Finite Group Databasebeta

← #14425257

Subgroups — #14425257

Order 1920.

1448 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5964C211yesmaximal, characteristic, complemented
2#11756581C211yesmaximal, characteristic, complemented
3#11754572C211yesmaximal, characteristic, complemented
4#11754145C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6#11749466C212yesmaximal, complemented
7#11749459C212yesmaximal, complemented
8#11749423C212yesmaximal, complemented
9#11749420C212yesmaximal, complemented
10C2×#90979C211yesmaximal, characteristic, complemented
11#11748355C211yesmaximal, characteristic, complemented
12#10615852—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic, complemented
15C5×#1010—21no—
16C5×#1010C2212yes—
17C5×#1009—21no—
18C5×#1009C2212yes—
19C5×D3×#41—22no—
20C5×D3×#41—22no—
21C5×#1007—21no—
22C5×#1004—21no—
23C5×#1004—22no—
24C2×C5×#235—22no—
25C2×C5×#235C2211yescharacteristic
26C2×C5×#235C2211yescharacteristic
27#91840C2212yescomplemented
28#91839—22no—
29#91838C2212yescomplemented
30#91831—21no—
31#91821—21no—
32C2×#6710C2211yescharacteristic, complemented
33C2×C3×C4×Dic5C2211yescharacteristic, complemented
34C2×C3×#681C2211yescharacteristic, complemented
35#91566—22no—
36#91451C2211yescharacteristic, complemented
37C4×#1203—22no—
38#91376C2211yescharacteristic, complemented
39#91375C2211yescharacteristic, complemented
40#91373C2211yescharacteristic, complemented
41#91322C2212yescomplemented
42#91321—21no—
43#91305C2212yescomplemented
44#91304—21no—
45#91303—22no—
46C3×#3969C2212yescomplemented
47C3×#3969C2212yescomplemented
48#90979C2212yescomplemented
49#90979C2212yescomplemented
50#90962C2212yescomplemented
51#90959C2212yescomplemented
52#78986—51nomaximal, Hall
53C5×#585—31no—
54#66166—31no—
55#66156—31no—
56#66156—31no—
57#65535—32no—
58#65534—32no—
59#65531—32no—
60#65530—32no—
61#65526—31no—
62C2×#3969—31no—
63C2×#3969D311yescharacteristic, complemented
64C3×C5×#41—21no—
65C3×C5×#41—21no—
66C3×C5×#41D412yescomplemented
67C3×C5×#41C2312yes—
68C2×C3×C5×Q8D411yescharacteristic, complemented
69C2×C3×C5×D4—21no—
70C2×C3×C5×D4D411yescharacteristic, complemented
71C22×C3×C4×C5—21no—
72C22×C3×C4×C5C2311yescharacteristic
73C2×#1220—21no—
74#6817—21no—
75#6817—21no—
76#6817—21no—
77#6817—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C2×C5×#67—24no—
82C2×C5×#67—21no—
83C2×C5×#67D412yes—
84C5×#239—22no—
85C5×#239—22no—
86C5×D3×Q8—22no—
87C5×D3×Q8—22no—
88C5×#237—24no—
89C5×#237—22no—
90C5×#237—22no—
91C5×#237—24no—
92C5×D3×D4—24no—
93C5×D3×D4—22no—
94C5×D3×D4—24no—
95C5×D3×D4—22no—
96C5×#235—24no—
97C5×#235—24no—
98C5×#235—21no—
99C5×#235—21no—
100C5×#235—21no—
101C5×#235—21no—
102C5×#235—21no—
103C5×#235—21no—
104C5×#235—22no—
105C5×#235—22no—
106C5×#235D412yescomplemented
107C5×#235C2312yes—
108C2×C5×D12—22no—
109C2×C5×D12D411yescharacteristic, complemented
110C2×C5×D12C2311yescharacteristic
111C2×C4×C5×D3—24no—
112C2×C4×C5×D3—21no—
113C2×C4×C5×D3D412yes—
114C2×C5×Dic6—22no—
115C2×C5×Dic6D411yescharacteristic, complemented
116C2×C5×Dic6C2311yescharacteristic
117C22×C3×Dic5—21no—
118C2×#1203—22no—
119#6718—22no—
120#6717—22no—
121#6716—22no—
122#6715—22no—
123#6710—21no—
124#6710C2312yes—
125C2×C3⋊#168—21no—
126C3×C4×Dic5—21no—
127C3×C4×Dic5C2311yescharacteristic
128C3×C4×Dic5C2311yescharacteristic
129C3×#681—21no—
130C3×#681C2312yes—
131C2×C3×#168—21no—
132#6668—22no—
133#6667—22no—
134(C2×D3)⋊Dic5—22no—
135#6663—22no—
136#6660—22no—
137#6659—22no—
138#6654—22no—
139#5964D511yescharacteristic, complemented
140#5822—51no—
141#5748—51no—
142#5477—51no—
143C2×C3×#104—51no—
144#5132—51no—
145C2×#805—51no—
146#4827—52no—
147#4826—52no—
148#4825—52no—
149#4822—52no—
150C5×2−1+4—32no—
151C5×2−1+4—61no—
152C5×2−1+4—61no—
153C5×H(5,𝔽2)—32no—
154C5×H(5,𝔽2)—62no—
155C5×H(5,𝔽2)—61no—
156C5×H(5,𝔽2)—61no—
157C2×C5×#41—31no—
158C2×C5×#41—31no—
159C2×C5×#41—62no—
160C2×C5×#41—62no—
161C2×C5×#41—62no—
162C2×C5×#41C2×D311yescharacteristic
163C2×#709—31no—
164#4097—32no—
165#4097—32no—
166#4096—62no—
167#4096—62no—
168#4095—32no—
169#4095—32no—
170#4093—31no—
171#4090—31no—
172#4088—61no—
173#4088—61no—
174#4086—31no—
175#4085—62no—
176#4082—31no—
177#4078—61no—
178#4078—61no—
179C4×C22⋊D5—62no—
180C2×C4×Dic5C2×D311yescharacteristic, complemented
181C2×#681—31no—
182C2×#681C2×D311yescharacteristic, complemented
183#3969—32no—
184#3969—32no—
185#3969C2×D312yescomplemented
186#3969C2×D312yescomplemented
187#3968—32no—
188#3965—32no—
189#3018—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5C2×D411yescharacteristic
192C22×D15—21no—
193C22×C5×D3—24no—
194C22×C5×D3—21no—
195C22×C5×D3C2×D412yes—
196C3×C5×Q8—21no—
197C3×C5×Q8C2×D412yes—
198C3×C5×D4—22no—
199C3×C5×D4—22no—
200C3×C5×D4—21no—
201C3×C5×D4C2×D412yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—22no—
204C2×C3×C4×C5—22no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211#1220—41no—
212#1220—41no—
213C2×Dic15—21no—
214D60—21no—
215D60—21no—
216C4×D15—41no—
217C4×D15—41no—
218Dic30—21no—
219Dic30—21no—
220C5×#67—24no—
221C5×#67—24no—
222C5×#67—22no—
223C5×#67—22no—
224C5×#67—22no—
225C5×#67—22no—
226C2×C5×Dic3—24no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3C2×D412yes—
229C5×D12—24no—
230C5×D12—21no—
231C5×D12—21no—
232C5×D12—21no—
233C5×D12C2×D412yes—
234C4×C5×D3—24no—
235C4×C5×D3—24no—
236C4×C5×D3—22no—
237C4×C5×D3—22no—
238C4×C5×D3—22no—
239C4×C5×D3—22no—
240C5×Dic6—24no—
241C5×Dic6—21no—
242C5×Dic6—21no—
243C5×Dic6—21no—
244C5×Dic6C2×D412yes—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—42no—
248#1203—44no—
249C3⋊#168—22no—
250C3×#168—22no—
251C2×C3×#41C2×D511yescharacteristic
252#1010—21no—
253#1010C2×D512yes—
254#1009—21no—
255#1009C2×D512yes—
256D3×#41—22no—
257D3×#41—22no—
258#1007—21no—
259#1004—21no—
260#1004—22no—
261C2×#235—22no—
262C2×#235—51no—
263C2×#235C2×D511yescharacteristic
264C2×#235C2×D511yescharacteristic
265C2×C3×M16—51no—
266C2×C3×C42—51no—
267#951—52no—
268#950—102no—
269#949—52no—
270#942—101no—
271#932—101no—
272#930—102no—
273C2×#208—51no—
274#909—52no—
275#909—101no—
276#908—52no—
277#908—101no—
278#904—102no—
279#875—51no—
280#875—51no—
281#874—51no—
282C4×D12—102no—
283#869—51no—
284C3×#104—52no—
285C3×#104—52no—
286#824—52no—
287#823—52no—
288#805—52no—
289#805—52no—
290C5×#41—21no—
291C5×#41—21no—
292C5×#41—32no—
293C5×#41—32no—
294C5×#41—62no—
295C5×#41—62no—
296C5×#41—64no—
297C5×#41—64no—
298C5×#41—64no—
299C5×#41—64no—
300C5×#41—62no—
301C5×#41—62no—
302C5×#41—62no—
303C5×#41—62no—
304C5×#41—61no—
305C5×#41—61no—
306C5×#41—61no—
307C5×#41—61no—
308C5×#41—61no—
309C5×#41—61no—
310C5×#41D1212yescomplemented
311C5×#41C22×D312yes—
312C2×C5×Q8—31no—
313C2×C5×Q8—31no—
314C2×C5×Q8—62no—
315C2×C5×Q8—62no—
316C2×C5×Q8—62no—
317C2×C5×Q8D1211yescharacteristic, complemented
318C2×C5×D4—21no—
319C2×C5×D4—32no—
320C2×C5×D4—31no—
321C2×C5×D4—31no—
322C2×C5×D4—62no—
323C2×C5×D4—64no—
324C2×C5×D4—64no—
325C2×C5×D4—62no—
326C2×C5×D4—64no—
327C2×C5×D4—61no—
328C2×C5×D4—62no—
329C2×C5×D4D1211yescharacteristic, complemented
330C22×C4×C5—21no—
331C22×C4×C5—32no—
332C22×C4×C5—64no—
333C22×C4×C5—61no—
334C22×C4×C5C22×D311yescharacteristic
335C2×C22⋊D5—62no—
336C2×C22⋊D5—61no—
337C22×Dic5—21no—
338#709—61no—
339#709—61no—
340#709—61no—
341#709—61no—
342C2×D20—31no—
343C2×C4×D5—61no—
344C2×Dic10—31no—
345C22⋊Dic5—62no—
346#689—62no—
347#689—62no—
348#688—62no—
349#688—62no—
350#687—62no—
351#687—62no—
352#686—62no—
353#686—62no—
354#685—62no—
355#683—62no—
356C4×Dic5—21no—
357C4×Dic5C22×D311yescharacteristic
358C4×Dic5C22×D311yescharacteristic
359#681—21no—
360#681—32no—
361#681—61no—
362#681C22×D312yes—
363C2×#168—21no—
364C2×#168—61no—
365#585—31no—
366#575—151no—
367#575—151no—
368#532—151no—
369#456—152no—
370#455—152no—
371#454—152no—
372#453—152no—
373C2×#104—51no—
374C2×#104—151no—
375#413—151no—
376C22×C3×C5—22no—
377C22×C3×C5—41no—
378C22×C3×C5—81no—
379C22×C3×C5#12011yescharacteristic
380C22×C3×C5#12011yescharacteristic
381C22×C3×C5C22×D411yescharacteristic
382C2×D15—42no—
383C2×D15—41no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—42no—
387C2×C5×D3—81no—
388C2×C5×D3—84no—
389C3×C4×C5—22no—
390C3×C4×C5#12011yescharacteristic
391C3×C4×C5#12011yescharacteristic
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5C22×D411yescharacteristic
394Dic15—41no—
395C3×Dic5—22no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C3×#41—21no—
400C3×#41—21no—
401C3×#41C22⋊D512yescomplemented
402C3×#41C22×D512yes—
403C2×C3×Q8C22⋊D511yescharacteristic, complemented
404C2×C3×D4—21no—
405C2×C3×D4C22⋊D511yescharacteristic, complemented
406C22×C3×C4—21no—
407C22×C3×C4—101no—
408C22×C3×C4C22×D511yescharacteristic
409C2×#67—24no—
410C2×#67—21no—
411C2×#67—101no—
412C2×#67C22⋊D512yes—
413#239—22no—
414#239—22no—
415D3×Q8—22no—
416D3×Q8—22no—
417#237—24no—
418#237—22no—
419#237—22no—
420#237—24no—
421D3×D4—24no—
422D3×D4—22no—
423D3×D4—24no—
424D3×D4—22no—
425#235—24no—
426#235—24no—
427#235—21no—
428#235—21no—
429#235—21no—
430#235—21no—
431#235—21no—
432#235—21no—
433#235—22no—
434#235—22no—
435#235—101no—
436#235—101no—
437#235—101no—
438#235—101no—
439#235C22⋊D512yescomplemented
440#235C22×D512yes—
441C2×D12—22no—
442C2×D12—51no—
443C2×D12—102no—
444C2×D12C22⋊D511yescharacteristic, complemented
445C2×D12C22×D511yescharacteristic
446C2×C4×D3—24no—
447C2×C4×D3—21no—
448C2×C4×D3—101no—
449C2×C4×D3C22⋊D512yes—
450C2×Dic6—22no—
451C2×Dic6—51no—
452C2×Dic6C22⋊D511yescharacteristic, complemented
453C2×Dic6C22×D511yescharacteristic
454C3×M16—52no—
455C3×M16—101no—
456C2×C3×C8—101no—
457C3×C42—51no—
458C3×C42—51no—
459C3×C42—101no—
460#216—102no—
461#215—102no—
462#214—102no—
463#213—102no—
464(C2×D3)⋊C4—102no—
465(C2×D3)⋊C4—102no—
466C4⋊Dic3—102no—
467#208—52no—
468#208—101no—
469C2×C3⋊C8—101no—
470Dic12—102no—
471D24—102no—
472#204—102no—
473#204—102no—
474C23×C5—21no—
475C23×C5—32no—
476C23×C5—64no—
477C23×C5—61no—
478C23×C5D3×D411yescharacteristic
479C22×D5—61no—
480C5×Q8—21no—
481C5×Q8—32no—
482C5×Q8—64no—
483C5×Q8—61no—
484C5×Q8—61no—
485C5×Q8—61no—
486C5×Q8C2×D1212yes—
487C5×D4—22no—
488C5×D4—22no—
489C5×D4—21no—
490C5×D4—32no—
491C5×D4—64no—
492C5×D4—64no—
493C5×D4—64no—
494C5×D4—62no—
495C5×D4—62no—
496C5×D4—62no—
497C5×D4—62no—
498C5×D4—61no—
499C5×D4—61no—
500C5×D4—61no—
501C5×D4C2×D1212yes—
502C2×C4×C5—21no—
503C2×C4×C5—22no—
504C2×C4×C5—22no—
505C2×C4×C5—32no—
506C2×C4×C5—64no—
507C2×C4×C5—64no—
508C2×C4×C5—64no—
509C2×C4×C5—61no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—62no—
514C2×C4×C5C2×D1211yescharacteristic
515C2×C4×C5C2×D1211yescharacteristic
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5D3×D411yescharacteristic
518C2×C4×C5D3×D411yescharacteristic
519C2×C4×C5C23×D311yescharacteristic
520C22⋊D5—124no—
521C22⋊D5—121no—
522C22⋊D5—121no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—42no—
526C2×Dic5—61no—
527D20—61no—
528D20—61no—
529C4×D5—121no—
530C4×D5—121no—
531Dic10—61no—
532Dic10—61no—
533#168—22no—
534#168—62no—
5352−1+4—32no—
5362−1+4—61no—
5372−1+4—61no—
538H(5,𝔽2)—32no—
539H(5,𝔽2)—62no—
540H(5,𝔽2)—61no—
541H(5,𝔽2)—61no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—62no—
545C2×#41—62no—
546C2×#41—62no—
547C2×#41—151no—
548C2×#41D3×D511yescharacteristic
549#137—152no—
550#137—152no—
551#137—301no—
552#137—301no—
553AGL(1,ℤ/8)—152no—
554AGL(1,ℤ/8)—152no—
555AGL(1,ℤ/8)—301no—
556AGL(1,ℤ/8)—301no—
557#135—302no—
558#135—302no—
559C2×M16—51no—
560C2×M16—151no—
561C4⋊Q8—151no—
562#127—151no—
563#124—151no—
564#124—151no—
565#121—302no—
566C4×D4—302no—
567C2×C42—51no—
568#104—52no—
569#104—52no—
570#104—152no—
571#104—152no—
572#101—152no—
573#100—152no—
574C2×C3×C5—21no—
575C2×C3×C5—21no—
576C2×C3×C5—21no—
577C2×C3×C5—42no—
578C2×C3×C5C2×#12011yescharacteristic
579D15—81no—
580C5×D3—42no—
581C5×D3—42no—
582C23×C3—21no—
583C23×C3C2×C22⋊D511yescharacteristic
584C22×D3—24no—
585C22×D3—21no—
586C22×D3—101no—
587C22×D3C2×C22⋊D512yes—
588C3×Q8—21no—
589C3×Q8C2×C22⋊D512yes—
590C3×D4—22no—
591C3×D4—22no—
592C3×D4—21no—
593C3×D4C2×C22⋊D512yes—
594C2×C3×C4—21no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—202no—
600C2×C3×C4C2×C22⋊D511yescharacteristic
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C2×C22⋊D511yescharacteristic
603C2×C3×C4C2×C22⋊D511yescharacteristic
604C2×C3×C4C2×C22⋊D511yescharacteristic
605C2×C3×C4C23×D511yescharacteristic
606#67—24no—
607#67—24no—
608#67—22no—
609#67—22no—
610#67—22no—
611#67—22no—
612#67—201no—
613#67—201no—
614C2×Dic3—24no—
615C2×Dic3—21no—
616C2×Dic3—101no—
617C2×Dic3C2×C22⋊D512yes—
618D12—24no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—101no—
623D12—101no—
624D12—204no—
625D12C2×C22⋊D512yes—
626C4×D3—24no—
627C4×D3—24no—
628C4×D3—22no—
629C4×D3—22no—
630C4×D3—22no—
631C4×D3—22no—
632C4×D3—201no—
633C4×D3—201no—
634Dic6—24no—
635Dic6—21no—
636Dic6—21no—
637Dic6—21no—
638Dic6—101no—
639Dic6—101no—
640Dic6C2×C22⋊D512yes—
641C3×C8—102no—
642C3⋊C8—102no—
643C22×C5—22no—
644C22×C5—41no—
645C22×C5—62no—
646C22×C5—62no—
647C22×C5—81no—
648C22×C5—122no—
649C22×C5—241no—
650C22×C5—244no—
651C22×C5#88211yescharacteristic
652C22×C5#88211yescharacteristic
653C22×C5C2×D3×D411yescharacteristic
654C2×D5—122no—
655C2×D5—121no—
656C4×C5—22no—
657C4×C5—62no—
658C4×C5—62no—
659C4×C5#88211yescharacteristic
660C4×C5#88211yescharacteristic
661C4×C5C22×D1211yescharacteristic
662C4×C5C2×D3×D411yescharacteristic
663Dic5—22no—
664Dic5—41no—
665Dic5—121no—
666#41—21no—
667#41—21no—
668#41—32no—
669#41—32no—
670#41—62no—
671#41—62no—
672#41—64no—
673#41—64no—
674#41—64no—
675#41—64no—
676#41—62no—
677#41—62no—
678#41—62no—
679#41—62no—
680#41—61no—
681#41—61no—
682#41—61no—
683#41—61no—
684#41—61no—
685#41—61no—
686#41—301no—
687#41—301no—
688#41—301no—
689#41—301no—
690#41#120312yescomplemented
691#41C2×D3×D512yes—
692C2×Q8—31no—
693C2×Q8—31no—
694C2×Q8—62no—
695C2×Q8—62no—
696C2×Q8—62no—
697C2×Q8—151no—
698C2×Q8#120311yescharacteristic, complemented
699C2×D4—21no—
700C2×D4—32no—
701C2×D4—31no—
702C2×D4—31no—
703C2×D4—62no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—62no—
707C2×D4—64no—
708C2×D4—61no—
709C2×D4—62no—
710C2×D4—151no—
711C2×D4—302no—
712C2×D4—301no—
713C2×D4#120311yescharacteristic, complemented
714C22×C4—21no—
715C22×C4—32no—
716C22×C4—64no—
717C22×C4—61no—
718C22×C4—101no—
719C22×C4—301no—
720C22×C4C2×D3×D511yescharacteristic
721Q16—302no—
722Q16—302no—
723SD16—302no—
724SD16—302no—
725SD16—302no—
726SD16—302no—
727D8—302no—
728D8—302no—
729M16—52no—
730M16—101no—
731M16—152no—
732M16—301no—
733C2×C8—101no—
734C2×C8—301no—
735C4⋊C4—302no—
736C22⋊C4—302no—
737C22⋊C4—302no—
738C42—51no—
739C42—51no—
740C42—101no—
741C3×C5#301811yescharacteristic, complemented, Hall
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—81no—
745C22×C3#409911yescharacteristic
746C22×C3#409911yescharacteristic
747C22×C3C22×C22⋊D511yescharacteristic
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—42no—
751C2×D3—81no—
752C2×D3—84no—
753C2×D3—202no—
754C2×D3—201no—
755C3×C4—22no—
756C3×C4—102no—
757C3×C4—201no—
758C3×C4#409911yescharacteristic
759C3×C4#409911yescharacteristic
760C3×C4C22×C22⋊D511yescharacteristic
761C3×C4C22×C22⋊D511yescharacteristic
762Dic3—22no—
763Dic3—22no—
764Dic3—201no—
765C2×C5—21no—
766C2×C5—21no—
767C2×C5—21no—
768C2×C5—42no—
769C2×C5—122no—
770C2×C5—122no—
771C2×C5C2×#88211yescharacteristic
772D5—241no—
773C23—21no—
774C23—32no—
775C23—64no—
776C23—61no—
777C23—301no—
778C23D3×C22⋊D511yescharacteristic
779Q8—21no—
780Q8—32no—
781Q8—64no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—301no—
786Q8—301no—
787Q8C2×#120312yes—
788D4—22no—
789D4—22no—
790D4—21no—
791D4—32no—
792D4—64no—
793D4—64no—
794D4—64no—
795D4—62no—
796D4—62no—
797D4—62no—
798D4—62no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—301no—
803D4—301no—
804D4—604no—
805D4—601no—
806D4—601no—
807D4C2×#120312yes—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—32no—
812C2×C4—64no—
813C2×C4—64no—
814C2×C4—64no—
815C2×C4—61no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—202no—
823C2×C4—301no—
824C2×C4—601no—
825C2×C4—601no—
826C2×C4C2×#120311yescharacteristic
827C2×C4C2×#120311yescharacteristic
828C2×C4D3×C22⋊D511yescharacteristic
829C2×C4D3×C22⋊D511yescharacteristic
830C2×C4D3×C22⋊D511yescharacteristic
831C2×C4C22×D3×D511yescharacteristic
832C8—102no—
833C8—302no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—42no—
838C2×C3C2×#409911yescharacteristic
839D3—42no—
840D3—42no—
841D3—401no—
842C5#7898611yescharacteristic, complemented, Sylow
843C22—22no—
844C22—41no—
845C22—62no—
846C22—62no—
847C22—81no—
848C22—122no—
849C22—241no—
850C22—244no—
851C22—602no—
852C22—601no—
853C22#9157011yescharacteristic
854C22#9157011yescharacteristic
855C22C2×D3×C22⋊D511yescharacteristic
856C4—22no—
857C4—62no—
858C4—62no—
859C4—102no—
860C4—201no—
861C4—601no—
862C4#9157011yescharacteristic
863C4#9157011yescharacteristic
864C4C22×#120311yescharacteristic
865C4C2×D3×C22⋊D511yescharacteristic
866C3#1061585211yescharacteristic, complemented, Sylow
867C2—21no—
868C2—21no—
869C2—21no—
870C2—42no—
871C2—122no—
872C2—122no—
873C2—1201no—
874C2C2×#9157011yescharacteristic
subgroupG/H
centerC4#91570
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3018
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C5×#5964C2semidirect
2. #11756581C2semidirect
3. #11754572C2semidirect
4. #11754145C2semidirect
5. C2×C3×#3969C2semidirect
6. #11749466C2semidirect
7. #11749459C2semidirect
8. #11749423C2semidirect
9. #11749420C2semidirect
10. C2×#90979C2semidirect
11. #11748355C2semidirect
14. C2×#6817C22semidirect
27. #91840C22semidirect
29. #91838C22semidirect
32. C2×#6710C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. C2×C3×#681C22semidirect
36. #91451C22semidirect
38. #91376C22semidirect
39. #91375C22semidirect
40. #91373C22semidirect
41. #91322C22semidirect
43. #91305C22semidirect
46. C3×#3969C22semidirect
47. C3×#3969C22semidirect
48. #90979C22semidirect
49. #90979C22semidirect
50. #90962C22semidirect
51. #90959C22semidirect
63. C2×#3969D3semidirect
66. C3×C5×#41D4semidirect
68. C2×C3×C5×Q8D4semidirect
70. C2×C3×C5×D4D4semidirect
106. C5×#235D4semidirect
109. C2×C5×D12D4semidirect
115. C2×C5×Dic6D4semidirect
139. #5964D5semidirect
180. C2×C4×Dic5C2×D3semidirect
182. C2×#681C2×D3semidirect
185. #3969C2×D3semidirect
186. #3969C2×D3semidirect
310. C5×#41D12semidirect
317. C2×C5×Q8D12semidirect
329. C2×C5×D4D12semidirect
401. C3×#41C22⋊D5semidirect
403. C2×C3×Q8C22⋊D5semidirect
405. C2×C3×D4C22⋊D5semidirect
439. #235C22⋊D5semidirect
444. C2×D12C22⋊D5semidirect
452. C2×Dic6C22⋊D5semidirect
690. #41#1203semidirect
698. C2×Q8#1203semidirect
713. C2×D4#1203semidirect
741. C3×C5#3018semidirect
842. C5#78986semidirect
866. C3#10615852semidirect

Maximal subgroups

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

subgroupindex
C5×#59642
#117565812
#117545722
#117541452
C2×C3×#39692
#117494662
#117494592
#117494232
#117494202
C2×#909792
#117483552
#106158523
#789865