Finite Group Databasebeta

← #14329808

Subgroups — #14329808

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic
2C5×#5229C211yesmaximal, characteristic, complemented
3C3×#65519C211yesmaximal, characteristic, complemented
4#11748902C211yesmaximal, characteristic
5#11748898C211yesmaximal, characteristic
6#11748888C211yesmaximal, characteristic
7#11748881C211yesmaximal, characteristic
8#11748875C211yesmaximal, characteristic
9#11748689C211yesmaximal, characteristic, complemented
10#11748688C211yesmaximal, characteristic, complemented
11#11748687C211yesmaximal, characteristic, complemented
12#11748674C211yesmaximal, characteristic, complemented
13#11748670C211yesmaximal, characteristic
14#11748645C211yesmaximal, characteristic, complemented
15#11748640C211yesmaximal, characteristic, complemented
16#10608347—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21#91835C418yescomplemented
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×#6669C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C5×C3⋊#95C2211yescharacteristic
40C5×C3⋊#95C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#76616—51nomaximal, Hall
54C2×#4092—31no—
55C5×#391—31no—
56#65519D311yescharacteristic, complemented
57#65278—31no—
58#65267—31no—
59C4×#685—31no—
60C4×#683—31no—
61#64957—31no—
62#64955—31no—
63#64955—31no—
64D5×#95—31no—
65#64944—31no—
66#64943—31no—
67#64942—31no—
68#64938—31no—
69C23×D15C2311yescharacteristic
70C2×C3×C5×Q8—41no—
71C2×C3×C5×Q8—41no—
72C2×C3×C5×Q8C2×C414yescomplemented
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C4×D15—41no—
80C2×C4×D15—41no—
81C2×C4×D15C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×#1200—22no—
91C2×#1200—22no—
92C2×#1200—22no—
93C2×#1200—22no—
94C2×#1200—41no—
95C2×#1200—41no—
96#6714C2×C414yes—
97#6714C2×C414yes—
98C4⋊Dic15C2×C414yescomplemented
99#6712C2×C414yescomplemented
100#6712C2×C414yescomplemented
101C5×C4⋊Dic3—41no—
102C4×C5×Dic3—41no—
103C3×C4⋊Dic5—41no—
104C3×C4×Dic5—41no—
105#6669—22no—
106#6669—22no—
107#6667—22no—
108#6667Q814yescomplemented
109Dic3×Dic5—22no—
110Dic3×Dic5—22no—
111Dic3×Dic5—41no—
112Dic3×Dic5—41no—
113C2×#946—51no—
114C3×#391—51no—
115#5229D511yescharacteristic, complemented
116#4989—51no—
117#4978—51no—
118C4×(C2×D3)⋊C4—51no—
119C4×Dic3⋊C4—51no—
120#4668—51no—
121#4666—51no—
122#4666—51no—
123D3×#95—51no—
124#4655—51no—
125#4654—51no—
126#4653—51no—
127#4649—51no—
128C22×C5×Q8C2×D311yescharacteristic
129C22×C4×D5—31no—
130C22×C4×D5—31no—
131C22×C4×D5—31no—
132C2×C5×C4⋊C4—31no—
133C2×C42×C5—31no—
134#4092—38no—
135C2×#685—31no—
136C2×#685—31no—
137C2×#685—31no—
138C2×#685—31no—
139C2×C4⋊Dic5—31no—
140C2×C4⋊Dic5C2×D311yescharacteristic
141C2×#683—31no—
142C2×#683—31no—
143C2×#683—31no—
144C2×#683—31no—
145C2×C4×Dic5—31no—
146C2×C4×Dic5—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5C2×D311yescharacteristic
150C5×#95—31no—
151C5×#95—31no—
152C5×#95—31no—
153C5×#95—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963C2×D311yescharacteristic
161#3963C2×D311yescharacteristic
162#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#2368—151noSylow
165C23×C3×C5C2411yescharacteristic
166C22×D15—21no—
167C22×D15—21no—
168C22×D15—21no—
169C22×D15—21no—
170C22×D15C22×C412yes—
171C22×D15C2×Q812yes—
172C22×D15#4112yes—
173C3×C5×Q8—44no—
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×C5C22×C412yes—
181C2×C3×C4×C5C22×C412yes—
182C2×C3×C4×C5C22×C412yes—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15C22×C412yes—
190C2×Dic15C22×C412yes—
191C2×Dic15C22×C412yes—
192C4×D15—44no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3C2×Q812yes—
204C2×C5×Dic3#4112yes—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5C2×Q812yes—
216C2×C3×Dic5#4112yes—
217#1200—44no—
218#1200—44no—
219C22×C3×Q8C2×D511yescharacteristic
220C22×C4×D3—51no—
221C22×C4×D3—51no—
222C22×C4×D3—51no—
223C2×C3×C4⋊C4—51no—
224C2×C3×C42—51no—
225#946—58no—
226C2×(C2×D3)⋊C4—51no—
227C2×(C2×D3)⋊C4—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×(C2×D3)⋊C4—51no—
230C2×C4⋊Dic3—51no—
231C2×C4⋊Dic3C2×D511yescharacteristic
232C2×Dic3⋊C4—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×C4×Dic3—51no—
237C2×C4×Dic3—51no—
238C2×C4×Dic3—51no—
239C2×C4×Dic3—51no—
240C2×C4×Dic3C2×D511yescharacteristic
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—
250C3⋊#95—51no—
251C3⋊#95C2×D511yescharacteristic
252C3⋊#95C2×D511yescharacteristic
253C3⋊#95C2×D511yescharacteristic
254C3⋊#95C2×D511yescharacteristic
255C23×D5—31no—
256C2×C5×Q8—41no—
257C2×C5×Q8—41no—
258C2×C5×Q8C4×D314yescomplemented
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×Dic5—31no—
267C22×Dic5—31no—
268C22×Dic5—31no—
269C22×Dic5C22×D311yescharacteristic
270C22×Dic5C22×D311yescharacteristic
271C22×Dic5C22×D311yescharacteristic
272C22×Dic5C22×D311yescharacteristic
273C2×C4×D5—34no—
274C2×C4×D5—62no—
275C2×C4×D5—62no—
276C2×C4×D5—62no—
277C2×C4×D5—62no—
278C2×C4×D5—121no—
279C2×C4×D5—121no—
280C2×C4×D5—121no—
281C2×C4×D5—121no—
282C5×C4⋊C4—121no—
283C42×C5—121no—
284#685—34no—
285#685—34no—
286#685—34no—
287#685—62no—
288C4⋊Dic5—34no—
289C4⋊Dic5—41no—
290#683—34no—
291#683—34no—
292#683—62no—
293#683—62no—
294C4×Dic5—41no—
295C4×Dic5—62no—
296C4×Dic5—62no—
297C4×Dic5—121no—
298C4×Dic5—121no—
299C2×C22⋊Q8—151no—
300#391—31no—
301#391—51no—
302#387—151no—
303#387—151no—
304#387—151no—
305#387—151no—
306#385—151no—
307#385—151no—
308C4×C4⋊C4—151no—
309C4×C4⋊C4—151no—
310C4×C22⋊C4—151no—
311C4×C22⋊C4—151no—
312C4×C22⋊C4—151no—
313C2×#95—151no—
314C22×C3×C5C23×C411yescharacteristic
315C22×C3×C5C22×Q811yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5C2×#4111yescharacteristic
318C22×C3×C5C2×#4111yescharacteristic
319C22×C3×C5H(5,𝔽2)11yescharacteristic
320C22×C3×C5H(5,𝔽2)11yescharacteristic
321C2×D15—22no—
322C2×D15—22no—
323C2×D15—22no—
324C2×D15—22no—
325C2×D15—22no—
326C2×D15—22no—
327C2×D15C4×Q814yes—
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330C3×C4×C5—22no—
331Dic15—22no—
332Dic15—22no—
333Dic15—22no—
334C3×Dic5—22no—
335C3×Dic5—22no—
336C3×Dic5—41no—
337C3×Dic5—41no—
338C5×Dic3—22no—
339C5×Dic3—22no—
340C5×Dic3—41no—
341C5×Dic3—41no—
342C23×D3—51no—
343C2×C3×Q8—41no—
344C2×C3×Q8—41no—
345C2×C3×Q8C4×D514yescomplemented
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C22×Dic3—51no—
354C22×Dic3—51no—
355C22×Dic3—51no—
356C22×Dic3C22×D511yescharacteristic
357C22×Dic3C22×D511yescharacteristic
358C22×Dic3C22×D511yescharacteristic
359C22×Dic3C22×D511yescharacteristic
360C2×C4×D3—54no—
361C2×C4×D3—102no—
362C2×C4×D3—102no—
363C2×C4×D3—102no—
364C2×C4×D3—102no—
365C2×C4×D3—201no—
366C2×C4×D3—201no—
367C2×C4×D3—201no—
368C2×C4×D3—201no—
369C3×C4⋊C4—201no—
370C3×C42—201no—
371(C2×D3)⋊C4—54no—
372(C2×D3)⋊C4—54no—
373(C2×D3)⋊C4—54no—
374(C2×D3)⋊C4—102no—
375C4⋊Dic3—41no—
376C4⋊Dic3—54no—
377Dic3⋊C4—54no—
378Dic3⋊C4—54no—
379Dic3⋊C4—102no—
380Dic3⋊C4—102no—
381C4×Dic3—41no—
382C4×Dic3—102no—
383C4×Dic3—102no—
384C4×Dic3—201no—
385C4×Dic3—201no—
386C23×C5C23×D311yescharacteristic
387C22×D5—32no—
388C22×D5—32no—
389C22×D5—32no—
390C22×D5—61no—
391C22×D5—61no—
392C22×D5—61no—
393C22×D5—61no—
394C5×Q8—44no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—32no—
402C2×C4×C5—32no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5C2×C4×D312yes—
414C2×C4×C5C2×C4×D312yes—
415C2×C4×C5C2×C4×D312yes—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—32no—
427C2×Dic5—32no—
428C2×Dic5—32no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5D3×Q812yes—
436C2×Dic5#23912yes—
437C4×D5—124no—
438C4×D5—124no—
439C4×D5—124no—
440C22×Q8D3×D511yescharacteristic
441C23×C4—151no—
442C23×C4—151no—
443C23×C4—151no—
444C22⋊Q8—158no—
445C2×C4⋊C4—31no—
446C2×C4⋊C4—51no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4—151no—
452C2×C22⋊C4—151no—
453C2×C22⋊C4—151no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C42—31no—
457C2×C42—51no—
458C2×C42—151no—
459C2×C42—151no—
460C2×C42—151no—
461C2×C42—151no—
462#95—31no—
463#95—31no—
464#95—31no—
465#95—31no—
466#95—51no—
467#95—51no—
468#95—51no—
469#95—51no—
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474#95—151no—
475#95—151no—
476C2×C3×C5C2×C4×Q811yescharacteristic
477C2×C3×C5C4×#4111yescharacteristic
478C2×C3×C5#51811yescharacteristic
479C2×C3×C5#55111yescharacteristic
480C2×C3×C5#55111yescharacteristic
481C2×C3×C5#55411yescharacteristic
482C2×C3×C5#55411yescharacteristic
483D15—24no—
484C23×C3C23×D511yescharacteristic
485C22×D3—52no—
486C22×D3—52no—
487C22×D3—52no—
488C22×D3—101no—
489C22×D3—101no—
490C22×D3—101no—
491C22×D3—101no—
492C3×Q8—44no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—52no—
500C2×C3×C4—52no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4C2×C4×D512yes—
512C2×C3×C4C2×C4×D512yes—
513C2×C3×C4C2×C4×D512yes—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—52no—
525C2×Dic3—52no—
526C2×Dic3—52no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3Q8×D512yes—
534C2×Dic3#71312yes—
535C4×D3—204no—
536C4×D3—204no—
537C4×D3—204no—
538C22×C5C22×C4×D311yescharacteristic
539C22×C5#100411yescharacteristic
540C22×C5#100411yescharacteristic
541C22×C5C2×D3×Q811yescharacteristic
542C22×C5C2×#23911yescharacteristic
543C22×C5D3×#4111yescharacteristic
544C22×C5D3×#4111yescharacteristic
545C2×D5—34no—
546C2×D5—62no—
547C2×D5—62no—
548C2×D5—62no—
549C2×D5—62no—
550C2×D5—62no—
551C2×D5—62no—
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—62no—
556C4×C5—62no—
557C4×C5—121no—
558C4×C5—121no—
559Dic5—22no—
560Dic5—22no—
561Dic5—41no—
562Dic5—41no—
563Dic5—62no—
564Dic5—62no—
565Dic5—62no—
566C24—151no—
567C2×Q8—41no—
568C2×Q8—41no—
569C2×Q8#120014yescomplemented
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—151no—
579C22×C4—151no—
580C22×C4—151no—
581C22×C4—154no—
582C22×C4—302no—
583C22×C4—302no—
584C22×C4—302no—
585C22×C4—302no—
586C22×C4—601no—
587C22×C4—601no—
588C22×C4—601no—
589C22×C4—601no—
590C22×C4C2×D3×D511yescharacteristic
591C22×C4C2×D3×D511yescharacteristic
592C22×C4C2×D3×D511yescharacteristic
593C4⋊C4—121no—
594C4⋊C4—154no—
595C4⋊C4—154no—
596C4⋊C4—154no—
597C4⋊C4—201no—
598C4⋊C4—302no—
599C4⋊C4—302no—
600C22⋊C4—154no—
601C22⋊C4—154no—
602C22⋊C4—154no—
603C22⋊C4—302no—
604C42—121no—
605C42—201no—
606C42—302no—
607C42—302no—
608C42—601no—
609C42—601no—
610C3×C5#236811yescharacteristic, complemented, Hall
611C22×C3C22×C4×D511yescharacteristic
612C22×C3#414411yescharacteristic
613C22×C3#414411yescharacteristic
614C22×C3C2×Q8×D511yescharacteristic
615C22×C3C2×#71311yescharacteristic
616C22×C3D5×#4111yescharacteristic
617C22×C3D5×#4111yescharacteristic
618C2×D3—54no—
619C2×D3—102no—
620C2×D3—102no—
621C2×D3—102no—
622C2×D3—102no—
623C2×D3—102no—
624C2×D3—102no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—102no—
629C3×C4—102no—
630C3×C4—201no—
631C3×C4—201no—
632Dic3—22no—
633Dic3—22no—
634Dic3—41no—
635Dic3—41no—
636Dic3—102no—
637Dic3—102no—
638Dic3—102no—
639C2×C5#548611yescharacteristic
640C2×C5C4×D3×Q811yescharacteristic
641C2×C5C4×#23911yescharacteristic
642C2×C5#563611yescharacteristic
643C2×C5#563711yescharacteristic
644C2×C5#567911yescharacteristic
645C2×C5#573011yescharacteristic
646D5—64no—
647C23—152no—
648C23—152no—
649C23—152no—
650C23—301no—
651C23—301no—
652C23—301no—
653C23—301no—
654C23C22×D3×D511yescharacteristic
655Q8—44no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—52no—
665C2×C4—52no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—152no—
687C2×C4—152no—
688C2×C4—152no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—604no—
696C2×C4—604no—
697C2×C4—604no—
698C2×C4C2×#120012yes—
699C2×C4C2×#120012yes—
700C2×C4C2×#120012yes—
701C2×C3#6582011yescharacteristic
702C2×C3C4×Q8×D511yescharacteristic
703C2×C3C4×#71311yescharacteristic
704C2×C3#6597011yescharacteristic
705C2×C3#6597111yescharacteristic
706C2×C3#6601311yescharacteristic
707C2×C3#6606411yescharacteristic
708D3—104no—
709C5#7661611yescharacteristic, complemented, Sylow
710C22—154no—
711C22—302no—
712C22—302no—
713C22—302no—
714C22—302no—
715C22—302no—
716C22—302no—
717C22D3×Q8×D511yescharacteristic
718C22D5×#23911yescharacteristic
719C22D3×#71311yescharacteristic
720C22#9203411yescharacteristic
721C22C22×#120011yescharacteristic
722C22#9204911yescharacteristic
723C22#9204911yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—62no—
728C4—62no—
729C4—102no—
730C4—102no—
731C4—121no—
732C4—121no—
733C4—201no—
734C4—201no—
735C4—302no—
736C4—302no—
737C4—302no—
738C3#1060834711yescharacteristic, complemented, Sylow
739C2—304no—
740C2#1175517811yescharacteristic
741C2Q8×#120011yescharacteristic
742C2#1175518811yescharacteristic
743C2#1175520011yescharacteristic
744C2#1175529011yescharacteristic
745C2#1175529211yescharacteristic
746C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2368
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5229C2semidirect
3. C3×#65519C2semidirect
9. #11748689C2semidirect
10. #11748688C2semidirect
11. #11748687C2semidirect
12. #11748674C2semidirect
14. #11748645C2semidirect
15. #11748640C2semidirect
21. #91835C4semidirect
56. #65519D3semidirect
72. C2×C3×C5×Q8C2×C4semidirect
98. C4⋊Dic15C2×C4semidirect
99. #6712C2×C4semidirect
100. #6712C2×C4semidirect
108. #6667Q8semidirect
115. #5229D5semidirect
258. C2×C5×Q8C4×D3semidirect
345. C2×C3×Q8C4×D5semidirect
569. C2×Q8#1200semidirect
610. C3×C5#2368semidirect
709. C5#76616semidirect
738. C3#10608347semidirect

Maximal subgroups

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

subgroupindex
C2×#918352
C5×#52292
C3×#655192
#117489022
#117488982
#117488882
#117488812
#117488752
#117486892
#117486882
#117486872
#117486742
#117486702
#117486452
#117486402
#106083473
#766165