Finite Group Databasebeta

← C2×#11750849 #14429291

Subgroups — C2×#11750849 #14429291

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×#6716C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic
3C2×#91798C211yesmaximal, characteristic, complemented
4C2×#91796C211yesmaximal, characteristic, complemented
5C2×C3×C5×#100C211yesmaximal, characteristic, complemented
6C2×#91108C211yesmaximal, characteristic, complemented
7C2×#91106C211yesmaximal, characteristic, complemented
8#11750849C218yesmaximal, direct product factor
9C2×#65037—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C2×#6817C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×#6716—21no—
16C2×#6716—21no—
17C2×#6716—21no—
18C2×#6716—22no—
19C2×#6716C2214yescomplemented
20#91821—22no—
21#91821C2214yes—
22C2×#6715—21no—
23C2×#6710C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25#91798—22no—
26#91798C2214yescomplemented
27#91796—22no—
28#91796C2214yescomplemented
29C2×Dic60—21no—
30C2×#6706—21no—
31C2×#6705—21no—
32C2×C8×D15—21no—
33C3×C5×#100C2214yescomplemented
34#91108C2214yescomplemented
35#91106C2214yescomplemented
36C2×#4748—51nomaximal, Hall
37C22×#687—31no—
38C2×#4078—31no—
39C2×#4055—31no—
40C2×#4053—31no—
41C2×C5×#100D311yescharacteristic, complemented
42C2×#3956—31no—
43C2×#3954—31no—
44#65037—38no—
45C24×C3×C5—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C2×#1220—21no—
54C22×Dic15—21no—
55#6817—21no—
56#6817—21no—
57#6817D412yes—
58#6817C2312yes—
59C2×D60D411yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30—21no—
62C2×Dic30—21no—
63C2×Dic30—21no—
64C2×Dic30—21no—
65C2×Dic30—21no—
66C2×Dic30D411yescharacteristic
67C2×Dic30C2312yes—
68C3×C5×M16—21no—
69C3×C5×M16—21no—
70C3×C5×M16C2312yes—
71C3×C5×M16C2312yes—
72C2×C3×C5×C8—21no—
73C2×C3×C5×C8—21no—
74#6716—24no—
75#6716—24no—
76#6716—24no—
77#6715—24no—
78#6710—21no—
79#6710C2312yes—
80C2×C3⋊#168—21no—
81C2×C3⋊#168D411yescharacteristic
82C2×C3⋊#168D411yescharacteristic
83C2×C3⋊#168D412yes—
84C2×C3⋊#168C2312yes—
85Dic60—24no—
86#6706—24no—
87#6705—24no—
88C8×D15—24no—
89C22×#214—51no—
90C2×#932—51no—
91C2×#909—51no—
92C2×#907—51no—
93C2×C3×#100D511yescharacteristic, complemented
94C2×#824—51no—
95C2×#822—51no—
96#4748—58no—
97C22×C5×D4C2×D311yescharacteristic
98C2×#709—31no—
99C22×Dic10—31no—
100C2×C5×M16C2×D311yescharacteristic
101C2×C5×M16C2×D311yescharacteristic
102C2×#687—34no—
103C2×#687—61no—
104C2×#687—61no—
105C2×#687—62no—
106C2×#687—61no—
107#4078—34no—
108#4078—62no—
109C2×#686—61no—
110C2×#681—31no—
111C22×#168—31no—
112#4055—34no—
113#4055—62no—
114#4053—34no—
115#4053—62no—
116C2×Dic20—61no—
117C2×#677—61no—
118C2×#676—61no—
119C2×C8×D5—61no—
120C5×#100C2×D314yescomplemented
121#3956—34no—
122#3954—34no—
123C2×#471—151noSylow
124C23×C3×C5—22no—
125C23×C3×C5—41no—
126C23×C3×C5—41no—
127C23×C3×C5—82no—
128C23×C3×C5#4111yescharacteristic
129C22×D15—21no—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—41no—
133C3×C5×D4—41no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—22no—
141#1220—22no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—41no—
145C2×Dic15—41no—
146D60—21no—
147D60C2×D412yes—
148C4×D15—22no—
149C4×D15—22no—
150Dic30—21no—
151Dic30—22no—
152Dic30—22no—
153Dic30—41no—
154Dic30—41no—
155Dic30C2×D412yes—
156C3×C5×C8—22no—
157C3×C5×C8—22no—
158C3⋊#168—22no—
159C3⋊#168C2×D412yes—
160C3⋊#168C2×D412yes—
161C22×C3×D4C2×D511yescharacteristic
162C2×#235—51no—
163C22×Dic6—51no—
164C2×C3×M16C2×D511yescharacteristic
165C2×C3×M16C2×D511yescharacteristic
166C2×#214—54no—
167C2×#214—101no—
168C2×#214—101no—
169C2×#214—102no—
170C2×#214—101no—
171#932—54no—
172#932—102no—
173C2×#213—101no—
174C2×#208—51no—
175C22×C3⋊C8—51no—
176#909—54no—
177#909—102no—
178#907—54no—
179#907—102no—
180C2×Dic12—101no—
181C2×#204—101no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#100C2×D514yescomplemented
185#824—54no—
186#822—54no—
187C24×C5—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4C22×D312yes—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—61no—
196C22×Dic5—61no—
197#709—32no—
198#709—32no—
199#709—61no—
200#709—61no—
201C2×D20—31no—
202C2×C4×D5—61no—
203C2×Dic10—31no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10—61no—
210C5×M16—21no—
211C5×M16—21no—
212C5×M16C22×D312yes—
213C5×M16C22×D312yes—
214C2×C5×C8—21no—
215C2×C5×C8—21no—
216#687—64no—
217#687—64no—
218#687—64no—
219#686—64no—
220#681—32no—
221#681—61no—
222C2×#168—31no—
223C2×#168—31no—
224C2×#168—32no—
225C2×#168—32no—
226C2×#168—61no—
227Dic20—64no—
228#677—64no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100D1511yescharacteristic, complemented
239C22×C3×C5—22no—
240C22×C3×C5—42no—
241C22×C3×C5—82no—
242C22×C3×C5—82no—
243C22×C3×C5—82no—
244C22×C3×C5#12111yescharacteristic
245C22×C3×C5#12111yescharacteristic
246C22×C3×C5C2×#4111yescharacteristic
247C2×D15—22no—
248C2×D15—42no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—22no—
254Dic15—42no—
255C24×C3—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4C22×D512yes—
262C22×C3×C4C22×D511yescharacteristic
263C2×#67—101no—
264C22×Dic3—101no—
265#235—52no—
266#235—52no—
267#235—101no—
268#235—101no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×Dic6—51no—
272C2×Dic6—52no—
273C2×Dic6—101no—
274C2×Dic6—101no—
275C2×Dic6—101no—
276C2×Dic6—101no—
277C2×Dic6—101no—
278C3×M16—21no—
279C3×M16—21no—
280C3×M16C22×D512yes—
281C3×M16C22×D512yes—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284#214—104no—
285#214—104no—
286#214—104no—
287#213—104no—
288#208—52no—
289#208—101no—
290C2×C3⋊C8—51no—
291C2×C3⋊C8—51no—
292C2×C3⋊C8—52no—
293C2×C3⋊C8—52no—
294C2×C3⋊C8—101no—
295Dic12—104no—
296#204—104no—
297ΓL(1,𝔽25)—104no—
298D3×C8—104no—
299C23×C5—22no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—82no—
303C23×C5#23511yescharacteristic
304C22×D5—61no—
305C5×D4—22no—
306C5×D4—22no—
307C5×D4—41no—
308C5×D4—41no—
309C2×C4×C5#23511yescharacteristic
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—62no—
316C22⋊D5—62no—
317C2×Dic5—61no—
318C2×Dic5—62no—
319C2×Dic5—121no—
320C2×Dic5—121no—
321D20—32no—
322D20—61no—
323C4×D5—62no—
324C4×D5—62no—
325Dic10—32no—
326Dic10—61no—
327Dic10—62no—
328Dic10—62no—
329Dic10—121no—
330Dic10—121no—
331C5×C8—22no—
332C5×C8—22no—
333#168—32no—
334#168—32no—
335#168—62no—
336C2×#41—151no—
337C22×Q8—151no—
338C22×D4C2×D1511yescharacteristic
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—154no—
345C2×SD16—301no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—154no—
352#131—302no—
353C2×M16—151no—
354C2×M16—301no—
355C2×M16C2×D1511yescharacteristic
356C2×M16C2×D1511yescharacteristic
357C22×C8—151no—
358C22×C8—301no—
359#108—154no—
360#101—154no—
361#100C2×D1514yescomplemented
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—82no—
365C2×C3×C5#47112yescomplemented
366C2×C3×C5C2×#12111yescharacteristic
367D15—42no—
368C23×C3—22no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—82no—
372C23×C3#70911yescharacteristic
373C22×D3—101no—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—41no—
377C3×D4—41no—
378C2×C3×C4#70911yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4D4×D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—102no—
385#67—102no—
386C2×Dic3—101no—
387C2×Dic3—102no—
388C2×Dic3—201no—
389C2×Dic3—201no—
390D12—52no—
391D12—101no—
392C4×D3—102no—
393C4×D3—102no—
394Dic6—52no—
395Dic6—101no—
396Dic6—102no—
397Dic6—102no—
398Dic6—201no—
399Dic6—201no—
400C3×C8—22no—
401C3×C8—22no—
402C3⋊C8—52no—
403C3⋊C8—52no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—42no—
407C22×C5—82no—
408C22×C5—82no—
409C22×C5—82no—
410C22×C5#88411yescharacteristic
411C22×C5#88411yescharacteristic
412C22×C5C2×#23511yescharacteristic
413C2×D5—62no—
414C2×D5—122no—
415C4×C5#88411yescharacteristic
416C4×C5#88411yescharacteristic
417C4×C5C2×D3×D411yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419Dic5—62no—
420Dic5—122no—
421C24—21no—
422#41—152no—
423#41—152no—
424#41—301no—
425#41—301no—
426C2×Q8—151no—
427C2×Q8—152no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8—301no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—151no—
439C2×D4—301no—
440C2×D4C22×D1512yes—
441C22×C4—301no—
442C22×C4—301no—
443C22×C4C22×D1511yescharacteristic
444Q16—304no—
445SD16—304no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—21no—
451M16—21no—
452M16—152no—
453M16—304no—
454M16—301no—
455M16C22×D1512yes—
456M16C22×D1512yes—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—151no—
460C2×C8—151no—
461C2×C8—152no—
462C2×C8—152no—
463C2×C8—304no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—42no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—82no—
471C22×C3#403011yescharacteristic
472C22×C3#403011yescharacteristic
473C22×C3C2×#70911yescharacteristic
474C2×D3—102no—
475C2×D3—202no—
476C3×C4#403011yescharacteristic
477C3×C4#403011yescharacteristic
478C3×C4C2×D4×D511yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480Dic3—102no—
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—82no—
485C2×C5#474812yescomplemented
486C2×C5C2×#88411yescharacteristic
487D5—122no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—82no—
492C23—301no—
493C23#681711yescharacteristic
494Q8—152no—
495Q8—301no—
496Q8—302no—
497Q8—302no—
498Q8—601no—
499Q8—601no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504D4—152no—
505D4—302no—
506D4—302no—
507D4—301no—
508C2×C4—301no—
509C2×C4—302no—
510C2×C4—302no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4#681711yescharacteristic
515C2×C4D4×D1511yescharacteristic
516C2×C4D4×D1511yescharacteristic
517C2×C4D4×D1511yescharacteristic
518C2×C4D4×D1511yescharacteristic
519C2×C4C23×D1511yescharacteristic
520C8—22no—
521C8—22no—
522C8—152no—
523C8—152no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—82no—
528C2×C3#6503712yescomplemented
529C2×C3C2×#403011yescharacteristic
530D3—202no—
531C5C2×#474811yescharacteristic, complemented, Sylow
532C22—22no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—302no—
538C22—602no—
539C22#9177311yescharacteristic
540C22#9177311yescharacteristic
541C22C2×#681711yescharacteristic
542C4—302no—
543C4—602no—
544C4#9177311yescharacteristic
545C4#9177311yescharacteristic
546C4C2×D4×D1511yescharacteristic
547C4C2×D4×D1511yescharacteristic
548C3C2×#6503711yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—82no—
552C2—602no—
553C2#1175084912yesdirect product factor
554C2C2×#9177311yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5#121
prime radicalC2×#91821C2
hypercenterC2×#100D15
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C22×#6716C2semidirect
3. C2×#91798C2semidirect
4. C2×#91796C2semidirect
5. C2×C3×C5×#100C2semidirect
6. C2×#91108C2semidirect
7. C2×#91106C2semidirect
8. #11750849C2direct (N × H)
19. C2×#6716C22semidirect
26. #91798C22semidirect
28. #91796C22semidirect
33. C3×C5×#100C22semidirect
34. #91108C22semidirect
35. #91106C22semidirect
41. C2×C5×#100D3semidirect
93. C2×C3×#100D5semidirect
120. C5×#100C2×D3semidirect
184. C3×#100C2×D5semidirect
238. C2×#100D15semidirect
361. #100C2×D15semidirect
365. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#4748semidirect
528. C2×C3#65037semidirect
531. C5C2×#4748semidirect
548. C3C2×#65037semidirect
553. C2#11750849direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67162
C2×#918212
C2×#917982
C2×#917962
C2×C3×C5×#1002
C2×#911082
C2×#911062
#117508492
C2×#650373
C2×#47485