Finite Group Databasebeta

← C2×#11754906 #14484763

Subgroups — C2×#11754906 #14484763

Order 1920.

2480 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
1C2×#91829C211yesmaximal, characteristic
2C2×C5×#935C211yesmaximal, characteristic, complemented
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×#91556C212yesmaximal, complemented
5C2×#91552C212yesmaximal, complemented
6C2×#91526C212yesmaximal, complemented
7C2×#91526C212yesmaximal, complemented
8#11754906C2116yesmaximal, direct product factor
9C2×#91433C212yesmaximal, complemented
10C2×#91325C212yesmaximal, complemented
11C2×#65998—31nomaximal, Hall
12C22×C3×C5×D4C2211yescharacteristic
13C22×#1220C2212yes—
14C22×#1220C2212yes—
15C22×D60C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C22×#1204C2212yes—
19C22×#1200C2212yes—
20#91829C2218yes—
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×#217C2211yescharacteristic
23C2×C5×#217C2212yes—
24C5×#935C2218yescomplemented
25C2×C5×Dic3⋊C4C2212yes—
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C3×#4081C2218yescomplemented
29C2×C3×#683C2212yes—
30#91556C22116yescomplemented
31#91552C22116yescomplemented
32C2×#6669C2212yes—
33C2×#6667C2212yes—
34C2×#6667C2212yes—
35C2×#6667C2212yes—
36C2×Dic3×Dic5C2212yes—
37C2×Dic3×Dic5C2212yes—
38#91526C22116yescomplemented
39#91526C22116yescomplemented
40#91433C22116yescomplemented
41#91325C22116yescomplemented
42C2×#5664—51nomaximal, Hall
43C2×C5×#123—31no—
44C2×#4086—31no—
45C2×#4081D311yescharacteristic, complemented
46C2×C4×C22⋊D5—32no—
47#65998—316no—
48C2×#4040—32no—
49C2×#4033—32no—
50C2×#4031—32no—
51C2×#4031—32no—
52C2×#4027—32no—
53C24×C3×C5C2311yescharacteristic
54C24×C3×C5C2311yescharacteristic
55C23×D15C2312yes—
56C2×C3×C5×D4—42no—
57C2×C3×C5×D4C2314yes—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—28no—
60C2×#1220—28no—
61C2×#1220C2318yes—
62C2×#1220C2318yes—
63C22×Dic15C2312yes—
64C2×D60—42no—
65C2×D60C2314yes—
66C22×C5×Dic3—42no—
67C22×C5×Dic3C2312yes—
68C22×C5×Dic3C2312yes—
69C22×C5×Dic3C2314yes—
70C22×C3×Dic5—42no—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2314yes—
74C2×#1204—28no—
75C2×#1204C2318yes—
76C2×#1200—44no—
77C2×#1200C2318yes—
78C4×Dic15C2314yes—
79C5×#217C2314yes—
80C5×#217C2318yes—
81C5×Dic3⋊C4C2318yes—
82C3×C22⋊Dic5C2314yes—
83C3×C22⋊Dic5C2318yes—
84C3×#683C2318yes—
85#6669C2318yes—
86#6667C2318yes—
87#6667C2318yes—
88#6667C2318yes—
89Dic3×Dic5C2318yes—
90Dic3×Dic5C2318yes—
91C2×C3×#123—51no—
92C2×#940—51no—
93C2×#935D511yescharacteristic, complemented
94C2×C4×#67—52no—
95#5664—516no—
96C2×#894—52no—
97C2×#887—52no—
98C2×#885—52no—
99C2×#885—52no—
100C2×#67⋊C4—52no—
101C22×C5×D4C2×D311yescharacteristic
102C23×C4×C5—31no—
103C22×C22⋊D5—32no—
104C22×C22⋊D5—32no—
105C23×Dic5C2×D311yescharacteristic
106C22×D20—31no—
107C22×C4×D5—32no—
108C22×Dic10—32no—
109C5×#123—38no—
110C2×C5×C4⋊C4—32no—
111C2×C5×C22⋊C4—32no—
112C2×C5×C22⋊C4—31no—
113C2×C22⋊Dic5C2×D311yescharacteristic
114C2×C22⋊Dic5C2×D312yes—
115#4086—38no—
116#4081C2×D318yescomplemented
117C4×C22⋊D5—316no—
118C2×#685—32no—
119C2×#685—32no—
120C2×#685—32no—
121C2×#683—32no—
122C2×#683C2×D312yes—
123C2×C4×Dic5—31no—
124C2×C4×Dic5—32no—
125C2×C4×Dic5—32no—
126#4040—316no—
127#4033—316no—
128#4031—316no—
129#4031—316no—
130#4027—316no—
131C2×#559—151noSylow
132C23×C3×C5—24no—
133C23×C3×C5—24no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5C2412yes—
137C23×C3×C5C2412yes—
138C23×C3×C5C2411yescharacteristic
139C22×D15—24no—
140C22×D15—24no—
141C22×D15—24no—
142C22×D15C2414yes—
143C3×C5×D4—44no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2412yes—
146#1220—216no—
147#1220—216no—
148C2×Dic15#4118yes—
149C2×Dic15C2414yes—
150D60—44no—
151C2×C5×Dic3—24no—
152C2×C5×Dic3—24no—
153C2×C5×Dic3—44no—
154C2×C5×Dic3C2414yes—
155C2×C5×Dic3C2414yes—
156C2×C3×Dic5—24no—
157C2×C3×Dic5—24no—
158C2×C3×Dic5—44no—
159C2×C3×Dic5C2414yes—
160C2×C3×Dic5C2414yes—
161#1204—216no—
162#1200—48no—
163C22×C3×D4C2×D511yescharacteristic
164C23×C3×C4—51no—
165C22×#67—52no—
166C22×#67—52no—
167C23×Dic3C2×D511yescharacteristic
168C22×D12—51no—
169C22×C4×D3—52no—
170C22×Dic6—52no—
171C3×#123—58no—
172C2×C3×C4⋊C4—52no—
173C2×C3×C22⋊C4—52no—
174C2×C3×C22⋊C4—51no—
175C2×#217C2×D511yescharacteristic
176C2×#217C2×D512yes—
177#940—58no—
178#935C2×D518yescomplemented
179C4×#67—516no—
180C2×(C2×D3)⋊C4—52no—
181C2×(C2×D3)⋊C4—52no—
182C2×(C2×D3)⋊C4—52no—
183C2×Dic3⋊C4—52no—
184C2×Dic3⋊C4C2×D512yes—
185C2×C4×Dic3—51no—
186C2×C4×Dic3—52no—
187C2×C4×Dic3—52no—
188#894—516no—
189#887—516no—
190#885—516no—
191#885—516no—
192#67⋊C4—516no—
193C24×C5C22×D311yescharacteristic
194C24×C5C22×D311yescharacteristic
195C23×D5—32no—
196C2×C5×D4—42no—
197C2×C5×D4C22×D314yes—
198C22×C4×C5—32no—
199C22×C4×C5—32no—
200C22×C4×C5—34no—
201C22×C4×C5—122no—
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—38no—
204C2×C22⋊D5—38no—
205C2×C22⋊D5—68no—
206C2×C22⋊D5—68no—
207C22×Dic5—32no—
208C22×Dic5—42no—
209C22×Dic5C22×D312yes—
210C22×Dic5C22×D312yes—
211C22×Dic5C22×D314yes—
212C2×D20—34no—
213C2×D20—122no—
214C2×C4×D5—38no—
215C2×C4×D5—124no—
216C2×Dic10—38no—
217C2×Dic10—68no—
218C5×C4⋊C4—38no—
219C5×C22⋊C4—38no—
220C5×C22⋊C4—34no—
221C22⋊Dic5C22×D314yes—
222C22⋊Dic5C22×D318yes—
223#685—38no—
224#685—38no—
225#685—38no—
226#683—38no—
227#683C22×D318yes—
228C4×Dic5—34no—
229C4×Dic5—38no—
230C4×Dic5—38no—
231#559—1516no—
232C2×#127—151no—
233C2×#124—152no—
234C2×#124—152no—
235C2×#123—31no—
236C2×#123—51no—
237C2×#123—152no—
238C2×C4×Q8—152no—
239C2×C4×D4—152no—
240C2×C4×D4—152no—
241C22×C3×C5—24no—
242C22×C3×C5—24no—
243C22×C3×C5—22no—
244C22×C3×C5—22no—
245C22×C3×C5—44no—
246C22×C3×C5—44no—
247C22×C3×C5C2×#4114yes—
248C22×C3×C5H(5,𝔽2)12yes—
249C22×C3×C5C2511yescharacteristic
250C2×D15—24no—
251C2×D15—24no—
252C2×D15—24no—
253C2×D15—48no—
254C3×C4×C5—22no—
255Dic15C2×#4118yes—
256C3×Dic5—24no—
257C3×Dic5—24no—
258C5×Dic3—24no—
259C5×Dic3—24no—
260C24×C3C22×D511yescharacteristic
261C24×C3C22×D511yescharacteristic
262C23×D3—52no—
263C2×C3×D4—42no—
264C2×C3×D4C22×D514yes—
265C22×C3×C4—52no—
266C22×C3×C4—52no—
267C22×C3×C4—54no—
268C22×C3×C4—202no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—58no—
271C2×#67—58no—
272C2×#67—108no—
273C2×#67—108no—
274C22×Dic3—42no—
275C22×Dic3—52no—
276C22×Dic3C22×D512yes—
277C22×Dic3C22×D512yes—
278C22×Dic3C22×D514yes—
279C2×D12—54no—
280C2×D12—202no—
281C2×C4×D3—58no—
282C2×C4×D3—204no—
283C2×Dic6—58no—
284C2×Dic6—108no—
285C3×C4⋊C4—58no—
286C3×C22⋊C4—58no—
287C3×C22⋊C4—54no—
288#217C22×D514yes—
289#217C22×D518yes—
290(C2×D3)⋊C4—58no—
291(C2×D3)⋊C4—58no—
292(C2×D3)⋊C4—58no—
293Dic3⋊C4—58no—
294Dic3⋊C4C22×D518yes—
295C4×Dic3—54no—
296C4×Dic3—58no—
297C4×Dic3—58no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—24no—
301C23×C5—24no—
302C23×C5C23×D312yes—
303C23×C5C23×D312yes—
304C23×C5C23×D311yescharacteristic
305C22×D5—34no—
306C22×D5—64no—
307C22×D5—64no—
308C22×D5—64no—
309C5×D4—44no—
310C2×C4×C5—22no—
311C2×C4×C5—34no—
312C2×C4×C5—34no—
313C2×C4×C5—64no—
314C2×C4×C5—64no—
315C2×C4×C5—124no—
316C2×C4×C5C23×D312yes—
317C22⋊D5—616no—
318C22⋊D5—616no—
319C2×Dic5—24no—
320C2×Dic5—24no—
321C2×Dic5—38no—
322C2×Dic5—34no—
323C2×Dic5—44no—
324C2×Dic5C23×D314yes—
325C2×Dic5C23×D314yes—
326D20—124no—
327C4×D5—128no—
328Dic10—616no—
329C22×Q8—152no—
330C22×D4—152no—
331C22×D4—152no—
332C22×D4—151no—
333C22×D4D3×D511yescharacteristic
334C23×C4—31no—
335C23×C4—51no—
336C23×C4—152no—
337#127—158no—
338#124—1516no—
339#124—1516no—
340#123—38no—
341#123—58no—
342#123—1516no—
343C4×Q8—1516no—
344C4×D4—1516no—
345C4×D4—1516no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—52no—
348C2×C4⋊C4—152no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—52no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4—152no—
354C2×C22⋊C4—152no—
355C2×C22⋊C4—152no—
356C2×C42—152no—
357C2×C42—152no—
358C2×C42—151no—
359C2×C3×C5—42no—
360C2×C3×C5—42no—
361C2×C3×C5#55914yescomplemented
362C2×C3×C5C22×#4112yes—
363C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
364D15—44no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3C23×D512yes—
370C23×C3C23×D512yes—
371C23×C3C23×D511yescharacteristic
372C22×D3—54no—
373C22×D3—104no—
374C22×D3—104no—
375C22×D3—104no—
376C3×D4—44no—
377C2×C3×C4—22no—
378C2×C3×C4—54no—
379C2×C3×C4—54no—
380C2×C3×C4—104no—
381C2×C3×C4—104no—
382C2×C3×C4—204no—
383C2×C3×C4C23×D512yes—
384#67—1016no—
385#67—1016no—
386C2×Dic3—24no—
387C2×Dic3—24no—
388C2×Dic3—44no—
389C2×Dic3—58no—
390C2×Dic3—54no—
391C2×Dic3C23×D514yes—
392C2×Dic3C23×D514yes—
393D12—204no—
394C4×D3—208no—
395Dic6—1016no—
396C22×C5—22no—
397C22×C5—22no—
398C22×C5—24no—
399C22×C5—24no—
400C22×C5—44no—
401C22×C5—44no—
402C22×C5#100412yes—
403C22×C5D3×#4114yes—
404C22×C5C24×D311yescharacteristic
405C2×D5—64no—
406C2×D5—64no—
407C2×D5—64no—
408C2×D5—128no—
409C4×C5—22no—
410C4×C5—64no—
411C4×C5—64no—
412Dic5—24no—
413Dic5—24no—
414Dic5—38no—
415C24—152no—
416C24C2×D3×D511yescharacteristic
417C24C2×D3×D511yescharacteristic
418C2×Q8—158no—
419C2×Q8—308no—
420C2×D4—42no—
421C2×D4—158no—
422C2×D4—158no—
423C2×D4—154no—
424C2×D4—308no—
425C2×D4—308no—
426C2×D4—602no—
427C2×D4C2×D3×D514yes—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—34no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—54no—
434C22×C4—122no—
435C22×C4—158no—
436C22×C4—152no—
437C22×C4—202no—
438C22×C4—604no—
439C22×C4C2×D3×D511yescharacteristic
440C4⋊C4—38no—
441C4⋊C4—58no—
442C4⋊C4—158no—
443C22⋊C4—38no—
444C22⋊C4—34no—
445C22⋊C4—58no—
446C22⋊C4—54no—
447C22⋊C4—158no—
448C22⋊C4—158no—
449C22⋊C4—158no—
450C42—158no—
451C42—158no—
452C42—154no—
453C3×C5C2×#55911yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—44no—
459C22×C3—44no—
460C22×C3#414412yes—
461C22×C3D5×#4114yes—
462C22×C3C24×D511yescharacteristic
463C2×D3—104no—
464C2×D3—104no—
465C2×D3—104no—
466C2×D3—208no—
467C3×C4—22no—
468C3×C4—104no—
469C3×C4—104no—
470Dic3—24no—
471Dic3—24no—
472Dic3—58no—
473C2×C5—42no—
474C2×C5—42no—
475C2×C5#566414yescomplemented
476C2×C5C2×#100411yescharacteristic
477C2×C5C2×D3×#4112yes—
478D5—124no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—154no—
484C23—304no—
485C23—304no—
486C23—304no—
487C23C22×D3×D512yes—
488C23C22×D3×D512yes—
489C23C22×D3×D511yescharacteristic
490Q8—3016no—
491D4—44no—
492D4—3016no—
493D4—3016no—
494D4—604no—
495C2×C4—22no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—54no—
499C2×C4—54no—
500C2×C4—64no—
501C2×C4—64no—
502C2×C4—104no—
503C2×C4—104no—
504C2×C4—124no—
505C2×C4—158no—
506C2×C4—154no—
507C2×C4—204no—
508C2×C4—608no—
509C2×C4C22×D3×D512yes—
510C2×C3—42no—
511C2×C3—42no—
512C2×C3#6599814yescomplemented
513C2×C3C2×#414411yescharacteristic
514C2×C3C2×D5×#4112yes—
515D3—204no—
516C5C2×#566411yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—24no—
520C22—24no—
521C22—44no—
522C22—44no—
523C22—304no—
524C22—304no—
525C22—304no—
526C22—608no—
527C22#9202414yes—
528C22#9204912yes—
529C22C23×D3×D511yescharacteristic
530C4—22no—
531C4—64no—
532C4—64no—
533C4—104no—
534C4—104no—
535C4—158no—
536C3C2×#6599811yescharacteristic, complemented, Sylow
537C2—42no—
538C2—42no—
539C2—604no—
540C2#1175490614yesdirect product factor
541C2C2×#9202412yes—
542C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×#91829C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#935C2semidirect
3. C2×C3×#4081C2semidirect
4. C2×#91556C2semidirect
5. C2×#91552C2semidirect
6. C2×#91526C2semidirect
7. C2×#91526C2semidirect
8. #11754906C2direct (N × H)
9. C2×#91433C2semidirect
10. C2×#91325C2semidirect
24. C5×#935C22semidirect
28. C3×#4081C22semidirect
30. #91556C22semidirect
31. #91552C22semidirect
38. #91526C22semidirect
39. #91526C22semidirect
40. #91433C22semidirect
41. #91325C22semidirect
45. C2×#4081D3semidirect
93. C2×#935D5semidirect
116. #4081C2×D3semidirect
178. #935C2×D5semidirect
361. C2×C3×C5#559semidirect
453. C3×C5C2×#559semidirect
475. C2×C5#5664semidirect
512. C2×C3#65998semidirect
516. C5C2×#5664semidirect
536. C3C2×#65998semidirect
540. C2#11754906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C5×#9352
C2×C3×#40812
C2×#915562
C2×#915522
C2×#915262
#117549062
C2×#914332
C2×#913252
C2×#659983
C2×#56645