Finite Group Databasebeta

← #14458359

Subgroups — #14458359

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×#65943C211yesmaximal, characteristic, complemented
2#11754325C211yesmaximal, characteristic, complemented
3#11751139C211yesmaximal, characteristic, complemented
4C5×#5033C211yesmaximal, characteristic, complemented
5#11749102C211yesmaximal, characteristic, complemented
6#11749022C211yesmaximal, characteristic, complemented
7#11748976C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic, complemented
9#11748512C211yesmaximal, characteristic, complemented
10#11748493C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12#11747442C211yesmaximal, characteristic, complemented
13#11747410C211yesmaximal, characteristic, complemented
14#11747223C211yesmaximal, characteristic, complemented
15#11747192C211yesmaximal, characteristic, complemented
16#10613033—31nomaximal, Hall
17C2×C3×D4×D5—21no—
18C2×C3×D4×D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C2×#6779—21no—
21C3×C5×#121C2211yescharacteristic
22C2×#6715C2211yescharacteristic, complemented
23#91819C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C3×#4086C2211yescharacteristic
27C3×#4083—21no—
28C3×C4×C22⋊D5C2211yescharacteristic
29C3×#4041C2211yescharacteristic
30C3×#4039C2211yescharacteristic
31C3×#4030—21no—
32C3×#4028—21no—
33#91542—21no—
34#91468C2211yescharacteristic, complemented
35#91450C2211yescharacteristic, complemented
36#91419—21no—
37#91418C2211yescharacteristic, complemented
38#91413—21no—
39D5×C4⋊Dic3C2211yescharacteristic, complemented
40C2×#6653C2211yescharacteristic
41C2×#6653C2211yescharacteristic, complemented
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91116C2211yescharacteristic, complemented
44#91093C2211yescharacteristic, complemented
45#91091C2211yescharacteristic, complemented
46C5×#832C2211yescharacteristic, complemented
47C5×#832C2211yescharacteristic, complemented
48C5×#830C2211yescharacteristic, complemented
49C5×#807C2211yescharacteristic, complemented
50C5×#807C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90965C2211yescharacteristic
53#90965C2211yescharacteristic, complemented
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56#90964C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83482—51nomaximal, Hall
61#65943D311yescharacteristic, complemented
62#65841—31no—
63C5×#480—31no—
64#65327—31no—
65C2×#3941—31no—
66#65179—31no—
67#65172—31no—
68#65171—31no—
69#65161—31no—
70#65075—31no—
71#65062—31no—
72D5×#102—31no—
73#65049—31no—
74#65021—31no—
75#65014—31no—
76C23×C3×D5—21no—
77C23×C3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×D60C2311yescharacteristic
83C22×C5×Dic3—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5D411yescharacteristic
88C3×D4×D5—22no—
89C3×D4×D5—41no—
90C3×D4×D5—44no—
91C2×C3×D20—22no—
92C2×C3×D20—21no—
93C2×C3×D20—21no—
94C2×C3×D20—41no—
95C2×C3×D20C2311yescharacteristic
96C2×C3×D20C2311yescharacteristic
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5C2311yescharacteristic
99C2×#1204—21no—
100C2×#1202—21no—
101C2×#1200—21no—
102#6779—44no—
103C2×D5×Dic3—21no—
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106#6715—41no—
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C2×C3⋊#168—41no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×C4⋊Dic3—21no—
113C5×C4⋊Dic3C2311yescharacteristic
114C5×C4⋊Dic3C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C3×C22⋊Dic5D411yescharacteristic
118C3×#685—21no—
119C3×#685—21no—
120C3×#685D411yescharacteristic
121C3×#683D411yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123#6668—21no—
124#6668—21no—
125#6667—21no—
126#6667—21no—
127#6653—22no—
128#6653—41no—
129D5×C3⋊C8—41no—
130C3×D42—51no—
131#5555—51no—
132#5217—51no—
133#5217—51no—
134C2×#832—51no—
135C2×#832—51no—
136#5072—51no—
137#5070—51no—
138#5038—51no—
139#5038—51no—
140#5033—51no—
141#5033D511yescharacteristic, complemented
142C4×#213—51no—
143D4×C3⋊C8—51no—
144#5007—51no—
145C2×D4×D5—21no—
146C2×D4×D5C2×D311yescharacteristic
147C2×#709—61no—
148C22×D20C2×D311yescharacteristic
149C5×#121C2×D311yescharacteristic
150C2×C5×C4⋊C4—31no—
151#4086C2×D311yescharacteristic
152#4083—21no—
153C2×#686—31no—
154#4076—31no—
155#4075—61no—
156C4×C22⋊D5C2×D311yescharacteristic
157C22×#168—31no—
158C2×D40—31no—
159C2×D40—31no—
160C2×C8×D5—31no—
161#4042—61no—
162#4041—31no—
163#4041C2×D311yescharacteristic
164#4040—61no—
165#4039—31no—
166#4039C2×D311yescharacteristic
167D5×C4⋊C4—31no—
168#4034—31no—
169#4030—21no—
170#4028—21no—
171C5×#107—31no—
172C5×#107—31no—
173C5×#102—31no—
174C5×#102—31no—
175C5×C22⋊C8—31no—
176#3964—31no—
177#3953—31no—
178#3953—31no—
179#3952—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3941—31no—
186#3941—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5C2×D411yescharacteristic
191C22×D15—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—42no—
195C22×C3×D5—42no—
196C22×C3×D5—42no—
197C22×C3×D5—42no—
198C22×C3×D5—81no—
199C22×C3×D5—81no—
200C22×C3×D5C2×D411yescharacteristic
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—42no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209#1220—42no—
210C2×Dic15—21no—
211D60—21no—
212D60—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—42no—
216C3×C22⋊D5—42no—
217C3×C22⋊D5—42no—
218C3×C22⋊D5—81no—
219C3×C22⋊D5D814yescomplemented
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C3×D20—21no—
224C3×D20—21no—
225C3×D20—21no—
226C3×D20—42no—
227C3×D20—42no—
228C3×D20#4112yescomplemented
229C3×C4×D5—21no—
230C3×C4×D5—21no—
231C3×C4×D5—42no—
232#1204—42no—
233#1202—42no—
234#1200—42no—
235D5×Dic3—42no—
236C3⋊#168—21no—
237C3⋊#168—21no—
238C5×C3⋊C8—21no—
239C5×C3⋊C8—21no—
240C22×C3×D4—51no—
241C22×C3×D4—51no—
242C22×C3×D4—101no—
243C2×#237—101no—
244C3×#127—51no—
245C3×#121—51no—
246C3×#121—101no—
247C3×#121C2×D511yescharacteristic
248C3×#120—101no—
249C3×#120—101no—
250C3×C4×D4—51no—
251C3×C4×D4—51no—
252C2×#213—51no—
253C2×#213—51no—
254C2×#213—51no—
255#930—51no—
256#930—51no—
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3C2×D511yescharacteristic, complemented
259C22×C3⋊C8—51no—
260C22×C3⋊C8—51no—
261#897—101no—
262#886—101no—
263#886—101no—
264C4×D12—51no—
265#869—51no—
266#832—51no—
267#832—51no—
268#832—51no—
269#832—51no—
270#832—51no—
271#832—51no—
272#832—51no—
273#832C2×D511yescharacteristic, complemented
274#832C2×D511yescharacteristic, complemented
275#830—51no—
276#830C2×D511yescharacteristic, complemented
277#809—51no—
278#807—51no—
279#807C2×D511yescharacteristic, complemented
280#807C2×D511yescharacteristic, complemented
281C4⋊(C3⋊C8)—51no—
282C4×C3⋊C8—51no—
283C23×D5—21no—
284C23×D5—21no—
285C2×C5×D4—21no—
286C2×C5×D4C22×D311yescharacteristic
287C22×C4×C5—61no—
288C22×C4×C5C22×D311yescharacteristic
289C2×C22⋊D5—21no—
290C2×C22⋊D5—21no—
291C2×C22⋊D5—21no—
292C2×C22⋊D5—61no—
293C2×C22⋊D5#6711yescharacteristic
294D4×D5—22no—
295D4×D5—41no—
296D4×D5—44no—
297#709—124no—
298C2×D20—22no—
299C2×D20—21no—
300C2×D20—21no—
301C2×D20—31no—
302C2×D20—41no—
303C2×D20—61no—
304C2×D20C22×D311yescharacteristic
305C2×D20C22×D311yescharacteristic
306C2×C4×D5—21no—
307C2×C4×D5—61no—
308C2×C4×D5—61no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—61no—
311C2×C5×C8—31no—
312C2×C5×C8—31no—
313C5×C4⋊C4—31no—
314C5×C4⋊C4—31no—
315C5×C4⋊C4—61no—
316C5×C4⋊C4C22×D311yescharacteristic
317C5×C22⋊C4—21no—
318C22⋊Dic5#6711yescharacteristic
319#686—121no—
320#685—21no—
321#685—21no—
322#685—61no—
323#685—61no—
324#685—61no—
325#685#6711yescharacteristic
326C4⋊Dic5—31no—
327#683—61no—
328#683—61no—
329#683#6711yescharacteristic
330C4×Dic5C22×D311yescharacteristic
331C2×#168—31no—
332C2×#168—31no—
333C2×#168—121no—
334D40—62no—
335D40—121no—
336C8×D5—121no—
337#547—151no—
338D42—51no—
339#486—151no—
340#480—31no—
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—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—41no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5C2×D812yes—
358C22×C3×C5C22×D411yescharacteristic
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×C3×D5—21no—
363C2×C3×D5—21no—
364C2×C3×D5—22no—
365C2×C3×D5—41no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—84no—
371C2×C3×D5—84no—
372C2×C3×D5C2×D812yes—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5C2×#4111yescharacteristic
376C3×C4×C5H(5,𝔽2)11yescharacteristic
377Dic15—41no—
378C3×Dic5—21no—
379C3×Dic5—21no—
380C3×Dic5C2×D812yes—
381C5×Dic3—41no—
382C5×Dic3—41no—
383C24×C3—101no—
384C24×C3—101no—
385C2×C3×D4—21no—
386C2×C3×D4—51no—
387C2×C3×D4—51no—
388C2×C3×D4—51no—
389C2×C3×D4—102no—
390C2×C3×D4—101no—
391C2×C3×D4—101no—
392C2×C3×D4—101no—
393C2×C3×D4—101no—
394C2×C3×D4—102no—
395C2×C3×D4—101no—
396C2×C3×D4—201no—
397C2×C3×D4—201no—
398C2×C3×D4—204no—
399C2×C3×D4C22×D511yescharacteristic
400C22×C3×C4—51no—
401C22×C3×C4—101no—
402C22×C3×C4C22×D511yescharacteristic
403C2×#67—101no—
404C2×#67—101no—
405C22×Dic3—21no—
406C22×Dic3—101no—
407#237—204no—
408C2×D12—51no—
409C2×C4×D3—101no—
410C2×Dic6—101no—
411C3×C4⋊C4—51no—
412C3×C4⋊C4C22×D511yescharacteristic
413C3×C22⋊C4—21no—
414C3×C22⋊C4—51no—
415C3×C22⋊C4—51no—
416C3×C22⋊C4—101no—
417C3×C22⋊C4—101no—
418C3×C42—51no—
419#213—102no—
420#213—201no—
421#213—201no—
422(C2×D3)⋊C4—101no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425C4⋊Dic3—21no—
426C4⋊Dic3—51no—
427C4⋊Dic3—101no—
428C4⋊Dic3—101no—
429C4⋊Dic3C22×D511yescharacteristic
430C4⋊Dic3C22×D511yescharacteristic
431C2×C3⋊C8—51no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—201no—
434C2×C3⋊C8—201no—
435C2×C3⋊C8C22×D511yescharacteristic
436C2×C3⋊C8C22×D511yescharacteristic
437C23×C5—21no—
438C23×C5C2×#6711yescharacteristic
439C22×D5—21no—
440C22×D5—21no—
441C22×D5—42no—
442C22×D5—42no—
443C22×D5—42no—
444C22×D5—42no—
445C22×D5—61no—
446C22×D5—81no—
447C22×D5—81no—
448C22×D5C2×#6711yescharacteristic
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—42no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—61no—
456C2×C4×C5—61no—
457C2×C4×C5—122no—
458C2×C4×C5C2×#6711yescharacteristic
459C2×C4×C5C23×D311yescharacteristic
460C22⋊D5—42no—
461C22⋊D5—42no—
462C22⋊D5—81no—
463C22⋊D5—122no—
464C22⋊D5#21314yescomplemented
465C2×Dic5—61no—
466C2×Dic5C2×#6711yescharacteristic
467C2×Dic5C2×#6711yescharacteristic
468C2×Dic5C2×#6711yescharacteristic
469D20—21no—
470D20—21no—
471D20—21no—
472D20—42no—
473D20—42no—
474D20—61no—
475D20—61no—
476D20—122no—
477D20#23712yescomplemented
478C4×D5—21no—
479C4×D5—21no—
480C4×D5—42no—
481C4×D5—122no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—61no—
485C5×C8—61no—
486#168—61no—
487#168—61no—
488C2×#41—301no—
489C22×D4—51no—
490C22×D4—51no—
491C22×D4—101no—
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—151no—
498#127—51no—
499#123—301no—
500#123—301no—
501C22⋊Q8—301no—
502#121—51no—
503#121—101no—
504#121—151no—
505#121—151no—
506#121D3×D511yescharacteristic
507#120—101no—
508#120—101no—
509C4×D4—51no—
510C4×D4—51no—
511C4×D4—151no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—151no—
514#107—31no—
515#107—31no—
516#107—151no—
517C4⋊C8—151no—
518#102—31no—
519#102—31no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102—151no—
527#102—151no—
528C22⋊C8—31no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—81no—
533C2×C3×C5#54611yescharacteristic
534C2×C3×C5C22×D811yescharacteristic
535C2×C3×C5#57711yescharacteristic
536D15—81no—
537C3×D5—22no—
538C3×D5—42no—
539C3×D5—81no—
540C23×C3—21no—
541C23×C3—51no—
542C23×C3—101no—
543C23×C3—101no—
544C23×C3—202no—
545C23×C3—202no—
546C23×C3—202no—
547C23×C3—202no—
548C23×C3—401no—
549C23×C3—401no—
550C23×C3D4×D511yescharacteristic
551C22×D3—101no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—42no—
555C3×D4—54no—
556C3×D4—52no—
557C3×D4—101no—
558C3×D4—101no—
559C3×D4—101no—
560C3×D4—202no—
561C3×D4—202no—
562C3×D4—202no—
563C3×D4—202no—
564C3×D4—401no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—51no—
569C2×C3×C4—51no—
570C2×C3×C4—51no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—202no—
574C2×C3×C4D4×D511yescharacteristic
575C2×C3×C4C23×D511yescharacteristic
576#67—202no—
577#67—202no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—42no—
581C2×Dic3—101no—
582C2×Dic3—202no—
583D12—101no—
584D12—101no—
585C4×D3—202no—
586Dic6—202no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5C2×#21312yes—
597C22×C5C22×#6711yescharacteristic
598C2×D5—21no—
599C2×D5—21no—
600C2×D5—22no—
601C2×D5—41no—
602C2×D5—41no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—84no—
607C2×D5—84no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—121no—
611C2×D5C2×#21312yes—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5—121no—
615C4×C5—121no—
616C4×C5C2×#23711yescharacteristic
617C4×C5#100411yescharacteristic
618Dic5—21no—
619Dic5—21no—
620Dic5—121no—
621Dic5C2×#21312yes—
622C24—101no—
623C24—101no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—21no—
627C2×D4—51no—
628C2×D4—51no—
629C2×D4—51no—
630C2×D4—102no—
631C2×D4—101no—
632C2×D4—101no—
633C2×D4—101no—
634C2×D4—101no—
635C2×D4—102no—
636C2×D4—101no—
637C2×D4—151no—
638C2×D4—201no—
639C2×D4—201no—
640C2×D4—204no—
641C2×D4—301no—
642C2×D4—301no—
643C2×D4C2×D3×D511yescharacteristic
644C22×C4—51no—
645C22×C4—61no—
646C22×C4—101no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—151no—
656C2×C8—151no—
657C2×C8—601no—
658C2×C8—601no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—51no—
662C4⋊C4—61no—
663C4⋊C4—151no—
664C4⋊C4—301no—
665C4⋊C4—301no—
666C4⋊C4C2×D3×D511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—51no—
669C22⋊C4—51no—
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—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—52no—
683C22×C3—101no—
684C22×C3—101no—
685C22×C3—102no—
686C22×C3—201no—
687C22×C3—201no—
688C22×C3—201no—
689C22×C3—201no—
690C22×C3—201no—
691C22×C3—404no—
692C22×C3—404no—
693C22×C3D5×D812yes—
694C22×C3C2×D4×D511yescharacteristic
695C2×D3—201no—
696C2×D3—201no—
697C2×D3—201no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—52no—
701C3×C4—101no—
702C3×C4—101no—
703C3×C4D5×#4111yescharacteristic
704C3×C4#414911yescharacteristic
705Dic3—41no—
706Dic3—41no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—81no—
710C2×C5C22×#21311yescharacteristic
711C2×C5#580611yescharacteristic
712C2×C5#583611yescharacteristic
713D5—22no—
714D5—42no—
715D5—81no—
716D5—241no—
717C23—21no—
718C23—51no—
719C23—101no—
720C23—101no—
721C23—202no—
722C23—202no—
723C23—202no—
724C23—202no—
725C23—301no—
726C23—401no—
727C23—401no—
728C23D5×#6711yescharacteristic
729Q8—602no—
730D4—21no—
731D4—21no—
732D4—42no—
733D4—54no—
734D4—52no—
735D4—101no—
736D4—101no—
737D4—101no—
738D4—202no—
739D4—202no—
740D4—202no—
741D4—202no—
742D4—301no—
743D4—301no—
744D4—401no—
745D4—602no—
746D4—602no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—51no—
751C2×C4—51no—
752C2×C4—51no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—122no—
758C2×C4—202no—
759C2×C4—301no—
760C2×C4—602no—
761C2×C4—602no—
762C2×C4D5×#6711yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—61no—
765C8—61no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—81no—
770C2×C3—102no—
771C2×C3—202no—
772C2×C3—401no—
773C2×C3#6598811yescharacteristic
774C2×C3C2×D5×D811yescharacteristic
775C2×C3#6611211yescharacteristic
776D3—401no—
777C5#8348211yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—52no—
784C22—101no—
785C22—101no—
786C22—102no—
787C22—201no—
788C22—201no—
789C22—201no—
790C22—201no—
791C22—201no—
792C22—404no—
793C22—404no—
794C22—601no—
795C22—601no—
796C22—601no—
797C22D5×#21312yes—
798C22C2×D5×#6711yescharacteristic
799C4—21no—
800C4—41no—
801C4—52no—
802C4—101no—
803C4—101no—
804C4—121no—
805C4—121no—
806C4—601no—
807C4D5×#23711yescharacteristic
808C4#9202611yescharacteristic
809C3#1061303311yescharacteristic, complemented, Sylow
810C2—22no—
811C2—81no—
812C2—102no—
813C2—202no—
814C2—401no—
815C2—1201no—
816C2C2×D5×#21311yescharacteristic
817C2#1175478911yescharacteristic
818C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#65943C2semidirect
2. #11754325C2semidirect
3. #11751139C2semidirect
4. C5×#5033C2semidirect
5. #11749102C2semidirect
6. #11749022C2semidirect
7. #11748976C2semidirect
8. D5×#832C2semidirect
9. #11748512C2semidirect
10. #11748493C2semidirect
11. C2×#90964C2semidirect
12. #11747442C2semidirect
13. #11747410C2semidirect
14. #11747223C2semidirect
15. #11747192C2semidirect
22. C2×#6715C22semidirect
23. #91819C22semidirect
24. C22×C3⋊#168C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
34. #91468C22semidirect
35. #91450C22semidirect
37. #91418C22semidirect
39. D5×C4⋊Dic3C22semidirect
41. C2×#6653C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91116C22semidirect
44. #91093C22semidirect
45. #91091C22semidirect
46. C5×#832C22semidirect
47. C5×#832C22semidirect
48. C5×#830C22semidirect
49. C5×#807C22semidirect
50. C5×#807C22semidirect
51. #90982C22semidirect
53. #90965C22semidirect
56. #90964C22semidirect
57. #90964C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
61. #65943D3semidirect
141. #5033D5semidirect
219. C3×C22⋊D5D8semidirect
228. C3×D20#41semidirect
258. C2×C4⋊Dic3C2×D5semidirect
273. #832C2×D5semidirect
274. #832C2×D5semidirect
276. #830C2×D5semidirect
279. #807C2×D5semidirect
280. #807C2×D5semidirect
464. C22⋊D5#213semidirect
477. D20#237semidirect
676. C3×C5#3294semidirect
777. C5#83482semidirect
809. C3#10613033semidirect

Maximal subgroups

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

subgroupindex
C3×#659432
#117543252
#117511392
C5×#50332
#117491022
#117490222
#117489762
D5×#8322
#117485122
#117484932
C2×#909642
#117474422
#117474102
#117472232
#117471922
#106130333
#834825