Finite Group Databasebeta

← #14459066

Subgroups — #14459066

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5676C211yesmaximal, characteristic, complemented
2#11752617C211yesmaximal, characteristic, complemented
3#11751158C211yesmaximal, characteristic, complemented
4C3×#65345C211yesmaximal, characteristic, complemented
5#11749282C211yesmaximal, characteristic, complemented
6#11749280C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749202C211yesmaximal, characteristic, complemented
9#11749034C211yesmaximal, characteristic, complemented
10#11749033C211yesmaximal, characteristic, complemented
11#11748966C211yesmaximal, characteristic, complemented
12D3×#3964C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14D12×#168C211yesmaximal, characteristic, complemented
15#11746902C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C2×#6717C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic
22C4×D60C2211yescharacteristic, complemented
23C5×#946C2211yescharacteristic
24C5×#938C2211yescharacteristic
25C5×#884—21no—
26C5×#883—21no—
27C5×#882—21no—
28C5×D3×C22⋊C4—21no—
29C4×C5×D12C2211yescharacteristic
30C4×C5×D12C2211yescharacteristic
31C3×#4016C2211yescharacteristic, complemented
32#91460C2211yescharacteristic
33#91460C2211yescharacteristic, complemented
34D3×C4⋊Dic5C2211yescharacteristic
35#91416—21no—
36#91406—21no—
37#91355—21no—
38#91338C2211yescharacteristic, complemented
39#91337—21no—
40C2×#6654C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91116C2211yescharacteristic
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×#3967C2211yescharacteristic, complemented
48C3×#3964C2211yescharacteristic
49C3×#3964C2211yescharacteristic
50C3×C4×#168C2211yescharacteristic, complemented
51#90989C2211yescharacteristic, complemented
52#90988C2211yescharacteristic, complemented
53#90986C2211yescharacteristic, complemented
54#90969C2211yescharacteristic, complemented
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#81653—51nomaximal, Hall
61C5×#546—31no—
62#65899—31no—
63#65527—31no—
64#65522—31no—
65#65506—31no—
66C2×#3964—31no—
67#65346—31no—
68#65345D311yescharacteristic, complemented
69#65337—31no—
70#65333—31no—
71#65327—31no—
72#65324—31no—
73C4×#686—31no—
74D4×#168—31no—
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×#67—21no—
82C2×C5×#67—21no—
83C5×#239—22no—
84C5×#239—41no—
85C5×D3×D4—22no—
86C5×D3×D4—41no—
87C2×C5×D12—21no—
88C2×C5×D12D411yescharacteristic
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C4×C5×D3C2311yescharacteristic
94C2×#1203—21no—
95C2×#1203—21no—
96C2×D3×Dic5—21no—
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C42×C5C2311yescharacteristic
100#6717—41no—
101#6715—41no—
102#6714—21no—
103C4⋊Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#217—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4D411yescharacteristic
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×C4⋊Dic3D411yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6667—21no—
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124Dic3×Dic5—21no—
125#6654—22no—
126D3×#168—41no—
127D3×#168—41no—
128#5695—51no—
129#5676D511yescharacteristic, complemented
130C3×#488—51no—
131#5066—51no—
132#5057—51no—
133#4811—51no—
134#4810—51no—
135#4807—51no—
136#4804—51no—
137#4784—51no—
138#4775—51no—
139#4773—51no—
140D3×#102—51no—
141C4×D24—51no—
142C8×D12—51no—
143C2×C5×#41—31no—
144C22×C5×D4—31no—
145C5×#124C2×D311yescharacteristic
146C5×#123—61no—
147C5×C22⋊Q8—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C2×C5×C22⋊C4—61no—
154C2×#688—31no—
155#4085—61no—
156C2×#686—31no—
157C2×#686—31no—
158#4076—31no—
159#4076—31no—
160#4072—31no—
161C2×C4⋊Dic5—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4044—61no—
165#4029—61no—
166#4027—61no—
167C4×D20—31no—
168#4016C2×D311yescharacteristic, complemented
169#3967—31no—
170#3967C2×D311yescharacteristic, complemented
171#3967C2×D311yescharacteristic, complemented
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964C2×D311yescharacteristic
177#3964C2×D311yescharacteristic
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168C2×D311yescharacteristic, complemented
186#3297—151noSylow
187C23×C3×C5—21no—
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C5×D3—42no—
191C22×C5×D3—42no—
192C22×C5×D3—81no—
193C22×C5×D3C2×D411yescharacteristic
194C22×C5×D3C2×D411yescharacteristic
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204D60—21no—
205D60—21no—
206C4×D15—81no—
207C5×#67—42no—
208C5×#67—81no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—22no—
213C5×D12—21no—
214C5×D12—42no—
215C5×D12#4112yes—
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C4×C5×D3—21no—
220C4×C5×D3—42no—
221C4×C5×D3—81no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224#1203—42no—
225#1203—81no—
226D3×Dic5—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#239C2×D511yescharacteristic
232C2×D3×D4C2×D511yescharacteristic
233C3×#125—51no—
234C3×#124C2×D511yescharacteristic
235#946C2×D511yescharacteristic
236C2×#215—51no—
237#938C2×D511yescharacteristic
238C2×#213—51no—
239C2×D24—51no—
240C2×D3×C8—51no—
241C2×D3×C8—51no—
242#898—101no—
243#895—51no—
244#895—51no—
245#895—101no—
246#894—101no—
247#893—101no—
248#892—51no—
249D3×C4⋊C4—51no—
250#884—21no—
251#883—21no—
252#882—21no—
253D3×C22⋊C4—21no—
254C4×D12—51no—
255C4×D12C2×D511yescharacteristic
256C4×D12C2×D511yescharacteristic
257C3×#103—51no—
258C3×#103—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×C4×C8—51no—
262#835—51no—
263#832—51no—
264#821—51no—
265#821—51no—
266(C2×D3)⋊C8—51no—
267(C2×D3)⋊C8—51no—
268#818—51no—
269#809—51no—
270#809—51no—
271#808—51no—
272#807—51no—
273C4⋊(C3⋊C8)—51no—
274C24×C5—61no—
275C5×#41—62no—
276C5×#41—121no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4—31no—
279C2×C5×D4—31no—
280C2×C5×D4—61no—
281C2×C5×D4—61no—
282C2×C5×D4—62no—
283C2×C5×D4—61no—
284C2×C5×D4—121no—
285C2×C5×D4C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—61no—
289C22×C4×C5—61no—
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C22×Dic5—61no—
293C2×D20—31no—
294C2×C4×D5—61no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—61no—
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—31no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C5×C22⋊C4—61no—
305C42×C5C22×D311yescharacteristic
306C22⋊Dic5—61no—
307#688—121no—
308#686—62no—
309#686—121no—
310#685—61no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—61no—
315C4⋊Dic5C22×D311yescharacteristic
316C4⋊Dic5C22×D311yescharacteristic
317#683—21no—
318#683—21no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—151no—
327#546—31no—
328#488—51no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—41no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3—21no—
351C2×C5×D3—22no—
352C2×C5×D3—21no—
353C2×C5×D3—21no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—84no—
357C2×C5×D3#13512yes—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364C3×Dic5—41no—
365C3×Dic5—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C23×D3—21no—
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4C22×D511yescharacteristic
372C2×#67—21no—
373C2×#67—21no—
374#239—22no—
375#239—41no—
376D3×D4—22no—
377D3×D4—41no—
378C2×D12—21no—
379C2×D12—51no—
380C2×D12—101no—
381C2×D12—101no—
382C2×D12C22⋊D511yescharacteristic
383C2×D12C22×D511yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×C4×D3C22×D511yescharacteristic
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C42C22×D511yescharacteristic
399#217—21no—
400#215—201no—
401#213—201no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4C22⋊D511yescharacteristic
409(C2×D3)⋊C4C22⋊D511yescharacteristic
410C4⋊Dic3—51no—
411C4⋊Dic3C22⋊D511yescharacteristic
412C4⋊Dic3C22×D511yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—101no—
415C4×Dic3—101no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418D24—102no—
419D3×C8—201no—
420D3×C8—201no—
421C23×C5—21no—
422C23×C5—31no—
423C23×C5—31no—
424C23×C5—61no—
425C23×C5—122no—
426C23×C5—122no—
427C23×C5—241no—
428C22×D5—61no—
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—21no—
432C5×D4—21no—
433C5×D4—32no—
434C5×D4—62no—
435C5×D4—61no—
436C5×D4—122no—
437C5×D4—122no—
438C5×D4—241no—
439C2×C4×C5—21no—
440C2×C4×C5—31no—
441C2×C4×C5—31no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—122no—
448C2×C4×C5—241no—
449C2×C4×C5D3×D411yescharacteristic
450C2×C4×C5D3×D411yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—122no—
453C22⋊D5—241no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—61no—
459D20—61no—
460C4×D5—241no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—31no—
466C22×D4—31no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—301no—
473#125—51no—
474#124D3×D511yescharacteristic
475#123—61no—
476#123—301no—
477C22⋊Q8—31no—
478#121—31no—
479#121—61no—
480#121—151no—
481#121—151no—
482#121—301no—
483#120—61no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—61no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—51no—
496#103—51no—
497#103—151no—
498#102—51no—
499#102—51no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—51no—
508C2×C3×C5—81no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512D15—81no—
513C5×D3—22no—
514C5×D3—41no—
515C5×D3—42no—
516C23×C3—21no—
517C22×D3—21no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—81no—
521C22×D3—101no—
522C22×D3C2×C22⋊D511yescharacteristic
523C22×D3C2×C22⋊D511yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—21no—
527C3×D4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4C2×C22⋊D511yescharacteristic
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—42no—
535#67—81no—
536C2×Dic3—21no—
537C2×Dic3—101no—
538C2×Dic3C2×C22⋊D511yescharacteristic
539C2×Dic3C2×C22⋊D511yescharacteristic
540D12—22no—
541D12—21no—
542D12—42no—
543D12—101no—
544D12—101no—
545D12—202no—
546D12—401no—
547D12#71112yes—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—42no—
553C4×D3—81no—
554C4×D3—401no—
555C4×D3—401no—
556C3×C8—101no—
557C3×C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—32no—
561C22×C5—41no—
562C22×C5—41no—
563C22×C5—41no—
564C22×C5—61no—
565C22×C5—61no—
566C22×C5—61no—
567C22×C5—62no—
568C22×C5—61no—
569C22×C5—61no—
570C22×C5—121no—
571C22×C5—121no—
572C22×C5—244no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—121no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—41no—
580C4×C5—61no—
581C4×C5—61no—
582C4×C5—121no—
583C4×C5D3×#4111yescharacteristic
584C4×C5#100911yescharacteristic
585Dic5—41no—
586Dic5—41no—
587Dic5—121no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8C2×D3×D511yescharacteristic
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—151no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—301no—
608C22×C4—301no—
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—61no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—151no—
626C4⋊C4—301no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—301no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3C22×C22⋊D511yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—22no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—84no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3#409612yes—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—201no—
662C3×C4—201no—
663C3×C4C2×#71111yescharacteristic
664C3×C4#414411yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—201no—
669C2×C5—62no—
670C2×C5—81no—
671C2×C5—121no—
672C2×C5—122no—
673C2×C5#567611yescharacteristic
674C2×C5D3×#13511yescharacteristic
675C2×C5#576911yescharacteristic
676D5—241no—
677C23—21no—
678C23—31no—
679C23—31no—
680C23—61no—
681C23—122no—
682C23—122no—
683C23—241no—
684C23—301no—
685Q8—21no—
686Q8—21no—
687D4—21no—
688D4—21no—
689D4—32no—
690D4—62no—
691D4—61no—
692D4—122no—
693D4—122no—
694D4—241no—
695D4—301no—
696D4—301no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—122no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—1201no—
713C2×C4—1201no—
714C2×C4D3×C22⋊D511yescharacteristic
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—81no—
722C2×C3#6614011yescharacteristic
723C2×C3C2×#409611yescharacteristic
724C2×C3#6616911yescharacteristic
725D3—22no—
726D3—41no—
727D3—42no—
728D3—401no—
729C5#8165311yescharacteristic, complemented, Sylow
730C22—32no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—62no—
740C22—121no—
741C22—121no—
742C22—244no—
743C22—601no—
744C22—601no—
745C22—601no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—201no—
754C4—201no—
755C4—601no—
756C4D3×#71111yescharacteristic
757C4#9202711yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—62no—
760C2—81no—
761C2—121no—
762C2—122no—
763C2—1201no—
764C2#1175494911yescharacteristic
765C2D3×#409611yescharacteristic
766C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5676C2semidirect
2. #11752617C2semidirect
3. #11751158C2semidirect
4. C3×#65345C2semidirect
5. #11749282C2semidirect
6. #11749280C2semidirect
7. #11749211C2semidirect
8. #11749202C2semidirect
9. #11749034C2semidirect
10. #11749033C2semidirect
11. #11748966C2semidirect
12. D3×#3964C2semidirect
13. C4×#6654C2semidirect
14. D12×#168C2semidirect
15. #11746902C2semidirect
20. C2×#6717C22semidirect
22. C4×D60C22semidirect
31. C3×#4016C22semidirect
33. #91460C22semidirect
38. #91338C22semidirect
42. C2×D3×#168C22semidirect
43. #91119C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. C3×#3967C22semidirect
47. C3×#3967C22semidirect
50. C3×C4×#168C22semidirect
51. #90989C22semidirect
52. #90988C22semidirect
53. #90986C22semidirect
54. #90969C22semidirect
59. (C2×D3)⋊#168C22semidirect
68. #65345D3semidirect
129. #5676D5semidirect
168. #4016C2×D3semidirect
170. #3967C2×D3semidirect
171. #3967C2×D3semidirect
185. C4×#168C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#81653semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
C5×#56762
#117526172
#117511582
C3×#653452
#117492822
#117492802
#117492112
#117492022
#117490342
#117490332
#117489662
D3×#39642
C4×#66542
D12×#1682
#117469022
#106152263
#816535