Finite Group Databasebeta

← #14458316

Subgroups — #14458316

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
1#11754647C211yesmaximal, characteristic, complemented
2#11754325C211yesmaximal, characteristic, complemented
3#11750833C211yesmaximal, characteristic, complemented
4C5×#4736C211yesmaximal, characteristic, complemented
5C3×#65014C211yesmaximal, characteristic, complemented
6#11748514C211yesmaximal, characteristic, complemented
7C2×#90969C211yesmaximal, characteristic, complemented
8#11748117C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747995C211yesmaximal, characteristic, complemented
11#11747899C211yesmaximal, characteristic, complemented
12#11747768C211yesmaximal, characteristic, complemented
13#11747767C211yesmaximal, characteristic, complemented
14#11747766C211yesmaximal, characteristic, complemented
15#11747616C211yesmaximal, characteristic, complemented
16#10613033—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×#6779—21no—
20C2×D5×D12C2211yescharacteristic
21#91819C2211yescharacteristic, complemented
22C2×D120C2211yescharacteristic
23C2×D120C2211yescharacteristic, complemented
24C5×#930C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C3×C4×C22⋊D5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic, complemented
28C2×C3×C8×D5C2211yescharacteristic, complemented
29#91573—21no—
30#91542—21no—
31#91476—21no—
32#91468C2211yescharacteristic, complemented
33#91451C2211yescharacteristic
34#91450C2211yescharacteristic
35#91450C2211yescharacteristic, complemented
36#91420—21no—
37#91419—21no—
38#91418C2211yescharacteristic
39#91418C2211yescharacteristic, complemented
40#91413—21no—
41D5×C4⋊Dic3C2211yescharacteristic, complemented
42C2×#6654C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic
45#91105C2211yescharacteristic, complemented
46C5×#821C2211yescharacteristic, complemented
47C5×#821C2211yescharacteristic, complemented
48C5×#818C2211yescharacteristic, complemented
49C5×#818C2211yescharacteristic, complemented
50C3×#3952C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic
56#90969C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90969C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#79438—51nomaximal, Hall
61#65943—31no—
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#65014D311yescharacteristic, complemented
76C23×D15—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×D60C2311yescharacteristic
86C2×C5×#67—21no—
87C22×C5×Dic3—21no—
88C2×C5×D12C2311yescharacteristic
89C2×C3×C22⋊D5D411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91#6790—44no—
92C2×#1204—21no—
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1203—21no—
96C2×#1202—21no—
97C2×#1202—21no—
98C2×#1200—21no—
99C2×#1200—21no—
100#6779—44no—
101C2×D5×Dic3—21no—
102D5×D12—22no—
103D5×D12—41no—
104C2×C3×C5×C8C2311yescharacteristic
105C2×C3×C5×C8C2311yescharacteristic
106#6714—21no—
107C4⋊Dic15C2311yescharacteristic
108D120—22no—
109D120—41no—
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×C4⋊Dic3C2311yescharacteristic
115C3×C22⋊Dic5D411yescharacteristic
116C3×#685D411yescharacteristic
117C3×#683D411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168—41no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C3×C8×D5—41no—
123#6668—21no—
124#6668—21no—
125#6667—21no—
126#6667—21no—
127#6667—21no—
128#6667—21no—
129#6654—41no—
130#5555—51no—
131D4×D12—51no—
132C3×C8×D4—51no—
133#5115—51no—
134#5115—51no—
135C2×#821—51no—
136C2×#821—51no—
137#4846—51no—
138#4843—51no—
139#4736—51no—
140#4736D511yescharacteristic, complemented
141#4732—51no—
142#4732—51no—
143#4694—51no—
144C4×D24—51no—
145C2×D4×D5—31no—
146C2×D4×D5—61no—
147C2×#709—61no—
148C22×D20—31no—
149C5×#121—31no—
150C2×C5×C4⋊C4—31no—
151#4086—31no—
152#4083—61no—
153C2×#686—31no—
154#4076—31no—
155#4075—61no—
156C4×C22⋊D5C2×D311yescharacteristic
157C22×#168C2×D311yescharacteristic, complemented
158C2×D40—31no—
159C2×D40—31no—
160C2×C8×D5C2×D311yescharacteristic, complemented
161#4042—61no—
162#4041—31no—
163#4041—31no—
164#4040—61no—
165#4039—31no—
166#4039—31no—
167D5×C4⋊C4—31no—
168#4034—31no—
169#4030—61no—
170#4028—61no—
171C5×#107—31no—
172C5×#107—31no—
173C5×#102—31no—
174C5×#102—31no—
175C5×C22⋊C8C2×D311yescharacteristic, complemented
176#3964—31no—
177#3953—31no—
178#3953—31no—
179#3952C2×D311yescharacteristic, complemented
180#3946C2×D311yescharacteristic, complemented
181C8×Dic5C2×D311yescharacteristic, complemented
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3941—31no—
186#3941—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—42no—
194C22×D15—42no—
195C22×D15—81no—
196C22×C5×D3—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×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205#1220—42no—
206C2×Dic15—21no—
207D60—21no—
208D60—21no—
209D60—21no—
210D60—21no—
211D60—21no—
212D60—42no—
213D60#4112yescomplemented
214C5×#67—42no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—42no—
219C5×D12—21no—
220C5×D12—21no—
221C3×C22⋊D5D814yescomplemented
222C2×C3×Dic5C2×D411yescharacteristic
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227#1204—42no—
228#1203—42no—
229#1203—42no—
230#1203—81no—
231#1202—42no—
232#1202—42no—
233#1200—42no—
234#1200—42no—
235D5×Dic3—42no—
236C3×C5×C8—21no—
237C3×C5×C8—21no—
238C3×#168—21no—
239C3×#168—21no—
240C2×#237—101no—
241C2×D3×D4—101no—
242C22×D12—51no—
243C22×D12—51no—
244C22×C3×C8—51no—
245C22×C3×C8—51no—
246C3×C4×D4—51no—
247#930—51no—
248#930—51no—
249#930—51no—
250#930C2×D511yescharacteristic
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3C2×D511yescharacteristic, complemented
253C2×D24—51no—
254C2×D24—51no—
255C2×D24—51no—
256#897—101no—
257#895—101no—
258#886—101no—
259#886—101no—
260#882—101no—
261#882—101no—
262#874—51no—
263C4×D12—51no—
264C4×D12—51no—
265#869—51no—
266C3×C4⋊C8—51no—
267C3×C22⋊C8—51no—
268C3×C22⋊C8C2×D511yescharacteristic, complemented
269C3×C4×C8—51no—
270#821—51no—
271#821—51no—
272#821—51no—
273#821—51no—
274#821—51no—
275#821—51no—
276#821—51no—
277#821—51no—
278#821C2×D511yescharacteristic, complemented
279#821C2×D511yescharacteristic, complemented
280#818—51no—
281#818C2×D511yescharacteristic, complemented
282#818C2×D511yescharacteristic, complemented
283C23×D5—61no—
284C23×D5—61no—
285C2×C5×D4—31no—
286C2×C5×D4—61no—
287C22×C4×C5—61no—
288C22×C4×C5C22×D311yescharacteristic
289C2×C22⋊D5—61no—
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C2×C22⋊D5—61no—
293C2×C22⋊D5D1211yescharacteristic
294D4×D5—62no—
295D4×D5—121no—
296D4×D5—124no—
297#709—124no—
298C2×D20—31no—
299C2×D20—31no—
300C2×D20—31no—
301C2×D20—62no—
302C2×D20—61no—
303C2×D20—61no—
304C2×D20—61no—
305C2×D20—121no—
306C2×C4×D5—61no—
307C2×C4×D5—61no—
308C2×C4×D5—61no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—61no—
311C2×C5×C8C22×D311yescharacteristic
312C2×C5×C8C22×D311yescharacteristic
313C5×C4⋊C4—31no—
314C5×C4⋊C4—31no—
315C5×C4⋊C4—31no—
316C5×C4⋊C4—61no—
317C5×C22⋊C4—61no—
318C22⋊Dic5D1211yescharacteristic
319#686—121no—
320#685—61no—
321#685—61no—
322#685—61no—
323#685—61no—
324#685—61no—
325#685D1211yescharacteristic
326C4⋊Dic5—31no—
327#683—61no—
328#683—61no—
329#683D1211yescharacteristic
330C4×Dic5C22×D311yescharacteristic
331C2×#168—41no—
332C2×#168C22×D311yescharacteristic
333C2×#168C22×D311yescharacteristic
334D40—62no—
335D40—121no—
336C8×D5—41no—
337#547—151no—
338D42—151no—
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—51no—
350C2×#102—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5C2×D812yes—
355C22×C3×C5C22×D411yescharacteristic
356C2×D15—22no—
357C2×D15—41no—
358C2×D15—41no—
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×D15—41no—
363C2×D15—41no—
364C2×D15—41no—
365C2×D15—84no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C5×D3—41no—
369C2×C3×D5—21no—
370C2×C3×D5—21no—
371C2×C3×D5C2×D812yes—
372D3×D5—84no—
373C3×C4×C5—21no—
374C3×C4×C5C2×#4111yescharacteristic
375C3×C4×C5H(5,𝔽2)11yescharacteristic
376Dic15—41no—
377C3×Dic5—21no—
378C3×Dic5—21no—
379C3×Dic5C2×D812yes—
380C5×Dic3—41no—
381C5×Dic3—41no—
382C5×Dic3—41no—
383C23×D3—101no—
384C23×D3—101no—
385C2×C3×D4—51no—
386C22×C3×C4—51no—
387C22×C3×C4C22×D511yescharacteristic
388C2×#67—21no—
389C2×#67—101no—
390C2×#67—101no—
391C2×#67—101no—
392C22×Dic3—21no—
393C22×Dic3—101no—
394#237—204no—
395D3×D4—204no—
396C2×D12—51no—
397C2×D12—51no—
398C2×D12—51no—
399C2×D12—102no—
400C2×D12—102no—
401C2×D12—101no—
402C2×D12—101no—
403C2×D12—101no—
404C2×D12—101no—
405C2×D12—201no—
406C2×D12—201no—
407C2×D12C22×D511yescharacteristic
408C2×C4×D3—101no—
409C2×C4×D3—101no—
410C2×Dic6—101no—
411C2×C3×C8—51no—
412C2×C3×C8—51no—
413C2×C3×C8—201no—
414C2×C3×C8—201no—
415C2×C3×C8C22×D511yescharacteristic
416C2×C3×C8C22×D511yescharacteristic
417C3×C4⋊C4—51no—
418C3×C22⋊C4—51no—
419C3×C22⋊C4—51no—
420C3×C42—51no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—101no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4—101no—
426(C2×D3)⋊C4—101no—
427C4⋊Dic3—21no—
428C4⋊Dic3—51no—
429C4⋊Dic3—101no—
430C4⋊Dic3—101no—
431C4⋊Dic3C22×D511yescharacteristic
432C4⋊Dic3C22×D511yescharacteristic
433C4⋊Dic3C22×D511yescharacteristic
434D24—102no—
435D24—201no—
436D24—201no—
437C23×C5—61no—
438C23×C5C2×D1211yescharacteristic
439C22×D5—61no—
440C22×D5—61no—
441C22×D5—61no—
442C22×D5—122no—
443C22×D5—122no—
444C22×D5—122no—
445C22×D5—122no—
446C22×D5—241no—
447C22×D5—241no—
448C22×D5C2×D1211yescharacteristic
449C5×D4—61no—
450C5×D4—61no—
451C5×D4—122no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—61no—
455C2×C4×C5—61no—
456C2×C4×C5—61no—
457C2×C4×C5—122no—
458C2×C4×C5C2×D1211yescharacteristic
459C2×C4×C5C23×D311yescharacteristic
460C22⋊D5—122no—
461C22⋊D5—122no—
462C22⋊D5—122no—
463C22⋊D5—241no—
464C22⋊D5D2414yescomplemented
465C2×Dic5—61no—
466C2×Dic5C2×D1211yescharacteristic
467C2×Dic5C2×D1211yescharacteristic
468C2×Dic5C2×D1211yescharacteristic
469D20—32no—
470D20—61no—
471D20—61no—
472D20—61no—
473D20—61no—
474D20—61no—
475D20—122no—
476D20—122no—
477D20—122no—
478C4×D5—21no—
479C4×D5—21no—
480C4×D5—122no—
481C4×D5—122no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—21no—
487#168—21no—
488C2×#41—301no—
489C22×D4—151no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—51no—
496C22×C8—51no—
497C4⋊Q8—151no—
498#127—151no—
499#123—301no—
500#123—301no—
501C22⋊Q8—301no—
502#121—31no—
503#121—151no—
504#121—151no—
505#121—151no—
506#121—301no—
507#120—301no—
508#120—301no—
509C4×D4—51no—
510C4×D4—151no—
511C4×D4—151no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—151no—
514#107—31no—
515#107—31no—
516#107—151no—
517C4⋊C8—51no—
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—51no—
529C22⋊C8D3×D511yescharacteristic, complemented
530C4×C8—51no—
531C2×C3×C5—22no—
532C2×C3×C5#54611yescharacteristic
533C2×C3×C5C22×D811yescharacteristic
534C2×C3×C5#57711yescharacteristic
535D15—42no—
536D15—81no—
537D15—81no—
538C3×D5—22no—
539C5×D3—81no—
540C23×C3—51no—
541C23×C3D4×D511yescharacteristic
542C22×D3—21no—
543C22×D3—101no—
544C22×D3—101no—
545C22×D3—101no—
546C22×D3—202no—
547C22×D3—202no—
548C22×D3—202no—
549C22×D3—202no—
550C22×D3—401no—
551C22×D3—401no—
552C3×D4—54no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—51no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4D4×D511yescharacteristic
561C2×C3×C4C23×D511yescharacteristic
562#67—42no—
563#67—202no—
564#67—202no—
565#67—202no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—42no—
570C2×Dic3—101no—
571C2×Dic3—202no—
572D12—21no—
573D12—21no—
574D12—52no—
575D12—101no—
576D12—101no—
577D12—101no—
578D12—101no—
579D12—101no—
580D12—202no—
581D12—202no—
582D12—202no—
583D12—401no—
584C4×D3—202no—
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—121no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5C2×D2412yes—
597C22×C5C22×D1211yescharacteristic
598C2×D5—21no—
599C2×D5—21no—
600C2×D5—62no—
601C2×D5—121no—
602C2×D5—121no—
603C2×D5—121no—
604C2×D5—121no—
605C2×D5—121no—
606C2×D5—121no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—244no—
610C2×D5—244no—
611C2×D5C2×D2412yes—
612C4×C5—21no—
613C4×C5—121no—
614C4×C5—121no—
615C4×C5—121no—
616C4×C5#100411yescharacteristic
617C4×C5D3×#4111yescharacteristic
618Dic5—21no—
619Dic5—21no—
620Dic5—121no—
621Dic5C2×D2412yes—
622C24—301no—
623C24—301no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—31no—
627C2×D4—51no—
628C2×D4—61no—
629C2×D4—151no—
630C2×D4—151no—
631C2×D4—151no—
632C2×D4—302no—
633C2×D4—301no—
634C2×D4—301no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—302no—
639C2×D4—301no—
640C2×D4—301no—
641C2×D4—601no—
642C2×D4—601no—
643C2×D4—604no—
644C22×C4—51no—
645C22×C4—61no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—201no—
656C2×C8—201no—
657C2×C8C2×D3×D511yescharacteristic
658C2×C8C2×D3×D511yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—51no—
663C4⋊C4—61no—
664C4⋊C4—151no—
665C4⋊C4—301no—
666C4⋊C4—301no—
667C22⋊C4—51no—
668C22⋊C4—51no—
669C22⋊C4—61no—
670C22⋊C4—301no—
671C22⋊C4—301no—
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×C3D5×D812yes—
683C22×C3C2×D4×D511yescharacteristic
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—201no—
691C2×D3—201no—
692C2×D3—201no—
693C2×D3—201no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—404no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—52no—
700C3×C4—101no—
701C3×C4—101no—
702C3×C4D5×#4111yescharacteristic
703C3×C4#414911yescharacteristic
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—241no—
710C2×C5#555411yescharacteristic
711C2×C5C22×D2411yescharacteristic
712C2×C5#575111yescharacteristic
713D5—22no—
714D5—122no—
715D5—241no—
716D5—241no—
717C23—51no—
718C23—61no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—602no—
723C23—602no—
724C23—602no—
725C23—602no—
726C23—1201no—
727C23—1201no—
728C23D5×D1211yescharacteristic
729Q8—602no—
730D4—54no—
731D4—61no—
732D4—61no—
733D4—122no—
734D4—152no—
735D4—301no—
736D4—301no—
737D4—301no—
738D4—301no—
739D4—301no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—602no—
746D4—1201no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—51no—
750C2×C4—51no—
751C2×C4—51no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—122no—
758C2×C4—301no—
759C2×C4—602no—
760C2×C4—602no—
761C2×C4—602no—
762C2×C4D5×D1211yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—21no—
765C8—21no—
766C8—101no—
767C8—101no—
768C2×C3—22no—
769C2×C3—102no—
770C2×C3#6598811yescharacteristic
771C2×C3C2×D5×D811yescharacteristic
772C2×C3#6611211yescharacteristic
773D3—81no—
774D3—202no—
775D3—401no—
776D3—401no—
777C5#7943811yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—52no—
781C22—101no—
782C22—101no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—302no—
787C22—601no—
788C22—601no—
789C22—601no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—1204no—
796C22—1204no—
797C22D5×D2412yes—
798C22C2×D5×D1211yescharacteristic
799C4—21no—
800C4—52no—
801C4—101no—
802C4—101no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—601no—
807C4#9202411yescharacteristic
808C4#9202611yescharacteristic
809C3#1061303311yescharacteristic, complemented, Sylow
810C2—22no—
811C2—102no—
812C2—241no—
813C2—602no—
814C2—1201no—
815C2—1201no—
816C2#1175326611yescharacteristic
817C2C2×D5×D2411yescharacteristic
818C2#1175402511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #11754647C2semidirect
2. #11754325C2semidirect
3. #11750833C2semidirect
4. C5×#4736C2semidirect
5. C3×#65014C2semidirect
6. #11748514C2semidirect
7. C2×#90969C2semidirect
8. #11748117C2semidirect
9. D5×#821C2semidirect
10. #11747995C2semidirect
11. #11747899C2semidirect
12. #11747768C2semidirect
13. #11747767C2semidirect
14. #11747766C2semidirect
15. #11747616C2semidirect
21. #91819C22semidirect
23. C2×D120C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
27. C22×C3×#168C22semidirect
28. C2×C3×C8×D5C22semidirect
32. #91468C22semidirect
35. #91450C22semidirect
39. #91418C22semidirect
41. D5×C4⋊Dic3C22semidirect
42. C2×#6654C22semidirect
43. C3×C5×C22⋊C8C22semidirect
45. #91105C22semidirect
46. C5×#821C22semidirect
47. C5×#821C22semidirect
48. C5×#818C22semidirect
49. C5×#818C22semidirect
50. C3×#3952C22semidirect
51. C3×#3946C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90988C22semidirect
56. #90969C22semidirect
57. #90969C22semidirect
58. #90969C22semidirect
59. #90967C22semidirect
75. #65014D3semidirect
140. #4736D5semidirect
157. C22×#168C2×D3semidirect
160. C2×C8×D5C2×D3semidirect
175. C5×C22⋊C8C2×D3semidirect
179. #3952C2×D3semidirect
180. #3946C2×D3semidirect
181. C8×Dic5C2×D3semidirect
213. D60#41semidirect
221. C3×C22⋊D5D8semidirect
252. C2×C4⋊Dic3C2×D5semidirect
268. C3×C22⋊C8C2×D5semidirect
278. #821C2×D5semidirect
279. #821C2×D5semidirect
281. #818C2×D5semidirect
282. #818C2×D5semidirect
464. C22⋊D5D24semidirect
529. C22⋊C8D3×D5semidirect
676. C3×C5#3294semidirect
777. C5#79438semidirect
809. C3#10613033semidirect

Maximal subgroups

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

subgroupindex
#117546472
#117543252
#117508332
C5×#47362
C3×#650142
#117485142
C2×#909692
#117481172
D5×#8212
#117479952
#117478992
#117477682
#117477672
#117477662
#117476162
#106130333
#794385