Finite Group Databasebeta

← #14325882

Subgroups — #14325882

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91836C211yesmaximal, characteristic
2C5×#5229C211yesmaximal, characteristic, complemented
3C3×#65519C211yesmaximal, characteristic, complemented
4#11748904C211yesmaximal, characteristic
5#11748904C211yesmaximal, characteristic
6#11748902C211yesmaximal, characteristic, complemented
7#11748898C211yesmaximal, characteristic, complemented
8#11748881C211yesmaximal, characteristic, complemented
9#11748875C211yesmaximal, characteristic, complemented
10#11748854C211yesmaximal, characteristic, complemented
11#11748829C211yesmaximal, characteristic, complemented
12#11748685C211yesmaximal, characteristic, complemented
13#11748678C211yesmaximal, characteristic, complemented
14#11748663C211yesmaximal, characteristic, complemented
15#11748621C211yesmaximal, characteristic, complemented
16#10608219—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21#91836C418yescomplemented
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
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×#6667C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#76488—51nomaximal, Hall
54C2×#4093—31no—
55C5×#391—31no—
56#65519D311yescharacteristic, complemented
57#65279—31no—
58#65278—31no—
59#65229—31no—
60C4×#685—31no—
61#64959—31no—
62#64958—31no—
63#64957—31no—
64#64955—31no—
65#64954—31no—
66#64954—31no—
67#64940—31no—
68#64938—31no—
69C23×D15C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C2×C3×C5×Q8—41no—
72C2×C3×C5×Q8—41no—
73C2×C3×C5×Q8C2×C414yescomplemented
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×D60—41no—
80C2×D60—41no—
81C2×D60C2×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—41no—
93C2×#1200—41no—
94C2×#1200—41no—
95C2×#1200—41no—
96#6714C2×C414yescomplemented
97#6714C2×C414yescomplemented
98#6714C2×C414yescomplemented
99#6714C2×C414yescomplemented
100C4×Dic15C2×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#6667—22no—
109#6667—41no—
110#6667—41no—
111#6667—41no—
112#6667—41no—
113Dic3×Dic5—41no—
114Dic3×Dic5—41no—
115C2×#947—51no—
116C3×#391—51no—
117#5229D511yescharacteristic, complemented
118#4990—51no—
119#4989—51no—
120#4940—51no—
121C4×(C2×D3)⋊C4—51no—
122#4670—51no—
123#4669—51no—
124#4668—51no—
125#4666—51no—
126#4665—51no—
127#4665—51no—
128#4651—51no—
129#4649—51no—
130C22×C5×Q8C2×D311yescharacteristic
131C22×D20—31no—
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C2×C5×C4⋊C4—31no—
135C2×C42×C5—31no—
136#4093—38no—
137C2×#685—31no—
138C2×#685—31no—
139C2×#685—31no—
140C2×#685—31no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#685—31no—
147C2×C4⋊Dic5C2×D311yescharacteristic
148C2×#683—31no—
149C2×#683—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5C2×D311yescharacteristic
154C5×#95—31no—
155C5×#95—31no—
156C5×#95—31no—
157C5×#95—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2337—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×D15—21no—
169C22×D15—21no—
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15—21no—
175C22×D15—21no—
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15C22×C412yes—
181C22×D15C22×C412yes—
182C3×C5×Q8—44no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C22×C412yes—
190C2×C3×C4×C5C22×C412yes—
191C2×C3×C4×C5C22×C412yes—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C22×C412yes—
197C2×Dic15C22×C412yes—
198D60—44no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3#4112yes—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5#4112yes—
223#1200—44no—
224#1200—44no—
225C22×C3×Q8C2×D511yescharacteristic
226C22×D12—51no—
227C22×C4×D3—51no—
228C22×C4×D3—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C42—51no—
231#947—58no—
232C2×(C2×D3)⋊C4—51no—
233C2×(C2×D3)⋊C4—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4—51no—
241C2×(C2×D3)⋊C4—51no—
242C2×C4⋊Dic3C2×D511yescharacteristic
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249C3×#95—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3×#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95C2×D511yescharacteristic
258C3⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C3⋊#95C2×D511yescharacteristic
261C23×D5—31no—
262C23×D5—31no—
263C2×C5×Q8—41no—
264C2×C5×Q8—41no—
265C2×C5×Q8C4×D314yescomplemented
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C2×D20—34no—
280C2×D20—121no—
281C2×D20—121no—
282C2×C4×D5—62no—
283C2×C4×D5—62no—
284C2×C4×D5—121no—
285C2×C4×D5—121no—
286C2×C4×D5—121no—
287C2×C4×D5—121no—
288C5×C4⋊C4—121no—
289C42×C5—121no—
290#685—34no—
291#685—34no—
292#685—34no—
293#685—34no—
294#685—62no—
295#685—62no—
296#685—121no—
297#685—121no—
298#685—121no—
299#685—121no—
300C4⋊Dic5—41no—
301#683—62no—
302#683—62no—
303C4×Dic5—34no—
304C4×Dic5—41no—
305C4×Dic5—121no—
306C4×Dic5—121no—
307C2×#124—151no—
308#391—31no—
309#391—51no—
310#388—151no—
311#388—151no—
312#388—151no—
313#388—151no—
314#386—151no—
315#386—151no—
316#385—151no—
317#385—151no—
318#383—151no—
319C4×C4⋊C4—151no—
320C4×C22⋊C4—151no—
321C4×C22⋊C4—151no—
322C22×C3×C5C23×C411yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C22×C3×C52−1+411yescharacteristic
329C2×D15—22no—
330C2×D15—22no—
331C2×D15—22no—
332C2×D15—22no—
333C2×D15—22no—
334C2×D15—22no—
335C2×D15—41no—
336C2×D15—41no—
337C2×D15—41no—
338C2×D15—41no—
339C2×D15—41no—
340C2×D15—41no—
341C2×D15—41no—
342C2×D15—41no—
343C3×C4×C5—22no—
344C3×C4×C5—22no—
345C3×C4×C5—22no—
346Dic15—22no—
347Dic15—22no—
348C3×Dic5—22no—
349C3×Dic5—41no—
350C3×Dic5—41no—
351C3×Dic5—41no—
352C5×Dic3—22no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C5×Dic3—41no—
356C23×D3—51no—
357C23×D3—51no—
358C2×C3×Q8—41no—
359C2×C3×Q8—41no—
360C2×C3×Q8C4×D514yescomplemented
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3C22×D511yescharacteristic
371C22×Dic3C22×D511yescharacteristic
372C22×Dic3C22×D511yescharacteristic
373C22×Dic3C22×D511yescharacteristic
374C2×D12—54no—
375C2×D12—201no—
376C2×D12—201no—
377C2×C4×D3—102no—
378C2×C4×D3—102no—
379C2×C4×D3—201no—
380C2×C4×D3—201no—
381C2×C4×D3—201no—
382C2×C4×D3—201no—
383C3×C4⋊C4—201no—
384C3×C42—201no—
385(C2×D3)⋊C4—54no—
386(C2×D3)⋊C4—54no—
387(C2×D3)⋊C4—54no—
388(C2×D3)⋊C4—54no—
389(C2×D3)⋊C4—102no—
390(C2×D3)⋊C4—102no—
391(C2×D3)⋊C4—201no—
392(C2×D3)⋊C4—201no—
393(C2×D3)⋊C4—201no—
394(C2×D3)⋊C4—201no—
395C4⋊Dic3—41no—
396Dic3⋊C4—102no—
397Dic3⋊C4—102no—
398C4×Dic3—41no—
399C4×Dic3—54no—
400C4×Dic3—201no—
401C4×Dic3—201no—
402C23×C5C23×D311yescharacteristic
403C22×D5—32no—
404C22×D5—32no—
405C22×D5—61no—
406C22×D5—61no—
407C22×D5—61no—
408C22×D5—61no—
409C22×D5—61no—
410C22×D5—61no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—61no—
416C22×D5—61no—
417C5×Q8—44no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—32no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5C2×C4×D312yes—
437C2×C4×C5C2×C4×D312yes—
438C2×C4×C5C2×C4×D312yes—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—32no—
451C2×Dic5—32no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5#23912yes—
457D20—124no—
458C4×D5—124no—
459C4×D5—124no—
460C22×Q8D3×D511yescharacteristic
461C22×D4—151no—
462C23×C4—151no—
463C23×C4—151no—
464#124—158no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C22⋊C4—151no—
470C2×C22⋊C4—151no—
471C2×C22⋊C4—151no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—31no—
480C2×C42—51no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—51no—
489#95—51no—
490#95—51no—
491#95—51no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5C4×#4111yescharacteristic
497C2×C3×C5#51811yescharacteristic
498C2×C3×C5#52011yescharacteristic
499C2×C3×C5#53811yescharacteristic
500C2×C3×C5#53811yescharacteristic
501C2×C3×C5#54211yescharacteristic
502C2×C3×C5#54211yescharacteristic
503D15—42no—
504D15—42no—
505C23×C3C23×D511yescharacteristic
506C22×D3—52no—
507C22×D3—52no—
508C22×D3—101no—
509C22×D3—101no—
510C22×D3—101no—
511C22×D3—101no—
512C22×D3—101no—
513C22×D3—101no—
514C22×D3—101no—
515C22×D3—101no—
516C22×D3—101no—
517C22×D3—101no—
518C22×D3—101no—
519C22×D3—101no—
520C3×Q8—44no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—52no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4C2×C4×D512yes—
540C2×C3×C4C2×C4×D512yes—
541C2×C3×C4C2×C4×D512yes—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—52no—
554C2×Dic3—52no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3#71312yes—
560D12—204no—
561C4×D3—204no—
562C4×D3—204no—
563C22×C5C22×C4×D311yescharacteristic
564C22×C5#100411yescharacteristic
565C22×C5#100411yescharacteristic
566C22×C5C2×#23911yescharacteristic
567C22×C5#100711yescharacteristic
568C22×C5D3×#4111yescharacteristic
569C22×C5#100911yescharacteristic
570C2×D5—62no—
571C2×D5—62no—
572C2×D5—62no—
573C2×D5—62no—
574C2×D5—62no—
575C2×D5—62no—
576C2×D5—121no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5—121no—
581C2×D5—121no—
582C2×D5—121no—
583C2×D5—121no—
584C4×C5—22no—
585C4×C5—22no—
586C4×C5—22no—
587C4×C5—62no—
588C4×C5—121no—
589C4×C5—121no—
590C4×C5—121no—
591Dic5—22no—
592Dic5—41no—
593Dic5—41no—
594Dic5—41no—
595Dic5—62no—
596Dic5—62no—
597C24—151no—
598C24—151no—
599C2×Q8—41no—
600C2×Q8—41no—
601C2×Q8#120014yescomplemented
602C2×D4—154no—
603C2×D4—601no—
604C2×D4—601no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—151no—
614C22×C4—151no—
615C22×C4—302no—
616C22×C4—302no—
617C22×C4—601no—
618C22×C4—601no—
619C22×C4—601no—
620C22×C4—601no—
621C22×C4C2×D3×D511yescharacteristic
622C22×C4C2×D3×D511yescharacteristic
623C22×C4C2×D3×D511yescharacteristic
624C4⋊C4—121no—
625C4⋊C4—201no—
626C4⋊C4—302no—
627C4⋊C4—302no—
628C22⋊C4—154no—
629C22⋊C4—154no—
630C22⋊C4—154no—
631C22⋊C4—154no—
632C22⋊C4—302no—
633C22⋊C4—302no—
634C22⋊C4—601no—
635C22⋊C4—601no—
636C22⋊C4—601no—
637C22⋊C4—601no—
638C42—121no—
639C42—154no—
640C42—201no—
641C42—601no—
642C42—601no—
643C3×C5#233711yescharacteristic, complemented, Hall
644C22×C3C22×C4×D511yescharacteristic
645C22×C3#414411yescharacteristic
646C22×C3#414411yescharacteristic
647C22×C3C2×#71311yescharacteristic
648C22×C3#414711yescharacteristic
649C22×C3D5×#4111yescharacteristic
650C22×C3#414911yescharacteristic
651C2×D3—102no—
652C2×D3—102no—
653C2×D3—102no—
654C2×D3—102no—
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—201no—
658C2×D3—201no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3—201no—
662C2×D3—201no—
663C2×D3—201no—
664C2×D3—201no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—102no—
669C3×C4—201no—
670C3×C4—201no—
671C3×C4—201no—
672Dic3—22no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—102no—
677Dic3—102no—
678C2×C5#548611yescharacteristic
679C2×C5C4×#23911yescharacteristic
680C2×C5#557411yescharacteristic
681C2×C5#564011yescharacteristic
682C2×C5#564411yescharacteristic
683C2×C5#567811yescharacteristic
684C2×C5#573311yescharacteristic
685D5—122no—
686D5—122no—
687C23—152no—
688C23—152no—
689C23—301no—
690C23—301no—
691C23—301no—
692C23—301no—
693C23—301no—
694C23—301no—
695C23—301no—
696C23—301no—
697C23—301no—
698C23—301no—
699C23—301no—
700C23—301no—
701C23C22×D3×D511yescharacteristic
702Q8—44no—
703D4—604no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—52no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—604no—
741C2×C4—604no—
742C2×C4C2×#120012yes—
743C2×C4C2×#120012yes—
744C2×C4C2×#120012yes—
745C2×C3#6582011yescharacteristic
746C2×C3C4×#71311yescharacteristic
747C2×C3#6590811yescharacteristic
748C2×C3#6597411yescharacteristic
749C2×C3#6597811yescharacteristic
750C2×C3#6601211yescharacteristic
751C2×C3#6606711yescharacteristic
752D3—202no—
753D3—202no—
754C5#7648811yescharacteristic, complemented, Sylow
755C22—302no—
756C22—302no—
757C22—302no—
758C22—302no—
759C22—302no—
760C22—302no—
761C22—601no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22—601no—
766C22—601no—
767C22—601no—
768C22—601no—
769C22#9202911yescharacteristic
770C22D5×#23911yescharacteristic
771C22D3×#71311yescharacteristic
772C22#9203511yescharacteristic
773C22C22×#120011yescharacteristic
774C22#9204911yescharacteristic
775C22#9204911yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—62no—
780C4—102no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—201no—
785C4—201no—
786C4—201no—
787C4—302no—
788C4—302no—
789C3#1060821911yescharacteristic, complemented, Sylow
790C2—602no—
791C2—602no—
792C2#1175512911yescharacteristic
793C2#1175513011yescharacteristic
794C2#1175514911yescharacteristic
795C2#1175520011yescharacteristic
796C2#1175528811yescharacteristic
797C2#1175529111yescharacteristic
798C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2337
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
6. #11748902C2semidirect
7. #11748898C2semidirect
8. #11748881C2semidirect
9. #11748875C2semidirect
10. #11748854C2semidirect
11. #11748829C2semidirect
12. #11748685C2semidirect
13. #11748678C2semidirect
14. #11748663C2semidirect
15. #11748621C2semidirect
21. #91836C4semidirect
56. #65519D3semidirect
73. C2×C3×C5×Q8C2×C4semidirect
96. #6714C2×C4semidirect
97. #6714C2×C4semidirect
98. #6714C2×C4semidirect
99. #6714C2×C4semidirect
100. C4×Dic15C2×C4semidirect
117. #5229D5semidirect
265. C2×C5×Q8C4×D3semidirect
360. C2×C3×Q8C4×D5semidirect
601. C2×Q8#1200semidirect
643. C3×C5#2337semidirect
754. C5#76488semidirect
789. C3#10608219semidirect

Maximal subgroups

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

subgroupindex
C2×#918362
C5×#52292
C3×#655192
#117489042
#117489022
#117488982
#117488812
#117488752
#117488542
#117488292
#117486852
#117486782
#117486632
#117486212
#106082193
#764885