Finite Group Databasebeta

← C2×#11752585 #14484050

Subgroups — C2×#11752585 #14484050

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C5×#875C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×Dic5×D12C211yesmaximal, characteristic
5C2×#91410C212yesmaximal, complemented
6C2×#91400C212yesmaximal, complemented
7C2×#91376C211yesmaximal, characteristic, complemented
8C2×#91373C211yesmaximal, characteristic
9C2×#91367C212yesmaximal, complemented
10C2×#91341C212yesmaximal, complemented
11C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
12#11752585C2116yesmaximal, direct product factor
13C2×#66005—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2212yes—
22C2×C4×Dic15C2212yes—
23C4×Dic30C2218yescomplemented
24C2×C5×(C2×D3)⋊C4C2212yes—
25C2×C5×(C2×D3)⋊C4C2212yes—
26C5×#875C2218yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×C4×Dic10C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×#6668C2212yes—
35C2×#6668C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40Dic5×D12C2218yes—
41#91410C22116yescomplemented
42#91400C22116yescomplemented
43#91376C2218yescomplemented
44#91373C2218yes—
45#91367C22116yescomplemented
46#91341C22116yescomplemented
47Dic5×Dic6C2218yescomplemented
48C2×#5584—51nomaximal, Hall
49C2×C5×#124—31no—
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4082—31no—
53C2×D4×Dic5—31no—
54#66005—316no—
55C2×#4025—32no—
56C2×#4025—32no—
57C2×#4024—32no—
58C2×#4023—32no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×C5×D3C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C2×Dic30—24no—
68C2×Dic30C2314yes—
69C22×C5×Dic3C2312yes—
70C2×C5×D12—24no—
71C2×C5×D12C2314yes—
72C2×C5×Dic6—24no—
73C2×C5×Dic6C2314yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5C2318yes—
82C3×C42×C5C2314yes—
83C4⋊Dic15C2314yes—
84#6712C2318yes—
85C4×Dic15C2318yes—
86C5×(C2×D3)⋊C4C2318yes—
87C5×(C2×D3)⋊C4C2318yes—
88C3×C4⋊Dic5C2314yes—
89C3×#683C2314yes—
90C3×#683C2314yes—
91C3×C4×Dic5C2314yes—
92C3×C4×Dic5C2314yes—
93Dic3⋊Dic5C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96(C2×D3)⋊Dic5C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4×Q8—51no—
101C2×#946—52no—
102#5584—516no—
103C2×#898—52no—
104C2×#898—52no—
105C2×#892—52no—
106C2×#875—51no—
107C2×#875D511yescharacteristic
108C2×C4×D12—51no—
109C2×#869—51no—
110C2×C4×Dic6—51no—
111C2×C4×Dic6—51no—
112C22×C5×Q8—31no—
113C22×C5×D4—31no—
114C23×Dic5—32no—
115C22×Dic10—31no—
116C22×Dic10C2×D311yescharacteristic
117C5×#124—38no—
118C2×C5×C22⋊C4—32no—
119C2×C5×C22⋊C4—32no—
120C2×C42×C5C2×D311yescharacteristic
121C2×C22⋊Dic5—32no—
122C2×C22⋊Dic5—32no—
123C2×C22⋊Dic5—32no—
124Q8×Dic5—38no—
125#4090—38no—
126#4082—38no—
127D4×Dic5—38no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×#683—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683C2×D311yescharacteristic
135C2×#683C2×D311yescharacteristic
136C2×C4×Dic5—32no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5C2×D311yescharacteristic
139C2×C4×Dic5C2×D311yescharacteristic
140#4025—316no—
141#4025—316no—
142#4024—316no—
143#4023—316no—
144C4×Dic10—38no—
145C4×Dic10C2×D318yescomplemented
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C5×D3—24no—
149C22×C5×D3—24no—
150C22×C5×D3—24no—
151C22×C5×D3C2414yes—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2412yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×Dic15—24no—
159C2×Dic15—24no—
160C2×Dic15C2414yes—
161C2×Dic15C2414yes—
162Dic30—28no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3C2414yes—
165C5×D12—28no—
166C5×Dic6—28no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5#4114yes—
171C2×C3×Dic5C2412yes—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2412yes—
175C3×Dic10—28no—
176D3×Dic5—216no—
177C22×C3×Q8—51no—
178C22×D12C2×D511yescharacteristic
179C22×C4×D3—52no—
180C22×Dic6—51no—
181C22×Dic6C2×D511yescharacteristic
182C3×C4×Q8—58no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C4⋊C4—51no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C42—51no—
187C2×C3×C42—51no—
188C2×C3×C42C2×D511yescharacteristic
189#946—516no—
190C2×(C2×D3)⋊C4—52no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×(C2×D3)⋊C4C2×D512yes—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—52no—
201C2×C4×Dic3—52no—
202#898—516no—
203#898—516no—
204#892—516no—
205#875—58no—
206#875C2×D518yes—
207C4×D12—58no—
208#869—58no—
209C4×Dic6—58no—
210C4×Dic6—58no—
211C24×C5—32no—
212C2×C5×Q8—34no—
213C2×C5×Q8—64no—
214C2×C5×D4—34no—
215C2×C5×D4—64no—
216C22×C4×C5—32no—
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—32no—
221C22×Dic5—32no—
222C22×Dic5—38no—
223C22×Dic5—68no—
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D311yescharacteristic
226C22×Dic5C22×D311yescharacteristic
227C22×Dic5C22×D311yescharacteristic
228C2×Dic10—24no—
229C2×Dic10—34no—
230C2×Dic10—64no—
231C2×Dic10C22×D314yes—
232C5×C22⋊C4—38no—
233C5×C22⋊C4—38no—
234C42×C5C22×D314yes—
235C22⋊Dic5—38no—
236C22⋊Dic5—38no—
237C22⋊Dic5—38no—
238C4⋊Dic5—34no—
239C4⋊Dic5—38no—
240C4⋊Dic5C22×D314yes—
241#683—38no—
242#683—38no—
243#683—38no—
244#683C22×D314yes—
245#683C22×D314yes—
246C4×Dic5—38no—
247C4×Dic5—38no—
248C4×Dic5C22×D314yes—
249C4×Dic5C22×D314yes—
250#556—1516no—
251C2×C4⋊Q8—151no—
252C2×#126—152no—
253C2×#126—152no—
254C2×#124—31no—
255C2×#124—151no—
256C2×C22⋊Q8—152no—
257C2×C4×Q8—51no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C22×C3×C5C2×#4112yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C52−1+412yes—
265C22×C3×C5C2511yescharacteristic
266C2×C5×D3—24no—
267C2×C5×D3—24no—
268C2×C5×D3—24no—
269C2×C5×D3—48no—
270C3×C4×C5—22no—
271C3×C4×C5—22no—
272C3×C4×C5C2×#4114yes—
273Dic15—24no—
274Dic15—24no—
275C3×Dic5—22no—
276C3×Dic5—22no—
277C3×Dic5—22no—
278C3×Dic5C2×#4114yes—
279C5×Dic3—24no—
280C23×D3C22×D512yes—
281C2×C3×Q8—54no—
282C2×C3×Q8—104no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×C3×C4C22×D511yescharacteristic
290C22×Dic3—52no—
291C22×Dic3—52no—
292C22×Dic3C22×D512yes—
293C2×D12—24no—
294C2×D12C22×D514yes—
295C2×C4×D3—58no—
296C2×C4×D3—108no—
297C2×Dic6—24no—
298C2×Dic6—54no—
299C2×Dic6—104no—
300C2×Dic6C22×D514yes—
301C3×C4⋊C4—54no—
302C3×C4⋊C4—54no—
303C3×C4⋊C4—54no—
304C3×C42—54no—
305C3×C42—54no—
306C3×C42C22×D514yes—
307(C2×D3)⋊C4—58no—
308(C2×D3)⋊C4—58no—
309(C2×D3)⋊C4—58no—
310(C2×D3)⋊C4C22×D518yes—
311(C2×D3)⋊C4C22×D518yes—
312C4⋊Dic3—54no—
313C4⋊Dic3—58no—
314C4⋊Dic3—58no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317C4×Dic3—58no—
318C4×Dic3—58no—
319C23×C5—34no—
320C23×C5—64no—
321C23×C5—64no—
322C23×C5—64no—
323C23×C5C23×D311yescharacteristic
324C5×Q8—68no—
325C5×D4—68no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—34no—
329C2×C4×C5—64no—
330C2×C4×C5#23914yes—
331C2×C4×C5C23×D312yes—
332C2×C4×C5C23×D312yes—
333C2×C4×C5C23×D312yes—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—34no—
338C2×Dic5—34no—
339C2×Dic5—64no—
340C2×Dic5—64no—
341C2×Dic5—616no—
342C2×Dic5#23514yes—
343C2×Dic5C23×D312yes—
344C2×Dic5C23×D312yes—
345C2×Dic5C23×D312yes—
346C2×Dic5C23×D312yes—
347Dic10—28no—
348Dic10—68no—
349C22×Q8—31no—
350C22×Q8—51no—
351C22×Q8—151no—
352C22×D4—31no—
353C23×C4—152no—
354C4⋊Q8—158no—
355#126—1516no—
356#126—1516no—
357#124—38no—
358#124—158no—
359C22⋊Q8—1516no—
360C4×Q8—58no—
361C4×Q8—158no—
362C4×Q8—158no—
363C4×D4—158no—
364#117—1516no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—152no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—152no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C22⋊C4—152no—
378C2×C42—51no—
379C2×C42—51no—
380C2×C42—152no—
381C2×C42—152no—
382C2×C42D3×D511yescharacteristic
383C2×C3×C5#55614yescomplemented
384C2×C3×C5C22×#4111yescharacteristic
385C2×C3×C5C22×#4111yescharacteristic
386C2×C3×C5C2×2−1+411yescharacteristic
387C5×D3—44no—
388C23×C3C23×D511yescharacteristic
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3C23×D514yes—
393C3×Q8—108no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—54no—
397C2×C3×C4—52no—
398C2×C3×C4—52no—
399C2×C3×C4—52no—
400C2×C3×C4—52no—
401C2×C3×C4—102no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4#71114yes—
405C2×C3×C4C23×D512yes—
406C2×C3×C4C23×D512yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—24no—
409C2×Dic3—54no—
410C2×Dic3—54no—
411C2×Dic3—104no—
412C2×Dic3—104no—
413C2×Dic3C23×D514yes—
414D12—28no—
415C4×D3—1016no—
416Dic6—28no—
417Dic6—108no—
418C22×C5—64no—
419C22×C5—64no—
420C22×C5—64no—
421C22×C5—128no—
422C22×C5C2×#23512yes—
423C22×C5C2×#23912yes—
424C22×C5#101012yes—
425C22×C5C24×D311yescharacteristic
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—64no—
429C4×C5C2×#23914yes—
430Dic5—22no—
431Dic5—22no—
432Dic5—22no—
433Dic5—64no—
434Dic5—64no—
435Dic5C2×#23514yes—
436C24—32no—
437C2×Q8—34no—
438C2×Q8—54no—
439C2×Q8—64no—
440C2×Q8—104no—
441C2×Q8—154no—
442C2×Q8—304no—
443C2×D4—34no—
444C2×D4—64no—
445C22×C4—32no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—158no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—308no—
454C22×C4C2×D3×D511yescharacteristic
455C22×C4C2×D3×D511yescharacteristic
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—54no—
458C4⋊C4—54no—
459C4⋊C4—54no—
460C4⋊C4—158no—
461C4⋊C4—158no—
462C4⋊C4—158no—
463C4⋊C4—154no—
464C4⋊C4—158no—
465C22⋊C4—38no—
466C22⋊C4—38no—
467C22⋊C4—158no—
468C22⋊C4—158no—
469C22⋊C4—158no—
470C42—54no—
471C42—54no—
472C42—158no—
473C42—158no—
474C42C2×D3×D514yes—
475C3×C5C2×#55611yescharacteristic, complemented, Hall
476C22×C3C2×#71112yes—
477C22×C3D5×#4112yes—
478C22×C3#415012yes—
479C22×C3C24×D511yescharacteristic
480C2×D3—24no—
481C2×D3—24no—
482C2×D3—24no—
483C2×D3—48no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—54no—
487C3×C4—102no—
488C3×C4—102no—
489C3×C4—102no—
490C3×C4C2×#71114yes—
491Dic3—24no—
492Dic3—104no—
493Dic3—104no—
494C2×C5—124no—
495C2×C5#558414yescomplemented
496C2×C5C22×#23511yescharacteristic
497C2×C5C22×#23911yescharacteristic
498C2×C5C2×#101011yescharacteristic
499C23—34no—
500C23—64no—
501C23—64no—
502C23—64no—
503C23C22×D3×D511yescharacteristic
504Q8—68no—
505Q8—108no—
506Q8—308no—
507D4—68no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—34no—
511C2×C4—54no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—52no—
515C2×C4—52no—
516C2×C4—64no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—154no—
521C2×C4—154no—
522C2×C4—3016no—
523C2×C4—304no—
524C2×C4—304no—
525C2×C4#676814yes—
526C2×C4C22×D3×D512yes—
527C2×C4C22×D3×D512yes—
528C2×C4C22×D3×D512yes—
529C2×C3#6600514yescomplemented
530C2×C3C22×#71111yescharacteristic
531C2×C3C2×D5×#4111yescharacteristic
532C2×C3C2×#415011yescharacteristic
533D3—44no—
534C5C2×#558411yescharacteristic, complemented, Sylow
535C22—64no—
536C22—64no—
537C22—64no—
538C22—128no—
539C22#9200112yes—
540C22C2×#676812yes—
541C22D5×#23512yes—
542C22C23×D3×D511yescharacteristic
543C4—22no—
544C4—22no—
545C4—54no—
546C4—64no—
547C4—102no—
548C4—102no—
549C4—102no—
550C4—304no—
551C4—304no—
552C4C2×#676814yes—
553C3C2×#6600511yescharacteristic, complemented, Sylow
554C2—124no—
555C2#1175258514yesdirect product factor
556C2C2×#9200111yescharacteristic
557C2C22×#676811yescharacteristic
558C2C2×D5×#23511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#556
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic30C2semidirect
3. C2×C3×C4×Dic10C2semidirect
5. C2×#91410C2semidirect
6. C2×#91400C2semidirect
7. C2×#91376C2semidirect
9. C2×#91367C2semidirect
10. C2×#91341C2semidirect
11. C2×Dic5×Dic6C2semidirect
12. #11752585C2direct (N × H)
23. C4×Dic30C22semidirect
32. C3×C4×Dic10C22semidirect
41. #91410C22semidirect
42. #91400C22semidirect
43. #91376C22semidirect
45. #91367C22semidirect
46. #91341C22semidirect
47. Dic5×Dic6C22semidirect
60. C2×C4×Dic10D3semidirect
145. C4×Dic10C2×D3semidirect
383. C2×C3×C5#556semidirect
475. C3×C5C2×#556semidirect
495. C2×C5#5584semidirect
529. C2×C3#66005semidirect
534. C5C2×#5584semidirect
553. C3C2×#66005semidirect
555. C2#11752585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C5×#8752
C2×C3×C4×Dic102
C2×Dic5×D122
C2×#914102
C2×#914002
C2×#913762
C2×#913732
C2×#913672
C2×#913412
C2×Dic5×Dic62
#117525852
C2×#660053
C2×#55845