Finite Group Databasebeta

← #14458311

Subgroups — #14458311

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
1D12×C22⋊D5C211yesmaximal, characteristic, complemented
2#11754326C211yesmaximal, characteristic, complemented
3#11750837C211yesmaximal, characteristic, complemented
4C5×#4732C211yesmaximal, characteristic, complemented
5C3×#65014C211yesmaximal, characteristic, complemented
6#11748514C211yesmaximal, characteristic, complemented
7C2×#90967C211yesmaximal, characteristic, complemented
8#11748116C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747995C211yesmaximal, characteristic, complemented
11#11747898C211yesmaximal, characteristic, complemented
12#11747765C211yesmaximal, characteristic, complemented
13#11747764C211yesmaximal, characteristic, complemented
14Dic5×D24C211yesmaximal, characteristic, complemented
15#11747617C211yesmaximal, characteristic, complemented
16#10611745—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×D3×C22⋊D5—21no—
19C2×#6780—21no—
20C2×D5×D12C2211yescharacteristic
21#91819C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic, complemented
23C5×#930C2211yescharacteristic, complemented
24C2×C5×D24C2211yescharacteristic
25C2×C5×D24C2211yescharacteristic, complemented
26C3×C4×C22⋊D5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic, complemented
28C2×C3×C8×D5C2211yescharacteristic, complemented
29#91570—21no—
30#91543—21no—
31#91475—21no—
32#91468C2211yescharacteristic, complemented
33#91451C2211yescharacteristic
34#91449C2211yescharacteristic
35#91449C2211yescharacteristic, complemented
36#91417—21no—
37#91416—21no—
38Dic5×D12C2211yescharacteristic
39Dic5×D12C2211yescharacteristic, complemented
40#91414—21no—
41D5×C4⋊Dic3C2211yescharacteristic, complemented
42C2×#6654C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic, complemented
45#91105C2211yescharacteristic, complemented
46#91102C2211yescharacteristic, complemented
47#91102C2211yescharacteristic, complemented
48C5×#821C2211yescharacteristic
49C5×#821C2211yescharacteristic, complemented
50C3×#3952C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90969C2211yescharacteristic, complemented
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90967C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#79438—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65945—31no—
63C5×#447—31no—
64C2×#3964—31no—
65#65446—31no—
66#65445—31no—
67#65439—31no—
68D8×Dic5—31no—
69#65327—31no—
70#65063—31no—
71D5×#102—31no—
72#65049—31no—
73#65048—31no—
74#65025—31no—
75#65014D311yescharacteristic, complemented
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C22×Dic15—21no—
81C2×D60C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×D12—22no—
84C2×C5×D12—21no—
85C2×C5×D12—41no—
86C2×C5×D12C2311yescharacteristic
87C2×C5×D12C2311yescharacteristic
88C2×C5×D12C2311yescharacteristic
89C2×C3×C22⋊D5D411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91D3×C22⋊D5—44no—
92C2×#1204—21no—
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1203—21no—
96C2×#1201—21no—
97C2×#1201—21no—
98C2×D3×Dic5—21no—
99C2×D3×Dic5—21no—
100#6780—44no—
101C2×D5×Dic3—21no—
102D5×D12—22no—
103D5×D12—41no—
104C2×C3×C5×C8C2311yescharacteristic
105C2×C3×C5×C8C2311yescharacteristic
106#6714—21no—
107C4⋊Dic15—21no—
108C4⋊Dic15C2311yescharacteristic
109C4⋊Dic15C2311yescharacteristic
110C4⋊Dic15C2311yescharacteristic
111C5×(C2×D3)⋊C4—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×D24—22no—
114C5×D24—41no—
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(C2×D3)⋊Dic5—21no—
126(C2×D3)⋊Dic5—21no—
127(C2×D3)⋊Dic5—21no—
128(C2×D3)⋊Dic5—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#4736—51no—
141#4732—51no—
142#4732D511yescharacteristic, complemented
143#4694—51no—
144C4×D24—51no—
145C22×C5×D4—31no—
146C22×C22⋊D5—61no—
147C2×#711—61no—
148C2×D4×D5—31no—
149C2×C5×D8—31no—
150C2×C5×D8—31no—
151C5×#121—31no—
152#4099—61no—
153#4086—31no—
154#4085—61no—
155#4084—31no—
156#4084—31no—
157#4083—61no—
158#4081—61no—
159D4×Dic5—31no—
160D4×Dic5—31no—
161C2×#686—31no—
162#4076—31no—
163C4×C22⋊D5C2×D311yescharacteristic
164C2×C4⋊Dic5—31no—
165C22×#168C2×D311yescharacteristic, complemented
166C2×C8×D5C2×D311yescharacteristic, complemented
167D5×C4⋊C4—31no—
168#4034—31no—
169#4029—61no—
170#4024—61no—
171C5×#102—31no—
172C5×#102—31no—
173C5×C22⋊C8C2×D311yescharacteristic, complemented
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3952C2×D311yescharacteristic, complemented
182#3950—31no—
183#3950—31no—
184#3946C2×D311yescharacteristic, complemented
185C8×Dic5C2×D311yescharacteristic, complemented
186#3941—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—21no—
194C22×C5×D3—42no—
195C22×C5×D3—42no—
196C22×C5×D3—81no—
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—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—42no—
210D60—21no—
211D60—21no—
212C5×#67—42no—
213C2×C5×Dic3—21no—
214C5×D12—21no—
215C5×D12—21no—
216C5×D12—21no—
217C5×D12—21no—
218C5×D12—21no—
219C5×D12—42no—
220C5×D12#4112yescomplemented
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#1201—42no—
232#1201—42no—
233D3×Dic5—42no—
234D3×Dic5—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×D12C2×D511yescharacteristic
244C22×C3×C8—51no—
245C22×C3×C8—51no—
246C3×C4×D4—51no—
247#930—51no—
248#930—51no—
249#930—51no—
250#930C2×D511yescharacteristic, complemented
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3—51no—
253C2×D24—51no—
254C2×D24C2×D511yescharacteristic
255C2×D24C2×D511yescharacteristic, complemented
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
279#821C2×D511yescharacteristic, complemented
280#818—51no—
281#818—51no—
282#818—51no—
283C24×C5—61no—
284C23×D5—61no—
285C2×C5×D4—31no—
286C2×C5×D4—31no—
287C2×C5×D4—31no—
288C2×C5×D4—62no—
289C2×C5×D4—61no—
290C2×C5×D4—61no—
291C2×C5×D4—121no—
292C22×C4×C5C22×D311yescharacteristic
293C2×C22⋊D5—61no—
294C2×C22⋊D5—61no—
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—61no—
299C2×C22⋊D5—124no—
300C2×C22⋊D5D1211yescharacteristic
301C22×Dic5—61no—
302C22×Dic5—61no—
303C22×Dic5—61no—
304#711—124no—
305D4×D5—62no—
306D4×D5—121no—
307C2×D20—31no—
308C2×C4×D5—61no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—61no—
311C5×D8—62no—
312C5×D8—121no—
313C2×C5×C8C22×D311yescharacteristic
314C2×C5×C8C22×D311yescharacteristic
315C5×C4⋊C4—31no—
316C5×C22⋊C4—61no—
317C22⋊Dic5—61no—
318C22⋊Dic5—61no—
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321C22⋊Dic5D1211yescharacteristic
322#686—121no—
323#685—61no—
324#685D1211yescharacteristic
325C4⋊Dic5—31no—
326C4⋊Dic5—31no—
327C4⋊Dic5—31no—
328C4⋊Dic5—61no—
329#683—61no—
330#683—61no—
331#683D1211yescharacteristic
332C4×Dic5C22×D311yescharacteristic
333C2×#168—41no—
334C2×#168C22×D311yescharacteristic
335C2×#168C22×D311yescharacteristic
336C8×D5—41no—
337#547—151no—
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—31no—
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—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—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C5×D3—84no—
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—
377Dic15—41no—
378Dic15—41no—
379C3×Dic5—21no—
380C3×Dic5—21no—
381C3×Dic5C2×D812yes—
382C5×Dic3—41no—
383C23×D3—21no—
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—101no—
393C22×Dic3—101no—
394#237—204no—
395D3×D4—204no—
396C2×D12—22no—
397C2×D12—21no—
398C2×D12—41no—
399C2×D12—51no—
400C2×D12—102no—
401C2×D12—101no—
402C2×D12—101no—
403C2×D12—101no—
404C2×D12—201no—
405C2×D12C22×D511yescharacteristic
406C2×D12C22×D511yescharacteristic
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—51no—
428C4⋊Dic3—51no—
429C4⋊Dic3—51no—
430C4⋊Dic3—101no—
431C4⋊Dic3—101no—
432C4⋊Dic3—101no—
433C4⋊Dic3C22×D511yescharacteristic
434D24—22no—
435D24—41no—
436D24—201no—
437C23×C5—61no—
438C23×C5—61no—
439C23×C5—61no—
440C23×C5—122no—
441C23×C5—122no—
442C23×C5—241no—
443C23×C5C2×D1211yescharacteristic
444C22×D5—61no—
445C22×D5—122no—
446C22×D5—122no—
447C22×D5—241no—
448C22×D5C2×D1211yescharacteristic
449C5×D4—32no—
450C5×D4—61no—
451C5×D4—61no—
452C5×D4—61no—
453C5×D4—61no—
454C5×D4—61no—
455C5×D4—122no—
456C5×D4—122no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—61no—
460C2×C4×C5C2×D1211yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—122no—
463C22⋊D5—122no—
464C22⋊D5—122no—
465C22⋊D5—122no—
466C22⋊D5—122no—
467C22⋊D5—241no—
468C22⋊D5D2414yescomplemented
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—122no—
473C2×Dic5—122no—
474C2×Dic5—122no—
475C2×Dic5C2×D1211yescharacteristic
476C2×Dic5C2×D1211yescharacteristic
477C2×Dic5C2×D1211yescharacteristic
478D20—61no—
479D20—61no—
480C4×D5—21no—
481C4×D5—21no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—21no—
487#168—21no—
488C2×#41—301no—
489C22×D4—31no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—31no—
493C2×D8—31no—
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—151no—
513C2×C4⋊C4—151no—
514#107—151no—
515#107—151no—
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—81no—
536C3×D5—22no—
537C5×D3—42no—
538C5×D3—81no—
539C5×D3—81no—
540C23×C3—51no—
541C23×C3D4×D511yescharacteristic
542C22×D3—21no—
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×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—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—202no—
571C2×Dic3—202no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—42no—
578D12—101no—
579D12—101no—
580D12—202no—
581D12—202no—
582D12—401no—
583D12#71112yescomplemented
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—62no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5—121no—
597C22×C5—121no—
598C22×C5—121no—
599C22×C5—121no—
600C22×C5—121no—
601C22×C5—121no—
602C22×C5—244no—
603C22×C5C2×D2412yes—
604C22×C5C22×D1211yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—244no—
611C2×D5C2×D2412yes—
612C4×C5—21no—
613C4×C5—121no—
614C4×C5#100411yescharacteristic
615C4×C5D3×#4111yescharacteristic
616Dic5—21no—
617Dic5—21no—
618Dic5—121no—
619Dic5—121no—
620Dic5—121no—
621Dic5C2×D2412yes—
622C24—61no—
623C24—301no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—51no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—121no—
634C2×D4—151no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—302no—
639C2×D4—301no—
640C2×D4—301no—
641C2×D4—301no—
642C2×D4—601no—
643C2×D4—604no—
644C22×C4—51no—
645C22×C4—301no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—62no—
651D8—121no—
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—51no—
661C4⋊C4—151no—
662C4⋊C4—151no—
663C4⋊C4—151no—
664C4⋊C4—301no—
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—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
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—52no—
700C3×C4—101no—
701C3×C4—101no—
702C3×C4C2×#71111yescharacteristic
703C3×C4#414411yescharacteristic
704Dic3—41no—
705Dic3—201no—
706Dic3—201no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—122no—
710C2×C5—241no—
711C2×C5—241no—
712C2×C5#555411yescharacteristic
713C2×C5C22×D2411yescharacteristic
714C2×C5#575111yescharacteristic
715D5—22no—
716D5—241no—
717C23—51no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—122no—
722C23—122no—
723C23—241no—
724C23—301no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D5×D1211yescharacteristic
729Q8—602no—
730D4—32no—
731D4—54no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—122no—
738D4—122no—
739D4—301no—
740D4—301no—
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—101no—
754C2×C4—101no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—602no—
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#6592511yescharacteristic
771C2×C3C2×D5×D811yescharacteristic
772C2×C3#6610911yescharacteristic
773D3—42no—
774D3—81no—
775D3—81no—
776D3—401no—
777C5#7943811yescharacteristic, 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—121no—
790C22—121no—
791C22—121no—
792C22—244no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D5×D2412yes—
798C22C2×D5×D1211yescharacteristic
799C4—21no—
800C4—52no—
801C4—101no—
802C4—101no—
803C4—121no—
804C4—601no—
805C4—601no—
806C4—601no—
807C4D3×#71111yescharacteristic
808C4#9202511yescharacteristic
809C3#1061174511yescharacteristic, complemented, Sylow
810C2—22no—
811C2—102no—
812C2—122no—
813C2—241no—
814C2—241no—
815C2—1201no—
816C2#1175326511yescharacteristic
817C2C2×D5×D2411yescharacteristic
818C2#1175402311yescharacteristic
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. D12×C22⋊D5C2semidirect
2. #11754326C2semidirect
3. #11750837C2semidirect
4. C5×#4732C2semidirect
5. C3×#65014C2semidirect
6. #11748514C2semidirect
7. C2×#90967C2semidirect
8. #11748116C2semidirect
9. D5×#821C2semidirect
10. #11747995C2semidirect
11. #11747898C2semidirect
12. #11747765C2semidirect
13. #11747764C2semidirect
14. Dic5×D24C2semidirect
15. #11747617C2semidirect
22. C2×C4⋊Dic15C22semidirect
23. C5×#930C22semidirect
25. C2×C5×D24C22semidirect
27. C22×C3×#168C22semidirect
28. C2×C3×C8×D5C22semidirect
32. #91468C22semidirect
35. #91449C22semidirect
39. Dic5×D12C22semidirect
41. D5×C4⋊Dic3C22semidirect
42. C2×#6654C22semidirect
43. C3×C5×C22⋊C8C22semidirect
44. #91105C22semidirect
45. #91105C22semidirect
46. #91102C22semidirect
47. #91102C22semidirect
49. C5×#821C22semidirect
50. C3×#3952C22semidirect
51. C3×#3946C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90988C22semidirect
54. #90969C22semidirect
57. #90967C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
75. #65014D3semidirect
142. #4732D5semidirect
165. C22×#168C2×D3semidirect
166. C2×C8×D5C2×D3semidirect
173. C5×C22⋊C8C2×D3semidirect
181. #3952C2×D3semidirect
184. #3946C2×D3semidirect
185. C8×Dic5C2×D3semidirect
220. C5×D12#41semidirect
221. C3×C22⋊D5D8semidirect
250. #930C2×D5semidirect
255. C2×D24C2×D5semidirect
268. C3×C22⋊C8C2×D5semidirect
279. #821C2×D5semidirect
468. C22⋊D5D24semidirect
529. C22⋊C8D3×D5semidirect
583. D12#711semidirect
676. C3×C5#3294semidirect
777. C5#79438semidirect
809. C3#10611745semidirect

Maximal subgroups

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

subgroupindex
D12×C22⋊D52
#117543262
#117508372
C5×#47322
C3×#650142
#117485142
C2×#909672
#117481162
D5×#8212
#117479952
#117478982
#117477652
#117477642
Dic5×D242
#117476172
#106117453
#794385