Finite Group Databasebeta

← #14458907

Subgroups — #14458907

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×#65864C211yesmaximal, characteristic, complemented
2#11754665C211yesmaximal, characteristic, complemented
3#11751103C211yesmaximal, characteristic, complemented
4C5×#5003C211yesmaximal, characteristic, complemented
5#11748550C211yesmaximal, characteristic, complemented
6#11748522C211yesmaximal, characteristic, complemented
7#11748493C211yesmaximal, characteristic, complemented
8#11747480C211yesmaximal, characteristic, complemented
9D5×#809C211yesmaximal, characteristic, complemented
10#11747444C211yesmaximal, characteristic, complemented
11#11747368C211yesmaximal, characteristic, complemented
12#11747244C211yesmaximal, characteristic, complemented
13#11747223C211yesmaximal, characteristic, complemented
14#11747169C211yesmaximal, characteristic, complemented
15#11747142C211yesmaximal, characteristic, complemented
16#10613113—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C3×C5×#117C2211yescharacteristic, complemented
20C22×C3⋊#168C2211yescharacteristic, complemented
21C5×#930C2211yescharacteristic
22C3×#4076C2211yescharacteristic, complemented
23C3×C4×C22⋊D5C2211yescharacteristic
24C3×#4041C2211yescharacteristic
25C3×#4039C2211yescharacteristic, complemented
26C3×D5×C4⋊C4C2211yescharacteristic
27C3×#4036C2211yescharacteristic, complemented
28C3×#4030—21no—
29C3×#4029—21no—
30C3×#4022—21no—
31C3×C4×D20—21no—
32#91577—21no—
33#91557—21no—
34#91473—21no—
35#91418C2211yescharacteristic
36#91373C2211yescharacteristic
37#91360C2211yescharacteristic
38#91355—21no—
39C2×#6657C2211yescharacteristic, complemented
40C2×#6653C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic
43#91094C2211yescharacteristic, complemented
44#91094C2211yescharacteristic, complemented
45#91093C2211yescharacteristic
46#91093C2211yescharacteristic
47C5×#830C2211yescharacteristic, complemented
48C5×#809C2211yescharacteristic
49C5×#809C2211yescharacteristic
50C5×#808C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52#90989C2211yescharacteristic, complemented
53#90982C2211yescharacteristic, complemented
54#90974C2211yescharacteristic, complemented
55#90968C2211yescharacteristic
56#90966C2211yescharacteristic
57#90964C2211yescharacteristic, complemented
58#90955C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61#65946—31no—
62#65864D311yescharacteristic, complemented
63C5×#482—31no—
64#65327—31no—
65#65291—31no—
66#65173—31no—
67#65161—31no—
68#65160—31no—
69#65153—31no—
70#65076—31no—
71#65062—31no—
72D5×#102—31no—
73#65057—31no—
74#65023—31no—
75#65014—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×D12C2311yescharacteristic
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5D411yescharacteristic
88C2×C3×D20—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×#1203—21no—
94C2×#1200—21no—
95D5×D12—22no—
96D5×D12—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×(C2×D3)⋊C4—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C2×C5×C3⋊C8C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C3×C22⋊Dic5D411yescharacteristic
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685D411yescharacteristic
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683D411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119Dic3⋊Dic5—21no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123#6665—21no—
124#6657—41no—
125#6653—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#5003D511yescharacteristic, complemented
140#5002—51no—
141#4970—51no—
142C2×#809—51no—
143C2×D4×D5—31no—
144C2×#709—31no—
145C5×#121—31no—
146C5×#117C2×D311yescharacteristic, complemented
147#4084—61no—
148#4083—61no—
149#4082—31no—
150C2×#686—31no—
151#4076C2×D311yescharacteristic, complemented
152C4×C22⋊D5C2×D311yescharacteristic
153C22×#168—31no—
154C2×D40—31no—
155C2×#677—31no—
156C2×C8×D5—31no—
157#4043—31no—
158#4041C2×D311yescharacteristic
159#4039—31no—
160#4039C2×D311yescharacteristic, complemented
161D5×C4⋊C4C2×D311yescharacteristic
162#4036C2×D311yescharacteristic, complemented
163#4030—21no—
164#4029—21no—
165#4029—61no—
166D5×C22⋊C4—61no—
167#4022—21no—
168C4×D20—21no—
169C5×#107—31no—
170C5×#106—31no—
171C5×#102—31no—
172C5×#102—31no—
173C5×C22⋊C8—31no—
174#3964—31no—
175#3953—31no—
176#3952—31no—
177#3948—31no—
178#3946—31no—
179C8×Dic5—31no—
180#3942—31no—
181#3942—31no—
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C3×D5—21no—
191C22×C3×D5C2×D411yescharacteristic
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—81no—
209C2×C5×Dic3—21no—
210C5×D12—21no—
211C5×D12—21no—
212C3×C22⋊D5—22no—
213C3×C22⋊D5—81no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—42no—
221C3×C4×D5—21no—
222C3×C4×D5—21no—
223C3×C4×D5—81no—
224C3×C4×D5—81no—
225#1203—42no—
226#1200—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×#235—51no—
232C22×D12—51no—
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×#117C2×D511yescharacteristic, complemented
243C2×C3×C4⋊C4—51no—
244#937—101no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213—51no—
248#930C2×D511yescharacteristic
249#924—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#894—101no—
253#884—101no—
254D3×C22⋊C4—101no—
255#875—51no—
256C4×D12—51no—
257#832—51no—
258#830—51no—
259#830C2×D511yescharacteristic, complemented
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809C2×D511yescharacteristic
268#809C2×D511yescharacteristic
269#808C2×D511yescharacteristic, complemented
270#807—51no—
271#807C2×D511yescharacteristic, complemented
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—61no—
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—21no—
279C2×C22⋊D5—61no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5#6711yescharacteristic
282D4×D5—62no—
283D4×D5—121no—
284#709—62no—
285#709—121no—
286C2×D20—21no—
287C2×D20—31no—
288C2×D20C22×D311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10—31no—
295C2×C5×C8—31no—
296C2×C5×C8—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C22⋊C4—21no—
301C5×C22⋊C4—61no—
302C42×C5—21no—
303C22⋊Dic5—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5#6711yescharacteristic
306#686—121no—
307#685—21no—
308#685—21no—
309#685—21no—
310#685—61no—
311#685—61no—
312#685#6711yescharacteristic
313C4⋊Dic5—21no—
314C4⋊Dic5—61no—
315C4⋊Dic5C22×D311yescharacteristic
316#683—21no—
317#683—21no—
318#683#6711yescharacteristic
319C4×Dic5C22×D311yescharacteristic
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—121no—
323D40—62no—
324#677—121no—
325C8×D5—121no—
326#553—51no—
327#546—151no—
328#488—151no—
329#484—151no—
330#482—31no—
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—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5#13512yes—
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—21no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C5×Dic3—41no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—101no—
373C2×C3×D4—101no—
374C22×C3×C4—51no—
375C22×C3×C4—101no—
376C22×C3×C4—101no—
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—21no—
379C2×#67—101no—
380#235—102no—
381#235—201no—
382C2×D12—51no—
383C2×D12—102no—
384C2×D12—101no—
385C2×D12—201no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—101no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—51no—
399C3×C22⋊C4—51no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C42—21no—
404C3×C42—51no—
405#217—101no—
406#214—201no—
407#213—102no—
408#213—201no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—201no—
418C2×C3⋊C8—201no—
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5—61no—
422C23×C5C2×#6711yescharacteristic
423C22×D5—21no—
424C22×D5—61no—
425C22×D5—122no—
426C22×D5—122no—
427C22×D5—241no—
428C22×D5C2×#6711yescharacteristic
429C5×D4—61no—
430C5×D4—61no—
431C5×D4—241no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—61no—
437C2×C4×C5C2×#6711yescharacteristic
438C2×C4×C5C23×D311yescharacteristic
439C22⋊D5—22no—
440C22⋊D5—81no—
441C22⋊D5—122no—
442C22⋊D5—122no—
443C2×Dic5—21no—
444C2×Dic5—61no—
445C2×Dic5C2×#6711yescharacteristic
446C2×Dic5C2×#6711yescharacteristic
447C2×Dic5C2×#6711yescharacteristic
448D20—21no—
449D20—21no—
450D20—32no—
451D20—42no—
452D20—61no—
453C4×D5—21no—
454C4×D5—21no—
455C4×D5—81no—
456C4×D5—81no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—61no—
462C5×C8—61no—
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—101no—
473#125—51no—
474#124—151no—
475#123—101no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—51no—
480#121—51no—
481#121—101no—
482#121—301no—
483#120—301no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—101no—
487C4×D4—151no—
488#117D3×D511yescharacteristic, complemented
489C2×C4⋊C4—51no—
490C2×C22⋊C4—301no—
491#107—31no—
492#107—151no—
493#106—31no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—31no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—31no—
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—22no—
514C3×D5—81no—
515C5×D3—81no—
516C23×C3—51no—
517C23×C3—101no—
518C23×C3D4×D511yescharacteristic
519C22×D3—21no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
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—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—401no—
540C2×C3×C4—401no—
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—81no—
544#67—202no—
545C2×Dic3—21no—
546C2×Dic3—101no—
547D12—21no—
548D12—21no—
549D12—52no—
550D12—101no—
551D12—202no—
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—21no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5C22×#6711yescharacteristic
567C2×D5—21no—
568C2×D5—21no—
569C2×D5—41no—
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—62no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—244no—
576C2×D5#95012yes—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5—121no—
581C4×C5D3×#4111yescharacteristic
582C4×C5#100911yescharacteristic
583Dic5—21no—
584Dic5—21no—
585Dic5—21no—
586Dic5—41no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—101no—
597C2×D4—101no—
598C2×D4—151no—
599C2×D4—301no—
600C2×D4—302no—
601C2×D4—301no—
602C2×D4—601no—
603C22×C4—51no—
604C22×C4—101no—
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—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—301no—
625C4⋊C4C2×D3×D511yescharacteristic
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—51no—
629C22⋊C4—51no—
630C22⋊C4—61no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—21no—
639C42—51no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—52no—
645C22×C3—101no—
646C22×C3—101no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3C2×D4×D511yescharacteristic
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—102no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—101no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4—201no—
665C3×C4D5×#4111yescharacteristic
666C3×C4#414911yescharacteristic
667Dic3—41no—
668Dic3—201no—
669C2×C5—41no—
670C2×C5—241no—
671C2×C5C2×#95011yescharacteristic
672C2×C5#582911yescharacteristic
673C2×C5#583511yescharacteristic
674D5—22no—
675D5—81no—
676D5—122no—
677C23—51no—
678C23—61no—
679C23—101no—
680C23—301no—
681C23—602no—
682C23—602no—
683C23—1201no—
684C23D5×#6711yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—61no—
688D4—61no—
689D4—102no—
690D4—101no—
691D4—101no—
692D4—152no—
693D4—202no—
694D4—241no—
695D4—301no—
696D4—401no—
697D4—602no—
698D4—602no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—51no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—301no—
711C2×C4—401no—
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—41no—
722C2×C3—102no—
723C2×C3—401no—
724C2×C3#6598811yescharacteristic
725C2×C3D5×#13511yescharacteristic
726C2×C3#6610811yescharacteristic
727D3—81no—
728D3—202no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—52no—
734C22—101no—
735C22—101no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—101no—
751C4—101no—
752C4—101no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4#9201611yescharacteristic
757C4#9201911yescharacteristic
758C3#1061311311yescharacteristic, complemented, Sylow
759C2—41no—
760C2—102no—
761C2—241no—
762C2—401no—
763C2—602no—
764C2#1175463911yescharacteristic
765C2D5×#95011yescharacteristic
766C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. C3×#65864C2semidirect
2. #11754665C2semidirect
3. #11751103C2semidirect
4. C5×#5003C2semidirect
5. #11748550C2semidirect
6. #11748522C2semidirect
7. #11748493C2semidirect
8. #11747480C2semidirect
9. D5×#809C2semidirect
10. #11747444C2semidirect
11. #11747368C2semidirect
12. #11747244C2semidirect
13. #11747223C2semidirect
14. #11747169C2semidirect
15. #11747142C2semidirect
19. C3×C5×#117C22semidirect
20. C22×C3⋊#168C22semidirect
22. C3×#4076C22semidirect
25. C3×#4039C22semidirect
27. C3×#4036C22semidirect
39. C2×#6657C22semidirect
43. #91094C22semidirect
44. #91094C22semidirect
47. C5×#830C22semidirect
50. C5×#808C22semidirect
51. C5×#807C22semidirect
52. #90989C22semidirect
53. #90982C22semidirect
54. #90974C22semidirect
57. #90964C22semidirect
59. Dic5×C3⋊C8C22semidirect
62. #65864D3semidirect
139. #5003D5semidirect
146. C5×#117C2×D3semidirect
151. #4076C2×D3semidirect
160. #4039C2×D3semidirect
162. #4036C2×D3semidirect
242. C3×#117C2×D5semidirect
259. #830C2×D5semidirect
269. #808C2×D5semidirect
271. #807C2×D5semidirect
488. #117D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10613113semidirect

Maximal subgroups

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

subgroupindex
C3×#658642
#117546652
#117511032
C5×#50032
#117485502
#117485222
#117484932
#117474802
D5×#8092
#117474442
#117473682
#117472442
#117472232
#117471692
#117471422
#106131133
#836145