Finite Group Databasebeta

← C2×#11751301 #14429288

Subgroups — C2×#11751301 #14429288

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91837C211yesmaximal, characteristic, complemented
4C22×#6716C211yesmaximal, characteristic, complemented
5C2×#91117C211yesmaximal, characteristic, complemented
6#11751301C218yesmaximal, direct product factor
7C2×#91108C211yesmaximal, characteristic, complemented
8C2×#91106C211yesmaximal, characteristic, complemented
9C2×#65489—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C3×C5×AGL(1,ℤ/8)—22no—
14C3×C5×AGL(1,ℤ/8)C2214yes—
15C2×C3×C5×SD16—21no—
16C2×C3×C5×D8—21no—
17C2×C3×C5×M16C2211yescharacteristic
18#91840—22no—
19#91840C2214yescomplemented
20#91837—22no—
21#91837C2214yescomplemented
22C2×#6718—21no—
23C2×#6716—21no—
24C2×#6716—21no—
25C2×#6716—21no—
26C2×#6716—22no—
27C2×#6716C2214yescomplemented
28C2×#6710—21no—
29C2×#6710C2211yescharacteristic
30C2×#6710C2211yescharacteristic
31C22×C3⋊#168—21no—
32C22×C3⋊#168C2211yescharacteristic
33#91117C2214yescomplemented
34#91108C2214yescomplemented
35#91106C2214yescomplemented
36C2×#5200—51nomaximal, Hall
37C2×C5×AGL(1,ℤ/8)D311yescharacteristic
38C2×#4097—31no—
39C2×#4094—31no—
40C22×#687—31no—
41C2×#3965—31no—
42#65489—38no—
43C2×#3956—31no—
44C2×#3954—31no—
45C24×C3×C5—21no—
46C3×C5×#41—21no—
47C3×C5×#41—21no—
48C3×C5×#41D412yes—
49C3×C5×#41C2312yes—
50C2×C3×C5×Q8D411yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4D411yescharacteristic
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15—21no—
62C2×Dic30—21no—
63C2×Dic30—21no—
64C2×Dic30—21no—
65C2×Dic30—21no—
66C2×Dic30—21no—
67C2×Dic30C2312yes—
68C3×C5×SD16—24no—
69C3×C5×D8—24no—
70C3×C5×M16—21no—
71C3×C5×M16C2312yes—
72C2×C3×C5×C8—21no—
73#6718—24no—
74#6716—24no—
75#6716—24no—
76#6716—24no—
77#6710—21no—
78#6710—21no—
79#6710—24no—
80#6710C2312yes—
81#6710C2312yes—
82C2×C3⋊#168—21no—
83C2×C3⋊#168—21no—
84C2×C3⋊#168—24no—
85C2×C3⋊#168D411yescharacteristic
86C2×C3⋊#168D411yescharacteristic
87C2×C3⋊#168D412yes—
88C2×C3⋊#168C2312yes—
89C2×C3×AGL(1,ℤ/8)D511yescharacteristic
90C2×#951—51no—
91C2×#948—51no—
92C22×#214—51no—
93C2×#833—51no—
94#5200—58no—
95C2×#824—51no—
96C2×#822—51no—
97C2×C5×#41C2×D311yescharacteristic
98C22×C5×D4C2×D311yescharacteristic
99C22×Dic10—31no—
100C5×AGL(1,ℤ/8)—22no—
101C5×AGL(1,ℤ/8)C2×D314yes—
102C2×C5×SD16—21no—
103C2×C5×D8—21no—
104C2×C5×M16C2×D311yescharacteristic
105#4097—34no—
106#4097—62no—
107#4094—34no—
108#4094—62no—
109C2×#689—61no—
110C2×#687—34no—
111C2×#687—61no—
112C2×#687—61no—
113C2×#687—62no—
114C2×#687—61no—
115C2×#681—31no—
116C2×#681—31no—
117C2×#681—61no—
118C22×#168—31no—
119C22×#168—61no—
120#3965—34no—
121#3956—34no—
122#3954—34no—
123C2×#471—151noSylow
124C23×C3×C5—21no—
125C23×C3×C5—22no—
126C23×C3×C5—41no—
127C23×C3×C5—41no—
128C23×C3×C5—82no—
129C23×C3×C5#4111yescharacteristic
130C3×C5×Q8—21no—
131C3×C5×Q8C2×D412yes—
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—21no—
135C3×C5×D4—22no—
136C3×C5×D4—22no—
137C3×C5×D4—41no—
138C3×C5×D4—41no—
139C3×C5×D4C2×D412yes—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5#4111yescharacteristic
148C2×C3×C4×C5C2411yescharacteristic
149C2×Dic15—22no—
150C2×Dic15—41no—
151C2×Dic15—41no—
152Dic30—22no—
153Dic30—22no—
154Dic30—41no—
155Dic30—41no—
156C3×C5×C8—22no—
157C3⋊#168—22no—
158C3⋊#168—22no—
159C3⋊#168C2×D412yes—
160C3⋊#168C2×D412yes—
161C2×C3×#41C2×D511yescharacteristic
162C22×C3×D4C2×D511yescharacteristic
163C22×Dic6—51no—
164C3×AGL(1,ℤ/8)—22no—
165C3×AGL(1,ℤ/8)C2×D514yes—
166C2×C3×SD16—21no—
167C2×C3×D8—21no—
168C2×C3×M16C2×D511yescharacteristic
169#951—54no—
170#951—102no—
171#948—54no—
172#948—102no—
173C2×#216—101no—
174C2×#214—54no—
175C2×#214—101no—
176C2×#214—101no—
177C2×#214—102no—
178C2×#214—101no—
179C2×#208—51no—
180C2×#208—51no—
181C2×#208—101no—
182C22×C3⋊C8—51no—
183C22×C3⋊C8—101no—
184#833—54no—
185#824—54no—
186#822—54no—
187C24×C5—21no—
188C5×#41—21no—
189C5×#41—21no—
190C5×#41#6712yes—
191C5×#41C22×D312yes—
192C2×C5×Q8#6711yescharacteristic
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4#6711yescharacteristic
200C2×C5×D4C22×D312yes—
201C22×C4×C5—21no—
202C22×C4×C5C22×D311yescharacteristic
203C22×Dic5—61no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10—61no—
210C5×SD16—24no—
211C5×D8—24no—
212C5×M16—21no—
213C5×M16C22×D312yes—
214C2×C5×C8—21no—
215#689—64no—
216#687—64no—
217#687—64no—
218#687—64no—
219#681—32no—
220#681—32no—
221#681—64no—
222#681—61no—
223#681—61no—
224C2×#168—31no—
225C2×#168—31no—
226C2×#168—32no—
227C2×#168—32no—
228C2×#168—64no—
229C2×#168—61no—
230C2×#168—61no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)D1511yescharacteristic
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5—82no—
244C22×C3×C5—82no—
245C22×C3×C5—82no—
246C22×C3×C5#12111yescharacteristic
247C22×C3×C5#12111yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C3×C4×C5—22no—
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5#12111yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254Dic15—42no—
255C24×C3—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41C22⋊D512yes—
259C3×#41C22×D512yes—
260C2×C3×Q8C22⋊D511yescharacteristic
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4C22⋊D511yescharacteristic
268C2×C3×D4C22×D512yes—
269C22×C3×C4—21no—
270C22×C3×C4C22×D511yescharacteristic
271C22×Dic3—101no—
272C2×Dic6—52no—
273C2×Dic6—101no—
274C2×Dic6—101no—
275C2×Dic6—101no—
276C2×Dic6—101no—
277C2×Dic6—101no—
278C3×SD16—24no—
279C3×D8—24no—
280C3×M16—21no—
281C3×M16C22×D512yes—
282C2×C3×C8—21no—
283#216—104no—
284#214—104no—
285#214—104no—
286#214—104no—
287#208—52no—
288#208—52no—
289#208—104no—
290#208—101no—
291#208—101no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—52no—
295C2×C3⋊C8—52no—
296C2×C3⋊C8—104no—
297C2×C3⋊C8—101no—
298C2×C3⋊C8—101no—
299C23×C5—21no—
300C23×C5—22no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—82no—
304C23×C5#23711yescharacteristic
305C5×Q8—21no—
306C5×Q8C2×#6712yes—
307C5×D4—22no—
308C5×D4—22no—
309C5×D4—21no—
310C5×D4—22no—
311C5×D4—22no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4C2×#6712yes—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5#23711yescharacteristic
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C2×#6711yescharacteristic
323C2×C4×C5C23×D311yescharacteristic
324C2×Dic5—62no—
325C2×Dic5—121no—
326C2×Dic5—121no—
327Dic10—62no—
328Dic10—62no—
329Dic10—121no—
330Dic10—121no—
331C5×C8—22no—
332#168—32no—
333#168—32no—
334#168—62no—
335#168—62no—
336C2×#41C2×D1511yescharacteristic
337C22×Q8—151no—
338C22×D4C2×D1511yescharacteristic
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—22no—
342AGL(1,ℤ/8)C2×D1514yes—
343C2×Q16—301no—
344C2×SD16—21no—
345C2×SD16—154no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—21no—
351#131—154no—
352#131—302no—
353C2×M16—151no—
354C2×M16—151no—
355C2×M16—301no—
356C2×M16C2×D1511yescharacteristic
357C22×C8—151no—
358C22×C8—301no—
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—42no—
365C2×C3×C5—82no—
366C2×C3×C5#47112yescomplemented
367C2×C3×C5C2×#12111yescharacteristic
368C23×C3—21no—
369C23×C3—22no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—82no—
373C23×C3#71111yescharacteristic
374C3×Q8—21no—
375C3×Q8C2×C22⋊D512yes—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—22no—
380C3×D4—21no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4C2×C22⋊D512yes—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4#71111yescharacteristic
390C2×C3×C4C2×C22⋊D511yescharacteristic
391C2×C3×C4C2×C22⋊D511yescharacteristic
392C2×C3×C4C23×D511yescharacteristic
393C2×Dic3—102no—
394C2×Dic3—201no—
395C2×Dic3—201no—
396Dic6—102no—
397Dic6—102no—
398Dic6—201no—
399Dic6—201no—
400C3×C8—22no—
401C3⋊C8—52no—
402C3⋊C8—52no—
403C3⋊C8—102no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—82no—
410C22×C5—82no—
411C22×C5—82no—
412C22×C5#93911yescharacteristic
413C22×C5#93911yescharacteristic
414C22×C5C2×#23711yescharacteristic
415C4×C5—22no—
416C4×C5#93911yescharacteristic
417C4×C5#93911yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—122no—
421C24—21no—
422#41—21no—
423#41—21no—
424#41#122012yes—
425#41C22×D1512yes—
426C2×Q8—152no—
427C2×Q8—301no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8#122011yescharacteristic
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4#122011yescharacteristic
440C2×D4C22×D1512yes—
441C22×C4—21no—
442C22×C4—301no—
443C22×C4C22×D1511yescharacteristic
444Q16—304no—
445SD16—24no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—24no—
450M16—21no—
451M16—152no—
452M16—152no—
453M16—304no—
454M16—301no—
455M16—301no—
456M16C22×D1512yes—
457C2×C8—21no—
458C2×C8—151no—
459C2×C8—151no—
460C2×C8—152no—
461C2×C8—152no—
462C2×C8—304no—
463C2×C8—301no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—82no—
471C22×C3—82no—
472C22×C3—82no—
473C22×C3#408511yescharacteristic
474C22×C3#408511yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C3×C4—22no—
477C3×C4#408511yescharacteristic
478C3×C4#408511yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480C3×C4C22×C22⋊D511yescharacteristic
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—42no—
485C2×C5—82no—
486C2×C5#520012yescomplemented
487C2×C5C2×#93911yescharacteristic
488C23—21no—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—82no—
493C23#681911yescharacteristic
494Q8—21no—
495Q8—302no—
496Q8—302no—
497Q8—601no—
498Q8—601no—
499Q8C2×#122012yes—
500D4—22no—
501D4—22no—
502D4—21no—
503D4—22no—
504D4—22no—
505D4—41no—
506D4—41no—
507D4C2×#122012yes—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4D4×D1511yescharacteristic
515C2×C4D4×D1511yescharacteristic
516C2×C4#681911yescharacteristic
517C2×C4C2×#122011yescharacteristic
518C2×C4C2×#122011yescharacteristic
519C2×C4C23×D1511yescharacteristic
520C8—22no—
521C8—152no—
522C8—152no—
523C8—302no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—42no—
528C2×C3—82no—
529C2×C3#6548912yescomplemented
530C2×C3C2×#408511yescharacteristic
531C5C2×#520011yescharacteristic, complemented, Sylow
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22#9182811yescharacteristic
540C22#9182811yescharacteristic
541C22C2×#681911yescharacteristic
542C4—22no—
543C4—602no—
544C4#9182811yescharacteristic
545C4#9182811yescharacteristic
546C4C2×D4×D1511yescharacteristic
547C4C22×#122011yescharacteristic
548C3C2×#6548911yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—42no—
552C2—82no—
553C2#1175130112yesdirect product factor
554C2C2×#9182811yescharacteristic
subgroupG/H
centerC22#91828
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5#121
hypercenterC2×AGL(1,ℤ/8)D15
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C2×#91837C2semidirect
4. C22×#6716C2semidirect
5. C2×#91117C2semidirect
6. #11751301C2direct (N × H)
7. C2×#91108C2semidirect
8. C2×#91106C2semidirect
19. #91840C22semidirect
21. #91837C22semidirect
27. C2×#6716C22semidirect
33. #91117C22semidirect
34. #91108C22semidirect
35. #91106C22semidirect
366. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
486. C2×C5#5200semidirect
529. C2×C3#65489semidirect
531. C5C2×#5200semidirect
548. C3C2×#65489semidirect
553. C2#11751301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
C2×#918402
C2×#918372
C22×#67162
C2×#911172
#117513012
C2×#911082
C2×#911062
C2×#654893
C2×#52005