Finite Group Databasebeta

← #14458952

Subgroups — #14458952

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
1C3×#65848C211yesmaximal, characteristic, complemented
2#11754540C211yesmaximal, characteristic, complemented
3#11751071C211yesmaximal, characteristic, complemented
4C2×C5×#809C211yesmaximal, characteristic, complemented
5#11748539C211yesmaximal, characteristic, complemented
6#11748516C211yesmaximal, characteristic, complemented
7C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
8#11747510C211yesmaximal, characteristic, complemented
9#11747499C211yesmaximal, characteristic, complemented
10#11747368C211yesmaximal, characteristic, complemented
11#11747310C211yesmaximal, characteristic, complemented
12#11747307C211yesmaximal, characteristic, complemented
13#11747241C211yesmaximal, characteristic, complemented
14#11747216C211yesmaximal, characteristic, complemented
15#11747142C211yesmaximal, characteristic, complemented
16#10610491—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20#91813C2211yescharacteristic
21C22×C5×C3⋊C8C2211yescharacteristic
22C3×#4076—21no—
23C3×#4076C2211yescharacteristic
24C3×C4×C22⋊D5—21no—
25C3×C4×C22⋊D5C2211yescharacteristic
26C3×#4044—21no—
27C3×#4041C2211yescharacteristic, complemented
28C3×#4040—21no—
29C3×#4039C2211yescharacteristic, complemented
30C3×#4038C2211yescharacteristic, complemented
31C3×#4036C2211yescharacteristic, complemented
32#91568—21no—
33D3×C22⋊Dic5—21no—
34#91453—21no—
35#91449C2211yescharacteristic
36#91423—21no—
37Dic5×D12C2211yescharacteristic
38#91373C2211yescharacteristic
39C2×#6657C2211yescharacteristic, complemented
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91114C2211yescharacteristic
44#91094C2211yescharacteristic, complemented
45#91094C2211yescharacteristic, complemented
46#91091C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C5×#809C2211yescharacteristic
49C5×#809C2211yescharacteristic
50C5×#809C2211yescharacteristic
51C5×#809C2211yescharacteristic
52#90987C2211yescharacteristic, complemented
53#90982C2211yescharacteristic, complemented
54#90974C2211yescharacteristic, complemented
55#90966C2211yescharacteristic
56#90966C2211yescharacteristic
57#90965C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61#66140—31no—
62#65848D311yescharacteristic, complemented
63C2×C5×#102—31no—
64#65506—31no—
65#65403—31no—
66C8×C22⋊D5—31no—
67#65259—31no—
68#65076—31no—
69#65070—31no—
70#65068—31no—
71#65064—31no—
72#65061—31no—
73#65057—31no—
74#65052—31no—
75#65045—31no—
76C23×C5×D3—21no—
77C22×C3×C4×C5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×D12—22no—
81C2×C5×D12—21no—
82C2×C5×D12—41no—
83C2×C5×D12C2311yescharacteristic
84C2×C5×D12C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5D411yescharacteristic
87C2×C3×D20—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×#1201—21no—
92C2×#1201—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5—21no—
95#6772—22no—
96#6772—41no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100#6719—21no—
101C4⋊Dic15C2311yescharacteristic
102#6712—21no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C5×C3⋊C8—41no—
106C2×C5×C3⋊C8C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C3×C22⋊Dic5D411yescharacteristic
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683D411yescharacteristic
118C3×C4×Dic5—21no—
119C3×C4×Dic5C2311yescharacteristic
120(C2×D3)⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124#6657—41no—
125#6652—22no—
126#6652—41no—
127D5×C3⋊C8—41no—
128C3×#553—51no—
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5041—51no—
133#5038—51no—
134#5037—51no—
135#5036—51no—
136#5016—51no—
137C4×#213—51no—
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4970—51no—
142C2×#809D511yescharacteristic, complemented
143C22×C5×D4—31no—
144C2×#711—31no—
145C22×C5×C8—31no—
146C2×C5×C4⋊C4C2×D311yescharacteristic
147#4099—61no—
148C2×C22⋊Dic5—61no—
149#4085—61no—
150#4084—31no—
151#4082—31no—
152#4081—61no—
153D4×Dic5—31no—
154C2×#686—31no—
155C2×#686—31no—
156#4076—21no—
157#4076C2×D311yescharacteristic
158C4×C22⋊D5—21no—
159C4×C22⋊D5C2×D311yescharacteristic
160#4070—31no—
161C2×#677—31no—
162C2×C8×D5—31no—
163#4044—21no—
164#4041C2×D311yescharacteristic, complemented
165#4040—21no—
166#4039C2×D311yescharacteristic, complemented
167#4038C2×D311yescharacteristic, complemented
168#4036C2×D311yescharacteristic, complemented
169C5×#102—31no—
170C5×#102—31no—
171C5×#102—31no—
172C5×#102—31no—
173#3964—31no—
174#3964—31no—
175C22⋊#168—31no—
176#3953—31no—
177#3952—31no—
178#3949—31no—
179#3948—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3942—31no—
183#3942—31no—
184#3939—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—42no—
191C22×C5×D3—42no—
192C22×C5×D3—81no—
193C22×C3×D5—21no—
194C22×C3×D5C2×D411yescharacteristic
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—21no—
204Dic30—21no—
205Dic30—21no—
206C5×D12—21no—
207C5×D12—21no—
208C5×D12—21no—
209C5×D12—42no—
210C5×D12#4112yes—
211C3×C22⋊D5—22no—
212C3×C22⋊D5—42no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—21no—
218C3×D20—21no—
219C3×D20—81no—
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—81no—
223#1201—42no—
224#1201—81no—
225D3×Dic5—42no—
226D3×Dic5—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×#235—51no—
232C22×D12C2×D511yescharacteristic
233C3×#126—101no—
234C3×#125—51no—
235C3×#123—101no—
236C3×#121—51no—
237C3×#121—51no—
238C3×#121—101no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—101no—
242C3×#117—51no—
243C2×C3×C4⋊C4C2×D511yescharacteristic
244#937—101no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213—51no—
248#930—51no—
249#924—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8C2×D511yescharacteristic
252#894—101no—
253#884—101no—
254D3×C22⋊C4—101no—
255#875—51no—
256C4×D12—51no—
257#832—51no—
258#830—51no—
259#830—51no—
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809C2×D511yescharacteristic
266#809C2×D511yescharacteristic
267#809C2×D511yescharacteristic
268#809C2×D511yescharacteristic
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C24×C5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—62no—
278C2×C5×D4—61no—
279C2×C5×D4—121no—
280C22×C4×C5—21no—
281C22×C4×C5C22×D311yescharacteristic
282C2×C22⋊D5—21no—
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5#6711yescharacteristic
286C22×Dic5—61no—
287C22×Dic5—61no—
288#711—62no—
289#711—121no—
290C2×D20—21no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10—31no—
295C2×C5×C8—31no—
296C2×C5×C8—31no—
297C2×C5×C8—121no—
298C5×C4⋊C4—21no—
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C4⋊C4C22×D311yescharacteristic
301C22⋊Dic5—61no—
302C22⋊Dic5—61no—
303C22⋊Dic5—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306C22⋊Dic5#6711yescharacteristic
307#686—62no—
308#686—121no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685#6711yescharacteristic
314C4⋊Dic5—21no—
315C4⋊Dic5—31no—
316C4⋊Dic5C22×D311yescharacteristic
317#683—21no—
318#683—61no—
319#683#6711yescharacteristic
320C4×Dic5—21no—
321C4×Dic5C22×D311yescharacteristic
322C2×#168—31no—
323C2×#168—31no—
324#677—121no—
325C8×D5—121no—
326#553—51no—
327#546—151no—
328#488—151no—
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—31no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—22no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C5×D3—84no—
352C2×C3×D5—21no—
353C2×C3×D5—21no—
354C2×C3×D5—21no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364Dic15—41no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—21no—
368C3×Dic5—41no—
369C23×D3—21no—
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—101no—
373C2×C3×D4—101no—
374C22×C3×C4—21no—
375C22×C3×C4—51no—
376C22×C3×C4—101no—
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—101no—
379C2×#67—101no—
380#235—102no—
381#235—201no—
382C2×D12—22no—
383C2×D12—21no—
384C2×D12—41no—
385C2×D12C22×D511yescharacteristic
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—51no—
398C3×C22⋊C4—51no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C42—51no—
404C3×C42—101no—
405#217—101no—
406#214—201no—
407#213—102no—
408#213—201no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413C4⋊Dic3—51no—
414Dic3⋊C4—101no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—201no—
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—122no—
424C23×C5—122no—
425C23×C5—241no—
426C23×C5C2×#6711yescharacteristic
427C22×D5—21no—
428C22×D5C2×#6711yescharacteristic
429C5×D4—32no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—61no—
433C5×D4—122no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—81no—
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—22no—
442C22⋊D5—42no—
443C22⋊D5—122no—
444C22⋊D5—241no—
445C2×Dic5—21no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—122no—
449C2×Dic5—241no—
450C2×Dic5C2×#6711yescharacteristic
451C2×Dic5C2×#6711yescharacteristic
452C2×Dic5C2×#6711yescharacteristic
453D20—21no—
454D20—21no—
455D20—81no—
456C4×D5—21no—
457C4×D5—21no—
458C4×D5—81no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—61no—
462C5×C8—61no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—31no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—31no—
471C22×C8—151no—
472#126—101no—
473#125—51no—
474#124—151no—
475#123—101no—
476#123—301no—
477C22⋊Q8—151no—
478#121—51no—
479#121—51no—
480#121—101no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—101no—
487C4×D4—151no—
488#117—51no—
489C2×C4⋊C4D3×D511yescharacteristic
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C3×D5—41no—
513C3×D5—81no—
514C5×D3—42no—
515C5×D3—81no—
516C23×C3—51no—
517C23×C3—101no—
518C23×C3D4×D511yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—81no—
524C3×D4—102no—
525C3×D4—101no—
526C3×D4—101no—
527C3×D4—202no—
528C3×D4—401no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—51no—
534C2×C3×C4—51no—
535C2×C3×C4—51no—
536C2×C3×C4—81no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4—401no—
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—202no—
544#67—401no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12#70912yes—
552C4×D3—202no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—62no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—244no—
569C22×C5#95012yes—
570C22×C5C22×#6711yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—21no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5D3×#4111yescharacteristic
581C4×C5#100911yescharacteristic
582Dic5—21no—
583Dic5—21no—
584Dic5—21no—
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—61no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—121no—
601C2×D4—301no—
602C2×D4—301no—
603C22×C4—21no—
604C22×C4—51no—
605C22×C4—101no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—121no—
615C2×C8—151no—
616C2×C8—151no—
617C2×C8—601no—
618C4⋊C4—21no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—151no—
624C4⋊C4—301no—
625C4⋊C4C2×D3×D511yescharacteristic
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—51no—
628C22⋊C4—51no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—51no—
639C42—101no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—101no—
644C22×C3—101no—
645C22×C3—101no—
646C22×C3—201no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3#406212yes—
650C22×C3C2×D4×D511yescharacteristic
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—101no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4—201no—
665C3×C4C2×#70911yescharacteristic
666C3×C4#414411yescharacteristic
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—122no—
671C2×C5—241no—
672C2×C5C2×#95011yescharacteristic
673C2×C5#582911yescharacteristic
674C2×C5#583511yescharacteristic
675D5—41no—
676D5—81no—
677C23—51no—
678C23—61no—
679C23—61no—
680C23—101no—
681C23—122no—
682C23—122no—
683C23—241no—
684C23D5×#6711yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—32no—
688D4—61no—
689D4—61no—
690D4—61no—
691D4—102no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—202no—
696D4—401no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—51no—
706C2×C4—81no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—401no—
713C2×C4—602no—
714C2×C4—1201no—
715C2×C4D5×#6711yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—61no—
718C8—61no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—201no—
723C2×C3—401no—
724C2×C3#6582411yescharacteristic
725C2×C3#6609111yescharacteristic
726C2×C3C2×#406211yescharacteristic
727D3—42no—
728D3—81no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—62no—
733C22—101no—
734C22—101no—
735C22—101no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—244no—
745C22#9151412yes—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—101no—
751C4—101no—
752C4—101no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4D3×#70911yescharacteristic
757C4#9201811yescharacteristic
758C3#1061049111yescharacteristic, complemented, Sylow
759C2—22no—
760C2—122no—
761C2—201no—
762C2—241no—
763C2—401no—
764C2#1175463611yescharacteristic
765C2#1175469111yescharacteristic
766C2C2×#9151411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65848C2semidirect
2. #11754540C2semidirect
3. #11751071C2semidirect
4. C2×C5×#809C2semidirect
5. #11748539C2semidirect
6. #11748516C2semidirect
7. C3⋊C8×C22⋊D5C2semidirect
8. #11747510C2semidirect
9. #11747499C2semidirect
10. #11747368C2semidirect
11. #11747310C2semidirect
12. #11747307C2semidirect
13. #11747241C2semidirect
14. #11747216C2semidirect
15. #11747142C2semidirect
27. C3×#4041C22semidirect
29. C3×#4039C22semidirect
30. C3×#4038C22semidirect
31. C3×#4036C22semidirect
39. C2×#6657C22semidirect
42. C2×D5×C3⋊C8C22semidirect
44. #91094C22semidirect
45. #91094C22semidirect
46. #91091C22semidirect
47. #91091C22semidirect
52. #90987C22semidirect
53. #90982C22semidirect
54. #90974C22semidirect
57. #90965C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
62. #65848D3semidirect
142. C2×#809D5semidirect
164. #4041C2×D3semidirect
166. #4039C2×D3semidirect
167. #4038C2×D3semidirect
168. #4036C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10610491semidirect

Maximal subgroups

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

subgroupindex
C3×#658482
#117545402
#117510712
C2×C5×#8092
#117485392
#117485162
C3⋊C8×C22⋊D52
#117475102
#117474992
#117473682
#117473102
#117473072
#117472412
#117472162
#117471422
#106104913
#836145