Finite Group Databasebeta

← C2×#11748080 #14429325

Subgroups — C2×#11748080 #14429325

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
1C22×C5×#204C211yesmaximal, characteristic, complemented
2C2×C3×#4047C211yesmaximal, characteristic, complemented
3C2×#91307C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic
5C2×#91103C211yesmaximal, characteristic, complemented
6C2×#90962C211yesmaximal, characteristic, complemented
7C2×#90959C211yesmaximal, characteristic, complemented
8#11748080C218yesmaximal, direct product factor
9C2×#65466—31nomaximal, Hall
10C22×C5×D12C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×#204—21no—
17C2×C5×#204—21no—
18C2×C5×#204—22no—
19C2×C5×#204C2214yescomplemented
20C2×C3×#681C2211yescharacteristic
21C3×#4047—22no—
22C3×#4047C2214yescomplemented
23C2×C3×#676—21no—
24C2×C3×C8×D5—21no—
25C2×#6661—21no—
26C2×#6656—21no—
27#91307—22no—
28#91307C2214yescomplemented
29C2×#6655—21no—
30#91299—22no—
31#91299C2214yes—
32C2×#6652—21no—
33#91103C2214yescomplemented
34#90962C2214yescomplemented
35#90959C2214yescomplemented
36C2×#5141—51nomaximal, Hall
37C22×C5×SD16—31no—
38C2×#4088—31no—
39C2×#4078—31no—
40C2×#4047D311yescharacteristic, complemented
41C2×#3968—31no—
42C2×#3965—31no—
43#65466—38no—
44C2×#3951—31no—
45C23×C5×D3—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×C5×Dic3—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12—21no—
53C2×C5×D12C2312yes—
54C2×C5×Dic6—21no—
55C2×C5×Dic6—21no—
56C2×C5×Dic6—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6C2312yes—
60C2×C3×C22⋊D5—21no—
61C3×#709—21no—
62C3×#709—21no—
63C3×#709D412yes—
64C3×#709C2312yes—
65C2×C3×D20D411yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10D411yescharacteristic
68C2×C3×C5×C8D411yescharacteristic
69C2×C3×C5×C8D411yescharacteristic
70C2×C3×C5×C8D412yes—
71C2×C3×C5×C8C2312yes—
72#6710—21no—
73#6710—21no—
74#6710C2312yes—
75#6710C2312yes—
76C2×C3⋊#168—21no—
77C2×C3⋊#168—21no—
78C5×#204—24no—
79C5×#204—24no—
80C3×#681—21no—
81C3×#681C2312yes—
82C2×C3×#168—21no—
83C3×#676—24no—
84C3×C8×D5—24no—
85#6661—24no—
86#6656—24no—
87#6655—24no—
88#6652—24no—
89C2×C3×#131—51no—
90C2×#951—51no—
91C2×#949—51no—
92C22×#204D511yescharacteristic, complemented
93#5141—58no—
94C2×#824—51no—
95C2×#823—51no—
96C2×#819—51no—
97C22×C5×Q8—31no—
98C22×C5×D4—31no—
99C2×#709C2×D311yescharacteristic
100C2×C5×SD16—34no—
101C2×C5×SD16—61no—
102C2×C5×SD16—61no—
103C2×C5×SD16—62no—
104C22×C5×C8C2×D311yescharacteristic
105C2×#689—61no—
106#4088—34no—
107#4088—62no—
108C2×#688—61no—
109C2×#687—61no—
110#4078—34no—
111#4078—62no—
112C2×#686—61no—
113C2×#681—31no—
114C2×#681—31no—
115C2×#681C2×D311yescharacteristic
116#4047—22no—
117#4047C2×D314yescomplemented
118C2×#676—21no—
119C2×C8×D5—21no—
120#3968—34no—
121#3965—34no—
122#3951—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×C5×D3—22no—
126C22×C5×D3—41no—
127C22×C5×D3—41no—
128C22×C5×D3—82no—
129C22×C3×D5—21no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×C5×Dic3—22no—
137C2×C5×Dic3—41no—
138C2×C5×Dic3—41no—
139C5×D12—22no—
140C5×D12—22no—
141C5×D12—41no—
142C5×D12—41no—
143C5×Dic6—22no—
144C5×Dic6—22no—
145C5×Dic6—41no—
146C5×Dic6—41no—
147C3×C22⋊D5—22no—
148C3×C22⋊D5—22no—
149C2×C3×Dic5—21no—
150C3×D20—21no—
151C3×D20C2×D412yes—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×Dic10—21no—
155C3×Dic10C2×D412yes—
156C3×C5×C8C2×D412yes—
157C3×C5×C8C2×D412yes—
158C3⋊#168—22no—
159C3⋊#168—22no—
160C3×#168—22no—
161C2×C3×#41—51no—
162C22×D12C2×D511yescharacteristic
163C22×Dic6C2×D511yescharacteristic
164C3×#131—54no—
165C3×#131—102no—
166C2×C3×M16—51no—
167C2×C3×M16—101no—
168C22×C3×C8—101no—
169C22×C3×C8C2×D511yescharacteristic
170#951—54no—
171#951—102no—
172#949—54no—
173#949—102no—
174C2×#216—101no—
175C2×#215—101no—
176C2×#214—101no—
177C2×#213—101no—
178C2×#208—51no—
179C2×#208—51no—
180C2×#204—21no—
181C2×#204—21no—
182C2×#204—22no—
183C2×#204C2×D514yescomplemented
184#824—54no—
185#823—54no—
186#819—54no—
187C24×C5—61no—
188C2×C5×Q8—32no—
189C2×C5×Q8—61no—
190C2×C5×Q8—61no—
191C2×C5×Q8—61no—
192C2×C5×Q8—61no—
193C2×C5×Q8—61no—
194C2×C5×D4—32no—
195C2×C5×D4—61no—
196C2×C5×D4—61no—
197C2×C5×D4—61no—
198C2×C5×D4—61no—
199C2×C5×D4—61no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—21no—
203#709—21no—
204#709—21no—
205#709D1212yes—
206#709C22×D312yes—
207C2×D20D1211yescharacteristic
208C2×C4×D5—21no—
209C2×Dic10D1211yescharacteristic
210C5×SD16—64no—
211C5×SD16—64no—
212C2×C5×C8#6711yescharacteristic
213C2×C5×C8#6711yescharacteristic
214C2×C5×C8#6712yes—
215C2×C5×C8C22×D312yes—
216#689—64no—
217#688—64no—
218#687—64no—
219#686—64no—
220#681—21no—
221#681—32no—
222#681—32no—
223#681—61no—
224#681—61no—
225#681C22×D312yes—
226C2×#168—21no—
227C2×#168—61no—
228C2×#168—61no—
229#676—24no—
230C8×D5—24no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—31no—
234C2×#131—51no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×C5×D3—42no—
244C2×C5×D3—82no—
245C2×C5×D3—82no—
246C2×C5×D3—82no—
247C2×C3×D5—22no—
248C2×C3×D5—42no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×Dic5—22no—
254C5×Dic3—42no—
255C23×D3—21no—
256C3×#41—52no—
257C3×#41—52no—
258C3×#41—101no—
259C3×#41—101no—
260C2×C3×Q8—51no—
261C2×C3×D4—51no—
262C2×C3×D4—101no—
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C22×Dic3—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12C22×D512yes—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6C22×D512yes—
278C3×M16—52no—
279C3×M16—101no—
280C3×M16—104no—
281C2×C3×C8—101no—
282C2×C3×C8—104no—
283C2×C3×C8C22⋊D511yescharacteristic
284C2×C3×C8C22⋊D511yescharacteristic
285C2×C3×C8C22⋊D512yes—
286C2×C3×C8C22×D512yes—
287#216—104no—
288#215—104no—
289#214—104no—
290#213—104no—
291#208—52no—
292#208—52no—
293#208—101no—
294#208—101no—
295C2×C3⋊C8—101no—
296C2×C3⋊C8—101no—
297#204—24no—
298#204—24no—
299C23×C5—62no—
300C23×C5—121no—
301C23×C5—121no—
302C23×C5—242no—
303C23×C5#23511yescharacteristic
304C22×D5—21no—
305C5×Q8—62no—
306C5×Q8—62no—
307C5×Q8—121no—
308C5×Q8—121no—
309C5×D4—62no—
310C5×D4—62no—
311C5×D4—121no—
312C5×D4—121no—
313C2×C4×C5—62no—
314C2×C4×C5—121no—
315C2×C4×C5—121no—
316C2×C4×C5C2×D1211yescharacteristic
317C2×C4×C5C2×D1211yescharacteristic
318C2×C4×C5#23511yescharacteristic
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C2×#6711yescharacteristic
321C2×C4×C5C23×D311yescharacteristic
322C22⋊D5—22no—
323C22⋊D5—22no—
324C2×Dic5—21no—
325D20—21no—
326D20C2×D1212yes—
327C4×D5—22no—
328C4×D5—22no—
329Dic10—21no—
330Dic10C2×D1212yes—
331C5×C8C2×#6712yes—
332C5×C8C2×#6712yes—
333#168—22no—
334#168—62no—
335#168—62no—
336C2×#41—51no—
337C22×Q8—31no—
338C22×D4—31no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—34no—
345C2×SD16—61no—
346C2×SD16—61no—
347C2×SD16—62no—
348C2×SD16—301no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—54no—
352#131—102no—
353C2×M16—51no—
354C2×M16—101no—
355C2×M16—151no—
356C2×M16—151no—
357C22×C8—101no—
358C22×C8D3×D511yescharacteristic
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366C3×D5—42no—
367C5×D3—82no—
368C23×C3—101no—
369C23×C3#71111yescharacteristic
370C22×D3—22no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—82no—
374C3×Q8—52no—
375C3×Q8—101no—
376C3×D4—52no—
377C3×D4—102no—
378C3×D4—102no—
379C3×D4—101no—
380C2×C3×C4—101no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4#71111yescharacteristic
386C2×C3×C4C2×C22⋊D511yescharacteristic
387C2×C3×C4C2×C22⋊D511yescharacteristic
388C2×C3×C4C23×D511yescharacteristic
389C2×Dic3—22no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400C3×C8—102no—
401C3×C8C2×C22⋊D512yes—
402C3×C8C2×C22⋊D512yes—
403C3⋊C8—102no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—122no—
407C22×C5—242no—
408C22×C5—242no—
409C22×C5—242no—
410C22×C5#93011yescharacteristic
411C22×C5#93011yescharacteristic
412C22×C5C2×#23511yescharacteristic
413C2×D5—22no—
414C2×D5—42no—
415C4×C5—122no—
416C4×C5#93011yescharacteristic
417C4×C5#93011yescharacteristic
418C4×C5C22×D1211yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—22no—
421C24—61no—
422#41—52no—
423#41—52no—
424#41—101no—
425#41—101no—
426C2×Q8—32no—
427C2×Q8—51no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×D4—32no—
434C2×D4—51no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—101no—
441C22×C4—61no—
442C22×C4—101no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—64no—
446SD16—64no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—52no—
451M16—101no—
452M16—104no—
453M16—152no—
454M16—152no—
455M16—301no—
456M16—301no—
457C2×C8—101no—
458C2×C8—104no—
459C2×C8—301no—
460C2×C8—301no—
461C2×C8#120111yescharacteristic
462C2×C8#120111yescharacteristic
463C2×C8#120112yes—
464C2×C8C2×D3×D512yes—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—102no—
468C22×C3—202no—
469C22×C3#408411yescharacteristic
470C22×C3#408411yescharacteristic
471C22×C3C2×#71111yescharacteristic
472C2×D3—42no—
473C2×D3—82no—
474C2×D3—82no—
475C2×D3—82no—
476C3×C4—102no—
477C3×C4#408411yescharacteristic
478C3×C4#408411yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480C3×C4C22×C22⋊D511yescharacteristic
481Dic3—42no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—242no—
485C2×C5#514112yescomplemented
486C2×C5C2×#93011yescharacteristic
487D5—42no—
488C23—62no—
489C23—101no—
490C23—121no—
491C23—121no—
492C23—242no—
493C23#677211yescharacteristic
494Q8—52no—
495Q8—62no—
496Q8—62no—
497Q8—101no—
498Q8—121no—
499Q8—121no—
500D4—52no—
501D4—62no—
502D4—62no—
503D4—102no—
504D4—102no—
505D4—101no—
506D4—121no—
507D4—121no—
508C2×C4—62no—
509C2×C4—101no—
510C2×C4—102no—
511C2×C4—102no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4#677211yescharacteristic
515C2×C4D5×D1211yescharacteristic
516C2×C4D5×D1211yescharacteristic
517C2×C4C2×#120111yescharacteristic
518C2×C4C2×#120111yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—102no—
521C8—302no—
522C8—302no—
523C8C2×#120112yes—
524C8C2×#120112yes—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—202no—
528C2×C3#6546612yescomplemented
529C2×C3C2×#408411yescharacteristic
530D3—82no—
531C5C2×#514111yescharacteristic, complemented, Sylow
532C22—22no—
533C22—102no—
534C22—122no—
535C22—202no—
536C22—242no—
537C22—242no—
538C22—242no—
539C22#9144911yescharacteristic
540C22#9144911yescharacteristic
541C22C2×#677211yescharacteristic
542C4—102no—
543C4—122no—
544C4#9144911yescharacteristic
545C4#9144911yescharacteristic
546C4C2×D5×D1211yescharacteristic
547C4C22×#120111yescharacteristic
548C3C2×#6546611yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—202no—
552C2—242no—
553C2#1174808012yesdirect product factor
554C2C2×#9144911yescharacteristic
subgroupG/H
centerC22#91449
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5#121
prime radicalC2×#91299C2
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#204C2semidirect
2. C2×C3×#4047C2semidirect
3. C2×#91307C2semidirect
5. C2×#91103C2semidirect
6. C2×#90962C2semidirect
7. C2×#90959C2semidirect
8. #11748080C2direct (N × H)
19. C2×C5×#204C22semidirect
22. C3×#4047C22semidirect
28. #91307C22semidirect
33. #91103C22semidirect
34. #90962C22semidirect
35. #90959C22semidirect
40. C2×#4047D3semidirect
92. C22×#204D5semidirect
117. #4047C2×D3semidirect
183. C2×#204C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#5141semidirect
528. C2×C3#65466semidirect
531. C5C2×#5141semidirect
548. C3C2×#65466semidirect
553. C2#11748080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2042
C2×C3×#40472
C2×#913072
C2×#912992
C2×#911032
C2×#909622
C2×#909592
#117480802
C2×#654663
C2×#51415