Finite Group Databasebeta

← C4×#91271 #14416249

Subgroups — C4×#91271 #14416249

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91271C211yesmaximal, characteristic
2C4×#6773C212yesmaximal, complemented
3C4×D120C211yesmaximal, characteristic, complemented
4C4×C5×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×C8×D5C211yesmaximal, characteristic, complemented
6Dic5×Dic12C211yesmaximal, characteristic, complemented
7#11747833C212yesmaximal, complemented
8#11747766C211yesmaximal, characteristic, complemented
9#11747672C211yesmaximal, characteristic, complemented
10#11747642C212yesmaximal, complemented
11C4×#6660C212yesmaximal, complemented
12C4×#4065—31nomaximal, Hall
13C2×#6773C2212yes—
14C2×D120C2211yescharacteristic
15C4×D60C2212yes—
16C2×C5×Dic12C2211yescharacteristic
17C4×C5×Dic6C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21#91444—22no—
22C4×#1202—22no—
23#91418C2212yes—
24#91402—22no—
25C4×#1200—22no—
26#91358C2212yes—
27Dic5×Dic6C2212yes—
28C2×#6660C2212yes—
29#91271C418yesdirect product factor
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91102C2211yescharacteristic
33C5×#818C2211yescharacteristic
34C5×#816C2212yes—
35C3×C8×Dic5C2211yescharacteristic
36C3×C8×Dic5C2211yescharacteristic
37C3×C4×#168C2211yescharacteristic
38#90985C2212yes—
39#90973C2212yes—
40#90969C2212yes—
41C4×#904—51nomaximal, Hall
42C2×#4065—31no—
43C4×#713—32no—
44C4×C5×Q16—31no—
45Q16×Dic5—31no—
46C4×#688—32no—
47#65169—31no—
48#65161—31no—
49#65093—32no—
50#65077—32no—
51C4×D40—31no—
52C4×C8×D5D311yescharacteristic, complemented
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C5×Dic6C2312yes—
56C2×C3×C4×D5D411yescharacteristic
57C2×C3×C4×D5D411yescharacteristic
58C2×C3×C4×D5C2311yescharacteristic
59C2×#1202—22no—
60C2×#1200—22no—
61C2×#1200—22no—
62#6773—24no—
63#6773C2×C418yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67#6714—22no—
68C4⋊Dic15C2312yes—
69D120C2×C414yescomplemented
70C5×C4⋊Dic3C2312yes—
71C5×Dic3⋊C4—22no—
72C4×C5×Dic3—22no—
73C5×Dic12C2×C414yescomplemented
74C3×C4×Dic5D411yescharacteristic
75C3×C4×Dic5D411yescharacteristic
76C3×C4×Dic5C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78C2×C3×#168C2311yescharacteristic
79C3×C8×D5—22no—
80C3×C8×D5C2×C414yescomplemented
81Dic3⋊Dic5—22no—
82#6667—22no—
83#6665—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6660C2×C418yescomplemented
87C2×#904—51no—
88C4×#235—52no—
89C2×C3×C4×C8—51no—
90#5113—52no—
91#5106—51no—
92C4×Dic12—51no—
93C4×Dic12D511yescharacteristic, complemented
94C4×D24—51no—
95C4×D24—51no—
96C4×#204—52no—
97C4×#204—52no—
98C2×#713—32no—
99C2×C5×Q16—31no—
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#688—32no—
103#4065—38no—
104C2×D40—31no—
105C2×C8×D5C2×D311yescharacteristic
106C2×C8×D5C2×D311yescharacteristic
107#4039—32no—
108#4039—62no—
109#4038—32no—
110#4038—62no—
111C4×D20—32no—
112C4×D20—62no—
113C42×D5—62no—
114C42×D5C2×D311yescharacteristic
115C5×#107—31no—
116C5×#103—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953—32no—
120#3950—31no—
121C8×Dic5C2×D311yescharacteristic
122C8×Dic5C2×D311yescharacteristic
123#3941—32no—
124#3940—32no—
125C4×#168C2×D311yescharacteristic
126C4×#135—151noSylow
127C22×D15—22no—
128C22×C3×D5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133D60—22no—
134D60C22×C414yes—
135C4×D15—44no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C5×Dic6—22no—
139C5×Dic6C22×C414yes—
140C2×C3×Dic5C2×D411yescharacteristic
141C2×C3×Dic5C2×D411yescharacteristic
142C2×C3×Dic5C2×D411yescharacteristic
143C3×C4×D5—22no—
144C3×C4×D5—22no—
145C3×C4×D5C22×C412yes—
146C3×C4×D5#4112yes—
147#1202—28no—
148#1200—28no—
149#1200—44no—
150C3×C5×C8—21no—
151C3×C5×C8C22×C412yes—
152C3×#168—21no—
153C3×#168C22×C412yes—
154C2×#235—52no—
155C22×C3×C8—51no—
156C22×C3×C8—51no—
157C2×C3×C42—51no—
158C4×#67—102no—
159C4×#67—102no—
160#926—52no—
161C2×Dic12C2×D511yescharacteristic
162#904—58no—
163C2×D24—51no—
164C2×#204—52no—
165C4×D12—52no—
166C4×D12—52no—
167#872—102no—
168C42×D3—102no—
169C4×Dic6—52no—
170C4×Dic6C2×D512yes—
171C3×C4×C8—51no—
172C3×C4×C8—51no—
173C3×C4×C8—51no—
174C3×C4×C8C2×D511yescharacteristic
175#821—52no—
176#821—52no—
177#818—51no—
178#818C2×D511yescharacteristic
179#817—52no—
180#816—52no—
181#816C2×D512yes—
182C2×C5×Q8—32no—
183#713—38no—
184#713—64no—
185C2×D20—32no—
186C2×D20—62no—
187C2×C4×D5—62no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×C4×D5D1211yescharacteristic
191C2×C4×D5D1211yescharacteristic
192C2×C4×D5C22×D311yescharacteristic
193C5×Q16—34no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—32no—
197C5×C4⋊C4—62no—
198C42×C5—62no—
199C42×C5C22×D311yescharacteristic
200#688—38no—
201#685—62no—
202#685—62no—
203#685—62no—
204C4⋊Dic5—32no—
205C4⋊Dic5—62no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5D1211yescharacteristic
209C4×Dic5D1211yescharacteristic
210C4×Dic5C22×D311yescharacteristic
211C2×#168C22×D311yescharacteristic
212C2×#168C22×D311yescharacteristic
213D40—34no—
214C8×D5—22no—
215C8×D5C4×D314yescomplemented
216C2×#135—151no—
217C4×#41—152no—
218C4×Q16—31no—
219C4×Q16—151no—
220C4×SD16—152no—
221C4×SD16—152no—
222C4×D8—151no—
223C4×D8—151no—
224#427—151no—
225#416—152no—
226C2×C4×C8—51no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—24no—
229C2×D15—42no—
230C2×D15—42no—
231C2×C3×D5—21no—
232C2×C3×D5—21no—
233C2×C3×D5C4×D412yes—
234C3×C4×C5—21no—
235C3×C4×C5#13512yescomplemented
236C3×C4×C5C23×C411yescharacteristic
237C3×C4×C5C2×#4111yescharacteristic
238Dic15—42no—
239C3×Dic5—21no—
240C3×Dic5C4×D412yes—
241C3×Dic5#13512yescomplemented
242C5×Dic3—24no—
243C5×Dic3—42no—
244C22×C3×C4—51no—
245C22×C3×C4—51no—
246C22×C3×C4—51no—
247C2×#67—102no—
248#235—58no—
249#235—104no—
250C2×D12—52no—
251C2×C4×D3—102no—
252C2×C4×D3—102no—
253C2×C4×D3—102no—
254C2×Dic6C22×D512yes—
255C2×C3×C8—51no—
256C2×C3×C8—54no—
257C2×C3×C8—51no—
258C2×C3×C8—102no—
259C2×C3×C8C22×D511yescharacteristic
260C2×C3×C8C22×D511yescharacteristic
261C3×C42—51no—
262C3×C42—51no—
263C3×C42—51no—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266(C2×D3)⋊C4—102no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—52no—
269C4⋊Dic3C22×D512yes—
270Dic3⋊C4—22no—
271Dic3⋊C4—102no—
272C4×Dic3—22no—
273C4×Dic3—102no—
274C4×Dic3—102no—
275Dic12C4×D514yescomplemented
276D24—54no—
277#204—58no—
278C22×D5—62no—
279C22×D5C2×D1211yescharacteristic
280C5×Q8—34no—
281C5×Q8—62no—
282C2×C4×C5—62no—
283C2×C4×C5—62no—
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5C2×D1211yescharacteristic
286C2×C4×C5C23×D311yescharacteristic
287C2×Dic5—62no—
288C2×Dic5C2×D1211yescharacteristic
289C2×Dic5C2×D1211yescharacteristic
290C2×Dic5C2×D1211yescharacteristic
291D20—34no—
292D20—68no—
293D20—62no—
294C4×D5—22no—
295C4×D5—22no—
296C4×D5—68no—
297C4×D5—124no—
298C4×D5—124no—
299C4×D5C2×C4×D312yes—
300C4×D5#23512yes—
301C5×C8—21no—
302C5×C8C2×C4×D312yes—
303#168—21no—
304#168C2×C4×D312yes—
305C2×#41—152no—
306#135—158no—
307C2×Q16—31no—
308C2×SD16—152no—
309C2×D8—151no—
310C22×C8—51no—
311C22×C8—51no—
312C4×Q8—32no—
313C4×Q8—152no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—302no—
317C4×D4—302no—
318#117—152no—
319#117—302no—
320C2×C42—51no—
321C2×C42—302no—
322#107—31no—
323#107—151no—
324#106—152no—
325#103—32no—
326#103—152no—
327#102—152no—
328#102—152no—
329C4×C8—51no—
330C4×C8—51no—
331C4×C8—51no—
332C4×C8D3×D511yescharacteristic
333C2×C3×C5C2×C4×D411yescharacteristic
334C2×C3×C5C2×#13511yescharacteristic
335C2×C3×C5C2×#13511yescharacteristic
336D15—44no—
337C3×D5—22no—
338C23×C3—51no—
339C22×D3—102no—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—52no—
343C2×C3×C4—52no—
344C2×C3×C4—51no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4C23×D511yescharacteristic
350#67—108no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—102no—
354D12—54no—
355D12—102no—
356C4×D3—108no—
357C4×D3—204no—
358C4×D3—204no—
359Dic6—22no—
360Dic6C2×C4×D514yes—
361C3×C8—21no—
362C3×C8—52no—
363C3×C8—101no—
364C3×C8C2×C4×D512yes—
365C22×C5C22×D1211yescharacteristic
366C2×D5—21no—
367C2×D5—21no—
368C2×D5—64no—
369C2×D5—122no—
370C2×D5—122no—
371C2×D5C4×D1212yes—
372C4×C5—21no—
373C4×C5—64no—
374C4×C5—122no—
375C4×C5#90412yescomplemented
376C4×C5C22×C4×D311yescharacteristic
377C4×C5C2×#23511yescharacteristic
378Dic5—21no—
379Dic5—122no—
380Dic5C4×D1212yes—
381Dic5#90412yescomplemented
382#41—158no—
383#41—304no—
384C2×Q8—32no—
385C2×D4—152no—
386C2×D4—302no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—51no—
390C22×C4—302no—
391C22×C4—302no—
392C22×C4—302no—
393Q16—34no—
394SD16—158no—
395D8—154no—
396C2×C8—51no—
397C2×C8—54no—
398C2×C8—51no—
399C2×C8—102no—
400C2×C8C2×D3×D511yescharacteristic
401C2×C8C2×D3×D511yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—62no—
404C4⋊C4—152no—
405C4⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—51no—
410C42—51no—
411C42—51no—
412C42—62no—
413C42—302no—
414C42—302no—
415C42C2×D3×D511yescharacteristic
416C3×C5C4×#13511yescharacteristic, complemented, Hall
417C22×C3—52no—
418C22×C3—101no—
419C22×C3—101no—
420C22×C3C2×D4×D511yescharacteristic
421C2×D3—104no—
422C2×D3—202no—
423C2×D3—202no—
424C3×C4—21no—
425C3×C4—52no—
426C3×C4—52no—
427C3×C4—101no—
428C3×C4#406512yescomplemented
429C3×C4C22×C4×D511yescharacteristic
430C3×C4D5×#4111yescharacteristic
431Dic3—24no—
432Dic3—42no—
433Dic3—202no—
434C2×C5C2×C4×D1211yescharacteristic
435C2×C5C2×#90411yescharacteristic
436C2×C5C2×#90411yescharacteristic
437D5—22no—
438D5—124no—
439C23—51no—
440C23—302no—
441Q8—34no—
442Q8—62no—
443D4—154no—
444D4—308no—
445D4—302no—
446C2×C4—51no—
447C2×C4—51no—
448C2×C4—52no—
449C2×C4—52no—
450C2×C4—51no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—102no—
454C2×C4—102no—
455C2×C4—308no—
456C2×C4—302no—
457C2×C4—604no—
458C2×C4—604no—
459C2×C4D5×D1211yescharacteristic
460C2×C4D5×D1211yescharacteristic
461C2×C4C22×D3×D511yescharacteristic
462C8—21no—
463C8—52no—
464C8—101no—
465C8C4×D3×D512yes—
466C2×C3—102no—
467C2×C3C4×D4×D511yescharacteristic
468C2×C3C2×#406511yescharacteristic
469C2×C3D5×#13511yescharacteristic
470D3—204no—
471C5C4×#90411yescharacteristic, complemented, Sylow
472C22—52no—
473C22—101no—
474C22—101no—
475C22—304no—
476C22—602no—
477C22—602no—
478C22C2×D5×D1211yescharacteristic
479C4—21no—
480C4—52no—
481C4—52no—
482C4—64no—
483C4—101no—
484C4—122no—
485C4—602no—
486C4#9127112yesdirect product factor
487C4C2×C4×D3×D511yescharacteristic
488C4D5×#23511yescharacteristic
489C3C4×#406511yescharacteristic, complemented, Sylow
490C2—102no—
491C2—604no—
492C2C4×D5×D1211yescharacteristic
493C2D5×#90411yescharacteristic
494C2C2×#9127111yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91271C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#6773C2semidirect
3. C4×D120C2semidirect
4. C4×C5×Dic12C2semidirect
5. C3×C4×C8×D5C2semidirect
6. Dic5×Dic12C2semidirect
7. #11747833C2semidirect
8. #11747766C2semidirect
9. #11747672C2semidirect
10. #11747642C2semidirect
11. C4×#6660C2semidirect
29. #91271C4direct (N × H)
52. C4×C8×D5D3semidirect
63. #6773C2×C4semidirect
69. D120C2×C4semidirect
73. C5×Dic12C2×C4semidirect
80. C3×C8×D5C2×C4semidirect
86. #6660C2×C4semidirect
93. C4×Dic12D5semidirect
215. C8×D5C4×D3semidirect
235. C3×C4×C5#135semidirect
241. C3×Dic5#135semidirect
275. Dic12C4×D5semidirect
375. C4×C5#904semidirect
381. Dic5#904semidirect
416. C3×C5C4×#135semidirect
428. C3×C4#4065semidirect
471. C5C4×#904semidirect
486. C4#91271direct (N × H)
489. C3C4×#4065semidirect

Maximal subgroups

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

subgroupindex
C2×#912712
C4×#67732
C4×D1202
C4×C5×Dic122
C3×C4×C8×D52
Dic5×Dic122
#117478332
#117477662
#117476722
#117476422
C4×#66602
C4×#40653
C4×#9045