Finite Group Databasebeta

← C2×#11749134 #14429320

Subgroups — C2×#11749134 #14429320

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×#91821C211yesmaximal, characteristic
2C22×C5×#214C211yesmaximal, characteristic, complemented
3C2×#91321C211yesmaximal, characteristic, complemented
4C2×#91291C211yesmaximal, characteristic, complemented
5C2×C3×#3965C211yesmaximal, characteristic, complemented
6#11749134C218yesmaximal, direct product factor
7C2×#90993C211yesmaximal, characteristic, complemented
8C2×#90962C211yesmaximal, characteristic, complemented
9C2×#65466—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C2×#6817C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C2×#6716—21no—
14#91821—22no—
15#91821C2214yes—
16C2×#6715—21no—
17C2×#6710C2211yescharacteristic
18C2×C5×#214—21no—
19C2×C5×#214—22no—
20C2×C5×#214—21no—
21C2×C5×#214C2214yescomplemented
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91321—22no—
26#91321C2214yescomplemented
27C2×#6663—21no—
28C2×#6660—21no—
29C2×#6651—21no—
30#91291—22no—
31#91291C2214yescomplemented
32C2×#6648—21no—
33C3×#3965C2214yescomplemented
34#90993C2214yescomplemented
35#90962C2214yescomplemented
36C2×#4748—51nomaximal, Hall
37C22×C5×SD16—31no—
38C2×#4088—31no—
39C2×#4078—31no—
40C2×#4047—31no—
41C2×#3968—31no—
42C2×#3965D311yescharacteristic, complemented
43#65466—38no—
44C2×#3951—31no—
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—
54#6817—21no—
55#6817—21no—
56#6817D412yes—
57#6817C2312yes—
58C2×D60D411yescharacteristic
59C2×C4×D15—21no—
60C2×Dic30D411yescharacteristic
61C22×C5×Dic3—21no—
62C2×C5×Dic6—21no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6—21no—
65C2×C5×Dic6—21no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6C2312yes—
68#6716—24no—
69#6715—24no—
70#6710—21no—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C5×#214—24no—
74C5×#214—24no—
75C2×C5×C3⋊C8D411yescharacteristic
76C2×C5×C3⋊C8D412yes—
77C2×C5×C3⋊C8D411yescharacteristic
78C2×C5×C3⋊C8C2312yes—
79C3×#681—21no—
80C3×#681—21no—
81C3×#681C2312yes—
82C3×#681C2312yes—
83C2×C3×#168—21no—
84C2×C3×#168—21no—
85#6663—24no—
86#6660—24no—
87#6651—24no—
88#6648—24no—
89C22×#214D511yescharacteristic, complemented
90C2×#932—51no—
91C2×#909—51no—
92C2×#907—51no—
93C2×C3×#100—51no—
94C2×#824—51no—
95C2×#822—51no—
96#4748—58no—
97C22×C5×Q8—31no—
98C22×C5×D4C2×D311yescharacteristic
99C2×#709—31no—
100C2×C5×SD16—34no—
101C2×C5×SD16—61no—
102C2×C5×SD16—61no—
103C2×C5×SD16—62no—
104C22×C5×C8—31no—
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×#681C2×D311yescharacteristic
115C2×#681C2×D311yescharacteristic
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120#3968—34no—
121#3965C2×D314yescomplemented
122#3951—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—
143D60—21no—
144D60C2×D412yes—
145C4×D15—22no—
146C4×D15—22no—
147Dic30—21no—
148Dic30C2×D412yes—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—41no—
151C2×C5×Dic3—41no—
152C5×Dic6—22no—
153C5×Dic6—22no—
154C5×Dic6—41no—
155C5×Dic6—41no—
156C3⋊#168—22no—
157C3×#168—22no—
158C3×#168—22no—
159C5×C3⋊C8C2×D412yes—
160C5×C3⋊C8C2×D412yes—
161C22×C3×D4C2×D511yescharacteristic
162C2×#235—51no—
163C22×Dic6C2×D511yescharacteristic
164C2×C3×M16—51no—
165C2×C3×M16—51no—
166C2×#214—21no—
167C2×#214—21no—
168C2×#214—22no—
169C2×#214—101no—
170C2×#214C2×D514yescomplemented
171#932—54no—
172#932—102no—
173C2×#213—101no—
174C2×#208—51no—
175C22×C3⋊C8C2×D511yescharacteristic
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×#100—54no—
185#824—54no—
186#822—54no—
187C24×C5—21no—
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—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4C22×D312yes—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—61no—
203#709—32no—
204#709—32no—
205#709—61no—
206#709—61no—
207C2×D20—31no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×SD16—64no—
211C5×SD16—64no—
212C2×C5×C8—31no—
213C2×C5×C8—31no—
214C2×C5×C8—32no—
215C2×C5×C8—32no—
216#689—64no—
217#688—64no—
218#687—64no—
219#686—64no—
220#681—21no—
221#681—21no—
222#681—32no—
223#681—61no—
224#681C22×D312yes—
225#681C22×D312yes—
226C2×#168—21no—
227C2×#168—21no—
228C2×#168—61no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—31no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—51no—
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—
254C5×Dic3—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—21no—
265#235—52no—
266#235—52no—
267#235—101no—
268#235—101no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—51no—
277C2×Dic6C22×D512yes—
278C3×M16—52no—
279C3×M16—52no—
280C3×M16—101no—
281C3×M16—101no—
282C2×C3×C8—101no—
283C2×C3×C8—101no—
284#214—24no—
285#214—24no—
286#214—104no—
287#213—104no—
288#208—52no—
289#208—101no—
290C2×C3⋊C8—101no—
291C2×C3⋊C8C22⋊D511yescharacteristic
292C2×C3⋊C8C22⋊D511yescharacteristic
293C2×C3⋊C8C22⋊D512yes—
294C2×C3⋊C8C22×D512yes—
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×Q8—62no—
306C5×Q8—62no—
307C5×Q8—121no—
308C5×Q8—121no—
309C5×D4—22no—
310C5×D4—22no—
311C5×D4—41no—
312C5×D4—41no—
313C2×C4×C5—62no—
314C2×C4×C5—121no—
315C2×C4×C5—121no—
316C2×C4×C5#23511yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5D3×D411yescharacteristic
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5C23×D311yescharacteristic
322C22⋊D5—62no—
323C22⋊D5—62no—
324C2×Dic5—61no—
325D20—32no—
326D20—61no—
327C4×D5—62no—
328C4×D5—62no—
329Dic10—32no—
330Dic10—61no—
331C5×C8—32no—
332C5×C8—32no—
333#168—22no—
334#168—22no—
335#168—62no—
336C2×#41—151no—
337C22×Q8—31no—
338C22×D4D3×D511yescharacteristic
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—154no—
352#131—302no—
353C2×M16—51no—
354C2×M16—51no—
355C2×M16—151no—
356C2×M16—301no—
357C22×C8—31no—
358C22×C8—301no—
359#108—154no—
360#101—154no—
361#100—54no—
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#71111yescharacteristic
373C22×D3—101no—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—41no—
377C3×D4—41no—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4#71111yescharacteristic
381C2×C3×C4C2×C22⋊D511yescharacteristic
382C2×C3×C4C2×C22⋊D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—102no—
385#67—102no—
386C2×Dic3—22no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—101no—
390D12—52no—
391D12—101no—
392C4×D3—102no—
393C4×D3—102no—
394Dic6—22no—
395Dic6—22no—
396Dic6—41no—
397Dic6—41no—
398Dic6—52no—
399Dic6—101no—
400C3×C8—102no—
401C3×C8—102no—
402C3⋊C8—102no—
403C3⋊C8C2×C22⋊D512yes—
404C3⋊C8C2×C22⋊D512yes—
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—122no—
416C4×C5#88411yescharacteristic
417C4×C5#88411yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C2×D3×D411yescharacteristic
420Dic5—62no—
421C24—21no—
422#41—152no—
423#41—152no—
424#41—301no—
425#41—301no—
426C2×Q8—32no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—151no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—151no—
439C2×D4—301no—
440C2×D4C2×D3×D512yes—
441C22×C4—61no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—64no—
446SD16—64no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—52no—
451M16—52no—
452M16—101no—
453M16—101no—
454M16—152no—
455M16—304no—
456M16—301no—
457C2×C8—31no—
458C2×C8—31no—
459C2×C8—32no—
460C2×C8—32no—
461C2×C8—101no—
462C2×C8—101no—
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#408411yescharacteristic
472C22×C3#408411yescharacteristic
473C22×C3C2×#71111yescharacteristic
474C2×D3—102no—
475C2×D3—202no—
476C3×C4#408411yescharacteristic
477C3×C4#408411yescharacteristic
478C3×C4C2×D4×D511yescharacteristic
479C3×C4C22×C22⋊D511yescharacteristic
480Dic3—42no—
481Dic3—102no—
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#678211yescharacteristic
494Q8—62no—
495Q8—62no—
496Q8—121no—
497Q8—121no—
498Q8—152no—
499Q8—301no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504D4—152no—
505D4—302no—
506D4—302no—
507D4—301no—
508C2×C4—62no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—301no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4#678211yescharacteristic
515C2×C4D3×C22⋊D511yescharacteristic
516C2×C4D3×C22⋊D511yescharacteristic
517C2×C4#679011yescharacteristic
518C2×C4#679011yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—32no—
521C8—32no—
522C8—102no—
523C8—102no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—82no—
528C2×C3#6546612yescomplemented
529C2×C3C2×#408411yescharacteristic
530D3—202no—
531C5C2×#474811yescharacteristic, complemented, Sylow
532C22—22no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—302no—
538C22—602no—
539C22#9155711yescharacteristic
540C22#9155711yescharacteristic
541C22C2×#678211yescharacteristic
542C4—122no—
543C4—302no—
544C4#9155711yescharacteristic
545C4#9155711yescharacteristic
546C4C2×D3×C22⋊D511yescharacteristic
547C4C2×#679011yescharacteristic
548C3C2×#6546611yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—82no—
552C2—602no—
553C2#1174913412yesdirect product factor
554C2C2×#9155711yescharacteristic
subgroupG/H
centerC22#91557
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#121
prime radicalC2×#91821C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C5×#214C2semidirect
3. C2×#91321C2semidirect
4. C2×#91291C2semidirect
5. C2×C3×#3965C2semidirect
6. #11749134C2direct (N × H)
7. C2×#90993C2semidirect
8. C2×#90962C2semidirect
21. C2×C5×#214C22semidirect
26. #91321C22semidirect
31. #91291C22semidirect
33. C3×#3965C22semidirect
34. #90993C22semidirect
35. #90962C22semidirect
42. C2×#3965D3semidirect
89. C22×#214D5semidirect
121. #3965C2×D3semidirect
170. C2×#214C2×D5semidirect
365. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#4748semidirect
528. C2×C3#65466semidirect
531. C5C2×#4748semidirect
548. C3C2×#65466semidirect
553. C2#11749134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918212
C22×C5×#2142
C2×#913212
C2×#912912
C2×C3×#39652
#117491342
C2×#909932
C2×#909622
C2×#654663
C2×#47485