Finite Group Databasebeta

← C2×#11748087 #14429329

Subgroups — C2×#11748087 #14429329

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×#91790C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic, complemented
4C2×#91312C211yesmaximal, characteristic
5C2×C5×#819C211yesmaximal, characteristic, complemented
6C2×#90961C211yesmaximal, characteristic, complemented
7C2×#90958C211yesmaximal, characteristic, complemented
8#11748087C218yesmaximal, direct product factor
9C2×#65187—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C22×C3×D20C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15#91790—22no—
16#91790C2214yescomplemented
17C2×#6705—21no—
18C2×C8×D15—21no—
19C2×C5×#208C2211yescharacteristic
20C2×C5×#208C2211yescharacteristic
21C2×C3×#677—21no—
22C2×C3×#677—21no—
23C2×C3×#677—22no—
24C2×C3×#677C2214yescomplemented
25C2×#6662—21no—
26#91315—22no—
27#91315C2214yescomplemented
28C2×#6658—21no—
29#91312—22no—
30#91312C2214yes—
31C2×#6657—21no—
32C2×#6653—21no—
33C5×#819C2214yescomplemented
34#90961C2214yescomplemented
35#90958C2214yescomplemented
36C2×#5177—51nomaximal, Hall
37C2×#4055—31no—
38C2×#4054—31no—
39C22×#677D311yescharacteristic, complemented
40C2×#4047—31no—
41C2×C5×#108—31no—
42C2×#3956—31no—
43C2×#3955—31no—
44#65187—38no—
45C23×C3×D5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48#6817—21no—
49#6817—21no—
50#6817D412yes—
51#6817C2312yes—
52C2×D60D411yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30D411yescharacteristic
55C22×C3×Dic5—21no—
56C2×C3×D20—21no—
57C2×C3×D20—21no—
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20—21no—
61C2×C3×D20C2312yes—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—21no—
67C2×C3×Dic10C2312yes—
68C2×C3×C5×C8D411yescharacteristic
69C2×C3×C5×C8D411yescharacteristic
70C2×C3×C5×C8D412yes—
71C2×C3×C5×C8C2312yes—
72#6710—21no—
73#6710C2312yes—
74C2×C3⋊#168—21no—
75#6705—24no—
76C8×D15—24no—
77C5×#208—21no—
78C5×#208—21no—
79C5×#208C2312yes—
80C5×#208C2312yes—
81C2×C5×C3⋊C8—21no—
82C2×C5×C3⋊C8—21no—
83C3×#677—24no—
84C3×#677—24no—
85#6662—24no—
86#6658—24no—
87#6657—24no—
88#6653—24no—
89C22×C3×SD16—51no—
90C2×#942—51no—
91C2×#932—51no—
92C2×#901—51no—
93C2×#836—51no—
94C2×#833—51no—
95#5177—58no—
96C2×#819D511yescharacteristic, complemented
97C2×#709—31no—
98C22×D20C2×D311yescharacteristic
99C22×Dic10C2×D311yescharacteristic
100C2×C5×M16—31no—
101C2×C5×M16—31no—
102C22×C5×C8C2×D311yescharacteristic
103C2×#681—31no—
104#4055—34no—
105#4055—62no—
106#4054—34no—
107#4054—62no—
108C2×Dic20—61no—
109C2×D40—61no—
110C2×#677—21no—
111C2×#677—21no—
112C2×#677—22no—
113C2×#677—61no—
114C2×#677—61no—
115C2×#677C2×D314yescomplemented
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120C5×#108—34no—
121#3956—34no—
122#3955—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×D15—21no—
126C22×C3×D5—22no—
127C22×C3×D5—41no—
128C22×C3×D5—41no—
129C22×C3×D5—82no—
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
136#1220—22no—
137#1220—22no—
138C2×Dic15—21no—
139D60—21no—
140D60C2×D412yes—
141C4×D15—22no—
142C4×D15—22no—
143Dic30—21no—
144Dic30C2×D412yes—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—41no—
147C2×C3×Dic5—41no—
148C3×D20—22no—
149C3×D20—22no—
150C3×D20—41no—
151C3×D20—41no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C3×Dic10—41no—
155C3×Dic10—41no—
156C3×C5×C8C2×D412yes—
157C3×C5×C8C2×D412yes—
158C3⋊#168—22no—
159C5×C3⋊C8—22no—
160C5×C3⋊C8—22no—
161C22×C3×Q8—51no—
162C22×C3×D4—51no—
163C2×#235—51no—
164C2×C3×SD16—54no—
165C2×C3×SD16—101no—
166C2×C3×SD16—101no—
167C2×C3×SD16—102no—
168C22×C3×C8C2×D511yescharacteristic
169C2×#216—101no—
170#942—54no—
171#942—102no—
172C2×#215—101no—
173C2×#214—101no—
174#932—54no—
175#932—102no—
176C2×#213—101no—
177C2×#208—51no—
178C2×#208C2×D511yescharacteristic
179C2×#208C2×D511yescharacteristic
180#901—54no—
181#901—102no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184#836—54no—
185#833—54no—
186#819C2×D514yescomplemented
187C23×D5—21no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—61no—
190C22×Dic5—21no—
191#709—32no—
192#709—32no—
193#709—61no—
194#709—61no—
195C2×D20—21no—
196C2×D20—21no—
197C2×D20—21no—
198C2×D20—21no—
199C2×D20—21no—
200C2×D20—31no—
201C2×D20C22×D312yes—
202C2×C4×D5—61no—
203C2×Dic10—21no—
204C2×Dic10—21no—
205C2×Dic10—21no—
206C2×Dic10—21no—
207C2×Dic10—21no—
208C2×Dic10—31no—
209C2×Dic10C22×D312yes—
210C5×M16—32no—
211C5×M16—32no—
212C5×M16—61no—
213C5×M16—61no—
214C2×C5×C8—61no—
215C2×C5×C8—61no—
216C2×C5×C8#6711yescharacteristic
217C2×C5×C8#6711yescharacteristic
218C2×C5×C8#6712yes—
219C2×C5×C8C22×D312yes—
220#681—32no—
221#681—61no—
222C2×#168—61no—
223Dic20—64no—
224D40—64no—
225#677—24no—
226#677—24no—
227#677—64no—
228#677—64no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—51no—
234C2×#131—151no—
235#471—158no—
236C2×#108—31no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×D15—22no—
244C2×D15—42no—
245C2×C3×D5—42no—
246C2×C3×D5—82no—
247C2×C3×D5—82no—
248C2×C3×D5—82no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—22no—
254C3×Dic5—42no—
255C24×C3—101no—
256C2×C3×Q8—52no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8—101no—
260C2×C3×Q8—101no—
261C2×C3×Q8—101no—
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4—101no—
267C2×C3×D4—101no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271#235—52no—
272#235—52no—
273#235—101no—
274#235—101no—
275C2×D12—51no—
276C2×C4×D3—101no—
277C2×Dic6—51no—
278C3×SD16—104no—
279C3×SD16—104no—
280C2×C3×C8D2011yescharacteristic
281C2×C3×C8D2011yescharacteristic
282C2×C3×C8D2012yes—
283C2×C3×C8C22×D512yes—
284#216—104no—
285#215—104no—
286#214—104no—
287#213—104no—
288#208—21no—
289#208—21no—
290#208—52no—
291#208—101no—
292#208C22×D512yes—
293#208C22×D512yes—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—101no—
297ΓL(1,𝔽25)—104no—
298D3×C8—104no—
299C23×C5#23711yescharacteristic
300C22×D5—22no—
301C22×D5—41no—
302C22×D5—41no—
303C22×D5—61no—
304C22×D5—82no—
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5#23711yescharacteristic
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C2×#6711yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—62no—
312C22⋊D5—62no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—61no—
317D20—22no—
318D20—22no—
319D20—32no—
320D20—41no—
321D20—41no—
322D20—61no—
323C4×D5—62no—
324C4×D5—62no—
325Dic10—22no—
326Dic10—22no—
327Dic10—32no—
328Dic10—41no—
329Dic10—41no—
330Dic10—61no—
331C5×C8—62no—
332C5×C8—62no—
333C5×C8C2×#6712yes—
334C5×C8C2×#6712yes—
335#168—62no—
336C2×#41—151no—
337C22×Q8—51no—
338C22×D4—51no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—54no—
345C2×SD16—101no—
346C2×SD16—101no—
347C2×SD16—102no—
348C2×SD16—301no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—154no—
352#131—302no—
353C2×M16—31no—
354C2×M16—31no—
355C2×M16—151no—
356C2×M16—301no—
357C22×C8—301no—
358C22×C8D3×D511yescharacteristic
359#108—34no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366D15—42no—
367C3×D5—82no—
368C23×C3—102no—
369C23×C3—201no—
370C23×C3—201no—
371C23×C3—402no—
372C23×C3#71311yescharacteristic
373C22×D3—101no—
374C3×Q8—102no—
375C3×Q8—102no—
376C3×Q8—201no—
377C3×Q8—201no—
378C3×D4—102no—
379C3×D4—102no—
380C3×D4—201no—
381C3×D4—201no—
382C2×C3×C4—102no—
383C2×C3×C4—201no—
384C2×C3×C4—201no—
385C2×C3×C4C2×D2011yescharacteristic
386C2×C3×C4C2×D2011yescharacteristic
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4#71311yescharacteristic
390C2×C3×C4C23×D511yescharacteristic
391#67—102no—
392#67—102no—
393C2×Dic3—101no—
394D12—52no—
395D12—101no—
396C4×D3—102no—
397C4×D3—102no—
398Dic6—52no—
399Dic6—101no—
400C3×C8C2×D2012yes—
401C3×C8C2×D2012yes—
402C3⋊C8—22no—
403C3⋊C8—22no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5#93811yescharacteristic
407C22×C5#93811yescharacteristic
408C22×C5C2×#23711yescharacteristic
409C2×D5—42no—
410C2×D5—62no—
411C2×D5—82no—
412C2×D5—82no—
413C2×D5—82no—
414C2×D5—122no—
415C4×C5#93811yescharacteristic
416C4×C5#93811yescharacteristic
417C4×C5C2×D3×D411yescharacteristic
418C4×C5C22×#6711yescharacteristic
419Dic5—42no—
420Dic5—62no—
421C24—101no—
422#41—152no—
423#41—152no—
424#41—301no—
425#41—301no—
426C2×Q8—52no—
427C2×Q8—101no—
428C2×Q8—101no—
429C2×Q8—101no—
430C2×Q8—101no—
431C2×Q8—101no—
432C2×Q8—151no—
433C2×D4—52no—
434C2×D4—101no—
435C2×D4—101no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—101no—
439C2×D4—151no—
440C2×D4—301no—
441C22×C4—101no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—104no—
446SD16—104no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—32no—
451M16—32no—
452M16—61no—
453M16—61no—
454M16—152no—
455M16—301no—
456M16—304no—
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—301no—
460C2×C8—304no—
461C2×C8#120211yescharacteristic
462C2×C8#120211yescharacteristic
463C2×C8#120212yes—
464C2×C8C2×D3×D512yes—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—202no—
468C22×C3—402no—
469C22×C3—402no—
470C22×C3—402no—
471C22×C3#404111yescharacteristic
472C22×C3#404111yescharacteristic
473C22×C3C2×#71311yescharacteristic
474C2×D3—102no—
475C2×D3—202no—
476C3×C4—202no—
477C3×C4#404111yescharacteristic
478C3×C4#404111yescharacteristic
479C3×C4C22×D2011yescharacteristic
480C3×C4C2×D4×D511yescharacteristic
481Dic3—102no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5#517712yescomplemented
485C2×C5C2×#93811yescharacteristic
486D5—82no—
487D5—122no—
488C23—102no—
489C23—201no—
490C23—201no—
491C23—301no—
492C23—402no—
493C23#676611yescharacteristic
494Q8—102no—
495Q8—102no—
496Q8—152no—
497Q8—201no—
498Q8—201no—
499Q8—301no—
500D4—102no—
501D4—102no—
502D4—152no—
503D4—201no—
504D4—201no—
505D4—302no—
506D4—302no—
507D4—301no—
508C2×C4—102no—
509C2×C4—201no—
510C2×C4—201no—
511C2×C4—301no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4#676611yescharacteristic
515C2×C4#677711yescharacteristic
516C2×C4#677711yescharacteristic
517C2×C4C2×#120211yescharacteristic
518C2×C4C2×#120211yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—62no—
521C8—62no—
522C8—302no—
523C8C2×#120212yes—
524C8C2×#120212yes—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—402no—
528C2×C3#6518712yescomplemented
529C2×C3C2×#404111yescharacteristic
530D3—202no—
531C5C2×#517711yescharacteristic, complemented, Sylow
532C22—22no—
533C22—202no—
534C22—302no—
535C22—402no—
536C22—402no—
537C22—402no—
538C22—602no—
539C22#9146511yescharacteristic
540C22#9146511yescharacteristic
541C22C2×#676611yescharacteristic
542C4—202no—
543C4—302no—
544C4#9146511yescharacteristic
545C4#9146511yescharacteristic
546C4C2×#677711yescharacteristic
547C4C22×#120211yescharacteristic
548C3C2×#6518711yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—402no—
552C2—602no—
553C2#1174808712yesdirect product factor
554C2C2×#9146511yescharacteristic
subgroupG/H
centerC22#91465
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5#121
prime radicalC2×#91312C2
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. C2×#91790C2semidirect
2. C22×C3×#677C2semidirect
3. C2×#91315C2semidirect
5. C2×C5×#819C2semidirect
6. C2×#90961C2semidirect
7. C2×#90958C2semidirect
8. #11748087C2direct (N × H)
16. #91790C22semidirect
24. C2×C3×#677C22semidirect
27. #91315C22semidirect
33. C5×#819C22semidirect
34. #90961C22semidirect
35. #90958C22semidirect
39. C22×#677D3semidirect
96. C2×#819D5semidirect
115. C2×#677C2×D3semidirect
186. #819C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
484. C2×C5#5177semidirect
528. C2×C3#65187semidirect
531. C5C2×#5177semidirect
548. C3C2×#65187semidirect
553. C2#11748087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917902
C22×C3×#6772
C2×#913152
C2×#913122
C2×C5×#8192
C2×#909612
C2×#909582
#117480872
C2×#651873
C2×#51775