Finite Group Databasebeta

← #14459067

Subgroups — #14459067

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#11752696C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic, complemented
4C3×#65346C211yesmaximal, characteristic, complemented
5#11749281C211yesmaximal, characteristic, complemented
6#11749274C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749202C211yesmaximal, characteristic, complemented
9#11749032C211yesmaximal, characteristic, complemented
10#11749028C211yesmaximal, characteristic, complemented
11#11748968C211yesmaximal, characteristic, complemented
12D3×#3964C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746998C211yesmaximal, characteristic, complemented
15#11746894C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20#91759C2211yescharacteristic, complemented
21C5×#946C2211yescharacteristic
22C5×#938C2211yescharacteristic
23C5×#884—21no—
24C5×#883—21no—
25C5×#882—21no—
26C5×D3×C22⋊C4—21no—
27C4×C5×D12C2211yescharacteristic
28C4×C5×D12C2211yescharacteristic
29C2×C3×#688C2211yescharacteristic, complemented
30C2×C3×#686C2211yescharacteristic
31C3×C4×D20C2211yescharacteristic, complemented
32#91456C2211yescharacteristic
33#91456C2211yescharacteristic, complemented
34#91453—21no—
35#91447—21no—
36#91440—21no—
37D3×C4⋊Dic5C2211yescharacteristic
38#91361—21no—
39#91338C2211yescharacteristic, complemented
40C2×#6652C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91119C2211yescharacteristic, complemented
45#91116C2211yescharacteristic
46#91116C2211yescharacteristic
47C4×C3⋊#168C2211yescharacteristic, complemented
48C3×#3967C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×C4⋊#168C2211yescharacteristic, complemented
51#90989C2211yescharacteristic, complemented
52#90988C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90967C2211yescharacteristic
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90964C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#80559—51nomaximal, Hall
61C5×#546—31no—
62#65899—31no—
63#65527—31no—
64#65522—31no—
65#65506—31no—
66C2×#3964—31no—
67#65346D311yescharacteristic, complemented
68#65345—31no—
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×C5×#67—21no—
80C2×C5×#67—21no—
81C5×#239—22no—
82C5×#239—41no—
83C5×D3×D4—22no—
84C5×D3×D4—41no—
85C2×C5×D12—21no—
86C2×C5×D12D411yescharacteristic
87C2×C5×D12C2311yescharacteristic
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3C2311yescharacteristic
91C2×C4×C5×D3C2311yescharacteristic
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5—21no—
94C2×#1201—21no—
95C2×#1201—21no—
96C2×D3×Dic5—21no—
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C42×C5C2311yescharacteristic
100C4⋊Dic15C2311yescharacteristic
101C4⋊Dic15C2311yescharacteristic
102#6712—21no—
103#6712—21no—
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×#688—41no—
115C3×#686—41no—
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120Dic3⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125#6652—22no—
126D3×#168—41no—
127D3×#168—41no—
128#5676D511yescharacteristic, complemented
129#5558—51no—
130C3×#463—51no—
131#5172—51no—
132#5171—51no—
133#5157—51no—
134#5156—51no—
135#5056—51no—
136C4×#213—51no—
137#4847—51no—
138#4834—51no—
139#4811—51no—
140#4804—51no—
141#4779—51no—
142D3×#102—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×#688C2×D311yescharacteristic, complemented
155#4085—61no—
156C2×#686—31no—
157C2×#686C2×D311yescharacteristic
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×D20C2×D311yescharacteristic, complemented
168#4016—31no—
169#3967—31no—
170#3967—31no—
171#3967C2×D311yescharacteristic, complemented
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964C2×D311yescharacteristic
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168C2×D311yescharacteristic, complemented
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C22×C5×D3—21no—
189C22×C5×D3—42no—
190C22×C5×D3—42no—
191C22×C5×D3—81no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C5×D3C2×D411yescharacteristic
194C22×C3×D5—21no—
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—
204C2×Dic15—21no—
205C5×#67—42no—
206C5×#67—81no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C5×D12—22no—
211C5×D12—21no—
212C5×D12—42no—
213C5×D12#4112yes—
214C4×C5×D3—21no—
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C4×C5×D3—42no—
219C4×C5×D3—81no—
220C2×C3×Dic5—21no—
221C3×D20—21no—
222C3×D20—21no—
223C3×C4×D5—81no—
224#1201—42no—
225#1201—81no—
226D3×Dic5—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#239C2×D511yescharacteristic
232C2×D3×D4C2×D511yescharacteristic
233C2×C3×SD16—51no—
234C2×C3×D8—51no—
235C3×#124C2×D511yescharacteristic
236C3×C4×D4—51no—
237#946C2×D511yescharacteristic
238#938—51no—
239#938—51no—
240#938C2×D511yescharacteristic
241C2×#213—51no—
242#929—101no—
243C4×#67—101no—
244C2×D3×C8—51no—
245C2×D3×C8—51no—
246#892—51no—
247D3×C4⋊C4—51no—
248#884—21no—
249#884—101no—
250#883—21no—
251#882—21no—
252D3×C22⋊C4—21no—
253#879—101no—
254C4×D12C2×D511yescharacteristic
255C4×D12C2×D511yescharacteristic
256#870—51no—
257C3×C4⋊C8—51no—
258C3×#103—51no—
259C3×#102—51no—
260#835—51no—
261#835—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#821—51no—
266#821—51no—
267(C2×D3)⋊C8—51no—
268(C2×D3)⋊C8—51no—
269#818—51no—
270#817—51no—
271#809—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×D20C22×D311yescharacteristic
294C2×C4×D5—21no—
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—41no—
308#686—41no—
309#686—62no—
310#685—21no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5C22×D311yescharacteristic
317#683—61no—
318#683—61no—
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—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—51no—
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×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—22no—
349C2×C5×D3—21no—
350C2×C5×D3—21no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3—84no—
354C2×C5×D3#13512yes—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364Dic15—41no—
365C3×Dic5—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C23×D3—21no—
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—101no—
377C2×#67—101no—
378#239—22no—
379#239—41no—
380D3×D4—22no—
381D3×D4—41no—
382C2×D12—21no—
383C2×D12C22⋊D511yescharacteristic
384C2×D12C22×D511yescharacteristic
385C2×C4×D3—21no—
386C2×C4×D3—21no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×C4×D3C22×D511yescharacteristic
390C3×SD16—201no—
391C3×D8—201no—
392C2×C3×C8—51no—
393C2×C3×C8—51no—
394C3×C4⋊C4—51no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—101no—
398C3×C42C22×D511yescharacteristic
399#217—21no—
400#217—101no—
401#217—101no—
402#213—102no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4C22⋊D511yescharacteristic
407(C2×D3)⋊C4C22⋊D511yescharacteristic
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3C22⋊D511yescharacteristic
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—101no—
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416C4×Dic3—101no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
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—21no—
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—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—21no—
459D20—21no—
460C4×D5—81no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—31no—
466C22×D4—31no—
467C2×SD16—51no—
468C2×D8—51no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
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—51no—
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—51no—
495#103—51no—
496#103—151no—
497#103—151no—
498#102—51no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—81no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C3×D5—81no—
513C5×D3—22no—
514C5×D3—41no—
515C5×D3—42no—
516C23×C3—21no—
517C23×C3—101no—
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—81no—
522C22×D3C2×C22⋊D511yescharacteristic
523C22×D3C2×C22⋊D511yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—101no—
529C3×D4—101no—
530C2×C3×C4—21no—
531C2×C3×C4—101no—
532C2×C3×C4—401no—
533C2×C3×C4C2×C22⋊D511yescharacteristic
534C2×C3×C4C2×C22⋊D511yescharacteristic
535C2×C3×C4C23×D511yescharacteristic
536#67—42no—
537#67—81no—
538#67—202no—
539#67—401no—
540C2×Dic3—21no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3C2×C22⋊D511yescharacteristic
544C2×Dic3C2×C22⋊D511yescharacteristic
545D12—22no—
546D12—21no—
547D12—42no—
548D12#71112yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—42no—
554C4×D3—81no—
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—61no—
568C22×C5—61no—
569C22×C5—62no—
570C22×C5—121no—
571C22×C5—121no—
572C22×C5—244no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—41no—
580C4×C5—61no—
581C4×C5—61no—
582C4×C5—121no—
583C4×C5#100411yescharacteristic
584C4×C5D3×#4111yescharacteristic
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8C2×D3×D511yescharacteristic
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—61no—
599C2×D4—121no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—101no—
608C22×C4—301no—
609SD16—201no—
610D8—201no—
611D8—302no—
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—61no—
622C4⋊C4—151no—
623C4⋊C4—151no—
624C4⋊C4—301no—
625C4⋊C4—301no—
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—101no—
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×C3—201no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3C22×C22⋊D511yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—22no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—84no—
657C2×D3#409612yes—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—201no—
662C3×C4C2×#71111yescharacteristic
663C3×C4#414411yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—62no—
670C2×C5—81no—
671C2×C5—121no—
672C2×C5—122no—
673C2×C5#561211yescharacteristic
674C2×C5D3×#13511yescharacteristic
675C2×C5#577411yescharacteristic
676D5—81no—
677C23—21no—
678C23—31no—
679C23—31no—
680C23—61no—
681C23—101no—
682C23—122no—
683C23—122no—
684C23—241no—
685Q8—21no—
686Q8—21no—
687D4—21no—
688D4—21no—
689D4—32no—
690D4—62no—
691D4—61no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—122no—
696D4—241no—
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—122no—
709C2×C4—241no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—401no—
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—401no—
723C2×C3#6614011yescharacteristic
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616911yescharacteristic
726D3—22no—
727D3—41no—
728D3—42no—
729C5#8055911yescharacteristic, 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—201no—
743C22—201no—
744C22—201no—
745C22—244no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4D3×#71111yescharacteristic
757C4#9202511yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—62no—
760C2—81no—
761C2—121no—
762C2—122no—
763C2—401no—
764C2#1175494611yescharacteristic
765C2D3×#409611yescharacteristic
766C2#1175532311yescharacteristic
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. #11752696C2semidirect
3. #11751157C2semidirect
4. C3×#65346C2semidirect
5. #11749281C2semidirect
6. #11749274C2semidirect
7. #11749211C2semidirect
8. #11749202C2semidirect
9. #11749032C2semidirect
10. #11749028C2semidirect
11. #11748968C2semidirect
12. D3×#3964C2semidirect
13. C4×#6652C2semidirect
14. #11746998C2semidirect
15. #11746894C2semidirect
20. #91759C22semidirect
29. C2×C3×#688C22semidirect
31. C3×C4×D20C22semidirect
33. #91456C22semidirect
39. #91338C22semidirect
42. C2×D3×#168C22semidirect
43. #91119C22semidirect
44. #91119C22semidirect
47. C4×C3⋊#168C22semidirect
48. C3×#3967C22semidirect
50. C3×C4⋊#168C22semidirect
51. #90989C22semidirect
52. #90988C22semidirect
53. #90985C22semidirect
57. #90964C22semidirect
59. (C2×D3)⋊#168C22semidirect
67. #65346D3semidirect
128. #5676D5semidirect
154. C2×#688C2×D3semidirect
167. C4×D20C2×D3semidirect
171. #3967C2×D3semidirect
184. C4⋊#168C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#80559semidirect
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
#117526962
#117511572
C3×#653462
#117492812
#117492742
#117492112
#117492022
#117490322
#117490282
#117489682
D3×#39642
C4×#66522
#117469982
#117468942
#106152263
#805595