Finite Group Databasebeta

← #14458317

Subgroups — #14458317

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65841C211yesmaximal, characteristic, complemented
2D12×C22⋊D5C211yesmaximal, characteristic, complemented
3#11751068C211yesmaximal, characteristic, complemented
4C2×C5×#809C211yesmaximal, characteristic, complemented
5#11748518C211yesmaximal, characteristic, complemented
6#11748516C211yesmaximal, characteristic, complemented
7C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
8#11747480C211yesmaximal, characteristic, complemented
9D5×#809C211yesmaximal, characteristic, complemented
10#11747399C211yesmaximal, characteristic, complemented
11#11747307C211yesmaximal, characteristic, complemented
12#11747306C211yesmaximal, characteristic, complemented
13#11747237C211yesmaximal, characteristic, complemented
14#11747216C211yesmaximal, characteristic, complemented
15#11747138C211yesmaximal, characteristic, complemented
16#10610488—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×C3×#709—21no—
19C2×D3×C22⋊D5—21no—
20C2×D5×D12C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
22#91819C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C3×#4076C2211yescharacteristic, complemented
25C3×#4075—21no—
26C3×C4×C22⋊D5C2211yescharacteristic
27C3×#4042—21no—
28C3×#4041C2211yescharacteristic, complemented
29C3×#4040—21no—
30C3×#4039C2211yescharacteristic, complemented
31C3×D5×C4⋊C4C2211yescharacteristic, complemented
32C3×#4034C2211yescharacteristic, complemented
33#91570—21no—
34#91475—21no—
35#91451C2211yescharacteristic
36#91449C2211yescharacteristic
37#91416—21no—
38Dic5×D12C2211yescharacteristic
39C2×#6653C2211yescharacteristic, complemented
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic, complemented
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91114C2211yescharacteristic, complemented
44#91093C2211yescharacteristic, complemented
45#91093C2211yescharacteristic, complemented
46#91091C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C5×#809C2211yescharacteristic
49C5×#809C2211yescharacteristic
50C5×#809C2211yescharacteristic, complemented
51C5×#809C2211yescharacteristic, complemented
52#90990C2211yescharacteristic, complemented
53#90982C2211yescharacteristic, complemented
54#90968C2211yescharacteristic, complemented
55#90966C2211yescharacteristic
56#90966C2211yescharacteristic, complemented
57#90965C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83525—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65841D311yescharacteristic, complemented
63C2×C5×#102—31no—
64#65506—31no—
65#65404—31no—
66C8×C22⋊D5—31no—
67#65256—31no—
68#65075—31no—
69#65064—31no—
70#65063—31no—
71#65062—31no—
72D5×#102—31no—
73#65049—31no—
74#65048—31no—
75#65045—31no—
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×D60C2311yescharacteristic
82C2×C5×D12—22no—
83C2×C5×D12—21no—
84C2×C5×D12—41no—
85C2×C5×D12C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5D411yescharacteristic
89C3×#709—44no—
90C2×C3×D20—21no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5C2311yescharacteristic
95C2×C3×Dic10—21no—
96D3×C22⋊D5—44no—
97C2×#1203—21no—
98C2×#1203—21no—
99C2×#1203—21no—
100C2×#1201—21no—
101C2×D3×Dic5—21no—
102D5×D12—22no—
103D5×D12—41no—
104C3×C5×C4⋊C4—21no—
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C4⋊C4C2311yescharacteristic
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111C2×C5×C3⋊C8—41no—
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C22⋊Dic5D411yescharacteristic
115C3×#685—21no—
116C3×#685—21no—
117C3×#685—21no—
118C3×#685D411yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×#683—21no—
121C3×#683—21no—
122C3×#683D411yescharacteristic
123C3×C4×Dic5C2311yescharacteristic
124(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126#6653—41no—
127#6652—22no—
128#6652—41no—
129D5×C3⋊C8—41no—
130C3×#547—51no—
131D4×D12—51no—
132#5088—51no—
133#5087—51no—
134#5038—51no—
135#5038—51no—
136#5036—51no—
137#5036—51no—
138#5015—51no—
139C4×#213—51no—
140D4×C3⋊C8—51no—
141#4967—51no—
142#4967—51no—
143C2×#809—51no—
144C2×#809D511yescharacteristic, complemented
145C22×C5×D4—31no—
146C22×C22⋊D5—61no—
147C2×D4×D5—31no—
148C2×#709—21no—
149C22×C5×C8—31no—
150C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
151#4099—61no—
152#4086—31no—
153#4085—61no—
154#4084—31no—
155#4083—61no—
156D4×Dic5—31no—
157C2×#686—31no—
158C2×#686—31no—
159#4076—31no—
160#4076C2×D311yescharacteristic, complemented
161#4075—21no—
162C4×C22⋊D5C2×D311yescharacteristic
163C2×D40—31no—
164C2×C8×D5—31no—
165#4042—21no—
166#4041C2×D311yescharacteristic, complemented
167#4040—21no—
168#4039C2×D311yescharacteristic, complemented
169D5×C4⋊C4C2×D311yescharacteristic, complemented
170#4034C2×D311yescharacteristic, complemented
171C5×#102—31no—
172C5×#102—31no—
173C5×#102—31no—
174C5×#102—31no—
175#3964—31no—
176#3964—31no—
177C22⋊#168—31no—
178#3953—31no—
179#3953—31no—
180#3952—31no—
181#3950—31no—
182#3946—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941—31no—
186#3939—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—42no—
194C22×C5×D3—42no—
195C22×C5×D3—81no—
196C22×C3×D5—21no—
197C22×C3×D5C2×D411yescharacteristic
198C2×D3×D5—42no—
199C2×D3×D5—42no—
200C2×D3×D5—81no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208#1220—42no—
209C2×Dic15—21no—
210D60—21no—
211D60—21no—
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—21no—
215C5×D12—42no—
216C5×D12#4112yescomplemented
217C3×C22⋊D5—42no—
218C3×C22⋊D5D814yescomplemented
219C2×C3×Dic5—21no—
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C3×D20—21no—
224C3×D20—21no—
225C3×D20—42no—
226C3×C4×D5—21no—
227C3×C4×D5—21no—
228C3×C4×D5—42no—
229C3×C4×D5—42no—
230C3×Dic10—42no—
231#1203—42no—
232#1203—42no—
233#1203—81no—
234#1201—42no—
235D3×Dic5—42no—
236C3⋊#168—21no—
237C3⋊#168—21no—
238C5×C3⋊C8—21no—
239C5×C3⋊C8—21no—
240C2×C3×#41—101no—
241C2×D3×D4—101no—
242C22×D12—51no—
243C22×D12C2×D511yescharacteristic
244C3×C4⋊Q8—51no—
245C3×#123—101no—
246C3×#123—101no—
247C3×C22⋊Q8—101no—
248C3×#121—51no—
249C3×#121—51no—
250C3×C4×D4—51no—
251C3×C4×D4—51no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
254C2×#213—51no—
255C2×#213—51no—
256C2×#213—51no—
257#930—51no—
258#930—51no—
259C22×C3⋊C8—51no—
260C22×C3⋊C8C2×D511yescharacteristic, complemented
261#895—101no—
262#882—101no—
263#882—101no—
264#874—51no—
265C4×D12—51no—
266#832—51no—
267#830—51no—
268#830—51no—
269#809—51no—
270#809—51no—
271#809—51no—
272#809—51no—
273#809—51no—
274#809C2×D511yescharacteristic
275#809C2×D511yescharacteristic
276#809C2×D511yescharacteristic, complemented
277#809C2×D511yescharacteristic, complemented
278#807—51no—
279#807—51no—
280#807—51no—
281C4⋊(C3⋊C8)—51no—
282C4×C3⋊C8—51no—
283C24×C5—61no—
284C23×D5—61no—
285C2×C5×D4—31no—
286C2×C5×D4—31no—
287C2×C5×D4—62no—
288C2×C5×D4—61no—
289C2×C5×D4—121no—
290C22×C4×C5—21no—
291C22×C4×C5C22×D311yescharacteristic
292C2×C22⋊D5—21no—
293C2×C22⋊D5—61no—
294C2×C22⋊D5—61no—
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—124no—
299C2×C22⋊D5#6711yescharacteristic
300C22×Dic5—61no—
301D4×D5—62no—
302D4×D5—121no—
303#709—44no—
304C2×D20—21no—
305C2×D20—31no—
306C2×D20C22×D311yescharacteristic
307C2×C4×D5—21no—
308C2×C4×D5—21no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—21no—
311C2×C5×C8—31no—
312C2×C5×C8—31no—
313C2×C5×C8—121no—
314C5×C4⋊C4—21no—
315C5×C4⋊C4C22×D311yescharacteristic
316C5×C4⋊C4C22×D311yescharacteristic
317C22⋊Dic5—61no—
318C22⋊Dic5—61no—
319C22⋊Dic5#6711yescharacteristic
320#686—62no—
321#686—121no—
322#685—21no—
323#685—21no—
324#685—21no—
325#685—61no—
326#685#6711yescharacteristic
327C4⋊Dic5—31no—
328C4⋊Dic5C22×D311yescharacteristic
329#683—21no—
330#683—21no—
331#683#6711yescharacteristic
332C4×Dic5C22×D311yescharacteristic
333C2×#168—31no—
334C2×#168—31no—
335D40—121no—
336C8×D5—121no—
337#547—51no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—151no—
347#447—151no—
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—31no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5C2×D812yes—
355C22×C3×C5C22×D411yescharacteristic
356C2×D15—41no—
357C2×D15—41no—
358C2×D15—41no—
359C2×C5×D3—22no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—41no—
363C2×C5×D3—41no—
364C2×C5×D3—41no—
365C2×C5×D3—84no—
366C2×C3×D5—21no—
367C2×C3×D5—21no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—41no—
371C2×C3×D5C2×D812yes—
372D3×D5—84no—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5—41no—
376C3×C4×C5C2×#4111yescharacteristic
377C3×C4×C5H(5,𝔽2)11yescharacteristic
378Dic15—41no—
379C3×Dic5—21no—
380C3×Dic5—21no—
381C3×Dic5—41no—
382C3×Dic5C2×D812yes—
383C23×D3—21no—
384C23×D3—101no—
385C3×#41—204no—
386C2×C3×Q8—101no—
387C2×C3×D4—51no—
388C2×C3×D4—51no—
389C2×C3×D4—101no—
390C2×C3×D4—101no—
391C22×C3×C4—21no—
392C22×C3×C4—51no—
393C22×C3×C4—101no—
394C22×C3×C4—101no—
395C22×C3×C4C22×D511yescharacteristic
396C2×#67—101no—
397C2×#67—101no—
398D3×D4—204no—
399C2×D12—22no—
400C2×D12—21no—
401C2×D12—41no—
402C2×D12—51no—
403C2×D12—102no—
404C2×D12—101no—
405C2×D12—101no—
406C2×D12—101no—
407C2×D12—201no—
408C2×D12C22×D511yescharacteristic
409C2×D12C22×D511yescharacteristic
410C2×C4×D3—101no—
411C3×C4⋊C4—21no—
412C3×C4⋊C4—51no—
413C3×C4⋊C4—51no—
414C3×C4⋊C4—101no—
415C3×C4⋊C4—101no—
416C3×C4⋊C4C22×D511yescharacteristic
417C3×C4⋊C4C22×D511yescharacteristic
418C3×C22⋊C4—51no—
419C3×C22⋊C4—51no—
420C3×C22⋊C4—101no—
421C3×C22⋊C4—101no—
422C3×C22⋊C4—101no—
423C3×C42—51no—
424#213—102no—
425#213—201no—
426#213—201no—
427(C2×D3)⋊C4—101no—
428(C2×D3)⋊C4—101no—
429(C2×D3)⋊C4—101no—
430C4⋊Dic3—51no—
431C2×C3⋊C8—41no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—51no—
434C2×C3⋊C8—201no—
435C2×C3⋊C8C22×D511yescharacteristic
436C2×C3⋊C8C22×D511yescharacteristic
437C23×C5—61no—
438C23×C5—61no—
439C23×C5—122no—
440C23×C5—122no—
441C23×C5—241no—
442C23×C5C2×#6711yescharacteristic
443C22×D5—21no—
444C22×D5—61no—
445C22×D5—122no—
446C22×D5—122no—
447C22×D5—241no—
448C22×D5C2×#6711yescharacteristic
449C5×D4—32no—
450C5×D4—61no—
451C5×D4—61no—
452C5×D4—61no—
453C5×D4—122no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—42no—
459C2×C4×C5C2×#6711yescharacteristic
460C2×C4×C5C23×D311yescharacteristic
461C22⋊D5—42no—
462C22⋊D5—122no—
463C22⋊D5—122no—
464C22⋊D5—122no—
465C22⋊D5—122no—
466C22⋊D5—241no—
467C22⋊D5#21314yescomplemented
468C2×Dic5—21no—
469C2×Dic5—61no—
470C2×Dic5—122no—
471C2×Dic5C2×#6711yescharacteristic
472C2×Dic5C2×#6711yescharacteristic
473C2×Dic5C2×#6711yescharacteristic
474D20—21no—
475D20—21no—
476D20—42no—
477D20—61no—
478D20—61no—
479C4×D5—21no—
480C4×D5—21no—
481C4×D5—42no—
482C4×D5—42no—
483Dic10—42no—
484C5×C8—61no—
485C5×C8—61no—
486#168—61no—
487#168—61no—
488C2×#41—101no—
489C22×D4—31no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—31no—
496C22×C8—151no—
497C4⋊Q8—51no—
498#127—151no—
499#123—101no—
500#123—101no—
501C22⋊Q8—101no—
502#121—51no—
503#121—51no—
504#121—151no—
505#121—151no—
506#121—301no—
507#120—301no—
508#120—301no—
509C4×D4—51no—
510C4×D4—51no—
511C4×D4—151no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4D3×D511yescharacteristic, complemented
514#107—151no—
515#107—151no—
516#107—151no—
517C4⋊C8—151no—
518#102—31no—
519#102—31no—
520#102—31no—
521#102—31no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102—151no—
527#102—151no—
528C22⋊C8—151no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5#54611yescharacteristic
533C2×C3×C5C22×D811yescharacteristic
534C2×C3×C5#57711yescharacteristic
535D15—81no—
536C3×D5—22no—
537C3×D5—81no—
538C5×D3—42no—
539C5×D3—81no—
540C23×C3—51no—
541C23×C3—101no—
542C23×C3D4×D511yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—81no—
548C22×D3—101no—
549C22×D3—202no—
550C22×D3—202no—
551C22×D3—401no—
552C3×Q8—202no—
553C3×D4—54no—
554C3×D4—101no—
555C3×D4—101no—
556C3×D4—202no—
557C3×D4—202no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—42no—
563C2×C3×C4—51no—
564C2×C3×C4—51no—
565C2×C3×C4—51no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—202no—
570C2×C3×C4—202no—
571C2×C3×C4D4×D511yescharacteristic
572C2×C3×C4C23×D511yescharacteristic
573#67—202no—
574#67—202no—
575C2×Dic3—101no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—42no—
580D12—101no—
581D12—101no—
582D12—202no—
583D12—202no—
584D12—401no—
585D12#70912yescomplemented
586C4×D3—202no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—62no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5—121no—
597C22×C5—121no—
598C22×C5—121no—
599C22×C5—244no—
600C22×C5C2×#21312yes—
601C22×C5C22×#6711yescharacteristic
602C2×D5—21no—
603C2×D5—21no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—244no—
611C2×D5C2×#21312yes—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5—41no—
615C4×C5D3×#4111yescharacteristic
616C4×C5#100911yescharacteristic
617Dic5—21no—
618Dic5—21no—
619Dic5—41no—
620Dic5—121no—
621Dic5C2×#21312yes—
622C24—61no—
623C24—301no—
624#41—204no—
625C2×Q8—101no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—51no—
629C2×D4—51no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—101no—
633C2×D4—101no—
634C2×D4—121no—
635C2×D4—151no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—302no—
640C2×D4—301no—
641C2×D4—301no—
642C2×D4—601no—
643C2×D4—604no—
644C22×C4—21no—
645C22×C4—51no—
646C22×C4—101no—
647C22×C4—101no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—121no—
656C2×C8—151no—
657C2×C8—151no—
658C2×C8—601no—
659C4⋊C4—21no—
660C4⋊C4—51no—
661C4⋊C4—51no—
662C4⋊C4—101no—
663C4⋊C4—101no—
664C4⋊C4—151no—
665C4⋊C4C2×D3×D511yescharacteristic
666C4⋊C4C2×D3×D511yescharacteristic
667C22⋊C4—51no—
668C22⋊C4—51no—
669C22⋊C4—101no—
670C22⋊C4—101no—
671C22⋊C4—101no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—51no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—52no—
680C22×C3—101no—
681C22×C3—101no—
682C22×C3—201no—
683C22×C3—201no—
684C22×C3—201no—
685C22×C3D5×D812yes—
686C22×C3C2×D4×D511yescharacteristic
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—84no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—201no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—52no—
702C3×C4—101no—
703C3×C4—101no—
704C3×C4—201no—
705C3×C4C2×#70911yescharacteristic
706C3×C4#414411yescharacteristic
707Dic3—201no—
708C2×C5—22no—
709C2×C5—122no—
710C2×C5—241no—
711C2×C5C22×#21311yescharacteristic
712C2×C5#582911yescharacteristic
713C2×C5#583711yescharacteristic
714D5—22no—
715D5—81no—
716D5—241no—
717C23—51no—
718C23—61no—
719C23—61no—
720C23—101no—
721C23—122no—
722C23—122no—
723C23—241no—
724C23—301no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D5×#6711yescharacteristic
729Q8—202no—
730D4—32no—
731D4—54no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—101no—
736D4—101no—
737D4—122no—
738D4—202no—
739D4—202no—
740D4—301no—
741D4—301no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—602no—
746D4—1201no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—42no—
752C2×C4—51no—
753C2×C4—51no—
754C2×C4—51no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4D5×#6711yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—61no—
765C8—61no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—102no—
770C2×C3—401no—
771C2×C3#6582411yescharacteristic
772C2×C3C2×D5×D811yescharacteristic
773C2×C3#6609611yescharacteristic
774D3—42no—
775D3—81no—
776D3—401no—
777C5#8352511yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—52no—
781C22—62no—
782C22—101no—
783C22—101no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—201no—
790C22—201no—
791C22—201no—
792C22—244no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D5×#21312yes—
798C22C2×D5×#6711yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—52no—
803C4—101no—
804C4—101no—
805C4—201no—
806C4—601no—
807C4D3×#70911yescharacteristic
808C4#9201811yescharacteristic
809C3#1061048811yescharacteristic, complemented, Sylow
810C2—22no—
811C2—102no—
812C2—122no—
813C2—241no—
814C2—401no—
815C2—1201no—
816C2#1175463611yescharacteristic
817C2C2×D5×#21311yescharacteristic
818C2#1175508511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65841C2semidirect
2. D12×C22⋊D5C2semidirect
3. #11751068C2semidirect
4. C2×C5×#809C2semidirect
5. #11748518C2semidirect
6. #11748516C2semidirect
7. C3⋊C8×C22⋊D5C2semidirect
8. #11747480C2semidirect
9. D5×#809C2semidirect
10. #11747399C2semidirect
11. #11747307C2semidirect
12. #11747306C2semidirect
13. #11747237C2semidirect
14. #11747216C2semidirect
15. #11747138C2semidirect
21. C2×C3×C5×C4⋊C4C22semidirect
23. C22×C5×C3⋊C8C22semidirect
24. C3×#4076C22semidirect
28. C3×#4041C22semidirect
30. C3×#4039C22semidirect
31. C3×D5×C4⋊C4C22semidirect
32. C3×#4034C22semidirect
39. C2×#6653C22semidirect
41. C2×#6652C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91114C22semidirect
44. #91093C22semidirect
45. #91093C22semidirect
46. #91091C22semidirect
47. #91091C22semidirect
50. C5×#809C22semidirect
51. C5×#809C22semidirect
52. #90990C22semidirect
53. #90982C22semidirect
54. #90968C22semidirect
56. #90966C22semidirect
57. #90965C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
62. #65841D3semidirect
144. C2×#809D5semidirect
150. C2×C5×C4⋊C4C2×D3semidirect
160. #4076C2×D3semidirect
166. #4041C2×D3semidirect
168. #4039C2×D3semidirect
169. D5×C4⋊C4C2×D3semidirect
170. #4034C2×D3semidirect
216. C5×D12#41semidirect
218. C3×C22⋊D5D8semidirect
253. C2×C3×C4⋊C4C2×D5semidirect
260. C22×C3⋊C8C2×D5semidirect
276. #809C2×D5semidirect
277. #809C2×D5semidirect
467. C22⋊D5#213semidirect
513. C2×C4⋊C4D3×D5semidirect
585. D12#709semidirect
676. C3×C5#3294semidirect
777. C5#83525semidirect
809. C3#10610488semidirect

Maximal subgroups

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

subgroupindex
C3×#658412
D12×C22⋊D52
#117510682
C2×C5×#8092
#117485182
#117485162
C3⋊C8×C22⋊D52
#117474802
D5×#8092
#117473992
#117473072
#117473062
#117472372
#117472162
#117471382
#106104883
#835255