Finite Group Databasebeta

← #14453338

Subgroups — #14453338

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5676C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#11752745C211yesmaximal, characteristic, complemented
5#11751158C211yesmaximal, characteristic, complemented
6C3×#65347C211yesmaximal, characteristic, complemented
7#11749398C211yesmaximal, characteristic, complemented
8#11749281C211yesmaximal, characteristic, complemented
9#11749274C211yesmaximal, characteristic, complemented
10#11749152C211yesmaximal, characteristic, complemented
11#11749032C211yesmaximal, characteristic, complemented
12#11749029C211yesmaximal, characteristic, complemented
13#11747033C211yesmaximal, characteristic, complemented
14#11747025C211yesmaximal, characteristic, complemented
15#11746987C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic, complemented
18C2×C5×D3×D4C2211yescharacteristic, complemented
19C2×#6777—21no—
20C2×D3×D20C2211yescharacteristic
21C2×D3×D20C2211yescharacteristic, complemented
22C3×C5×#124C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic, complemented
24C2×#6715C2211yescharacteristic
25C4×D60C2211yescharacteristic, complemented
26C5×#946C2211yescharacteristic, complemented
27C5×#938C2211yescharacteristic, complemented
28C5×#884—21no—
29C5×#883—21no—
30C5×#882—21no—
31C5×D3×C22⋊C4—21no—
32C4×C5×D12C2211yescharacteristic
33C4×C5×D12C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic, complemented
35C2×C3×#688C2211yescharacteristic, complemented
36C2×C3×#686C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic, complemented
38C3×#4020C2211yescharacteristic, complemented
39#91504—24no—
40D3×#686—24no—
41#91474—21no—
42#91474—21no—
43#91465—21no—
44#91456C2211yescharacteristic
45#91456C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic
47C2×#6652C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90985C2211yescharacteristic, complemented
56#90969C2211yescharacteristic, complemented
57#90967C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#81856—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20—31no—
67#65527—31no—
68#65506—31no—
69#65347D311yescharacteristic, complemented
70#65346—31no—
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325—31no—
75#65304—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C22×D3×D5—21no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C5×#239—22no—
88C5×#239—41no—
89C5×D3×D4—22no—
90C5×D3×D4—41no—
91C2×C5×D12—21no—
92C2×C5×D12D411yescharacteristic
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C4×C5×D3C2311yescharacteristic
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×#1202—21no—
103C2×#1202—21no—
104C2×#1201—21no—
105C2×#1201—21no—
106#6777—44no—
107D3×D20—22no—
108D3×D20—22no—
109D3×D20—41no—
110D3×D20—41no—
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C42×C5C2311yescharacteristic
114#6717—22no—
115#6715—22no—
116#6714—21no—
117C4⋊Dic15C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C5×#217—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4D411yescharacteristic
124C5×(C2×D3)⋊C4D411yescharacteristic
125C5×C4⋊Dic3D411yescharacteristic
126C5×C4⋊Dic3C2311yescharacteristic
127C5×Dic3⋊C4—21no—
128C3×#688—22no—
129C3×#688—41no—
130C3×#686—22no—
131C3×#686—41no—
132C2×C3×#168C2311yescharacteristic
133C2×C3×#168C2311yescharacteristic
134#6665—21no—
135#6665—21no—
136#6654D414yescomplemented
137#6652—22no—
138#6652—22no—
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×D8—51no—
143#5717—51no—
144#5676D511yescharacteristic, complemented
145C3×#496—51no—
146#5172—51no—
147#5171—51no—
148#5169—51no—
149#5159—51no—
150#5156—51no—
151#5156—51no—
152#5072—51no—
153#5057—51no—
154#4711—51no—
155#4706—51no—
156C2×C5×#41—31no—
157C22×C5×D4—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124C2×D311yescharacteristic, complemented
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—31no—
165C5×#121—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169C2×C5×C22⋊C4—61no—
170#4095—64no—
171C2×#688—31no—
172C2×#688C2×D311yescharacteristic, complemented
173C2×#688C2×D311yescharacteristic, complemented
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—64no—
179C2×#686C2×D311yescharacteristic, complemented
180C2×#686C2×D311yescharacteristic, complemented
181#4076—31no—
182#4076—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020C2×D311yescharacteristic, complemented
189C4×D20—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3940—31no—
199C4⋊#168—31no—
200#3935C2×D311yescharacteristic, complemented
201#3264—151noSylow
202C23×C3×C5—21no—
203C22×D15—21no—
204C22×C5×D3—21no—
205C22×C5×D3—42no—
206C22×C5×D3—42no—
207C22×C5×D3—81no—
208C22×C5×D3C2×D411yescharacteristic
209C22×C5×D3C2×D411yescharacteristic
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C2×D3×D5—42no—
213C2×D3×D5—42no—
214C2×D3×D5—42no—
215C2×D3×D5—42no—
216C2×D3×D5—81no—
217C2×D3×D5—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226C2×Dic15—21no—
227D60—21no—
228D60C2×D412yes—
229C4×D15—42no—
230C5×#67—42no—
231C5×#67—81no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3C2×D411yescharacteristic
234C2×C5×Dic3C2×D411yescharacteristic
235C5×D12—22no—
236C5×D12—21no—
237C5×D12—42no—
238C5×D12C2×D412yescomplemented
239C4×C5×D3—21no—
240C4×C5×D3—21no—
241C4×C5×D3—21no—
242C4×C5×D3—21no—
243C4×C5×D3—42no—
244C4×C5×D3—81no—
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×D20—42no—
250C3×D20—81no—
251#1202—42no—
252#1202—42no—
253#1201—42no—
254#1201—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×#239C2×D511yescharacteristic, complemented
260C2×D3×D4—51no—
261C2×D3×D4—51no—
262C2×D3×D4—101no—
263C2×D3×D4C2×D511yescharacteristic, complemented
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C3×#127—51no—
269C3×#124C2×D511yescharacteristic, complemented
270#946C2×D511yescharacteristic, complemented
271C2×#215—51no—
272#938—51no—
273#938—51no—
274#938—101no—
275#938C2×D511yescharacteristic, complemented
276#937—101no—
277#937—101no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#914—104no—
282D3×D8—104no—
283C2×D24—51no—
284C2×ΓL(1,𝔽25)—51no—
285C2×D3×C8—51no—
286#884—21no—
287#883—21no—
288#882—21no—
289D3×C22⋊C4—21no—
290C4×D12—51no—
291C4×D12C2×D511yescharacteristic
292C4×D12C2×D511yescharacteristic, complemented
293C3×#97—51no—
294#835—51no—
295#832—51no—
296#832—51no—
297#832—51no—
298#821—51no—
299#821—51no—
300(C2×D3)⋊C8—51no—
301(C2×D3)⋊C8—51no—
302#817—51no—
303C4⋊(C3⋊C8)—51no—
304C24×C5—61no—
305C23×D5—61no—
306C23×D5—61no—
307C5×#41—62no—
308C5×#41—121no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—31no—
311C2×C5×D4—31no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—62no—
315C2×C5×D4—61no—
316C2×C5×D4—121no—
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—31no—
319C22×C4×C5—31no—
320C22×C4×C5—61no—
321C22×C4×C5—61no—
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324D4×D5—124no—
325C2×D20—21no—
326C2×D20—21no—
327C2×D20—31no—
328C2×D20—62no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—121no—
333C2×D20—121no—
334C2×D20C22×D311yescharacteristic
335C2×D20C22×D311yescharacteristic
336C2×C4×D5—61no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4—31no—
339C5×C4⋊C4—61no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—31no—
343C5×C22⋊C4—31no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4—61no—
346C5×C22⋊C4—61no—
347C42×C5C22×D311yescharacteristic
348#688—22no—
349#688—41no—
350#688—62no—
351#686—22no—
352#686—34no—
353#686—41no—
354#686—62no—
355#686—62no—
356#686—62no—
357#685—61no—
358#685—61no—
359#685—61no—
360C4⋊Dic5—31no—
361#681—62no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—62no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—31no—
370D42—151no—
371#496—51no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—21no—
390C2×C5×D3—21no—
391C2×C5×D3—21no—
392C2×C5×D3—22no—
393C2×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—84no—
398C2×C5×D3AGL(1,ℤ/8)12yescomplemented
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405D3×D5—84no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—41no—
410C3×C4×C5C22×D411yescharacteristic
411C3×C4×C5H(5,𝔽2)11yescharacteristic
412Dic15—41no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C23×D3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C2×C3×Q8C22×D511yescharacteristic
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4C22×D511yescharacteristic
425C2×#67—21no—
426C2×#67—21no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—101no—
431#239—22no—
432#239—41no—
433D3×D4—22no—
434D3×D4—41no—
435D3×D4—102no—
436D3×D4—102no—
437D3×D4—201no—
438D3×D4—201no—
439D3×D4—204no—
440C2×D12—21no—
441C2×D12—51no—
442C2×D12C22⋊D511yescharacteristic
443C2×D12C22×D511yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—21no—
446C2×C4×D3—101no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—201no—
451C3×D8—102no—
452C3×D8—201no—
453C2×C3×C8—51no—
454C2×C3×C8—51no—
455C3×C22⋊C4—21no—
456C3×C22⋊C4—21no—
457C3×C42C22×D511yescharacteristic
458#217—21no—
459#217—101no—
460#217—101no—
461#215—102no—
462#213—102no—
463#213—102no—
464#213—102no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—21no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4C22⋊D511yescharacteristic
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3—51no—
471C4⋊Dic3C22⋊D511yescharacteristic
472C4⋊Dic3C22×D511yescharacteristic
473Dic3⋊C4—21no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476D24—54no—
477ΓL(1,𝔽25)—102no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—31no—
481C23×C5—31no—
482C23×C5—61no—
483C23×C5—122no—
484C23×C5—122no—
485C23×C5—241no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—61no—
489C22×D5—122no—
490C22×D5—122no—
491C22×D5—122no—
492C22×D5—122no—
493C22×D5—241no—
494C22×D5—241no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—32no—
500C5×D4—62no—
501C5×D4—61no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—241no—
505C2×C4×C5—21no—
506C2×C4×C5—31no—
507C2×C4×C5—31no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—122no—
514C2×C4×C5—241no—
515C2×C4×C5D3×D411yescharacteristic
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—122no—
519C22⋊D5—122no—
520C2×Dic5—61no—
521D20—21no—
522D20—21no—
523D20—21no—
524D20—21no—
525D20—32no—
526D20—42no—
527D20—61no—
528D20—81no—
529D20—122no—
530D20—122no—
531C4×D5—122no—
532#168—21no—
533#168—61no—
534#168—61no—
535#168D3×D412yescomplemented
536C2×#41—31no—
537C22×D4—31no—
538C22×D4—151no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127—51no—
555#124D3×D511yescharacteristic, complemented
556#123—61no—
557C22⋊Q8—31no—
558#121—31no—
559#121—61no—
560#121—151no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—301no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—61no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—151no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—51no—
581C2×C3×C5—81no—
582C2×C3×C5D4211yescharacteristic
583C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
584C2×C3×C5#57611yescharacteristic
585D15—42no—
586C3×D5—81no—
587C3×D5—81no—
588C5×D3—22no—
589C5×D3—41no—
590C5×D3—42no—
591C23×C3—21no—
592C23×C3—101no—
593C23×C3—101no—
594C22×D3—21no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—81no—
598C22×D3—101no—
599C22×D3—202no—
600C22×D3—202no—
601C22×D3—202no—
602C22×D3—202no—
603C22×D3—401no—
604C22×D3—401no—
605C22×D3C2×C22⋊D511yescharacteristic
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—101no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—101no—
615C3×D4—202no—
616C3×D4—401no—
617C2×C3×C4—21no—
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C2×C22⋊D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621#67—42no—
622#67—81no—
623#67—202no—
624#67—202no—
625#67—202no—
626#67—202no—
627C2×Dic3—21no—
628C2×Dic3—101no—
629C2×Dic3C2×C22⋊D511yescharacteristic
630C2×Dic3C2×C22⋊D511yescharacteristic
631D12—22no—
632D12—21no—
633D12—42no—
634D12—52no—
635D12—101no—
636D12D4×D512yescomplemented
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—81no—
643C4×D3—202no—
644C3×C8—52no—
645C3×C8—101no—
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—32no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—61no—
653C22×C5—61no—
654C22×C5—61no—
655C22×C5—62no—
656C22×C5—61no—
657C22×C5—61no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—244no—
661C22×C5C2×D3×D411yescharacteristic
662C2×D5—41no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—62no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—244no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5—61no—
677C4×C5—61no—
678C4×C5—121no—
679C4×C5C2×D3×D411yescharacteristic
680C4×C5#100411yescharacteristic
681Dic5—121no—
682C24—61no—
683C24—301no—
684C24—301no—
685#41—62no—
686#41—121no—
687C2×Q8C2×D3×D511yescharacteristic
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—62no—
695C2×D4—61no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—121no—
699C2×D4—151no—
700C2×D4—301no—
701C2×D4—301no—
702C2×D4—302no—
703C2×D4—302no—
704C2×D4—301no—
705C2×D4—301no—
706C2×D4—601no—
707C2×D4—601no—
708C2×D4—604no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—301no—
715SD16—102no—
716SD16—201no—
717SD16—302no—
718D8—102no—
719D8—154no—
720D8—201no—
721D8—302no—
722D8—302no—
723D8—302no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—61no—
733C4⋊C4—151no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—31no—
737C22⋊C4—31no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42C2×D3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—201no—
750C22×C3—201no—
751C22×C3—201no—
752C22×C3—201no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3C22×C22⋊D511yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—22no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3—102no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—404no—
769C2×D3—404no—
770C2×D3#409512yescomplemented
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4C2×D4×D511yescharacteristic
775C3×C4#414411yescharacteristic
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—201no—
780C2×C5—62no—
781C2×C5—81no—
782C2×C5—121no—
783C2×C5—122no—
784C2×C5#571711yescharacteristic
785C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
786C2×C5#577411yescharacteristic
787D5—81no—
788D5—81no—
789D5—122no—
790C23—21no—
791C23—31no—
792C23—31no—
793C23—61no—
794C23—101no—
795C23—101no—
796C23—122no—
797C23—122no—
798C23—241no—
799C23—301no—
800C23—602no—
801C23—602no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23—1201no—
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—62no—
812D4—61no—
813D4—101no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—122no—
818D4—122no—
819D4—152no—
820D4—202no—
821D4—241no—
822D4—301no—
823D4—401no—
824D4—602no—
825D4—602no—
826D4—602no—
827D4—602no—
828C2×C4—21no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—122no—
837C2×C4—241no—
838C2×C4—301no—
839C2×C4—602no—
840C2×C4D3×C22⋊D511yescharacteristic
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—301no—
846C8—301no—
847C2×C3—81no—
848C2×C3—401no—
849C2×C3—401no—
850C2×C3D4×C22⋊D511yescharacteristic
851C2×C3C2×#409511yescharacteristic
852C2×C3#6616911yescharacteristic
853D3—22no—
854D3—41no—
855D3—42no—
856D3—202no—
857C5#8185611yescharacteristic, complemented, Sylow
858C22—32no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—62no—
866C22—61no—
867C22—61no—
868C22—121no—
869C22—121no—
870C22—201no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—302no—
878C22—601no—
879C22—601no—
880C22—1204no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—61no—
887C4—61no—
888C4—121no—
889C4—601no—
890C4D3×D4×D511yescharacteristic
891C4#9202511yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—62no—
894C2—81no—
895C2—121no—
896C2—122no—
897C2—401no—
898C2—401no—
899C2—602no—
900C2#1175505711yescharacteristic
901C2D3×#409511yescharacteristic
902C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5676C2semidirect
2. C2×#91504C2semidirect
3. C2×D3×#686C2semidirect
4. #11752745C2semidirect
5. #11751158C2semidirect
6. C3×#65347C2semidirect
7. #11749398C2semidirect
8. #11749281C2semidirect
9. #11749274C2semidirect
10. #11749152C2semidirect
11. #11749032C2semidirect
12. #11749029C2semidirect
13. #11747033C2semidirect
14. #11747025C2semidirect
15. #11746987C2semidirect
17. C2×C5×#239C22semidirect
18. C2×C5×D3×D4C22semidirect
21. C2×D3×D20C22semidirect
22. C3×C5×#124C22semidirect
23. C2×#6717C22semidirect
25. C4×D60C22semidirect
26. C5×#946C22semidirect
27. C5×#938C22semidirect
33. C4×C5×D12C22semidirect
34. C2×C3×#688C22semidirect
35. C2×C3×#688C22semidirect
36. C2×C3×#686C22semidirect
37. C2×C3×#686C22semidirect
38. C3×#4020C22semidirect
45. #91456C22semidirect
47. C2×#6652C22semidirect
48. C2×#6652C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. C3×#3935C22semidirect
55. #90985C22semidirect
56. #90969C22semidirect
57. #90967C22semidirect
58. #90964C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
69. #65347D3semidirect
136. #6654D4semidirect
144. #5676D5semidirect
161. C5×#124C2×D3semidirect
172. C2×#688C2×D3semidirect
173. C2×#688C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C2×#686C2×D3semidirect
188. #4020C2×D3semidirect
200. #3935C2×D3semidirect
238. C5×D12C2×D4semidirect
258. C3×#168C2×D4semidirect
259. C2×#239C2×D5semidirect
263. C2×D3×D4C2×D5semidirect
269. C3×#124C2×D5semidirect
270. #946C2×D5semidirect
275. #938C2×D5semidirect
292. C4×D12C2×D5semidirect
398. C2×C5×D3AGL(1,ℤ/8)semidirect
535. #168D3×D4semidirect
555. #124D3×D5semidirect
636. D12D4×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4095semidirect
857. C5#81856semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#56762
C2×#915042
C2×D3×#6862
#117527452
#117511582
C3×#653472
#117493982
#117492812
#117492742
#117491522
#117490322
#117490292
#117470332
#117470252
#117469872
#106152333
#818565