
690C22—154no—
691C22—302no—
692C22—302no—
693C22—302no—
694C22—302no—
695C22—302no—
696C22—302no—
697C22C2×C4×D3×D511yescharacteristic
698C22D3×#70911yescharacteristic
699C22#9202411yescharacteristic
700C22#9202711yescharacteristic
701C22#9202911yescharacteristic
702C22#9203411yescharacteristic
703C22C2×#677911yescharacteristic
704C4—22no—
705C4—22no—
706C4—41no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—102no—
711C4—102no—
712C4—121no—
713C4—201no—
714C4—201no—
715C4—302no—
716C4—601no—
717C4—601no—
718C3#1060549711yescharacteristic, complemented, Sylow
719C2—304no—
720C2#1175333711yescharacteristic
721C2#1175338411yescharacteristic
722C2#1175383511yescharacteristic
723C2#1175392011yescharacteristic
724C2C4×#677911yescharacteristic
725C2#1175473711yescharacteristic
726C2#1175513211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×Dic3×C4⋊C4C2semidirect
4. C3×#65267C2semidirect
9. #11748807C2semidirect
10. #11748806C2semidirect
12. #11748690C2semidirect
13. #11748644C2semidirect
14. #11748635C2semidirect
15. #11748618C2semidirect
36. #91403C4semidirect
59. #65267D3semidirect
100. C4×C5×Dic3C2×C4semidirect
101. C3×#683C2×C4semidirect
104. #6668C2×C4semidirect
108. Dic3×Dic5C2×C4semidirect
113. Dic3×C4⋊C4D5semidirect
286. #683C4×D3semidirect
372. C4×Dic3C4×D5semidirect
591. C3×C5#2343semidirect
689. C5#75303semidirect
718. C3#10605497semidirect

Maximal subgroups

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

subgroupindex
C2×#914032
#117510902
C5×Dic3×C4⋊C42
C3×#652672
#117489022
#117488892
#117488882
#117488812
#117488072
#117488062
C4×#66672
#117486902
#117486442
#117486352
#117486182
#106054973
#753035