Finite Group Databasebeta

← #14458905

Subgroups — #14458905

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×#5530C211yesmaximal, characteristic, complemented
2#11754667C211yesmaximal, characteristic, complemented
3#11751103C211yesmaximal, characteristic, complemented
4C3×#65292C211yesmaximal, characteristic, complemented
5#11748526C211yesmaximal, characteristic, complemented
6#11748522C211yesmaximal, characteristic, complemented
7#67⋊#168C211yesmaximal, characteristic, complemented
8#11747482C211yesmaximal, characteristic, complemented
9D3×#3941C211yesmaximal, characteristic, complemented
10#11747448C211yesmaximal, characteristic, complemented
11#11747375C211yesmaximal, characteristic, complemented
12#11747374C211yesmaximal, characteristic, complemented
13#11747252C211yesmaximal, characteristic, complemented
14#11747230C211yesmaximal, characteristic, complemented
15#11747178C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C3×C5×#117C2211yescharacteristic, complemented
20C22×C3⋊#168C2211yescharacteristic, complemented
21C5×#930C2211yescharacteristic, complemented
22C4×C5×#67C2211yescharacteristic
23C5×#895C2211yescharacteristic
24C5×#893C2211yescharacteristic, complemented
25C5×D3×C4⋊C4C2211yescharacteristic
26C5×#890C2211yescharacteristic, complemented
27C5×#884—21no—
28C5×#883—21no—
29C5×#876—21no—
30C4×C5×D12—21no—
31C3×#4076C2211yescharacteristic
32#91577—21no—
33#91533—21no—
34#91473—21no—
35#91428C2211yescharacteristic
36#91365C2211yescharacteristic
37#91364C2211yescharacteristic
38#91354—21no—
39C2×#6659C2211yescharacteristic, complemented
40C2×#6654C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43#91094C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91093C2211yescharacteristic
46#91093C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3940C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52#90989C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90969C2211yescharacteristic
56#90966C2211yescharacteristic, complemented
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic, complemented
60#81382—51nomaximal, Hall
61C5×#553—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292D311yescharacteristic, complemented
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C22×D3×D5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79#6817—22no—
80#6817—41no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67D411yescharacteristic
86C2×C5×D12—21no—
87C2×C5×D12C2311yescharacteristic
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×D20C2311yescharacteristic
93C2×#1202—21no—
94C2×#1200—21no—
95D3×D20—22no—
96D3×D20—41no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C42×C5—21no—
101C2×C3⋊#168—41no—
102C2×C3⋊#168C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C5×#217D411yescharacteristic
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4D411yescharacteristic
114C4×C5×Dic3C2311yescharacteristic
115C3×#685—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119#6668—21no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123#6665—21no—
124#6659—41no—
125#6654—22no—
126#6652—41no—
127D3×#168—41no—
128#5612—51no—
129#5530D511yescharacteristic, complemented
130C3×#482—51no—
131#5038—51no—
132#5002—51no—
133#4884—51no—
134#4872—51no—
135#4871—51no—
136#4864—51no—
137#4787—51no—
138#4773—51no—
139D3×#102—51no—
140#4768—51no—
141#4734—51no—
142#67⋊C8—51no—
143C2×#709—31no—
144C22×D20—31no—
145C5×#126—61no—
146C5×#125—31no—
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C4×C5×D4—61no—
154C5×#117C2×D311yescharacteristic, complemented
155C2×C5×C4⋊C4—31no—
156#4083—61no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076C2×D311yescharacteristic
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#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic
181#3940C2×D311yescharacteristic, complemented
182#3939—31no—
183#3939C2×D311yescharacteristic, complemented
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C2×D3×D5—42no—
193C2×D3×D5—42no—
194C2×D3×D5—81no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201#1220—42no—
202C2×Dic15—21no—
203D60—21no—
204D60#4112yes—
205C4×D15—42no—
206Dic30—21no—
207Dic30—21no—
208C5×#67—22no—
209C5×#67—81no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C5×D12—21no—
215C5×D12—21no—
216C5×D12—42no—
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C4×C5×D3—81no—
220C4×C5×D3—81no—
221C3×C22⋊D5—81no—
222C2×C3×Dic5—21no—
223C3×D20—21no—
224C3×D20—21no—
225#1202—42no—
226#1200—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×D3×D4—51no—
232C2×#235—51no—
233C3×#121—51no—
234C3×#117C2×D511yescharacteristic, complemented
235#938—101no—
236#937—101no—
237#936—51no—
238C2×#213—51no—
239#930C2×D511yescharacteristic, complemented
240C4×#67C2×D511yescharacteristic
241C22×C3⋊C8—51no—
242C2×D24—51no—
243C2×#204—51no—
244C2×D3×C8—51no—
245#897—51no—
246#895C2×D511yescharacteristic
247#893—51no—
248#893C2×D511yescharacteristic, complemented
249D3×C4⋊C4C2×D511yescharacteristic
250#890C2×D511yescharacteristic, complemented
251#884—21no—
252#883—21no—
253#883—101no—
254D3×C22⋊C4—101no—
255#876—21no—
256C4×D12—21no—
257C3×#107—51no—
258C3×#106—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×C22⋊C8—51no—
262#832—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265#816—51no—
266Dic3⋊C8—51no—
267C8×Dic3—51no—
268#810—51no—
269#810—51no—
270#809—51no—
271#809—51no—
272#809—51no—
273#807—51no—
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
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—62no—
286#709—121no—
287C2×D20—31no—
288C2×D20—62no—
289C2×D20—61no—
290C2×D20—121no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—61no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4C22×D311yescharacteristic
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—21no—
309C42×C5—31no—
310C22⋊Dic5—61no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5C22×D311yescharacteristic
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—51no—
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—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—21no—
349C2×C5×D3—21no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3#13512yes—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364C3×Dic5—41no—
365C5×Dic3—21no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—21no—
374C2×#67—101no—
375C2×#67—101no—
376C2×#67C22⋊D511yescharacteristic
377D3×D4—102no—
378D3×D4—201no—
379#235—102no—
380#235—201no—
381C2×D12—21no—
382C2×D12—51no—
383C2×D12C22×D511yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×Dic6—51no—
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4C22×D511yescharacteristic
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—101no—
397C3×C42—21no—
398#217—101no—
399#217—101no—
400#217C22⋊D511yescharacteristic
401#213—201no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4C22⋊D511yescharacteristic
408C4⋊Dic3—21no—
409C4⋊Dic3—101no—
410C4⋊Dic3C22×D511yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4C22⋊D511yescharacteristic
414C4×Dic3C22×D511yescharacteristic
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—201no—
418D24—102no—
419#204—201no—
420D3×C8—201no—
421C23×C5—31no—
422C23×C5—61no—
423C23×C5D3×D411yescharacteristic
424C22×D5—21no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—62no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—122no—
433C5×D4—241no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—31no—
439C2×C4×C5—31no—
440C2×C4×C5—31no—
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—81no—
449C22⋊D5—122no—
450C2×Dic5—21no—
451C2×Dic5—61no—
452D20—21no—
453D20—21no—
454D20—32no—
455D20—61no—
456D20—122no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
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—31no—
480#121—51no—
481#121—61no—
482#121—301no—
483#120—301no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—61no—
487C4×D4—151no—
488#117D3×D511yescharacteristic, complemented
489C2×C4⋊C4—31no—
490C2×C22⋊C4—301no—
491#107—51no—
492#107—151no—
493#106—51no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
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—51no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—41no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512D15—42no—
513C3×D5—81no—
514C5×D3—22no—
515C5×D3—81no—
516C23×C3—101no—
517C23×C3C2×C22⋊D511yescharacteristic
518C22×D3—21no—
519C22×D3—101no—
520C22×D3—202no—
521C22×D3—202no—
522C22×D3—401no—
523C22×D3C2×C22⋊D511yescharacteristic
524C3×D4—101no—
525C3×D4—101no—
526C3×D4—401no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—101no—
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—22no—
535#67—81no—
536#67—202no—
537#67—202no—
538C2×Dic3—21no—
539C2×Dic3—101no—
540C2×Dic3C2×C22⋊D511yescharacteristic
541C2×Dic3C2×C22⋊D511yescharacteristic
542C2×Dic3C2×C22⋊D511yescharacteristic
543D12—21no—
544D12—21no—
545D12—42no—
546D12—52no—
547D12—101no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3—202no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
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—61no—
565C22×C5—61no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5C2×D3×D411yescharacteristic
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—62no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5—61no—
581C4×C5—61no—
582C4×C5—61no—
583C4×C5—121no—
584C4×C5D3×#4111yescharacteristic
585C4×C5#100911yescharacteristic
586Dic5—41no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—101no—
598C2×D4—151no—
599C2×D4—301no—
600C2×D4—302no—
601C2×D4—301no—
602C2×D4—601no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
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—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—301no—
625C4⋊C4C2×D3×D511yescharacteristic
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—101no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—21no—
639C42—31no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—201no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3C22×C22⋊D511yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—102no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—404no—
657C2×D3#409612yes—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—201no—
662C3×C4D5×#4111yescharacteristic
663C3×C4#414911yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—201no—
669C2×C5—41no—
670C2×C5—62no—
671C2×C5—241no—
672C2×C5#565411yescharacteristic
673C2×C5D3×#13511yescharacteristic
674C2×C5#577411yescharacteristic
675D5—81no—
676D5—122no—
677C23—31no—
678C23—61no—
679C23—101no—
680C23—301no—
681C23—602no—
682C23—602no—
683C23—1201no—
684C23D3×C22⋊D511yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—62no—
688D4—61no—
689D4—61no—
690D4—101no—
691D4—101no—
692D4—122no—
693D4—152no—
694D4—241no—
695D4—301no—
696D4—401no—
697D4—602no—
698D4—602no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—101no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—301no—
713C2×C4—602no—
714C2×C4—1201no—
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—41no—
722C2×C3—401no—
723C2×C3C2×#409611yescharacteristic
724C2×C3#6616311yescharacteristic
725C2×C3#6616911yescharacteristic
726D3—22no—
727D3—81no—
728D3—202no—
729C5#8138211yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—32no—
734C22—61no—
735C22—61no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4#9201611yescharacteristic
757C4#9201911yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—41no—
760C2—62no—
761C2—241no—
762C2—401no—
763C2—602no—
764C2#1175465611yescharacteristic
765C2D3×#409611yescharacteristic
766C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5530C2semidirect
2. #11754667C2semidirect
3. #11751103C2semidirect
4. C3×#65292C2semidirect
5. #11748526C2semidirect
6. #11748522C2semidirect
7. #67⋊#168C2semidirect
8. #11747482C2semidirect
9. D3×#3941C2semidirect
10. #11747448C2semidirect
11. #11747375C2semidirect
12. #11747374C2semidirect
13. #11747252C2semidirect
14. #11747230C2semidirect
15. #11747178C2semidirect
19. C3×C5×#117C22semidirect
20. C22×C3⋊#168C22semidirect
21. C5×#930C22semidirect
24. C5×#893C22semidirect
26. C5×#890C22semidirect
39. C2×#6659C22semidirect
43. #91094C22semidirect
44. #91094C22semidirect
47. C3×C22⋊#168C22semidirect
50. C3×#3940C22semidirect
51. C3×#3939C22semidirect
52. #90989C22semidirect
53. Dic3⋊#168C22semidirect
54. #90975C22semidirect
56. #90966C22semidirect
59. Dic3×#168C22semidirect
72. #65292D3semidirect
129. #5530D5semidirect
154. C5×#117C2×D3semidirect
171. C22⋊#168C2×D3semidirect
181. #3940C2×D3semidirect
183. #3939C2×D3semidirect
234. C3×#117C2×D5semidirect
239. #930C2×D5semidirect
248. #893C2×D5semidirect
250. #890C2×D5semidirect
488. #117D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#81382semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C5×#55302
#117546672
#117511032
C3×#652922
#117485262
#117485222
#67⋊#1682
#117474822
D3×#39412
#117474482
#117473752
#117473742
#117472522
#117472302
#117471782
#106153453
#813825