Finite Group Databasebeta

← #14412692

Subgroups — #14412692

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92035C211yesmaximal, characteristic
2C2×#91266C211yesmaximal, characteristic, complemented
3#11753669C211yesmaximal, characteristic, complemented
4#11750904C211yesmaximal, characteristic, complemented
5C5×#4803C211yesmaximal, characteristic, complemented
6C3×#65093C211yesmaximal, characteristic, complemented
7#11749215C211yesmaximal, characteristic, complemented
8#11749211C211yesmaximal, characteristic, complemented
9#11749198C211yesmaximal, characteristic, complemented
10#11748109C211yesmaximal, characteristic, complemented
11#11748107C211yesmaximal, characteristic, complemented
12D5×#821C211yesmaximal, characteristic, complemented
13#11747478C211yesmaximal, characteristic, complemented
14D3×#3941C211yesmaximal, characteristic, complemented
15#11747475C211yesmaximal, characteristic, complemented
16#10610613—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20#92035—24no—
21#92035C418yescomplemented
22C2×#6777—21no—
23C2×#6777C2211yescharacteristic
24C2×D3×D20—21no—
25C2×D3×D20C2211yescharacteristic
26C2×D5×D12—21no—
27C2×D5×D12C2211yescharacteristic
28C2×#6771—21no—
29C2×#6771C2211yescharacteristic
30C2×#6705C2211yescharacteristic, complemented
31C4⋊C4×D15C2211yescharacteristic, complemented
32C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33C5×D3×C4⋊C4C2211yescharacteristic, complemented
34C2×C3×C8×D5C2211yescharacteristic, complemented
35C3×#4038C2211yescharacteristic, complemented
36C4×#1203—21no—
37#91441—21no—
38D5×C4⋊Dic3C2211yescharacteristic, complemented
39#91396—21no—
40#91347C2211yescharacteristic, complemented
41#91338C2211yescharacteristic, complemented
42#91323—21no—
43C2×#6649C2211yescharacteristic, complemented
44C2×#6648C2211yescharacteristic, complemented
45C2×D3×#168C2211yescharacteristic, complemented
46#91266—24no—
47C3×C5×#103C2211yescharacteristic, complemented
48#91119C2211yescharacteristic, complemented
49#91105C2211yescharacteristic, complemented
50#91093C2211yescharacteristic, complemented
51C5×#835C2211yescharacteristic, complemented
52C5×#821C2211yescharacteristic, complemented
53C5×#809C2211yescharacteristic, complemented
54C3×#3967C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90968C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#90966C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62#90964C2211yescharacteristic, complemented
63#78831—51nomaximal, Hall
64C2×#4149—31no—
65C2×#4053—31no—
66#65838—31no—
67C5×#417—31no—
68#65522—31no—
69#65420—31no—
70C2×#3941—31no—
71#65093—31no—
72#65093D311yescharacteristic, complemented
73#65092—31no—
74#65092—31no—
75#65059—31no—
76#65059—31no—
77D5×#102—31no—
78D5×#102—31no—
79C22×D3×D5—21no—
80C22×D3×D5—21no—
81C22×D3×D5—21no—
82C2×C3×C5×Q8C2311yescharacteristic
83#6821—22no—
84#6821C2×C414yescomplemented
85C2×D60—21no—
86C2×D60C2311yescharacteristic
87C2×C4×D15—21no—
88C2×C4×D15—21no—
89C2×C4×D15C2311yescharacteristic
90C5×#239—22no—
91C5×#239C2×C414yescomplemented
92C2×C5×D12—21no—
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C3×#713—22no—
98C3×#713C2×C414yescomplemented
99C2×C3×D20—21no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5C2311yescharacteristic
103C2×#1204D411yescharacteristic
104C2×#1203—21no—
105C2×#1203D411yescharacteristic
106C2×#1202—21no—
107C2×#1202D411yescharacteristic
108C2×#1201—21no—
109C2×#1201D411yescharacteristic
110C2×D5×Dic3—21no—
111#6777—22no—
112#6777—28no—
113#6777C2×C414yescomplemented
114D3×D20—22no—
115D3×D20—28no—
116D3×D20C2×C414yescomplemented
117D5×D12—22no—
118D5×D12—28no—
119D5×D12C2×C414yescomplemented
120#6771—28no—
121#6771C2×C414yes—
122#6771D414yes—
123C2×C3×C5×C8C2311yescharacteristic
124C3×C5×C4⋊C4C2311yescharacteristic
125C4⋊Dic15C2311yescharacteristic
126#6712—21no—
127C2×C3⋊#168C2311yescharacteristic
128#6705—22no—
129C5×C4⋊Dic3C2311yescharacteristic
130C5×Dic3⋊C4—21no—
131C2×C5×C3⋊C8C2311yescharacteristic
132C5×ΓL(1,𝔽25)—22no—
133C3×#685—21no—
134C3×C4⋊Dic5C2311yescharacteristic
135C3×C4×Dic5—21no—
136C2×C3×#168C2311yescharacteristic
137C3×C8×D5—22no—
138#6668—21no—
139#6667—21no—
140(C2×D3)⋊Dic5—21no—
141Dic3×Dic5—21no—
142Dic3×Dic5—21no—
143#6649—22no—
144#6648—22no—
145D3×#168—22no—
146C2×#1009—51no—
147C2×#901—51no—
148#5523—51no—
149C3×#416—51no—
150#5232—51no—
151C2×#821—51no—
152#5001—51no—
153#4804—51no—
154#4804—51no—
155#4803—51no—
156#4803D511yescharacteristic, complemented
157#4770—51no—
158#4770—51no—
159D3×#102—51no—
160D3×#102—51no—
161C2×C5×#41—31no—
162#4149—38no—
163#4149—64no—
164C2×#713—31no—
165C2×#713C2×D311yescharacteristic
166C2×D4×D5—31no—
167C2×D4×D5—31no—
168C2×D4×D5—61no—
169C2×D4×D5—61no—
170C2×#709—31no—
171C2×#709—61no—
172C22×D20—31no—
173C22×D20—61no—
174C2×C5×M16—31no—
175C2×C5×C4⋊C4—31no—
176C4×C22⋊D5—61no—
177C4×C22⋊D5—61no—
178#4072—31no—
179C22×#168—31no—
180#4053—64no—
181C2×#676—31no—
182C2×#676—31no—
183C2×C8×D5—31no—
184C2×C8×D5C2×D311yescharacteristic, complemented
185#4039—61no—
186#4038—31no—
187#4038C2×D311yescharacteristic, complemented
188D5×C4⋊C4—31no—
189D5×C4⋊C4—31no—
190#4033—61no—
191C5×#103—31no—
192C5×#103C2×D311yescharacteristic, complemented
193C5×#102—31no—
194C5×#102—31no—
195#3967—31no—
196#3967C2×D311yescharacteristic, complemented
197#3964—31no—
198#3964—31no—
199#3953—31no—
200#3953—31no—
201#3953—31no—
202#3953C2×D311yescharacteristic, complemented
203#3941—31no—
204#3941—31no—
205#3941—31no—
206#3941C2×D311yescharacteristic, complemented
207#2897—151noSylow
208C22×D15—21no—
209C22×D15C2×D411yescharacteristic
210C22×C5×D3—21no—
211C22×C5×D3C2×D411yescharacteristic
212C22×C3×D5—21no—
213C22×C3×D5C2×D411yescharacteristic
214C2×D3×D5—24no—
215C2×D3×D5—24no—
216C2×D3×D5—24no—
217C2×D3×D5—81no—
218C2×D3×D5—81no—
219C2×D3×D5—81no—
220C2×D3×D5—81no—
221C2×D3×D5—81no—
222C2×D3×D5—81no—
223C3×C5×Q8—21no—
224C3×C5×Q8C22×C412yes—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5C2411yescharacteristic
228C2×Dic15—21no—
229C2×Dic15C2×D411yescharacteristic
230D60—24no—
231D60—21no—
232D60C22×C412yes—
233C4×D15—24no—
234C4×D15—81no—
235C4×D15C22×C412yes—
236C4×D15C2×D412yes—
237C2×C5×Dic3—21no—
238C2×C5×Dic3C2×D411yescharacteristic
239C5×D12—24no—
240C5×D12—21no—
241C5×D12C22×C412yes—
242C4×C5×D3—24no—
243C4×C5×D3—81no—
244C4×C5×D3C22×C412yes—
245C4×C5×D3C2×D412yes—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C2×D411yescharacteristic
248C3×D20—24no—
249C3×D20—21no—
250C3×D20C22×C412yes—
251C3×C4×D5—24no—
252C3×C4×D5C22×C412yes—
253C3×C4×D5C2×D412yes—
254#1204C22⋊C414yes—
255#1203—24no—
256#1203C22⋊C414yes—
257#1202—24no—
258#1202C22⋊C414yes—
259#1201—24no—
260#1201C22⋊C414yes—
261D5×Dic3—81no—
262C3×C5×C8—21no—
263C3⋊#168—21no—
264C3×#168—21no—
265C5×C3⋊C8—21no—
266C2×C3×#41—51no—
267#1009—58no—
268#1009—104no—
269C2×#239—51no—
270C2×#239C2×D511yescharacteristic
271C2×D3×D4—51no—
272C2×D3×D4—51no—
273C2×D3×D4—101no—
274C2×D3×D4—101no—
275C2×#235—51no—
276C2×#235—101no—
277C22×D12—51no—
278C22×D12—101no—
279C22×C3×C8—51no—
280C3×#117—51no—
281C2×C4⋊Dic3—51no—
282C2×#208—51no—
283#901—104no—
284C2×ΓL(1,𝔽25)—51no—
285C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
286C2×D3×C8—51no—
287C2×D3×C8—51no—
288#892—51no—
289#892—51no—
290D3×C4⋊C4—51no—
291D3×C4⋊C4C2×D511yescharacteristic, complemented
292#67⋊C4—101no—
293#67⋊C4—101no—
294C4×D12—101no—
295C4×Dic6—101no—
296C3×#103—51no—
297C3×#103C2×D511yescharacteristic, complemented
298C3×#102—51no—
299C3×#102—51no—
300#835—51no—
301#835C2×D511yescharacteristic, complemented
302#832—51no—
303#832—51no—
304#821—51no—
305#821—51no—
306#821—51no—
307#821C2×D511yescharacteristic, complemented
308#809—51no—
309#809—51no—
310#809—51no—
311#809C2×D511yescharacteristic, complemented
312C23×D5—61no—
313C23×D5—61no—
314C23×D5—61no—
315C5×#41—34no—
316C5×#41—62no—
317C2×C5×Q8C22×D311yescharacteristic
318C2×C5×D4—31no—
319C2×C5×D4—61no—
320C22×C4×C5—31no—
321C22×C4×C5—61no—
322C22×C4×C5—61no—
323C2×C22⋊D5—31no—
324C2×C22⋊D5—31no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5—61no—
327#713—22no—
328#713—34no—
329#713—62no—
330#713C4×D314yescomplemented
331D4×D5—34no—
332D4×D5—34no—
333D4×D5—68no—
334D4×D5—62no—
335D4×D5—68no—
336D4×D5—62no—
337#709—34no—
338#709—34no—
339#709—68no—
340C2×D20—21no—
341C2×D20—31no—
342C2×D20—31no—
343C2×D20—34no—
344C2×D20—68no—
345C2×D20—62no—
346C2×D20—61no—
347C2×D20—61no—
348C2×D20C22×D311yescharacteristic
349C2×C4×D5—21no—
350C2×C4×D5—31no—
351C2×C4×D5—61no—
352C2×C4×D5—61no—
353C2×C4×D5—61no—
354C2×C4×D5C22×D311yescharacteristic
355C2×Dic10—31no—
356C5×M16—62no—
357C2×C5×C8—31no—
358C2×C5×C8C22×D311yescharacteristic
359C5×C4⋊C4—31no—
360C5×C4⋊C4—61no—
361C5×C4⋊C4C22×D311yescharacteristic
362C22⋊Dic5—61no—
363#685—21no—
364#685—61no—
365C4⋊Dic5—31no—
366C4⋊Dic5C22×D311yescharacteristic
367#683—61no—
368#683—61no—
369C4×Dic5—21no—
370C4×Dic5—61no—
371C4×Dic5—61no—
372C2×#168—31no—
373C2×#168—62no—
374C2×#168C22×D311yescharacteristic
375#676—62no—
376#676—62no—
377C8×D5—22no—
378C8×D5—62no—
379C2×H(5,𝔽2)—151no—
380C2×#131—151no—
381#520—151no—
382#418—151no—
383#418—151no—
384#418—151no—
385#417—31no—
386#417—151no—
387#417—151no—
388#416—51no—
389#416—151no—
390#416—151no—
391C2×#102—151no—
392C2×#102—151no—
393C2×#102—151no—
394C22×C3×C5C22×D411yescharacteristic
395C2×D15—21no—
396C2×D15—21no—
397C2×D15—22no—
398C2×D15—41no—
399C2×D15—41no—
400C2×D15C2×C22⋊C412yes—
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—22no—
404C2×C5×D3—41no—
405C2×C5×D3—41no—
406C2×C5×D3C2×C22⋊C412yes—
407C2×C3×D5—21no—
408C2×C3×D5—21no—
409C2×C3×D5—22no—
410C2×C3×D5—41no—
411C2×C3×D5—41no—
412C2×C3×D5C2×C22⋊C412yes—
413D3×D5—84no—
414D3×D5—84no—
415D3×D5—84no—
416C3×C4×C5—22no—
417C3×C4×C5—41no—
418C3×C4×C5C23×C411yescharacteristic
419C3×C4×C5C22×D411yescharacteristic
420Dic15—41no—
421Dic15C2×C22⋊C412yes—
422C3×Dic5—41no—
423C3×Dic5C2×C22⋊C412yes—
424C5×Dic3—41no—
425C5×Dic3C2×C22⋊C412yes—
426C23×D3—101no—
427C23×D3—101no—
428C23×D3—101no—
429C3×#41—54no—
430C3×#41—102no—
431C2×C3×Q8C22×D511yescharacteristic
432C2×C3×D4—51no—
433C2×C3×D4—101no—
434C22×C3×C4—51no—
435C22×C3×C4—101no—
436C2×#67—51no—
437C2×#67—51no—
438C2×#67—101no—
439C2×#67—101no—
440C22×Dic3—101no—
441#239—22no—
442#239—54no—
443#239—102no—
444#239C4×D514yescomplemented
445D3×D4—54no—
446D3×D4—54no—
447D3×D4—108no—
448D3×D4—102no—
449D3×D4—108no—
450D3×D4—102no—
451#235—54no—
452#235—54no—
453#235—108no—
454C2×D12—21no—
455C2×D12—51no—
456C2×D12—51no—
457C2×D12—54no—
458C2×D12—108no—
459C2×D12—102no—
460C2×D12—101no—
461C2×D12—101no—
462C2×D12C22×D511yescharacteristic
463C2×C4×D3—21no—
464C2×C4×D3—21no—
465C2×C4×D3—51no—
466C2×C4×D3—101no—
467C2×C4×D3—101no—
468C2×C4×D3C22×D511yescharacteristic
469C2×Dic6—51no—
470C2×C3×C8—51no—
471C2×C3×C8—102no—
472C2×C3×C8C22×D511yescharacteristic
473C3×C4⋊C4—51no—
474C3×C4⋊C4C22×D511yescharacteristic
475C3×C22⋊C4—101no—
476C3×C42—101no—
477(C2×D3)⋊C4—101no—
478(C2×D3)⋊C4—101no—
479C4⋊Dic3—51no—
480C4⋊Dic3—101no—
481C4⋊Dic3C22×D511yescharacteristic
482Dic3⋊C4—21no—
483Dic3⋊C4—101no—
484C4×Dic3—101no—
485C4×Dic3—101no—
486#208—102no—
487C2×C3⋊C8—51no—
488C2×C3⋊C8C22×D511yescharacteristic
489ΓL(1,𝔽25)—22no—
490ΓL(1,𝔽25)—102no—
491D3×C8—102no—
492D3×C8—102no—
493C23×C5—31no—
494C23×C5—61no—
495C22×D5—21no—
496C22×D5—31no—
497C22×D5—64no—
498C22×D5—64no—
499C22×D5—61no—
500C22×D5—64no—
501C22×D5—241no—
502C22×D5—241no—
503C22×D5—241no—
504C22×D5—241no—
505C22×D5—241no—
506C22×D5—241no—
507C22×D5D3×D411yescharacteristic
508C5×Q8—21no—
509C5×Q8C2×C4×D312yes—
510C5×D4—32no—
511C5×D4—64no—
512C5×D4—61no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—31no—
516C2×C4×C5—32no—
517C2×C4×C5—32no—
518C2×C4×C5—64no—
519C2×C4×C5—61no—
520C2×C4×C5—241no—
521C2×C4×C5C23×D311yescharacteristic
522C22⋊D5—34no—
523C22⋊D5—34no—
524C22⋊D5—64no—
525C22⋊D5—64no—
526C2×Dic5—21no—
527C2×Dic5—31no—
528C2×Dic5—61no—
529C2×Dic5D3×D411yescharacteristic
530D20—24no—
531D20—21no—
532D20—34no—
533D20—32no—
534D20—64no—
535D20—64no—
536D20—61no—
537D20C2×C4×D312yes—
538C4×D5—24no—
539C4×D5—32no—
540C4×D5—32no—
541C4×D5—64no—
542C4×D5—241no—
543C4×D5—241no—
544C4×D5C2×C4×D312yes—
545C4×D5D3×D412yes—
546Dic10—34no—
547C5×C8—21no—
548C5×C8—61no—
549#168—21no—
550#168—61no—
551H(5,𝔽2)—158no—
552H(5,𝔽2)—304no—
553C2×#41—31no—
554C2×#41—51no—
555C2×#41—151no—
556C2×#41—151no—
557C2×#41—301no—
558C22×D4—151no—
559C22×D4—151no—
560C22×D4—151no—
561C22×D4—301no—
562C22×D4—301no—
563C22×D4—301no—
564#131—304no—
565C2×M16—31no—
566C2×M16—151no—
567C2×M16—151no—
568C22×C8—51no—
569C22×C8—151no—
570C22×C8—151no—
571C4×Q8—301no—
572C4×D4—301no—
573C4×D4—301no—
574C4×D4—301no—
575#117—51no—
576#117—151no—
577#117—151no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—151no—
580C2×C4⋊C4—151no—
581#103—31no—
582#103—51no—
583#103—151no—
584#103D3×D511yescharacteristic, complemented
585#102—31no—
586#102—31no—
587#102—51no—
588#102—51no—
589#102—151no—
590#102—151no—
591#102—151no—
592#102—151no—
593#102—151no—
594#102—151no—
595#102—151no—
596#102—151no—
597C2×C3×C5C22×C22⋊C411yescharacteristic
598C2×C3×C5#57611yescharacteristic
599C2×C3×C5#57711yescharacteristic
600D15—22no—
601D15—42no—
602C3×D5—22no—
603C3×D5—42no—
604C5×D3—22no—
605C5×D3—42no—
606C23×C3—51no—
607C23×C3—101no—
608C22×D3—21no—
609C22×D3—51no—
610C22×D3—104no—
611C22×D3—104no—
612C22×D3—101no—
613C22×D3—104no—
614C22×D3—401no—
615C22×D3—401no—
616C22×D3—401no—
617C22×D3—401no—
618C22×D3—401no—
619C22×D3—401no—
620C22×D3D4×D511yescharacteristic
621C3×Q8—21no—
622C3×Q8C2×C4×D512yes—
623C3×D4—52no—
624C3×D4—104no—
625C3×D4—101no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—51no—
629C2×C3×C4—52no—
630C2×C3×C4—52no—
631C2×C3×C4—104no—
632C2×C3×C4—101no—
633C2×C3×C4C23×D511yescharacteristic
634#67—54no—
635#67—54no—
636#67—104no—
637#67—104no—
638C2×Dic3—21no—
639C2×Dic3—51no—
640C2×Dic3—101no—
641C2×Dic3—401no—
642C2×Dic3D4×D511yescharacteristic
643D12—24no—
644D12—21no—
645D12—54no—
646D12—52no—
647D12—104no—
648D12—104no—
649D12—101no—
650D12C2×C4×D512yes—
651C4×D3—24no—
652C4×D3—52no—
653C4×D3—52no—
654C4×D3—81no—
655C4×D3—104no—
656C4×D3—401no—
657C4×D3C2×C4×D512yes—
658C4×D3D4×D512yes—
659Dic6—54no—
660C3×C8—21no—
661C3×C8—101no—
662C3⋊C8—21no—
663C3⋊C8—101no—
664C22×C5—32no—
665C22×C5—61no—
666C22×C5—61no—
667C22×C5—62no—
668C22×C5—121no—
669C22×C5—121no—
670C22×C5C2×D3×D411yescharacteristic
671C2×D5—21no—
672C2×D5—21no—
673C2×D5—22no—
674C2×D5—32no—
675C2×D5—41no—
676C2×D5—41no—
677C2×D5—61no—
678C2×D5—61no—
679C2×D5—62no—
680C2×D5—121no—
681C2×D5—121no—
682C2×D5—244no—
683C2×D5—244no—
684C2×D5—244no—
685C2×D5D3×C22⋊C412yes—
686C4×C5—22no—
687C4×C5—32no—
688C4×C5—41no—
689C4×C5—121no—
690C4×C5C22×C4×D311yescharacteristic
691C4×C5C2×D3×D411yescharacteristic
692Dic5—32no—
693Dic5—41no—
694Dic5—121no—
695Dic5D3×C22⋊C412yes—
696C24—301no—
697C24—301no—
698C24—301no—
699#41—34no—
700#41—54no—
701#41—62no—
702#41—102no—
703#41—154no—
704#41—154no—
705#41—154no—
706#41—308no—
707#41—302no—
708C2×Q8—151no—
709C2×Q8C2×D3×D511yescharacteristic
710C2×D4—31no—
711C2×D4—51no—
712C2×D4—61no—
713C2×D4—101no—
714C2×D4—154no—
715C2×D4—151no—
716C2×D4—154no—
717C2×D4—151no—
718C2×D4—154no—
719C2×D4—151no—
720C2×D4—151no—
721C2×D4—301no—
722C2×D4—302no—
723C2×D4—301no—
724C2×D4—302no—
725C2×D4—301no—
726C2×D4—308no—
727C2×D4—308no—
728C2×D4—302no—
729C2×D4—301no—
730C2×D4—308no—
731C22×C4—31no—
732C22×C4—51no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—101no—
736C22×C4—151no—
737C22×C4—301no—
738C22×C4—301no—
739C22×C4—301no—
740M16—62no—
741M16—302no—
742M16—302no—
743C2×C8—31no—
744C2×C8—51no—
745C2×C8—102no—
746C2×C8—151no—
747C2×C8—302no—
748C2×C8—302no—
749C2×C8C2×D3×D511yescharacteristic
750C4⋊C4—31no—
751C4⋊C4—51no—
752C4⋊C4—61no—
753C4⋊C4—151no—
754C4⋊C4—301no—
755C4⋊C4—301no—
756C4⋊C4C2×D3×D511yescharacteristic
757C22⋊C4—101no—
758C22⋊C4—301no—
759C22⋊C4—301no—
760C42—101no—
761C42—301no—
762C42—301no—
763C3×C5#289711yescharacteristic, complemented, Hall
764C22×C3—52no—
765C22×C3—101no—
766C22×C3—101no—
767C22×C3—102no—
768C22×C3—201no—
769C22×C3—201no—
770C22×C3C2×D4×D511yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—52no—
777C2×D3—101no—
778C2×D3—101no—
779C2×D3—102no—
780C2×D3—201no—
781C2×D3—201no—
782C2×D3—404no—
783C2×D3—404no—
784C2×D3—404no—
785C2×D3D5×C22⋊C412yes—
786C3×C4—22no—
787C3×C4—41no—
788C3×C4—52no—
789C3×C4—201no—
790C3×C4C22×C4×D511yescharacteristic
791C3×C4C2×D4×D511yescharacteristic
792Dic3—41no—
793Dic3—52no—
794Dic3—201no—
795Dic3D5×C22⋊C412yes—
796C2×C5—62no—
797C2×C5—122no—
798C2×C5C2×D3×C22⋊C411yescharacteristic
799C2×C5#576911yescharacteristic
800C2×C5#577011yescharacteristic
801D5—22no—
802D5—42no—
803D5—62no—
804D5—122no—
805C23—31no—
806C23—51no—
807C23—61no—
808C23—101no—
809C23—151no—
810C23—304no—
811C23—304no—
812C23—304no—
813C23—301no—
814C23—1201no—
815C23—1201no—
816C23—1201no—
817C23—1201no—
818C23—1201no—
819C23—1201no—
820Q8—21no—
821Q8—154no—
822Q8C4×D3×D512yes—
823D4—32no—
824D4—52no—
825D4—64no—
826D4—61no—
827D4—104no—
828D4—101no—
829D4—154no—
830D4—154no—
831D4—154no—
832D4—152no—
833D4—304no—
834D4—304no—
835D4—304no—
836D4—304no—
837D4—301no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—31no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—51no—
844C2×C4—52no—
845C2×C4—52no—
846C2×C4—64no—
847C2×C4—61no—
848C2×C4—104no—
849C2×C4—101no—
850C2×C4—151no—
851C2×C4—152no—
852C2×C4—152no—
853C2×C4—241no—
854C2×C4—304no—
855C2×C4—301no—
856C2×C4—1201no—
857C2×C4—1201no—
858C2×C4C22×D3×D511yescharacteristic
859C8—21no—
860C8—61no—
861C8—101no—
862C8—301no—
863C2×C3—102no—
864C2×C3—202no—
865C2×C3C2×D5×C22⋊C411yescharacteristic
866C2×C3#6610811yescharacteristic
867C2×C3#6611211yescharacteristic
868D3—22no—
869D3—42no—
870D3—102no—
871D3—202no—
872C5#7883111yescharacteristic, complemented, Sylow
873C22—32no—
874C22—52no—
875C22—61no—
876C22—61no—
877C22—62no—
878C22—101no—
879C22—101no—
880C22—102no—
881C22—121no—
882C22—121no—
883C22—152no—
884C22—201no—
885C22—201no—
886C22—301no—
887C22—301no—
888C22—302no—
889C22—601no—
890C22—601no—
891C22—1204no—
892C22—1204no—
893C22—1204no—
894C22D3×D4×D511yescharacteristic
895C4—22no—
896C4—32no—
897C4—41no—
898C4—52no—
899C4—121no—
900C4—152no—
901C4—201no—
902C4—601no—
903C4C2×C4×D3×D511yescharacteristic
904C4D3×D4×D511yescharacteristic
905C3#1061061311yescharacteristic, complemented, Sylow
906C2—62no—
907C2—102no—
908C2—122no—
909C2—202no—
910C2—302no—
911C2—602no—
912C2D3×D5×C22⋊C411yescharacteristic
913C2#1175409311yescharacteristic
914C2#1175411411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#92035C2
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#91266C2semidirect
3. #11753669C2semidirect
4. #11750904C2semidirect
5. C5×#4803C2semidirect
6. C3×#65093C2semidirect
7. #11749215C2semidirect
8. #11749211C2semidirect
9. #11749198C2semidirect
10. #11748109C2semidirect
11. #11748107C2semidirect
12. D5×#821C2semidirect
13. #11747478C2semidirect
14. D3×#3941C2semidirect
15. #11747475C2semidirect
21. #92035C4semidirect
30. C2×#6705C22semidirect
31. C4⋊C4×D15C22semidirect
32. C2×C5×ΓL(1,𝔽25)C22semidirect
33. C5×D3×C4⋊C4C22semidirect
34. C2×C3×C8×D5C22semidirect
35. C3×#4038C22semidirect
38. D5×C4⋊Dic3C22semidirect
40. #91347C22semidirect
41. #91338C22semidirect
43. C2×#6649C22semidirect
44. C2×#6648C22semidirect
45. C2×D3×#168C22semidirect
47. C3×C5×#103C22semidirect
48. #91119C22semidirect
49. #91105C22semidirect
50. #91093C22semidirect
51. C5×#835C22semidirect
52. C5×#821C22semidirect
53. C5×#809C22semidirect
54. C3×#3967C22semidirect
55. C3×#3953C22semidirect
56. C3×#3941C22semidirect
57. #90969C22semidirect
58. #90968C22semidirect
59. #90967C22semidirect
60. #90966C22semidirect
61. #90965C22semidirect
62. #90964C22semidirect
72. #65093D3semidirect
84. #6821C2×C4semidirect
91. C5×#239C2×C4semidirect
98. C3×#713C2×C4semidirect
113. #6777C2×C4semidirect
116. D3×D20C2×C4semidirect
119. D5×D12C2×C4semidirect
156. #4803D5semidirect
184. C2×C8×D5C2×D3semidirect
187. #4038C2×D3semidirect
192. C5×#103C2×D3semidirect
196. #3967C2×D3semidirect
202. #3953C2×D3semidirect
206. #3941C2×D3semidirect
285. C2×ΓL(1,𝔽25)C2×D5semidirect
291. D3×C4⋊C4C2×D5semidirect
297. C3×#103C2×D5semidirect
301. #835C2×D5semidirect
307. #821C2×D5semidirect
311. #809C2×D5semidirect
330. #713C4×D3semidirect
444. #239C4×D5semidirect
584. #103D3×D5semidirect
763. C3×C5#2897semidirect
872. C5#78831semidirect
905. C3#10610613semidirect

Maximal subgroups

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

subgroupindex
C2×#920352
C2×#912662
#117536692
#117509042
C5×#48032
C3×#650932
#117492152
#117492112
#117491982
#117481092
#117481072
D5×#8212
#117474782
D3×#39412
#117474752
#106106133
#788315