Finite Group Databasebeta

← #14426285

Subgroups — #14426285

Order 1920.

992 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×#950C211yesmaximal, characteristic, complemented
2C3×#66166C211yesmaximal, characteristic, complemented
3Dic5×#235C211yesmaximal, characteristic, complemented
4C2×#91297C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749249C211yesmaximal, characteristic, complemented
7#11749245C211yesmaximal, characteristic, complemented
8#11749224C211yesmaximal, characteristic, complemented
9#11749220C211yesmaximal, characteristic, complemented
10#11749003C211yesmaximal, characteristic, complemented
11#11748999C211yesmaximal, characteristic, complemented
12#11748978C211yesmaximal, characteristic, complemented
13#11748974C211yesmaximal, characteristic, complemented
14C2×#90982C211yesmaximal, characteristic, complemented
15#11748365C211yesmaximal, characteristic, complemented
16#10615631—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C5×#235C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20#91815C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C5×#950—24no—
23C2×C5×#216C2211yescharacteristic
24C2×C5×#215C2211yescharacteristic
25C2×C5×#214C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4093C2211yescharacteristic
29C3×#4090C2211yescharacteristic
30C3×#4086C2211yescharacteristic
31C3×#4085—21no—
32C3×#4085—21no—
33C3×#4082C2211yescharacteristic
34C3×C4×C22⋊D5—21no—
35C3×C4×C22⋊D5—21no—
36C2×C3×C4×Dic5C2211yescharacteristic
37Dic5×#67—21no—
38Dic5×#67—21no—
39Dic5×D12C2211yescharacteristic
40Dic5×D12C2211yescharacteristic
41C4×D3×Dic5—21no—
42#91371—21no—
43Dic5×Dic6C2211yescharacteristic
44Dic5×Dic6C2211yescharacteristic
45C2×#6661C2211yescharacteristic
46C2×#6656C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48#91297—24no—
49C2×#6652C2211yescharacteristic
50#91119C2211yescharacteristic
51#91119C2211yescharacteristic
52#91116C2211yescharacteristic
53#91116C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90982C2211yescharacteristic
57#90982C2211yescharacteristic
58#90971C2211yescharacteristic
59#90971C2211yescharacteristic
60#90965C2211yescharacteristic
61#90965C2211yescharacteristic
62#83296—51nomaximal, Hall
63C2×C5×#135—31no—
64#66166D311yescharacteristic, complemented
65#41×Dic5—31no—
66C2×#4096—31no—
67#65522—31no—
68#65474—31no—
69#65471—31no—
70#65455—31no—
71#65454—31no—
72#65452—31no—
73#65451—31no—
74#65442—31no—
75#65439—31no—
76#65402—31no—
77C2×#3946—31no—
78C3×C5×#41—22no—
79C3×C5×#41—22no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×C5×#67—21no—
86C5×#235—22no—
87C5×#235D414yescomplemented
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C5×Dic6C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C22×C3×Dic5D411yescharacteristic
95C22×C3×Dic5D411yescharacteristic
96C3×#709—22no—
97C3×#709—22no—
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×Dic10C2311yescharacteristic
101C2×D3×Dic5—21no—
102C2×D3×Dic5—21no—
103#6719—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15—21no—
107C2×C3⋊#168—22no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#216—22no—
111C5×#215—22no—
112C5×#214—22no—
113C5×#213—22no—
114C2×C5×C3⋊C8—22no—
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#683—21no—
122C3×#683—21no—
123C3×C4×Dic5D411yescharacteristic
124C3×C4×Dic5D411yescharacteristic
125C3×C4×Dic5C2311yescharacteristic
126C3×C4×Dic5C2311yescharacteristic
127Dic3⋊Dic5—21no—
128Dic3⋊Dic5—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131Dic3×Dic5—21no—
132Dic3×Dic5—21no—
133#6661—22no—
134#6656—22no—
135#6655—22no—
136#6652—22no—
137C3×#532—51no—
138C2×#950—51no—
139C2×#950D511yescharacteristic, complemented
140C4×#235—51no—
141#5233—51no—
142#5233—51no—
143#5090—51no—
144#5083—51no—
145#5075—51no—
146#5072—51no—
147#5057—51no—
148#5057—51no—
149#5054—51no—
150#5054—51no—
151C2×C4⋊(C3⋊C8)—51no—
152C2×C5×#41—31no—
153C2×C5×#41C2×D311yescharacteristic
154C2×#709C2×D311yescharacteristic
155C5×#135—64no—
156C2×C5×Q16—31no—
157C2×C5×SD16—31no—
158C2×C5×SD16—31no—
159C2×C5×D8—31no—
160C22×C5×C8—31no—
161#4096—64no—
162#4093C2×D311yescharacteristic
163Q8×Dic5—31no—
164Q8×Dic5—31no—
165#4090C2×D311yescharacteristic
166C2×#689—31no—
167C2×#688—31no—
168#4086C2×D311yescharacteristic
169#4085—21no—
170#4085—21no—
171#4082C2×D311yescharacteristic
172D4×Dic5—31no—
173D4×Dic5—31no—
174D4×Dic5—61no—
175D4×Dic5—61no—
176C2×#687—31no—
177C2×#686—31no—
178C4×C22⋊D5—21no—
179C4×C22⋊D5—21no—
180#4072—31no—
181#4072—61no—
182C2×C4×Dic5—61no—
183C2×C4×Dic5C2×D311yescharacteristic
184C22×#168—31no—
185#3967—31no—
186#3967—31no—
187#3964—31no—
188#3964—31no—
189#3953—31no—
190#3953—31no—
191#3948—31no—
192#3948—31no—
193#3946—31no—
194#3946—31no—
195#3946—31no—
196#3946—31no—
197#3035—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×C5×D3—21no—
201C22×C3×D5—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8—21no—
204C3×C5×D4—21no—
205C3×C5×D4—21no—
206C3×C5×D4—42no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—42no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5#4112yes—
212C2×C3×C4×C5C2411yescharacteristic
213C2×Dic15—21no—
214C2×Dic15—21no—
215C5×#67—24no—
216C2×C5×Dic3—21no—
217C5×D12—21no—
218C5×D12C2×D412yes—
219C4×C5×D3—24no—
220C5×Dic6—21no—
221C5×Dic6C2×D412yes—
222C3×C22⋊D5—42no—
223C3×C22⋊D5—42no—
224C3×C22⋊D5—42no—
225C2×C3×Dic5—22no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—41no—
228C2×C3×Dic5C2×D411yescharacteristic
229C2×C3×Dic5C2×D411yescharacteristic
230C2×C3×Dic5C2×D411yescharacteristic
231C2×C3×Dic5C2×D411yescharacteristic
232C3×D20—21no—
233C3×D20—21no—
234C3×C4×D5—42no—
235C3×Dic10—21no—
236C3×Dic10—21no—
237D3×Dic5—42no—
238D3×Dic5—42no—
239C3⋊#168—21no—
240C3⋊#168—21no—
241C5×C3⋊C8—21no—
242C5×C3⋊C8—21no—
243C2×C3×#41—51no—
244C2×C3×#41C2×D511yescharacteristic
245C2×#235C2×D511yescharacteristic
246C3×C4⋊Q8—51no—
247C3×#127—51no—
248C3×#124—51no—
249C3×#124—51no—
250C3×#121—101no—
251C3×#121—101no—
252C3×C4×D4—101no—
253C3×C4×D4—101no—
254C2×C3×C42—51no—
255#950—24no—
256#950—104no—
257C2×#216—51no—
258C2×#216C2×D511yescharacteristic
259C2×#215—51no—
260C2×#215C2×D511yescharacteristic
261C2×#214—51no—
262C2×#214C2×D511yescharacteristic
263C2×#213—51no—
264C2×#213C2×D511yescharacteristic
265C4×#67—101no—
266C4×#67—101no—
267#926—51no—
268C22×C3⋊C8—51no—
269C22×C3⋊C8C2×D511yescharacteristic
270C4×D12—51no—
271C4×D12—51no—
272#872—101no—
273C42×D3—101no—
274C4×Dic6—51no—
275C4×Dic6—51no—
276#835—51no—
277#835—51no—
278#835—51no—
279#835—51no—
280#832—51no—
281#832—51no—
282#832—51no—
283#832—51no—
284C4⋊(C3⋊C8)—51no—
285C4⋊(C3⋊C8)—51no—
286C4⋊(C3⋊C8)—51no—
287C4⋊(C3⋊C8)—51no—
288C5×#41—22no—
289C5×#41—22no—
290C5×#41—34no—
291C5×#41—62no—
292C2×C5×Q8—31no—
293C2×C5×Q8C22×D311yescharacteristic
294C2×C5×D4—21no—
295C2×C5×D4—31no—
296C2×C5×D4—61no—
297C2×C5×D4C22×D311yescharacteristic
298C22×C4×C5—21no—
299C22×C4×C5—61no—
300C22×C4×C5C22×D311yescharacteristic
301C2×C22⋊D5—21no—
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304C22×Dic5—61no—
305C22×Dic5—61no—
306C22×Dic5#6711yescharacteristic
307C22×Dic5#6711yescharacteristic
308#709—22no—
309#709—22no—
310C2×D20C22×D311yescharacteristic
311C2×C4×D5—21no—
312C2×Dic10C22×D311yescharacteristic
313C5×Q16—62no—
314C5×SD16—62no—
315C5×SD16—62no—
316C5×D8—62no—
317C2×C5×C8—31no—
318C2×C5×C8—31no—
319C2×C5×C8—62no—
320C22⋊Dic5—21no—
321C22⋊Dic5—21no—
322C22⋊Dic5—61no—
323C22⋊Dic5—61no—
324C22⋊Dic5—61no—
325#689—62no—
326#688—62no—
327#687—62no—
328#686—62no—
329#685—21no—
330#685—21no—
331C4⋊Dic5—31no—
332C4⋊Dic5—31no—
333C4⋊Dic5—61no—
334C4⋊Dic5—61no—
335#683—21no—
336#683—21no—
337C4×Dic5—61no—
338C4×Dic5—61no—
339C4×Dic5—61no—
340C4×Dic5#6711yescharacteristic
341C4×Dic5#6711yescharacteristic
342C4×Dic5C22×D311yescharacteristic
343C4×Dic5C22×D311yescharacteristic
344C2×#168—31no—
345C2×#168—31no—
346C2×#168—62no—
347C2×#135—31no—
348C2×#135—151no—
349#532—51no—
350C4×#41—151no—
351#464—151no—
352#464—151no—
353#463—151no—
354#463—151no—
355#462—151no—
356#461—151no—
357#460—151no—
358#459—151no—
359C2×C4⋊C8—151no—
360#416—151no—
361#416—151no—
362C22×C3×C5—21no—
363C22×C3×C5—21no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5#12112yes—
368C22×C3×C5C22×D411yescharacteristic
369C2×C5×D3—22no—
370C2×C5×D3—41no—
371C2×C5×D3—41no—
372C2×C3×D5—41no—
373C2×C3×D5—41no—
374C2×C3×D5—41no—
375C3×C4×C5—41no—
376C3×C4×C5#12112yes—
377C3×C4×C5C22×D411yescharacteristic
378C3×C4×C5C2×#4111yescharacteristic
379Dic15—41no—
380Dic15—41no—
381C3×Dic5—21no—
382C3×Dic5—21no—
383C3×Dic5—21no—
384C3×Dic5—41no—
385C3×Dic5#13512yescomplemented
386C5×Dic3—22no—
387C3×#41—22no—
388C3×#41—22no—
389C3×#41—102no—
390C3×#41—102no—
391C2×C3×Q8—51no—
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C2×C3×D4—101no—
397C2×C3×D4—101no—
398C2×C3×D4C22×D511yescharacteristic
399C22×C3×C4—21no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—101no—
403C22×C3×C4C22×D511yescharacteristic
404C2×#67—21no—
405#235—22no—
406#235C22⋊D514yescomplemented
407C2×D12C22×D511yescharacteristic
408C2×C4×D3—21no—
409C2×C4×D3—101no—
410C2×C4×D3—101no—
411C2×Dic6C22×D511yescharacteristic
412C3×C4⋊C4—101no—
413C3×C4⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C22⋊C4—101no—
416C3×C22⋊C4—101no—
417C3×C22⋊C4—101no—
418C3×C42—51no—
419C3×C42—51no—
420C3×C42—51no—
421C3×C42—51no—
422#217—101no—
423#216—22no—
424#216—102no—
425#215—22no—
426#215—102no—
427#214—22no—
428#214—102no—
429#213—22no—
430#213—102no—
431(C2×D3)⋊C4—101no—
432(C2×D3)⋊C4—101no—
433C4⋊Dic3—51no—
434C4⋊Dic3—51no—
435Dic3⋊C4—101no—
436Dic3⋊C4—101no—
437C4×Dic3—101no—
438C4×Dic3—101no—
439C4×Dic3—101no—
440C2×C3⋊C8—22no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—102no—
444C2×C3⋊C8C22×D511yescharacteristic
445C2×C3⋊C8C22×D511yescharacteristic
446C23×C5—21no—
447C23×C5—61no—
448C23×C5C2×#6711yescharacteristic
449C22×D5—21no—
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—32no—
453C5×Q8—61no—
454C5×D4—21no—
455C5×D4—21no—
456C5×D4—32no—
457C5×D4—42no—
458C5×D4—64no—
459C5×D4—61no—
460C2×C4×C5—21no—
461C2×C4×C5—42no—
462C2×C4×C5—61no—
463C2×C4×C5—64no—
464C2×C4×C5D3×D412yes—
465C2×C4×C5#23712yes—
466C2×C4×C5C2×#6711yescharacteristic
467C2×C4×C5C23×D311yescharacteristic
468C22⋊D5—42no—
469C22⋊D5—42no—
470C22⋊D5—42no—
471C2×Dic5—22no—
472C2×Dic5—21no—
473C2×Dic5—41no—
474C2×Dic5—61no—
475C2×Dic5—61no—
476C2×Dic5—122no—
477C2×Dic5—122no—
478C2×Dic5C2×#6711yescharacteristic
479C2×Dic5C2×#6711yescharacteristic
480C2×Dic5C2×#6711yescharacteristic
481C2×Dic5C2×#6711yescharacteristic
482D20—21no—
483D20—21no—
484C4×D5—42no—
485Dic10—21no—
486Dic10—21no—
487C5×C8—61no—
488C5×C8—61no—
489#168—61no—
490#168—61no—
491C2×#41—31no—
492C2×#41—51no—
493C2×#41D3×D511yescharacteristic
494#135—64no—
495#135—304no—
496C2×Q16—31no—
497C2×Q16—151no—
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16—151no—
501C2×SD16—151no—
502C2×D8—31no—
503C2×D8—151no—
504C22×C8—31no—
505C22×C8—151no—
506C4⋊Q8—51no—
507#127—51no—
508#124—51no—
509#124—51no—
510#121—101no—
511#121—101no—
512C4×Q8—151no—
513C4×Q8—151no—
514C4×D4—101no—
515C4×D4—101no—
516C4×D4—151no—
517C4×D4—151no—
518C4×D4—301no—
519C4×D4—301no—
520#117—151no—
521#117—301no—
522C2×C42—51no—
523C2×C42—301no—
524C4⋊C8—151no—
525C4⋊C8—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528#103—151no—
529#103—151no—
530#103—151no—
531#103—151no—
532#102—151no—
533#102—151no—
534#102—151no—
535#102—151no—
536C2×C3×C5—22no—
537C2×C3×C5—81no—
538C2×C3×C5C2×#12111yescharacteristic
539C2×C3×C5C2×#13511yescharacteristic
540C2×C3×C5#57511yescharacteristic
541C3×D5—81no—
542C5×D3—42no—
543C23×C3—21no—
544C23×C3—101no—
545C23×C3D4×D511yescharacteristic
546C22×D3—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—101no—
550C3×Q8—101no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—42no—
554C3×D4—101no—
555C3×D4—101no—
556C3×D4—202no—
557C3×D4—202no—
558C3×D4—202no—
559C2×C3×C4—21no—
560C2×C3×C4—42no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—51no—
564C2×C3×C4—51no—
565C2×C3×C4—102no—
566C2×C3×C4—101no—
567C2×C3×C4—201no—
568C2×C3×C4—202no—
569C2×C3×C4D4×D511yescharacteristic
570C2×C3×C4#71112yes—
571C2×C3×C4C2×C22⋊D512yes—
572C2×C3×C4C23×D511yescharacteristic
573#67—24no—
574C2×Dic3—21no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577D12—21no—
578D12C2×C22⋊D512yes—
579C4×D3—24no—
580C4×D3—202no—
581C4×D3—202no—
582Dic6—21no—
583Dic6C2×C22⋊D512yes—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—101no—
587C3⋊C8—101no—
588C22×C5—21no—
589C22×C5—21no—
590C22×C5—41no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5—62no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5#93812yes—
597C22×C5C22×#6711yescharacteristic
598C2×D5—41no—
599C2×D5—41no—
600C2×D5—41no—
601C4×C5—41no—
602C4×C5—62no—
603C4×C5#93812yes—
604C4×C5C2×D3×D411yescharacteristic
605C4×C5C2×#23711yescharacteristic
606Dic5—21no—
607Dic5—21no—
608Dic5—21no—
609Dic5—41no—
610Dic5—121no—
611Dic5—121no—
612Dic5#95012yescomplemented
613#41—22no—
614#41—22no—
615#41—34no—
616#41—62no—
617#41—102no—
618#41—102no—
619C2×Q8—31no—
620C2×Q8—51no—
621C2×Q8C2×D3×D511yescharacteristic
622C2×D4—21no—
623C2×D4—31no—
624C2×D4—51no—
625C2×D4—61no—
626C2×D4—101no—
627C2×D4—101no—
628C2×D4—101no—
629C2×D4C2×D3×D511yescharacteristic
630C22×C4—21no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—61no—
634C22×C4—101no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4C2×D3×D511yescharacteristic
638Q16—62no—
639Q16—302no—
640SD16—62no—
641SD16—62no—
642SD16—302no—
643SD16—302no—
644D8—62no—
645D8—302no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—62no—
649C2×C8—151no—
650C2×C8—151no—
651C2×C8—302no—
652C4⋊C4—101no—
653C4⋊C4—101no—
654C4⋊C4—151no—
655C4⋊C4—151no—
656C4⋊C4—301no—
657C4⋊C4—301no—
658C22⋊C4—101no—
659C22⋊C4—101no—
660C22⋊C4—101no—
661C22⋊C4—101no—
662C22⋊C4—301no—
663C22⋊C4—301no—
664C22⋊C4—301no—
665C42—51no—
666C42—51no—
667C42—51no—
668C42—51no—
669C42—301no—
670C42—301no—
671C42—301no—
672C3×C5#303511yescharacteristic, complemented, Hall
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—201no—
679C22×C3—201no—
680C22×C3—201no—
681C22×C3#408512yes—
682C22×C3C2×D4×D511yescharacteristic
683C2×D3—22no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—41no—
687C3×C4—52no—
688C3×C4—101no—
689C3×C4—101no—
690C3×C4—101no—
691C3×C4—201no—
692C3×C4#408512yes—
693C3×C4C2×#71111yescharacteristic
694C3×C4C22×C22⋊D511yescharacteristic
695Dic3—22no—
696Dic3—201no—
697Dic3—201no—
698C2×C5—22no—
699C2×C5—81no—
700C2×C5—122no—
701C2×C5C2×#93811yescharacteristic
702C2×C5C2×#95011yescharacteristic
703C2×C5#582211yescharacteristic
704D5—81no—
705C23—21no—
706C23—61no—
707C23—101no—
708C23D5×#6711yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—32no—
712Q8—61no—
713Q8—101no—
714Q8—101no—
715D4—21no—
716D4—21no—
717D4—32no—
718D4—42no—
719D4—64no—
720D4—61no—
721D4—101no—
722D4—101no—
723D4—202no—
724D4—202no—
725D4—202no—
726C2×C4—21no—
727C2×C4—42no—
728C2×C4—51no—
729C2×C4—51no—
730C2×C4—51no—
731C2×C4—51no—
732C2×C4—61no—
733C2×C4—64no—
734C2×C4—102no—
735C2×C4—101no—
736C2×C4—201no—
737C2×C4—202no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—602no—
741C2×C4—602no—
742C2×C4#678012yes—
743C2×C4D5×#6711yescharacteristic
744C2×C4D3×C22⋊D512yes—
745C2×C4C22×D3×D511yescharacteristic
746C8—61no—
747C8—61no—
748C8—301no—
749C8—301no—
750C2×C3—22no—
751C2×C3—81no—
752C2×C3—401no—
753C2×C3D5×#13511yescharacteristic
754C2×C3#6610211yescharacteristic
755C2×C3C2×#408511yescharacteristic
756D3—42no—
757C5#8329611yescharacteristic, complemented, Sylow
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—62no—
764C22—121no—
765C22—121no—
766C22—201no—
767C22—201no—
768C22—201no—
769C22#9156512yes—
770C22C2×D5×#6711yescharacteristic
771C4—41no—
772C4—52no—
773C4—62no—
774C4—101no—
775C4—101no—
776C4—101no—
777C4—201no—
778C4—601no—
779C4—601no—
780C4#9156512yes—
781C4C2×#678011yescharacteristic
782C4C2×D3×C22⋊D511yescharacteristic
783C3#1061563111yescharacteristic, complemented, Sylow
784C2—22no—
785C2—81no—
786C2—122no—
787C2—401no—
788C2D5×#95011yescharacteristic
789C2#1175531511yescharacteristic
790C2C2×#9156511yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#950C2semidirect
2. C3×#66166C2semidirect
3. Dic5×#235C2semidirect
4. C2×#91297C2semidirect
5. #11751334C2semidirect
6. #11749249C2semidirect
7. #11749245C2semidirect
8. #11749224C2semidirect
9. #11749220C2semidirect
10. #11749003C2semidirect
11. #11748999C2semidirect
12. #11748978C2semidirect
13. #11748974C2semidirect
14. C2×#90982C2semidirect
15. #11748365C2semidirect
64. #66166D3semidirect
87. C5×#235D4semidirect
139. C2×#950D5semidirect
385. C3×Dic5#135semidirect
406. #235C22⋊D5semidirect
612. Dic5#950semidirect
672. C3×C5#3035semidirect
757. C5#83296semidirect
783. C3#10615631semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9502
C3×#661662
Dic5×#2352
C2×#912972
#117513342
#117492492
#117492452
#117492242
#117492202
#117490032
#117489992
#117489782
#117489742
C2×#909822
#117483652
#106156313
#832965