Finite Group Databasebeta

← C2×C3×#65114 #14425024

Subgroups — C2×C3×#65114 #14425024

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3C2×C3×#4055C211yesmaximal, characteristic, complemented
4C2×C3×#4021C211yesmaximal, characteristic, complemented
5C2×C3×C5×#104C211yesmaximal, characteristic, complemented
6C2×C3×#3955C211yesmaximal, characteristic, complemented
7C2×C3×#3937C211yesmaximal, characteristic, complemented
8C3×#65114C218yesmaximal, direct product factor
9C2×#65114C311yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C3×#4149—22no—
12C3×#4149—22no—
13C3×#4149—22no—
14C3×#4149C2214yes—
15C2×C3×#713—21no—
16C2×C3×D4×D5—22no—
17C2×C3×D4×D5—21no—
18C2×C3×#709—21no—
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20—21no—
21C22×C3×D20C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic, complemented
23C2×C3×C5×M16C2211yescharacteristic, complemented
24C2×C3×C42×C5C2211yescharacteristic, complemented
25C3×#4097—22no—
26C3×#4097C2214yescomplemented
27C2×C3×#689—21no—
28C2×C3×#687—21no—
29C2×C3×#685—22no—
30C2×C3×#681C2211yescharacteristic, complemented
31C3×#4055—22no—
32C3×#4055C2214yescomplemented
33C2×C3×Dic20—21no—
34C2×C3×#677—21no—
35C3×#4021—22no—
36C3×#4021C2214yescomplemented
37C3×C5×#104C2214yescomplemented
38C3×#3955C2214yescomplemented
39C3×#3937C2214yescomplemented
40C2×C3×#455—51nomaximal, Hall
41C2×#4149C2×C311yescharacteristic
42C2×#4097C2×C311yescharacteristic, complemented
43C2×#4055C2×C311yescharacteristic, complemented
44C2×#4021C2×C311yescharacteristic, complemented
45C2×C5×#104C2×C311yescharacteristic, complemented
46C2×#3955C2×C311yescharacteristic, complemented
47C2×#3937C2×C311yescharacteristic, complemented
48#65114C2×C318yesdirect product factor
49C23×C3×D5—22no—
50C23×C3×D5D412yes—
51C3×C5×#41—21no—
52C3×C5×#41—21no—
53C3×C5×#41D412yes—
54C3×C5×#41C2312yes—
55C2×C3×C5×Q8D411yescharacteristic
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4D411yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5—21no—
63C22×C3×Dic5—21no—
64C3×#713—24no—
65C3×#713—24no—
66C3×D4×D5—28no—
67C3×D4×D5—24no—
68C3×D4×D5—28no—
69C3×D4×D5—24no—
70C3×#709—24no—
71C3×#709—21no—
72C3×#709—21no—
73C3×#709—24no—
74C3×#709D412yes—
75C3×#709C2312yes—
76C2×C3×D20—22no—
77C2×C3×D20—24no—
78C2×C3×D20—21no—
79C2×C3×D20—21no—
80C2×C3×D20—21no—
81C2×C3×D20—21no—
82C2×C3×D20—24no—
83C2×C3×D20D412yes—
84C2×C3×D20D411yescharacteristic
85C2×C3×D20C2312yes—
86C2×C3×C4×D5—22no—
87C2×C3×C4×D5—21no—
88C2×C3×Dic10—21no—
89C2×C3×Dic10—21no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10—21no—
92C2×C3×Dic10—21no—
93C2×C3×Dic10D411yescharacteristic
94C2×C3×Dic10C2312yescomplemented
95C3×C5×M16—21no—
96C3×C5×M16C2312yescomplemented
97C2×C3×C5×C8—21no—
98C3×C42×C5—21no—
99C3×C42×C5C2312yescomplemented
100C3×#689—24no—
101C3×#687—24no—
102C3×#685—28no—
103C3×#681—21no—
104C3×#681C2312yescomplemented
105C2×C3×#168—21no—
106C3×Dic20—24no—
107C3×#677—24no—
108C2×C3×H(5,𝔽2)—51no—
109C2×C3×#137—51no—
110C2×C3×#137—51no—
111C2×C3×#124—51no—
112C3×#455—58no—
113C2×C3×#104—51no—
114C2×C3×#104D511yescharacteristic, complemented
115C2×C3×#100—51no—
116C2×C5×#41C22×C311yescharacteristic
117#4149—22no—
118#4149—22no—
119#4149—22no—
120#4149C22×C314yes—
121C2×#713—21no—
122C2×D4×D5—22no—
123C2×D4×D5—21no—
124C2×#709—21no—
125C2×#709C22×C311yescharacteristic
126C22×D20—21no—
127C22×D20C22×C311yescharacteristic
128C22×Dic10C22×C311yescharacteristic, complemented
129C2×C5×M16C22×C311yescharacteristic, complemented
130C2×C42×C5C22×C311yescharacteristic, complemented
131#4097—22no—
132#4097C22×C314yescomplemented
133C2×#689—21no—
134C2×#687—21no—
135C2×#685—22no—
136C2×#681C22×C311yescharacteristic, complemented
137#4055—22no—
138#4055C22×C314yescomplemented
139C2×Dic20—21no—
140C2×#677—21no—
141#4021—22no—
142#4021C22×C314yescomplemented
143C5×#104C22×C314yescomplemented
144#3955C22×C314yescomplemented
145#3937C22×C314yescomplemented
146C2×#455—51noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×C3×D5—22no—
150C22×C3×D5—21no—
151C22×C3×D5—28no—
152C22×C3×D5—22no—
153C22×C3×D5—44no—
154C22×C3×D5—84no—
155C22×C3×D5C2×D414yes—
156C3×C5×Q8—21no—
157C3×C5×Q8C2×D412yes—
158C3×C5×D4—22no—
159C3×C5×D4—22no—
160C3×C5×D4—21no—
161C3×C5×D4C2×D412yes—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—42no—
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2×D411yescharacteristic
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2×D411yescharacteristic
171C2×C3×C4×C5C2×D411yescharacteristic
172C2×C3×C4×C5C2411yescharacteristic
173C3×C22⋊D5—28no—
174C3×C22⋊D5—22no—
175C3×C22⋊D5—22no—
176C2×C3×Dic5—21no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—41no—
179C2×C3×Dic5—41no—
180C3×D20—28no—
181C3×D20—22no—
182C3×D20—21no—
183C3×D20—22no—
184C3×D20—22no—
185C3×D20—22no—
186C3×D20C2×D412yes—
187C3×C4×D5—28no—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×Dic10—21no—
191C3×Dic10—22no—
192C3×Dic10—22no—
193C3×Dic10—41no—
194C3×Dic10—41no—
195C3×Dic10C2×D412yes—
196C3×C5×C8—22no—
197C3×#168—22no—
198C3×H(5,𝔽2)—54no—
199C3×H(5,𝔽2)—102no—
200C3×H(5,𝔽2)—102no—
201C3×H(5,𝔽2)—102no—
202C2×C3×#41—51no—
203C2×C3×#41—101no—
204C2×C3×#41—101no—
205C2×C3×#41C2×D511yescharacteristic
206C22×C3×Q8—51no—
207C22×C3×D4—51no—
208C22×C3×D4—101no—
209C22×C3×D4—102no—
210C22×C3×D4—101no—
211C3×#137—54no—
212C3×#137—54no—
213C3×#137—102no—
214C3×#137—102no—
215C2×C3×Q16—101no—
216C2×C3×Q16—101no—
217C2×C3×SD16—101no—
218C2×C3×SD16—101no—
219C2×C3×M16—51no—
220C2×C3×M16C2×D511yescharacteristic, complemented
221C3×#124—54no—
222C3×#124—102no—
223C2×C3×C22⋊C4—102no—
224C2×C3×C42C2×D511yescharacteristic, complemented
225C3×#104—54no—
226C3×#104C2×D514yescomplemented
227C3×#100—54no—
228C23×D5—22no—
229C23×D5C3×D412yes—
230C5×#41—21no—
231C5×#41—21no—
232C5×#41C3×D412yes—
233C5×#41C23×C312yes—
234C2×C5×Q8C3×D411yescharacteristic
235C2×C5×D4—21no—
236C2×C5×D4C3×D411yescharacteristic
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5C23×C311yescharacteristic
240C2×C22⋊D5—22no—
241C2×C22⋊D5—21no—
242C22×Dic5—21no—
243#713—24no—
244#713—24no—
245D4×D5—28no—
246D4×D5—24no—
247D4×D5—28no—
248D4×D5—24no—
249#709—24no—
250#709—21no—
251#709—21no—
252#709—24no—
253#709C3×D412yes—
254#709C23×C312yes—
255C2×D20—22no—
256C2×D20—24no—
257C2×D20—21no—
258C2×D20—21no—
259C2×D20—21no—
260C2×D20—21no—
261C2×D20—24no—
262C2×D20C3×D412yes—
263C2×D20C3×D411yescharacteristic
264C2×D20C23×C312yes—
265C2×C4×D5—22no—
266C2×C4×D5—21no—
267C2×Dic10—21no—
268C2×Dic10—21no—
269C2×Dic10—21no—
270C2×Dic10—21no—
271C2×Dic10—21no—
272C2×Dic10C3×D411yescharacteristic
273C2×Dic10C23×C312yescomplemented
274C5×M16—21no—
275C5×M16C23×C312yescomplemented
276C2×C5×C8—21no—
277C42×C5—21no—
278C42×C5C23×C312yescomplemented
279#689—24no—
280#687—24no—
281#685—28no—
282#681—21no—
283#681C23×C312yescomplemented
284C2×#168—21no—
285Dic20—24no—
286#677—24no—
287C2×H(5,𝔽2)—51no—
288C2×#137—51no—
289C2×#137—51no—
290C2×#124—51no—
291#455—58no—
292C2×#104—51no—
293C2×#104C3×D511yescharacteristic, complemented
294C2×#100—51no—
295C22×C3×C5—22no—
296C22×C3×C5—22no—
297C22×C3×C5—42no—
298C22×C3×C5#12011yescharacteristic
299C22×C3×C5#12011yescharacteristic
300C22×C3×C5C22×D411yescharacteristic
301C2×C3×D5—24no—
302C2×C3×D5—22no—
303C2×C3×D5—44no—
304C2×C3×D5—42no—
305C2×C3×D5—44no—
306C2×C3×D5—82no—
307C2×C3×D5—88no—
308C3×C4×C5—22no—
309C3×C4×C5—42no—
310C3×C4×C5#12011yescharacteristic
311C3×C4×C5#12011yescharacteristic
312C3×C4×C5C22×D411yescharacteristic
313C3×C4×C5C22×D411yescharacteristic
314C3×Dic5—22no—
315C3×Dic5—42no—
316C24×C3—52no—
317C24×C3—102no—
318C3×#41—21no—
319C3×#41—21no—
320C3×#41—52no—
321C3×#41—52no—
322C3×#41—104no—
323C3×#41—104no—
324C3×#41—104no—
325C3×#41—104no—
326C3×#41—101no—
327C3×#41—101no—
328C3×#41D2012yes—
329C3×#41C22×D512yes—
330C2×C3×Q8—51no—
331C2×C3×Q8—52no—
332C2×C3×Q8—101no—
333C2×C3×Q8—101no—
334C2×C3×Q8—101no—
335C2×C3×Q8—101no—
336C2×C3×Q8—101no—
337C2×C3×Q8D2011yescharacteristic
338C2×C3×D4—21no—
339C2×C3×D4—51no—
340C2×C3×D4—52no—
341C2×C3×D4—52no—
342C2×C3×D4—104no—
343C2×C3×D4—102no—
344C2×C3×D4—104no—
345C2×C3×D4—108no—
346C2×C3×D4—108no—
347C2×C3×D4—104no—
348C2×C3×D4—102no—
349C2×C3×D4—101no—
350C2×C3×D4—104no—
351C2×C3×D4—101no—
352C2×C3×D4—101no—
353C2×C3×D4—101no—
354C2×C3×D4—101no—
355C2×C3×D4D2011yescharacteristic
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—102no—
359C22×C3×C4—101no—
360C22×C3×C4—101no—
361C22×C3×C4C22×D511yescharacteristic
362C3×Q16—104no—
363C3×Q16—104no—
364C3×SD16—104no—
365C3×SD16—104no—
366C3×M16—21no—
367C3×M16—52no—
368C3×M16—101no—
369C3×M16C22×D512yescomplemented
370C2×C3×C8—21no—
371C2×C3×C8—101no—
372C3×C22⋊C4—108no—
373C3×C42—21no—
374C3×C42C22×D512yescomplemented
375C23×C5—21no—
376C23×C5C2×C3×D411yescharacteristic
377C22×D5—22no—
378C22×D5—21no—
379C22×D5—28no—
380C22×D5—22no—
381C22×D5—44no—
382C22×D5—84no—
383C22×D5C2×C3×D414yes—
384C5×Q8—21no—
385C5×Q8C2×C3×D412yes—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—21no—
389C5×D4C2×C3×D412yes—
390C2×C4×C5—21no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—42no—
395C2×C4×C5C2×C3×D411yescharacteristic
396C2×C4×C5C2×C3×D411yescharacteristic
397C2×C4×C5C2×C3×D411yescharacteristic
398C2×C4×C5C2×C3×D411yescharacteristic
399C2×C4×C5C2×C3×D411yescharacteristic
400C2×C4×C5C24×C311yescharacteristic
401C22⋊D5—28no—
402C22⋊D5—22no—
403C22⋊D5—22no—
404C2×Dic5—21no—
405C2×Dic5—22no—
406C2×Dic5—41no—
407C2×Dic5—41no—
408D20—28no—
409D20—22no—
410D20—21no—
411D20—22no—
412D20—22no—
413D20—22no—
414D20C2×C3×D412yes—
415C4×D5—28no—
416C4×D5—22no—
417C4×D5—22no—
418Dic10—21no—
419Dic10—22no—
420Dic10—22no—
421Dic10—41no—
422Dic10—41no—
423Dic10C2×C3×D412yes—
424C5×C8—22no—
425#168—22no—
426H(5,𝔽2)—54no—
427H(5,𝔽2)—102no—
428H(5,𝔽2)—102no—
429H(5,𝔽2)—102no—
430C2×#41—51no—
431C2×#41—101no—
432C2×#41—101no—
433C2×#41C2×C3×D511yescharacteristic
434C22×Q8—51no—
435C22×D4—51no—
436C22×D4—101no—
437C22×D4—102no—
438C22×D4—101no—
439#137—54no—
440#137—54no—
441#137—102no—
442#137—102no—
443C2×Q16—101no—
444C2×Q16—101no—
445C2×SD16—101no—
446C2×SD16—101no—
447C2×M16—51no—
448C2×M16C2×C3×D511yescharacteristic, complemented
449#124—54no—
450#124—102no—
451C2×C22⋊C4—102no—
452C2×C42C2×C3×D511yescharacteristic, complemented
453#104—54no—
454#104C2×C3×D514yescomplemented
455#100—54no—
456C2×C3×C5—21no—
457C2×C3×C5—21no—
458C2×C3×C5—42no—
459C2×C3×C5#45512yescomplemented
460C2×C3×C5C2×#12011yescharacteristic
461C3×D5—44no—
462C3×D5—42no—
463C23×C3—21no—
464C23×C3—54no—
465C23×C3—108no—
466C23×C3—101no—
467C23×C3—102no—
468C23×C3—102no—
469C23×C3—204no—
470C23×C3—404no—
471C23×C3D4×D511yescharacteristic
472C3×Q8—21no—
473C3×Q8—52no—
474C3×Q8—101no—
475C3×Q8—102no—
476C3×Q8—102no—
477C3×Q8—201no—
478C3×Q8—201no—
479C3×Q8C2×D2012yes—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—21no—
483C3×D4—52no—
484C3×D4—108no—
485C3×D4—108no—
486C3×D4—102no—
487C3×D4—102no—
488C3×D4—102no—
489C3×D4—102no—
490C3×D4—101no—
491C3×D4—102no—
492C3×D4—102no—
493C3×D4C2×D2012yes—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—42no—
499C2×C3×C4—108no—
500C2×C3×C4—101no—
501C2×C3×C4—102no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4—201no—
505C2×C3×C4—201no—
506C2×C3×C4C2×D2011yescharacteristic
507C2×C3×C4C2×D2011yescharacteristic
508C2×C3×C4D4×D511yescharacteristic
509C2×C3×C4D4×D511yescharacteristic
510C2×C3×C4D4×D511yescharacteristic
511C2×C3×C4C23×D511yescharacteristic
512C3×C8—22no—
513C3×C8—102no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—42no—
517C22×C5C3×#12011yescharacteristic
518C22×C5C3×#12011yescharacteristic
519C22×C5C22×C3×D411yescharacteristic
520C2×D5—24no—
521C2×D5—22no—
522C2×D5—44no—
523C2×D5—42no—
524C2×D5—44no—
525C2×D5—82no—
526C2×D5—88no—
527C4×C5—22no—
528C4×C5—42no—
529C4×C5C3×#12011yescharacteristic
530C4×C5C3×#12011yescharacteristic
531C4×C5C22×C3×D411yescharacteristic
532C4×C5C22×C3×D411yescharacteristic
533Dic5—22no—
534Dic5—42no—
535C24—52no—
536C24—102no—
537#41—21no—
538#41—21no—
539#41—52no—
540#41—52no—
541#41—104no—
542#41—104no—
543#41—104no—
544#41—104no—
545#41—101no—
546#41—101no—
547#41C3×D2012yes—
548#41C22×C3×D512yes—
549C2×Q8—51no—
550C2×Q8—52no—
551C2×Q8—101no—
552C2×Q8—101no—
553C2×Q8—101no—
554C2×Q8—101no—
555C2×Q8—101no—
556C2×Q8C3×D2011yescharacteristic
557C2×D4—21no—
558C2×D4—51no—
559C2×D4—52no—
560C2×D4—52no—
561C2×D4—104no—
562C2×D4—102no—
563C2×D4—104no—
564C2×D4—108no—
565C2×D4—108no—
566C2×D4—104no—
567C2×D4—102no—
568C2×D4—101no—
569C2×D4—104no—
570C2×D4—101no—
571C2×D4—101no—
572C2×D4—101no—
573C2×D4—101no—
574C2×D4C3×D2011yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—102no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4C22×C3×D511yescharacteristic
581Q16—104no—
582Q16—104no—
583SD16—104no—
584SD16—104no—
585M16—21no—
586M16—52no—
587M16—101no—
588M16C22×C3×D512yescomplemented
589C2×C8—21no—
590C2×C8—101no—
591C22⋊C4—108no—
592C42—21no—
593C42C22×C3×D512yescomplemented
594C3×C5C2×#45511yescharacteristic, complemented, Hall
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—42no—
598C22×C3—102no—
599C22×C3—104no—
600C22×C3—204no—
601C22×C3—204no—
602C22×C3—202no—
603C22×C3—402no—
604C22×C3—408no—
605C22×C3#402811yescharacteristic
606C22×C3#402811yescharacteristic
607C22×C3C2×D4×D511yescharacteristic
608C3×C4—22no—
609C3×C4—42no—
610C3×C4—102no—
611C3×C4—202no—
612C3×C4#402811yescharacteristic
613C3×C4#402811yescharacteristic
614C3×C4C22×D2011yescharacteristic
615C3×C4C2×D4×D511yescharacteristic
616C2×C5—21no—
617C2×C5—21no—
618C2×C5—42no—
619C2×C5C3×#45512yescomplemented
620C2×C5C2×C3×#12011yescharacteristic
621D5—44no—
622D5—42no—
623C23—21no—
624C23—54no—
625C23—108no—
626C23—101no—
627C23—102no—
628C23—102no—
629C23—204no—
630C23—404no—
631C23C3×D4×D511yescharacteristic
632Q8—21no—
633Q8—52no—
634Q8—101no—
635Q8—102no—
636Q8—102no—
637Q8—201no—
638Q8—201no—
639Q8C2×C3×D2012yes—
640D4—22no—
641D4—22no—
642D4—21no—
643D4—52no—
644D4—108no—
645D4—108no—
646D4—102no—
647D4—102no—
648D4—102no—
649D4—102no—
650D4—101no—
651D4—102no—
652D4—102no—
653D4C2×C3×D2012yes—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—108no—
660C2×C4—101no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—201no—
665C2×C4—201no—
666C2×C4C2×C3×D2011yescharacteristic
667C2×C4C2×C3×D2011yescharacteristic
668C2×C4C3×D4×D511yescharacteristic
669C2×C4C3×D4×D511yescharacteristic
670C2×C4C3×D4×D511yescharacteristic
671C2×C4C23×C3×D511yescharacteristic
672C8—22no—
673C8—102no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—42no—
677C2×C3—204no—
678C2×C3—202no—
679C2×C3#6511412yesdirect product factor
680C2×C3C2×#402811yescharacteristic
681C5C2×C3×#45511yescharacteristic, complemented, Sylow
682C22—22no—
683C22—22no—
684C22—42no—
685C22—102no—
686C22—104no—
687C22—204no—
688C22—204no—
689C22—202no—
690C22—402no—
691C22—408no—
692C22C3×#402811yescharacteristic
693C22C3×#402811yescharacteristic
694C22C2×C3×D4×D511yescharacteristic
695C4—22no—
696C4—42no—
697C4—102no—
698C4—202no—
699C4C3×#402811yescharacteristic
700C4C3×#402811yescharacteristic
701C4C22×C3×D2011yescharacteristic
702C4C2×C3×D4×D511yescharacteristic
703C3C2×#6511411yescharacteristic, direct product factor, Sylow
704C2—21no—
705C2—21no—
706C2—42no—
707C2—204no—
708C2—202no—
709C2C3×#6511412yesdirect product factor
710C2C2×C3×#402811yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×C3×#4149C2
hypercenterC2×C3×#104D5
hypocenterC5C2×C3×#455
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C2×C3×#4055C2semidirect
4. C2×C3×#4021C2semidirect
5. C2×C3×C5×#104C2semidirect
6. C2×C3×#3955C2semidirect
7. C2×C3×#3937C2semidirect
8. C3×#65114C2direct (N × H)
9. C2×#65114C3direct (N × H)
22. C22×C3×Dic10C22semidirect
23. C2×C3×C5×M16C22semidirect
24. C2×C3×C42×C5C22semidirect
26. C3×#4097C22semidirect
30. C2×C3×#681C22semidirect
32. C3×#4055C22semidirect
36. C3×#4021C22semidirect
37. C3×C5×#104C22semidirect
38. C3×#3955C22semidirect
39. C3×#3937C22semidirect
42. C2×#4097C2×C3semidirect
43. C2×#4055C2×C3semidirect
44. C2×#4021C2×C3semidirect
45. C2×C5×#104C2×C3semidirect
46. C2×#3955C2×C3semidirect
47. C2×#3937C2×C3semidirect
48. #65114C2×C3direct (N × H)
94. C2×C3×Dic10C23semidirect
96. C3×C5×M16C23semidirect
99. C3×C42×C5C23semidirect
104. C3×#681C23semidirect
114. C2×C3×#104D5semidirect
128. C22×Dic10C22×C3semidirect
129. C2×C5×M16C22×C3semidirect
130. C2×C42×C5C22×C3semidirect
132. #4097C22×C3semidirect
136. C2×#681C22×C3semidirect
138. #4055C22×C3semidirect
142. #4021C22×C3semidirect
143. C5×#104C22×C3semidirect
144. #3955C22×C3semidirect
145. #3937C22×C3semidirect
220. C2×C3×M16C2×D5semidirect
224. C2×C3×C42C2×D5semidirect
226. C3×#104C2×D5semidirect
273. C2×Dic10C23×C3semidirect
275. C5×M16C23×C3semidirect
278. C42×C5C23×C3semidirect
283. #681C23×C3semidirect
293. C2×#104C3×D5semidirect
369. C3×M16C22×D5semidirect
374. C3×C42C22×D5semidirect
448. C2×M16C2×C3×D5semidirect
452. C2×C42C2×C3×D5semidirect
454. #104C2×C3×D5semidirect
459. C2×C3×C5#455semidirect
588. M16C22×C3×D5semidirect
593. C42C22×C3×D5semidirect
594. C3×C5C2×#455semidirect
619. C2×C5C3×#455semidirect
679. C2×C3#65114direct (N × H)
681. C5C2×C3×#455semidirect
703. C3C2×#65114direct (N × H)
709. C2C3×#65114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41492
C2×C3×#40972
C2×C3×#40552
C2×C3×#40212
C2×C3×C5×#1042
C2×C3×#39552
C2×C3×#39372
C3×#651142
C2×#651143
C2×C3×#4555