Finite Group Databasebeta

← #14458892

Subgroups — #14458892

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×#5614C211yesmaximal, characteristic, complemented
2#11754638C211yesmaximal, characteristic, complemented
3#11751139C211yesmaximal, characteristic, complemented
4C3×#65326C211yesmaximal, characteristic, complemented
5#11749152C211yesmaximal, characteristic, complemented
6#11749080C211yesmaximal, characteristic, complemented
7#11749050C211yesmaximal, characteristic, complemented
8Dic3×#686C211yesmaximal, characteristic, complemented
9#67⋊#168C211yesmaximal, characteristic, complemented
10#11748373C211yesmaximal, characteristic, complemented
11#11748364C211yesmaximal, characteristic, complemented
12D3×#3941C211yesmaximal, characteristic, complemented
13#11747379C211yesmaximal, characteristic, complemented
14#11747349C211yesmaximal, characteristic, complemented
15#11747249C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C5×#121C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21#91819C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic, complemented
23C5×#938—21no—
24C5×#938C2211yescharacteristic
25C5×#935—21no—
26C5×D4×Dic3C2211yescharacteristic, complemented
27C4×C5×#67C2211yescharacteristic
28C5×#926C2211yescharacteristic, complemented
29C5×D3×C4⋊C4C2211yescharacteristic
30C5×#890C2211yescharacteristic, complemented
31C5×#67⋊C4—21no—
32C5×#879—21no—
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic
35#91577—21no—
36#91550—21no—
37D5×(C2×D3)⋊C4—21no—
38Dic3×D20C2211yescharacteristic
39#91374C2211yescharacteristic
40#91369C2211yescharacteristic
41#91348—21no—
42C2×D3×#168C2211yescharacteristic
43#91116C2211yescharacteristic, complemented
44#91093C2211yescharacteristic
45#91091C2211yescharacteristic, complemented
46C3×C22⋊#168C2211yescharacteristic, complemented
47C3×#3942C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49#90988C2211yescharacteristic, complemented
50#90985C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90970C2211yescharacteristic, complemented
53#90970C2211yescharacteristic, complemented
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic, complemented
60#80102—51nomaximal, Hall
61C5×#553—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326D311yescharacteristic, complemented
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C22×D3×D5—21no—
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×D60C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×#67D411yescharacteristic
84C22×C5×Dic3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C3×#709—22no—
89C3×#709—41no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—21no—
92C2×C3×Dic10C2311yescharacteristic
93C2×#1202—21no—
94C2×D5×Dic3—21no—
95D3×D20—22no—
96D3×D20—41no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99#6715—41no—
100#6714—21no—
101C4⋊Dic15C2311yescharacteristic
102C2×C3⋊#168—41no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#217—21no—
106C5×#217—21no—
107C5×#217—21no—
108C5×#217D411yescharacteristic
109C5×(C2×D3)⋊C4D411yescharacteristic
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4D411yescharacteristic
116C4×C5×Dic3—21no—
117C4×C5×Dic3C2311yescharacteristic
118C3×#687—41no—
119C3×#686—22no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6669—21no—
123#6667—21no—
124#6667—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127D3×#168—41no—
128#5829—51no—
129#5614D511yescharacteristic, complemented
130C3×#449—51no—
131#5233—51no—
132#5171—51no—
133#5165—51no—
134#5156—51no—
135Dic3×D8—51no—
136#5038—51no—
137#4811—51no—
138#4800—51no—
139D3×#102—51no—
140#4763—51no—
141#4737—51no—
142#67⋊C8—51no—
143C2×#709C2×D311yescharacteristic
144C22×D20—31no—
145C5×#126—61no—
146C5×#125—31no—
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#121C2×D311yescharacteristic, complemented
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C4×C5×D4—61no—
154C5×#117—31no—
155C2×C5×C4⋊C4—31no—
156#4083—61no—
157C2×#687C2×D311yescharacteristic, complemented
158C2×#686—31no—
159C2×#686C2×D311yescharacteristic
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3964—31no—
170C22⋊#168—31no—
171C22⋊#168C2×D311yescharacteristic, complemented
172#3942—31no—
173#3942—31no—
174#3942C2×D311yescharacteristic, complemented
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C2×D3×D5—42no—
193C2×D3×D5—42no—
194C2×D3×D5—81no—
195C3×C5×D4—21no—
196C3×C5×D4—21no—
197C3×C5×D4—81no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203#1220—81no—
204C2×Dic15—21no—
205D60—21no—
206D60—21no—
207C5×#67—22no—
208C5×#67—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—81no—
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—81no—
218C3×C22⋊D5—42no—
219C2×C3×Dic5—21no—
220C3×D20—21no—
221C3×D20#4112yes—
222C3×C4×D5—42no—
223C3×Dic10—21no—
224C3×Dic10—21no—
225#1202—42no—
226D5×Dic3—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×C3×#41—51no—
232C2×D3×D4—51no—
233C2×C3×SD16—51no—
234C2×C3×D8—51no—
235C3×#121C2×D511yescharacteristic, complemented
236#947—51no—
237#946—51no—
238#939—101no—
239#938—21no—
240#938C2×D511yescharacteristic
241#937—101no—
242#935—21no—
243D4×Dic3—51no—
244D4×Dic3C2×D511yescharacteristic, complemented
245C2×#213—51no—
246#930—51no—
247#929—101no—
248C4×#67C2×D511yescharacteristic
249C2×(C2×D3)⋊C4—101no—
250#926C2×D511yescharacteristic, complemented
251C22×C3⋊C8—51no—
252C2×D3×C8—51no—
253D3×C4⋊C4C2×D511yescharacteristic
254#890C2×D511yescharacteristic, complemented
255#67⋊C4—21no—
256#879—21no—
257C3×#103—51no—
258C3×#102—51no—
259C3×C22⋊C8—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#818—51no—
269#817—51no—
270Dic3⋊C8—51no—
271C8×Dic3—51no—
272#809—51no—
273#807—51no—
274C23×D5—61no—
275C2×C5×D4—21no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—31no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—21no—
284C2×C22⋊D5—61no—
285#709—22no—
286#709—41no—
287C2×D20—31no—
288C2×D20—62no—
289C2×D20—61no—
290C2×D20—121no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—61no—
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—31no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C5×C22⋊C4—61no—
308C42×C5—31no—
309C42×C5—61no—
310C22⋊Dic5—61no—
311#687—41no—
312#686—22no—
313#686—121no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319#683—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—31no—
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—51no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—21no—
352C2×C5×D3—21no—
353C2×C5×D3#13512yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5C2×#4111yescharacteristic
361C3×C4×C5H(5,𝔽2)11yescharacteristic
362Dic15—41no—
363C3×Dic5—41no—
364C5×Dic3—21no—
365C5×Dic3—21no—
366C5×Dic3—21no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C23×D3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8—51no—
373C2×C3×D4—21no—
374C2×C3×D4—51no—
375C2×C3×D4—101no—
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—101no—
378C22×C3×C4C22×D511yescharacteristic
379C2×#67—21no—
380C2×#67—101no—
381C2×#67—101no—
382C2×#67C22⋊D511yescharacteristic
383C22×Dic3—21no—
384C22×Dic3—101no—
385D3×D4—102no—
386D3×D4—201no—
387C2×D12—51no—
388C2×C4×D3—21no—
389C2×C4×D3C22×D511yescharacteristic
390C3×SD16—201no—
391C3×D8—102no—
392C2×C3×C8—51no—
393C2×C3×C8—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—21no—
396#217—21no—
397#217—21no—
398#217—21no—
399#217—101no—
400#217C22⋊D511yescharacteristic
401#213—201no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4C22⋊D511yescharacteristic
407C4⋊Dic3—21no—
408C4⋊Dic3—51no—
409C4⋊Dic3C22×D511yescharacteristic
410C4⋊Dic3C22×D511yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—101no—
414Dic3⋊C4C22⋊D511yescharacteristic
415C4×Dic3—21no—
416C4×Dic3C22×D511yescharacteristic
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420D3×C8—201no—
421C23×C5—21no—
422C23×C5—31no—
423C23×C5D3×D411yescharacteristic
424C22×D5—21no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—21no—
430C5×D4—21no—
431C5×D4—62no—
432C5×D4—81no—
433C5×D4—122no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—31no—
438C2×C4×C5—31no—
439C2×C4×C5—31no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—241no—
445C2×C4×C5—241no—
446C2×C4×C5D3×D411yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—42no—
449C22⋊D5—241no—
450C2×Dic5—21no—
451C2×Dic5—61no—
452D20—21no—
453D20—61no—
454D20—61no—
455D20—122no—
456D20#23712yes—
457C4×D5—42no—
458C4×D5—241no—
459Dic10—21no—
460Dic10—21no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—51no—
466C22×D4—151no—
467C2×SD16—51no—
468C2×D8—51no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—61no—
473#125—31no—
474#124—151no—
475#123—61no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—61no—
480#121—151no—
481#121—301no—
482#121D3×D511yescharacteristic, complemented
483#120—301no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—61no—
487C4×D4—151no—
488#117—31no—
489C2×C4⋊C4—31no—
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
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—51no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—41no—
509C2×C3×C5—81no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513D15—81no—
514C3×D5—42no—
515C5×D3—22no—
516C23×C3—21no—
517C23×C3—101no—
518C23×C3C2×C22⋊D511yescharacteristic
519C22×D3—101no—
520C22×D3—202no—
521C22×D3—202no—
522C22×D3—401no—
523C22×D3C2×C22⋊D511yescharacteristic
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—52no—
529C3×D4—81no—
530C3×D4—101no—
531C3×D4—202no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—101no—
536C2×C3×C4—202no—
537C2×C3×C4C2×C22⋊D511yescharacteristic
538C2×C3×C4C23×D511yescharacteristic
539#67—22no—
540#67—42no—
541#67—202no—
542#67—401no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—81no—
546C2×Dic3—101no—
547C2×Dic3—401no—
548C2×Dic3C2×C22⋊D511yescharacteristic
549C2×Dic3C2×C22⋊D511yescharacteristic
550C2×Dic3C2×C22⋊D511yescharacteristic
551D12—101no—
552D12—101no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—81no—
556C3×C8—101no—
557C3×C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—32no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5—61no—
568C22×C5—61no—
569C22×C5C2×D3×D411yescharacteristic
570C2×D5—22no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—61no—
580C4×C5—61no—
581C4×C5—61no—
582C4×C5—121no—
583C4×C5—121no—
584C4×C5C2×#23711yescharacteristic
585C4×C5#100411yescharacteristic
586Dic5—41no—
587Dic5—121no—
588C24—301no—
589#41—102no—
590#41—201no—
591C2×Q8—51no—
592C2×D4—21no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—101no—
597C2×D4—151no—
598C2×D4—301no—
599C2×D4—302no—
600C2×D4—301no—
601C2×D4—601no—
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—101no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—201no—
610D8—102no—
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—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—151no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—31no—
639C42—61no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—102no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3C22×C22⋊D511yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—404no—
657C2×D3#409612yes—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—201no—
661C3×C4D5×#4111yescharacteristic
662C3×C4#414911yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—201no—
669C2×C5—41no—
670C2×C5—62no—
671C2×C5—81no—
672C2×C5#559111yescharacteristic
673C2×C5D3×#13511yescharacteristic
674C2×C5#577411yescharacteristic
675D5—42no—
676D5—241no—
677C23—21no—
678C23—31no—
679C23—101no—
680C23—301no—
681C23—602no—
682C23—602no—
683C23—1201no—
684C23D3×C22⋊D511yescharacteristic
685Q8—101no—
686Q8—101no—
687D4—21no—
688D4—21no—
689D4—52no—
690D4—62no—
691D4—81no—
692D4—101no—
693D4—122no—
694D4—202no—
695D4—301no—
696D4—301no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—101no—
710C2×C4—202no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—301no—
714C2×C4—1201no—
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—41no—
722C2×C3—81no—
723C2×C3—202no—
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616311yescharacteristic
726C2×C3#6616911yescharacteristic
727D3—22no—
728D3—401no—
729C5#8010211yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—32no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—61no—
738C22—61no—
739C22—102no—
740C22—201no—
741C22—201no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4D5×#23711yescharacteristic
757C4#9202611yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—41no—
760C2—62no—
761C2—81no—
762C2—202no—
763C2—1201no—
764C2#1175469811yescharacteristic
765C2#1175506611yescharacteristic
766C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C5×#5614C2semidirect
2. #11754638C2semidirect
3. #11751139C2semidirect
4. C3×#65326C2semidirect
5. #11749152C2semidirect
6. #11749080C2semidirect
7. #11749050C2semidirect
8. Dic3×#686C2semidirect
9. #67⋊#168C2semidirect
10. #11748373C2semidirect
11. #11748364C2semidirect
12. D3×#3941C2semidirect
13. #11747379C2semidirect
14. #11747349C2semidirect
15. #11747249C2semidirect
19. C3×C5×#121C22semidirect
22. C22×C3⋊#168C22semidirect
26. C5×D4×Dic3C22semidirect
28. C5×#926C22semidirect
30. C5×#890C22semidirect
33. C2×C3×#687C22semidirect
43. #91116C22semidirect
45. #91091C22semidirect
46. C3×C22⋊#168C22semidirect
47. C3×#3942C22semidirect
49. #90988C22semidirect
50. #90985C22semidirect
51. Dic3⋊#168C22semidirect
52. #90970C22semidirect
53. #90970C22semidirect
59. Dic3×#168C22semidirect
67. #65326D3semidirect
129. #5614D5semidirect
150. C5×#121C2×D3semidirect
157. C2×#687C2×D3semidirect
171. C22⋊#168C2×D3semidirect
174. #3942C2×D3semidirect
235. C3×#121C2×D5semidirect
244. D4×Dic3C2×D5semidirect
250. #926C2×D5semidirect
254. #890C2×D5semidirect
482. #121D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#80102semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C5×#56142
#117546382
#117511392
C3×#653262
#117491522
#117490802
#117490502
Dic3×#6862
#67⋊#1682
#117483732
#117483642
D3×#39412
#117473792
#117473492
#117472492
#106153453
#801025