Finite Group Databasebeta

← C2×#11755199 #14483976

Subgroups — C2×#11755199 #14483976

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91836C211yesmaximal, characteristic, complemented
2C2×C5×#947C211yesmaximal, characteristic, complemented
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4#11755199C2116yesmaximal, direct product factor
5C2×#91420C212yesmaximal, complemented
6C2×#91416C212yesmaximal, complemented
7C2×#91405C212yesmaximal, complemented
8C2×#91403C212yesmaximal, complemented
9C2×#91400C212yesmaximal, complemented
10C2×#91326C212yesmaximal, complemented
11C2×#66004—31nomaximal, Hall
12C22×C3×C5×Q8C2211yescharacteristic
13C22×D60C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C22×#1203C2212yes—
17C22×#1203C2212yes—
18C22×#1200C2212yes—
19C22×D3×Dic5C2212yes—
20#91836C2218yescomplemented
21C2×#6714C2212yes—
22C2×#6714C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24C5×#947C2218yescomplemented
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C3×#4090C2218yescomplemented
29C2×C3×#683C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×#6668C2212yes—
33C2×#6667C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×Dic3×Dic5C2212yes—
36#91420C22116yescomplemented
37#91416C22116yescomplemented
38#91405C22116yescomplemented
39#91403C22116yescomplemented
40#91400C22116yescomplemented
41#91326C22116yescomplemented
42C2×#5734—51nomaximal, Hall
43C2×C5×#124—31no—
44C2×#4093—31no—
45C2×#4090D311yescharacteristic, complemented
46C2×#4085—32no—
47#66004—316no—
48C2×#4031—32no—
49C2×#4030—32no—
50C2×#4027—32no—
51C2×#4023—32no—
52C2×#4018—32no—
53C23×D15C2312yes—
54C23×C5×D3C2312yes—
55C2×C3×C5×Q8—42no—
56C2×C3×C5×Q8C2314yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15C2312yes—
61C2×D60—42no—
62C2×D60C2314yes—
63C22×C5×Dic3C2312yes—
64C2×C5×D12—42no—
65C2×C5×D12C2314yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×C3×Dic10—42no—
69C2×C3×Dic10C2314yes—
70C2×#1203—28no—
71C2×#1203—44no—
72C2×#1203C2318yes—
73C2×#1203C2318yes—
74C2×#1200—28no—
75C2×#1200C2318yes—
76C2×D3×Dic5—28no—
77C2×D3×Dic5C2318yes—
78#6714C2318yes—
79#6714C2318yes—
80C4×Dic15C2314yes—
81C5×(C2×D3)⋊C4C2318yes—
82C5×(C2×D3)⋊C4C2318yes—
83C4×C5×Dic3C2314yes—
84C3×#683C2318yes—
85C3×#683C2318yes—
86C3×C4×Dic5C2314yes—
87#6668C2318yes—
88#6667C2318yes—
89(C2×D3)⋊Dic5C2318yes—
90Dic3×Dic5C2318yes—
91C2×C3×C4⋊Q8—51no—
92C2×#947—51no—
93C2×#947—52no—
94C2×#947D511yescharacteristic, complemented
95#5734—516no—
96C2×#895—52no—
97C2×#895—52no—
98C2×#892—52no—
99C2×#892—52no—
100C2×C4×D12—52no—
101C22×C5×Q8C2×D311yescharacteristic
102C22×C5×D4—31no—
103C22×C22⋊D5—32no—
104C22×C22⋊D5—32no—
105C23×Dic5—32no—
106C22×D20—31no—
107C22×C4×D5—32no—
108C22×Dic10C2×D311yescharacteristic
109C5×#124—38no—
110C2×C5×C22⋊C4—32no—
111C2×C5×C22⋊C4—32no—
112C2×C42×C5—31no—
113C2×C22⋊Dic5—32no—
114#4093—38no—
115#4090C2×D318yescomplemented
116#4085—316no—
117C2×#685—32no—
118C2×#685—32no—
119C2×#685—32no—
120C2×#683—32no—
121C2×#683C2×D312yes—
122C2×#683C2×D312yes—
123C2×C4×Dic5—31no—
124C2×C4×Dic5—32no—
125C2×C4×Dic5C2×D311yescharacteristic
126#4031—316no—
127#4030—316no—
128#4027—316no—
129#4023—316no—
130#4018—316no—
131C2×#555—151noSylow
132C23×C3×C5C2411yescharacteristic
133C22×D15—24no—
134C22×D15—24no—
135C22×D15—24no—
136C22×D15C2414yes—
137C22×C5×D3—24no—
138C22×C5×D3—24no—
139C22×C5×D3—24no—
140C22×C5×D3C2414yes—
141C3×C5×Q8—44no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2412yes—
146C2×C3×C4×C5C2412yes—
147C2×C3×C4×C5C2412yes—
148C2×Dic15—24no—
149C2×Dic15C2414yes—
150D60—44no—
151C2×C5×Dic3—24no—
152C2×C5×Dic3C2414yes—
153C5×D12—44no—
154C2×C3×Dic5—24no—
155C2×C3×Dic5#4118yes—
156C2×C3×Dic5C2414yes—
157C2×C3×Dic5C2414yes—
158C3×Dic10—44no—
159#1203—216no—
160#1203—48no—
161#1200—216no—
162D3×Dic5—216no—
163C22×C3×Q8—51no—
164C22×C3×Q8C2×D511yescharacteristic
165C22×D12—52no—
166C22×D12—52no—
167C22×D12—51no—
168C22×D12C2×D511yescharacteristic
169C22×C4×D3—52no—
170C22×C4×D3—52no—
171C3×C4⋊Q8—58no—
172C2×C3×C4⋊C4—52no—
173C2×C3×C4⋊C4—52no—
174C2×C3×C42—51no—
175#947—58no—
176#947—516no—
177#947C2×D518yescomplemented
178C2×(C2×D3)⋊C4—52no—
179C2×(C2×D3)⋊C4—52no—
180C2×(C2×D3)⋊C4—52no—
181C2×(C2×D3)⋊C4—52no—
182C2×(C2×D3)⋊C4C2×D512yes—
183C2×(C2×D3)⋊C4C2×D512yes—
184C2×C4⋊Dic3—52no—
185C2×C4×Dic3—51no—
186C2×C4×Dic3—52no—
187C2×C4×Dic3C2×D511yescharacteristic
188#895—516no—
189#895—516no—
190#892—516no—
191#892—516no—
192C4×D12—516no—
193C24×C5—32no—
194C23×D5—32no—
195C2×C5×Q8—42no—
196C2×C5×Q8C22×D314yes—
197C2×C5×D4—34no—
198C2×C5×D4—122no—
199C22×C4×C5—32no—
200C22×C4×C5C22×D311yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—38no—
204C2×C22⋊D5—38no—
205C2×C22⋊D5—68no—
206C2×C22⋊D5—124no—
207C22×Dic5—32no—
208C22×Dic5—38no—
209C22×Dic5—68no—
210C22×Dic5C22×D312yes—
211C22×Dic5C22×D312yes—
212C2×D20—34no—
213C2×D20—122no—
214C2×C4×D5—38no—
215C2×C4×D5—68no—
216C2×Dic10—42no—
217C2×Dic10C22×D314yes—
218C5×C22⋊C4—38no—
219C5×C22⋊C4—38no—
220C42×C5—34no—
221C22⋊Dic5—38no—
222#685—38no—
223#685—38no—
224#685—38no—
225#683—38no—
226#683C22×D318yes—
227#683C22×D318yes—
228C4×Dic5—34no—
229C4×Dic5—38no—
230C4×Dic5C22×D314yes—
231#555—1516no—
232C2×C4⋊Q8—51no—
233C2×#124—31no—
234C2×#124—152no—
235C2×#124—151no—
236C2×#121—152no—
237C2×#121—152no—
238C2×C4×D4—152no—
239C2×#117—152no—
240C2×#117—152no—
241C22×C3×C5C2×#4114yes—
242C22×C3×C5H(5,𝔽2)12yes—
243C22×C3×C5C2511yescharacteristic
244C2×D15—24no—
245C2×D15—24no—
246C2×D15—24no—
247C2×D15—48no—
248C2×C5×D3—24no—
249C2×C5×D3—24no—
250C2×C5×D3—24no—
251C2×C5×D3—48no—
252C3×C4×C5—22no—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255Dic15—24no—
256C3×Dic5—24no—
257C3×Dic5C2×#4118yes—
258C5×Dic3—24no—
259C23×D3—52no—
260C23×D3C22×D512yes—
261C2×C3×Q8—42no—
262C2×C3×Q8—54no—
263C2×C3×Q8—202no—
264C2×C3×Q8C22×D514yes—
265C22×C3×C4—52no—
266C22×C3×C4—52no—
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C22×Dic3—52no—
271C22×Dic3C22×D512yes—
272C2×D12—42no—
273C2×D12—58no—
274C2×D12—58no—
275C2×D12—54no—
276C2×D12—108no—
277C2×D12—202no—
278C2×D12—204no—
279C2×D12C22×D514yes—
280C2×C4×D3—58no—
281C2×C4×D3—58no—
282C2×C4×D3—108no—
283C2×C4×D3—108no—
284C3×C4⋊C4—58no—
285C3×C4⋊C4—58no—
286C3×C42—54no—
287(C2×D3)⋊C4—58no—
288(C2×D3)⋊C4—58no—
289(C2×D3)⋊C4—58no—
290(C2×D3)⋊C4—58no—
291(C2×D3)⋊C4C22×D518yes—
292(C2×D3)⋊C4C22×D518yes—
293C4⋊Dic3—58no—
294C4×Dic3—54no—
295C4×Dic3—58no—
296C4×Dic3C22×D514yes—
297C23×C5—34no—
298C23×C5—64no—
299C23×C5—64no—
300C23×C5—64no—
301C23×C5C23×D311yescharacteristic
302C22×D5—34no—
303C22×D5—64no—
304C22×D5—64no—
305C22×D5—64no—
306C5×Q8—44no—
307C5×D4—124no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—34no—
312C2×C4×C5—64no—
313C2×C4×C5C23×D312yes—
314C2×C4×C5C23×D312yes—
315C2×C4×C5C23×D312yes—
316C22⋊D5—616no—
317C22⋊D5—128no—
318C2×Dic5—24no—
319C2×Dic5—34no—
320C2×Dic5—64no—
321C2×Dic5—616no—
322C2×Dic5#23918yes—
323C2×Dic5C23×D314yes—
324C2×Dic5C23×D314yes—
325D20—124no—
326C4×D5—616no—
327Dic10—44no—
328C22×Q8—51no—
329C22×Q8D3×D511yescharacteristic
330C22×D4—31no—
331C22×D4—152no—
332C22×D4—152no—
333C22×D4—151no—
334C23×C4—152no—
335C23×C4—152no—
336C4⋊Q8—58no—
337#124—38no—
338#124—1516no—
339#124—158no—
340#121—1516no—
341#121—1516no—
342C4×D4—1516no—
343#117—1516no—
344#117—1516no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—52no—
347C2×C4⋊C4—152no—
348C2×C22⋊C4—32no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C22⋊C4—152no—
353C2×C22⋊C4—152no—
354C2×C42—31no—
355C2×C42—51no—
356C2×C42—152no—
357C2×C42—151no—
358C2×C3×C5#55514yescomplemented
359C2×C3×C5C22×#4112yes—
360C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
361D15—44no—
362C5×D3—44no—
363C23×C3C23×D511yescharacteristic
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—24no—
367C22×D3—54no—
368C22×D3—104no—
369C22×D3—104no—
370C22×D3—104no—
371C22×D3C23×D514yes—
372C3×Q8—44no—
373C3×Q8—204no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—58no—
378C2×C3×C4—54no—
379C2×C3×C4—54no—
380C2×C3×C4—104no—
381C2×C3×C4C23×D512yes—
382C2×C3×C4C23×D512yes—
383C2×C3×C4C23×D512yes—
384C2×Dic3—24no—
385C2×Dic3—54no—
386C2×Dic3—104no—
387C2×Dic3C23×D514yes—
388D12—44no—
389D12—1016no—
390D12—204no—
391D12—208no—
392C4×D3—1016no—
393C4×D3—1016no—
394C22×C5—64no—
395C22×C5—64no—
396C22×C5—64no—
397C22×C5—128no—
398C22×C5#100412yes—
399C22×C5C2×#23914yes—
400C22×C5C24×D311yescharacteristic
401C2×D5—64no—
402C2×D5—64no—
403C2×D5—64no—
404C2×D5—128no—
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—22no—
408C4×C5—64no—
409Dic5—24no—
410Dic5—64no—
411Dic5C2×#23918yes—
412C24—32no—
413C24—152no—
414C2×Q8—42no—
415C2×Q8—54no—
416C2×Q8—202no—
417C2×Q8C2×D3×D514yes—
418C2×D4—34no—
419C2×D4—122no—
420C2×D4—158no—
421C2×D4—158no—
422C2×D4—154no—
423C2×D4—308no—
424C2×D4—602no—
425C2×D4—604no—
426C22×C4—32no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—158no—
430C22×C4—158no—
431C22×C4—152no—
432C22×C4—308no—
433C22×C4—308no—
434C22×C4C2×D3×D511yescharacteristic
435C22×C4C2×D3×D511yescharacteristic
436C22×C4C2×D3×D511yescharacteristic
437C4⋊C4—58no—
438C4⋊C4—58no—
439C4⋊C4—158no—
440C22⋊C4—38no—
441C22⋊C4—38no—
442C22⋊C4—158no—
443C22⋊C4—158no—
444C22⋊C4—158no—
445C22⋊C4—158no—
446C42—34no—
447C42—54no—
448C42—158no—
449C42—154no—
450C3×C5C2×#55511yescharacteristic, complemented, Hall
451C22×C3#414412yes—
452C22×C3D5×#4114yes—
453C22×C3C24×D511yescharacteristic
454C2×D3—24no—
455C2×D3—24no—
456C2×D3—24no—
457C2×D3—48no—
458C2×D3—104no—
459C2×D3—104no—
460C2×D3—104no—
461C2×D3—208no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—58no—
466C3×C4—104no—
467Dic3—24no—
468Dic3—104no—
469C2×C5—124no—
470C2×C5#573414yescomplemented
471C2×C5C2×#100411yescharacteristic
472C2×C5C22×#23912yes—
473D5—124no—
474C23—34no—
475C23—64no—
476C23—64no—
477C23—64no—
478C23—154no—
479C23—304no—
480C23—304no—
481C23—304no—
482C23C22×D3×D511yescharacteristic
483Q8—44no—
484Q8—204no—
485D4—124no—
486D4—3016no—
487D4—604no—
488D4—608no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—34no—
493C2×C4—58no—
494C2×C4—54no—
495C2×C4—54no—
496C2×C4—64no—
497C2×C4—104no—
498C2×C4—154no—
499C2×C4—3016no—
500C2×C4—3016no—
501C2×C4—304no—
502C2×C4C22×D3×D512yes—
503C2×C4C22×D3×D512yes—
504C2×C4C22×D3×D512yes—
505C2×C3#6600414yescomplemented
506C2×C3C2×#414411yescharacteristic
507C2×C3C2×D5×#4112yes—
508D3—44no—
509D3—204no—
510C5C2×#573411yescharacteristic, complemented, Sylow
511C22—64no—
512C22—64no—
513C22—64no—
514C22—128no—
515C22—304no—
516C22—304no—
517C22—304no—
518C22—608no—
519C22D5×#23914yes—
520C22#9204912yes—
521C22C23×D3×D511yescharacteristic
522C4—22no—
523C4—22no—
524C4—22no—
525C4—58no—
526C4—64no—
527C4—104no—
528C4—304no—
529C3C2×#6600411yescharacteristic, complemented, Sylow
530C2—124no—
531C2—604no—
532C2#1175519914yesdirect product factor
533C2C2×D5×#23912yes—
534C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#91836C2semidirect
2. C2×C5×#947C2semidirect
3. C2×C3×#4090C2semidirect
4. #11755199C2direct (N × H)
5. C2×#91420C2semidirect
6. C2×#91416C2semidirect
7. C2×#91405C2semidirect
8. C2×#91403C2semidirect
9. C2×#91400C2semidirect
10. C2×#91326C2semidirect
20. #91836C22semidirect
24. C5×#947C22semidirect
28. C3×#4090C22semidirect
36. #91420C22semidirect
37. #91416C22semidirect
38. #91405C22semidirect
39. #91403C22semidirect
40. #91400C22semidirect
41. #91326C22semidirect
45. C2×#4090D3semidirect
94. C2×#947D5semidirect
115. #4090C2×D3semidirect
177. #947C2×D5semidirect
358. C2×C3×C5#555semidirect
450. C3×C5C2×#555semidirect
470. C2×C5#5734semidirect
505. C2×C3#66004semidirect
510. C5C2×#5734semidirect
529. C3C2×#66004semidirect
532. C2#11755199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918362
C2×C5×#9472
C2×C3×#40902
#117551992
C2×#914202
C2×#914162
C2×#914052
C2×#914032
C2×#914002
C2×#913262
C2×#660043
C2×#57345