Finite Group Databasebeta

← C3×D5×#462 #14426062

Subgroups — C3×D5×#462 #14426062

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×Q16C212yesmaximal
2C3×D5×C4⋊Q8C211yesmaximal, characteristic
3C3×C4×Q8×D5C211yesmaximal, characteristic
4C3×C5×#462C211yesmaximal, characteristic, complemented
5C3×#65471C212yesmaximal, complemented
6C3×#65379C211yesmaximal, characteristic, complemented
7C3×#65320C211yesmaximal, characteristic, complemented
8C3×#65138C211yesmaximal, characteristic, complemented
9C3×D5×C4⋊C8C211yesmaximal, characteristic
10C3×D5×#103C212yesmaximal
11C3×#65082C212yesmaximal, complemented
12D5×#462C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×Q8×D5C2212yes—
14C2×C3×Q8×D5C2211yescharacteristic
15C2×C3×C5×Q16C2212yes—
16C3×C5×C4⋊Q8C2211yescharacteristic
17C3×C4×C5×Q8C2211yescharacteristic
18C3×Q8×Dic5C2211yescharacteristic
19C3×#4090C2212yes—
20C2×C3×#689C2212yes—
21C2×C3×#689C2212yes—
22C3×D5×Q16—28no—
23C2×C3×Dic20C2212yes—
24C2×C3×C8×D5C2212yes—
25C3×D5×C4⋊C4—21no—
26C3×D5×C4⋊C4—21no—
27C3×D5×C4⋊C4—21no—
28C3×D5×C4⋊C4C2211yescharacteristic
29C3×#4034—21no—
30C3×#4034—21no—
31C3×#4033—21no—
32C3×#4033C2211yescharacteristic
33C3×C42×D5—21no—
34C3×C42×D5C2211yescharacteristic
35C3×#4015C2211yescharacteristic
36C3×C4×Dic10—21no—
37C3×C4×Dic10C2211yescharacteristic
38C3×C5×C4⋊C8C2211yescharacteristic
39C3×C5×#103C2212yes—
40C3×#3967C2212yes—
41C3×#3948C2212yes—
42C3×#3946C2212yes—
43C3×#3942C2212yes—
44C3×C4⋊#168C2211yescharacteristic
45C2×C3×#462—51nomaximal, Hall
46C2×D5×Q16C2×C312yes—
47D5×C4⋊Q8C2×C311yescharacteristic
48C4×Q8×D5C2×C311yescharacteristic
49C5×#462C2×C311yescharacteristic, complemented
50#65471C2×C312yescomplemented
51#65379C2×C311yescharacteristic, complemented
52#65320C2×C311yescharacteristic, complemented
53#65138C2×C311yescharacteristic, complemented
54D5×C4⋊C8C2×C311yescharacteristic
55D5×#103C2×C312yes—
56#65082C2×C312yescomplemented
57C2×C3×C5×Q8C2312yes—
58C2×C3×C5×Q8C2311yescharacteristic
59C3×Q8×D5—22no—
60C3×Q8×D5—24no—
61C3×Q8×D5—24no—
62C3×Q8×D5D414yes—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5D411yescharacteristic
67C2×C3×C4×D5D411yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×Dic10—21no—
70C2×C3×Dic10—22no—
71C2×C3×Dic10C2312yes—
72C2×C3×Dic10C2311yescharacteristic
73C3×C5×Q16—24no—
74C2×C3×C5×C8C2312yes—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2311yescharacteristic
79C3×C42×C5—21no—
80C3×C42×C5C2311yescharacteristic
81C3×#689—24no—
82C3×#689—24no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C3×#683—21no—
88C3×#683—22no—
89C3×#683—22no—
90C3×#683—21no—
91C3×#683—21no—
92C3×C4×Dic5—21no—
93C3×C4×Dic5—21no—
94C3×C4×Dic5—21no—
95C3×C4×Dic5D411yescharacteristic
96C3×C4×Dic5D411yescharacteristic
97C3×C4×Dic5C2311yescharacteristic
98C2×C3×#168C2312yes—
99C3×Dic20—24no—
100C3×C8×D5—24no—
101C22×C3×Q16—52no—
102C2×C3×C4⋊Q8—51no—
103C2×C3×C4×Q8—51no—
104C3×#462—52no—
105C3×#462—51no—
106C3×#462—51no—
107C3×#462—51no—
108C3×#462—52no—
109C3×#462D511yescharacteristic, direct product factor
110C2×C3×C4⋊C8—51no—
111C2×C3×#103—52no—
112C2×Q8×D5C22×C312yes—
113C2×Q8×D5C22×C311yescharacteristic
114C2×C5×Q16C22×C312yes—
115C5×C4⋊Q8C22×C311yescharacteristic
116C4×C5×Q8C22×C311yescharacteristic
117Q8×Dic5C22×C311yescharacteristic
118#4090C22×C312yes—
119C2×#689C22×C312yes—
120C2×#689C22×C312yes—
121D5×Q16—28no—
122C2×Dic20C22×C312yes—
123C2×C8×D5C22×C312yes—
124D5×C4⋊C4—21no—
125D5×C4⋊C4—21no—
126D5×C4⋊C4—21no—
127D5×C4⋊C4C22×C311yescharacteristic
128#4034—21no—
129#4034—21no—
130#4033—21no—
131#4033C22×C311yescharacteristic
132C42×D5—21no—
133C42×D5C22×C311yescharacteristic
134#4015C22×C311yescharacteristic
135C4×Dic10—21no—
136C4×Dic10C22×C311yescharacteristic
137C5×C4⋊C8C22×C311yescharacteristic
138C5×#103C22×C312yes—
139#3967C22×C312yes—
140#3948C22×C312yes—
141#3946C22×C312yes—
142#3942C22×C312yes—
143C4⋊#168C22×C311yescharacteristic
144C2×#462—51noSylow
145C22×C3×D5C2×D411yescharacteristic
146C3×C5×Q8—21no—
147C3×C5×Q8—22no—
148C3×C5×Q8—22no—
149C3×C5×Q8C2×D412yes—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2411yescharacteristic
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161C2×C3×Dic5C2×D411yescharacteristic
162C3×C4×D5—24no—
163C3×C4×D5—22no—
164C3×C4×D5—44no—
165C3×C4×D5—42no—
166C3×C4×D5Q1614yescomplemented
167C3×C4×D5C2×D412yes—
168C3×C4×D5#4112yes—
169C3×Dic10—21no—
170C3×Dic10—24no—
171C3×Dic10—22no—
172C3×Dic10—22no—
173C3×Dic10—44no—
174C3×Dic10C2×D412yes—
175C3×C5×C8—22no—
176C3×#168—22no—
177C22×C3×Q8—51no—
178C22×C3×Q8—52no—
179C2×C3×Q16—52no—
180C2×C3×Q16—52no—
181C2×C3×Q16—52no—
182C2×C3×Q16—108no—
183C2×C3×Q16C2×D512yes—
184C22×C3×C8—52no—
185C3×C4⋊Q8—52no—
186C3×C4⋊Q8—51no—
187C3×C4⋊Q8—101no—
188C3×C4⋊Q8—101no—
189C3×C4⋊Q8C2×D511yescharacteristic
190C3×C4×Q8—51no—
191C3×C4×Q8—51no—
192C3×C4×Q8—51no—
193C3×C4×Q8—101no—
194C3×C4×Q8—101no—
195C3×C4×Q8C2×D511yescharacteristic
196C2×C3×C4⋊C4—51no—
197C2×C3×C4⋊C4—101no—
198C2×C3×C4⋊C4—101no—
199C2×C3×C4⋊C4—101no—
200C2×C3×C42—51no—
201C2×C3×C42—101no—
202C3×C4⋊C8—52no—
203C3×C4⋊C8—51no—
204C3×C4⋊C8C2×D511yescharacteristic
205C3×#103—52no—
206C3×#103—52no—
207C3×#103—52no—
208C3×#103C2×D512yes—
209C2×C5×Q8C23×C312yes—
210C2×C5×Q8C23×C311yescharacteristic
211Q8×D5—22no—
212Q8×D5—24no—
213Q8×D5—24no—
214Q8×D5C3×D414yes—
215C2×C4×D5—21no—
216C2×C4×D5—22no—
217C2×C4×D5—21no—
218C2×C4×D5C3×D411yescharacteristic
219C2×C4×D5C3×D411yescharacteristic
220C2×C4×D5C23×C311yescharacteristic
221C2×Dic10—21no—
222C2×Dic10—22no—
223C2×Dic10C23×C312yes—
224C2×Dic10C23×C311yescharacteristic
225C5×Q16—24no—
226C2×C5×C8C23×C312yes—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4C23×C311yescharacteristic
231C42×C5—21no—
232C42×C5C23×C311yescharacteristic
233#689—24no—
234#689—24no—
235C4⋊Dic5—21no—
236C4⋊Dic5—21no—
237C4⋊Dic5—21no—
238C4⋊Dic5C23×C311yescharacteristic
239#683—21no—
240#683—21no—
241#683—21no—
242#683—22no—
243#683—22no—
244C4×Dic5—21no—
245C4×Dic5—21no—
246C4×Dic5—21no—
247C4×Dic5C3×D411yescharacteristic
248C4×Dic5C3×D411yescharacteristic
249C4×Dic5C23×C311yescharacteristic
250C2×#168C23×C312yes—
251Dic20—24no—
252C8×D5—24no—
253C22×Q16—52no—
254C2×C4⋊Q8—51no—
255C2×C4×Q8—51no—
256#462—52no—
257#462—51no—
258#462—51no—
259#462—51no—
260#462—52no—
261#462C3×D511yescharacteristic, direct product factor
262C2×C4⋊C8—51no—
263C2×#103—52no—
264C22×C3×C5C22×D411yescharacteristic
265C2×C3×D5#12112yes—
266C2×C3×D5C2×Q1612yes—
267C2×C3×D5#13712yes—
268C3×C4×C5—22no—
269C3×C4×C5—21no—
270C3×C4×C5—42no—
271C3×C4×C5—41no—
272C3×C4×C5C2×Q1612yescomplemented
273C3×C4×C5C22×D411yescharacteristic
274C3×C4×C5C2×#4111yescharacteristic
275C3×Dic5—22no—
276C3×Dic5—21no—
277C3×Dic5—42no—
278C3×Dic5—41no—
279C3×Dic5#12112yes—
280C3×Dic5C2×Q1612yescomplemented
281C2×C3×Q8—54no—
282C2×C3×Q8—51no—
283C2×C3×Q8—52no—
284C2×C3×Q8—101no—
285C2×C3×Q8—102no—
286C2×C3×Q8—102no—
287C2×C3×Q8—104no—
288C2×C3×Q8—104no—
289C2×C3×Q8C22×D512yes—
290C2×C3×Q8C22×D511yescharacteristic
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—101no—
295C22×C3×C4—101no—
296C22×C3×C4—102no—
297C3×Q16—24no—
298C3×Q16—104no—
299C3×Q16—104no—
300C3×Q16—104no—
301C2×C3×C8—52no—
302C2×C3×C8—104no—
303C2×C3×C8C22×D512yes—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—51no—
308C3×C4⋊C4—101no—
309C3×C4⋊C4—101no—
310C3×C4⋊C4—102no—
311C3×C4⋊C4—102no—
312C3×C4⋊C4—101no—
313C3×C4⋊C4—101no—
314C3×C4⋊C4—101no—
315C3×C4⋊C4—101no—
316C3×C4⋊C4C22×D511yescharacteristic
317C3×C42—21no—
318C3×C42—51no—
319C3×C42—51no—
320C3×C42—51no—
321C3×C42—101no—
322C3×C42—101no—
323C3×C42—101no—
324C3×C42C22×D511yescharacteristic
325C22×D5C2×C3×D411yescharacteristic
326C5×Q8—21no—
327C5×Q8—22no—
328C5×Q8—22no—
329C5×Q8C2×C3×D412yes—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5C2×C3×D411yescharacteristic
334C2×C4×C5C2×C3×D411yescharacteristic
335C2×C4×C5C24×C311yescharacteristic
336C2×Dic5—21no—
337C2×Dic5—21no—
338C2×Dic5—22no—
339C2×Dic5C2×C3×D411yescharacteristic
340C2×Dic5C2×C3×D411yescharacteristic
341C2×Dic5C2×C3×D411yescharacteristic
342C4×D5—24no—
343C4×D5—22no—
344C4×D5—44no—
345C4×D5—42no—
346C4×D5C3×Q1614yescomplemented
347C4×D5C2×C3×D412yes—
348C4×D5C3×#4112yes—
349Dic10—21no—
350Dic10—24no—
351Dic10—22no—
352Dic10—22no—
353Dic10—44no—
354Dic10C2×C3×D412yes—
355C5×C8—22no—
356#168—22no—
357C22×Q8—51no—
358C22×Q8—52no—
359C2×Q16—52no—
360C2×Q16—52no—
361C2×Q16—52no—
362C2×Q16—108no—
363C2×Q16C2×C3×D512yes—
364C22×C8—52no—
365C4⋊Q8—52no—
366C4⋊Q8—51no—
367C4⋊Q8—101no—
368C4⋊Q8—101no—
369C4⋊Q8C2×C3×D511yescharacteristic
370C4×Q8—51no—
371C4×Q8—51no—
372C4×Q8—51no—
373C4×Q8—101no—
374C4×Q8—101no—
375C4×Q8C2×C3×D511yescharacteristic
376C2×C4⋊C4—51no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4—101no—
380C2×C42—51no—
381C2×C42—101no—
382C4⋊C8—52no—
383C4⋊C8—51no—
384C4⋊C8C2×C3×D511yescharacteristic
385#103—52no—
386#103—52no—
387#103—52no—
388#103C2×C3×D512yes—
389C2×C3×C5C2×#12111yescharacteristic
390C2×C3×C5C22×Q1611yescharacteristic
391C2×C3×C5C2×#13711yescharacteristic
392C3×D5#46214yesdirect product factor
393C23×C3—51no—
394C3×Q8—21no—
395C3×Q8—22no—
396C3×Q8—22no—
397C3×Q8—52no—
398C3×Q8—104no—
399C3×Q8—101no—
400C3×Q8—102no—
401C3×Q8—102no—
402C3×Q8—204no—
403C3×Q8D4×D512yes—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—51no—
408C2×C3×C4—51no—
409C2×C3×C4—52no—
410C2×C3×C4—52no—
411C2×C3×C4—54no—
412C2×C3×C4—51no—
413C2×C3×C4—102no—
414C2×C3×C4—104no—
415C2×C3×C4—101no—
416C2×C3×C4—101no—
417C2×C3×C4—102no—
418C2×C3×C4—202no—
419C2×C3×C4—204no—
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4D4×D511yescharacteristic
422C2×C3×C4C23×D511yescharacteristic
423C3×C8—22no—
424C3×C8—102no—
425C22×C5C22×C3×D411yescharacteristic
426C2×D5C3×#12112yes—
427C2×D5C2×C3×Q1612yes—
428C2×D5C3×#13712yes—
429C4×C5—21no—
430C4×C5—22no—
431C4×C5—41no—
432C4×C5—42no—
433C4×C5C2×C3×Q1612yescomplemented
434C4×C5C22×C3×D411yescharacteristic
435C4×C5C2×C3×#4111yescharacteristic
436Dic5—21no—
437Dic5—22no—
438Dic5—41no—
439Dic5—42no—
440Dic5C3×#12112yes—
441Dic5C2×C3×Q1612yescomplemented
442C2×Q8—54no—
443C2×Q8—51no—
444C2×Q8—52no—
445C2×Q8—101no—
446C2×Q8—102no—
447C2×Q8—102no—
448C2×Q8—104no—
449C2×Q8—104no—
450C2×Q8C22×C3×D512yes—
451C2×Q8C22×C3×D511yescharacteristic
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—102no—
458Q16—24no—
459Q16—104no—
460Q16—104no—
461Q16—104no—
462C2×C8—52no—
463C2×C8—104no—
464C2×C8C22×C3×D512yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—51no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—102no—
473C4⋊C4—102no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4C22×C3×D511yescharacteristic
478C42—21no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—101no—
483C42—101no—
484C42—101no—
485C42C22×C3×D511yescharacteristic
486C3×C5C2×#46211yescharacteristic, complemented, Hall
487C22×C3—52no—
488C22×C3—52no—
489C22×C3—52no—
490C22×C3C2×D4×D511yescharacteristic
491C3×C4—21no—
492C3×C4—22no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—52no—
496C3×C4—52no—
497C3×C4—101no—
498C3×C4—102no—
499C3×C4—201no—
500C3×C4—202no—
501C3×C4D5×Q1612yescomplemented
502C3×C4C2×D4×D511yescharacteristic
503C3×C4D5×#4111yescharacteristic
504C2×C5C2×C3×#12111yescharacteristic
505C2×C5C22×C3×Q1611yescharacteristic
506C2×C5C2×C3×#13711yescharacteristic
507D5C3×#46214yesdirect product factor
508C23—51no—
509Q8—21no—
510Q8—22no—
511Q8—22no—
512Q8—52no—
513Q8—104no—
514Q8—101no—
515Q8—102no—
516Q8—102no—
517Q8—204no—
518Q8C3×D4×D512yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—51no—
523C2×C4—51no—
524C2×C4—52no—
525C2×C4—52no—
526C2×C4—54no—
527C2×C4—51no—
528C2×C4—102no—
529C2×C4—104no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—102no—
533C2×C4—204no—
534C2×C4—202no—
535C2×C4C3×D4×D511yescharacteristic
536C2×C4C3×D4×D511yescharacteristic
537C2×C4C23×C3×D511yescharacteristic
538C8—22no—
539C8—102no—
540C2×C3—54no—
541C2×C3D5×#12111yescharacteristic
542C2×C3C2×D5×Q1611yescharacteristic
543C2×C3D5×#13711yescharacteristic
544C5C2×C3×#46211yescharacteristic, complemented, Sylow
545C22—52no—
546C22—52no—
547C22—52no—
548C22C2×C3×D4×D511yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—42no—
553C4—52no—
554C4—52no—
555C4—101no—
556C4—102no—
557C4—201no—
558C4—202no—
559C4C3×D5×Q1612yescomplemented
560C4C2×C3×D4×D511yescharacteristic
561C4C3×D5×#4111yescharacteristic
562C3D5×#46211yescharacteristic, direct product factor, Sylow
563C2—54no—
564C2C3×D5×#12111yescharacteristic
565C2C2×C3×D5×Q1611yescharacteristic
566C2C3×D5×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#462C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC3×#462D5
hypocenterC5C2×C3×#462
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
4. C3×C5×#462C2semidirect
5. C3×#65471C2semidirect
6. C3×#65379C2semidirect
7. C3×#65320C2semidirect
8. C3×#65138C2semidirect
11. C3×#65082C2semidirect
12. D5×#462C3direct (N × H)
49. C5×#462C2×C3semidirect
50. #65471C2×C3semidirect
51. #65379C2×C3semidirect
52. #65320C2×C3semidirect
53. #65138C2×C3semidirect
56. #65082C2×C3semidirect
109. C3×#462D5direct (N × H)
166. C3×C4×D5Q16semidirect
261. #462C3×D5direct (N × H)
272. C3×C4×C5C2×Q16semidirect
280. C3×Dic5C2×Q16semidirect
346. C4×D5C3×Q16semidirect
392. C3×D5#462direct (N × H)
433. C4×C5C2×C3×Q16semidirect
441. Dic5C2×C3×Q16semidirect
486. C3×C5C2×#462semidirect
501. C3×C4D5×Q16semidirect
507. D5C3×#462direct (N × H)
544. C5C2×C3×#462semidirect
559. C4C3×D5×Q16semidirect
562. C3D5×#462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
C3×D5×C4⋊Q82
C3×C4×Q8×D52
C3×C5×#4622
C3×#654712
C3×#653792
C3×#653202
C3×#651382
C3×D5×C4⋊C82
C3×D5×#1032
C3×#650822
D5×#4623
C2×C3×#4625