Finite Group Databasebeta

← #14417126

Subgroups — #14417126

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754916C211yesmaximal, characteristic, complemented
2C2×#91482C211yesmaximal, characteristic
3#11753841C211yesmaximal, characteristic, complemented
4#11750873C211yesmaximal, characteristic, complemented
5C5×#4756C211yesmaximal, characteristic, complemented
6C3×#65045C211yesmaximal, characteristic, complemented
7#11748988C211yesmaximal, characteristic, complemented
8#11748977C211yesmaximal, characteristic, complemented
9#11748108C211yesmaximal, characteristic, complemented
10#11747744C211yesmaximal, characteristic, complemented
11#11747739C211yesmaximal, characteristic, complemented
12#11747657C211yesmaximal, characteristic, complemented
13#11747473C211yesmaximal, characteristic, complemented
14#11747472C211yesmaximal, characteristic, complemented
15#11747456C211yesmaximal, characteristic, complemented
16#10611318—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20#91781C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic, complemented
22C2×C5×#213C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic, complemented
25C2×C3×#686C2211yescharacteristic
26C3×#4039C2211yescharacteristic
27#91556—21no—
28#91552—21no—
29C2×#6669—21no—
30#91532—21no—
31#91482C418yescomplemented
32D3×#685—21no—
33D5×(C2×D3)⋊C4—21no—
34#91442—21no—
35C4×#1201—21no—
36#91437C2211yescharacteristic
37Dic3×D20C2211yescharacteristic
38Dic5×D12C2211yescharacteristic
39#91386C2211yescharacteristic
40#91340C2211yescharacteristic, complemented
41#91333C2211yescharacteristic, complemented
42C2×#6659C2211yescharacteristic
43C2×#6657C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91116C2211yescharacteristic, complemented
47#91100C2211yescharacteristic, complemented
48#91094C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×C8×Dic3C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90987C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90966C2211yescharacteristic
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60#90952C2211yescharacteristic, complemented
61#79587—51nomaximal, Hall
62C2×#4057—31no—
63#65880—31no—
64#65879—31no—
65C4×C5×D8—31no—
66#65441—31no—
67#65307—31no—
68#65303—31no—
69#65178—31no—
70#65170—31no—
71#65061—31no—
72D5×#102—31no—
73#65047—31no—
74#65045D311yescharacteristic, complemented
75C4×#677—31no—
76#64978—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×#1220—21no—
80C22×Dic15—21no—
81#6819—22no—
82#6819C2×C414yescomplemented
83C2×C4×D15C2311yescharacteristic
84C2×Dic30C2311yescharacteristic
85C22×C5×Dic3—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3—21no—
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×#1201—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95#6777—22no—
96#6777C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99#6714—21no—
100C4⋊Dic15C2311yescharacteristic
101C4×Dic15—21no—
102C2×C3⋊#168C2311yescharacteristic
103C8×D15—22no—
104C5×#217—21no—
105C5×#213C2×C414yescomplemented
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C4×C5×Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C3×C22⋊Dic5—21no—
111C3×#686C2×C414yescomplemented
112C3×#685—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116#6669—21no—
117#6669—21no—
118#6669—21no—
119#6669D411yescharacteristic
120#6669D411yescharacteristic
121#6667D411yescharacteristic
122#6667D411yescharacteristic
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6659C2×C414yescomplemented
128#6657C2×C414yescomplemented
129#6651C2×C414yescomplemented
130C2×#911—51no—
131#5546—51no—
132#5545—51no—
133C3×C4×D8—51no—
134#5152—51no—
135#5018—51no—
136#5014—51no—
137#4889—51no—
138#4881—51no—
139#4772—51no—
140D3×#102—51no—
141#4758—51no—
142#4756D511yescharacteristic, complemented
143C4×#204—51no—
144#4689—51no—
145C2×#711—31no—
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5C2×D311yescharacteristic, complemented
152C2×#687—31no—
153C2×#686C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#683—61no—
158#4057—38no—
159C2×#677—31no—
160C2×#676—31no—
161C2×C8×D5—31no—
162#4039C2×D311yescharacteristic
163#4038—31no—
164D5×C4⋊C4—31no—
165#4033—31no—
166#4027—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169#4023—61no—
170C4×D20—31no—
171#4018—31no—
172C4×Dic10—31no—
173C5×#107—31no—
174C5×#102—31no—
175C5×#102C2×D311yescharacteristic, complemented
176C4×C5×C8—31no—
177#3964—31no—
178#3964—31no—
179#3953C2×D311yescharacteristic
180#3949—31no—
181#3948—31no—
182#3947—31no—
183C8×Dic5C2×D311yescharacteristic, complemented
184#3942—31no—
185#3941—31no—
186#3940—31no—
187#3939C2×D311yescharacteristic, complemented
188#3935—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15C2×D411yescharacteristic
192C22×C5×D3—21no—
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201#1220—24no—
202C2×Dic15—21no—
203C2×Dic15—24no—
204C2×Dic15—21no—
205C2×Dic15C2×D411yescharacteristic
206C4×D15C22×C412yes—
207C4×D15#4112yes—
208Dic30—21no—
209Dic30C22×C412yes—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—81no—
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C5×D12—21no—
215C5×D12C22×C412yes—
216C4×C5×D3—81no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—81no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20C22×C412yes—
223C3×C4×D5—81no—
224#1201—24no—
225#1200—81no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×C5×C8—21no—
229C3⋊#168—21no—
230C3×#168C22×C412yes—
231C5×C3⋊C8C22×C412yes—
232C2×#237—51no—
233C2×D3×D4—51no—
234C2×C3×D8—51no—
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237D4×Dic3—51no—
238D4×Dic3C2×D511yescharacteristic, complemented
239C2×#214—51no—
240C2×#213C2×D511yescharacteristic
241C4×#67—101no—
242C4×#67—101no—
243C2×(C2×D3)⋊C4—101no—
244C2×Dic3⋊C4—101no—
245#911—58no—
246C2×#204—51no—
247C2×ΓL(1,𝔽25)—51no—
248C2×D3×C8—51no—
249#893C2×D511yescharacteristic
250#892—51no—
251D3×C4⋊C4—51no—
252#887—51no—
253#67⋊C4—101no—
254#67⋊C4—101no—
255D3×C22⋊C4—101no—
256#877—101no—
257C4×D12—51no—
258#872—51no—
259C4×Dic6—51no—
260C3×#107—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic, complemented
263C3×C4×C8—51no—
264#832—51no—
265#832—51no—
266#821C2×D511yescharacteristic
267#817—51no—
268#816—51no—
269#815—51no—
270C8×Dic3C2×D511yescharacteristic, complemented
271#810—51no—
272#809—51no—
273#808—51no—
274#807C2×D511yescharacteristic, complemented
275#803—51no—
276C23×D5—61no—
277C2×C5×D4—31no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C2×C22⋊D5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—21no—
284C22×Dic5—61no—
285C22×Dic5—61no—
286#711—34no—
287#711—62no—
288D4×D5—34no—
289D4×D5—62no—
290C2×D20C22×D311yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5—31no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×Dic10—31no—
296C5×D8—34no—
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C22⋊Dic5—21no—
305C22⋊Dic5—61no—
306#687—34no—
307#686C4×D314yescomplemented
308#685—21no—
309#685—31no—
310#685—31no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5C22×D311yescharacteristic
315#683—31no—
316#683—31no—
317#683—61no—
318#683—61no—
319#683—61no—
320C4×Dic5—61no—
321C4×Dic5—61no—
322C4×Dic5—61no—
323C4×Dic5C22×D311yescharacteristic
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326#677—34no—
327#676—34no—
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—31no—
339C4×D8—51no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—21no—
349C2×D15—21no—
350C2×D15C4×D412yes—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—41no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—22no—
362Dic15—41no—
363Dic15C4×D412yes—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C5×Dic3—21no—
368C5×Dic3—21no—
369C5×Dic3—41no—
370C23×D3—101no—
371C2×C3×D4—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C22×C3×C4—101no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—21no—
378C22×Dic3—101no—
379C22×Dic3—101no—
380#237—54no—
381#237—102no—
382D3×D4—54no—
383D3×D4—102no—
384C2×D12C22×D511yescharacteristic
385C2×C4×D3—21no—
386C2×C4×D3—51no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×D8—54no—
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C42—51no—
398#217—21no—
399#217—101no—
400#214—54no—
401#213C4×D514yescomplemented
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—51no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407C4⋊Dic3—51no—
408C4⋊Dic3C22×D511yescharacteristic
409Dic3⋊C4—51no—
410Dic3⋊C4—51no—
411Dic3⋊C4—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—101no—
415C4×Dic3—101no—
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8C22×D511yescharacteristic
420#204—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—21no—
424C23×C5—61no—
425C22×D5—21no—
426C22×D5—31no—
427C22×D5—64no—
428C22×D5—241no—
429C22×D5—241no—
430C5×D4—21no—
431C5×D4—32no—
432C5×D4—61no—
433C5×D4C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—31no—
436C2×C4×C5—31no—
437C2×C4×C5—61no—
438C2×C4×C5—241no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—31no—
445C2×Dic5—64no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—81no—
449C2×Dic5—241no—
450C2×Dic5D3×D411yescharacteristic
451C2×Dic5D3×D411yescharacteristic
452D20—21no—
453D20C2×C4×D312yes—
454C4×D5—32no—
455C4×D5—32no—
456C4×D5—81no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—32no—
460Dic10—61no—
461C5×C8—21no—
462C5×C8—32no—
463#168—61no—
464#168C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—151no—
469C2×SD16—151no—
470C2×D8—31no—
471C2×D8—51no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—151no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—31no—
478C4×D4—51no—
479C4×D4—51no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—31no—
494#107—51no—
495#106—151no—
496#106—151no—
497#103—151no—
498#103—151no—
499#102—31no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102D3×D511yescharacteristic, complemented
505#97—151no—
506#97—151no—
507C4×C8—31no—
508C4×C8—51no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—22no—
514C3×D5—42no—
515C5×D3—42no—
516C23×C3—21no—
517C23×C3—101no—
518C22×D3—21no—
519C22×D3—51no—
520C22×D3—104no—
521C22×D3—401no—
522C22×D3—401no—
523C3×D4—21no—
524C3×D4—52no—
525C3×D4—101no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—401no—
532C2×C3×C4—401no—
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535#67—104no—
536C2×Dic3—21no—
537C2×Dic3—51no—
538C2×Dic3—81no—
539C2×Dic3—104no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—401no—
543C2×Dic3D4×D511yescharacteristic
544C2×Dic3D4×D511yescharacteristic
545D12—21no—
546D12C2×C4×D512yes—
547C4×D3—52no—
548C4×D3—52no—
549C4×D3—81no—
550C4×D3—401no—
551C4×D3—401no—
552Dic6—52no—
553Dic6—101no—
554C3×C8—21no—
555C3×C8—52no—
556C3⋊C8—101no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5—62no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—22no—
566C2×D5—32no—
567C2×D5—41no—
568C2×D5—41no—
569C2×D5—61no—
570C2×D5—61no—
571C2×D5—244no—
572C4×C5—41no—
573C4×C5—61no—
574C4×C5—61no—
575C4×C5—121no—
576C4×C5C22×C4×D311yescharacteristic
577C4×C5D3×#4111yescharacteristic
578Dic5—21no—
579Dic5—21no—
580Dic5—32no—
581Dic5—41no—
582Dic5—62no—
583Dic5—121no—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8—151no—
588C2×D4—31no—
589C2×D4—51no—
590C2×D4—154no—
591C2×D4—302no—
592C2×D4—301no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—151no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16—154no—
606D8—34no—
607D8—54no—
608M16—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—302no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—51no—
616C4⋊C4—151no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—301no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—101no—
626C22⋊C4—101no—
627C22⋊C4—151no—
628C22⋊C4—151no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—51no—
634C42—301no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—102no—
642C22×C3—201no—
643C22×C3—201no—
644C22×C3C2×D4×D511yescharacteristic
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—52no—
649C2×D3—101no—
650C2×D3—101no—
651C2×D3—404no—
652C3×C4—41no—
653C3×C4—101no—
654C3×C4—101no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4D5×#4111yescharacteristic
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—52no—
662Dic3—102no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5—122no—
666C2×C5C4×D3×D411yescharacteristic
667C2×C5#575711yescharacteristic
668C2×C5#577011yescharacteristic
669D5—42no—
670D5—62no—
671C23—21no—
672C23—61no—
673C23—101no—
674C23—151no—
675C23—304no—
676C23—1201no—
677C23—1201no—
678Q8—152no—
679Q8—301no—
680D4—21no—
681D4—32no—
682D4—52no—
683D4—61no—
684D4—101no—
685D4—304no—
686D4—304no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—51no—
692C2×C4—51no—
693C2×C4—61no—
694C2×C4—101no—
695C2×C4—151no—
696C2×C4—152no—
697C2×C4—152no—
698C2×C4—241no—
699C2×C4—241no—
700C2×C4—304no—
701C2×C4—301no—
702C2×C4—301no—
703C2×C4—401no—
704C2×C4—401no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—32no—
711C8—52no—
712C8—301no—
713C2×C3—42no—
714C2×C3—202no—
715C2×C3C4×D4×D511yescharacteristic
716C2×C3#6609111yescharacteristic
717C2×C3#6610411yescharacteristic
718D3—42no—
719D3—102no—
720C5#7958711yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—62no—
725C22—102no—
726C22—121no—
727C22—121no—
728C22—152no—
729C22—201no—
730C22—201no—
731C22—301no—
732C22—301no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—41no—
736C4—61no—
737C4—61no—
738C4—101no—
739C4—101no—
740C4—121no—
741C4—152no—
742C4—201no—
743C4—302no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4#9202411yescharacteristic
747C3#1061131811yescharacteristic, complemented, Sylow
748C2—42no—
749C2—122no—
750C2—202no—
751C2—302no—
752C2#1175320311yescharacteristic
753C2#1175405411yescharacteristic
754C2#1175409511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91482C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #11754916C2semidirect
3. #11753841C2semidirect
4. #11750873C2semidirect
5. C5×#4756C2semidirect
6. C3×#65045C2semidirect
7. #11748988C2semidirect
8. #11748977C2semidirect
9. #11748108C2semidirect
10. #11747744C2semidirect
11. #11747739C2semidirect
12. #11747657C2semidirect
13. #11747473C2semidirect
14. #11747472C2semidirect
15. #11747456C2semidirect
21. C5×D4×Dic3C22semidirect
24. C3×D4×Dic5C22semidirect
31. #91482C4semidirect
40. #91340C22semidirect
41. #91333C22semidirect
45. C3×C5×#102C22semidirect
46. #91116C22semidirect
47. #91100C22semidirect
48. #91094C22semidirect
50. C5×C8×Dic3C22semidirect
51. C5×#807C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3939C22semidirect
55. #90987C22semidirect
56. #90985C22semidirect
59. #90953C22semidirect
60. #90952C22semidirect
74. #65045D3semidirect
82. #6819C2×C4semidirect
96. #6777C2×C4semidirect
105. C5×#213C2×C4semidirect
111. C3×#686C2×C4semidirect
127. #6659C2×C4semidirect
128. #6657C2×C4semidirect
129. #6651C2×C4semidirect
142. #4756D5semidirect
151. D4×Dic5C2×D3semidirect
175. C5×#102C2×D3semidirect
183. C8×Dic5C2×D3semidirect
187. #3939C2×D3semidirect
238. D4×Dic3C2×D5semidirect
262. C3×#102C2×D5semidirect
270. C8×Dic3C2×D5semidirect
274. #807C2×D5semidirect
307. #686C4×D3semidirect
401. #213C4×D5semidirect
504. #102D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79587semidirect
747. C3#10611318semidirect

Maximal subgroups

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

subgroupindex
#117549162
C2×#914822
#117538412
#117508732
C5×#47562
C3×#650452
#117489882
#117489772
#117481082
#117477442
#117477392
#117476572
#117474732
#117474722
#117474562
#106113183
#795875