Finite Group Databasebeta

← C2×D3×#4005 #14412089

Subgroups — C2×D3×#4005 #14412089

Order 1920.

1472 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
1C22×D3×Dic10C211yesmaximal, characteristic
2C2×D3×#704C212yesmaximal
3C2×#91234C211yesmaximal, characteristic, complemented
4C2×C3×#4005C211yesmaximal, characteristic, complemented
5C2×#91175C212yesmaximal, complemented
6D3×#4005C218yesmaximal, direct product factor
7C22×#4005—31nomaximal, Hall
8C22×Dic30C411yescharacteristic
9C22×C4×C5×D3C411yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×#1204C411yescharacteristic
12C22×#1204C2211yescharacteristic
13C22×D3×Dic5C411yescharacteristic
14C22×D3×Dic5C2211yescharacteristic
15C2×D3×Dic10—22no—
16C2×D3×Dic10—24no—
17C2×D3×Dic10—22no—
18C2×D3×Dic10C414yes—
19C2×D3×Dic10C2214yes—
20C2×#6762C2212yes—
21C2×C3×#704C2212yes—
22C2×#6739—22no—
23D3×#704—24no—
24D3×#704C2218yes—
25C2×D3×#170—22no—
26#91234C2214yescomplemented
27C3×#4005C2214yescomplemented
28#91175C2218yescomplemented
29C2×D3×#101—51nomaximal, Hall
30C23×Dic10—31no—
31C22×#704—32no—
32C2×#4005—38no—
33C2×#4005—31no—
34C2×#4005—32no—
35C2×#4005D311yescharacteristic, direct product factor
36C23×C5×D3C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C2×Dic30—22no—
41C2×Dic30—22no—
42C2×Dic30C2×C414yes—
43C22×C5×Dic3C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3—22no—
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3C2×C414yes—
48C22×C3×Dic5C2×C411yescharacteristic
49C22×C3×Dic5C2311yescharacteristic
50C2×C3×Dic10—22no—
51C2×C3×Dic10—22no—
52C2×C3×Dic10C2×C412yes—
53C2×C3×Dic10C2312yes—
54C2×#1204—22no—
55C2×#1204—22no—
56C2×#1204—22no—
57C2×#1204—22no—
58C2×#1204C2×C412yes—
59C2×#1204C2×C414yes—
60C2×#1204C2312yes—
61C2×D3×Dic5—21no—
62C2×D3×Dic5—22no—
63C2×D3×Dic5—21no—
64C2×D3×Dic5C2×C414yes—
65C2×D3×Dic5C2×C412yes—
66C2×D3×Dic5D412yes—
67C2×D3×Dic5D414yes—
68C2×D3×Dic5D412yes—
69C2×D3×Dic5C2312yes—
70D3×Dic10—28no—
71D3×Dic10—28no—
72D3×Dic10—28no—
73D3×Dic10—28no—
74#6762—22no—
75#6762C2314yes—
76C2×C3⋊#170—22no—
77C3×#704—22no—
78C3×#704C2314yes—
79C2×C3×#170—22no—
80#6739—28no—
81D3×#170—28no—
82C22×D3×Q8—51no—
83C2×D3×M16—52no—
84C2×C3×#101—51no—
85C2×#836—51no—
86C2×#824—52no—
87D3×#101—58no—
88C23×C4×C5—31no—
89C23×Dic5—31no—
90C23×Dic5—31no—
91C22×Dic10—31no—
92C22×Dic10—31no—
93C22×Dic10—31no—
94C22×Dic10—34no—
95C22×Dic10—34no—
96C22×Dic10—62no—
97C22×Dic10—62no—
98C22×Dic10—64no—
99C22×Dic10C2×D311yescharacteristic
100C2×#704—32no—
101C2×#704—38no—
102C2×#704—62no—
103C2×#704—64no—
104C2×#704C2×D312yes—
105C22×#170—62no—
106#4005—34no—
107#4005—38no—
108#4005C2×D314yesdirect product factor
109C22×#101—151noSylow
110C23×C3×C5C22×C411yescharacteristic
111C22×C5×D3—24no—
112C22×C5×D3C22⋊C411yescharacteristic
113C22×C5×D3C22⋊C412yes—
114C22×C5×D3C22⋊C411yescharacteristic
115C22×C5×D3C22×C412yes—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5C22×C412yes—
119C2×Dic15—21no—
120C2×Dic15—21no—
121C2×Dic15C22⋊C412yes—
122C2×Dic15C22⋊C412yes—
123C2×Dic15C22×C412yes—
124C2×Dic15C22×C412yes—
125Dic30—28no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3C22×C412yes—
129C4×C5×D3—24no—
130C4×C5×D3—24no—
131C2×C3×Dic5—21no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5C22×C412yes—
134C2×C3×Dic5C22×C411yescharacteristic
135C2×C3×Dic5C2×D412yes—
136C2×C3×Dic5C2×D412yes—
137C2×C3×Dic5C2411yescharacteristic
138C3×Dic10—24no—
139C3×Dic10—24no—
140#1204—28no—
141#1204—24no—
142#1204—24no—
143D3×Dic5—24no—
144D3×Dic5—24no—
145D3×Dic5C22⋊C414yes—
146D3×Dic5C22⋊C414yes—
147D3×Dic5C2×D414yes—
148D3×Dic5C2×D414yes—
149C3⋊#170—24no—
150C3×#170—24no—
151C22×C3×Q8—51no—
152C2×D3×Q8—54no—
153C2×D3×Q8—54no—
154C2×D3×Q8—102no—
155C2×D3×Q8—102no—
156C2×D3×Q8—104no—
157C22×C4×D3—51no—
158C22×C4×D3—51no—
159C22×C4×D3AGL(1,𝔽5)11yescharacteristic
160C22×Dic6—51no—
161C22×Dic6—51no—
162C22×Dic6—51no—
163C2×C3×M16—52no—
164C2×#208—52no—
165D3×M16—58no—
166D3×M16—104no—
167C2×ΓL(1,𝔽25)—102no—
168C2×D3×C8—102no—
169C3×#101—54no—
170#836—54no—
171#824—58no—
172C24×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—34no—
175C22×C4×C5—61no—
176C22×C4×C5—62no—
177C22×C4×C5—61no—
178C22×C4×C5C4×D311yescharacteristic
179C22×Dic5—31no—
180C22×Dic5—32no—
181C22×Dic5—32no—
182C22×Dic5—34no—
183C22×Dic5—32no—
184C22×Dic5—32no—
185C22×Dic5—31no—
186C22×Dic5—34no—
187C22×Dic5—61no—
188C22×Dic5—62no—
189C22×Dic5—61no—
190C22×Dic5C4×D311yescharacteristic
191C22×Dic5C22×D311yescharacteristic
192C2×Dic10—22no—
193C2×Dic10—22no—
194C2×Dic10—34no—
195C2×Dic10—34no—
196C2×Dic10—32no—
197C2×Dic10—32no—
198C2×Dic10—68no—
199C2×Dic10—68no—
200C2×Dic10—68no—
201C2×Dic10—68no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C2×Dic10—62no—
205C2×Dic10—62no—
206C2×Dic10—62no—
207C2×Dic10—62no—
208C2×Dic10C4×D312yes—
209C2×Dic10C22×D312yes—
210#704—22no—
211#704—34no—
212#704—68no—
213#704—62no—
214#704C22×D314yes—
215C2×#170—22no—
216C2×#170—68no—
217C2×#170—62no—
218C23×Q8—151no—
219C22×M16—152no—
220C2×#101—51no—
221C2×#101—158no—
222C2×#101—152no—
223C2×#101—151no—
224C22×C3×C5—22no—
225C22×C3×C5C2×C22⋊C411yescharacteristic
226C22×C3×C5C2×C22⋊C411yescharacteristic
227C22×C3×C5C23×C411yescharacteristic
228C2×C5×D3—22no—
229C2×C5×D3—24no—
230C2×C5×D3—24no—
231C2×C5×D3#10114yescomplemented
232C2×C5×D3C2×C22⋊C412yes—
233C2×C5×D3C2×C22⋊C412yes—
234C3×C4×C5—22no—
235Dic15—22no—
236Dic15C2×C22⋊C414yes—
237C3×Dic5—22no—
238C3×Dic5C2×C22⋊C412yes—
239C3×Dic5C22×D412yes—
240C5×Dic3—22no—
241C23×D3C2×AGL(1,𝔽5)11yescharacteristic
242C2×C3×Q8—52no—
243C2×C3×Q8—52no—
244C2×C3×Q8—102no—
245C2×C3×Q8—102no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
249C22×Dic3—51no—
250C22×Dic3—51no—
251C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
252D3×Q8—108no—
253D3×Q8—108no—
254D3×Q8—108no—
255D3×Q8—108no—
256C2×C4×D3—22no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—52no—
260C2×C4×D3—52no—
261C2×C4×D3—54no—
262C2×C4×D3—52no—
263C2×C4×D3—52no—
264C2×C4×D3—54no—
265C2×C4×D3—102no—
266C2×C4×D3—101no—
267C2×C4×D3—101no—
268C2×C4×D3C2×AGL(1,𝔽5)14yes—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—54no—
272C2×Dic6—52no—
273C2×Dic6—102no—
274C2×Dic6—102no—
275C2×Dic6—102no—
276C2×Dic6—102no—
277C2×Dic6—102no—
278C2×Dic6—102no—
279C3×M16—54no—
280C3×M16—102no—
281C2×C3×C8—102no—
282#208—54no—
283#208—102no—
284C2×C3⋊C8—102no—
285ΓL(1,𝔽25)—108no—
286D3×C8—108no—
287C23×C5—31no—
288C23×C5—32no—
289C23×C5—31no—
290C23×C5—32no—
291C23×C5—64no—
292C23×C5C2×C4×D311yescharacteristic
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—32no—
296C2×C4×C5—64no—
297C2×C4×C5—64no—
298C2×C4×C5—61no—
299C2×C4×C5—61no—
300C2×C4×C5C2×C4×D312yes—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—32no—
304C2×Dic5—32no—
305C2×Dic5—32no—
306C2×Dic5—34no—
307C2×Dic5—34no—
308C2×Dic5—34no—
309C2×Dic5—34no—
310C2×Dic5—32no—
311C2×Dic5—64no—
312C2×Dic5—64no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315C2×Dic5C2×C4×D312yes—
316C2×Dic5C2×C4×D311yescharacteristic
317C2×Dic5D3×D412yes—
318C2×Dic5D3×D412yes—
319C2×Dic5C23×D311yescharacteristic
320Dic10—24no—
321Dic10—24no—
322Dic10—68no—
323Dic10—68no—
324Dic10—64no—
325Dic10—64no—
326#170—24no—
327#170—64no—
328C22×Q8—51no—
329C22×Q8—151no—
330C22×Q8—151no—
331C22×Q8—154no—
332C22×Q8—154no—
333C22×Q8—151no—
334C22×Q8—302no—
335C22×Q8—304no—
336C22×Q8—302no—
337C23×C4—31no—
338C23×C4—151no—
339C23×C4—151no—
340C2×M16—52no—
341C2×M16—158no—
342C2×M16—152no—
343C2×M16—302no—
344C2×M16—304no—
345C22×C8—302no—
346#101—54no—
347#101—158no—
348#101—154no—
349C2×C3×C5—21no—
350C2×C3×C5—21no—
351C2×C3×C5C2×#10112yescomplemented
352C2×C3×C5C22×C22⋊C411yescharacteristic
353C5×D3—22no—
354C5×D3C2×#10114yescomplemented
355C23×C3C22×AGL(1,𝔽5)11yescharacteristic
356C22×D3—24no—
357C22×D3C22⋊AGL(1,𝔽5)12yes—
358C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
359C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
360C22×D3C22×AGL(1,𝔽5)12yes—
361C3×Q8—104no—
362C3×Q8—104no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—52no—
366C2×C3×C4—52no—
367C2×C3×C4—51no—
368C2×C3×C4—51no—
369C2×C3×C4—52no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4C22×AGL(1,𝔽5)12yes—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—52no—
376C2×Dic3—52no—
377C2×Dic3—52no—
378C2×Dic3—52no—
379C2×Dic3—101no—
380C2×Dic3—101no—
381C2×Dic3C22×AGL(1,𝔽5)12yes—
382C4×D3—24no—
383C4×D3—24no—
384C4×D3—54no—
385C4×D3—54no—
386C4×D3—54no—
387C4×D3—54no—
388C4×D3—104no—
389C4×D3—104no—
390Dic6—108no—
391Dic6—104no—
392Dic6—104no—
393Dic6—108no—
394C3×C8—104no—
395C3⋊C8—104no—
396C22×C5—22no—
397C22×C5—32no—
398C22×C5—34no—
399C22×C5—32no—
400C22×C5—64no—
401C22×C5—64no—
402C22×C5—62no—
403C22×C5D3×C22⋊C411yescharacteristic
404C22×C5D3×C22⋊C411yescharacteristic
405C22×C5C22×C4×D311yescharacteristic
406C4×C5—22no—
407C4×C5—62no—
408Dic5—22no—
409Dic5—34no—
410Dic5—62no—
411Dic5D3×C22⋊C412yes—
412Dic5C2×D3×D412yes—
413C24—31no—
414C2×Q8—52no—
415C2×Q8—52no—
416C2×Q8—102no—
417C2×Q8—102no—
418C2×Q8—152no—
419C2×Q8—152no—
420C2×Q8—154no—
421C2×Q8—154no—
422C2×Q8—302no—
423C2×Q8—302no—
424C2×Q8—302no—
425C2×Q8—302no—
426C2×Q8—302no—
427C2×Q8—302no—
428C2×Q8—308no—
429C2×Q8—308no—
430C2×Q8—308no—
431C2×Q8—308no—
432C22×C4—31no—
433C22×C4—34no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—62no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—152no—
440C22×C4—152no—
441C22×C4—154no—
442C22×C4—152no—
443C22×C4—152no—
444C22×C4—154no—
445C22×C4—151no—
446C22×C4—151no—
447C22×C4—302no—
448C22×C4—301no—
449C22×C4—301no—
450C22×C4D3×AGL(1,𝔽5)11yescharacteristic
451M16—54no—
452M16—102no—
453M16—154no—
454M16—308no—
455M16—302no—
456C2×C8—102no—
457C2×C8—308no—
458C2×C8—302no—
459C3×C5C22×#10111yescharacteristic, complemented, Hall
460C22×C3—22no—
461C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
462C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
463C22×C3C23×AGL(1,𝔽5)11yescharacteristic
464C2×D3—22no—
465C2×D3—24no—
466C2×D3—24no—
467C2×D3#400514yesdirect product factor
468C2×D3C2×C22⋊AGL(1,𝔽5)12yes—
469C2×D3C2×C22⋊AGL(1,𝔽5)12yes—
470C3×C4—22no—
471C3×C4—52no—
472C3×C4—52no—
473C3×C4—102no—
474Dic3—22no—
475Dic3—54no—
476Dic3—102no—
477C2×C5—21no—
478C2×C5—21no—
479C2×C5—34no—
480C2×C5—62no—
481C2×C5D3×#10112yescomplemented
482C2×C5C2×D3×C22⋊C411yescharacteristic
483C23—31no—
484C23—32no—
485C23—31no—
486C23—32no—
487C23—64no—
488C23C2×D3×AGL(1,𝔽5)11yescharacteristic
489Q8—104no—
490Q8—104no—
491Q8—308no—
492Q8—304no—
493Q8—304no—
494Q8—308no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—32no—
498C2×C4—52no—
499C2×C4—52no—
500C2×C4—51no—
501C2×C4—51no—
502C2×C4—52no—
503C2×C4—64no—
504C2×C4—64no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—101no—
508C2×C4—101no—
509C2×C4—154no—
510C2×C4—154no—
511C2×C4—154no—
512C2×C4—154no—
513C2×C4—152no—
514C2×C4—152no—
515C2×C4—152no—
516C2×C4—152no—
517C2×C4—304no—
518C2×C4—304no—
519C2×C4—301no—
520C2×C4—301no—
521C2×C4C2×D3×AGL(1,𝔽5)12yes—
522C8—104no—
523C8—304no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3C2×#400512yescomplemented
527C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
528D3—22no—
529D3C2×#400514yesdirect product factor
530C5C2×D3×#10111yescharacteristic, complemented, Sylow
531C22—22no—
532C22—32no—
533C22—34no—
534C22—32no—
535C22—64no—
536C22—64no—
537C22—62no—
538C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
539C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
540C22C22×D3×AGL(1,𝔽5)11yescharacteristic
541C4—22no—
542C4—52no—
543C4—52no—
544C4—62no—
545C4—102no—
546C4—154no—
547C4—302no—
548C3C22×#400511yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—34no—
552C2—62no—
553C2D3×#400512yesdirect product factor
554C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C22×#101
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#91234C2semidirect
4. C2×C3×#4005C2semidirect
5. C2×#91175C2semidirect
6. D3×#4005C2direct (N × H)
26. #91234C22semidirect
27. C3×#4005C22semidirect
28. #91175C22semidirect
35. C2×#4005D3direct (N × H)
108. #4005C2×D3direct (N × H)
231. C2×C5×D3#101semidirect
351. C2×C3×C5C2×#101semidirect
354. C5×D3C2×#101semidirect
459. C3×C5C22×#101semidirect
467. C2×D3#4005direct (N × H)
481. C2×C5D3×#101semidirect
526. C2×C3C2×#4005semidirect
529. D3C2×#4005direct (N × H)
530. C5C2×D3×#101semidirect
548. C3C22×#4005semidirect
553. C2D3×#4005direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C2×D3×#7042
C2×#912342
C2×C3×#40052
C2×#911752
D3×#40052
C22×#40053
C2×D3×#1015