Finite Group Databasebeta

← C2×#11754814 #14480093

Subgroups — C2×#11754814 #14480093

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#237C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91829C211yesmaximal, characteristic, complemented
4C2×C3×#4082C211yesmaximal, characteristic, complemented
5C2×#91558C214yesmaximal, complemented
6C2×#91556C214yesmaximal, complemented
7#11754814C2116yesmaximal, direct product factor
8C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
9C2×#91385C211yesmaximal, characteristic, complemented
10C2×#91375C211yesmaximal, characteristic, complemented
11C2×#66166—31nomaximal, Hall
12C22×C3×C5×D4C2211yescharacteristic
13C22×#1220C2214yes—
14C22×D60C2211yescharacteristic
15C22×C5×#67C2212yes—
16C23×C5×Dic3C2212yes—
17C2×C5×#237—28no—
18C2×C5×#237C2218yescomplemented
19C22×C4×C5×D3C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic
22C22×#1203C2212yes—
23C22×#1200C2212yes—
24C22×D3×Dic5C2212yes—
25C2×#6769—28no—
26C2×#6769C2218yescomplemented
27#91829C2218yescomplemented
28C2×C4×Dic15C2211yescharacteristic
29C2×C3×C22⋊Dic5C2214yes—
30C3×#4082C2218yescomplemented
31C2×C3×C4×Dic5C2211yescharacteristic
32#91558C22132yescomplemented
33#91556C22132yescomplemented
34C2×#6669C2214yes—
35C2×#6667C2214yes—
36C2×Dic3×Dic5C2212yes—
37C4×D3×Dic5C2218yescomplemented
38#91385C2218yescomplemented
39#91375C2218yescomplemented
40C2×#5668—51nomaximal, Hall
41C22×C5×#41—31no—
42C22×#709—31no—
43#66166—316no—
44C2×#4093—31no—
45C2×#4090—31no—
46C2×#4086—31no—
47C2×#4085—34no—
48C2×#4082D311yescharacteristic, complemented
49C2×C4×C22⋊D5—34no—
50C22×C4×Dic5—31no—
51C24×C3×C5C2312yes—
52C23×D15C2312yes—
53C23×C5×D3C2311yescharacteristic
54C2×C3×C5×D4—24no—
55C2×C3×C5×D4C2314yes—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—216no—
58C2×#1220C23116yes—
59C22×Dic15C2312yes—
60C2×D60—24no—
61C2×D60C2314yes—
62C2×C5×#67—28no—
63C2×C5×#67C2318yes—
64C22×C5×Dic3—28no—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2318yes—
67C22×C5×Dic3C2311yescharacteristic
68C5×#237—232no—
69C2×C4×C5×D3D418yescomplemented
70C2×C4×C5×D3C2314yes—
71C2×C5×Dic6—24no—
72C2×C5×Dic6C2314yes—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2312yes—
75C2×C3×Dic10—24no—
76C2×C3×Dic10C2314yes—
77C2×#1203—28no—
78C2×#1203C2318yes—
79C2×#1200—28no—
80C2×#1200C2318yes—
81C2×D3×Dic5—28no—
82C2×D3×Dic5C2318yes—
83#6769—232no—
84C4×Dic15C2314yes—
85C3×C22⋊Dic5C23116yes—
86C3×C4×Dic5C2314yes—
87#6669C23116yes—
88#6667C23116yes—
89Dic3×Dic5C2318yes—
90C22×#239—51no—
91C22×#237D511yescharacteristic, complemented
92C2×C3×#124—51no—
93C2×#944—51no—
94C2×#940—51no—
95#5668—516no—
96C2×#884—54no—
97C2×#67⋊C4—54no—
98C2×#875—51no—
99C2×C42×D3—51no—
100C2×C5×#41—38no—
101C2×C5×#41—68no—
102C22×C5×Q8—31no—
103C22×C5×D4—32no—
104C22×C5×D4C2×D311yescharacteristic
105C23×C4×C5—31no—
106C23×C4×C5—32no—
107C22×C22⋊D5—34no—
108C22×C22⋊D5—32no—
109C23×Dic5—32no—
110C2×#709—38no—
111C2×#709—68no—
112C22×D20—31no—
113C22×C4×D5—32no—
114C22×Dic10C2×D311yescharacteristic
115C2×C22⋊Dic5C2×D314yes—
116#4093—38no—
117#4090—38no—
118#4086—38no—
119#4085—332no—
120#4082C2×D318yescomplemented
121C4×C22⋊D5—332no—
122C2×#685—34no—
123C2×#683—34no—
124C2×C4×Dic5—31no—
125C2×C4×Dic5—32no—
126C2×C4×Dic5—38no—
127C2×C4×Dic5C2×D311yescharacteristic
128C2×#532—151noSylow
129C23×C3×C5—24no—
130C23×C3×C5—28no—
131C23×C3×C5C2414yes—
132C23×C3×C5C2411yescharacteristic
133C22×D15—24no—
134C22×D15—28no—
135C22×D15C2414yes—
136C22×C5×D3—24no—
137C22×C5×D3C2×D414yes—
138C22×C5×D3C2412yes—
139C3×C5×D4—28no—
140C2×C3×C4×C5C2×D414yes—
141C2×C3×C4×C5C2412yes—
142#1220—232no—
143C2×Dic15#4118yescomplemented
144C2×Dic15C2414yes—
145D60—28no—
146C5×#67—216no—
147C2×C5×Dic3—24no—
148C2×C5×Dic3—216no—
149C2×C5×Dic3C2×D414yes—
150C2×C5×Dic3C2414yes—
151C2×C5×Dic3C2412yes—
152C4×C5×D3C2×D4116yescomplemented
153C5×Dic6—28no—
154C2×C3×Dic5—24no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5C2414yes—
157C2×C3×Dic5C2414yes—
158C3×Dic10—28no—
159#1203—216no—
160#1200—216no—
161D3×Dic5—216no—
162C22×C3×Q8—51no—
163C22×C3×D4C2×D511yescharacteristic
164C22×#67—54no—
165C22×#67C2×D512yes—
166C23×Dic3C2×D512yes—
167C2×#239—58no—
168C2×#239—108no—
169C2×#237—28no—
170C2×#237C2×D518yescomplemented
171C22×D12—52no—
172C22×D12—51no—
173C22×C4×D3—52no—
174C22×C4×D3—52no—
175C22×C4×D3C2×D511yescharacteristic
176C22×Dic6C2×D511yescharacteristic
177C3×#124—58no—
178C2×C3×C22⋊C4—54no—
179C2×C3×C42—51no—
180#944—58no—
181#940—58no—
182C2×(C2×D3)⋊C4—54no—
183C2×Dic3⋊C4—54no—
184C2×C4×Dic3—51no—
185C2×C4×Dic3—52no—
186#884—532no—
187#67⋊C4—532no—
188#875—58no—
189C42×D3—58no—
190C24×C5—31no—
191C24×C5C22×D312yes—
192C23×D5—32no—
193C5×#41—632no—
194C2×C5×Q8—34no—
195C2×C5×Q8—64no—
196C2×C5×D4—24no—
197C2×C5×D4—38no—
198C2×C5×D4—68no—
199C2×C5×D4C22×D314yes—
200C22×C4×C5—31no—
201C22×C4×C5—38no—
202C22×C4×C5—34no—
203C22×C4×C5—32no—
204C22×C4×C5—38no—
205C22×C4×C5—68no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—316no—
208C2×C22⋊D5—38no—
209C2×C22⋊D5—68no—
210C2×C22⋊D5—616no—
211C22×Dic5—32no—
212C22×Dic5—38no—
213C22×Dic5—68no—
214C22×Dic5C22×D312yes—
215C22×Dic5C22×D312yes—
216#709—632no—
217C2×D20—34no—
218C2×D20—64no—
219C2×C4×D5—38no—
220C2×C4×D5—68no—
221C2×Dic10—24no—
222C2×Dic10C22×D314yes—
223C22⋊Dic5C22×D3116yes—
224#685—316no—
225#683—316no—
226C4×Dic5—34no—
227C4×Dic5—38no—
228C4×Dic5C22×D314yes—
229C22×#41—31no—
230C22×#41—151no—
231#532—1516no—
232C2×C4⋊Q8—151no—
233C2×#127—151no—
234C2×#124—51no—
235C2×#124—151no—
236C2×#121—154no—
237C2×C4×D4—154no—
238C22×C42—151no—
239C22×C3×C5—24no—
240C22×C3×C5—28no—
241C22×C3×C5—48no—
242C22×C3×C5C22×D412yes—
243C22×C3×C5C2×#4114yes—
244C22×C3×C5C2511yescharacteristic
245C2×D15—24no—
246C2×D15—28no—
247C2×D15—48no—
248C2×C5×D3—28no—
249C2×C5×D3—24no—
250C2×C5×D3C22×D414yes—
251C3×C4×C5C22×D414yes—
252Dic15C2×#4118yescomplemented
253C3×Dic5—24no—
254C3×Dic5—24no—
255C5×Dic3—24no—
256C5×Dic3C22×D414yes—
257C24×C3C22×D512yes—
258C23×D3—52no—
259C23×D3C22×D511yescharacteristic
260C2×C3×Q8—54no—
261C2×C3×Q8—104no—
262C2×C3×D4—24no—
263C2×C3×D4C22×D514yes—
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4C22×D511yescharacteristic
267C2×#67—28no—
268C2×#67—516no—
269C2×#67—1016no—
270C2×#67C22×D518yes—
271C22×Dic3—28no—
272C22×Dic3—52no—
273C22×Dic3C22×D518yes—
274C22×Dic3C22×D512yes—
275C22×Dic3C22×D511yescharacteristic
276#239—1032no—
277#237—232no—
278C2×D12—58no—
279C2×D12—54no—
280C2×D12—108no—
281C2×D12—104no—
282C2×C4×D3—58no—
283C2×C4×D3—58no—
284C2×C4×D3—108no—
285C2×C4×D3—108no—
286C2×C4×D3C22⋊D518yescomplemented
287C2×C4×D3C22×D514yes—
288C2×Dic6—24no—
289C2×Dic6C22×D514yes—
290C3×C22⋊C4—516no—
291C3×C42—54no—
292(C2×D3)⋊C4—516no—
293Dic3⋊C4—516no—
294C4×Dic3—54no—
295C4×Dic3—58no—
296C23×C5—24no—
297C23×C5—28no—
298C23×C5—34no—
299C23×C5—32no—
300C23×C5—64no—
301C23×C5C23×D314yes—
302C23×C5C23×D311yescharacteristic
303C22×D5—34no—
304C22×D5—64no—
305C22×D5—68no—
306C5×Q8—68no—
307C5×D4—28no—
308C5×D4—616no—
309C2×C4×C5—34no—
310C2×C4×C5—32no—
311C2×C4×C5—316no—
312C2×C4×C5—34no—
313C2×C4×C5—616no—
314C2×C4×C5—64no—
315C2×C4×C5D3×D414yes—
316C2×C4×C5C23×D312yes—
317C22⋊D5—616no—
318C22⋊D5—632no—
319C2×Dic5—24no—
320C2×Dic5—24no—
321C2×Dic5—38no—
322C2×Dic5—34no—
323C2×Dic5—616no—
324C2×Dic5C23×D314yes—
325C2×Dic5C23×D314yes—
326D20—68no—
327C4×D5—616no—
328Dic10—28no—
329C2×#41—38no—
330C2×#41—68no—
331C2×#41—158no—
332C2×#41—308no—
333C22×Q8—31no—
334C22×Q8—51no—
335C22×D4—32no—
336C22×D4—152no—
337C22×D4—154no—
338C22×D4—151no—
339C22×D4D3×D511yescharacteristic
340C23×C4—31no—
341C23×C4—32no—
342C23×C4—152no—
343C23×C4—152no—
344C4⋊Q8—158no—
345#127—158no—
346#124—58no—
347#124—158no—
348#121—1532no—
349C4×D4—1532no—
350C2×C4⋊C4—154no—
351C2×C22⋊C4—54no—
352C2×C22⋊C4—154no—
353C2×C42—51no—
354C2×C42—158no—
355C2×C42—152no—
356C2×C42—151no—
357C2×C3×C5—44no—
358C2×C3×C5#53214yescomplemented
359C2×C3×C5C23×D411yescharacteristic
360C2×C3×C5C22×#4112yes—
361D15—44no—
362C5×D3—24no—
363C23×C3—28no—
364C23×C3—24no—
365C23×C3C23×D514yes—
366C23×C3C23×D511yescharacteristic
367C22×D3—24no—
368C22×D3—54no—
369C22×D3—108no—
370C22×D3—104no—
371C22×D3C2×C22⋊D514yes—
372C22×D3C23×D512yes—
373C3×Q8—108no—
374C3×D4—28no—
375C2×C3×C4—54no—
376C2×C3×C4—54no—
377C2×C3×C4—104no—
378C2×C3×C4—104no—
379C2×C3×C4C2×C22⋊D514yes—
380C2×C3×C4C23×D512yes—
381#67—216no—
382#67—1032no—
383C2×Dic3—24no—
384C2×Dic3—216no—
385C2×Dic3—58no—
386C2×Dic3—54no—
387C2×Dic3C2×C22⋊D514yes—
388C2×Dic3C23×D514yes—
389C2×Dic3C23×D512yes—
390D12—1016no—
391D12—108no—
392C4×D3—1016no—
393C4×D3—1016no—
394C4×D3C2×C22⋊D5116yescomplemented
395Dic6—28no—
396C22×C5—24no—
397C22×C5—28no—
398C22×C5—34no—
399C22×C5—48no—
400C22×C5—68no—
401C22×C5—64no—
402C22×C5C2×D3×D412yes—
403C22×C5D3×#4114yes—
404C22×C5C24×D311yescharacteristic
405C2×D5—64no—
406C2×D5—68no—
407C2×D5—128no—
408C4×C5—34no—
409C4×C5—64no—
410C4×C5C2×D3×D414yes—
411Dic5—24no—
412Dic5—24no—
413Dic5—38no—
414C24—31no—
415C24—152no—
416C24C2×D3×D512yes—
417#41—632no—
418#41—3032no—
419C2×Q8—34no—
420C2×Q8—54no—
421C2×Q8—64no—
422C2×Q8—104no—
423C2×D4—24no—
424C2×D4—38no—
425C2×D4—68no—
426C2×D4—158no—
427C2×D4—1516no—
428C2×D4—154no—
429C2×D4—308no—
430C2×D4—3016no—
431C2×D4—304no—
432C2×D4C2×D3×D514yes—
433C22×C4—31no—
434C22×C4—38no—
435C22×C4—34no—
436C22×C4—38no—
437C22×C4—32no—
438C22×C4—52no—
439C22×C4—52no—
440C22×C4—68no—
441C22×C4—158no—
442C22×C4—158no—
443C22×C4—152no—
444C22×C4—308no—
445C22×C4—308no—
446C22×C4C2×D3×D511yescharacteristic
447C4⋊C4—1516no—
448C22⋊C4—516no—
449C22⋊C4—1516no—
450C42—54no—
451C42—158no—
452C42—154no—
453C3×C5C2×#53211yescharacteristic, complemented, Hall
454C22×C3—28no—
455C22×C3—24no—
456C22×C3—48no—
457C22×C3D5×#4114yes—
458C22×C3C22×C22⋊D512yes—
459C22×C3C24×D511yescharacteristic
460C2×D3—28no—
461C2×D3—24no—
462C2×D3—108no—
463C2×D3—104no—
464C2×D3—208no—
465C2×D3C22×C22⋊D514yes—
466C3×C4—104no—
467C3×C4—104no—
468C3×C4C22×C22⋊D514yes—
469Dic3—24no—
470Dic3—58no—
471Dic3C22×C22⋊D514yes—
472C2×C5—44no—
473C2×C5—64no—
474C2×C5#566814yescomplemented
475C2×C5C22×D3×D411yescharacteristic
476C2×C5C2×D3×#4112yes—
477D5—124no—
478C23—28no—
479C23—24no—
480C23—34no—
481C23—32no—
482C23—64no—
483C23—154no—
484C23—308no—
485C23—304no—
486C23C22×D3×D514yes—
487C23C22×D3×D511yescharacteristic
488Q8—68no—
489Q8—108no—
490D4—28no—
491D4—616no—
492D4—3016no—
493D4—3032no—
494D4—308no—
495C2×C4—34no—
496C2×C4—32no—
497C2×C4—316no—
498C2×C4—34no—
499C2×C4—54no—
500C2×C4—54no—
501C2×C4—616no—
502C2×C4—64no—
503C2×C4—104no—
504C2×C4—104no—
505C2×C4—158no—
506C2×C4—154no—
507C2×C4—3016no—
508C2×C4—3016no—
509C2×C4D3×C22⋊D514yes—
510C2×C4C22×D3×D512yes—
511C2×C3—44no—
512C2×C3#6616614yescomplemented
513C2×C3C2×D5×#4112yes—
514C2×C3C23×C22⋊D511yescharacteristic
515D3—24no—
516D3—204no—
517C5C2×#566811yescharacteristic, complemented, Sylow
518C22—24no—
519C22—28no—
520C22—34no—
521C22—48no—
522C22—68no—
523C22—64no—
524C22—304no—
525C22—308no—
526C22—608no—
527C22#9202414yes—
528C22C2×D3×C22⋊D512yes—
529C22C23×D3×D511yescharacteristic
530C4—34no—
531C4—64no—
532C4—104no—
533C4—104no—
534C4—158no—
535C4C2×D3×C22⋊D514yes—
536C3C2×#6616611yescharacteristic, complemented, Sylow
537C2—44no—
538C2—64no—
539C2—604no—
540C2#1175481414yesdirect product factor
541C2C2×#9202412yes—
542C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#532
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#237C2semidirect
2. C22×#6769C2semidirect
3. C2×#91829C2semidirect
4. C2×C3×#4082C2semidirect
5. C2×#91558C2semidirect
6. C2×#91556C2semidirect
7. #11754814C2direct (N × H)
8. C2×C4×D3×Dic5C2semidirect
9. C2×#91385C2semidirect
10. C2×#91375C2semidirect
18. C2×C5×#237C22semidirect
26. C2×#6769C22semidirect
27. #91829C22semidirect
30. C3×#4082C22semidirect
32. #91558C22semidirect
33. #91556C22semidirect
37. C4×D3×Dic5C22semidirect
38. #91385C22semidirect
39. #91375C22semidirect
48. C2×#4082D3semidirect
69. C2×C4×C5×D3D4semidirect
91. C22×#237D5semidirect
120. #4082C2×D3semidirect
143. C2×Dic15#41semidirect
152. C4×C5×D3C2×D4semidirect
170. C2×#237C2×D5semidirect
252. Dic15C2×#41semidirect
286. C2×C4×D3C22⋊D5semidirect
358. C2×C3×C5#532semidirect
394. C4×D3C2×C22⋊D5semidirect
453. C3×C5C2×#532semidirect
474. C2×C5#5668semidirect
512. C2×C3#66166semidirect
517. C5C2×#5668semidirect
536. C3C2×#66166semidirect
540. C2#11754814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2372
C22×#67692
C2×#918292
C2×C3×#40822
C2×#915582
C2×#915562
#117548142
C2×C4×D3×Dic52
C2×#913852
C2×#913752
C2×#661663
C2×#56685