Finite Group Databasebeta

← #14425256

Subgroups — #14425256

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
2C3×#66156C211yesmaximal, characteristic, complemented
3#11754586C211yesmaximal, characteristic, complemented
4#11754138C211yesmaximal, characteristic, complemented
5C2×#91121C211yesmaximal, characteristic, complemented
6#11749465C212yesmaximal, complemented
7#11749458C212yesmaximal, complemented
8#11749419C212yesmaximal, complemented
9#11749416C212yesmaximal, complemented
10C2×#90978C211yesmaximal, characteristic, complemented
11#11748355C211yesmaximal, characteristic, complemented
12#10615852—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C5×#1010—21no—
15C5×#1010C2212yes—
16C5×#1009—21no—
17C5×#1009C2212yes—
18C5×D3×#41—22no—
19C5×D3×#41—22no—
20C5×#1007—21no—
21C5×#1004—21no—
22C5×#1004—22no—
23C2×C5×#235—22no—
24C2×C5×#235C2211yescharacteristic
25C2×C5×#235C2211yescharacteristic
26C2×C3×#709C2211yescharacteristic, complemented
27C2×C4×Dic15C2211yescharacteristic, complemented
28C2×#6710C2211yescharacteristic, complemented
29C3×#4097C2212yescomplemented
30C3×#4096—22no—
31C3×#4095C2212yescomplemented
32C3×#4088—21no—
33C3×#4078—21no—
34C2×C3×#681C2211yescharacteristic, complemented
35#91571—22no—
36#91463C2211yescharacteristic, complemented
37C4×#1201—22no—
38#91385C2211yescharacteristic, complemented
39#91370C2211yescharacteristic, complemented
40#91368C2211yescharacteristic, complemented
41#91309C2212yescomplemented
42#91307—21no—
43#91299—21no—
44#91298C2212yescomplemented
45#91297—22no—
46#91121C2212yescomplemented
47#91121C2212yescomplemented
48#90978C2212yescomplemented
49#90978C2212yescomplemented
50#90962C2212yescomplemented
51#90959C2212yescomplemented
52#84004—51nomaximal, Hall
53C5×#585—31no—
54#66166—31no—
55#66156—31no—
56#66156D311yescharacteristic, complemented
57#65535—32no—
58#65534—32no—
59#65531—32no—
60#65530—32no—
61#65526—31no—
62C2×#3969—31no—
63C2×#3969—31no—
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
73C22×Dic15—21no—
74C2×C5×#67—24no—
75C2×C5×#67—21no—
76C2×C5×#67D412yes—
77C5×#239—22no—
78C5×#239—22no—
79C5×D3×Q8—22no—
80C5×D3×Q8—22no—
81C5×#237—24no—
82C5×#237—22no—
83C5×#237—22no—
84C5×#237—24no—
85C5×D3×D4—24no—
86C5×D3×D4—22no—
87C5×D3×D4—24no—
88C5×D3×D4—22no—
89C5×#235—24no—
90C5×#235—24no—
91C5×#235—21no—
92C5×#235—21no—
93C5×#235—21no—
94C5×#235—21no—
95C5×#235—21no—
96C5×#235—21no—
97C5×#235—22no—
98C5×#235—22no—
99C5×#235D412yescomplemented
100C5×#235C2312yes—
101C2×C5×D12—22no—
102C2×C5×D12D411yescharacteristic, complemented
103C2×C5×D12C2311yescharacteristic
104C2×C4×C5×D3—24no—
105C2×C4×C5×D3—21no—
106C2×C4×C5×D3D412yes—
107C2×C5×Dic6—22no—
108C2×C5×Dic6D411yescharacteristic, complemented
109C2×C5×Dic6C2311yescharacteristic
110C2×C3×C22⋊D5—21no—
111C3×#709—21no—
112C3×#709—21no—
113C3×#709—21no—
114C3×#709—21no—
115C2×C3×D20C2311yescharacteristic
116C2×C3×C4×D5—21no—
117C2×C3×Dic10C2311yescharacteristic
118C2×#1201—22no—
119C4×Dic15—21no—
120C4×Dic15C2311yescharacteristic
121C4×Dic15C2311yescharacteristic
122#6710—21no—
123#6710C2312yes—
124C2×C3⋊#168—21no—
125C3×#689—22no—
126C3×#688—22no—
127C3×#687—22no—
128C3×#686—22no—
129C3×#681—21no—
130C3×#681C2312yes—
131C2×C3×#168—21no—
132#6669—22no—
133(C2×D3)⋊Dic5—22no—
134#6665—22no—
135#6661—22no—
136#6656—22no—
137#6655—22no—
138#6652—22no—
139#5964D511yescharacteristic, complemented
140C3×#575—51no—
141#5832—51no—
142#5822—51no—
143C2×#837—51no—
144#5205—52no—
145#5202—52no—
146#5201—52no—
147#5198—52no—
148C2×#825—51no—
149#5132—51no—
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×#709C2×D311yescharacteristic, complemented
164#4097—32no—
165#4097C2×D312yescomplemented
166#4096—22no—
167#4096—62no—
168#4095—32no—
169#4095C2×D312yescomplemented
170#4093—31no—
171#4090—31no—
172#4088—21no—
173#4088—61no—
174#4086—31no—
175#4085—62no—
176#4082—31no—
177#4078—21no—
178#4078—61no—
179C4×C22⋊D5—62no—
180C2×C4×Dic5—31no—
181C2×#681—31no—
182C2×#681C2×D311yescharacteristic, complemented
183#3969—32no—
184#3969—32no—
185#3969—32no—
186#3969—32no—
187#3968—32no—
188#3965—32no—
189#3018—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5C2×D411yescharacteristic
192C22×C5×D3—24no—
193C22×C5×D3—21no—
194C22×C5×D3C2×D412yes—
195C22×C3×D5—21no—
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
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—42no—
214C5×#67—24no—
215C5×#67—24no—
216C5×#67—22no—
217C5×#67—22no—
218C5×#67—22no—
219C5×#67—22no—
220C2×C5×Dic3—24no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3C2×D412yes—
223C5×D12—24no—
224C5×D12—21no—
225C5×D12—21no—
226C5×D12—21no—
227C5×D12C2×D412yes—
228C4×C5×D3—24no—
229C4×C5×D3—24no—
230C4×C5×D3—22no—
231C4×C5×D3—22no—
232C4×C5×D3—22no—
233C4×C5×D3—22no—
234C5×Dic6—24no—
235C5×Dic6—21no—
236C5×Dic6—21no—
237C5×Dic6—21no—
238C5×Dic6C2×D412yes—
239C3×C22⋊D5—41no—
240C3×C22⋊D5—41no—
241C2×C3×Dic5—21no—
242C3×D20—21no—
243C3×D20—21no—
244C3×C4×D5—41no—
245C3×C4×D5—41no—
246C3×Dic10—21no—
247C3×Dic10—21no—
248#1201—44no—
249C3⋊#168—22no—
250C3×#168—22no—
251C2×C3×#41—51no—
252C2×C3×#41C2×D511yescharacteristic
253#1010—21no—
254#1010C2×D512yes—
255#1009—21no—
256#1009C2×D512yes—
257D3×#41—22no—
258D3×#41—22no—
259#1007—21no—
260#1004—21no—
261#1004—22no—
262C2×#235—22no—
263C2×#235C2×D511yescharacteristic
264C2×#235C2×D511yescharacteristic
265C3×#137—52no—
266C3×#137—101no—
267C3×AGL(1,ℤ/8)—52no—
268C3×AGL(1,ℤ/8)—101no—
269C3×#135—102no—
270C2×C3×M16—51no—
271#951—101no—
272#950—102no—
273#949—101no—
274#947—51no—
275#944—51no—
276#942—52no—
277#940—51no—
278#939—102no—
279#936—51no—
280#932—52no—
281C4×#67—102no—
282C2×C4×Dic3—51no—
283C2×#208—51no—
284#837—52no—
285#837—52no—
286#825—52no—
287#825—52no—
288#824—52no—
289#823—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×#41#6712yescomplemented
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×Q8#6711yescharacteristic, 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×D4#6711yescharacteristic, complemented
330C22×C4×C5—21no—
331C22×C4×C5—32no—
332C22×C4×C5—64no—
333C22×C4×C5—61no—
334C22×C4×C5C22×D311yescharacteristic
335C2×C22⋊D5—21no—
336C2×C22⋊D5—62no—
337C22×Dic5—61no—
338#709—21no—
339#709—21no—
340#709—21no—
341#709—21no—
342C2×D20C22×D311yescharacteristic
343C2×C4×D5—21no—
344C2×Dic10C22×D311yescharacteristic
345C22⋊Dic5—62no—
346#689—22no—
347#689—62no—
348#688—22no—
349#688—62no—
350#687—22no—
351#687—62no—
352#686—22no—
353#686—62no—
354#685—62no—
355#683—62no—
356C4×Dic5—31no—
357C4×Dic5—31no—
358C4×Dic5—61no—
359#681—21no—
360#681—32no—
361#681—61no—
362#681C22×D312yes—
363C2×#168—21no—
364C2×#168—61no—
365#585—31no—
366#575—51no—
367#575—151no—
368#532—151no—
369#456—152no—
370#455—152no—
371#454—152no—
372#453—152no—
373C2×#104—151no—
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×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—42no—
385C2×C5×D3—81no—
386C2×C5×D3—84no—
387C2×C3×D5—42no—
388C2×C3×D5—41no—
389C3×C4×C5—22no—
390C3×C4×C5#12011yescharacteristic
391C3×C4×C5#12011yescharacteristic
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5C22×D411yescharacteristic
394Dic15—22no—
395Dic15—41no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C3×#41—21no—
400C3×#41—21no—
401C3×#41—101no—
402C3×#41—101no—
403C3×#41—101no—
404C3×#41—101no—
405C3×#41C22⋊D512yescomplemented
406C3×#41C22×D512yes—
407C2×C3×Q8—51no—
408C2×C3×Q8C22⋊D511yescharacteristic, complemented
409C2×C3×D4—21no—
410C2×C3×D4—51no—
411C2×C3×D4—101no—
412C2×C3×D4C22⋊D511yescharacteristic, complemented
413C22×C3×C4—21no—
414C22×C3×C4—101no—
415C22×C3×C4C22×D511yescharacteristic
416C2×#67—24no—
417C2×#67—21no—
418C2×#67—102no—
419C2×#67C22⋊D512yes—
420C22×Dic3—101no—
421#239—22no—
422#239—22no—
423D3×Q8—22no—
424D3×Q8—22no—
425#237—24no—
426#237—22no—
427#237—22no—
428#237—24no—
429D3×D4—24no—
430D3×D4—22no—
431D3×D4—24no—
432D3×D4—22no—
433#235—24no—
434#235—24no—
435#235—21no—
436#235—21no—
437#235—21no—
438#235—21no—
439#235—21no—
440#235—21no—
441#235—22no—
442#235—22no—
443#235C22⋊D512yescomplemented
444#235C22×D512yes—
445C2×D12—22no—
446C2×D12C22⋊D511yescharacteristic, complemented
447C2×D12C22×D511yescharacteristic
448C2×C4×D3—24no—
449C2×C4×D3—21no—
450C2×C4×D3C22⋊D512yes—
451C2×Dic6—22no—
452C2×Dic6C22⋊D511yescharacteristic, complemented
453C2×Dic6C22×D511yescharacteristic
454C3×Q16—102no—
455C3×SD16—102no—
456C3×SD16—102no—
457C3×D8—102no—
458C3×M16—52no—
459C3×M16—101no—
460C2×C3×C8—101no—
461#217—102no—
462#216—102no—
463#215—102no—
464#214—102no—
465#213—102no—
466(C2×D3)⋊C4—102no—
467Dic3⋊C4—102no—
468C4×Dic3—51no—
469C4×Dic3—51no—
470C4×Dic3—101no—
471#208—52no—
472#208—101no—
473C2×C3⋊C8—101no—
474C23×C5—21no—
475C23×C5—32no—
476C23×C5—64no—
477C23×C5—61no—
478C23×C5D3×D411yescharacteristic
479C22×D5—21no—
480C5×Q8—21no—
481C5×Q8—32no—
482C5×Q8—64no—
483C5×Q8—61no—
484C5×Q8—61no—
485C5×Q8—61no—
486C5×Q8C2×#6712yes—
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×#6712yes—
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×C5D3×D411yescharacteristic
515C2×C4×C5D3×D411yescharacteristic
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5C2×#6711yescharacteristic
518C2×C4×C5C2×#6711yescharacteristic
519C2×C4×C5C23×D311yescharacteristic
520C22⋊D5—41no—
521C22⋊D5—41no—
522C22⋊D5—124no—
523C2×Dic5—21no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—122no—
527D20—21no—
528D20—21no—
529C4×D5—41no—
530C4×D5—41no—
531Dic10—21no—
532Dic10—21no—
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—51no—
545C2×#41—62no—
546C2×#41—62no—
547C2×#41—62no—
548C2×#41D3×D511yescharacteristic
549#137—52no—
550#137—101no—
551#137—152no—
552#137—301no—
553AGL(1,ℤ/8)—52no—
554AGL(1,ℤ/8)—101no—
555AGL(1,ℤ/8)—152no—
556AGL(1,ℤ/8)—301no—
557#135—102no—
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—151no—
568#104—152no—
569#104—152no—
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
579C3×D5—81no—
580C5×D3—42no—
581C5×D3—42no—
582C23×C3—21no—
583C23×C3—101no—
584C23×C3C2×C22⋊D511yescharacteristic
585C22×D3—24no—
586C22×D3—21no—
587C22×D3C2×C22⋊D512yes—
588C3×Q8—21no—
589C3×Q8—101no—
590C3×Q8—101no—
591C3×Q8C2×C22⋊D512yes—
592C3×D4—22no—
593C3×D4—22no—
594C3×D4—21no—
595C3×D4—101no—
596C3×D4—101no—
597C3×D4—201no—
598C3×D4—201no—
599C3×D4C2×C22⋊D512yes—
600C2×C3×C4—21no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—101no—
604C2×C3×C4—201no—
605C2×C3×C4—201no—
606C2×C3×C4C2×C22⋊D511yescharacteristic
607C2×C3×C4C2×C22⋊D511yescharacteristic
608C2×C3×C4C2×C22⋊D511yescharacteristic
609C2×C3×C4C2×C22⋊D511yescharacteristic
610C2×C3×C4C2×C22⋊D511yescharacteristic
611C2×C3×C4C23×D511yescharacteristic
612#67—24no—
613#67—24no—
614#67—22no—
615#67—22no—
616#67—22no—
617#67—22no—
618#67—204no—
619C2×Dic3—24no—
620C2×Dic3—21no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—202no—
624C2×Dic3C2×C22⋊D512yes—
625D12—24no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12C2×C22⋊D512yes—
630C4×D3—24no—
631C4×D3—24no—
632C4×D3—22no—
633C4×D3—22no—
634C4×D3—22no—
635C4×D3—22no—
636Dic6—24no—
637Dic6—21no—
638Dic6—21no—
639Dic6—21no—
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#93711yescharacteristic
652C22×C5#93711yescharacteristic
653C22×C5C2×D3×D411yescharacteristic
654C2×D5—42no—
655C2×D5—41no—
656C4×C5—22no—
657C4×C5—62no—
658C4×C5—62no—
659C4×C5#93711yescharacteristic
660C4×C5#93711yescharacteristic
661C4×C5C2×D3×D411yescharacteristic
662C4×C5C22×#6711yescharacteristic
663Dic5—41no—
664Dic5—62no—
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—101no—
687#41—101no—
688#41—101no—
689#41—101no—
690#41#120112yescomplemented
691#41C2×D3×D512yes—
692C2×Q8—31no—
693C2×Q8—31no—
694C2×Q8—51no—
695C2×Q8—62no—
696C2×Q8—62no—
697C2×Q8—62no—
698C2×Q8#120111yescharacteristic, complemented
699C2×D4—21no—
700C2×D4—32no—
701C2×D4—31no—
702C2×D4—31no—
703C2×D4—51no—
704C2×D4—62no—
705C2×D4—64no—
706C2×D4—64no—
707C2×D4—62no—
708C2×D4—64no—
709C2×D4—61no—
710C2×D4—62no—
711C2×D4—101no—
712C2×D4—302no—
713C2×D4#120111yescharacteristic, complemented
714C22×C4—21no—
715C22×C4—32no—
716C22×C4—64no—
717C22×C4—61no—
718C22×C4—101no—
719C22×C4—301no—
720C22×C4C2×D3×D511yescharacteristic
721Q16—102no—
722Q16—302no—
723SD16—102no—
724SD16—102no—
725SD16—302no—
726SD16—302no—
727D8—102no—
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—151no—
739C42—151no—
740C42—301no—
741C3×C5#301811yescharacteristic, complemented, Hall
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—81no—
745C22×C3—202no—
746C22×C3—201no—
747C22×C3#409911yescharacteristic
748C22×C3#409911yescharacteristic
749C22×C3C22×C22⋊D511yescharacteristic
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—42no—
753C2×D3—81no—
754C2×D3—84no—
755C3×C4—22no—
756C3×C4—201no—
757C3×C4#409911yescharacteristic
758C3×C4#409911yescharacteristic
759C3×C4C22×C22⋊D511yescharacteristic
760C3×C4C22×C22⋊D511yescharacteristic
761Dic3—22no—
762Dic3—22no—
763Dic3—102no—
764Dic3—201no—
765C2×C5—21no—
766C2×C5—21no—
767C2×C5—21no—
768C2×C5—42no—
769C2×C5—122no—
770C2×C5—122no—
771C2×C5C2×#93711yescharacteristic
772D5—81no—
773C23—21no—
774C23—32no—
775C23—64no—
776C23—61no—
777C23—101no—
778C23D3×C22⋊D511yescharacteristic
779Q8—21no—
780Q8—32no—
781Q8—64no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—101no—
786Q8—101no—
787Q8C2×#120112yes—
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—101no—
803D4—101no—
804D4—201no—
805D4—201no—
806D4—604no—
807D4C2×#120112yes—
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—201no—
822C2×C4—201no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—602no—
826C2×C4C2×#120111yescharacteristic
827C2×C4C2×#120111yescharacteristic
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×C3—401no—
839C2×C3C2×#409911yescharacteristic
840D3—42no—
841D3—42no—
842C5#8400411yescharacteristic, complemented, Sylow
843C22—22no—
844C22—41no—
845C22—62no—
846C22—62no—
847C22—81no—
848C22—122no—
849C22—202no—
850C22—201no—
851C22—241no—
852C22—244no—
853C22#9156811yescharacteristic
854C22#9156811yescharacteristic
855C22C2×D3×C22⋊D511yescharacteristic
856C4—22no—
857C4—62no—
858C4—62no—
859C4—201no—
860C4—302no—
861C4—601no—
862C4#9156811yescharacteristic
863C4#9156811yescharacteristic
864C4C22×#120111yescharacteristic
865C4C2×D3×C22⋊D511yescharacteristic
866C3#1061585211yescharacteristic, complemented, Sylow
867C2—21no—
868C2—21no—
869C2—21no—
870C2—42no—
871C2—122no—
872C2—122no—
873C2—401no—
874C2C2×#9156811yescharacteristic
subgroupG/H
centerC4#91568
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. C3×#66156C2semidirect
3. #11754586C2semidirect
4. #11754138C2semidirect
5. C2×#91121C2semidirect
6. #11749465C2semidirect
7. #11749458C2semidirect
8. #11749419C2semidirect
9. #11749416C2semidirect
10. C2×#90978C2semidirect
11. #11748355C2semidirect
26. C2×C3×#709C22semidirect
27. C2×C4×Dic15C22semidirect
28. C2×#6710C22semidirect
29. C3×#4097C22semidirect
31. C3×#4095C22semidirect
34. C2×C3×#681C22semidirect
36. #91463C22semidirect
38. #91385C22semidirect
39. #91370C22semidirect
40. #91368C22semidirect
41. #91309C22semidirect
44. #91298C22semidirect
46. #91121C22semidirect
47. #91121C22semidirect
48. #90978C22semidirect
49. #90978C22semidirect
50. #90962C22semidirect
51. #90959C22semidirect
56. #66156D3semidirect
66. C3×C5×#41D4semidirect
68. C2×C3×C5×Q8D4semidirect
70. C2×C3×C5×D4D4semidirect
99. C5×#235D4semidirect
102. C2×C5×D12D4semidirect
108. C2×C5×Dic6D4semidirect
139. #5964D5semidirect
163. C2×#709C2×D3semidirect
165. #4097C2×D3semidirect
169. #4095C2×D3semidirect
182. C2×#681C2×D3semidirect
310. C5×#41#67semidirect
317. C2×C5×Q8#67semidirect
329. C2×C5×D4#67semidirect
405. C3×#41C22⋊D5semidirect
408. C2×C3×Q8C22⋊D5semidirect
412. C2×C3×D4C22⋊D5semidirect
443. #235C22⋊D5semidirect
446. C2×D12C22⋊D5semidirect
452. C2×Dic6C22⋊D5semidirect
690. #41#1201semidirect
698. C2×Q8#1201semidirect
713. C2×D4#1201semidirect
741. C3×C5#3018semidirect
842. C5#84004semidirect
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
C3×#661562
#117545862
#117541382
C2×#911212
#117494652
#117494582
#117494192
#117494162
C2×#909782
#117483552
#106158523
#840045