Finite Group Databasebeta

← #14425347

Subgroups — #14425347

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic, complemented
2C5×#5822C211yesmaximal, characteristic, complemented
3#11754600C211yesmaximal, characteristic, complemented
4#11754138C211yesmaximal, characteristic, complemented
5#11751337C211yesmaximal, characteristic, complemented
6#11749417C214yesmaximal, complemented
7#11749415C214yesmaximal, complemented
8#11748420C211yesmaximal, characteristic, complemented
9C2×#90958C211yesmaximal, characteristic, complemented
10#10615736—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic, complemented
13C3×#4149—22no—
14C3×#4149—22no—
15C3×#4149—22no—
16C3×#4149C2214yes—
17C2×C3×#713—21no—
18C2×C3×D4×D5—22no—
19C2×C3×D4×D5—21no—
20C2×C3×#709—21no—
21C2×C3×#709C2211yescharacteristic
22C22×C3×D20—21no—
23C22×C3×D20C2211yescharacteristic
24#91815C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C5×#951C2212yescomplemented
27C5×#950—22no—
28C5×#949C2212yescomplemented
29C5×#942—21no—
30C5×#932—21no—
31C2×C5×#208C2211yescharacteristic, complemented
32#91563—22no—
33#91463C2212yescomplemented
34#91456—22no—
35#91368C2212yescomplemented
36#91309—21no—
37#91307C2212yescomplemented
38#91299C2212yescomplemented
39#91298—21no—
40#91297—22no—
41#91121C2214yescomplemented
42#90976C2214yescomplemented
43#90958C2214yescomplemented
44#84104—51nomaximal, Hall
45C2×#4149D311yescharacteristic, complemented
46C5×#575—31no—
47#66164—31no—
48#66156—31no—
49#65525—31no—
50#65491—34no—
51#65487—34no—
52#65428—31no—
53C2×#3955—31no—
54C23×C3×D5—22no—
55C23×C3×D5D412yes—
56C3×C5×#41—21no—
57C3×C5×#41—21no—
58C3×C5×#41D412yescomplemented
59C3×C5×#41C2312yes—
60C2×C3×C5×Q8D411yescharacteristic, complemented
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4D411yescharacteristic, complemented
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×C5×#67—21no—
66C5×#235—21no—
67C5×#235—21no—
68C5×#235—21no—
69C5×#235—21no—
70C2×C5×D12C2311yescharacteristic, complemented
71C2×C4×C5×D3—21no—
72C2×C5×Dic6C2311yescharacteristic, complemented
73C2×C3×C22⋊D5—22no—
74C2×C3×C22⋊D5—21no—
75C3×#713—24no—
76C3×#713—24no—
77C3×D4×D5—28no—
78C3×D4×D5—24no—
79C3×D4×D5—28no—
80C3×D4×D5—24no—
81C3×#709—24no—
82C3×#709—21no—
83C3×#709—21no—
84C3×#709—24no—
85C3×#709D412yescomplemented
86C3×#709C2312yes—
87C2×C3×D20—22no—
88C2×C3×D20—24no—
89C2×C3×D20—21no—
90C2×C3×D20—21no—
91C2×C3×D20—21no—
92C2×C3×D20—21no—
93C2×C3×D20—24no—
94C2×C3×D20D412yes—
95C2×C3×D20D411yescharacteristic, complemented
96C2×C3×D20C2312yes—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—21no—
99C2×C3×Dic10D411yescharacteristic, complemented
100C2×#1201—24no—
101#6719—21no—
102C4⋊Dic15—21no—
103C4×Dic15C2312yescomplemented
104#6710—21no—
105#6710C2312yescomplemented
106C2×C3⋊#168—21no—
107C5×#216—22no—
108C5×#215—22no—
109C5×#214—22no—
110C5×#213—22no—
111C5×#208—21no—
112C5×#208C2312yescomplemented
113C2×C5×C3⋊C8—21no—
114#6665—24no—
115#6661—22no—
116#6656—22no—
117#6655—22no—
118#6652—22no—
119C2×C3×H(5,𝔽2)—51no—
120#5822—51no—
121#5822D511yescharacteristic, complemented
122#5805—51no—
123#5242—54no—
124#5241—54no—
125#5236—51no—
126#5236—51no—
127C2×#833—51no—
128C2×C5×#41—31no—
129C2×C5×#41C2×D311yescharacteristic
130#4149—22no—
131#4149—22no—
132#4149—22no—
133#4149C2×D314yes—
134C2×#713—21no—
135C2×D4×D5—22no—
136C2×D4×D5—21no—
137C2×#709—21no—
138C2×#709C2×D311yescharacteristic
139C22×D20—21no—
140C22×D20C2×D311yescharacteristic
141C5×#137—32no—
142C5×#137—61no—
143C5×AGL(1,ℤ/8)—32no—
144C5×AGL(1,ℤ/8)—61no—
145C5×#135—62no—
146C2×C5×M16—31no—
147#4097—61no—
148#4096—62no—
149#4095—61no—
150#4093—32no—
151#4088—32no—
152#4086—32no—
153#4083—62no—
154#4078—32no—
155#4076—62no—
156#4072—31no—
157C2×#681—31no—
158#3969—34no—
159#3957—34no—
160#3955—34no—
161#3019—151noSylow
162C23×C3×C5—21no—
163C23×C3×C5C2×D411yescharacteristic
164C22×C5×D3—21no—
165C22×C3×D5—22no—
166C22×C3×D5—21no—
167C22×C3×D5—28no—
168C22×C3×D5—22no—
169C22×C3×D5—82no—
170C22×C3×D5—84no—
171C22×C3×D5C2×D414yes—
172C3×C5×Q8—21no—
173C3×C5×Q8C2×D412yes—
174C3×C5×D4—22no—
175C3×C5×D4—22no—
176C3×C5×D4—21no—
177C3×C5×D4C2×D412yes—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5C2×D411yescharacteristic
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—22no—
188C5×#67—41no—
189C5×#67—41no—
190C2×C5×Dic3—21no—
191C5×D12—21no—
192C5×D12—21no—
193C4×C5×D3—41no—
194C4×C5×D3—41no—
195C5×Dic6—21no—
196C5×Dic6—21no—
197C3×C22⋊D5—28no—
198C3×C22⋊D5—22no—
199C3×C22⋊D5—22no—
200C2×C3×Dic5—21no—
201C3×D20—28no—
202C3×D20—22no—
203C3×D20—21no—
204C3×D20—22no—
205C3×D20—22no—
206C3×D20—22no—
207C3×D20C2×D412yes—
208C3×C4×D5—28no—
209C3×C4×D5—22no—
210C3×C4×D5—22no—
211C3×Dic10—21no—
212C3×Dic10C2×D412yes—
213#1201—84no—
214C3⋊#168—22no—
215C5×C3⋊C8—22no—
216C3×H(5,𝔽2)—54no—
217C3×H(5,𝔽2)—102no—
218C3×H(5,𝔽2)—102no—
219C3×H(5,𝔽2)—102no—
220C2×C3×#41—51no—
221C2×C3×#41—101no—
222C2×C3×#41—101no—
223C2×C3×#41C2×D511yescharacteristic
224C22×C3×D4—51no—
225C22×C3×D4—101no—
226C22×C3×D4—102no—
227C22×C3×D4—101no—
228C2×#235C2×D511yescharacteristic, complemented
229#953—102no—
230#951—52no—
231#951C2×D512yescomplemented
232#950—22no—
233#950—102no—
234#949—52no—
235#949C2×D512yescomplemented
236#942—21no—
237#942—101no—
238#940—52no—
239#938—102no—
240#936—52no—
241#932—21no—
242#932—101no—
243#926—51no—
244C2×#208—51no—
245C2×#208C2×D511yescharacteristic, complemented
246#837—54no—
247#837—54no—
248#833—54no—
249C23×D5—22no—
250C23×D5#6712yes—
251C5×#41—21no—
252C5×#41—21no—
253C5×#41—61no—
254C5×#41—61no—
255C5×#41—61no—
256C5×#41—61no—
257C5×#41#6712yescomplemented
258C5×#41C22×D312yes—
259C2×C5×Q8—31no—
260C2×C5×Q8#6711yescharacteristic, complemented
261C2×C5×D4—21no—
262C2×C5×D4—31no—
263C2×C5×D4—61no—
264C2×C5×D4#6711yescharacteristic, complemented
265C22×C4×C5—21no—
266C22×C4×C5—61no—
267C22×C4×C5C22×D311yescharacteristic
268C2×C22⋊D5—22no—
269C2×C22⋊D5—21no—
270C2×C22⋊D5—64no—
271#713—24no—
272#713—24no—
273D4×D5—28no—
274D4×D5—24no—
275D4×D5—28no—
276D4×D5—24no—
277#709—24no—
278#709—21no—
279#709—21no—
280#709—24no—
281#709#6712yescomplemented
282#709C22×D312yes—
283C2×D20—22no—
284C2×D20—24no—
285C2×D20—21no—
286C2×D20—21no—
287C2×D20—21no—
288C2×D20—21no—
289C2×D20—24no—
290C2×D20#6712yes—
291C2×D20#6711yescharacteristic, complemented
292C2×D20C22×D312yes—
293C2×C4×D5—22no—
294C2×C4×D5—21no—
295C2×Dic10#6711yescharacteristic, complemented
296C5×Q16—62no—
297C5×SD16—62no—
298C5×SD16—62no—
299C5×D8—62no—
300C5×M16—32no—
301C5×M16—61no—
302C2×C5×C8—61no—
303C22⋊Dic5—61no—
304#689—62no—
305#688—62no—
306#687—62no—
307#686—62no—
308#685—64no—
309C4⋊Dic5—61no—
310C4×Dic5—32no—
311#681—32no—
312#681—61no—
313C2×#168—61no—
314C2×H(5,𝔽2)—51no—
315#575—31no—
316#575—151no—
317#535—151no—
318#455—154no—
319#453—154no—
320#421—151no—
321#421—151no—
322C2×#100—151no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—42no—
326C22×C3×C5#12011yescharacteristic
327C22×C3×C5#12011yescharacteristic
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—42no—
330C2×C5×D3—41no—
331C2×C3×D5—24no—
332C2×C3×D5—22no—
333C2×C3×D5—44no—
334C2×C3×D5—42no—
335C2×C3×D5—44no—
336C2×C3×D5—82no—
337C2×C3×D5—88no—
338C3×C4×C5—22no—
339C3×C4×C5#12011yescharacteristic
340C3×C4×C5#12011yescharacteristic
341C3×C4×C5C22×D411yescharacteristic
342C3×C4×C5C22×D411yescharacteristic
343Dic15—42no—
344C3×Dic5—22no—
345C5×Dic3—41no—
346C24×C3—52no—
347C24×C3—102no—
348C3×#41—21no—
349C3×#41—21no—
350C3×#41—52no—
351C3×#41—52no—
352C3×#41—104no—
353C3×#41—104no—
354C3×#41—104no—
355C3×#41—104no—
356C3×#41—101no—
357C3×#41—101no—
358C3×#41C22⋊D512yescomplemented
359C3×#41C22×D512yes—
360C2×C3×Q8—51no—
361C2×C3×Q8C22⋊D511yescharacteristic, complemented
362C2×C3×D4—21no—
363C2×C3×D4—51no—
364C2×C3×D4—52no—
365C2×C3×D4—52no—
366C2×C3×D4—104no—
367C2×C3×D4—102no—
368C2×C3×D4—104no—
369C2×C3×D4—108no—
370C2×C3×D4—108no—
371C2×C3×D4—104no—
372C2×C3×D4—102no—
373C2×C3×D4—101no—
374C2×C3×D4—104no—
375C2×C3×D4—101no—
376C2×C3×D4—101no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4C22⋊D511yescharacteristic, complemented
380C22×C3×C4—21no—
381C22×C3×C4—102no—
382C22×C3×C4—101no—
383C22×C3×C4C22×D511yescharacteristic
384C2×#67—21no—
385C2×#67—104no—
386#235—21no—
387#235—21no—
388#235—21no—
389#235—21no—
390C2×D12C22×D511yescharacteristic, complemented
391C2×C4×D3—21no—
392C2×Dic6C22×D511yescharacteristic, complemented
393#217—104no—
394#217—101no—
395#216—22no—
396#216—102no—
397#215—22no—
398#215—102no—
399#214—22no—
400#214—102no—
401#213—22no—
402#213—102no—
403C4⋊Dic3—101no—
404C4×Dic3—52no—
405#208—21no—
406#208—52no—
407#208—101no—
408#208C22×D512yescomplemented
409C2×C3⋊C8—21no—
410C2×C3⋊C8—101no—
411C23×C5—21no—
412C23×C5—61no—
413C23×C5C2×#6711yescharacteristic
414C22×D5—22no—
415C22×D5—21no—
416C22×D5—28no—
417C22×D5—22no—
418C22×D5—82no—
419C22×D5—84no—
420C22×D5C2×#6714yes—
421C5×Q8—21no—
422C5×Q8—61no—
423C5×Q8—61no—
424C5×Q8C2×#6712yes—
425C5×D4—22no—
426C5×D4—22no—
427C5×D4—21no—
428C5×D4—61no—
429C5×D4—61no—
430C5×D4—121no—
431C5×D4—121no—
432C5×D4C2×#6712yes—
433C2×C4×C5—21no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—61no—
437C2×C4×C5—121no—
438C2×C4×C5—121no—
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C2×#6711yescharacteristic
441C2×C4×C5C2×#6711yescharacteristic
442C2×C4×C5C2×#6711yescharacteristic
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C23×D311yescharacteristic
445C22⋊D5—28no—
446C22⋊D5—22no—
447C22⋊D5—22no—
448C22⋊D5—244no—
449C2×Dic5—21no—
450C2×Dic5—62no—
451D20—28no—
452D20—22no—
453D20—21no—
454D20—22no—
455D20—22no—
456D20—22no—
457D20C2×#6712yes—
458C4×D5—28no—
459C4×D5—22no—
460C4×D5—22no—
461Dic10—21no—
462Dic10C2×#6712yes—
463C5×C8—62no—
464#168—62no—
465H(5,𝔽2)—54no—
466H(5,𝔽2)—102no—
467H(5,𝔽2)—102no—
468H(5,𝔽2)—102no—
469C2×#41—31no—
470C2×#41—51no—
471C2×#41—101no—
472C2×#41—101no—
473C2×#41D3×D511yescharacteristic
474C22×D4—51no—
475C22×D4—101no—
476C22×D4—102no—
477C22×D4—101no—
478#137—32no—
479#137—61no—
480#137—152no—
481#137—301no—
482AGL(1,ℤ/8)—32no—
483AGL(1,ℤ/8)—61no—
484AGL(1,ℤ/8)—152no—
485AGL(1,ℤ/8)—301no—
486#135—62no—
487#135—302no—
488C2×M16—31no—
489C2×M16—151no—
490#127—152no—
491#124—152no—
492#121—302no—
493#120—302no—
494#117—151no—
495#104—154no—
496#104—154no—
497#100—154no—
498C2×C3×C5—21no—
499C2×C3×C5—21no—
500C2×C3×C5—21no—
501C2×C3×C5—42no—
502C2×C3×C5C2×#12011yescharacteristic
503C3×D5—44no—
504C3×D5—42no—
505C5×D3—81no—
506C23×C3—21no—
507C23×C3—54no—
508C23×C3—108no—
509C23×C3—101no—
510C23×C3—102no—
511C23×C3—102no—
512C23×C3—402no—
513C23×C3—404no—
514C23×C3D4×D511yescharacteristic
515C22×D3—21no—
516C3×Q8—21no—
517C3×Q8—52no—
518C3×Q8—101no—
519C3×Q8C2×C22⋊D512yes—
520C3×D4—22no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—52no—
524C3×D4—108no—
525C3×D4—108no—
526C3×D4—102no—
527C3×D4—102no—
528C3×D4—102no—
529C3×D4—102no—
530C3×D4—101no—
531C3×D4—102no—
532C3×D4—102no—
533C3×D4C2×C22⋊D512yes—
534C2×C3×C4—21no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—108no—
538C2×C3×C4—101no—
539C2×C3×C4—102no—
540C2×C3×C4—102no—
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4D4×D511yescharacteristic
543C2×C3×C4D4×D511yescharacteristic
544C2×C3×C4C2×C22⋊D511yescharacteristic
545C2×C3×C4C2×C22⋊D511yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—41no—
548#67—41no—
549#67—404no—
550C2×Dic3—21no—
551C2×Dic3—102no—
552D12—21no—
553D12—21no—
554C4×D3—41no—
555C4×D3—41no—
556Dic6—21no—
557Dic6—21no—
558C3⋊C8—22no—
559C3⋊C8—102no—
560C22×C5—22no—
561C22×C5—41no—
562C22×C5—42no—
563C22×C5—122no—
564C22×C5—121no—
565C22×C5#95311yescharacteristic
566C22×C5#95311yescharacteristic
567C22×C5C22×#6711yescharacteristic
568C2×D5—24no—
569C2×D5—22no—
570C2×D5—44no—
571C2×D5—42no—
572C2×D5—44no—
573C2×D5—82no—
574C2×D5—88no—
575C4×C5—22no—
576C4×C5—121no—
577C4×C5#95311yescharacteristic
578C4×C5#95311yescharacteristic
579C4×C5C22×#6711yescharacteristic
580C4×C5C22×#6711yescharacteristic
581Dic5—22no—
582Dic5—122no—
583C24—52no—
584C24—102no—
585#41—21no—
586#41—21no—
587#41—52no—
588#41—52no—
589#41—61no—
590#41—61no—
591#41—61no—
592#41—61no—
593#41—104no—
594#41—104no—
595#41—104no—
596#41—104no—
597#41—101no—
598#41—101no—
599#41#120112yescomplemented
600#41C2×D3×D512yes—
601C2×Q8—31no—
602C2×Q8—51no—
603C2×Q8#120111yescharacteristic, complemented
604C2×D4—21no—
605C2×D4—31no—
606C2×D4—51no—
607C2×D4—52no—
608C2×D4—52no—
609C2×D4—61no—
610C2×D4—104no—
611C2×D4—102no—
612C2×D4—104no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—104no—
616C2×D4—102no—
617C2×D4—101no—
618C2×D4—104no—
619C2×D4—101no—
620C2×D4—101no—
621C2×D4—101no—
622C2×D4—101no—
623C2×D4—304no—
624C2×D4#120111yescharacteristic, complemented
625C22×C4—21no—
626C22×C4—61no—
627C22×C4—102no—
628C22×C4—101no—
629C22×C4C2×D3×D511yescharacteristic
630Q16—62no—
631Q16—302no—
632SD16—62no—
633SD16—62no—
634SD16—302no—
635SD16—302no—
636D8—62no—
637D8—302no—
638M16—32no—
639M16—61no—
640M16—152no—
641M16—301no—
642C2×C8—61no—
643C2×C8—301no—
644C4⋊C4—301no—
645C22⋊C4—304no—
646C22⋊C4—301no—
647C42—152no—
648C3×C5#301911yescharacteristic, complemented, Hall
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—102no—
653C22×C3—104no—
654C22×C3—204no—
655C22×C3—204no—
656C22×C3—202no—
657C22×C3—402no—
658C22×C3—408no—
659C22×C3#408311yescharacteristic
660C22×C3#408311yescharacteristic
661C22×C3C2×D4×D511yescharacteristic
662C2×D3—42no—
663C2×D3—41no—
664C3×C4—22no—
665C3×C4—102no—
666C3×C4#408311yescharacteristic
667C3×C4#408311yescharacteristic
668C3×C4C2×D4×D511yescharacteristic
669C3×C4C22×C22⋊D511yescharacteristic
670Dic3—41no—
671Dic3—202no—
672C2×C5—21no—
673C2×C5—21no—
674C2×C5—21no—
675C2×C5—42no—
676C2×C5—241no—
677C2×C5C2×#95311yescharacteristic
678D5—44no—
679D5—42no—
680C23—21no—
681C23—54no—
682C23—61no—
683C23—108no—
684C23—101no—
685C23—102no—
686C23—102no—
687C23—402no—
688C23—404no—
689C23D5×#6711yescharacteristic
690Q8—21no—
691Q8—52no—
692Q8—61no—
693Q8—61no—
694Q8—101no—
695Q8C2×#120112yes—
696D4—22no—
697D4—22no—
698D4—21no—
699D4—52no—
700D4—61no—
701D4—61no—
702D4—108no—
703D4—108no—
704D4—102no—
705D4—102no—
706D4—102no—
707D4—102no—
708D4—101no—
709D4—102no—
710D4—102no—
711D4—121no—
712D4—121no—
713D4—1204no—
714D4C2×#120112yes—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—61no—
719C2×C4—108no—
720C2×C4—101no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—302no—
726C2×C4C2×#120111yescharacteristic
727C2×C4C2×#120111yescharacteristic
728C2×C4D5×#6711yescharacteristic
729C2×C4D5×#6711yescharacteristic
730C2×C4D5×#6711yescharacteristic
731C2×C4C22×D3×D511yescharacteristic
732C8—62no—
733C8—302no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—204no—
739C2×C3—202no—
740C2×C3C2×#408311yescharacteristic
741D3—81no—
742C5#8410411yescharacteristic, complemented, Sylow
743C22—22no—
744C22—41no—
745C22—42no—
746C22—102no—
747C22—104no—
748C22—122no—
749C22—121no—
750C22—204no—
751C22—204no—
752C22—202no—
753C22—402no—
754C22—408no—
755C22#9156311yescharacteristic
756C22#9156311yescharacteristic
757C22C2×D5×#6711yescharacteristic
758C4—22no—
759C4—102no—
760C4—121no—
761C4—602no—
762C4#9156311yescharacteristic
763C4#9156311yescharacteristic
764C4C22×#120111yescharacteristic
765C4C2×D5×#6711yescharacteristic
766C3#1061573611yescharacteristic, complemented, Sylow
767C2—21no—
768C2—21no—
769C2—21no—
770C2—42no—
771C2—204no—
772C2—202no—
773C2—241no—
774C2C2×#9156311yescharacteristic
subgroupG/H
centerC2C2×#91563
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3019
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4149C2semidirect
2. C5×#5822C2semidirect
3. #11754600C2semidirect
4. #11754138C2semidirect
5. #11751337C2semidirect
6. #11749417C2semidirect
7. #11749415C2semidirect
8. #11748420C2semidirect
9. C2×#90958C2semidirect
12. C2×C5×#235C22semidirect
24. #91815C22semidirect
25. C2×#6710C22semidirect
26. C5×#951C22semidirect
28. C5×#949C22semidirect
31. C2×C5×#208C22semidirect
33. #91463C22semidirect
35. #91368C22semidirect
37. #91307C22semidirect
38. #91299C22semidirect
41. #91121C22semidirect
42. #90976C22semidirect
43. #90958C22semidirect
45. C2×#4149D3semidirect
58. C3×C5×#41D4semidirect
60. C2×C3×C5×Q8D4semidirect
62. C2×C3×C5×D4D4semidirect
70. C2×C5×D12C23semidirect
72. C2×C5×Dic6C23semidirect
85. C3×#709D4semidirect
95. C2×C3×D20D4semidirect
99. C2×C3×Dic10D4semidirect
103. C4×Dic15C23semidirect
105. #6710C23semidirect
112. C5×#208C23semidirect
121. #5822D5semidirect
228. C2×#235C2×D5semidirect
231. #951C2×D5semidirect
235. #949C2×D5semidirect
245. C2×#208C2×D5semidirect
257. C5×#41#67semidirect
260. C2×C5×Q8#67semidirect
264. C2×C5×D4#67semidirect
281. #709#67semidirect
291. C2×D20#67semidirect
295. C2×Dic10#67semidirect
358. C3×#41C22⋊D5semidirect
361. C2×C3×Q8C22⋊D5semidirect
379. C2×C3×D4C22⋊D5semidirect
390. C2×D12C22×D5semidirect
392. C2×Dic6C22×D5semidirect
408. #208C22×D5semidirect
599. #41#1201semidirect
603. C2×Q8#1201semidirect
624. C2×D4#1201semidirect
648. C3×C5#3019semidirect
742. C5#84104semidirect
766. C3#10615736semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41492
C5×#58222
#117546002
#117541382
#117513372
#117494172
#117494152
#117484202
C2×#909582
#106157363
#841045