Finite Group Databasebeta

← #14453771

Subgroups — #14453771

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5550C211yesmaximal, characteristic
2C3×D4×Dic10C211yesmaximal, characteristic, complemented
3C2×#91309C211yesmaximal, characteristic, complemented
4C22×#6656C211yesmaximal, characteristic, complemented
5#11751112C211yesmaximal, characteristic, complemented
6#11748562C211yesmaximal, characteristic, complemented
7#11748555C211yesmaximal, characteristic, complemented
8#11748548C211yesmaximal, characteristic, complemented
9#11748538C211yesmaximal, characteristic, complemented
10#11748537C211yesmaximal, characteristic, complemented
11#11748529C211yesmaximal, characteristic, complemented
12#11747082C211yesmaximal, characteristic, complemented
13#11747070C211yesmaximal, characteristic, complemented
14#11747061C211yesmaximal, characteristic, complemented
15#11747050C211yesmaximal, characteristic, complemented
16#10615237—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C2×#6710C2211yescharacteristic, complemented
23C22×C3⋊#168C2211yescharacteristic
24C5×#937—21no—
25C5×#930C2211yescharacteristic
26C5×#924C2211yescharacteristic
27C5×#894—21no—
28C5×#884—21no—
29C5×D3×C22⋊C4—21no—
30C5×#875C2211yescharacteristic
31C4×C5×D12C2211yescharacteristic
32C3×D4×Dic5—21no—
33C3×#4070C2211yescharacteristic
34C3×#4070C2211yescharacteristic, complemented
35C3×#4034—21no—
36C3×#4024—21no—
37C3×#4024—21no—
38C3×#4015C2211yescharacteristic, complemented
39C3×C4×Dic10C2211yescharacteristic, complemented
40C2×#6661C2211yescharacteristic, complemented
41C2×#6661C2211yescharacteristic, complemented
42C2×#6661C2211yescharacteristic, complemented
43#91309—24no—
44C2×#6656—24no—
45C2×#6656C2211yescharacteristic
46C2×#6656C2211yescharacteristic
47C2×#6656C2211yescharacteristic
48C2×#6656C2211yescharacteristic
49C2×#6656C2211yescharacteristic
50C2×#6656C2211yescharacteristic
51#91114C2211yescharacteristic
52#91114C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90970C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90966C2211yescharacteristic
61#90966C2211yescharacteristic
62#83559—51nomaximal, Hall
63C5×#546—31no—
64C2×#4097—31no—
65C22×#687—31no—
66D4×Dic10D311yescharacteristic, complemented
67#65528—31no—
68#65507—31no—
69#65349—31no—
70#65343—31no—
71#65340—31no—
72#65339—31no—
73#65331—31no—
74#65329—31no—
75#65308—31no—
76#65307—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×#67—21no—
84C5×#235—22no—
85C5×#235—41no—
86C2×C5×D12—22no—
87C2×C5×D12—21no—
88C2×C5×D12—41no—
89C2×C5×D12C2311yescharacteristic
90C2×C5×D12C2311yescharacteristic
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3—21no—
93C2×C5×Dic6C2311yescharacteristic
94C22×C3×Dic5—21no—
95C22×C3×Dic5—21no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10—22no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—21no—
100C2×C3×Dic10—41no—
101C2×C3×Dic10—41no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×C4⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C42×C5C2311yescharacteristic
109#6710—22no—
110C2×C3⋊#168—22no—
111C2×C3⋊#168C2311yescharacteristic
112C2×C3⋊#168C2311yescharacteristic
113C2×C3⋊#168C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C5×#217—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×(C2×D3)⋊C4—21no—
118C5×(C2×D3)⋊C4—21no—
119C5×(C2×D3)⋊C4—21no—
120C5×C4⋊Dic3C2311yescharacteristic
121C5×Dic3⋊C4—21no—
122C3×C22⋊Dic5—21no—
123C3×C22⋊Dic5—21no—
124C3×C4⋊Dic5—21no—
125C3×C4⋊Dic5—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C3×#683—21no—
128C3×#683—21no—
129C3×#683—21no—
130C3×C4×Dic5—21no—
131#6661—22no—
132#6661—22no—
133#6661—41no—
134#6656—22no—
135#6656—22no—
136#6656—22no—
137#6656—22no—
138#6656—41no—
139#6656D414yescomplemented
140C3×D4×Q8—51no—
141C2×#942—51no—
142C22×#215—51no—
143#5550D511yescharacteristic
144#5228—51no—
145#5227—51no—
146#5086—51no—
147#5083—51no—
148#5051—51no—
149#5049—51no—
150#5047—51no—
151#5046—51no—
152#5028—51no—
153#5026—51no—
154#5011—51no—
155C2×C5×#41—31no—
156C22×C5×D4—31no—
157C22×Dic10C2×D311yescharacteristic
158C22×Dic10C2×D311yescharacteristic, complemented
159C5×#124—31no—
160C5×#123—61no—
161C5×C22⋊Q8—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#120—61no—
165C4×C5×D4—31no—
166C4×C5×D4C2×D311yescharacteristic
167C2×C5×C22⋊C4—61no—
168#4097—64no—
169C2×#689—31no—
170C2×#689—31no—
171C2×#689—31no—
172D4×Dic5—21no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—31no—
177C2×#687—31no—
178C2×#687—31no—
179C2×#687—64no—
180#4070C2×D311yescharacteristic
181#4070C2×D311yescharacteristic, complemented
182C2×#681—31no—
183C22×#168—31no—
184#4034—21no—
185#4024—21no—
186#4024—21no—
187#4015C2×D311yescharacteristic, complemented
188C4×Dic10C2×D311yescharacteristic, complemented
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3942—31no—
196#3942—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—42no—
206C22×C5×D3—42no—
207C22×C5×D3—81no—
208C3×C5×D4—22no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218C5×#67—42no—
219C5×#67—81no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C5×D12—21no—
223C5×D12—21no—
224C5×D12—21no—
225C5×D12—42no—
226C5×D12C2×D412yes—
227C4×C5×D3—42no—
228C4×C5×D3—81no—
229C5×Dic6—21no—
230C5×Dic6—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—42no—
236C2×C3×Dic5—42no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yes—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3⋊#168C2×D412yes—
249C22×C3×Q8—51no—
250C22×C3×Q8—51no—
251C2×#235C2×D511yescharacteristic
252C22×D12C2×D511yescharacteristic
253C3×C4⋊Q8—51no—
254C3×C4⋊Q8—101no—
255C3×C22⋊Q8—51no—
256C3×C22⋊Q8—51no—
257C3×C22⋊Q8—101no—
258C3×C22⋊Q8—101no—
259C3×C4×Q8—51no—
260C3×C4×D4—101no—
261C3×C4×D4C2×D511yescharacteristic
262C2×#216—51no—
263C2×#216—51no—
264C2×#216—51no—
265#942—104no—
266C2×#215—51no—
267C2×#215—51no—
268C2×#215—51no—
269C2×#215—51no—
270C2×#215—51no—
271C2×#215—51no—
272C2×#215—104no—
273#937—21no—
274#930C2×D511yescharacteristic
275#924C2×D511yescharacteristic
276C2×#208—51no—
277C22×C3⋊C8—51no—
278#894—21no—
279#884—21no—
280D3×C22⋊C4—21no—
281#875C2×D511yescharacteristic
282C4×D12C2×D511yescharacteristic
283#835—51no—
284#835—51no—
285#835—51no—
286#830—51no—
287#830—51no—
288#810—51no—
289#809—51no—
290#809—51no—
291#807—51no—
292C4⋊(C3⋊C8)—51no—
293#803—51no—
294C24×C5—61no—
295C5×#41—62no—
296C5×#41—121no—
297C2×C5×Q8—31no—
298C2×C5×D4—31no—
299C2×C5×D4—31no—
300C2×C5×D4—62no—
301C2×C5×D4—61no—
302C2×C5×D4—61no—
303C2×C5×D4—61no—
304C2×C5×D4—121no—
305C2×C5×D4#6711yescharacteristic
306C22×C4×C5—61no—
307C22×C4×C5—61no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—21no—
311C22×Dic5—21no—
312C2×Dic10—22no—
313C2×Dic10—22no—
314C2×Dic10—21no—
315C2×Dic10—21no—
316C2×Dic10—41no—
317C2×Dic10—41no—
318C2×Dic10C22×D311yescharacteristic
319C2×Dic10C22×D311yescharacteristic
320C2×Dic10C22×D311yescharacteristic
321C5×C4⋊C4—31no—
322C5×C4⋊C4—61no—
323C5×C4⋊C4#6711yescharacteristic
324C5×C22⋊C4—61no—
325C5×C22⋊C4—61no—
326C5×C22⋊C4—61no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C5×C22⋊C4#6711yescharacteristic
330C5×C22⋊C4#6711yescharacteristic
331C42×C5C22×D311yescharacteristic
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334#689—62no—
335#689—62no—
336#689—121no—
337#687—34no—
338#687—62no—
339#687—62no—
340#687—62no—
341#687—62no—
342#687—121no—
343C4⋊Dic5—21no—
344C4⋊Dic5—21no—
345C4⋊Dic5C22×D311yescharacteristic
346#683—21no—
347#683—21no—
348#683—21no—
349C4×Dic5—21no—
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—31no—
355C2×#168—62no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—51no—
359#546—31no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×C5×D3—22no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391C3×Dic5—22no—
392C3×Dic5—41no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C23×D3—21no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×Q8—51no—
401C2×C3×Q8—102no—
402C2×C3×Q8—102no—
403C2×C3×Q8—101no—
404C2×C3×Q8—101no—
405C2×C3×Q8—201no—
406C2×C3×Q8—201no—
407C2×C3×D4C22⋊D511yescharacteristic
408C22×C3×C4—101no—
409C22×C3×C4—101no—
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C2×#67—21no—
413C2×#67—21no—
414#235—22no—
415#235—41no—
416C2×D12—22no—
417C2×D12—21no—
418C2×D12—41no—
419C2×D12C22×D511yescharacteristic
420C2×D12C22×D511yescharacteristic
421C2×C4×D3—21no—
422C2×C4×D3—21no—
423C2×Dic6C22×D511yescharacteristic
424C3×C4⋊C4—51no—
425C3×C4⋊C4—101no—
426C3×C4⋊C4—101no—
427C3×C4⋊C4—101no—
428C3×C4⋊C4—101no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4C22⋊D511yescharacteristic
431C3×C22⋊C4—101no—
432C3×C22⋊C4—101no—
433C3×C22⋊C4C22⋊D511yescharacteristic
434C3×C22⋊C4C22⋊D511yescharacteristic
435C3×C42—101no—
436C3×C42C22×D511yescharacteristic
437#217—21no—
438#216—102no—
439#216—102no—
440#216—201no—
441#215—54no—
442#215—102no—
443#215—102no—
444#215—102no—
445#215—102no—
446#215—201no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—21no—
449(C2×D3)⋊C4—21no—
450(C2×D3)⋊C4—21no—
451C4⋊Dic3C22×D511yescharacteristic
452Dic3⋊C4—21no—
453#208—102no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
457C2×C3⋊C8—51no—
458C2×C3⋊C8—102no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—122no—
462C23×C5—122no—
463C23×C5—241no—
464C23×C5C2×#6711yescharacteristic
465C23×C5C2×#6711yescharacteristic
466C5×Q8—61no—
467C5×Q8—61no—
468C5×D4—22no—
469C5×D4—32no—
470C5×D4—61no—
471C5×D4—61no—
472C5×D4—61no—
473C5×D4—122no—
474C5×D4—122no—
475C5×D4—241no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—122no—
483C2×C4×C5—241no—
484C2×C4×C5C2×#6711yescharacteristic
485C2×C4×C5C2×#6711yescharacteristic
486C2×C4×C5C2×#6711yescharacteristic
487C2×C4×C5C2×#6711yescharacteristic
488C2×C4×C5C23×D311yescharacteristic
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—42no—
494C2×Dic5—42no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—21no—
499Dic10—21no—
500Dic10—42no—
501Dic10—42no—
502Dic10D3×D412yes—
503#168—32no—
504#168—61no—
505#168—61no—
506#168—61no—
507C2×#41—31no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—31no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—31no—
527#123—61no—
528C22⋊Q8—31no—
529C22⋊Q8—51no—
530C22⋊Q8—51no—
531C22⋊Q8—101no—
532C22⋊Q8—101no—
533#121—31no—
534#121—61no—
535#120—61no—
536C4×Q8—51no—
537C4×D4—31no—
538C4×D4—101no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—61no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C5×D3—42no—
558C5×D3—81no—
559C23×C3C2×C22⋊D511yescharacteristic
560C23×C3C2×C22⋊D511yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—42no—
564C22×D3—42no—
565C22×D3—81no—
566C3×Q8—52no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—202no—
573C3×Q8—202no—
574C3×D4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—101no—
583C2×C3×C4—202no—
584C2×C3×C4—202no—
585C2×C3×C4C2×C22⋊D511yescharacteristic
586C2×C3×C4C2×C22⋊D511yescharacteristic
587C2×C3×C4C2×C22⋊D511yescharacteristic
588C2×C3×C4C2×C22⋊D511yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—42no—
591#67—81no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—42no—
598D12D4×D512yes—
599C4×D3—42no—
600C4×D3—81no—
601Dic6—21no—
602Dic6—21no—
603C3⋊C8—52no—
604C3⋊C8—101no—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5—62no—
613C22×C5—121no—
614C22×C5—121no—
615C22×C5—121no—
616C22×C5—121no—
617C22×C5—121no—
618C22×C5—244no—
619C22×C5#94212yescomplemented
620C22×C5C22×#6711yescharacteristic
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—121no—
626C4×C5—121no—
627C4×C5C2×D3×D411yescharacteristic
628C4×C5#100411yescharacteristic
629Dic5—22no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—61no—
634#41—62no—
635#41—121no—
636C2×Q8—31no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—51no—
640C2×Q8—102no—
641C2×Q8—102no—
642C2×Q8—101no—
643C2×Q8—101no—
644C2×Q8—201no—
645C2×Q8—201no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—121no—
653C2×D4#120111yescharacteristic
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4C2×D3×D511yescharacteristic
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—151no—
671C2×C8—151no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—31no—
676C4⋊C4—51no—
677C4⋊C4—61no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4#120111yescharacteristic
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4#120111yescharacteristic
692C22⋊C4#120111yescharacteristic
693C42—101no—
694C42C2×D3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3#409712yescomplemented
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—22no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—84no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—102no—
715C3×C4—201no—
716C3×C4—201no—
717C3×C4—201no—
718C3×C4C2×D4×D511yescharacteristic
719C3×C4#414411yescharacteristic
720Dic3—41no—
721Dic3—41no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5—122no—
725C2×C5—241no—
726C2×C5D4×#6711yescharacteristic
727C2×C5C2×#94211yescharacteristic
728C2×C5#583711yescharacteristic
729C23—61no—
730C23—61no—
731C23—122no—
732C23—122no—
733C23—241no—
734C23C2×#120111yescharacteristic
735C23C2×#120111yescharacteristic
736Q8—52no—
737Q8—61no—
738Q8—61no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8—202no—
746D4—22no—
747D4—32no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—122no—
765C2×C4—202no—
766C2×C4—202no—
767C2×C4—241no—
768C2×C4C2×#120111yescharacteristic
769C2×C4C2×#120111yescharacteristic
770C2×C4C2×#120111yescharacteristic
771C2×C4C2×#120111yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—152no—
774C8—301no—
775C8—301no—
776C8—301no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#409711yescharacteristic
781C2×C3#6617011yescharacteristic
782D3—42no—
783D3—81no—
784C5#8355911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—62no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22#9130912yescomplemented
798C22C22×#120111yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—102no—
804C4—121no—
805C4—121no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4D3×D4×D511yescharacteristic
810C4#9202511yescharacteristic
811C3#1061523711yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—122no—
815C2—241no—
816C2C2×#9130911yescharacteristic
817C2D4×#120111yescharacteristic
818C2#1175530411yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5550C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×Dic10C2semidirect
3. C2×#91309C2semidirect
4. C22×#6656C2semidirect
5. #11751112C2semidirect
6. #11748562C2semidirect
7. #11748555C2semidirect
8. #11748548C2semidirect
9. #11748538C2semidirect
10. #11748537C2semidirect
11. #11748529C2semidirect
12. #11747082C2semidirect
13. #11747070C2semidirect
14. #11747061C2semidirect
15. #11747050C2semidirect
20. C22×C3×Dic10C22semidirect
22. C2×#6710C22semidirect
34. C3×#4070C22semidirect
38. C3×#4015C22semidirect
39. C3×C4×Dic10C22semidirect
40. C2×#6661C22semidirect
41. C2×#6661C22semidirect
42. C2×#6661C22semidirect
52. #91114C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. #91087C22semidirect
55. #90989C22semidirect
56. #90972C22semidirect
57. #90970C22semidirect
58. #90970C22semidirect
59. #90970C22semidirect
66. D4×Dic10D3semidirect
139. #6656D4semidirect
158. C22×Dic10C2×D3semidirect
181. #4070C2×D3semidirect
187. #4015C2×D3semidirect
188. C4×Dic10C2×D3semidirect
376. C22×C3×C5#137semidirect
619. C22×C5#942semidirect
695. C3×C5#3266semidirect
701. C22×C3#4097semidirect
784. C5#83559semidirect
797. C22#91309semidirect
811. C3#10615237semidirect

Maximal subgroups

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

subgroupindex
C5×#55502
C3×D4×Dic102
C2×#913092
C22×#66562
#117511122
#117485622
#117485552
#117485482
#117485382
#117485372
#117485292
#117470822
#117470702
#117470612
#117470502
#106152373
#835595