Finite Group Databasebeta

← C3×D5⋊#407 #14411639

Subgroups — C3×D5⋊#407 #14411639

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C2×C3×D5⋊M16C212yesmaximal, complemented
3C3×#65798C212yesmaximal, complemented
4C3×#65756C214yesmaximal, complemented
5C3×#65755C212yesmaximal, complemented
6C3×D5⋊(C22⋊C8)C214yesmaximal, complemented
7D5⋊#407C311yesmaximal, characteristic, direct product factor, Hall
8C24×C3×D5C411yescharacteristic
9C23×C3×C4×C5C411yescharacteristic
10C23×C3×Dic5C2211yescharacteristic
11C22×C3×C4×D5—28no—
12C22×C3×C4×D5C411yescharacteristic
13C22×C3×C4×D5C411yescharacteristic
14C22×C3×C4×D5C412yes—
15C22×C3×C4×D5C412yes—
16C22×C3×C4×D5C2212yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C22×C3×C4×D5C2211yescharacteristic
20C2×C3×#704C2214yescomplemented
21C3×D5⋊M16—28no—
22C2×C3×#700C2214yescomplemented
23C2×C3×D5⋊C8C2214yescomplemented
24C3×C22⋊#170C2218yescomplemented
25C3×#4003C2218yescomplemented
26C2×C3×#407—51nomaximal, Hall
27C23×C4×D5C2×C311yescharacteristic
28C2×D5⋊M16C2×C312yescomplemented
29#65798C2×C312yescomplemented
30#65756C2×C314yescomplemented
31#65755C2×C312yescomplemented
32D5⋊(C22⋊C8)C2×C314yescomplemented
33C24×C3×C5C2×C411yescharacteristic
34C23×C3×D5—24no—
35C23×C3×D5—28no—
36C23×C3×D5C2×C411yescharacteristic
37C23×C3×D5C2×C412yes—
38C23×C3×D5C2×C411yescharacteristic
39C23×C3×D5C2×C412yes—
40C22×C3×C4×C5—24no—
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×C4×C5C2×C412yes—
43C22×C3×C4×C5C2×C412yes—
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×Dic5—24no—
46C22×C3×Dic5C2×C411yescharacteristic
47C22×C3×Dic5C2×C412yes—
48C22×C3×Dic5C2312yes—
49C22×C3×Dic5C2311yescharacteristic
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5—24no—
52C2×C3×C4×D5—24no—
53C2×C3×C4×D5—28no—
54C2×C3×C4×D5—28no—
55C2×C3×C4×D5—28no—
56C2×C3×C4×D5—28no—
57C2×C3×C4×D5C2×C412yes—
58C2×C3×C4×D5C2×C412yes—
59C2×C3×C4×D5C2×C412yes—
60C2×C3×C4×D5C2×C412yes—
61C2×C3×C4×D5C2×C412yes—
62C2×C3×C4×D5C2×C411yescharacteristic
63C2×C3×C4×D5C2×C411yescharacteristic
64C2×C3×C4×D5D418yes—
65C2×C3×C4×D5C2312yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C3×#704—28no—
69C2×C3×#170C2318yescomplemented
70C3×#700—28no—
71C3×D5⋊C8—28no—
72C24×C3×C4—51no—
73C22×C3×M16—52no—
74C3×#407—52no—
75C3×#407—54no—
76C3×#407—52no—
77C2×C3×C22⋊C8—54no—
78C24×D5C3×C411yescharacteristic
79C23×C4×C5C3×C411yescharacteristic
80C23×Dic5C22×C311yescharacteristic
81C22×C4×D5—28no—
82C22×C4×D5C3×C411yescharacteristic
83C22×C4×D5C3×C411yescharacteristic
84C22×C4×D5C3×C412yes—
85C22×C4×D5C3×C412yes—
86C22×C4×D5C22×C312yes—
87C22×C4×D5C22×C311yescharacteristic
88C22×C4×D5C22×C312yes—
89C22×C4×D5C22×C311yescharacteristic
90C2×#704C22×C314yescomplemented
91D5⋊M16—28no—
92C2×#700C22×C314yescomplemented
93C2×D5⋊C8C22×C314yescomplemented
94C22⋊#170C22×C318yescomplemented
95#4003C22×C318yescomplemented
96C2×#407—51noSylow
97C23×C3×C5—22no—
98C23×C3×C5—24no—
99C23×C3×C5C22×C411yescharacteristic
100C23×C3×C5C22×C412yes—
101C22×C3×D5—232no—
102C22×C3×D5—22no—
103C22×C3×D5—24no—
104C22×C3×D5—24no—
105C22×C3×D5—24no—
106C22×C3×D5—24no—
107C22×C3×D5—24no—
108C22×C3×D5—24no—
109C22×C3×D5—24no—
110C22×C3×D5C22⋊C414yes—
111C22×C3×D5M1618yescomplemented
112C22×C3×D5C22×C411yescharacteristic
113C22×C3×D5C22×C412yes—
114C22×C3×D5C22×C411yescharacteristic
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—24no—
117C2×C3×C4×C5—24no—
118C2×C3×C4×C5C22⋊C414yes—
119C2×C3×C4×C5C22×C412yes—
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×C3×C4×C5C22×C411yescharacteristic
122C2×C3×Dic5—22no—
123C2×C3×Dic5—24no—
124C2×C3×Dic5—24no—
125C2×C3×Dic5C22×C412yes—
126C2×C3×Dic5C22×C411yescharacteristic
127C2×C3×Dic5C2×D414yes—
128C2×C3×Dic5C2411yescharacteristic
129C3×C4×D5—24no—
130C3×C4×D5—24no—
131C3×C4×D5—24no—
132C3×C4×D5—24no—
133C3×C4×D5—24no—
134C3×C4×D5—24no—
135C3×C4×D5C22⋊C414yes—
136C3×C4×D5C22⋊C414yes—
137C3×C4×D5C2×D414yes—
138C3×C4×D5C2×D414yes—
139C3×#170—28no—
140C25×C3—51no—
141C23×C3×C4—51no—
142C23×C3×C4—51no—
143C23×C3×C4—52no—
144C23×C3×C4—52no—
145C23×C3×C4—51no—
146C23×C3×C4—51no—
147C23×C3×C4—52no—
148C23×C3×C4—51no—
149C23×C3×C4—52no—
150C23×C3×C4—108no—
151C23×C3×C4AGL(1,𝔽5)11yescharacteristic
152C2×C3×M16—54no—
153C2×C3×M16—54no—
154C2×C3×M16—108no—
155C22×C3×C8—54no—
156C3×C22⋊C8—58no—
157C3×C22⋊C8—58no—
158C24×C5C2×C3×C411yescharacteristic
159C23×D5—24no—
160C23×D5—28no—
161C23×D5C2×C3×C411yescharacteristic
162C23×D5C2×C3×C412yes—
163C23×D5C2×C3×C411yescharacteristic
164C23×D5C2×C3×C412yes—
165C22×C4×C5—24no—
166C22×C4×C5C2×C3×C411yescharacteristic
167C22×C4×C5C2×C3×C412yes—
168C22×C4×C5C2×C3×C412yes—
169C22×C4×C5C2×C3×C411yescharacteristic
170C22×Dic5—24no—
171C22×Dic5C2×C3×C411yescharacteristic
172C22×Dic5C2×C3×C412yes—
173C22×Dic5C23×C312yes—
174C22×Dic5C23×C311yescharacteristic
175C2×C4×D5—24no—
176C2×C4×D5—24no—
177C2×C4×D5—24no—
178C2×C4×D5—28no—
179C2×C4×D5—28no—
180C2×C4×D5—28no—
181C2×C4×D5—28no—
182C2×C4×D5C2×C3×C412yes—
183C2×C4×D5C2×C3×C412yes—
184C2×C4×D5C2×C3×C412yes—
185C2×C4×D5C2×C3×C412yes—
186C2×C4×D5C2×C3×C412yes—
187C2×C4×D5C2×C3×C411yescharacteristic
188C2×C4×D5C2×C3×C411yescharacteristic
189C2×C4×D5C3×D418yes—
190C2×C4×D5C23×C312yes—
191C2×C4×D5C23×C311yescharacteristic
192C2×C4×D5C23×C311yescharacteristic
193#704—28no—
194C2×#170C23×C318yescomplemented
195#700—28no—
196D5⋊C8—28no—
197C24×C4—51no—
198C22×M16—52no—
199#407—52no—
200#407—52no—
201#407—54no—
202C2×C22⋊C8—54no—
203C22×C3×C5—28no—
204C22×C3×C5—22no—
205C22×C3×C5—22no—
206C22×C3×C5—22no—
207C22×C3×C5C2×C22⋊C412yes—
208C22×C3×C5C2×M1614yescomplemented
209C22×C3×C5C23×C411yescharacteristic
210C2×C3×D5—216no—
211C2×C3×D5—28no—
212C2×C3×D5—22no—
213C2×C3×D5—22no—
214C2×C3×D5—22no—
215C2×C3×D5—28no—
216C2×C3×D5—216no—
217C2×C3×D5C2×C22⋊C412yes—
218C2×C3×D5C2×C22⋊C412yes—
219C2×C3×D5C2×M1614yes—
220C2×C3×D5C2×M1614yescomplemented
221C3×C4×C5—22no—
222C3×C4×C5C2×C22⋊C412yes—
223C3×C4×C5C2×C22⋊C412yes—
224C3×Dic5—22no—
225C3×Dic5C2×C22⋊C412yes—
226C3×Dic5C22×D412yes—
227C24×C3—52no—
228C24×C3—51no—
229C24×C3—52no—
230C24×C3—51no—
231C24×C3—108no—
232C24×C3—104no—
233C24×C3C2×AGL(1,𝔽5)11yescharacteristic
234C22×C3×C4—24no—
235C22×C3×C4—51no—
236C22×C3×C4—58no—
237C22×C3×C4—51no—
238C22×C3×C4—51no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—51no—
244C22×C3×C4—52no—
245C22×C3×C4—52no—
246C22×C3×C4—52no—
247C22×C3×C4—52no—
248C22×C3×C4—52no—
249C22×C3×C4—52no—
250C22×C3×C4—104no—
251C22×C3×C4—108no—
252C22×C3×C4—108no—
253C22×C3×C4—108no—
254C22×C3×C4—108no—
255C22×C3×C4—104no—
256C22×C3×C4—104no—
257C22×C3×C4—104no—
258C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
259C22×C3×C4C2×AGL(1,𝔽5)12yes—
260C22×C3×C4C2×AGL(1,𝔽5)12yes—
261C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
262C3×M16—108no—
263C3×M16—108no—
264C2×C3×C8—58no—
265C2×C3×C8—108no—
266C23×C5—22no—
267C23×C5—24no—
268C23×C5C22×C3×C411yescharacteristic
269C23×C5C22×C3×C412yes—
270C22×D5—232no—
271C22×D5—22no—
272C22×D5—24no—
273C22×D5—24no—
274C22×D5—24no—
275C22×D5—24no—
276C22×D5—24no—
277C22×D5—24no—
278C22×D5—24no—
279C22×D5C3×C22⋊C414yes—
280C22×D5C3×M1618yescomplemented
281C22×D5C22×C3×C411yescharacteristic
282C22×D5C22×C3×C412yes—
283C22×D5C22×C3×C411yescharacteristic
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5C3×C22⋊C414yes—
288C2×C4×C5C22×C3×C412yes—
289C2×C4×C5C22×C3×C411yescharacteristic
290C2×C4×C5C22×C3×C411yescharacteristic
291C2×Dic5—22no—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5C22×C3×C412yes—
295C2×Dic5C22×C3×C411yescharacteristic
296C2×Dic5C2×C3×D414yes—
297C2×Dic5C24×C311yescharacteristic
298C4×D5—24no—
299C4×D5—24no—
300C4×D5—24no—
301C4×D5—24no—
302C4×D5—24no—
303C4×D5—24no—
304C4×D5C3×C22⋊C414yes—
305C4×D5C3×C22⋊C414yes—
306C4×D5C2×C3×D414yes—
307C4×D5C2×C3×D414yes—
308#170—28no—
309C25—51no—
310C23×C4—51no—
311C23×C4—51no—
312C23×C4—52no—
313C23×C4—52no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4—52no—
317C23×C4—51no—
318C23×C4—52no—
319C23×C4—108no—
320C23×C4C3×AGL(1,𝔽5)11yescharacteristic
321C2×M16—54no—
322C2×M16—54no—
323C2×M16—108no—
324C22×C8—54no—
325C22⋊C8—58no—
326C22⋊C8—58no—
327C2×C3×C5—22no—
328C2×C3×C5—24no—
329C2×C3×C5C22×C22⋊C411yescharacteristic
330C2×C3×C5C22×M1612yes—
331C3×D5—22no—
332C3×D5—24no—
333C3×D5#40714yescomplemented
334C23×C3—24no—
335C23×C3—22no—
336C23×C3—51no—
337C23×C3—58no—
338C23×C3—54no—
339C23×C3—52no—
340C23×C3—51no—
341C23×C3—104no—
342C23×C3—104no—
343C23×C3—104no—
344C23×C3—104no—
345C23×C3—104no—
346C23×C3—104no—
347C23×C3—1032no—
348C23×C3—104no—
349C23×C3—102no—
350C23×C3C22×AGL(1,𝔽5)12yes—
351C23×C3C22×AGL(1,𝔽5)11yescharacteristic
352C2×C3×C4—22no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—54no—
356C2×C3×C4—51no—
357C2×C3×C4—51no—
358C2×C3×C4—54no—
359C2×C3×C4—54no—
360C2×C3×C4—54no—
361C2×C3×C4—54no—
362C2×C3×C4—52no—
363C2×C3×C4—104no—
364C2×C3×C4—104no—
365C2×C3×C4—104no—
366C2×C3×C4—104no—
367C2×C3×C4—104no—
368C2×C3×C4—104no—
369C2×C3×C4—102no—
370C2×C3×C4—104no—
371C2×C3×C4—104no—
372C2×C3×C4C22⋊AGL(1,𝔽5)14yes—
373C2×C3×C4C22×AGL(1,𝔽5)12yes—
374C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
375C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
376C3×C8—108no—
377C22×C5—28no—
378C22×C5—22no—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5C2×C3×C22⋊C412yes—
382C22×C5C2×C3×M1614yescomplemented
383C22×C5C23×C3×C411yescharacteristic
384C2×D5—216no—
385C2×D5—28no—
386C2×D5—22no—
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—28no—
390C2×D5—216no—
391C2×D5C2×C3×C22⋊C412yes—
392C2×D5C2×C3×C22⋊C412yes—
393C2×D5C2×C3×M1614yes—
394C2×D5C2×C3×M1614yescomplemented
395C4×C5—22no—
396C4×C5C2×C3×C22⋊C412yes—
397C4×C5C2×C3×C22⋊C412yes—
398Dic5—22no—
399Dic5C2×C3×C22⋊C412yes—
400Dic5C22×C3×D412yes—
401C24—52no—
402C24—51no—
403C24—52no—
404C24—51no—
405C24—104no—
406C24—108no—
407C24C2×C3×AGL(1,𝔽5)11yescharacteristic
408C22×C4—24no—
409C22×C4—51no—
410C22×C4—58no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—52no—
416C22×C4—52no—
417C22×C4—51no—
418C22×C4—52no—
419C22×C4—52no—
420C22×C4—52no—
421C22×C4—52no—
422C22×C4—52no—
423C22×C4—52no—
424C22×C4—104no—
425C22×C4—108no—
426C22×C4—108no—
427C22×C4—108no—
428C22×C4—108no—
429C22×C4—104no—
430C22×C4—104no—
431C22×C4—104no—
432C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
433C22×C4C2×C3×AGL(1,𝔽5)12yes—
434C22×C4C2×C3×AGL(1,𝔽5)12yes—
435C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
436M16—108no—
437M16—108no—
438C2×C8—58no—
439C2×C8—108no—
440C3×C5C2×#40711yescharacteristic, complemented, Hall
441C22×C3—28no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—54no—
446C22×C3—52no—
447C22×C3—54no—
448C22×C3—52no—
449C22×C3—1016no—
450C22×C3—108no—
451C22×C3—1016no—
452C22×C3—108no—
453C22×C3—102no—
454C22×C3—102no—
455C22×C3—102no—
456C22×C3D5⋊M1614yescomplemented
457C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
458C22×C3C23×AGL(1,𝔽5)11yescharacteristic
459C3×C4—22no—
460C3×C4—52no—
461C3×C4—52no—
462C3×C4—102no—
463C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
464C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
465C2×C5—22no—
466C2×C5—24no—
467C2×C5C22×C3×C22⋊C411yescharacteristic
468C2×C5C22×C3×M1612yes—
469D5—22no—
470D5—24no—
471D5C3×#40714yescomplemented
472C23—24no—
473C23—22no—
474C23—51no—
475C23—58no—
476C23—54no—
477C23—52no—
478C23—51no—
479C23—104no—
480C23—104no—
481C23—104no—
482C23—104no—
483C23—104no—
484C23—104no—
485C23—1032no—
486C23—104no—
487C23—102no—
488C23C22×C3×AGL(1,𝔽5)12yes—
489C23C22×C3×AGL(1,𝔽5)11yescharacteristic
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—54no—
494C2×C4—51no—
495C2×C4—51no—
496C2×C4—54no—
497C2×C4—54no—
498C2×C4—54no—
499C2×C4—54no—
500C2×C4—52no—
501C2×C4—104no—
502C2×C4—104no—
503C2×C4—104no—
504C2×C4—104no—
505C2×C4—104no—
506C2×C4—104no—
507C2×C4—102no—
508C2×C4—104no—
509C2×C4—104no—
510C2×C4C3×C22⋊AGL(1,𝔽5)14yes—
511C2×C4C22×C3×AGL(1,𝔽5)12yes—
512C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
513C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
514C8—108no—
515C2×C3—24no—
516C2×C3—22no—
517C2×C3—54no—
518C2×C3—104no—
519C2×C3—102no—
520C2×C3C2×D5⋊M1612yes—
521C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
522C5C2×C3×#40711yescharacteristic, complemented, Sylow
523C22—28no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—54no—
528C22—52no—
529C22—54no—
530C22—52no—
531C22—1016no—
532C22—108no—
533C22—1016no—
534C22—108no—
535C22—102no—
536C22—102no—
537C22—102no—
538C22C3×D5⋊M1614yescomplemented
539C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
540C22C23×C3×AGL(1,𝔽5)11yescharacteristic
541C4—22no—
542C4—52no—
543C4—52no—
544C4—102no—
545C4C2×C3×C22⋊AGL(1,𝔽5)12yes—
546C4C2×C3×C22⋊AGL(1,𝔽5)12yes—
547C3D5⋊#40711yescharacteristic, direct product factor, Sylow
548C2—24no—
549C2—22no—
550C2—54no—
551C2—104no—
552C2—102no—
553C2C2×C3×D5⋊M1612yes—
554C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C23×C4
prime radicalC24×C3×D5C4
cosocleC2×Dic5C24×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C2×C3×#407
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5⋊M16C2semidirect
3. C3×#65798C2semidirect
4. C3×#65756C2semidirect
5. C3×#65755C2semidirect
6. C3×D5⋊(C22⋊C8)C2semidirect
7. D5⋊#407C3direct (N × H)
20. C2×C3×#704C22semidirect
22. C2×C3×#700C22semidirect
23. C2×C3×D5⋊C8C22semidirect
24. C3×C22⋊#170C22semidirect
25. C3×#4003C22semidirect
28. C2×D5⋊M16C2×C3semidirect
29. #65798C2×C3semidirect
30. #65756C2×C3semidirect
31. #65755C2×C3semidirect
32. D5⋊(C22⋊C8)C2×C3semidirect
69. C2×C3×#170C23semidirect
90. C2×#704C22×C3semidirect
92. C2×#700C22×C3semidirect
93. C2×D5⋊C8C22×C3semidirect
94. C22⋊#170C22×C3semidirect
95. #4003C22×C3semidirect
111. C22×C3×D5M16semidirect
194. C2×#170C23×C3semidirect
208. C22×C3×C5C2×M16semidirect
220. C2×C3×D5C2×M16semidirect
280. C22×D5C3×M16semidirect
333. C3×D5#407semidirect
382. C22×C5C2×C3×M16semidirect
394. C2×D5C2×C3×M16semidirect
440. C3×C5C2×#407semidirect
456. C22×C3D5⋊M16semidirect
471. D5C3×#407semidirect
522. C5C2×C3×#407semidirect
538. C22C3×D5⋊M16semidirect
547. C3D5⋊#407direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C2×C3×D5⋊M162
C3×#657982
C3×#657562
C3×#657552
C3×D5⋊(C22⋊C8)2
D5⋊#4073
C2×C3×#4075