Finite Group Databasebeta

← #14417119

Subgroups — #14417119

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
1C2×#91250C211yesmaximal, characteristic
2#11753837C211yesmaximal, characteristic, complemented
3#11753671C211yesmaximal, characteristic, complemented
4#11750990C211yesmaximal, characteristic, complemented
5C5×#4872C211yesmaximal, characteristic, complemented
6C3×#65170C211yesmaximal, characteristic, complemented
7#11748050C211yesmaximal, characteristic, complemented
8#11747813C211yesmaximal, characteristic, complemented
9#11747789C211yesmaximal, characteristic, complemented
10#11747499C211yesmaximal, characteristic, complemented
11D5×#809C211yesmaximal, characteristic, complemented
12#11747473C211yesmaximal, characteristic, complemented
13#11747470C211yesmaximal, characteristic, complemented
14#11747234C211yesmaximal, characteristic, complemented
15#11747233C211yesmaximal, characteristic, complemented
16#10611318—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C2×#6706C2211yescharacteristic
20#91782C2211yescharacteristic
21#91776C2211yescharacteristic, complemented
22C2×C5×D24C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C5×#893C2211yescharacteristic, complemented
25C2×C3×#676C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27C3×D5×C4⋊C4C2211yescharacteristic
28#91473—21no—
29D3×#685—21no—
30C4×#1203—21no—
31#91440—21no—
32C4×#1201—21no—
33#91435C2211yescharacteristic
34#91435C2211yescharacteristic, complemented
35#91428C2211yescharacteristic
36#91405—21no—
37#91400—21no—
38D3×#683—21no—
39#91357C2211yescharacteristic
40#91340C2211yescharacteristic, complemented
41C2×#6659C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×D5×C3⋊C8C2211yescharacteristic
44#91250C418yescomplemented
45C3×C5×#107C2211yescharacteristic, complemented
46#91099C2211yescharacteristic, complemented
47#91094C2211yescharacteristic, complemented
48#91093C2211yescharacteristic
49C5×C8×Dic3C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic
51C5×#809C2211yescharacteristic, complemented
52C3×#3949C2211yescharacteristic, complemented
53C3×#3940C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90974C2211yescharacteristic, complemented
56#90968C2211yescharacteristic
57#90966C2211yescharacteristic
58#90966C2211yescharacteristic, complemented
59#90953C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79201—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#65170D311yescharacteristic, complemented
71#65061—31no—
72D5×#102—31no—
73#65047—31no—
74#65045—31no—
75C4×#677—31no—
76#64978—31no—
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C2×C5×D12C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1203—21no—
88C2×#1201—21no—
89C2×#1200—21no—
90C2×D3×Dic5—21no—
91C2×D3×Dic5—21no—
92C2×D3×Dic5—21no—
93D5×D12—22no—
94D5×D12C2×C414yescomplemented
95#6772—22no—
96#6772C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100#6714—21no—
101#6712—21no—
102C4×Dic15—21no—
103C4×Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105#6706C2×C414yescomplemented
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C4×C5×Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C5×D24C2×C414yescomplemented
111C3×#685—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C3×C4×Dic5—21no—
116C2×C3×#168C2311yescharacteristic
117C3×#676C2×C414yescomplemented
118#6669—21no—
119#6668D411yescharacteristic
120#6668D411yescharacteristic
121#6667—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124#6665D411yescharacteristic
125#6665D411yescharacteristic
126Dic3×Dic5—21no—
127#6659C2×C414yescomplemented
128#6654C2×C414yescomplemented
129D5×C3⋊C8—22no—
130C2×#908—51no—
131#5521—51no—
132#5504—51no—
133C3×#428—51no—
134#5122—51no—
135#5002—51no—
136C2×#809—51no—
137#4889—51no—
138#4889—51no—
139#4872—51no—
140#4872D511yescharacteristic, complemented
141#4869—51no—
142#4869—51no—
143#4852—51no—
144#4852—51no—
145C2×#711—31no—
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5—31no—
152C2×#687—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#683—61no—
158#4057—38no—
159C2×#677—31no—
160C2×#676C2×D311yescharacteristic
161C2×C8×D5—31no—
162#4039—31no—
163#4038C2×D311yescharacteristic
164D5×C4⋊C4C2×D311yescharacteristic
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×#107C2×D311yescharacteristic, complemented
174C5×#102—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3949C2×D311yescharacteristic, complemented
181#3948—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3941—31no—
186#3940C2×D311yescharacteristic, complemented
187#3939C2×D311yescharacteristic, complemented
188#3935—31no—
189#2946—151noSylow
190C22×D15—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C3×D5C2×D411yescharacteristic
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203D60—21no—
204D60C22×C412yes—
205C4×D15—81no—
206Dic30—21no—
207Dic30C22×C412yes—
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C5×D12—21no—
211C5×D12—21no—
212C5×D12C22×C412yes—
213C5×D12C22×C412yes—
214C4×C5×D3—81no—
215C4×C5×D3—81no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5C2×D411yescharacteristic
219C3×C4×D5—81no—
220C3×C4×D5C22×C412yes—
221C3×C4×D5#4112yes—
222#1203—24no—
223#1201—24no—
224#1200—81no—
225D3×Dic5—24no—
226D3×Dic5—81no—
227D3×Dic5—81no—
228C3×C5×C8C22×C412yes—
229C3⋊#168—21no—
230C3×#168C22×C412yes—
231C5×C3⋊C8—21no—
232C2×#235—51no—
233C22×D12—51no—
234C2×C3×M16—51no—
235C3×#117—51no—
236C2×C3×C4⋊C4—51no—
237C4×#67—101no—
238C4×#67—101no—
239#926—51no—
240C22×C3⋊C8—51no—
241#908—58no—
242C2×D24—51no—
243C2×D24C2×D511yescharacteristic
244C2×#204—51no—
245C2×#204—51no—
246#893—51no—
247#893—51no—
248#893—51no—
249#893—51no—
250#893C2×D511yescharacteristic
251#893C2×D511yescharacteristic, complemented
252#892—101no—
253D3×C4⋊C4—101no—
254#887—51no—
255#887—51no—
256D3×C22⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—101no—
259C4×D12—101no—
260C3×#107—51no—
261C3×#107C2×D511yescharacteristic, complemented
262C3×#106—51no—
263C3×#106—51no—
264#815—51no—
265#815—51no—
266C8×Dic3—51no—
267C8×Dic3C2×D511yescharacteristic, complemented
268#810—51no—
269#810—51no—
270#809—51no—
271#809—51no—
272#809—51no—
273#809—51no—
274#809C2×D511yescharacteristic
275#809C2×D511yescharacteristic, complemented
276C23×D5—61no—
277C2×C5×D4—31no—
278C2×C5×D4—31no—
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C2×C22⋊D5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—61no—
284C22×Dic5—61no—
285C22×Dic5—61no—
286#711—34no—
287#711—62no—
288D4×D5—34no—
289D4×D5—62no—
290C2×D20—31no—
291C2×C4×D5—21no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5C22×D311yescharacteristic
295C2×Dic10—31no—
296C5×D8—34no—
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306#687—34no—
307#686—34no—
308#685—21no—
309#685—31no—
310#685—31no—
311#685—61no—
312#685—61no—
313C4⋊Dic5C22×D311yescharacteristic
314C4⋊Dic5C22×D311yescharacteristic
315#683—21no—
316#683—31no—
317#683—31no—
318#683—61no—
319#683—61no—
320C4×Dic5—21no—
321C4×Dic5—31no—
322C4×Dic5—61no—
323C4×Dic5—61no—
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326#677—34no—
327#676C4×D314yescomplemented
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—151no—
340#428—51no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—22no—
349C2×C5×D3—22no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5C4×D412yes—
357D3×D5—84no—
358C3×C4×C5—41no—
359C3×C4×C5—41no—
360C3×C4×C5C23×C411yescharacteristic
361C3×C4×C5C2×#4111yescharacteristic
362Dic15—22no—
363Dic15—21no—
364Dic15—21no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C3×Dic5C4×D412yes—
368C5×Dic3—21no—
369C5×Dic3—21no—
370C23×D3—101no—
371C22×C3×C4—51no—
372C22×C3×C4—101no—
373C2×#67—101no—
374#235—54no—
375#235—102no—
376C2×D12—51no—
377C2×D12—54no—
378C2×D12—102no—
379C2×D12—101no—
380C2×D12C22×D511yescharacteristic
381C2×D12C22×D511yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—101no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×M16—54no—
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C4⋊C4C22×D511yescharacteristic
398C3×C22⋊C4—101no—
399C3×C42—101no—
400#217—51no—
401#217—51no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410Dic3⋊C4—101no—
411Dic3⋊C4—101no—
412C4×Dic3—51no—
413C4×Dic3—101no—
414C4×Dic3—101no—
415C4×Dic3C22×D511yescharacteristic
416C2×C3⋊C8—51no—
417C2×C3⋊C8—102no—
418C2×C3⋊C8C22×D511yescharacteristic
419D24—54no—
420D24C4×D514yescomplemented
421#204—54no—
422#204—54no—
423C23×C5—61no—
424C23×C5—61no—
425C22×D5—61no—
426C22×D5—64no—
427C22×D5—241no—
428C22×D5—241no—
429C22×D5D3×D411yescharacteristic
430C5×D4—32no—
431C5×D4—32no—
432C5×D4—61no—
433C5×D4—61no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—31no—
437C2×C4×C5—31no—
438C2×C4×C5—241no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—31no—
446C2×Dic5—31no—
447C2×Dic5—61no—
448C2×Dic5—64no—
449C2×Dic5—241no—
450C2×Dic5—241no—
451C2×Dic5D3×D411yescharacteristic
452D20—32no—
453D20—61no—
454C4×D5—81no—
455C4×D5—241no—
456C4×D5—241no—
457C4×D5C2×C4×D312yes—
458C4×D5#23912yes—
459Dic10—32no—
460Dic10—61no—
461C5×C8—61no—
462C5×C8C2×C4×D312yes—
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—151no—
472C2×M16—51no—
473C22×C8—151no—
474C4×Q8—151no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—31no—
478C4×D4—151no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—51no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—51no—
494#107D3×D511yescharacteristic, complemented
495#106—51no—
496#106—51no—
497#103—151no—
498#103—151no—
499#102—31no—
500#102—31no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—151no—
506#97—151no—
507C4×C8—31no—
508C4×C8—151no—
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—42no—
513C3×D5—22no—
514C5×D3—42no—
515C5×D3—42no—
516C23×C3—51no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—51no—
526C2×C3×C4—52no—
527C2×C3×C4—52no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—401no—
531C2×C3×C4C23×D511yescharacteristic
532#67—104no—
533C2×Dic3—51no—
534C2×Dic3—51no—
535C2×Dic3—101no—
536C2×Dic3D4×D511yescharacteristic
537C2×Dic3D4×D511yescharacteristic
538D12—21no—
539D12—21no—
540D12—52no—
541D12—104no—
542D12—101no—
543D12C2×C4×D512yes—
544D12C2×C4×D512yes—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—104no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3—401no—
551C4×D3—401no—
552Dic6—52no—
553Dic6—101no—
554C3×C8—52no—
555C3×C8C2×C4×D512yes—
556C3⋊C8—21no—
557C3⋊C8—101no—
558C22×C5—62no—
559C22×C5—62no—
560C22×C5—121no—
561C22×C5—121no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—21no—
566C2×D5—21no—
567C2×D5—62no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—244no—
571C2×D5#89312yes—
572C4×C5—41no—
573C4×C5—41no—
574C4×C5—61no—
575C4×C5—61no—
576C4×C5C22×C4×D311yescharacteristic
577C4×C5C2×#23911yescharacteristic
578Dic5—41no—
579Dic5—41no—
580Dic5—62no—
581Dic5—61no—
582Dic5—61no—
583Dic5#89312yes—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8—151no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—154no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4—301no—
595C22×C4—51no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—101no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16—154no—
606D8—34no—
607D8—154no—
608M16—54no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—151no—
612C2×C8—302no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—51no—
615C4⋊C4—51no—
616C4⋊C4—101no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—301no—
620C4⋊C4—301no—
621C4⋊C4C2×D3×D511yescharacteristic
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—101no—
626C22⋊C4—151no—
627C22⋊C4—151no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—101no—
634C42—151no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—52no—
639C22×C3—101no—
640C22×C3—101no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—52no—
655C3×C4—201no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4D5×#4111yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—101no—
662Dic3—101no—
663Dic3—102no—
664C2×C5—122no—
665C2×C5—122no—
666C2×C5C2×#89311yescharacteristic
667C2×C5#577411yescharacteristic
668C2×C5#577811yescharacteristic
669D5—22no—
670D5—122no—
671C23—51no—
672C23—61no—
673C23—61no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—152no—
679Q8—301no—
680D4—32no—
681D4—32no—
682D4—61no—
683D4—61no—
684D4—152no—
685D4—304no—
686D4—304no—
687D4—301no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—51no—
693C2×C4—52no—
694C2×C4—52no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—151no—
698C2×C4—151no—
699C2×C4—241no—
700C2×C4—241no—
701C2×C4—304no—
702C2×C4—301no—
703C2×C4—401no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—52no—
710C8—61no—
711C8—301no—
712C8C4×D3×D512yes—
713C2×C3—102no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3#6609111yescharacteristic
716C2×C3#6610411yescharacteristic
717D3—42no—
718D3—42no—
719D3—202no—
720C5#7920111yescharacteristic, complemented, Sylow
721C22—52no—
722C22—62no—
723C22—62no—
724C22—101no—
725C22—101no—
726C22—121no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—41no—
736C4—41no—
737C4—52no—
738C4—61no—
739C4—61no—
740C4—201no—
741C4—201no—
742C4—301no—
743C4—302no—
744C4—301no—
745C4C2×C4×D3×D511yescharacteristic
746C4D5×#23911yescharacteristic
747C3#1061131811yescharacteristic, complemented, Sylow
748C2—102no—
749C2—122no—
750C2—122no—
751C2—602no—
752C2D5×#89311yescharacteristic
753C2#1175405611yescharacteristic
754C2#1175411211yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91250C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11753837C2semidirect
3. #11753671C2semidirect
4. #11750990C2semidirect
5. C5×#4872C2semidirect
6. C3×#65170C2semidirect
7. #11748050C2semidirect
8. #11747813C2semidirect
9. #11747789C2semidirect
10. #11747499C2semidirect
11. D5×#809C2semidirect
12. #11747473C2semidirect
13. #11747470C2semidirect
14. #11747234C2semidirect
15. #11747233C2semidirect
21. #91776C22semidirect
24. C5×#893C22semidirect
34. #91435C22semidirect
40. #91340C22semidirect
44. #91250C4semidirect
45. C3×C5×#107C22semidirect
46. #91099C22semidirect
47. #91094C22semidirect
49. C5×C8×Dic3C22semidirect
51. C5×#809C22semidirect
52. C3×#3949C22semidirect
53. C3×#3940C22semidirect
54. C3×#3939C22semidirect
55. #90974C22semidirect
58. #90966C22semidirect
59. #90953C22semidirect
60. #90951C22semidirect
70. #65170D3semidirect
94. D5×D12C2×C4semidirect
96. #6772C2×C4semidirect
105. #6706C2×C4semidirect
110. C5×D24C2×C4semidirect
117. C3×#676C2×C4semidirect
127. #6659C2×C4semidirect
128. #6654C2×C4semidirect
140. #4872D5semidirect
173. C5×#107C2×D3semidirect
180. #3949C2×D3semidirect
186. #3940C2×D3semidirect
187. #3939C2×D3semidirect
251. #893C2×D5semidirect
261. C3×#107C2×D5semidirect
267. C8×Dic3C2×D5semidirect
275. #809C2×D5semidirect
327. #676C4×D3semidirect
420. D24C4×D5semidirect
494. #107D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79201semidirect
747. C3#10611318semidirect

Maximal subgroups

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

subgroupindex
C2×#912502
#117538372
#117536712
#117509902
C5×#48722
C3×#651702
#117480502
#117478132
#117477892
#117474992
D5×#8092
#117474732
#117474702
#117472342
#117472332
#106113183
#792015