Finite Group Databasebeta

← #14454102

Subgroups — #14454102

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5726C211yesmaximal, characteristic, complemented
2C2×#91517C211yesmaximal, characteristic, complemented
3C2×#91504C211yesmaximal, characteristic, complemented
4#11752736C211yesmaximal, characteristic, complemented
5#11751187C211yesmaximal, characteristic, complemented
6C3×#65372C211yesmaximal, characteristic, complemented
7#11749403C211yesmaximal, characteristic, complemented
8#11749398C211yesmaximal, characteristic, complemented
9#11749303C211yesmaximal, characteristic, complemented
10#11749300C211yesmaximal, characteristic, complemented
11#11749282C211yesmaximal, characteristic, complemented
12#11749280C211yesmaximal, characteristic, complemented
13#11747038C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615253—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic, complemented
19C2×D3×D20C2211yescharacteristic
20C2×#6765C2211yescharacteristic
21C3×C5×C4⋊Q8C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23C2×#6718C2211yescharacteristic, complemented
24C2×#6717C2211yescharacteristic
25C2×#6717C2211yescharacteristic
26#91764C2211yescharacteristic
27C5×#946C2211yescharacteristic
28C5×#946C2211yescharacteristic, complemented
29C5×#895—21no—
30C5×#894—21no—
31C5×#894—21no—
32C5×D3×C4⋊C4—21no—
33C4×C5×D12C2211yescharacteristic
34C4×C5×D12C2211yescharacteristic, complemented
35C2×C3×#688C2211yescharacteristic
36C2×C3×#688C2211yescharacteristic
37C3×C4×D20C2211yescharacteristic
38#91517—24no—
39#91504—24no—
40#91475—21no—
41D5×(C2×D3)⋊C4—21no—
42#91460C2211yescharacteristic
43#91448—21no—
44#91413—21no—
45#91365C2211yescharacteristic
46C2×#6659C2211yescharacteristic, complemented
47C2×#6654C2211yescharacteristic
48C2×#6652C2211yescharacteristic
49C2×#6650C2211yescharacteristic
50C2×D3×#168C2211yescharacteristic, complemented
51#91087C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3967C2211yescharacteristic, complemented
54C3×C4⋊#168C2211yescharacteristic, complemented
55#90986C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic
60(C2×D3)⋊#168C2211yescharacteristic
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80445—51nomaximal, Hall
63C5×#547—31no—
64C2×#4096—31no—
65C2×#4095—31no—
66#65884—31no—
67#65528—31no—
68#65527—31no—
69#65375—31no—
70#65372D311yescharacteristic, complemented
71#65341—31no—
72#65337—31no—
73#65336—31no—
74#65335—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×D60C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C5×#239—22no—
84C5×#239—22no—
85C5×#239—41no—
86C5×#239—41no—
87C2×C5×D12—21no—
88C2×C5×D12—21no—
89C2×C5×D12D411yescharacteristic
90C2×C5×D12C2311yescharacteristic
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3—21no—
93C2×C4×C5×D3—21no—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C4×C5×D3C2311yescharacteristic
96C2×C3×D20C2311yescharacteristic
97C2×C3×C4×D5—21no—
98C2×#1203—21no—
99C2×#1202—21no—
100C2×#1201—21no—
101C2×D5×Dic3—21no—
102D3×D20—22no—
103D3×D20—41no—
104#6765—22no—
105#6765—41no—
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4—21no—
108C3×C42×C5C2311yescharacteristic
109#6718—22no—
110#6718—41no—
111#6717—22no—
112#6717—41no—
113#6714—21no—
114#6714—21no—
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×(C2×D3)⋊C4—21no—
118C5×(C2×D3)⋊C4—21no—
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4D411yescharacteristic
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×C4⋊Dic3D411yescharacteristic
123C5×C4⋊Dic3C2311yescharacteristic
124C5×Dic3⋊C4—21no—
125C5×Dic3⋊C4—21no—
126C3×#688—22no—
127C3×#688—22no—
128C3×#685—21no—
129C3×C4⋊Dic5C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131C2×C3×#168C2311yescharacteristic
132#6668—21no—
133#6667—21no—
134(C2×D3)⋊Dic5—21no—
135#6659—22no—
136#6654—22no—
137#6652D414yescomplemented
138#6650—22no—
139D3×#168—22no—
140C2×#916—51no—
141C2×#914—51no—
142#5726D511yescharacteristic, complemented
143#5554—51no—
144C3×#461—51no—
145#5173—51no—
146#5169—51no—
147#5086—51no—
148#5014—51no—
149#4844—51no—
150#4836—51no—
151#4816—51no—
152#4810—51no—
153#4808—51no—
154#4807—51no—
155C2×C5×#41—31no—
156C2×C5×#41—31no—
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8C2×D311yescharacteristic, complemented
160C5×#123—61no—
161C5×#123—61no—
162C5×C22⋊Q8—31no—
163C5×C22⋊Q8—31no—
164C5×#121—61no—
165C4×C5×D4—31no—
166C4×C5×D4—31no—
167C2×C5×C4⋊C4—61no—
168#4096—64no—
169#4095—64no—
170C2×#689—31no—
171C2×#689—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688C2×D311yescharacteristic
175C2×#688C2×D311yescharacteristic
176#4083—61no—
177C2×#687—31no—
178C2×#686—31no—
179C2×#686—31no—
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20C2×D311yescharacteristic
189#3967C2×D311yescharacteristic, complemented
190#3967C2×D311yescharacteristic, complemented
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3940—31no—
198C4⋊#168C2×D311yescharacteristic, complemented
199#3935—31no—
200#3267—151noSylow
201C22×D15—21no—
202C22×C5×D3—21no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—81no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218C2×Dic15—21no—
219D60—21no—
220D60—21no—
221Dic30—21no—
222Dic30—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3C2×D411yescharacteristic
225C2×C5×Dic3C2×D411yescharacteristic
226C5×D12—21no—
227C5×D12—41no—
228C5×D12—42no—
229C5×D12—42no—
230C5×D12C2×D412yes—
231C4×C5×D3—21no—
232C4×C5×D3—21no—
233C4×C5×D3—21no—
234C4×C5×D3—21no—
235C4×C5×D3—42no—
236C4×C5×D3—42no—
237C4×C5×D3—42no—
238C2×C3×Dic5—21no—
239C3×D20—21no—
240C3×D20C2×D412yes—
241C3×C4×D5—81no—
242#1203—81no—
243#1202—42no—
244#1201—42no—
245D5×Dic3—42no—
246C3⋊#168—21no—
247C3⋊#168C2×D412yes—
248C3×#168—21no—
249C3×#168—21no—
250C2×#239C2×D511yescharacteristic
251C2×#239C2×D511yescharacteristic, complemented
252C2×#237—51no—
253C2×D3×D4—51no—
254C2×C3×SD16—51no—
255C2×C3×SD16—51no—
256C3×C4⋊Q8C2×D511yescharacteristic, complemented
257C3×C4×D4—51no—
258#946C2×D511yescharacteristic
259#946C2×D511yescharacteristic, complemented
260C2×#216—51no—
261C2×#216—51no—
262C2×#215—51no—
263C2×#215—51no—
264C2×#213—51no—
265#930—101no—
266C2×(C2×D3)⋊C4—101no—
267#916—104no—
268#914—104no—
269C2×D24—51no—
270C2×#204—51no—
271C2×ΓL(1,𝔽25)—51no—
272C2×D3×C8—51no—
273#897—51no—
274#895—21no—
275#895—51no—
276#894—21no—
277#894—21no—
278D3×C4⋊C4—21no—
279#886—101no—
280#882—101no—
281#875—51no—
282C4×D12C2×D511yescharacteristic
283C4×D12C2×D511yescharacteristic, complemented
284C3×C4⋊C8—51no—
285C3×#103—51no—
286C3×#103—51no—
287#832—51no—
288#821—51no—
289(C2×D3)⋊C8—51no—
290(C2×D3)⋊C8—51no—
291#816—51no—
292#809—51no—
293#808—51no—
294#803—51no—
295C23×D5—61no—
296C5×#41—62no—
297C5×#41—62no—
298C5×#41—121no—
299C5×#41—121no—
300C2×C5×Q8C22×D311yescharacteristic
301C2×C5×Q8C22×D311yescharacteristic
302C2×C5×D4—31no—
303C2×C5×D4—31no—
304C2×C5×D4—61no—
305C2×C5×D4—61no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—61no—
309C22×C4×C5—61no—
310C22×C4×C5—61no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313#709—62no—
314#709—121no—
315C2×D20—31no—
316C2×D20—62no—
317C2×D20—61no—
318C2×D20—121no—
319C2×D20C22×D311yescharacteristic
320C2×C4×D5—21no—
321C2×C4×D5—61no—
322C2×Dic10—31no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—31no—
326C5×C4⋊C4—31no—
327C5×C4⋊C4—61no—
328C5×C4⋊C4—61no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—31no—
331C5×C22⋊C4—61no—
332C5×C22⋊C4—61no—
333C5×C22⋊C4—61no—
334C42×C5C22×D311yescharacteristic
335C22⋊Dic5—61no—
336#689—62no—
337#689—121no—
338#688—22no—
339#688—22no—
340#688—62no—
341#688—121no—
342#687—62no—
343#686—34no—
344#686—62no—
345#685—21no—
346#685—61no—
347#685—61no—
348#685—61no—
349C4⋊Dic5C22×D311yescharacteristic
350#683—61no—
351#681—62no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—62no—
355C2×#168C22×D311yescharacteristic
356C2×#168C22×D311yescharacteristic
357C2×AGL(1,ℤ/8)—151no—
358C2×#135—151no—
359#547—31no—
360#546—151no—
361#497—151no—
362#470—151no—
363#465—151no—
364#463—151no—
365#461—51no—
366#452—151no—
367#452—151no—
368#450—151no—
369#449—151no—
370#442—151no—
371#435—151no—
372C22×C3×C5C22×D411yescharacteristic
373C2×D15—41no—
374C2×D15—41no—
375C2×D15—41no—
376C2×C5×D3—21no—
377C2×C5×D3—21no—
378C2×C5×D3—22no—
379C2×C5×D3—21no—
380C2×C5×D3—21no—
381C2×C5×D3—21no—
382C2×C5×D3—21no—
383C2×C5×D3—41no—
384C2×C5×D3—41no—
385C2×C3×D5—22no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388D3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395Dic15—41no—
396C3×Dic5—41no—
397C5×Dic3—21no—
398C5×Dic3—21no—
399C5×Dic3—41no—
400C23×D3—101no—
401C2×C3×Q8C22×D511yescharacteristic
402C2×C3×Q8C22×D511yescharacteristic
403C2×C3×D4—51no—
404C22×C3×C4—101no—
405C2×#67—101no—
406C2×#67—101no—
407C22×Dic3—101no—
408#239—22no—
409#239—22no—
410#239—41no—
411#239—41no—
412#237—102no—
413#237—201no—
414D3×D4—102no—
415D3×D4—201no—
416C2×D12—21no—
417C2×D12—21no—
418C2×D12—51no—
419C2×D12—101no—
420C2×D12C22⋊D511yescharacteristic
421C2×D12C22×D511yescharacteristic
422C2×C4×D3—21no—
423C2×C4×D3—21no—
424C2×C4×D3—21no—
425C2×C4×D3C22×D511yescharacteristic
426C2×C4×D3C22×D511yescharacteristic
427C2×Dic6—51no—
428C3×SD16—102no—
429C3×SD16—102no—
430C2×C3×C8—51no—
431C2×C3×C8—51no—
432C3×C4⋊C4—21no—
433C3×C4⋊C4—21no—
434C3×C4⋊C4—51no—
435C3×C22⋊C4—101no—
436C3×C42C22×D511yescharacteristic
437#216—102no—
438#216—201no—
439#215—102no—
440#215—201no—
441#213—54no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4—101no—
447(C2×D3)⋊C4—101no—
448(C2×D3)⋊C4—101no—
449(C2×D3)⋊C4C22⋊D511yescharacteristic
450(C2×D3)⋊C4C22⋊D511yescharacteristic
451C4⋊Dic3—101no—
452C4⋊Dic3C22⋊D511yescharacteristic
453C4⋊Dic3C22×D511yescharacteristic
454Dic3⋊C4—21no—
455Dic3⋊C4—21no—
456C2×C3⋊C8—51no—
457C2×C3⋊C8—51no—
458D24—102no—
459#204—102no—
460ΓL(1,𝔽25)—102no—
461D3×C8—102no—
462C23×C5—31no—
463C23×C5—31no—
464C23×C5—61no—
465C22×D5—21no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—241no—
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—21no—
473C5×Q8—21no—
474C5×D4—32no—
475C5×D4—61no—
476C5×D4—121no—
477C5×D4—122no—
478C5×D4—122no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—31no—
482C2×C4×C5—31no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5—61no—
488C2×C4×C5—122no—
489C2×C4×C5—122no—
490C2×C4×C5—122no—
491C2×C4×C5D3×D411yescharacteristic
492C2×C4×C5D3×D411yescharacteristic
493C2×C4×C5C23×D311yescharacteristic
494C22⋊D5—122no—
495C22⋊D5—241no—
496C2×Dic5—21no—
497C2×Dic5—61no—
498D20—21no—
499D20—61no—
500D20—61no—
501D20—122no—
502D20D3×D412yes—
503C4×D5—81no—
504C4×D5—122no—
505Dic10—61no—
506Dic10—61no—
507#168—21no—
508#168—21no—
509#168—32no—
510#168—61no—
511C2×#41—31no—
512C2×#41—31no—
513C2×#41—151no—
514C22×D4—151no—
515AGL(1,ℤ/8)—304no—
516#135—304no—
517C2×Q16—151no—
518C2×Q16—151no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—151no—
522C2×SD16—151no—
523C2×SD16—151no—
524C2×D8—151no—
525C2×D8—151no—
526C2×M16—151no—
527C22×C8—151no—
528C4⋊Q8D3×D511yescharacteristic, complemented
529#124—151no—
530#123—61no—
531#123—61no—
532#123—301no—
533C22⋊Q8—31no—
534C22⋊Q8—31no—
535C22⋊Q8—151no—
536#121—61no—
537#121—151no—
538#121—301no—
539#120—301no—
540C4×D4—31no—
541C4×D4—31no—
542C4×D4—51no—
543C2×C4⋊C4—61no—
544C2×C22⋊C4—301no—
545#106—151no—
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103—151no—
550#102—151no—
551#102—151no—
552#102—151no—
553C22⋊C8—151no—
554C22⋊C8—151no—
555#97—151no—
556C2×C3×C5D4211yescharacteristic
557C2×C3×C5#57511yescharacteristic
558C2×C3×C5#57711yescharacteristic
559D15—81no—
560C3×D5—42no—
561C5×D3—41no—
562C5×D3—41no—
563C5×D3—42no—
564C23×C3—101no—
565C22×D3—21no—
566C22×D3—101no—
567C22×D3—202no—
568C22×D3—202no—
569C22×D3—401no—
570C22×D3C2×C22⋊D511yescharacteristic
571C22×D3C2×C22⋊D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×D4—52no—
577C3×D4—101no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—101no—
581C2×C3×C4—401no—
582C2×C3×C4C2×C22⋊D511yescharacteristic
583C2×C3×C4C2×C22⋊D511yescharacteristic
584C2×C3×C4C23×D511yescharacteristic
585#67—202no—
586#67—202no—
587C2×Dic3—21no—
588C2×Dic3—101no—
589C2×Dic3—202no—
590C2×Dic3C2×C22⋊D511yescharacteristic
591C2×Dic3C2×C22⋊D511yescharacteristic
592D12—21no—
593D12—41no—
594D12—42no—
595D12—42no—
596D12—101no—
597D12—101no—
598D12—401no—
599D12D4×D512yes—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—42no—
606C4×D3—42no—
607Dic6—101no—
608Dic6—101no—
609C3×C8—101no—
610C3×C8—101no—
611C3⋊C8—52no—
612C3⋊C8—101no—
613C22×C5—61no—
614C22×C5—61no—
615C22×C5—61no—
616C22×C5—61no—
617C22×C5—61no—
618C22×C5—61no—
619C22×C5—62no—
620C22×C5—121no—
621C22×C5—121no—
622C22×C5C2×D3×D411yescharacteristic
623C2×D5—22no—
624C2×D5—41no—
625C2×D5—41no—
626C2×D5—121no—
627C2×D5—121no—
628C2×D5—121no—
629C2×D5—244no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—61no—
635C4×C5—61no—
636C4×C5—121no—
637C4×C5C2×D3×D411yescharacteristic
638C4×C5#100911yescharacteristic
639Dic5—41no—
640Dic5—121no—
641C24—301no—
642#41—62no—
643#41—62no—
644#41—121no—
645#41—121no—
646#41—302no—
647#41—601no—
648C2×Q8—151no—
649C2×Q8C2×D3×D511yescharacteristic
650C2×Q8C2×D3×D511yescharacteristic
651C2×D4—31no—
652C2×D4—31no—
653C2×D4—51no—
654C2×D4—61no—
655C2×D4—61no—
656C2×D4—151no—
657C2×D4—301no—
658C2×D4—302no—
659C2×D4—301no—
660C2×D4—301no—
661C2×D4—601no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—101no—
668C22×C4—301no—
669Q16—302no—
670Q16—601no—
671SD16—102no—
672SD16—102no—
673SD16—302no—
674SD16—302no—
675SD16—601no—
676D8—154no—
677D8—302no—
678M16—302no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—151no—
682C2×C8—151no—
683C2×C8—302no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—51no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—301no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—101no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C42C2×D3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—102no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3C22×C22⋊D511yescharacteristic
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—22no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—201no—
718C2×D3—201no—
719C2×D3—201no—
720C2×D3—404no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—201no—
726C3×C4C2×D4×D511yescharacteristic
727C3×C4#414411yescharacteristic
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—201no—
732C2×C5—121no—
733C2×C5—121no—
734C2×C5—122no—
735C2×C5#560911yescharacteristic
736C2×C5#576211yescharacteristic
737C2×C5#577711yescharacteristic
738D5—42no—
739D5—241no—
740C23—31no—
741C23—31no—
742C23—61no—
743C23—101no—
744C23—301no—
745C23—602no—
746C23—602no—
747C23—1201no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—301no—
753Q8—301no—
754D4—32no—
755D4—52no—
756D4—61no—
757D4—101no—
758D4—121no—
759D4—122no—
760D4—122no—
761D4—301no—
762D4—301no—
763D4—602no—
764D4—602no—
765D4—1201no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—101no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—301no—
780C2×C4—401no—
781C2×C4—602no—
782C2×C4D3×C22⋊D511yescharacteristic
783C2×C4D3×C22⋊D511yescharacteristic
784C2×C4C22×D3×D511yescharacteristic
785C8—101no—
786C8—101no—
787C8—152no—
788C8—301no—
789C2×C3—202no—
790C2×C3D4×C22⋊D511yescharacteristic
791C2×C3#6615611yescharacteristic
792C2×C3#6617111yescharacteristic
793D3—41no—
794D3—41no—
795D3—42no—
796D3—401no—
797C5#8044511yescharacteristic, complemented, Sylow
798C22—61no—
799C22—61no—
800C22—62no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—102no—
806C22—121no—
807C22—121no—
808C22—201no—
809C22—201no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22C2×D3×C22⋊D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—201no—
823C4—601no—
824C4D3×D4×D511yescharacteristic
825C4#9202711yescharacteristic
826C3#1061525311yescharacteristic, complemented, Sylow
827C2—121no—
828C2—121no—
829C2—122no—
830C2—202no—
831C2—1201no—
832C2#1175503611yescharacteristic
833C2#1175509011yescharacteristic
834C2#1175509111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3267
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5726C2semidirect
2. C2×#91517C2semidirect
3. C2×#91504C2semidirect
4. #11752736C2semidirect
5. #11751187C2semidirect
6. C3×#65372C2semidirect
7. #11749403C2semidirect
8. #11749398C2semidirect
9. #11749303C2semidirect
10. #11749300C2semidirect
11. #11749282C2semidirect
12. #11749280C2semidirect
13. #11747038C2semidirect
14. #11747021C2semidirect
15. #11746999C2semidirect
18. C2×C5×#239C22semidirect
21. C3×C5×C4⋊Q8C22semidirect
22. C2×#6718C22semidirect
23. C2×#6718C22semidirect
28. C5×#946C22semidirect
34. C4×C5×D12C22semidirect
46. C2×#6659C22semidirect
50. C2×D3×#168C22semidirect
51. #91087C22semidirect
52. C3×#3967C22semidirect
53. C3×#3967C22semidirect
54. C3×C4⋊#168C22semidirect
55. #90986C22semidirect
56. #90975C22semidirect
58. #90966C22semidirect
61. (C2×D3)⋊#168C22semidirect
70. #65372D3semidirect
137. #6652D4semidirect
142. #5726D5semidirect
159. C5×C4⋊Q8C2×D3semidirect
189. #3967C2×D3semidirect
190. #3967C2×D3semidirect
198. C4⋊#168C2×D3semidirect
251. C2×#239C2×D5semidirect
256. C3×C4⋊Q8C2×D5semidirect
259. #946C2×D5semidirect
283. C4×D12C2×D5semidirect
528. C4⋊Q8D3×D5semidirect
703. C3×C5#3267semidirect
797. C5#80445semidirect
826. C3#10615253semidirect

Maximal subgroups

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

subgroupindex
C5×#57262
C2×#915172
C2×#915042
#117527362
#117511872
C3×#653722
#117494032
#117493982
#117493032
#117493002
#117492822
#117492802
#117470382
#117470212
#117469992
#106152533
#804455