Finite Group Databasebeta

← #14412638

Subgroups — #14412638

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×#92027C211yesmaximal, characteristic
2C2×#91265C211yesmaximal, characteristic, complemented
3#11753669C211yesmaximal, characteristic, complemented
4D15×#102C211yesmaximal, characteristic, complemented
5C5×D3×#102C211yesmaximal, characteristic, complemented
6C3×#65061C211yesmaximal, characteristic, complemented
7#11748972C211yesmaximal, characteristic, complemented
8#11748967C211yesmaximal, characteristic, complemented
9#11748951C211yesmaximal, characteristic, complemented
10#11748145C211yesmaximal, characteristic, complemented
11D5×#821C211yesmaximal, characteristic, complemented
12#11747643C211yesmaximal, characteristic, complemented
13#11747509C211yesmaximal, characteristic, complemented
14#11747505C211yesmaximal, characteristic, complemented
15#11747475C211yesmaximal, characteristic, complemented
16#10610473—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic
20C2×#6790—21no—
21C2×D3×C22⋊D5—21no—
22C22×#1203—21no—
23C2×#6782—21no—
24#92027—24no—
25#92027C418yescomplemented
26C2×D5×D12C2211yescharacteristic
27C2×#6771C2211yescharacteristic
28C2×#6769C2211yescharacteristic
29C2×#6768C2211yescharacteristic
30C2×C8×D15C2211yescharacteristic, complemented
31C4⋊C4×D15C2211yescharacteristic, complemented
32C2×C5×D3×C8C2211yescharacteristic, 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×#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×#821C2211yescharacteristic, complemented
53C5×#809C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3948C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57#90971C2211yescharacteristic, complemented
58#90970C2211yescharacteristic, complemented
59#90969C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90967C2211yescharacteristic, complemented
62#90966C2211yescharacteristic, complemented
63#78831—51nomaximal, Hall
64C2×#4144—31no—
65C2×#4047—31no—
66#65838—31no—
67C2×C5×#102—31no—
68#65504—31no—
69#65402—31no—
70#65255—31no—
71#65061—31no—
72#65061D311yescharacteristic, complemented
73#65060—31no—
74#65060—31no—
75#65059—31no—
76#65059—31no—
77D5×#102—31no—
78D5×#102—31no—
79C23×D15—21no—
80C23×C5×D3—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—
90C5×D3×D4—22no—
91C5×D3×D4C2×C414yescomplemented
92C2×C5×D12C2311yescharacteristic
93C2×C4×C5×D3—21no—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C22×C3×Dic5—21no—
97C3×#711—22no—
98C3×#711C2×C414yescomplemented
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10C2311yescharacteristic
101#6790—28no—
102D3×C22⋊D5—28no—
103C2×#1204D411yescharacteristic
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1203—21no—
107C2×#1203—28no—
108C2×#1203D411yescharacteristic
109C2×#1202D411yescharacteristic
110C2×#1201D411yescharacteristic
111C2×#1200—21no—
112#6782—28no—
113C2×D3×Dic5—21no—
114C2×D5×Dic3—21no—
115D5×D12—22no—
116D5×D12C2×C414yescomplemented
117#6771C2×C414yes—
118#6771D414yes—
119#6769—22no—
120#6769C2×C414yescomplemented
121#6768—22no—
122#6768C2×C414yescomplemented
123C2×C3×C5×C8C2311yescharacteristic
124C3×C5×C4⋊C4C2311yescharacteristic
125C4⋊Dic15C2311yescharacteristic
126#6712—21no—
127C2×C3⋊#168C2311yescharacteristic
128C8×D15—22no—
129C5×C4⋊Dic3C2311yescharacteristic
130C5×Dic3⋊C4—21no—
131C2×C5×C3⋊C8C2311yescharacteristic
132C5×D3×C8—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#6651—22no—
144#6650—22no—
145#6649—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#4803—51no—
157#4770—51no—
158#4770—51no—
159D3×#102—51no—
160D3×#102D511yescharacteristic, complemented
161C22×C5×D4—31no—
162C22×C22⋊D5—61no—
163C22×C22⋊D5—61no—
164#4144—38no—
165#4144—64no—
166C2×#711—31no—
167C2×#711—61no—
168C2×#711C2×D311yescharacteristic
169C2×D4×D5—31no—
170C2×D4×D5—31no—
171C2×D4×D5—61no—
172C2×#709—31no—
173C2×#709—31no—
174C22×C5×C8—31no—
175C2×C5×C4⋊C4—31no—
176C4×C22⋊D5—61no—
177C4×C22⋊D5—61no—
178#4072—31no—
179C2×#681—31no—
180#4047—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×#102—31no—
192C5×#102—31no—
193C5×#102—31no—
194C5×#102C2×D311yescharacteristic, complemented
195#3964—31no—
196#3964—31no—
197#3964—31no—
198#3964C2×D311yescharacteristic, complemented
199#3953—31no—
200#3953—31no—
201#3948—31no—
202#3948C2×D311yescharacteristic, complemented
203#3942—31no—
204#3942C2×D311yescharacteristic, complemented
205#3941—31no—
206#3941—31no—
207#2897—151noSylow
208C23×C3×C5—21no—
209C22×D15—21no—
210C22×D15—24no—
211C22×D15—81no—
212C22×D15—81no—
213C22×D15C2×D411yescharacteristic
214C22×C5×D3—21no—
215C22×C5×D3—24no—
216C22×C5×D3—81no—
217C22×C5×D3—81no—
218C22×C5×D3C2×D411yescharacteristic
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×Dic3C2×D411yescharacteristic
238C5×D12—21no—
239C5×D12C22×C412yes—
240C4×C5×D3—81no—
241C4×C5×D3C22×C412yes—
242C4×C5×D3C2×D412yes—
243C3×C22⋊D5—24no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—24no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C2×D411yescharacteristic
248C3×C4×D5C22×C412yes—
249C3×C4×D5C2×D412yes—
250C3×Dic10—21no—
251C3×Dic10C22×C412yes—
252#1204C22⋊C414yes—
253#1203—24no—
254#1203—24no—
255#1203—24no—
256#1203C22⋊C414yes—
257#1202C22⋊C414yes—
258#1201C22⋊C414yes—
259#1200—24no—
260D3×Dic5—24no—
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×#239—51no—
271C2×D3×D4—51no—
272C2×D3×D4—101no—
273C2×D3×D4—101no—
274C2×D3×D4C2×D511yescharacteristic
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)—51no—
286C2×D3×C8—51no—
287C2×D3×C8C2×D511yescharacteristic, complemented
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×#103—51no—
298C3×#102—51no—
299C3×#102C2×D511yescharacteristic, complemented
300#835—51no—
301#835—51no—
302#832—51no—
303#832C2×D511yescharacteristic, complemented
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
312C24×C5—61no—
313C23×D5—61no—
314C23×D5—61no—
315C2×C5×D4—34no—
316C2×C5×D4—31no—
317C2×C5×D4—62no—
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—68no—
326C2×C22⋊D5—61no—
327C2×C22⋊D5—61no—
328C2×C22⋊D5—61no—
329C2×C22⋊D5—68no—
330C2×C22⋊D5—61no—
331C22×Dic5—21no—
332C22×Dic5—61no—
333#711—22no—
334#711—34no—
335#711—62no—
336#711—68no—
337#711C4×D314yescomplemented
338D4×D5—34no—
339D4×D5—34no—
340D4×D5—62no—
341D4×D5—68no—
342D4×D5—62no—
343#709—34no—
344#709—34no—
345#709—34no—
346#709—62no—
347C2×D20—31no—
348C2×D20—31no—
349C2×C4×D5—31no—
350C2×C4×D5—61no—
351C2×C4×D5—61no—
352C2×C4×D5—61no—
353C2×C4×D5C22×D311yescharacteristic
354C2×Dic10—31no—
355C2×Dic10C22×D311yescharacteristic
356C2×C5×C8—31no—
357C2×C5×C8—62no—
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—
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—51no—
389#416—151no—
390#416—151no—
391C2×#102—31no—
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×D3—22no—
408C2×C5×D3—41no—
409C2×C5×D3—41no—
410C2×C5×D3—84no—
411C2×C5×D3C2×C22⋊C412yes—
412C2×C3×D5—21no—
413C2×C3×D5—21no—
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—22no—
422C3×Dic5—41no—
423C3×Dic5C2×C22⋊C412yes—
424C5×Dic3—41no—
425C5×Dic3C2×C22⋊C412yes—
426C23×D3—21no—
427C23×D3—101no—
428C23×D3—101no—
429C3×#41—54no—
430C3×#41—102no—
431C2×C3×Q8—51no—
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—101no—
440C22×Dic3—101no—
441#239—54no—
442#239—54no—
443#239—102no—
444#239—102no—
445D3×D4—22no—
446D3×D4—54no—
447D3×D4—102no—
448D3×D4—108no—
449D3×D4—108no—
450D3×D4C4×D514yescomplemented
451#235—54no—
452#235—54no—
453#235—108no—
454C2×D12—51no—
455C2×D12—51no—
456C2×D12—54no—
457C2×D12—102no—
458C2×D12—108no—
459C2×D12—101no—
460C2×D12—101no—
461C2×D12—101no—
462C2×D12C22×D511yescharacteristic
463C2×C4×D3—21no—
464C2×C4×D3—51no—
465C2×C4×D3—101no—
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)—102no—
490ΓL(1,𝔽25)—102no—
491D3×C8—22no—
492D3×C8—102no—
493C23×C5—21no—
494C23×C5—31no—
495C23×C5—64no—
496C23×C5—61no—
497C23×C5—241no—
498C23×C5—241no—
499C22×D5—31no—
500C22×D5—64no—
501C22×D5—61no—
502C22×D5—64no—
503C22×D5—241no—
504C22×D5—241no—
505C22×D5—241no—
506C22×D5—241no—
507C22×D5D3×D411yescharacteristic
508C5×D4—21no—
509C5×D4—32no—
510C5×D4—64no—
511C5×D4—61no—
512C5×D4C2×C4×D312yes—
513C2×C4×C5—21no—
514C2×C4×C5—31no—
515C2×C4×C5—32no—
516C2×C4×C5—32no—
517C2×C4×C5—61no—
518C2×C4×C5—241no—
519C2×C4×C5C23×D311yescharacteristic
520C22⋊D5—24no—
521C22⋊D5—34no—
522C22⋊D5—34no—
523C22⋊D5—64no—
524C22⋊D5—64no—
525C22⋊D5—64no—
526C22⋊D5—64no—
527C2×Dic5—21no—
528C2×Dic5—24no—
529C2×Dic5—21no—
530C2×Dic5—31no—
531C2×Dic5—64no—
532C2×Dic5—61no—
533C2×Dic5D3×D411yescharacteristic
534D20—34no—
535D20—32no—
536D20—61no—
537C4×D5—32no—
538C4×D5—32no—
539C4×D5—64no—
540C4×D5—241no—
541C4×D5—241no—
542C4×D5C2×C4×D312yes—
543C4×D5D3×D412yes—
544Dic10—21no—
545Dic10—34no—
546Dic10C2×C4×D312yes—
547C5×C8—21no—
548C5×C8—61no—
549#168—21no—
550#168—61no—
551H(5,𝔽2)—158no—
552H(5,𝔽2)—304no—
553C2×#41—51no—
554C2×#41—151no—
555C2×#41—151no—
556C2×#41—151no—
557C2×#41—301no—
558C22×D4—31no—
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—51no—
576#117—151no—
577#117—151no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—151no—
580C2×C4⋊C4—151no—
581#103—51no—
582#103—51no—
583#103—151no—
584#103—151no—
585#102—31no—
586#102—31no—
587#102—31no—
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—
604C5×D3—22no—
605C5×D3—42no—
606C23×C3—21no—
607C23×C3—51no—
608C22×D3—21no—
609C22×D3—24no—
610C22×D3—51no—
611C22×D3—81no—
612C22×D3—81no—
613C22×D3—104no—
614C22×D3—104no—
615C22×D3—101no—
616C22×D3—401no—
617C22×D3—401no—
618C22×D3—401no—
619C22×D3—401no—
620C22×D3D4×D511yescharacteristic
621C3×Q8—52no—
622C3×Q8—101no—
623C3×D4—21no—
624C3×D4—104no—
625C3×D4C2×C4×D512yes—
626C2×C3×C4—21no—
627C2×C3×C4—51no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—104no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4C23×D511yescharacteristic
634#67—24no—
635#67—54no—
636#67—54no—
637#67—104no—
638C2×Dic3—21no—
639C2×Dic3—51no—
640C2×Dic3—101no—
641C2×Dic3—401no—
642C2×Dic3D4×D511yescharacteristic
643D12—21no—
644D12—54no—
645D12—52no—
646D12—104no—
647D12—104no—
648D12—104no—
649D12—101no—
650D12C2×C4×D512yes—
651C4×D3—52no—
652C4×D3—52no—
653C4×D3—81no—
654C4×D3—104no—
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—22no—
665C22×C5—32no—
666C22×C5—41no—
667C22×C5—41no—
668C22×C5—61no—
669C22×C5—61no—
670C22×C5—62no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5—244no—
674C22×C5C2×D3×D411yescharacteristic
675C2×D5—21no—
676C2×D5—21no—
677C2×D5—32no—
678C2×D5—61no—
679C2×D5—61no—
680C2×D5—62no—
681C2×D5—121no—
682C2×D5—121no—
683C2×D5—244no—
684C2×D5—244no—
685C2×D5D3×C22⋊C412yes—
686C4×C5—32no—
687C4×C5—41no—
688C4×C5—121no—
689C4×C5C22×C4×D311yescharacteristic
690C4×C5C2×D3×D411yescharacteristic
691Dic5—22no—
692Dic5—32no—
693Dic5—41no—
694Dic5—121no—
695Dic5D3×C22⋊C412yes—
696C24—61no—
697C24—301no—
698C24—301no—
699#41—54no—
700#41—102no—
701#41—154no—
702#41—154no—
703#41—154no—
704#41—154no—
705#41—302no—
706#41—308no—
707#41—302no—
708C2×Q8—51no—
709C2×Q8—151no—
710C2×D4—34no—
711C2×D4—31no—
712C2×D4—62no—
713C2×D4—61no—
714C2×D4—101no—
715C2×D4—151no—
716C2×D4—154no—
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—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—22no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—52no—
768C22×C3—101no—
769C22×C3—101no—
770C22×C3C2×D4×D511yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—52no—
777C2×D3—84no—
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—102no—
789C3×C4—201no—
790C3×C4C22×C4×D511yescharacteristic
791C3×C4C2×D4×D511yescharacteristic
792Dic3—41no—
793Dic3—52no—
794Dic3—201no—
795Dic3D5×C22⋊C412yes—
796C2×C5—42no—
797C2×C5—62no—
798C2×C5—122no—
799C2×C5C2×D3×C22⋊C411yescharacteristic
800C2×C5#576911yescharacteristic
801C2×C5#577011yescharacteristic
802D5—22no—
803D5—62no—
804D5—122no—
805C23—21no—
806C23—31no—
807C23—51no—
808C23—64no—
809C23—61no—
810C23—151no—
811C23—241no—
812C23—241no—
813C23—304no—
814C23—304no—
815C23—301no—
816C23—1201no—
817C23—1201no—
818C23—1201no—
819C23—1201no—
820Q8—52no—
821Q8—101no—
822Q8—154no—
823D4—21no—
824D4—32no—
825D4—64no—
826D4—61no—
827D4—104no—
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—61no—
846C2×C4—104no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—151no—
850C2×C4—152no—
851C2×C4—152no—
852C2×C4—241no—
853C2×C4—304no—
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—42no—
864C2×C3—102no—
865C2×C3C2×D5×C22⋊C411yescharacteristic
866C2×C3#6609111yescharacteristic
867C2×C3#6609611yescharacteristic
868D3—22no—
869D3—42no—
870D3—102no—
871D3—202no—
872C5#7883111yescharacteristic, complemented, Sylow
873C22—22no—
874C22—32no—
875C22—41no—
876C22—41no—
877C22—52no—
878C22—61no—
879C22—61no—
880C22—62no—
881C22—101no—
882C22—101no—
883C22—121no—
884C22—121no—
885C22—152no—
886C22—244no—
887C22—301no—
888C22—301no—
889C22—302no—
890C22—601no—
891C22—601no—
892C22—1204no—
893C22—1204no—
894C22D3×D4×D511yescharacteristic
895C4—32no—
896C4—41no—
897C4—52no—
898C4—102no—
899C4—121no—
900C4—152no—
901C4—201no—
902C4—601no—
903C4C2×C4×D3×D511yescharacteristic
904C4D3×D4×D511yescharacteristic
905C3#1061047311yescharacteristic, complemented, Sylow
906C2—42no—
907C2—62no—
908C2—102no—
909C2—122no—
910C2—302no—
911C2—602no—
912C2D3×D5×C22⋊C411yescharacteristic
913C2#1175406111yescharacteristic
914C2#1175409211yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#92027C2
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. #11753669C2semidirect
4. D15×#102C2semidirect
5. C5×D3×#102C2semidirect
6. C3×#65061C2semidirect
7. #11748972C2semidirect
8. #11748967C2semidirect
9. #11748951C2semidirect
10. #11748145C2semidirect
11. D5×#821C2semidirect
12. #11747643C2semidirect
13. #11747509C2semidirect
14. #11747505C2semidirect
15. #11747475C2semidirect
25. #92027C4semidirect
30. C2×C8×D15C22semidirect
31. C4⋊C4×D15C22semidirect
32. C2×C5×D3×C8C22semidirect
33. C5×D3×C4⋊C4C22semidirect
34. C2×C3×C8×D5C22semidirect
35. C3×#4038C22semidirect
38. D5×C4⋊Dic3C22semidirect
40. #91347C22semidirect
41. #91338C22semidirect
43. C2×#6651C22semidirect
44. C2×#6650C22semidirect
45. C2×#6649C22semidirect
47. C3×C5×#102C22semidirect
48. #91116C22semidirect
49. #91105C22semidirect
50. #91093C22semidirect
51. C5×#832C22semidirect
52. C5×#821C22semidirect
53. C5×#809C22semidirect
54. C3×#3964C22semidirect
55. C3×#3948C22semidirect
56. C3×#3942C22semidirect
57. #90971C22semidirect
58. #90970C22semidirect
59. #90969C22semidirect
60. #90968C22semidirect
61. #90967C22semidirect
62. #90966C22semidirect
72. #65061D3semidirect
85. D4×D15C2×C4semidirect
91. C5×D3×D4C2×C4semidirect
98. C3×#711C2×C4semidirect
116. D5×D12C2×C4semidirect
120. #6769C2×C4semidirect
122. #6768C2×C4semidirect
160. D3×#102D5semidirect
184. C2×C8×D5C2×D3semidirect
187. #4038C2×D3semidirect
194. C5×#102C2×D3semidirect
198. #3964C2×D3semidirect
202. #3948C2×D3semidirect
204. #3942C2×D3semidirect
287. C2×D3×C8C2×D5semidirect
291. D3×C4⋊C4C2×D5semidirect
299. C3×#102C2×D5semidirect
303. #832C2×D5semidirect
307. #821C2×D5semidirect
311. #809C2×D5semidirect
337. #711C4×D3semidirect
450. D3×D4C4×D5semidirect
596. #102D3×D5semidirect
763. C3×C5#2897semidirect
872. C5#78831semidirect
905. C3#10610473semidirect

Maximal subgroups

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

subgroupindex
C2×#920272
C2×#912652
#117536692
D15×#1022
C5×D3×#1022
C3×#650612
#117489722
#117489672
#117489512
#117481452
D5×#8212
#117476432
#117475092
#117475052
#117474752
#106104733
#788315