Finite Group Databasebeta

← C4×#91277 #14416248

Subgroups — C4×#91277 #14416248

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×#91277C211yesmaximal, characteristic
2C4×#6766C212yesmaximal, complemented
3C4×C8×D15C211yesmaximal, characteristic, complemented
4C4×C5×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×D40C211yesmaximal, characteristic, complemented
6#11748141C212yesmaximal, complemented
7#11747886C211yesmaximal, characteristic, complemented
8#11747809C211yesmaximal, characteristic, complemented
9#11747735C212yesmaximal, complemented
10#11747690C211yesmaximal, characteristic, complemented
11C4×#6655C212yesmaximal, complemented
12C4×#4065—31nomaximal, Hall
13C2×#6766C2212yes—
14C2×C8×D15C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16C42×D15C2211yescharacteristic
17C2×C5×Dic12C2211yescharacteristic
18C4×C5×Dic6C2212yes—
19C2×C3×D40C2211yescharacteristic
20C3×C4×D20C2212yes—
21C4×#1202—22no—
22#91434C2212yes—
23#91396—22no—
24#91394—22no—
25C4×D5×Dic3—22no—
26#91347C2212yes—
27#91344C2212yes—
28C2×#6655C2212yes—
29#91277C418yesdirect product factor
30C3×C4×C5×C8C2211yescharacteristic
31C8×Dic15C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#818C2211yescharacteristic
35C5×#816C2212yes—
36C3×#3953C2212yes—
37C3×#3950C2211yescharacteristic
38#90986C2212yes—
39#90972C2212yes—
40#90964C2212yes—
41C4×#912—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×D40D311yescharacteristic, complemented
52C4×C8×D5—31no—
53C2×C4×D15D411yescharacteristic
54C2×C4×D15D411yescharacteristic
55C2×C4×D15C2311yescharacteristic
56C2×C5×Dic6C2312yes—
57C2×C3×D20C2312yes—
58C2×C3×C4×D5—22no—
59C2×#1202—22no—
60C2×D5×Dic3—22no—
61C2×D5×Dic3—22no—
62#6766—24no—
63#6766C2×C418yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67C4×Dic15D411yescharacteristic
68C4×Dic15D411yescharacteristic
69C4×Dic15C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C8×D15—22no—
73C8×D15C2×C414yescomplemented
74C5×C4⋊Dic3C2312yes—
75C5×Dic3⋊C4—22no—
76C4×C5×Dic3—22no—
77C5×Dic12C2×C414yescomplemented
78C3×#685—22no—
79C3×C4⋊Dic5C2312yes—
80C3×D40C2×C414yescomplemented
81Dic3⋊Dic5—22no—
82#6667—22no—
83#6665—22no—
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6655C2×C418yescomplemented
87C2×#912—51no—
88C4×#237—52no—
89C3×C4×D8—51no—
90Dic3×D8—51no—
91C4×#214—52no—
92#4880—51no—
93#4873—51no—
94#4772—52no—
95#4758—52no—
96C4×Dic12D511yescharacteristic, complemented
97C4×D3×C8—51no—
98C2×#713—32no—
99C2×C5×Q16—31no—
100C4×C5×Q8—32no—
101Q8×Dic5—32no—
102C2×#688—32no—
103#4065—38no—
104C2×D40C2×D311yescharacteristic
105C2×C8×D5—31no—
106C2×C8×D5—31no—
107#4039—32no—
108#4039—62no—
109#4038—32no—
110#4038—62no—
111C4×D20—62no—
112C4×D20C2×D312yes—
113C42×D5—31no—
114C42×D5—62no—
115C5×#107—31no—
116C5×#103—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953C2×D312yes—
120#3950C2×D311yescharacteristic
121C8×Dic5—31no—
122C8×Dic5—31no—
123#3941—32no—
124#3940—32no—
125C4×#168—31no—
126C4×#135—151noSylow
127C22×D15C2×D411yescharacteristic
128C22×C3×D5—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133C2×Dic15C2×D411yescharacteristic
134C2×Dic15C2×D411yescharacteristic
135C4×D15—22no—
136C4×D15—22no—
137C4×D15C22×C412yes—
138C4×D15#4112yes—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C5×Dic6—22no—
142C5×Dic6C22×C414yes—
143C2×C3×Dic5—22no—
144C3×D20—22no—
145C3×D20C22×C414yes—
146C3×C4×D5—44no—
147#1202—28no—
148D5×Dic3—28no—
149D5×Dic3—44no—
150C3×C5×C8—21no—
151C3×C5×C8C22×C412yes—
152C3⋊#168—21no—
153C3⋊#168C22×C412yes—
154C2×#237—52no—
155C2×C3×D8—51no—
156C3×C4×D4—52no—
157D4×Dic3—52no—
158C2×#214—52no—
159C4×#67—102no—
160C2×C4×Dic3—102no—
161#912—58no—
162C2×Dic12C2×D511yescharacteristic
163C2×D3×C8—51no—
164C2×D3×C8—51no—
165#892—52no—
166#887—52no—
167#67⋊C4—102no—
168#877—102no—
169C42×D3—51no—
170C4×Dic6C2×D512yes—
171C3×#107—51no—
172C3×#102—52no—
173C3×C4×C8C2×D511yescharacteristic
174#832—52no—
175#818C2×D511yescharacteristic
176#816C2×D512yes—
177C8×Dic3—51no—
178C8×Dic3—51no—
179#810—52no—
180#808—52no—
181C4×C3⋊C8—51no—
182C2×C5×Q8—32no—
183#713—38no—
184#713—64no—
185C2×D20—62no—
186C2×D20C22×D312yes—
187C2×C4×D5—22no—
188C2×C4×D5—31no—
189C2×C4×D5—31no—
190C2×C4×D5—31no—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
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—22no—
202#685—62no—
203#685—62no—
204C4⋊Dic5—62no—
205C4⋊Dic5C22×D312yes—
206C4×Dic5—31no—
207C4×Dic5—31no—
208C4×Dic5—31no—
209C4×Dic5—62no—
210C4×Dic5—62no—
211C2×#168—31no—
212C2×#168—31no—
213D40C4×D314yescomplemented
214C8×D5—34no—
215C8×D5—62no—
216C2×#135—151no—
217C4×#41—152no—
218C4×Q16—31no—
219C4×Q16—151no—
220C4×SD16—152no—
221C4×SD16—152no—
222C4×D8—51no—
223C4×D8—151no—
224#427—151no—
225#416—152no—
226C2×C4×C8—151no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—21no—
229C2×D15—21no—
230C2×D15C4×D412yes—
231C2×C3×D5—24no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C3×C4×C5—21no—
235C3×C4×C5#13512yescomplemented
236C3×C4×C5C23×C411yescharacteristic
237C3×C4×C5C2×#4111yescharacteristic
238Dic15—21no—
239Dic15C4×D412yes—
240Dic15#13512yescomplemented
241C3×Dic5—42no—
242C5×Dic3—24no—
243C5×Dic3—42no—
244C2×C3×D4—52no—
245C22×C3×C4—102no—
246C2×#67—102no—
247C22×Dic3—102no—
248C22×Dic3—102no—
249#237—58no—
250#237—104no—
251C2×C4×D3—51no—
252C2×C4×D3—51no—
253C2×C4×D3—51no—
254C2×Dic6C22×D512yes—
255C3×D8—54no—
256C2×C3×C8C22×D511yescharacteristic
257C2×C3×C8C22×D511yescharacteristic
258C3×C4⋊C4—52no—
259C3×C22⋊C4—102no—
260C3×C42C22×D511yescharacteristic
261#217—102no—
262#214—58no—
263(C2×D3)⋊C4—102no—
264C4⋊Dic3C22×D512yes—
265Dic3⋊C4—22no—
266Dic3⋊C4—102no—
267C4×Dic3—22no—
268C4×Dic3—51no—
269C4×Dic3—51no—
270C4×Dic3—51no—
271C4×Dic3—102no—
272C4×Dic3—102no—
273C2×C3⋊C8—51no—
274C2×C3⋊C8—51no—
275Dic12C4×D514yescomplemented
276D3×C8—54no—
277D3×C8—102no—
278C22×D5—22no—
279C22×D5—31no—
280C5×Q8—34no—
281C5×Q8—62no—
282C2×C4×C5—62no—
283C2×C4×C5—62no—
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5C23×D311yescharacteristic
287C2×Dic5—22no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—31no—
291D20—22no—
292D20—68no—
293D20C2×C4×D314yes—
294C4×D5—32no—
295C4×D5—32no—
296C4×D5—44no—
297C4×D5—62no—
298C4×D5—68no—
299C4×D5—62no—
300C4×D5—124no—
301C5×C8—21no—
302C5×C8C2×C4×D312yes—
303#168—32no—
304#168—61no—
305C2×#41—152no—
306#135—158no—
307C2×Q16—31no—
308C2×SD16—152no—
309C2×D8—51no—
310C22×C8—151no—
311C22×C8—151no—
312C4×Q8—32no—
313C4×Q8—152no—
314C4×D4—52no—
315C4×D4—152no—
316C4×D4—302no—
317C4×D4—302no—
318#117—152no—
319#117—302no—
320C2×C42—151no—
321C2×C42—302no—
322#107—31no—
323#107—51no—
324#106—152no—
325#103—32no—
326#103—152no—
327#102—52no—
328#102—152no—
329C4×C8—151no—
330C4×C8—151no—
331C4×C8—151no—
332C4×C8D3×D511yescharacteristic
333C2×C3×C5C2×C4×D411yescharacteristic
334C2×C3×C5C2×#13511yescharacteristic
335C2×C3×C5C2×#13511yescharacteristic
336D15—22no—
337C3×D5—44no—
338C23×C3—102no—
339C22×D3—51no—
340C3×D4—54no—
341C3×D4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—204no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347#67—108no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—51no—
351C2×Dic3—51no—
352C2×Dic3—51no—
353C2×Dic3—108no—
354C2×Dic3—204no—
355C4×D3—52no—
356C4×D3—52no—
357C4×D3—102no—
358C4×D3—102no—
359Dic6—22no—
360Dic6C2×C4×D514yes—
361C3×C8—21no—
362C3×C8C2×C4×D512yes—
363C3⋊C8—52no—
364C3⋊C8—101no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—24no—
367C2×D5—32no—
368C2×D5—42no—
369C2×D5—42no—
370C2×D5—61no—
371C2×D5—61no—
372C4×C5—21no—
373C4×C5—64no—
374C4×C5—122no—
375C4×C5#91212yescomplemented
376C4×C5C22×C4×D311yescharacteristic
377C4×C5D3×#4111yescharacteristic
378Dic5—32no—
379Dic5—32no—
380Dic5—42no—
381Dic5—61no—
382#41—158no—
383#41—304no—
384C2×Q8—32no—
385C2×D4—52no—
386C2×D4—302no—
387C22×C4—102no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—151no—
391C22×C4—302no—
392C22×C4—302no—
393Q16—34no—
394SD16—158no—
395D8—54no—
396C2×C8—151no—
397C2×C8—154no—
398C2×C8—151no—
399C2×C8—302no—
400C2×C8C2×D3×D511yescharacteristic
401C2×C8C2×D3×D511yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—52no—
404C4⋊C4—62no—
405C4⋊C4—302no—
406C22⋊C4—102no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—62no—
410C42—151no—
411C42—151no—
412C42—151no—
413C42—302no—
414C42—302no—
415C42C2×D3×D511yescharacteristic
416C3×C5C4×#13511yescharacteristic, complemented, Hall
417C22×C3—104no—
418C22×C3—202no—
419C22×C3—202no—
420C22×C3C2×D4×D511yescharacteristic
421C2×D3—52no—
422C2×D3—101no—
423C2×D3—101no—
424C3×C4—21no—
425C3×C4—202no—
426C3×C4#406512yescomplemented
427C3×C4C22×C4×D511yescharacteristic
428C3×C4D5×#4111yescharacteristic
429Dic3—24no—
430Dic3—42no—
431Dic3—52no—
432Dic3—52no—
433Dic3—101no—
434C2×C5C4×D3×D411yescharacteristic
435C2×C5C2×#91211yescharacteristic
436C2×C5D3×#13511yescharacteristic
437D5—44no—
438D5—62no—
439C23—102no—
440C23—151no—
441Q8—34no—
442Q8—62no—
443D4—54no—
444D4—102no—
445D4—308no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—102no—
449C2×C4—151no—
450C2×C4—151no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—151no—
454C2×C4—204no—
455C2×C4—302no—
456C2×C4—308no—
457C2×C4—302no—
458C2×C4—604no—
459C2×C4#677711yescharacteristic
460C2×C4#677711yescharacteristic
461C2×C4C22×D3×D511yescharacteristic
462C8—21no—
463C8—152no—
464C8—301no—
465C8C4×D3×D512yes—
466C2×C3—204no—
467C2×C3C4×D4×D511yescharacteristic
468C2×C3C2×#406511yescharacteristic
469C2×C3D5×#13511yescharacteristic
470D3—102no—
471C5C4×#91211yescharacteristic, complemented, Sylow
472C22—104no—
473C22—152no—
474C22—202no—
475C22—202no—
476C22—301no—
477C22—301no—
478C22C2×#677711yescharacteristic
479C4—21no—
480C4—64no—
481C4—122no—
482C4—152no—
483C4—152no—
484C4—202no—
485C4—301no—
486C4#9127712yesdirect product factor
487C4C2×C4×D3×D511yescharacteristic
488C4#9201611yescharacteristic
489C3C4×#406511yescharacteristic, complemented, Sylow
490C2—204no—
491C2—302no—
492C2C4×#677711yescharacteristic
493C2#1175397811yescharacteristic
494C2C2×#9127711yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91277C2
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×#6766C2semidirect
3. C4×C8×D15C2semidirect
4. C4×C5×Dic12C2semidirect
5. C3×C4×D40C2semidirect
6. #11748141C2semidirect
7. #11747886C2semidirect
8. #11747809C2semidirect
9. #11747735C2semidirect
10. #11747690C2semidirect
11. C4×#6655C2semidirect
29. #91277C4direct (N × H)
51. C4×D40D3semidirect
63. #6766C2×C4semidirect
73. C8×D15C2×C4semidirect
77. C5×Dic12C2×C4semidirect
80. C3×D40C2×C4semidirect
86. #6655C2×C4semidirect
96. C4×Dic12D5semidirect
213. D40C4×D3semidirect
235. C3×C4×C5#135semidirect
240. Dic15#135semidirect
275. Dic12C4×D5semidirect
375. C4×C5#912semidirect
416. C3×C5C4×#135semidirect
426. C3×C4#4065semidirect
471. C5C4×#912semidirect
486. C4#91277direct (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×#912772
C4×#67662
C4×C8×D152
C4×C5×Dic122
C3×C4×D402
#117481412
#117478862
#117478092
#117477352
#117476902
C4×#66552
C4×#40653
C4×#9125