Finite Group Databasebeta

← C3×D5×#477 #14430061

Subgroups — C3×D5×#477 #14430061

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×C4×Q8×D5C211yesmaximal, characteristic
3C3×C5×#477C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5C3×#65310C211yesmaximal, characteristic, complemented
6C3×D5×#107C212yesmaximal
7C3×#65164C212yesmaximal, complemented
8C3×#65139C211yesmaximal, characteristic, complemented
9C3×D5×C4⋊C8C211yesmaximal, characteristic
10C3×D5×#103C212yesmaximal
11C3×#65083C212yesmaximal, complemented
12D5×#477C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×Q8×D5—21no—
14C2×C3×Q8×D5C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17C3×Q8×Dic5C2211yescharacteristic
18C3×#4090—21no—
19C2×C3×C8×D5C2212yes—
20C3×D5×C4⋊C4—21no—
21C3×D5×C4⋊C4—21no—
22C3×D5×C4⋊C4C2211yescharacteristic
23C3×D5×C4⋊C4C2212yes—
24C3×#4034—21no—
25C3×#4034C2212yes—
26C3×#4033—21no—
27C3×#4033C2211yescharacteristic
28C3×C42×D5—21no—
29C3×C42×D5C2211yescharacteristic
30C3×#4015C2211yescharacteristic
31C3×C4×Dic10—21no—
32C3×C4×Dic10C2211yescharacteristic
33C3×C5×#107C2212yes—
34C3×C5×C4⋊C8C2211yescharacteristic
35C3×C5×#103C2212yes—
36C3×#3967C2212yes—
37C3×#3950C2212yes—
38C3×#3948C2212yes—
39C3×#3946C2212yes—
40C3×#3942C2212yes—
41C3×#3939C2212yes—
42C3×#3939C2212yes—
43C3×C4⋊#168C2211yescharacteristic
44C2×C3×#477—51nomaximal, Hall
45D5×C4⋊Q8C2×C311yescharacteristic
46C4×Q8×D5C2×C311yescharacteristic
47C5×#477C2×C311yescharacteristic, complemented
48#65380C2×C311yescharacteristic, complemented
49#65310C2×C311yescharacteristic, complemented
50D5×#107C2×C312yes—
51#65164C2×C312yescomplemented
52#65139C2×C311yescharacteristic, complemented
53D5×C4⋊C8C2×C311yescharacteristic
54D5×#103C2×C312yes—
55#65083C2×C312yescomplemented
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8C2311yescharacteristic
58C3×Q8×D5—22no—
59C3×Q8×D5—44no—
60C3×Q8×D5Q814yescomplemented
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×Dic10—21no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10C2311yescharacteristic
71C2×C3×C5×C8C2312yes—
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2311yescharacteristic
75C3×C5×C4⋊C4C2312yes—
76C3×C42×C5—21no—
77C3×C42×C5C2311yescharacteristic
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2312yes—
82C3×#683—21no—
83C3×#683—22no—
84C3×#683—22no—
85C3×#683—21no—
86C3×#683—21no—
87C3×C4×Dic5—21no—
88C3×C4×Dic5—21no—
89C3×C4×Dic5—21no—
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5D411yescharacteristic
92C3×C4×Dic5C2311yescharacteristic
93C2×C3×#168C2312yes—
94C3×C8×D5—24no—
95C2×C3×C4⋊Q8—51no—
96C2×C3×C4×Q8—51no—
97C3×#477—51no—
98C3×#477—51no—
99C3×#477—52no—
100C3×#477—51no—
101C3×#477—52no—
102C3×#477D511yescharacteristic, direct product factor
103C2×C3×#107—52no—
104C2×C3×C4⋊C8—51no—
105C2×C3×#103—52no—
106C2×Q8×D5—21no—
107C2×Q8×D5C22×C311yescharacteristic
108C5×C4⋊Q8C22×C311yescharacteristic
109C4×C5×Q8C22×C311yescharacteristic
110Q8×Dic5C22×C311yescharacteristic
111#4090—21no—
112C2×C8×D5C22×C312yes—
113D5×C4⋊C4—21no—
114D5×C4⋊C4—21no—
115D5×C4⋊C4C22×C312yes—
116D5×C4⋊C4C22×C311yescharacteristic
117#4034—21no—
118#4034C22×C312yes—
119#4033—21no—
120#4033C22×C311yescharacteristic
121C42×D5—21no—
122C42×D5C22×C311yescharacteristic
123#4015C22×C311yescharacteristic
124C4×Dic10—21no—
125C4×Dic10C22×C311yescharacteristic
126C5×#107C22×C312yes—
127C5×C4⋊C8C22×C311yescharacteristic
128C5×#103C22×C312yes—
129#3967C22×C312yes—
130#3950C22×C312yes—
131#3948C22×C312yes—
132#3946C22×C312yes—
133#3942C22×C312yes—
134#3939C22×C312yes—
135#3939C22×C312yes—
136C4⋊#168C22×C311yescharacteristic
137C2×#477—51noSylow
138C22×C3×D5C2×D411yescharacteristic
139C3×C5×Q8—21no—
140C3×C5×Q8—42no—
141C3×C5×Q8C2×Q812yescomplemented
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5C2×D411yescharacteristic
152C2×C3×Dic5C2×D411yescharacteristic
153C2×C3×Dic5C2×D411yescharacteristic
154C3×C4×D5—24no—
155C3×C4×D5—22no—
156C3×C4×D5—42no—
157C3×C4×D5—44no—
158C3×C4×D5Q1614yes—
159C3×C4×D5C2×Q812yes—
160C3×C4×D5#4112yes—
161C3×Dic10—21no—
162C3×Dic10—24no—
163C3×Dic10—44no—
164C3×Dic10—42no—
165C3×Dic10C2×Q812yescomplemented
166C3×C5×C8—22no—
167C3×#168—22no—
168C22×C3×Q8—51no—
169C22×C3×Q8—101no—
170C22×C3×C8—52no—
171C3×C4⋊Q8—52no—
172C3×C4⋊Q8—51no—
173C3×C4⋊Q8—101no—
174C3×C4⋊Q8—101no—
175C3×C4⋊Q8C2×D511yescharacteristic
176C3×C4×Q8—51no—
177C3×C4×Q8—51no—
178C3×C4×Q8—51no—
179C3×C4×Q8—101no—
180C3×C4×Q8—101no—
181C3×C4×Q8C2×D511yescharacteristic
182C2×C3×C4⋊C4—52no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C4⋊C4—101no—
185C2×C3×C4⋊C4—101no—
186C2×C3×C42—51no—
187C2×C3×C42—101no—
188C3×#107—52no—
189C3×#107—52no—
190C3×#107—52no—
191C3×#107C2×D512yes—
192C3×C4⋊C8—52no—
193C3×C4⋊C8—51no—
194C3×C4⋊C8C2×D511yescharacteristic
195C3×#103—52no—
196C3×#103—52no—
197C3×#103—52no—
198C3×#103C2×D512yes—
199C2×C5×Q8—21no—
200C2×C5×Q8C23×C311yescharacteristic
201Q8×D5—22no—
202Q8×D5—44no—
203Q8×D5C3×Q814yescomplemented
204C2×C4×D5—21no—
205C2×C4×D5—22no—
206C2×C4×D5—21no—
207C2×C4×D5C3×D411yescharacteristic
208C2×C4×D5C3×D411yescharacteristic
209C2×C4×D5C23×C311yescharacteristic
210C2×Dic10—21no—
211C2×Dic10—21no—
212C2×Dic10—22no—
213C2×Dic10C23×C311yescharacteristic
214C2×C5×C8C23×C312yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4C23×C311yescharacteristic
218C5×C4⋊C4C23×C312yes—
219C42×C5—21no—
220C42×C5C23×C311yescharacteristic
221C4⋊Dic5—21no—
222C4⋊Dic5—21no—
223C4⋊Dic5C23×C311yescharacteristic
224C4⋊Dic5C23×C312yes—
225#683—21no—
226#683—21no—
227#683—21no—
228#683—22no—
229#683—22no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5C3×D411yescharacteristic
234C4×Dic5C3×D411yescharacteristic
235C4×Dic5C23×C311yescharacteristic
236C2×#168C23×C312yes—
237C8×D5—24no—
238C2×C4⋊Q8—51no—
239C2×C4×Q8—51no—
240#477—51no—
241#477—51no—
242#477—52no—
243#477—51no—
244#477—52no—
245#477C3×D511yescharacteristic, direct product factor
246C2×#107—52no—
247C2×C4⋊C8—51no—
248C2×#103—52no—
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5C22⋊Q812yes—
251C2×C3×D5C2×Q1612yes—
252C2×C3×D5AGL(1,ℤ/8)12yes—
253C3×C4×C5—22no—
254C3×C4×C5—21no—
255C3×C4×C5—42no—
256C3×C4×C5—41no—
257C3×C4×C5C2×Q1612yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260C3×Dic5—22no—
261C3×Dic5—21no—
262C3×Dic5—42no—
263C3×Dic5—41no—
264C3×Dic5C22⋊Q812yes—
265C3×Dic5C2×Q1612yes—
266C2×C3×Q8—21no—
267C2×C3×Q8—54no—
268C2×C3×Q8—51no—
269C2×C3×Q8—101no—
270C2×C3×Q8—102no—
271C2×C3×Q8—102no—
272C2×C3×Q8—101no—
273C2×C3×Q8—204no—
274C2×C3×Q8C22×D511yescharacteristic
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4—101no—
279C22×C3×C4—101no—
280C22×C3×C4—102no—
281C2×C3×C8—52no—
282C2×C3×C8—104no—
283C2×C3×C8C22×D512yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—52no—
287C3×C4⋊C4—51no—
288C3×C4⋊C4—101no—
289C3×C4⋊C4—102no—
290C3×C4⋊C4—101no—
291C3×C4⋊C4—102no—
292C3×C4⋊C4—101no—
293C3×C4⋊C4—101no—
294C3×C4⋊C4—101no—
295C3×C4⋊C4C22×D512yes—
296C3×C4⋊C4C22×D511yescharacteristic
297C3×C42—21no—
298C3×C42—51no—
299C3×C42—51no—
300C3×C42—51no—
301C3×C42—101no—
302C3×C42—101no—
303C3×C42—101no—
304C3×C42C22×D511yescharacteristic
305C22×D5C2×C3×D411yescharacteristic
306C5×Q8—21no—
307C5×Q8—42no—
308C5×Q8C2×C3×Q812yescomplemented
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5C2×C3×D411yescharacteristic
313C2×C4×C5C2×C3×D411yescharacteristic
314C2×C4×C5C24×C311yescharacteristic
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5C2×C3×D411yescharacteristic
319C2×Dic5C2×C3×D411yescharacteristic
320C2×Dic5C2×C3×D411yescharacteristic
321C4×D5—24no—
322C4×D5—22no—
323C4×D5—42no—
324C4×D5—44no—
325C4×D5C3×Q1614yes—
326C4×D5C2×C3×Q812yes—
327C4×D5C3×#4112yes—
328Dic10—21no—
329Dic10—24no—
330Dic10—44no—
331Dic10—42no—
332Dic10C2×C3×Q812yescomplemented
333C5×C8—22no—
334#168—22no—
335C22×Q8—51no—
336C22×Q8—101no—
337C22×C8—52no—
338C4⋊Q8—52no—
339C4⋊Q8—51no—
340C4⋊Q8—101no—
341C4⋊Q8—101no—
342C4⋊Q8C2×C3×D511yescharacteristic
343C4×Q8—51no—
344C4×Q8—51no—
345C4×Q8—51no—
346C4×Q8—101no—
347C4×Q8—101no—
348C4×Q8C2×C3×D511yescharacteristic
349C2×C4⋊C4—51no—
350C2×C4⋊C4—52no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C42—51no—
354C2×C42—101no—
355#107—52no—
356#107—52no—
357#107—52no—
358#107C2×C3×D512yes—
359C4⋊C8—52no—
360C4⋊C8—51no—
361C4⋊C8C2×C3×D511yescharacteristic
362#103—52no—
363#103—52no—
364#103—52no—
365#103C2×C3×D512yes—
366C2×C3×C5C2×C22⋊Q811yescharacteristic
367C2×C3×C5C22×Q1611yescharacteristic
368C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
369C3×D5#47714yesdirect product factor
370C23×C3—51no—
371C3×Q8—21no—
372C3×Q8—42no—
373C3×Q8—52no—
374C3×Q8—104no—
375C3×Q8—101no—
376C3×Q8—202no—
377C3×Q8—204no—
378C3×Q8Q8×D512yescomplemented
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—51no—
383C2×C3×C4—51no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—54no—
387C2×C3×C4—51no—
388C2×C3×C4—102no—
389C2×C3×C4—104no—
390C2×C3×C4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—102no—
393C2×C3×C4—202no—
394C2×C3×C4—204no—
395C2×C3×C4D4×D511yescharacteristic
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398C3×C8—22no—
399C3×C8—102no—
400C22×C5C22×C3×D411yescharacteristic
401C2×D5C3×C22⋊Q812yes—
402C2×D5C2×C3×Q1612yes—
403C2×D5C3×AGL(1,ℤ/8)12yes—
404C4×C5—21no—
405C4×C5—22no—
406C4×C5—42no—
407C4×C5—41no—
408C4×C5C2×C3×Q1612yes—
409C4×C5C22×C3×Q811yescharacteristic
410C4×C5C2×C3×#4111yescharacteristic
411Dic5—21no—
412Dic5—22no—
413Dic5—42no—
414Dic5—41no—
415Dic5C3×C22⋊Q812yes—
416Dic5C2×C3×Q1612yes—
417C2×Q8—21no—
418C2×Q8—54no—
419C2×Q8—51no—
420C2×Q8—101no—
421C2×Q8—102no—
422C2×Q8—102no—
423C2×Q8—101no—
424C2×Q8—204no—
425C2×Q8C22×C3×D511yescharacteristic
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—102no—
432C2×C8—52no—
433C2×C8—104no—
434C2×C8C22×C3×D512yes—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—52no—
438C4⋊C4—51no—
439C4⋊C4—101no—
440C4⋊C4—102no—
441C4⋊C4—101no—
442C4⋊C4—101no—
443C4⋊C4—102no—
444C4⋊C4—101no—
445C4⋊C4—101no—
446C4⋊C4C22×C3×D512yes—
447C4⋊C4C22×C3×D511yescharacteristic
448C42—21no—
449C42—51no—
450C42—51no—
451C42—51no—
452C42—101no—
453C42—101no—
454C42—101no—
455C42C22×C3×D511yescharacteristic
456C3×C5C2×#47711yescharacteristic, complemented, Hall
457C22×C3—52no—
458C22×C3—52no—
459C22×C3—52no—
460C22×C3C2×D4×D511yescharacteristic
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—42no—
465C3×C4—52no—
466C3×C4—52no—
467C3×C4—101no—
468C3×C4—102no—
469C3×C4—201no—
470C3×C4—202no—
471C3×C4D5×Q1612yes—
472C3×C4C2×Q8×D511yescharacteristic
473C3×C4D5×#4111yescharacteristic
474C2×C5C2×C3×C22⋊Q811yescharacteristic
475C2×C5C22×C3×Q1611yescharacteristic
476C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
477D5C3×#47714yesdirect product factor
478C23—51no—
479Q8—21no—
480Q8—42no—
481Q8—52no—
482Q8—104no—
483Q8—101no—
484Q8—202no—
485Q8—204no—
486Q8C3×Q8×D512yescomplemented
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—51no—
491C2×C4—51no—
492C2×C4—52no—
493C2×C4—52no—
494C2×C4—54no—
495C2×C4—51no—
496C2×C4—102no—
497C2×C4—104no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—102no—
501C2×C4—204no—
502C2×C4—202no—
503C2×C4C3×D4×D511yescharacteristic
504C2×C4C3×D4×D511yescharacteristic
505C2×C4C23×C3×D511yescharacteristic
506C8—22no—
507C8—102no—
508C2×C3—54no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×D5×Q1611yescharacteristic
511C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
512C5C2×C3×#47711yescharacteristic, complemented, Sylow
513C22—52no—
514C22—52no—
515C22—52no—
516C22C2×C3×D4×D511yescharacteristic
517C4—21no—
518C4—22no—
519C4—42no—
520C4—41no—
521C4—52no—
522C4—52no—
523C4—101no—
524C4—102no—
525C4—202no—
526C4—201no—
527C4C3×D5×Q1612yes—
528C4C2×C3×Q8×D511yescharacteristic
529C4C3×D5×#4111yescharacteristic
530C3D5×#47711yescharacteristic, direct product factor, Sylow
531C2—54no—
532C2C3×D5×C22⋊Q811yescharacteristic
533C2C2×C3×D5×Q1611yescharacteristic
534C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#477C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC3×#477D5
hypocenterC5C2×C3×#477
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
3. C3×C5×#477C2semidirect
4. C3×#65380C2semidirect
5. C3×#65310C2semidirect
7. C3×#65164C2semidirect
8. C3×#65139C2semidirect
11. C3×#65083C2semidirect
12. D5×#477C3direct (N × H)
47. C5×#477C2×C3semidirect
48. #65380C2×C3semidirect
49. #65310C2×C3semidirect
51. #65164C2×C3semidirect
52. #65139C2×C3semidirect
55. #65083C2×C3semidirect
60. C3×Q8×D5Q8semidirect
102. C3×#477D5direct (N × H)
141. C3×C5×Q8C2×Q8semidirect
165. C3×Dic10C2×Q8semidirect
203. Q8×D5C3×Q8semidirect
245. #477C3×D5direct (N × H)
308. C5×Q8C2×C3×Q8semidirect
332. Dic10C2×C3×Q8semidirect
369. C3×D5#477direct (N × H)
378. C3×Q8Q8×D5semidirect
456. C3×C5C2×#477semidirect
477. D5C3×#477direct (N × H)
486. Q8C3×Q8×D5semidirect
512. C5C2×C3×#477semidirect
530. C3D5×#477direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×C4×Q8×D52
C3×C5×#4772
C3×#653802
C3×#653102
C3×D5×#1072
C3×#651642
C3×#651392
C3×D5×C4⋊C82
C3×D5×#1032
C3×#650832
D5×#4773
C2×C3×#4775