Finite Group Databasebeta

← #14424153

Subgroups — #14424153

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91365C211yesmaximal, characteristic, complemented
4C2×#91322C211yesmaximal, characteristic, complemented
5C3×#65521C211yesmaximal, characteristic, complemented
6#11749302C212yesmaximal, complemented
7#11749300C212yesmaximal, complemented
8#11749056C212yesmaximal, complemented
9#11749054C212yesmaximal, complemented
10#11748384C211yesmaximal, characteristic, complemented
11#11748346C211yesmaximal, characteristic, complemented
12#10615815—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic, complemented
15C5×D3×#41—24no—
16C5×D3×#41—24no—
17C2×C5×#239C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C5×#237—21no—
20C2×C5×#237C2211yescharacteristic
21C2×C5×D3×D4—21no—
22C2×C5×D3×D4C2211yescharacteristic
23C2×C5×#235—21no—
24C2×C5×#235C2211yescharacteristic
25C22×C4×C5×D3—21no—
26C22×C4×C5×D3C2211yescharacteristic
27#91840—24no—
28C2×#6718C2212yescomplemented
29C2×#6716C2212yescomplemented
30C2×#6710C2211yescharacteristic, complemented
31C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
32C2×C3×#681C2211yescharacteristic, complemented
33C2×#6668—21no—
34C2×(C2×D3)⋊Dic5—21no—
35#91365—21no—
36#91365—21no—
37#91365C2212yes—
38#91365C2212yescomplemented
39#91322—24no—
40C2×#6663C2212yescomplemented
41C2×#6659C2212yescomplemented
42C3×#3967C2212yescomplemented
43C3×#3964C2212yescomplemented
44#90972C2212yescomplemented
45#90966C2212yescomplemented
46(C2×D3)⋊#168C2212yes—
47(C2×D3)⋊#168C2212yescomplemented
48#78885—51nomaximal, Hall
49C22×C5×#41—31no—
50C2×#4097—31no—
51C2×#4097—31no—
52C2×#4070—31no—
53#65528—32no—
54#65528—32no—
55#65521—31no—
56#65521D311yescharacteristic, complemented
57#65517—32no—
58#65507—32no—
59#65496—31no—
60C23×C5×D3—21no—
61C23×C5×D3D411yescharacteristic
62C3×C5×#41—22no—
63C3×C5×#41D414yes—
64C2×C3×C5×Q8C2311yescharacteristic
65C2×C3×C5×D4—21no—
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5C2311yescharacteristic
69C22×Dic15—21no—
70C2×Dic30—22no—
71C2×Dic30—22no—
72C2×Dic30—21no—
73C2×Dic30C2312yes—
74C2×C5×#67—21no—
75C2×C5×#67—21no—
76C2×C5×#67—21no—
77C22×C5×Dic3—21no—
78C22×C5×Dic3D411yescharacteristic
79C5×#239—22no—
80C5×#239—22no—
81C5×D3×Q8—22no—
82C5×D3×Q8—22no—
83C5×#237—28no—
84C5×#237—22no—
85C5×#237—22no—
86C5×D3×D4—28no—
87C5×D3×D4—22no—
88C5×D3×D4—22no—
89C5×#235—28no—
90C5×#235—22no—
91C5×#235D414yes—
92C2×C5×D12—21no—
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—28no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3—21no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—21no—
100C2×C4×C5×D3D411yescharacteristic
101C2×C4×C5×D3D411yescharacteristic
102C2×C4×C5×D3C2311yescharacteristic
103C2×C4×C5×D3C2311yescharacteristic
104C2×C5×Dic6—21no—
105C2×C5×Dic6C2311yescharacteristic
106C22×C3×Dic5—21no—
107#6718—24no—
108#6716—24no—
109#6710—22no—
110C2×C3⋊#168C2312yes—
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2312yes—
113C3×#681—22no—
114C2×C3×#168C2312yes—
115#6668—22no—
116#6668—22no—
117(C2×D3)⋊Dic5—22no—
118(C2×D3)⋊Dic5—22no—
119#6663—24no—
120#6659—24no—
121C2×D3×#41D511yescharacteristic
122C2×#951—51no—
123C2×#909—51no—
124C2×#897—51no—
125C3×#417—51no—
126#5126—51no—
127#4966—51no—
128#4809—52no—
129#4808—52no—
130#4783—52no—
131#4776—52no—
132C2×C5×#41—31no—
133C2×C5×#41—31no—
134C2×C5×#41—31no—
135C2×C5×#41—61no—
136C2×C5×#41—61no—
137C2×C5×#41—64no—
138C2×C5×#41—64no—
139C2×C5×#41C2×D311yescharacteristic
140C22×C5×Q8—31no—
141C22×C5×D4—31no—
142C22×C5×D4—61no—
143C23×C4×C5—31no—
144C23×C4×C5—61no—
145C22×Dic10—31no—
146C2×C22⋊Dic5—61no—
147#4097—64no—
148#4097—64no—
149C2×#689—32no—
150C2×#689—32no—
151C2×#687—32no—
152C2×#687—32no—
153C2×C4⋊Dic5C2×D311yescharacteristic, complemented
154#4070—32no—
155#4070—32no—
156#4070—61no—
157#4070—61no—
158C2×#683—61no—
159C2×#681—31no—
160C2×#681C2×D311yescharacteristic, complemented
161#3967—32no—
162#3967C2×D312yescomplemented
163#3964—32no—
164#3964C2×D312yescomplemented
165C22⋊#168—32no—
166C22⋊#168—32no—
167#3007—151noSylow
168C23×C3×C5—21no—
169C23×C3×C5C2×D411yescharacteristic
170C22×C5×D3—24no—
171C22×C5×D3—22no—
172C22×C5×D3—21no—
173C22×C5×D3—22no—
174C22×C5×D3—41no—
175C22×C5×D3—42no—
176C22×C5×D3—42no—
177C22×C5×D3C2×D411yescharacteristic
178C22×C5×D3C2×D411yescharacteristic
179C3×C5×Q8—21no—
180C3×C5×Q8C2×D412yes—
181C3×C5×D4—24no—
182C3×C5×D4—21no—
183C3×C5×D4C2×D412yes—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—24no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D412yes—
188C2×C3×C4×C5C2×D412yes—
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—22no—
191C2×Dic15—42no—
192Dic30—22no—
193Dic30—22no—
194Dic30—42no—
195C5×#67—24no—
196C5×#67—24no—
197C5×#67—24no—
198C2×C5×Dic3—24no—
199C2×C5×Dic3—22no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C5×D12—24no—
204C5×D12—21no—
205C5×D12C2×D412yes—
206C4×C5×D3—24no—
207C4×C5×D3—24no—
208C4×C5×D3—22no—
209C4×C5×D3—24no—
210C4×C5×D3—22no—
211C4×C5×D3—21no—
212C4×C5×D3—21no—
213C4×C5×D3—21no—
214C4×C5×D3—21no—
215C5×Dic6—24no—
216C5×Dic6—21no—
217C5×Dic6C2×D412yes—
218C2×C3×Dic5—22no—
219C2×C3×Dic5—42no—
220C3⋊#168—22no—
221C3×#168—22no—
222C2×C3×#41C2×D511yescharacteristic
223D3×#41—24no—
224D3×#41—24no—
225C2×#239C2×D511yescharacteristic
226C2×D3×Q8C2×D511yescharacteristic
227C2×#237—21no—
228C2×#237C2×D511yescharacteristic
229C2×D3×D4—21no—
230C2×D3×D4C2×D511yescharacteristic
231C2×#235—21no—
232C2×#235C2×D511yescharacteristic
233C22×C4×D3—21no—
234C22×C4×D3C2×D511yescharacteristic
235C22×Dic6—51no—
236C2×C3×M16—51no—
237C2×C3×C4⋊C4—51no—
238#951—104no—
239C2×#216—52no—
240C2×#214—52no—
241C2×(C2×D3)⋊C4—101no—
242C2×C4⋊Dic3—101no—
243C2×#208—51no—
244#909—104no—
245C2×Dic12—52no—
246C2×#204—52no—
247#897—52no—
248#897—52no—
249#897—101no—
250#897—101no—
251C3×#103—52no—
252C3×#102—52no—
253(C2×D3)⋊C8—52no—
254(C2×D3)⋊C8—52no—
255#810—52no—
256#809—52no—
257C24×C5—31no—
258C24×C5—61no—
259C5×#41—22no—
260C5×#41—34no—
261C5×#41—68no—
262C5×#41—62no—
263C5×#41—68no—
264C5×#41—62no—
265C5×#41—62no—
266C5×#41—62no—
267C5×#41—62no—
268C5×#41D1214yes—
269C2×C5×Q8—31no—
270C2×C5×Q8—61no—
271C2×C5×Q8—62no—
272C2×C5×Q8—62no—
273C2×C5×Q8C22×D311yescharacteristic
274C2×C5×D4—21no—
275C2×C5×D4—31no—
276C2×C5×D4—61no—
277C2×C5×D4—61no—
278C2×C5×D4—62no—
279C2×C5×D4—68no—
280C2×C5×D4—61no—
281C2×C5×D4—61no—
282C2×C5×D4—62no—
283C2×C5×D4C22×D311yescharacteristic
284C22×C4×C5—21no—
285C22×C4×C5—31no—
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5—31no—
290C22×C4×C5—61no—
291C22×C4×C5—61no—
292C22×C4×C5—68no—
293C22×C4×C5—61no—
294C22×C4×C5—62no—
295C22×C4×C5—62no—
296C22×C4×C5—61no—
297C22×C4×C5C22×D311yescharacteristic
298C22×Dic5—21no—
299C22×Dic5—61no—
300C2×Dic10—32no—
301C2×Dic10—62no—
302C2×Dic10—62no—
303C2×Dic10—61no—
304C22⋊Dic5—62no—
305C22⋊Dic5—62no—
306#689—64no—
307#689—64no—
308#687—64no—
309#687—64no—
310C4⋊Dic5—21no—
311C4⋊Dic5C22×D312yes—
312#683—62no—
313#683—62no—
314#681—22no—
315#681—62no—
316C2×#168—32no—
317C2×#168C22×D312yes—
318C22×#41—31no—
319C2×#137—151no—
320C2×#137—151no—
321C2×C22⋊Q8—151no—
322#452—152no—
323#452—152no—
324#451—152no—
325#450—152no—
326#417—51no—
327#417—151no—
328#407—151no—
329C22×C3×C5—21no—
330C22×C3×C5—21no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5#12012yes—
335C22×C3×C5C22×D411yescharacteristic
336C2×C5×D3—21no—
337C2×C5×D3—21no—
338C2×C5×D3—21no—
339C2×C5×D3—22no—
340C2×C5×D3—21no—
341C2×C5×D3—21no—
342C2×C5×D3—44no—
343C2×C5×D3—48no—
344C2×C5×D3—41no—
345C2×C5×D3—41no—
346C2×C5×D3#13712yescomplemented
347C3×C4×C5—22no—
348C3×C4×C5#12012yes—
349C3×C4×C5C22×D411yescharacteristic
350C3×C4×C5C22×D411yescharacteristic
351Dic15—42no—
352C3×Dic5—42no—
353C5×Dic3—21no—
354C5×Dic3—22no—
355C5×Dic3—21no—
356C23×D3—21no—
357C23×D3C22⋊D511yescharacteristic
358C3×#41—22no—
359C3×#41C22⋊D514yes—
360C2×C3×Q8C22×D511yescharacteristic
361C2×C3×D4—21no—
362C2×C3×D4C22×D511yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—101no—
365C22×C3×C4C22×D511yescharacteristic
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C22×Dic3—21no—
370C22×Dic3—101no—
371C22×Dic3C22⋊D511yescharacteristic
372#239—22no—
373#239—22no—
374D3×Q8—22no—
375D3×Q8—22no—
376#237—28no—
377#237—22no—
378#237—22no—
379D3×D4—28no—
380D3×D4—22no—
381D3×D4—22no—
382#235—28no—
383#235—22no—
384#235C22⋊D514yes—
385C2×D12—21no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—28no—
388C2×C4×D3—21no—
389C2×C4×D3—21no—
390C2×C4×D3—22no—
391C2×C4×D3—22no—
392C2×C4×D3—21no—
393C2×C4×D3C22⋊D511yescharacteristic
394C2×C4×D3C22⋊D511yescharacteristic
395C2×C4×D3C22×D511yescharacteristic
396C2×C4×D3C22×D511yescharacteristic
397C2×Dic6—21no—
398C2×Dic6—52no—
399C2×Dic6—102no—
400C2×Dic6—102no—
401C2×Dic6—101no—
402C2×Dic6C22×D511yescharacteristic
403C3×M16—102no—
404C2×C3×C8—52no—
405C3×C4⋊C4—52no—
406C3×C4⋊C4—101no—
407#216—104no—
408#214—104no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4—102no—
411C4⋊Dic3—102no—
412C4⋊Dic3—102no—
413#208—102no—
414C2×C3⋊C8—52no—
415Dic12—104no—
416#204—104no—
417C23×C5—21no—
418C23×C5—31no—
419C23×C5—31no—
420C23×C5—62no—
421C23×C5—64no—
422C23×C5—62no—
423C23×C5—61no—
424C23×C5—121no—
425C23×C5—122no—
426C23×C5—122no—
427C23×C5D3×D411yescharacteristic
428C5×Q8—21no—
429C5×Q8—32no—
430C5×Q8—64no—
431C5×Q8—61no—
432C5×Q8C2×D1212yes—
433C5×D4—24no—
434C5×D4—21no—
435C5×D4—32no—
436C5×D4—64no—
437C5×D4—64no—
438C5×D4—64no—
439C5×D4—64no—
440C5×D4—61no—
441C5×D4C2×D1212yes—
442C2×C4×C5—21no—
443C2×C4×C5—24no—
444C2×C4×C5—31no—
445C2×C4×C5—31no—
446C2×C4×C5—64no—
447C2×C4×C5—64no—
448C2×C4×C5—64no—
449C2×C4×C5—62no—
450C2×C4×C5—61no—
451C2×C4×C5—62no—
452C2×C4×C5—62no—
453C2×C4×C5—64no—
454C2×C4×C5—61no—
455C2×C4×C5—61no—
456C2×C4×C5—61no—
457C2×C4×C5—61no—
458C2×C4×C5C2×D1212yes—
459C2×C4×C5D3×D411yescharacteristic
460C2×C4×C5D3×D412yes—
461C2×C4×C5C23×D311yescharacteristic
462C2×Dic5—22no—
463C2×Dic5—42no—
464C2×Dic5—62no—
465C2×Dic5—122no—
466Dic10—62no—
467Dic10—62no—
468Dic10—122no—
469#168—22no—
470#168—62no—
471C2×#41—31no—
472C2×#41—31no—
473C2×#41—31no—
474C2×#41—61no—
475C2×#41—61no—
476C2×#41—64no—
477C2×#41—64no—
478C2×#41D3×D511yescharacteristic
479C22×Q8—31no—
480C22×Q8—151no—
481C22×D4—31no—
482C22×D4—61no—
483C23×C4—31no—
484C23×C4—61no—
485#137—304no—
486#137—304no—
487C2×Q16—152no—
488C2×Q16—152no—
489C2×SD16—152no—
490C2×SD16—152no—
491C2×M16—51no—
492C2×M16—151no—
493C22⋊Q8—152no—
494C22⋊Q8—152no—
495C22⋊Q8—301no—
496C22⋊Q8—301no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—301no—
499C2×C22⋊C4—301no—
500#103—52no—
501#103—152no—
502#102—52no—
503#102—152no—
504C22⋊C8—152no—
505C22⋊C8—152no—
506C2×C3×C5—22no—
507C2×C3×C5—42no—
508C2×C3×C5C2×#12011yescharacteristic
509C2×C3×C5C2×#13711yescharacteristic
510C2×C3×C5#57511yescharacteristic
511C5×D3—22no—
512C5×D3—41no—
513C5×D3—42no—
514C23×C3—21no—
515C23×C3C2×C22⋊D511yescharacteristic
516C22×D3—24no—
517C22×D3—22no—
518C22×D3—21no—
519C22×D3—22no—
520C22×D3—41no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3C2×C22⋊D511yescharacteristic
524C22×D3C2×C22⋊D511yescharacteristic
525C3×Q8—21no—
526C3×Q8C2×C22⋊D512yes—
527C3×D4—24no—
528C3×D4—21no—
529C3×D4C2×C22⋊D512yes—
530C2×C3×C4—21no—
531C2×C3×C4—24no—
532C2×C3×C4—102no—
533C2×C3×C4—202no—
534C2×C3×C4C2×C22⋊D512yes—
535C2×C3×C4C2×C22⋊D511yescharacteristic
536C2×C3×C4C2×C22⋊D512yes—
537C2×C3×C4C23×D511yescharacteristic
538#67—24no—
539#67—24no—
540#67—24no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—21no—
544C2×Dic3—102no—
545C2×Dic3—202no—
546C2×Dic3C2×C22⋊D511yescharacteristic
547C2×Dic3C2×C22⋊D511yescharacteristic
548D12—24no—
549D12—21no—
550D12C2×C22⋊D512yes—
551C4×D3—24no—
552C4×D3—24no—
553C4×D3—22no—
554C4×D3—24no—
555C4×D3—22no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560Dic6—24no—
561Dic6—21no—
562Dic6—102no—
563Dic6—102no—
564Dic6—202no—
565Dic6C2×C22⋊D512yes—
566C3×C8—102no—
567C3⋊C8—102no—
568C22×C5—21no—
569C22×C5—21no—
570C22×C5—22no—
571C22×C5—32no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—61no—
575C22×C5—61no—
576C22×C5—62no—
577C22×C5—61no—
578C22×C5—61no—
579C22×C5—61no—
580C22×C5—124no—
581C22×C5—128no—
582C22×C5—121no—
583C22×C5—121no—
584C22×C5#88212yes—
585C22×C5C2×D3×D411yescharacteristic
586C4×C5—22no—
587C4×C5—61no—
588C4×C5—61no—
589C4×C5—62no—
590C4×C5#88212yes—
591C4×C5C22×D1211yescharacteristic
592C4×C5C2×D3×D411yescharacteristic
593Dic5—42no—
594Dic5—122no—
595C24—31no—
596C24—61no—
597#41—22no—
598#41—34no—
599#41—68no—
600#41—62no—
601#41—68no—
602#41—62no—
603#41—62no—
604#41—62no—
605#41—62no—
606#41#120314yes—
607C2×Q8—31no—
608C2×Q8—61no—
609C2×Q8—62no—
610C2×Q8—62no—
611C2×Q8—152no—
612C2×Q8—301no—
613C2×Q8—302no—
614C2×Q8—302no—
615C2×Q8C2×D3×D511yescharacteristic
616C2×D4—21no—
617C2×D4—31no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—62no—
621C2×D4—68no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4—62no—
625C2×D4C2×D3×D511yescharacteristic
626C22×C4—21no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—68no—
635C22×C4—61no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—61no—
639C22×C4—101no—
640C22×C4—301no—
641C22×C4C2×D3×D511yescharacteristic
642Q16—304no—
643Q16—304no—
644SD16—304no—
645SD16—304no—
646M16—102no—
647M16—302no—
648C2×C8—52no—
649C2×C8—152no—
650C4⋊C4—52no—
651C4⋊C4—101no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C3×C5#300711yescharacteristic, complemented, Hall
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3#409912yes—
663C22×C3C22×C22⋊D511yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—44no—
671C2×D3—48no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3#409712yescomplemented
675C3×C4—22no—
676C3×C4—202no—
677C3×C4#409912yes—
678C3×C4C22×C22⋊D511yescharacteristic
679C3×C4C22×C22⋊D511yescharacteristic
680Dic3—21no—
681Dic3—22no—
682Dic3—21no—
683Dic3—202no—
684C2×C5—22no—
685C2×C5—42no—
686C2×C5—62no—
687C2×C5—121no—
688C2×C5—122no—
689C2×C5C2×#88211yescharacteristic
690C2×C5#577311yescharacteristic
691C2×C5D3×#13711yescharacteristic
692C23—21no—
693C23—31no—
694C23—31no—
695C23—62no—
696C23—64no—
697C23—61no—
698C23—62no—
699C23—121no—
700C23—122no—
701C23—122no—
702C23D3×C22⋊D511yescharacteristic
703Q8—21no—
704Q8—32no—
705Q8—64no—
706Q8—61no—
707Q8—302no—
708Q8—302no—
709Q8—602no—
710Q8C2×#120312yes—
711D4—24no—
712D4—21no—
713D4—32no—
714D4—64no—
715D4—64no—
716D4—64no—
717D4—64no—
718D4—61no—
719D4C2×#120312yes—
720C2×C4—21no—
721C2×C4—24no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—61no—
728C2×C4—62no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—102no—
737C2×C4—202no—
738C2×C4—302no—
739C2×C4—602no—
740C2×C4C2×#120312yes—
741C2×C4D3×C22⋊D512yes—
742C2×C4D3×C22⋊D511yescharacteristic
743C2×C4C22×D3×D511yescharacteristic
744C8—102no—
745C8—302no—
746C2×C3—22no—
747C2×C3—42no—
748C2×C3#6615611yescharacteristic
749C2×C3C2×#409711yescharacteristic
750C2×C3C2×#409911yescharacteristic
751D3—22no—
752D3—41no—
753D3—42no—
754C5#7888511yescharacteristic, complemented, Sylow
755C22—21no—
756C22—21no—
757C22—22no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—61no—
767C22—124no—
768C22—128no—
769C22—121no—
770C22—121no—
771C22#9157012yes—
772C22C2×D3×C22⋊D511yescharacteristic
773C4—22no—
774C4—61no—
775C4—61no—
776C4—62no—
777C4—202no—
778C4—602no—
779C4#9157012yes—
780C4C22×#120311yescharacteristic
781C4C2×D3×C22⋊D511yescharacteristic
782C3#1061581511yescharacteristic, complemented, Sylow
783C2—22no—
784C2—42no—
785C2—62no—
786C2—121no—
787C2—122no—
788C2D3×#409711yescharacteristic
789C2#1175534511yescharacteristic
790C2C2×#9157011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D3×#41C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C2×#91365C2semidirect
4. C2×#91322C2semidirect
5. C3×#65521C2semidirect
6. #11749302C2semidirect
7. #11749300C2semidirect
8. #11749056C2semidirect
9. #11749054C2semidirect
10. #11748384C2semidirect
11. #11748346C2semidirect
14. C22×Dic30C22semidirect
28. C2×#6718C22semidirect
29. C2×#6716C22semidirect
30. C2×#6710C22semidirect
31. C2×C3×C4⋊Dic5C22semidirect
32. C2×C3×#681C22semidirect
38. #91365C22semidirect
40. C2×#6663C22semidirect
41. C2×#6659C22semidirect
42. C3×#3967C22semidirect
43. C3×#3964C22semidirect
44. #90972C22semidirect
45. #90966C22semidirect
47. (C2×D3)⋊#168C22semidirect
56. #65521D3semidirect
153. C2×C4⋊Dic5C2×D3semidirect
160. C2×#681C2×D3semidirect
162. #3967C2×D3semidirect
164. #3964C2×D3semidirect
346. C2×C5×D3#137semidirect
656. C3×C5#3007semidirect
674. C2×D3#4097semidirect
754. C5#78885semidirect
782. C3#10615815semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C2×#918402
C2×#913652
C2×#913222
C3×#655212
#117493022
#117493002
#117490562
#117490542
#117483842
#117483462
#106158153
#788855