Finite Group Databasebeta

← C3×D5×#470 #14428030

Subgroups — C3×D5×#470 #14428030

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×Q16C211yesmaximal, characteristic, complemented
2C2×C3×D5×M16C211yesmaximal, characteristic
3C3×D5×C22⋊Q8C212yesmaximal
4C3×C5×#470C211yesmaximal, characteristic, complemented
5C3×#65478C211yesmaximal, characteristic, complemented
6C3×#65426C211yesmaximal, characteristic, complemented
7C3×#65341C212yesmaximal, complemented
8C3×#65157C211yesmaximal, characteristic, complemented
9C3×D5×#106C211yesmaximal, characteristic, complemented
10C3×#65105C212yesmaximal, complemented
11C3×D5×#103C212yesmaximal, complemented
12D5×#470C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×Q8×D5C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16C2×C3×C5×M16C2211yescharacteristic
17C3×C5×C22⋊Q8C2212yes—
18C3×#4092C2212yes—
19C2×C3×#689C2212yescomplemented
20C3×#4070C2212yes—
21C2×C3×#681C2211yescharacteristic
22C3×D5×Q16—24no—
23C3×D5×M16—24no—
24C2×C3×Dic20C2211yescharacteristic, complemented
25C2×C3×#676C2211yescharacteristic
26C2×C3×#676C2211yescharacteristic
27C2×C3×C8×D5C2211yescharacteristic
28C2×C3×C8×D5C2211yescharacteristic
29C3×#4043C2212yes—
30C3×#4042—22no—
31C3×D5×C4⋊C4—22no—
32C3×D5×C4⋊C4C2212yes—
33C3×D5×C22⋊C4—22no—
34C3×#4024—22no—
35C3×C5×#106C2211yescharacteristic, complemented
36C3×C5×#103C2212yescomplemented
37C3×#3967C2212yescomplemented
38C3×#3949C2211yescharacteristic, complemented
39C3×#3948C2212yescomplemented
40C3×#3942C2212yescomplemented
41C3×#3940C2212yescomplemented
42C2×C3×#470—51nomaximal, Hall
43C2×D5×Q16C2×C311yescharacteristic, complemented
44C2×D5×M16C2×C311yescharacteristic
45D5×C22⋊Q8C2×C312yes—
46C5×#470C2×C311yescharacteristic, complemented
47#65478C2×C311yescharacteristic, complemented
48#65426C2×C311yescharacteristic, complemented
49#65341C2×C312yescomplemented
50#65157C2×C311yescharacteristic, complemented
51D5×#106C2×C311yescharacteristic, complemented
52#65105C2×C312yescomplemented
53D5×#103C2×C312yescomplemented
54C23×C3×D5D411yescharacteristic
55C2×C3×C5×Q8C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×Dic5D411yescharacteristic
58C3×Q8×D5—24no—
59C3×Q8×D5—24no—
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×C3×Dic10—22no—
69C2×C3×Dic10C2312yes—
70C3×C5×Q16—22no—
71C3×C5×M16—22no—
72C2×C3×C5×C8C2311yescharacteristic
73C2×C3×C5×C8C2311yescharacteristic
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C22⋊C4—22no—
77C3×C22⋊Dic5—22no—
78C3×#689—24no—
79C3×#685—22no—
80C3×#685—22no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5C2312yes—
83C3×#683—22no—
84C3×#683—22no—
85C3×#683—22no—
86C3×#681—22no—
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89C3×Dic20—22no—
90C3×#676—22no—
91C3×#676—22no—
92C3×C8×D5—22no—
93C3×C8×D5D414yes—
94C22×C3×Q16—51no—
95C22×C3×M16—51no—
96C2×C3×C22⋊Q8—52no—
97C3×#470—51no—
98C3×#470—51no—
99C3×#470—52no—
100C3×#470—51no—
101C3×#470—52no—
102C3×#470D511yescharacteristic, direct product factor
103C2×C3×#106—51no—
104C2×C3×#103—52no—
105C2×Q8×D5C22×C312yes—
106C22×C4×D5C22×C311yescharacteristic
107C2×C5×Q16C22×C311yescharacteristic, complemented
108C2×C5×M16C22×C311yescharacteristic
109C5×C22⋊Q8C22×C312yes—
110#4092C22×C312yes—
111C2×#689C22×C312yescomplemented
112#4070C22×C312yes—
113C2×#681C22×C311yescharacteristic
114D5×Q16—24no—
115D5×M16—24no—
116C2×Dic20C22×C311yescharacteristic, complemented
117C2×#676C22×C311yescharacteristic
118C2×#676C22×C311yescharacteristic
119C2×C8×D5C22×C311yescharacteristic
120C2×C8×D5C22×C311yescharacteristic
121#4043C22×C312yes—
122#4042—22no—
123D5×C4⋊C4—22no—
124D5×C4⋊C4C22×C312yes—
125D5×C22⋊C4—22no—
126#4024—22no—
127C5×#106C22×C311yescharacteristic, complemented
128C5×#103C22×C312yescomplemented
129#3967C22×C312yescomplemented
130#3949C22×C311yescharacteristic, complemented
131#3948C22×C312yescomplemented
132#3942C22×C312yescomplemented
133#3940C22×C312yescomplemented
134C2×#470—51noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—22no—
137C22×C3×D5—24no—
138C22×C3×D5C2×D411yescharacteristic
139C22×C3×D5C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×Q8—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5C2×D411yescharacteristic
152C2×C3×Dic5C2×D411yescharacteristic
153C3×C4×D5—22no—
154C3×C4×D5—21no—
155C3×C4×D5—21no—
156C3×C4×D5—22no—
157C3×C4×D5—44no—
158C3×C4×D5—44no—
159C3×C4×D5C2×D412yes—
160C3×C4×D5#4112yes—
161C3×Dic10—22no—
162C3×Dic10—22no—
163C3×Dic10—44no—
164C3×C5×C8—21no—
165C3×C5×C8C2×D412yes—
166C3×#168—21no—
167C3×#168C2×D412yes—
168C22×C3×Q8—52no—
169C23×C3×C4—51no—
170C2×C3×Q16—52no—
171C2×C3×Q16—51no—
172C2×C3×Q16—104no—
173C2×C3×Q16C2×D511yescharacteristic, complemented
174C2×C3×M16—51no—
175C2×C3×M16—51no—
176C2×C3×M16—51no—
177C2×C3×M16—104no—
178C2×C3×M16C2×D511yescharacteristic
179C22×C3×C8—51no—
180C22×C3×C8—51no—
181C3×C22⋊Q8—52no—
182C3×C22⋊Q8—52no—
183C3×C22⋊Q8—52no—
184C3×C22⋊Q8—102no—
185C3×C22⋊Q8—102no—
186C3×C22⋊Q8C2×D512yes—
187C2×C3×C4⋊C4—52no—
188C2×C3×C4⋊C4—102no—
189C2×C3×C22⋊C4—102no—
190C3×#106—51no—
191C3×#106—52no—
192C3×#106C2×D511yescharacteristic, complemented
193C3×#103—52no—
194C3×#103—52no—
195C3×#103—52no—
196C3×#103C2×D512yescomplemented
197C23×D5C3×D411yescharacteristic
198C2×C5×Q8C23×C312yes—
199C22×C4×C5C23×C311yescharacteristic
200C22×Dic5C3×D411yescharacteristic
201Q8×D5—24no—
202Q8×D5—24no—
203C2×C4×D5—22no—
204C2×C4×D5—22no—
205C2×C4×D5—22no—
206C2×C4×D5—22no—
207C2×C4×D5C3×D411yescharacteristic
208C2×C4×D5C3×D411yescharacteristic
209C2×C4×D5C23×C311yescharacteristic
210C2×C4×D5C23×C311yescharacteristic
211C2×Dic10—22no—
212C2×Dic10C23×C312yes—
213C5×Q16—22no—
214C5×M16—22no—
215C2×C5×C8C23×C311yescharacteristic
216C2×C5×C8C23×C311yescharacteristic
217C5×C4⋊C4—22no—
218C5×C4⋊C4C23×C312yes—
219C5×C22⋊C4—22no—
220C22⋊Dic5—22no—
221#689—24no—
222#685—22no—
223#685—22no—
224C4⋊Dic5—22no—
225C4⋊Dic5C23×C312yes—
226#683—22no—
227#683—22no—
228#683—22no—
229#681—22no—
230C2×#168C23×C311yescharacteristic
231C2×#168C23×C311yescharacteristic
232Dic20—22no—
233#676—22no—
234#676—22no—
235C8×D5—22no—
236C8×D5C3×D414yes—
237C22×Q16—51no—
238C22×M16—51no—
239C2×C22⋊Q8—52no—
240#470—51no—
241#470—51no—
242#470—52no—
243#470—51no—
244#470—52no—
245#470C3×D511yescharacteristic, direct product factor
246C2×#106—51no—
247C2×#103—52no—
248C22×C3×C5—21no—
249C22×C3×C5—22no—
250C22×C3×C5C22×D411yescharacteristic
251C2×C3×D5—21no—
252C2×C3×D5—22no—
253C2×C3×D5—44no—
254C2×C3×D5#12112yes—
255C2×C3×D5#13714yes—
256C3×C4×C5—21no—
257C3×C4×C5—42no—
258C3×C4×C5—42no—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261C3×Dic5—21no—
262C3×Dic5—42no—
263C3×Dic5—42no—
264C3×Dic5#12112yes—
265C24×C3—51no—
266C2×C3×Q8—52no—
267C2×C3×Q8—102no—
268C2×C3×Q8—104no—
269C2×C3×Q8—104no—
270C2×C3×Q8C22×D512yes—
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×C3×C4—102no—
277C22×C3×C4—102no—
278C22×C3×C4—102no—
279C22×C3×C4—102no—
280C22×C3×C4C22×D511yescharacteristic
281C3×Q16—22no—
282C3×Q16—104no—
283C3×Q16—102no—
284C3×M16—22no—
285C3×M16—102no—
286C3×M16—102no—
287C3×M16—102no—
288C2×C3×C8—51no—
289C2×C3×C8—54no—
290C2×C3×C8—51no—
291C2×C3×C8—102no—
292C2×C3×C8C22×D511yescharacteristic
293C2×C3×C8C22×D511yescharacteristic
294C3×C4⋊C4—22no—
295C3×C4⋊C4—52no—
296C3×C4⋊C4—102no—
297C3×C4⋊C4—102no—
298C3×C4⋊C4—102no—
299C3×C4⋊C4—102no—
300C3×C4⋊C4C22×D512yes—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—102no—
303C3×C22⋊C4—102no—
304C3×C22⋊C4—102no—
305C23×C5C2×C3×D411yescharacteristic
306C22×D5—22no—
307C22×D5—24no—
308C22×D5C2×C3×D411yescharacteristic
309C22×D5C2×C3×D411yescharacteristic
310C5×Q8—22no—
311C5×Q8—22no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5C2×C3×D411yescharacteristic
317C2×C4×C5C24×C311yescharacteristic
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5C2×C3×D411yescharacteristic
322C2×Dic5C2×C3×D411yescharacteristic
323C4×D5—22no—
324C4×D5—21no—
325C4×D5—21no—
326C4×D5—22no—
327C4×D5—44no—
328C4×D5—44no—
329C4×D5C2×C3×D412yes—
330C4×D5C3×#4112yes—
331Dic10—22no—
332Dic10—22no—
333Dic10—44no—
334C5×C8—21no—
335C5×C8C2×C3×D412yes—
336#168—21no—
337#168C2×C3×D412yes—
338C22×Q8—52no—
339C23×C4—51no—
340C2×Q16—52no—
341C2×Q16—51no—
342C2×Q16—104no—
343C2×Q16C2×C3×D511yescharacteristic, complemented
344C2×M16—51no—
345C2×M16—51no—
346C2×M16—51no—
347C2×M16—104no—
348C2×M16C2×C3×D511yescharacteristic
349C22×C8—51no—
350C22×C8—51no—
351C22⋊Q8—52no—
352C22⋊Q8—52no—
353C22⋊Q8—52no—
354C22⋊Q8—102no—
355C22⋊Q8—102no—
356C22⋊Q8C2×C3×D512yes—
357C2×C4⋊C4—52no—
358C2×C4⋊C4—102no—
359C2×C22⋊C4—102no—
360#106—51no—
361#106—52no—
362#106C2×C3×D511yescharacteristic, complemented
363#103—52no—
364#103—52no—
365#103—52no—
366#103C2×C3×D512yescomplemented
367C2×C3×C5—41no—
368C2×C3×C5C2×#12111yescharacteristic
369C2×C3×C5C2×#13712yes—
370C3×D5—41no—
371C3×D5#47014yesdirect product factor
372C23×C3—51no—
373C23×C3—51no—
374C23×C3—102no—
375C23×C3—104no—
376C23×C3D4×D511yescharacteristic
377C3×Q8—22no—
378C3×Q8—22no—
379C3×Q8—102no—
380C3×Q8—102no—
381C3×Q8—204no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—51no—
387C2×C3×C4—52no—
388C2×C3×C4—52no—
389C2×C3×C4—51no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—101no—
394C2×C3×C4—101no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—204no—
398C2×C3×C4—204no—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4C23×D511yescharacteristic
401C3×C8—21no—
402C3×C8—52no—
403C3×C8—101no—
404C3×C8D4×D512yes—
405C22×C5—22no—
406C22×C5—21no—
407C22×C5C22×C3×D411yescharacteristic
408C2×D5—22no—
409C2×D5—21no—
410C2×D5—44no—
411C2×D5C3×#12112yes—
412C2×D5C3×#13714yes—
413C4×C5—21no—
414C4×C5—42no—
415C4×C5—42no—
416C4×C5C22×C3×D411yescharacteristic
417C4×C5C2×C3×#4111yescharacteristic
418Dic5—21no—
419Dic5—42no—
420Dic5—42no—
421Dic5C3×#12112yes—
422C24—51no—
423C2×Q8—52no—
424C2×Q8—102no—
425C2×Q8—104no—
426C2×Q8—104no—
427C2×Q8C22×C3×D512yes—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4C22×C3×D511yescharacteristic
438Q16—22no—
439Q16—104no—
440Q16—102no—
441M16—22no—
442M16—102no—
443M16—102no—
444M16—102no—
445C2×C8—51no—
446C2×C8—54no—
447C2×C8—51no—
448C2×C8—102no—
449C2×C8C22×C3×D511yescharacteristic
450C2×C8C22×C3×D511yescharacteristic
451C4⋊C4—22no—
452C4⋊C4—52no—
453C4⋊C4—102no—
454C4⋊C4—102no—
455C4⋊C4—102no—
456C4⋊C4—102no—
457C4⋊C4C22×C3×D512yes—
458C22⋊C4—22no—
459C22⋊C4—102no—
460C22⋊C4—102no—
461C22⋊C4—102no—
462C3×C5C2×#47011yescharacteristic, complemented, Hall
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—54no—
466C22×C3—52no—
467C22×C3—102no—
468C22×C3—101no—
469C22×C3—204no—
470C22×C3C2×D4×D511yescharacteristic
471C3×C4—21no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—52no—
475C3×C4—101no—
476C3×C4—202no—
477C3×C4—202no—
478C3×C4C2×D4×D511yescharacteristic
479C3×C4D5×#4111yescharacteristic
480C2×C5—41no—
481C2×C5C2×C3×#12111yescharacteristic
482C2×C5C2×C3×#13712yes—
483D5—41no—
484D5C3×#47014yesdirect product factor
485C23—51no—
486C23—51no—
487C23—102no—
488C23—104no—
489C23C3×D4×D511yescharacteristic
490Q8—22no—
491Q8—22no—
492Q8—102no—
493Q8—102no—
494Q8—204no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—51no—
500C2×C4—52no—
501C2×C4—52no—
502C2×C4—51no—
503C2×C4—102no—
504C2×C4—102no—
505C2×C4—102no—
506C2×C4—101no—
507C2×C4—101no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—204no—
511C2×C4—204no—
512C2×C4C3×D4×D511yescharacteristic
513C2×C4C23×C3×D511yescharacteristic
514C8—21no—
515C8—52no—
516C8—101no—
517C8C3×D4×D512yes—
518C2×C3—41no—
519C2×C3—54no—
520C2×C3—201no—
521C2×C3D5×#12111yescharacteristic
522C2×C3D5×#13712yes—
523C5C2×C3×#47011yescharacteristic, complemented, Sylow
524C22—22no—
525C22—21no—
526C22—54no—
527C22—52no—
528C22—102no—
529C22—101no—
530C22—204no—
531C22C2×C3×D4×D511yescharacteristic
532C4—21no—
533C4—42no—
534C4—42no—
535C4—52no—
536C4—101no—
537C4—202no—
538C4—202no—
539C4C2×C3×D4×D511yescharacteristic
540C4C3×D5×#4111yescharacteristic
541C3D5×#47011yescharacteristic, direct product factor, Sylow
542C2—41no—
543C2—54no—
544C2—201no—
545C2C3×D5×#12111yescharacteristic
546C2C3×D5×#13712yes—
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#470C2
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
hypercenterC3×#470D5
hypocenterC5C2×C3×#470
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×Q16C2semidirect
4. C3×C5×#470C2semidirect
5. C3×#65478C2semidirect
6. C3×#65426C2semidirect
7. C3×#65341C2semidirect
8. C3×#65157C2semidirect
9. C3×D5×#106C2semidirect
10. C3×#65105C2semidirect
11. C3×D5×#103C2semidirect
12. D5×#470C3direct (N × H)
15. C2×C3×C5×Q16C22semidirect
19. C2×C3×#689C22semidirect
24. C2×C3×Dic20C22semidirect
35. C3×C5×#106C22semidirect
36. C3×C5×#103C22semidirect
37. C3×#3967C22semidirect
38. C3×#3949C22semidirect
39. C3×#3948C22semidirect
40. C3×#3942C22semidirect
41. C3×#3940C22semidirect
43. C2×D5×Q16C2×C3semidirect
46. C5×#470C2×C3semidirect
47. #65478C2×C3semidirect
48. #65426C2×C3semidirect
49. #65341C2×C3semidirect
50. #65157C2×C3semidirect
51. D5×#106C2×C3semidirect
52. #65105C2×C3semidirect
53. D5×#103C2×C3semidirect
102. C3×#470D5direct (N × H)
107. C2×C5×Q16C22×C3semidirect
111. C2×#689C22×C3semidirect
116. C2×Dic20C22×C3semidirect
127. C5×#106C22×C3semidirect
128. C5×#103C22×C3semidirect
129. #3967C22×C3semidirect
130. #3949C22×C3semidirect
131. #3948C22×C3semidirect
132. #3942C22×C3semidirect
133. #3940C22×C3semidirect
173. C2×C3×Q16C2×D5semidirect
192. C3×#106C2×D5semidirect
196. C3×#103C2×D5semidirect
245. #470C3×D5direct (N × H)
343. C2×Q16C2×C3×D5semidirect
362. #106C2×C3×D5semidirect
366. #103C2×C3×D5semidirect
371. C3×D5#470direct (N × H)
462. C3×C5C2×#470semidirect
484. D5C3×#470direct (N × H)
523. C5C2×C3×#470semidirect
541. C3D5×#470direct (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
C2×C3×D5×M162
C3×D5×C22⋊Q82
C3×C5×#4702
C3×#654782
C3×#654262
C3×#653412
C3×#651572
C3×D5×#1062
C3×#651052
C3×D5×#1032
D5×#4703
C2×C3×#4705