Finite Group Databasebeta

← #14453236

Subgroups — #14453236

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×#5554C211yesmaximal, characteristic, complemented
2C2×#91480C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#11752745C211yesmaximal, characteristic, complemented
5#11751115C211yesmaximal, characteristic, complemented
6C3×#65304C211yesmaximal, characteristic, complemented
7#11749035C211yesmaximal, characteristic, complemented
8#11749032C211yesmaximal, characteristic, complemented
9#11747483C211yesmaximal, characteristic, complemented
10#11747482C211yesmaximal, characteristic, complemented
11#11747324C211yesmaximal, characteristic, complemented
12#11747321C211yesmaximal, characteristic, complemented
13#11747046C211yesmaximal, characteristic, complemented
14#11747041C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic, complemented
18C2×C5×D3×D4C2211yescharacteristic, complemented
19C2×#6777—21no—
20C2×D3×D20C2211yescharacteristic
21C2×D3×D20C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic
24C4×D60C2211yescharacteristic, complemented
25C5×#930—21no—
26C2×C5×(C2×D3)⋊C4—21no—
27C5×#897C2211yescharacteristic, complemented
28C5×#895C2211yescharacteristic, complemented
29C5×#886—21no—
30C5×#882—21no—
31C5×#875C2211yescharacteristic, complemented
32C4×C5×D12C2211yescharacteristic
33C2×C3×#686C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic, complemented
35C3×#4020C2211yescharacteristic, complemented
36#91480—24no—
37D3×#686—24no—
38#91474—21no—
39#91474—21no—
40#91465—21no—
41#91456C2211yescharacteristic
42#91456C2211yescharacteristic, complemented
43C2×#6660C2211yescharacteristic, complemented
44C2×#6655C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic
47C2×#6652C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80358—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20—31no—
67#65527—31no—
68#65506—31no—
69#65347—31no—
70#65346—31no—
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325—31no—
75#65304D311yescharacteristic, complemented
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C22×D3×D5—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C22×C5×Dic3—21no—
88C5×#237—22no—
89C5×#237—41no—
90C5×D3×D4—22no—
91C5×D3×D4—41no—
92C2×C5×D12—21no—
93C2×C5×D12D411yescharacteristic
94C2×C5×D12C2311yescharacteristic
95C2×C4×C5×D3C2311yescharacteristic
96C2×C4×C5×D3C2311yescharacteristic
97C2×C5×Dic6C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C42×C5C2311yescharacteristic
114#6715D414yescomplemented
115#6714—21no—
116C4⋊Dic15C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4D411yescharacteristic
124C5×(C2×D3)⋊C4D411yescharacteristic
125C5×C4⋊Dic3—21no—
126C5×C4⋊Dic3D411yescharacteristic
127C3×#686—22no—
128C3×#686—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6665—21no—
132#6665—21no—
133#6660—22no—
134#6655—22no—
135#6655—41no—
136#6654—22no—
137#6652—22no—
138#6652—41no—
139#6650—22no—
140D3×#168—22no—
141C2×#911—51no—
142C2×D3×D8—51no—
143#5717—51no—
144#5554D511yescharacteristic, complemented
145C3×#459—51no—
146#5158—51no—
147#5156—51no—
148#5074—51no—
149#5014—51no—
150#4844—51no—
151#4836—51no—
152#4782—51no—
153#4778—51no—
154#4776—51no—
155#4773—51no—
156C2×C5×#41—31no—
157C22×C5×D4—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124—31no—
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—31no—
165C5×#121—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4C2×D311yescharacteristic, complemented
169C2×C5×C22⋊C4—61no—
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
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#3941C2×D311yescharacteristic, complemented
197#3941C2×D311yescharacteristic, complemented
198#3940—31no—
199C4⋊#168C2×D311yescharacteristic, complemented
200#3935—31no—
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×D4—21no—
219C3×C5×D4C2×D412yescomplemented
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—81no—
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225C2×Dic15—21no—
226D60—21no—
227D60C2×D412yes—
228C4×D15—42no—
229C5×#67—42no—
230C5×#67—42no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—42no—
233C2×C5×Dic3C2×D411yescharacteristic
234C2×C5×Dic3C2×D411yescharacteristic
235C5×D12—22no—
236C5×D12—21no—
237C5×D12—21no—
238C5×D12—81no—
239C4×C5×D3—21no—
240C4×C5×D3—21no—
241C4×C5×D3—21no—
242C4×C5×D3—21no—
243C5×Dic6—21no—
244C5×Dic6—21no—
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⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×#237C2×D511yescharacteristic, complemented
260C2×D3×D4—51no—
261C2×D3×D4—51no—
262C2×D3×D4—101no—
263C2×D3×D4C2×D511yescharacteristic, complemented
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C3×#127—51no—
267C3×C4×D4C2×D511yescharacteristic, complemented
268#938—51no—
269#938—51no—
270#938—101no—
271#937—101no—
272#937—101no—
273C2×#214—51no—
274C2×#214—51no—
275C2×#213—51no—
276C2×#213—51no—
277C2×#213—51no—
278#930—21no—
279C2×(C2×D3)⋊C4—21no—
280#911—104no—
281D3×D8—104no—
282C2×D24—51no—
283C2×#204—51no—
284C2×ΓL(1,𝔽25)—51no—
285C2×D3×C8—51no—
286#897C2×D511yescharacteristic, complemented
287#895C2×D511yescharacteristic, complemented
288#886—21no—
289#882—21no—
290#875C2×D511yescharacteristic, complemented
291C4×D12—51no—
292C4×D12C2×D511yescharacteristic
293C3×C4⋊C8—51no—
294C3×#102—51no—
295C3×#102—51no—
296#832—51no—
297#821—51no—
298(C2×D3)⋊C8—51no—
299(C2×D3)⋊C8—51no—
300#816—51no—
301#809—51no—
302#808—51no—
303#803—51no—
304C24×C5—61no—
305C23×D5—61no—
306C23×D5—61no—
307C5×#41—62no—
308C5×#41—121no—
309C2×C5×Q8—31no—
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—21no—
319C22×C4×C5—31no—
320C22×C4×C5—31no—
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—61no—
339C5×C4⋊C4C22×D311yescharacteristic
340C5×C22⋊C4—21no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4—31no—
343C5×C22⋊C4—61no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4—61no—
346C5×C22⋊C4—61no—
347C42×C5C22×D311yescharacteristic
348#688—62no—
349#688—62no—
350#688—121no—
351#686—22no—
352#686—22no—
353#686—34no—
354#686—62no—
355#686—62no—
356#686—121no—
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—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—51no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—22no—
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—21no—
393C2×C5×D3—21no—
394C2×C5×D3—41no—
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×D4—51no—
420C2×C3×D4—51no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4C22×D511yescharacteristic
424C22×C3×C4—21no—
425C2×#67—21no—
426C2×#67—21no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—101no—
431C22×Dic3—21no—
432#237—22no—
433#237—41no—
434D3×D4—22no—
435D3×D4—41no—
436D3×D4—102no—
437D3×D4—102no—
438D3×D4—201no—
439D3×D4—201no—
440D3×D4—204no—
441C2×D12—21no—
442C2×D12—51no—
443C2×D12C22⋊D511yescharacteristic
444C2×D12C22×D511yescharacteristic
445C2×C4×D3—101no—
446C2×C4×D3C22×D511yescharacteristic
447C2×C4×D3C22×D511yescharacteristic
448C2×Dic6C22×D511yescharacteristic
449C3×D8—102no—
450C3×D8—102no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4C22×D511yescharacteristic
454C3×C22⋊C4—21no—
455C3×C42C22×D511yescharacteristic
456#217—101no—
457#217—101no—
458#214—102no—
459#214—201no—
460#213—54no—
461#213—102no—
462#213—201no—
463(C2×D3)⋊C4—21no—
464(C2×D3)⋊C4—21no—
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—21no—
471C4⋊Dic3—51no—
472C4⋊Dic3C22⋊D511yescharacteristic
473C2×C3⋊C8—51no—
474C2×C3⋊C8—51no—
475D24—102no—
476#204—102no—
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—61no—
496C5×Q8—61no—
497C5×D4—21no—
498C5×D4—62no—
499C5×D4—61no—
500C5×D4—61no—
501C5×D4—122no—
502C5×D4—122no—
503C5×D4—241no—
504C5×D4D3×D412yescomplemented
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—81no—
514C2×C4×C5—122no—
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—21no—
534#168—32no—
535#168—61no—
536C2×#41—31no—
537C22×D4—31no—
538C22×D4—151no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
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#124—31no—
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—151no—
568C4×D4D3×D511yescharacteristic, complemented
569C2×C22⋊C4—61no—
570#106—151no—
571C4⋊C8—51no—
572#103—151no—
573#102—51no—
574#102—51no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—42no—
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—81no—
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×D4—21no—
608C3×D4—101no—
609C3×D4—101no—
610C3×D4—101no—
611C3×D4—101no—
612C3×D4—202no—
613C3×D4—401no—
614C3×D4D4×D512yescomplemented
615C2×C3×C4—21no—
616C2×C3×C4—81no—
617C2×C3×C4C2×C22⋊D511yescharacteristic
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C23×D511yescharacteristic
620#67—42no—
621#67—42no—
622#67—202no—
623#67—202no—
624#67—202no—
625#67—202no—
626C2×Dic3—21no—
627C2×Dic3—42no—
628C2×Dic3—101no—
629C2×Dic3C2×C22⋊D511yescharacteristic
630C2×Dic3C2×C22⋊D511yescharacteristic
631D12—22no—
632D12—21no—
633D12—21no—
634D12—52no—
635D12—81no—
636D12—101no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—202no—
642Dic6—21no—
643Dic6—21no—
644C3×C8—101no—
645C3×C8—101no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—22no—
649C22×C5—32no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—61no—
653C22×C5—61no—
654C22×C5—61no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—121no—
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#100911yescharacteristic
681Dic5—121no—
682C24—61no—
683C24—301no—
684C24—301no—
685#41—62no—
686#41—121no—
687C2×Q8—31no—
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—21no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—61no—
714C22×C4—301no—
715SD16—302no—
716SD16—302no—
717SD16—601no—
718D8—102no—
719D8—102no—
720D8—154no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—61no—
732C4⋊C4—151no—
733C4⋊C4C2×D3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—31no—
736C22⋊C4—31no—
737C22⋊C4—61no—
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—22no—
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—21no—
760C2×D3—21no—
761C2×D3—41no—
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—42no—
781C2×C5—62no—
782C2×C5—121no—
783C2×C5—241no—
784C2×C5#560911yescharacteristic
785C2×C5#575711yescharacteristic
786C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
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—61no—
807Q8—61no—
808D4—21no—
809D4—62no—
810D4—61no—
811D4—61no—
812D4—101no—
813D4—101no—
814D4—101no—
815D4—101no—
816D4—122no—
817D4—122no—
818D4—152no—
819D4—202no—
820D4—241no—
821D4—301no—
822D4—401no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—602no—
827D4#677712yescomplemented
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—81no—
837C2×C4—122no—
838C2×C4—301no—
839C2×C4—602no—
840C2×C4D3×C22⋊D511yescharacteristic
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—101no—
844C8—101no—
845C8—152no—
846C8—301no—
847C2×C3—42no—
848C2×C3—401no—
849C2×C3—401no—
850C2×C3D4×C22⋊D511yescharacteristic
851C2×C3C2×#409511yescharacteristic
852C2×C3#6616911yescharacteristic
853D3—22no—
854D3—41no—
855D3—81no—
856D3—202no—
857C5#8035811yescharacteristic, complemented, Sylow
858C22—22no—
859C22—32no—
860C22—41no—
861C22—41no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—121no—
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—
890C4C2×#677711yescharacteristic
891C4#9201811yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—42no—
894C2—62no—
895C2—121no—
896C2—241no—
897C2—401no—
898C2—401no—
899C2—602no—
900C2#1175465711yescharacteristic
901C2#1175469711yescharacteristic
902C2D3×#409511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5554C2semidirect
2. C2×#91480C2semidirect
3. C2×D3×#686C2semidirect
4. #11752745C2semidirect
5. #11751115C2semidirect
6. C3×#65304C2semidirect
7. #11749035C2semidirect
8. #11749032C2semidirect
9. #11747483C2semidirect
10. #11747482C2semidirect
11. #11747324C2semidirect
12. #11747321C2semidirect
13. #11747046C2semidirect
14. #11747041C2semidirect
15. #11746999C2semidirect
17. C2×C5×#237C22semidirect
18. C2×C5×D3×D4C22semidirect
21. C2×D3×D20C22semidirect
22. C3×C4×C5×D4C22semidirect
24. C4×D60C22semidirect
27. C5×#897C22semidirect
28. C5×#895C22semidirect
31. C5×#875C22semidirect
33. C2×C3×#686C22semidirect
34. C2×C3×#686C22semidirect
35. C3×#4020C22semidirect
42. #91456C22semidirect
43. C2×#6660C22semidirect
44. C2×#6655C22semidirect
45. C2×#6655C22semidirect
47. C2×#6652C22semidirect
48. C2×#6652C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91093C22semidirect
53. #91092C22semidirect
54. #91087C22semidirect
55. C3×#3941C22semidirect
56. C3×#3941C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90973C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65304D3semidirect
114. #6715D4semidirect
144. #5554D5semidirect
168. C4×C5×D4C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C2×#686C2×D3semidirect
188. #4020C2×D3semidirect
196. #3941C2×D3semidirect
197. #3941C2×D3semidirect
199. C4⋊#168C2×D3semidirect
219. C3×C5×D4C2×D4semidirect
256. C3⋊#168C2×D4semidirect
259. C2×#237C2×D5semidirect
263. C2×D3×D4C2×D5semidirect
267. C3×C4×D4C2×D5semidirect
286. #897C2×D5semidirect
287. #895C2×D5semidirect
290. #875C2×D5semidirect
398. C2×C5×D3AGL(1,ℤ/8)semidirect
504. C5×D4D3×D4semidirect
568. C4×D4D3×D5semidirect
614. C3×D4D4×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4095semidirect
827. D4#6777semidirect
857. C5#80358semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#55542
C2×#914802
C2×D3×#6862
#117527452
#117511152
C3×#653042
#117490352
#117490322
#117474832
#117474822
#117473242
#117473212
#117470462
#117470412
#117469992
#106152333
#803585