Finite Group Databasebeta

← #14412639

Subgroups — #14412639

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×#92026C211yesmaximal, characteristic
2C2×#91265C211yesmaximal, characteristic, complemented
3#11753668C211yesmaximal, characteristic, complemented
4D15×#102C211yesmaximal, characteristic, complemented
5C5×#4772C211yesmaximal, characteristic, complemented
6C3×D5×#102C211yesmaximal, characteristic, complemented
7#11748972C211yesmaximal, characteristic, complemented
8#11748962C211yesmaximal, characteristic, complemented
9#11748955C211yesmaximal, characteristic, complemented
10#11748141C211yesmaximal, characteristic, complemented
11D3×#3953C211yesmaximal, characteristic, complemented
12#11747642C211yesmaximal, characteristic, complemented
13#11747507C211yesmaximal, characteristic, complemented
14#11747500C211yesmaximal, characteristic, complemented
15#11747477C211yesmaximal, characteristic, complemented
16#10610562—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×C5×#237C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic
20C2×#6790—21no—
21C2×D5×#67—21no—
22C22×#1202—21no—
23C2×#6779—21no—
24#92026—24no—
25#92026C418yescomplemented
26C2×D3×D20C2211yescharacteristic
27C2×#6773C2211yescharacteristic
28C2×#6771C2211yescharacteristic
29C2×#6766C2211yescharacteristic
30C2×C8×D15C2211yescharacteristic, complemented
31C4⋊C4×D15C2211yescharacteristic, complemented
32C2×C5×D3×C8C2211yescharacteristic, complemented
33C5×#892C2211yescharacteristic, complemented
34C2×C3×C8×D5C2211yescharacteristic, complemented
35C3×D5×C4⋊C4C2211yescharacteristic, complemented
36C4×#1202—21no—
37#91440—21no—
38D3×C4⋊Dic5C2211yescharacteristic, complemented
39#91406—21no—
40#91358C2211yescharacteristic, complemented
41#91347C2211yescharacteristic, complemented
42#91324—21no—
43C2×#6651C2211yescharacteristic, complemented
44C2×#6650C2211yescharacteristic, complemented
45C2×#6649C2211yescharacteristic, complemented
46#91265—24no—
47C3×C5×#102C2211yescharacteristic, complemented
48#91116C2211yescharacteristic, complemented
49#91105C2211yescharacteristic, complemented
50#91093C2211yescharacteristic, complemented
51C5×#832C2211yescharacteristic, complemented
52C5×#816C2211yescharacteristic, complemented
53C5×#810C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90972C2211yescharacteristic, complemented
59#90969C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62#90964C2211yescharacteristic, complemented
63#78742—51nomaximal, Hall
64C2×#4149—31no—
65C2×#4047—31no—
66#65857—31no—
67C5×#416—31no—
68#65521—31no—
69C2×#3953—31no—
70#65290—31no—
71#65093—31no—
72#65093—31no—
73#65092—31no—
74#65092—31no—
75#65059—31no—
76#65059—31no—
77D5×#102—31no—
78D5×#102D311yescharacteristic, complemented
79C23×D15—21no—
80C23×C3×D5—21no—
81C22×D3×D5—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×#1220—21no—
84D4×D15—22no—
85D4×D15C2×C414yescomplemented
86C2×D60C2311yescharacteristic
87C2×C4×D15—21no—
88C2×C4×D15C2311yescharacteristic
89C2×C5×#67—21no—
90C22×C5×Dic3—21no—
91C5×#237—22no—
92C5×#237C2×C414yescomplemented
93C2×C4×C5×D3C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C3×D4×D5—22no—
97C3×D4×D5C2×C414yescomplemented
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×C4×D5C2311yescharacteristic
101#6790—28no—
102D5×#67—28no—
103C2×#1204D411yescharacteristic
104C2×#1203D411yescharacteristic
105C2×#1202—21no—
106C2×#1202—21no—
107C2×#1202—21no—
108C2×#1202—28no—
109C2×#1202D411yescharacteristic
110C2×#1201D411yescharacteristic
111C2×#1200—21no—
112C2×D3×Dic5—21no—
113#6779—28no—
114C2×D5×Dic3—21no—
115D3×D20—22no—
116D3×D20C2×C414yescomplemented
117#6773—22no—
118#6773C2×C414yescomplemented
119#6771C2×C414yes—
120#6771D414yes—
121#6766—22no—
122#6766C2×C414yescomplemented
123C2×C3×C5×C8C2311yescharacteristic
124C3×C5×C4⋊C4C2311yescharacteristic
125C4⋊Dic15C2311yescharacteristic
126#6712—21no—
127C2×C3⋊#168C2311yescharacteristic
128C8×D15—22no—
129C5×(C2×D3)⋊C4—21no—
130C5×C4⋊Dic3C2311yescharacteristic
131C4×C5×Dic3—21no—
132C2×C5×C3⋊C8C2311yescharacteristic
133C5×D3×C8—22no—
134C3×C4⋊Dic5C2311yescharacteristic
135C3×#683—21no—
136C2×C3×#168C2311yescharacteristic
137C3×C8×D5—22no—
138Dic3⋊Dic5—21no—
139#6667—21no—
140#6665—21no—
141Dic3×Dic5—21no—
142Dic3×Dic5—21no—
143#6651—22no—
144#6650—22no—
145#6649—22no—
146C2×#1004—51no—
147C2×#901—51no—
148#5504—51no—
149C2×C3×#102—51no—
150#5215—51no—
151#5113—51no—
152#4966—51no—
153#4772—51no—
154#4772D511yescharacteristic, complemented
155#4771—51no—
156#4771—51no—
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×#713—31no—
166C2×D4×D5—31no—
167C2×D4×D5—61no—
168C2×D4×D5—61no—
169C2×D4×D5C2×D311yescharacteristic
170C2×#709—31no—
171C2×#709—61no—
172C22×D20—31no—
173C22×D20—61no—
174C22×C5×C8—31no—
175C5×#117—31no—
176C2×C4⋊Dic5—31no—
177C2×#681—31no—
178#4047—64no—
179C2×#676—31no—
180C2×#676—31no—
181C2×C8×D5—31no—
182C2×C8×D5C2×D311yescharacteristic, complemented
183#4038—31no—
184#4038—31no—
185D5×C4⋊C4—31no—
186D5×C4⋊C4C2×D311yescharacteristic, complemented
187#4027—61no—
188#4027—61no—
189C4×D20—61no—
190C4×Dic10—61no—
191C5×#103—31no—
192C5×#103—31no—
193C5×#102—31no—
194C5×#102C2×D311yescharacteristic, complemented
195#3967—31no—
196#3967—31no—
197#3964—31no—
198#3964C2×D311yescharacteristic, complemented
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
208C23×C3×C5—21no—
209C22×D15—21no—
210C22×D15—24no—
211C22×D15—81no—
212C22×D15—81no—
213C22×D15C2×D411yescharacteristic
214C22×C5×D3C2×D411yescharacteristic
215C22×C3×D5—21no—
216C22×C3×D5—24no—
217C22×C3×D5—81no—
218C22×C3×D5—81no—
219C22×C3×D5C2×D411yescharacteristic
220C2×D3×D5—24no—
221C2×D3×D5—81no—
222C2×D3×D5—81no—
223C3×C5×D4—21no—
224C3×C5×D4C22×C412yes—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5C2411yescharacteristic
227#1220—24no—
228C2×Dic15—21no—
229C2×Dic15C2×D411yescharacteristic
230D60—21no—
231D60C22×C412yes—
232C4×D15—81no—
233C4×D15C22×C412yes—
234C4×D15C2×D412yes—
235C5×#67—24no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—24no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3C2×D411yescharacteristic
240C4×C5×D3C22×C412yes—
241C4×C5×D3C2×D412yes—
242C5×Dic6—21no—
243C5×Dic6C22×C412yes—
244C3×C22⋊D5—24no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5C2×D411yescharacteristic
247C3×D20—21no—
248C3×D20C22×C412yes—
249C3×C4×D5—81no—
250C3×C4×D5C22×C412yes—
251C3×C4×D5C2×D412yes—
252#1204C22⋊C414yes—
253#1203C22⋊C414yes—
254#1202—24no—
255#1202—24no—
256#1202—24no—
257#1202C22⋊C414yes—
258#1201C22⋊C414yes—
259#1200—24no—
260D3×Dic5—81no—
261D5×Dic3—24no—
262C3×C5×C8—21no—
263C3⋊#168—21no—
264C3×#168—21no—
265C5×C3⋊C8—21no—
266C22×C3×D4—51no—
267C22×#67—101no—
268C22×#67—101no—
269#1004—58no—
270#1004—104no—
271C2×#237—51no—
272C2×#237—101no—
273C2×#237C2×D511yescharacteristic
274C2×D3×D4—51no—
275C2×D3×D4—51no—
276C2×D3×D4—101no—
277C2×#235—51no—
278C2×#235—51no—
279C22×C3×C8—51no—
280C2×C3×C4⋊C4—51no—
281C4×#67—101no—
282C4×#67—101no—
283#926—51no—
284C2×#208—51no—
285#901—104no—
286C2×ΓL(1,𝔽25)—51no—
287C2×ΓL(1,𝔽25)—51no—
288C2×D3×C8—51no—
289C2×D3×C8C2×D511yescharacteristic, complemented
290#893—101no—
291#892—51no—
292#892C2×D511yescharacteristic, complemented
293D3×C4⋊C4—51no—
294D3×C4⋊C4—51no—
295#887—101no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102C2×D511yescharacteristic, complemented
300#832—51no—
301#832—51no—
302#832—51no—
303#832C2×D511yescharacteristic, complemented
304#821—51no—
305#821—51no—
306#816—51no—
307#816C2×D511yescharacteristic, complemented
308#810—51no—
309#810C2×D511yescharacteristic, complemented
310#809—51no—
311#809—51no—
312C23×D5—21no—
313C23×D5—61no—
314C23×D5—61no—
315C5×#41—34no—
316C5×#41—62no—
317C2×C5×Q8—31no—
318C2×C5×D4—61no—
319C2×C5×D4C22×D311yescharacteristic
320C22×C4×C5—31no—
321C22×C4×C5—61no—
322C2×C22⋊D5—21no—
323C2×C22⋊D5—31no—
324C2×C22⋊D5—31no—
325C2×C22⋊D5—61no—
326C22×Dic5—61no—
327#713—34no—
328#713—34no—
329#713—62no—
330#713—62no—
331D4×D5—22no—
332D4×D5—34no—
333D4×D5—62no—
334D4×D5—68no—
335D4×D5—68no—
336D4×D5C4×D314yescomplemented
337#709—34no—
338#709—34no—
339#709—68no—
340C2×D20—31no—
341C2×D20—31no—
342C2×D20—34no—
343C2×D20—62no—
344C2×D20—68no—
345C2×D20—61no—
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—
356C2×C5×C8—31no—
357C2×C5×C8—62no—
358C2×C5×C8C22×D311yescharacteristic
359C5×C4⋊C4—31no—
360C5×C4⋊C4C22×D311yescharacteristic
361C5×C22⋊C4—61no—
362C42×C5—61no—
363#685—61no—
364#685—61no—
365C4⋊Dic5—31no—
366C4⋊Dic5—61no—
367C4⋊Dic5C22×D311yescharacteristic
368#683—21no—
369#683—61no—
370C4×Dic5—61no—
371C4×Dic5—61no—
372#681—62no—
373C2×#168—31no—
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—151no—
386#417—151no—
387#417—151no—
388#416—31no—
389#416—151no—
390#416—151no—
391C2×#102—51no—
392C2×#102—151no—
393C2×#102—151no—
394C22×C3×C5—22no—
395C22×C3×C5—41no—
396C22×C3×C5—41no—
397C22×C3×C5C22×D411yescharacteristic
398C2×D15—21no—
399C2×D15—21no—
400C2×D15—22no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—84no—
404C2×D15C2×C22⋊C412yes—
405C2×C5×D3—21no—
406C2×C5×D3—21no—
407C2×C5×D3C2×C22⋊C412yes—
408C2×C3×D5—21no—
409C2×C3×D5—21no—
410C2×C3×D5—22no—
411C2×C3×D5—41no—
412C2×C3×D5—41no—
413C2×C3×D5—84no—
414C2×C3×D5C2×C22⋊C412yes—
415D3×D5—84no—
416C3×C4×C5—41no—
417C3×C4×C5C23×C411yescharacteristic
418C3×C4×C5C22×D411yescharacteristic
419Dic15—41no—
420Dic15C2×C22⋊C412yes—
421C3×Dic5—41no—
422C3×Dic5C2×C22⋊C412yes—
423C5×Dic3—22no—
424C5×Dic3—41no—
425C5×Dic3C2×C22⋊C412yes—
426C24×C3—101no—
427C23×D3—101no—
428C23×D3—101no—
429C2×C3×D4—54no—
430C2×C3×D4—51no—
431C2×C3×D4—102no—
432C2×C3×D4—101no—
433C2×C3×D4C22×D511yescharacteristic
434C22×C3×C4—51no—
435C22×C3×C4—101no—
436C2×#67—21no—
437C2×#67—51no—
438C2×#67—51no—
439C2×#67—108no—
440C2×#67—101no—
441C2×#67—101no—
442C2×#67—101no—
443C2×#67—108no—
444C2×#67—101no—
445C22×Dic3—21no—
446C22×Dic3—101no—
447#237—22no—
448#237—54no—
449#237—102no—
450#237—108no—
451#237C4×D514yescomplemented
452D3×D4—54no—
453D3×D4—54no—
454D3×D4—102no—
455D3×D4—108no—
456D3×D4—102no—
457#235—54no—
458#235—54no—
459#235—54no—
460#235—102no—
461C2×D12—51no—
462C2×D12—51no—
463C2×C4×D3—51no—
464C2×C4×D3—101no—
465C2×C4×D3—101no—
466C2×C4×D3—101no—
467C2×C4×D3C22×D511yescharacteristic
468C2×Dic6—51no—
469C2×Dic6C22×D511yescharacteristic
470C2×C3×C8—51no—
471C2×C3×C8—102no—
472C2×C3×C8C22×D511yescharacteristic
473C3×C4⋊C4—51no—
474C3×C4⋊C4—101no—
475C3×C4⋊C4C22×D511yescharacteristic
476#217—101no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—101no—
479C4⋊Dic3—51no—
480C4⋊Dic3C22×D511yescharacteristic
481Dic3⋊C4—101no—
482Dic3⋊C4—101no—
483C4×Dic3—21no—
484C4×Dic3—101no—
485C4×Dic3—101no—
486#208—102no—
487C2×C3⋊C8—51no—
488C2×C3⋊C8C22×D511yescharacteristic
489ΓL(1,𝔽25)—102no—
490ΓL(1,𝔽25)—102no—
491D3×C8—22no—
492D3×C8—102no—
493C23×C5—21no—
494C23×C5—31no—
495C22×D5—21no—
496C22×D5—24no—
497C22×D5—31no—
498C22×D5—64no—
499C22×D5—64no—
500C22×D5—61no—
501C22×D5—81no—
502C22×D5—81no—
503C22×D5—241no—
504C22×D5—241no—
505C22×D5—241no—
506C22×D5—241no—
507C22×D5D3×D411yescharacteristic
508C5×Q8—32no—
509C5×Q8—61no—
510C5×D4—21no—
511C5×D4—64no—
512C5×D4C2×C4×D312yes—
513C2×C4×C5—21no—
514C2×C4×C5—31no—
515C2×C4×C5—32no—
516C2×C4×C5—32no—
517C2×C4×C5—64no—
518C2×C4×C5—61no—
519C2×C4×C5—61no—
520C2×C4×C5C23×D311yescharacteristic
521C22⋊D5—24no—
522C22⋊D5—34no—
523C22⋊D5—34no—
524C22⋊D5—64no—
525C2×Dic5—21no—
526C2×Dic5—31no—
527C2×Dic5—61no—
528C2×Dic5—241no—
529C2×Dic5D3×D411yescharacteristic
530D20—21no—
531D20—34no—
532D20—32no—
533D20—64no—
534D20—64no—
535D20—64no—
536D20—61no—
537D20C2×C4×D312yes—
538C4×D5—32no—
539C4×D5—32no—
540C4×D5—64no—
541C4×D5—64no—
542C4×D5—81no—
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—151no—
555C2×#41—151no—
556C2×#41—151no—
557C2×#41—301no—
558C22×D4—51no—
559C22×D4—151no—
560C22×D4—151no—
561C22×D4—301no—
562C22×D4—301no—
563C22×D4—301no—
564#131—304no—
565C2×M16—151no—
566C2×M16—151no—
567C2×M16—151no—
568C22×C8—31no—
569C22×C8—51no—
570C22×C8—151no—
571C4×Q8—301no—
572C4×D4—301no—
573C4×D4—301no—
574C4×D4—301no—
575#117—31no—
576#117—151no—
577#117—151no—
578C2×C4⋊C4—51no—
579C2×C4⋊C4—151no—
580C2×C4⋊C4—151no—
581#103—31no—
582#103—31no—
583#103—151no—
584#103—151no—
585#102—31no—
586#102—51no—
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#102D3×D511yescharacteristic, complemented
597C2×C3×C5—42no—
598C2×C3×C5C22×C22⋊C411yescharacteristic
599C2×C3×C5#57611yescharacteristic
600C2×C3×C5#57711yescharacteristic
601D15—22no—
602D15—42no—
603C3×D5—22no—
604C3×D5—42no—
605C5×D3—22no—
606C23×C3—21no—
607C23×C3—51no—
608C23×C3—104no—
609C23×C3—101no—
610C23×C3—401no—
611C23×C3—401no—
612C22×D3—51no—
613C22×D3—104no—
614C22×D3—101no—
615C22×D3—104no—
616C22×D3—401no—
617C22×D3—401no—
618C22×D3—401no—
619C22×D3—401no—
620C22×D3D4×D511yescharacteristic
621C3×D4—21no—
622C3×D4—52no—
623C3×D4—104no—
624C3×D4—101no—
625C3×D4C2×C4×D512yes—
626C2×C3×C4—21no—
627C2×C3×C4—51no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—101no—
631C2×C3×C4—401no—
632C2×C3×C4C23×D511yescharacteristic
633#67—24no—
634#67—54no—
635#67—54no—
636#67—104no—
637#67—104no—
638#67—104no—
639#67—104no—
640C2×Dic3—21no—
641C2×Dic3—24no—
642C2×Dic3—21no—
643C2×Dic3—51no—
644C2×Dic3—104no—
645C2×Dic3—101no—
646C2×Dic3D4×D511yescharacteristic
647D12—54no—
648D12—52no—
649D12—101no—
650C4×D3—52no—
651C4×D3—52no—
652C4×D3—104no—
653C4×D3—401no—
654C4×D3—401no—
655C4×D3C2×C4×D512yes—
656C4×D3D4×D512yes—
657Dic6—21no—
658Dic6—54no—
659Dic6C2×C4×D512yes—
660C3×C8—21no—
661C3×C8—101no—
662C3⋊C8—21no—
663C3⋊C8—101no—
664C22×C5—22no—
665C22×C5—32no—
666C22×C5—41no—
667C22×C5—41no—
668C22×C5—61no—
669C22×C5—61no—
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—84no—
681C2×D5—121no—
682C2×D5—121no—
683C2×D5—244no—
684C2×D5—244no—
685C2×D5D3×C22⋊C412yes—
686C4×C5—32no—
687C4×C5—41no—
688C4×C5—62no—
689C4×C5—121no—
690C4×C5C22×C4×D311yescharacteristic
691C4×C5C2×D3×D411yescharacteristic
692Dic5—32no—
693Dic5—41no—
694Dic5—121no—
695Dic5D3×C22⋊C412yes—
696C24—101no—
697C24—301no—
698C24—301no—
699#41—34no—
700#41—62no—
701#41—154no—
702#41—154no—
703#41—154no—
704#41—154no—
705#41—302no—
706#41—308no—
707#41—302no—
708C2×Q8—31no—
709C2×Q8—151no—
710C2×D4—54no—
711C2×D4—51no—
712C2×D4—61no—
713C2×D4—102no—
714C2×D4—101no—
715C2×D4—154no—
716C2×D4—151no—
717C2×D4—151no—
718C2×D4—151no—
719C2×D4—154no—
720C2×D4—151no—
721C2×D4—302no—
722C2×D4—301no—
723C2×D4—308no—
724C2×D4—301no—
725C2×D4—301no—
726C2×D4—302no—
727C2×D4—301no—
728C2×D4—308no—
729C2×D4—308no—
730C2×D4C2×D3×D511yescharacteristic
731C22×C4—31no—
732C22×C4—51no—
733C22×C4—61no—
734C22×C4—101no—
735C22×C4—151no—
736C22×C4—301no—
737C22×C4—301no—
738C22×C4—301no—
739C22×C4—301no—
740M16—302no—
741M16—302no—
742M16—302no—
743C2×C8—31no—
744C2×C8—51no—
745C2×C8—62no—
746C2×C8—102no—
747C2×C8—151no—
748C2×C8—302no—
749C2×C8C2×D3×D511yescharacteristic
750C4⋊C4—31no—
751C4⋊C4—51no—
752C4⋊C4—101no—
753C4⋊C4—151no—
754C4⋊C4—301no—
755C4⋊C4—301no—
756C4⋊C4C2×D3×D511yescharacteristic
757C22⋊C4—61no—
758C22⋊C4—301no—
759C22⋊C4—301no—
760C42—61no—
761C42—301no—
762C42—301no—
763C3×C5#289711yescharacteristic, complemented, Hall
764C22×C3—22no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—52no—
768C22×C3—101no—
769C22×C3—101no—
770C22×C3—102no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3—404no—
774C22×C3C2×D4×D511yescharacteristic
775C2×D3—21no—
776C2×D3—21no—
777C2×D3—52no—
778C2×D3—101no—
779C2×D3—101no—
780C2×D3—102no—
781C2×D3—201no—
782C2×D3—201no—
783C2×D3—404no—
784C2×D3—404no—
785C2×D3D5×C22⋊C412yes—
786C3×C4—41no—
787C3×C4—52no—
788C3×C4—201no—
789C3×C4C22×C4×D511yescharacteristic
790C3×C4C2×D4×D511yescharacteristic
791Dic3—22no—
792Dic3—41no—
793Dic3—52no—
794Dic3—201no—
795Dic3D5×C22⋊C412yes—
796C2×C5—42no—
797C2×C5—62no—
798C2×C5C2×D3×C22⋊C411yescharacteristic
799C2×C5#575711yescharacteristic
800C2×C5#576211yescharacteristic
801D5—22no—
802D5—42no—
803D5—62no—
804D5—122no—
805C23—21no—
806C23—31no—
807C23—51no—
808C23—104no—
809C23—101no—
810C23—151no—
811C23—304no—
812C23—304no—
813C23—301no—
814C23—401no—
815C23—401no—
816C23—1201no—
817C23—1201no—
818C23—1201no—
819C23—1201no—
820Q8—32no—
821Q8—61no—
822Q8—154no—
823D4—21no—
824D4—52no—
825D4—64no—
826D4—104no—
827D4—101no—
828D4—154no—
829D4—154no—
830D4—154no—
831D4—152no—
832D4—304no—
833D4—304no—
834D4—304no—
835D4—304no—
836D4—301no—
837D4C4×D3×D512yes—
838C2×C4—21no—
839C2×C4—31no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—51no—
843C2×C4—52no—
844C2×C4—52no—
845C2×C4—64no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—101no—
849C2×C4—151no—
850C2×C4—152no—
851C2×C4—152no—
852C2×C4—304no—
853C2×C4—304no—
854C2×C4—301no—
855C2×C4—401no—
856C2×C4—1201no—
857C2×C4—1201no—
858C2×C4C22×D3×D511yescharacteristic
859C8—21no—
860C8—61no—
861C8—101no—
862C8—301no—
863C2×C3—42no—
864C2×C3—102no—
865C2×C3—202no—
866C2×C3C2×D5×C22⋊C411yescharacteristic
867C2×C3#6610311yescharacteristic
868C2×C3#6610411yescharacteristic
869D3—22no—
870D3—102no—
871D3—202no—
872C5#7874211yescharacteristic, complemented, Sylow
873C22—22no—
874C22—32no—
875C22—41no—
876C22—41no—
877C22—52no—
878C22—61no—
879C22—61no—
880C22—101no—
881C22—101no—
882C22—102no—
883C22—152no—
884C22—201no—
885C22—201no—
886C22—301no—
887C22—301no—
888C22—302no—
889C22—404no—
890C22—601no—
891C22—601no—
892C22—1204no—
893C22—1204no—
894C22D3×D4×D511yescharacteristic
895C4—32no—
896C4—41no—
897C4—52no—
898C4—62no—
899C4—121no—
900C4—152no—
901C4—201no—
902C4—601no—
903C4C2×C4×D3×D511yescharacteristic
904C4D3×D4×D511yescharacteristic
905C3#1061056211yescharacteristic, complemented, Sylow
906C2—42no—
907C2—62no—
908C2—102no—
909C2—202no—
910C2—302no—
911C2—602no—
912C2D3×D5×C22⋊C411yescharacteristic
913C2#1175405811yescharacteristic
914C2#1175408711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#92026C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#91265C2semidirect
3. #11753668C2semidirect
4. D15×#102C2semidirect
5. C5×#4772C2semidirect
6. C3×D5×#102C2semidirect
7. #11748972C2semidirect
8. #11748962C2semidirect
9. #11748955C2semidirect
10. #11748141C2semidirect
11. D3×#3953C2semidirect
12. #11747642C2semidirect
13. #11747507C2semidirect
14. #11747500C2semidirect
15. #11747477C2semidirect
25. #92026C4semidirect
30. C2×C8×D15C22semidirect
31. C4⋊C4×D15C22semidirect
32. C2×C5×D3×C8C22semidirect
33. C5×#892C22semidirect
34. C2×C3×C8×D5C22semidirect
35. C3×D5×C4⋊C4C22semidirect
38. D3×C4⋊Dic5C22semidirect
40. #91358C22semidirect
41. #91347C22semidirect
43. C2×#6651C22semidirect
44. C2×#6650C22semidirect
45. C2×#6649C22semidirect
47. C3×C5×#102C22semidirect
48. #91116C22semidirect
49. #91105C22semidirect
50. #91093C22semidirect
51. C5×#832C22semidirect
52. C5×#816C22semidirect
53. C5×#810C22semidirect
54. C3×#3964C22semidirect
55. C3×#3953C22semidirect
56. C3×#3941C22semidirect
57. #90973C22semidirect
58. #90972C22semidirect
59. #90969C22semidirect
60. #90968C22semidirect
61. #90965C22semidirect
62. #90964C22semidirect
78. D5×#102D3semidirect
85. D4×D15C2×C4semidirect
92. C5×#237C2×C4semidirect
97. C3×D4×D5C2×C4semidirect
116. D3×D20C2×C4semidirect
118. #6773C2×C4semidirect
122. #6766C2×C4semidirect
154. #4772D5semidirect
182. C2×C8×D5C2×D3semidirect
186. D5×C4⋊C4C2×D3semidirect
194. C5×#102C2×D3semidirect
198. #3964C2×D3semidirect
202. #3953C2×D3semidirect
206. #3941C2×D3semidirect
289. C2×D3×C8C2×D5semidirect
292. #892C2×D5semidirect
299. C3×#102C2×D5semidirect
303. #832C2×D5semidirect
307. #816C2×D5semidirect
309. #810C2×D5semidirect
336. D4×D5C4×D3semidirect
451. #237C4×D5semidirect
596. #102D3×D5semidirect
763. C3×C5#2897semidirect
872. C5#78742semidirect
905. C3#10610562semidirect

Maximal subgroups

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

subgroupindex
C2×#920262
C2×#912652
#117536682
D15×#1022
C5×#47722
C3×D5×#1022
#117489722
#117489622
#117489552
#117481412
D3×#39532
#117476422
#117475072
#117475002
#117474772
#106105623
#787425