Finite Group Databasebeta

← C2×#11747017 #14417971

Subgroups — C2×#11747017 #14417971

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91311C211yesmaximal, characteristic
2C2×#91291C211yesmaximal, characteristic, complemented
3C2×#91283C211yesmaximal, characteristic, complemented
4C2×#91089C211yesmaximal, characteristic, complemented
5C2×C5×#803C211yesmaximal, characteristic, complemented
6C2×C3×#3937C211yesmaximal, characteristic, complemented
7C2×#90993C211yesmaximal, characteristic, complemented
8#11747017C218yesmaximal, direct product factor
9C2×#65006—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C2×C3×#709C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C2×#6662C411yescharacteristic, complemented
18C2×#6658C411yescharacteristic, complemented
19#91311C414yescomplemented
20#91311C2214yes—
21C2×#6657C411yescharacteristic, complemented
22C2×#6653C411yescharacteristic, complemented
23C2×#6651—21no—
24C2×#6649—21no—
25#91291—22no—
26#91291C2214yescomplemented
27C2×#6648—21no—
28#91283—22no—
29#91283C2214yescomplemented
30C2×D5×C3⋊C8—21no—
31#91089C2214yescomplemented
32C5×#803C2214yescomplemented
33C3×#3937C2214yescomplemented
34#90993C2214yescomplemented
35C2×#4823—51nomaximal, Hall
36C2×#4050—31no—
37C2×#4047—31no—
38C2×#4047—31no—
39C2×C5×#97—31no—
40C2×#3951—31no—
41C2×#3937—31no—
42C2×#3937D311yescharacteristic, complemented
43#65006—38no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220—21no—
47#6817—21no—
48#6817—21no—
49#6817C2×C412yes—
50#6817C2312yes—
51C2×D60C2×C411yescharacteristic
52C2×C4×D15—21no—
53C2×Dic30C2×C411yescharacteristic
54C2×C3×C22⋊D5—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709C2×C412yes—
58C3×#709C2312yes—
59C2×C3×D20C2×C411yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2×C411yescharacteristic
62C3×C42×C5—21no—
63C3×C42×C5C2312yes—
64#6710—21no—
65#6710C2312yes—
66C2×C3⋊#168—21no—
67C2×C5×C3⋊C8C2×C411yescharacteristic
68C2×C5×C3⋊C8C2×C411yescharacteristic
69C2×C5×C3⋊C8C2×C412yes—
70C2×C5×C3⋊C8D411yescharacteristic
71C2×C5×C3⋊C8D412yes—
72C2×C5×C3⋊C8D411yescharacteristic
73C2×C5×C3⋊C8C2312yes—
74C2×C5×C3⋊C8C2312yes—
75C3×#681—21no—
76C3×#681C2312yes—
77C2×C3×#168—21no—
78#6662C2×C414yescomplemented
79#6658C2×C414yescomplemented
80#6657C2×C414yescomplemented
81#6653C2×C414yescomplemented
82#6651—24no—
83#6649—24no—
84#6648—24no—
85D5×C3⋊C8—24no—
86C2×#950—51no—
87C2×#948—51no—
88C2×#907—51no—
89C2×C3×#104—51no—
90C2×#822—51no—
91C2×#805—51no—
92C2×#803D511yescharacteristic, complemented
93#4823—58no—
94C2×#709—31no—
95C2×#709C2×D311yescharacteristic
96C22×C5×C8—31no—
97C22×C5×C8—31no—
98C2×C42×C5C2×D311yescharacteristic
99C2×#681—31no—
100C2×#681C2×D311yescharacteristic
101C2×Dic20—31no—
102#4050—34no—
103#4050—34no—
104C2×D40—31no—
105C2×#677—31no—
106C2×#677—31no—
107#4047—34no—
108#4047—34no—
109#4047—62no—
110#4047—62no—
111C2×#676—61no—
112C2×#676—61no—
113C2×C8×D5—61no—
114C2×C8×D5—61no—
115C5×#97—34no—
116#3951—34no—
117#3937—34no—
118#3937C2×D314yescomplemented
119C2×#444—151noSylow
120C23×C3×C5#4111yescharacteristic
121C22×D15—21no—
122C22×C3×D5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—42no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131#1220—22no—
132#1220—22no—
133C2×Dic15—21no—
134D60—21no—
135D60C22×C412yes—
136C4×D15—22no—
137C4×D15—22no—
138Dic30—21no—
139Dic30C22×C412yes—
140C3×C22⋊D5—22no—
141C3×C22⋊D5—22no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20C22×C412yes—
145C3×C4×D5—22no—
146C3×C4×D5—22no—
147C3×Dic10—21no—
148C3×Dic10C22×C412yes—
149C3⋊#168—22no—
150C3×#168—22no—
151C5×C3⋊C8C22×C412yes—
152C5×C3⋊C8C22×C412yes—
153C5×C3⋊C8C2×D412yes—
154C5×C3⋊C8C2×D412yes—
155C2×C3×#41—51no—
156C2×#235—51no—
157C2×C3×M16—51no—
158C2×C3×C42C2×D511yescharacteristic
159#950—54no—
160#950—54no—
161#948—54no—
162#948—102no—
163C2×#216—51no—
164C2×#215—51no—
165C2×#214—51no—
166C2×#213—51no—
167C2×#208—51no—
168C2×#208—101no—
169C22×C3⋊C8—101no—
170C22×C3⋊C8C2×D511yescharacteristic
171C22×C3⋊C8C2×D511yescharacteristic
172#907—54no—
173#907—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176C3×#104—54no—
177#822—54no—
178#805—54no—
179#803C2×D514yescomplemented
180C22×C4×C5—21no—
181C22×C4×C5C22×D311yescharacteristic
182C2×C22⋊D5—21no—
183C2×C22⋊D5—61no—
184#709—21no—
185#709—21no—
186#709—32no—
187#709—32no—
188#709—61no—
189#709—61no—
190#709C4×D312yes—
191#709C22×D312yes—
192C2×D20—31no—
193C2×D20C4×D311yescharacteristic
194C2×C4×D5—21no—
195C2×C4×D5—61no—
196C2×Dic10—31no—
197C2×Dic10C4×D311yescharacteristic
198C2×C5×C8—31no—
199C2×C5×C8—31no—
200C2×C5×C8—32no—
201C2×C5×C8—31no—
202C2×C5×C8—31no—
203C2×C5×C8—32no—
204C2×C5×C8—32no—
205C2×C5×C8—32no—
206C42×C5—21no—
207C42×C5C22×D312yes—
208#681—21no—
209#681—32no—
210#681—61no—
211#681C22×D312yes—
212C2×#168—21no—
213C2×#168—61no—
214Dic20—34no—
215D40—34no—
216#677—34no—
217#677—34no—
218#676—64no—
219#676—64no—
220C8×D5—64no—
221C8×D5—64no—
222C2×#135—151no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—51no—
228C2×#104—151no—
229C2×#97—31no—
230C22×C3×C5—22no—
231C22×C3×C5C4×D411yescharacteristic
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C2×D15—22no—
235C2×D15—42no—
236C2×C3×D5—22no—
237C2×C3×D5—42no—
238C3×C4×C5—42no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243Dic15—22no—
244C3×Dic5—22no—
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—101no—
248C3×#41—101no—
249C2×C3×Q8—51no—
250C2×C3×D4—51no—
251C2×C3×D4—101no—
252C22×C3×C4—21no—
253C22×C3×C4—101no—
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—101no—
256#235—52no—
257#235—52no—
258#235—101no—
259#235—101no—
260C2×D12—51no—
261C2×C4×D3—101no—
262C2×Dic6—51no—
263C3×M16—52no—
264C3×M16—101no—
265C2×C3×C8—101no—
266C3×C42—21no—
267C3×C42C22×D512yes—
268#216—54no—
269#215—54no—
270#214—54no—
271#213—54no—
272#208—52no—
273#208—101no—
274#208—104no—
275C2×C3⋊C8—101no—
276C2×C3⋊C8—104no—
277C2×C3⋊C8C4×D511yescharacteristic
278C2×C3⋊C8C4×D511yescharacteristic
279C2×C3⋊C8C4×D512yes—
280C2×C3⋊C8D2011yescharacteristic
281C2×C3⋊C8D2011yescharacteristic
282C2×C3⋊C8D2012yes—
283C2×C3⋊C8C22×D512yes—
284C2×C3⋊C8C22×D512yes—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5#23711yescharacteristic
288C22×D5—21no—
289C22×D5—61no—
290C2×C4×C5—22no—
291C2×C4×C5—42no—
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5C2×C4×D311yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5#23711yescharacteristic
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—22no—
299C22⋊D5—22no—
300C22⋊D5—62no—
301C22⋊D5—62no—
302C2×Dic5—21no—
303C2×Dic5—61no—
304D20—21no—
305D20—32no—
306D20—61no—
307D20C2×C4×D312yes—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—62no—
311C4×D5—62no—
312Dic10—21no—
313Dic10—32no—
314Dic10—61no—
315Dic10C2×C4×D312yes—
316C5×C8—32no—
317C5×C8—32no—
318C5×C8—32no—
319C5×C8—32no—
320#168—22no—
321#168—62no—
322C2×#41—51no—
323C2×#41—151no—
324#135—154no—
325#135—154no—
326C2×Q16—151no—
327C2×SD16—151no—
328C2×SD16—151no—
329C2×D8—151no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—51no—
335C2×M16—151no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42D3×D511yescharacteristic
343#108—154no—
344#104—54no—
345#104—154no—
346#97—34no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5#44412yescomplemented
350C2×C3×C5C2×C4×D411yescharacteristic
351D15—42no—
352C3×D5—42no—
353C23×C3—101no—
354C23×C3#70911yescharacteristic
355C22×D3—101no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—52no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—101no—
362C2×C3×C4—22no—
363C2×C3×C4—42no—
364C2×C3×C4—101no—
365C2×C3×C4—102no—
366C2×C3×C4—102no—
367C2×C3×C4C2×C4×D511yescharacteristic
368C2×C3×C4C2×C4×D511yescharacteristic
369C2×C3×C4C2×D2011yescharacteristic
370C2×C3×C4C2×D2011yescharacteristic
371C2×C3×C4#70911yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—102no—
374#67—102no—
375C2×Dic3—101no—
376D12—52no—
377D12—101no—
378C4×D3—102no—
379C4×D3—102no—
380Dic6—52no—
381Dic6—101no—
382C3×C8—102no—
383C3⋊C8—102no—
384C3⋊C8C2×C4×D512yes—
385C3⋊C8C2×C4×D512yes—
386C3⋊C8C2×D2012yes—
387C3⋊C8C2×D2012yes—
388C22×C5—22no—
389C22×C5#67⋊C411yescharacteristic
390C22×C5#67⋊C411yescharacteristic
391C22×C5C2×#23711yescharacteristic
392C2×D5—22no—
393C2×D5—42no—
394C2×D5—62no—
395C2×D5—122no—
396C4×C5—42no—
397C4×C5#67⋊C411yescharacteristic
398C4×C5#67⋊C411yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×D3×D411yescharacteristic
401Dic5—22no—
402Dic5—62no—
403#41—52no—
404#41—52no—
405#41—101no—
406#41—101no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—51no—
412C2×Q8—151no—
413C2×D4—51no—
414C2×D4—101no—
415C2×D4—151no—
416C2×D4—301no—
417C22×C4—21no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—52no—
426M16—101no—
427M16—152no—
428M16—304no—
429M16—304no—
430M16—301no—
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—32no—
434C2×C8—32no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—32no—
438C2×C8—32no—
439C2×C8—101no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8—301no—
443C42—21no—
444C42C2×D3×D512yes—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—102no—
448C22×C3—202no—
449C22×C3C4×D2011yescharacteristic
450C22×C3C4×D2011yescharacteristic
451C22×C3C2×#70911yescharacteristic
452C2×D3—102no—
453C2×D3—202no—
454C3×C4—42no—
455C3×C4—102no—
456C3×C4C4×D2011yescharacteristic
457C3×C4C4×D2011yescharacteristic
458C3×C4C22×C4×D511yescharacteristic
459C3×C4C22×D2011yescharacteristic
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5#482312yescomplemented
464C2×C5C2×#67⋊C411yescharacteristic
465D5—42no—
466D5—122no—
467C23—101no—
468C23—301no—
469C23#677911yescharacteristic
470Q8—52no—
471Q8—101no—
472Q8—152no—
473Q8—301no—
474D4—52no—
475D4—102no—
476D4—102no—
477D4—101no—
478D4—152no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—101no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—301no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4C4×D3×D511yescharacteristic
491C2×C4C4×D3×D511yescharacteristic
492C2×C4D3×D2011yescharacteristic
493C2×C4D3×D2011yescharacteristic
494C2×C4#677911yescharacteristic
495C2×C4C22×D3×D511yescharacteristic
496C8—32no—
497C8—32no—
498C8—32no—
499C8—32no—
500C8—102no—
501C8—302no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3#6500612yescomplemented
506C2×C3C2×C4×D2011yescharacteristic
507D3—202no—
508C5C2×#482311yescharacteristic, complemented, Sylow
509C22—22no—
510C22—102no—
511C22—202no—
512C22—302no—
513C22—602no—
514C22#9139511yescharacteristic
515C22#9139511yescharacteristic
516C22C2×#677911yescharacteristic
517C4—42no—
518C4—102no—
519C4—302no—
520C4#9139511yescharacteristic
521C4#9139511yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×D3×D2011yescharacteristic
524C3C2×#6500611yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—202no—
528C2—602no—
529C2#1174701712yesdirect product factor
530C2C2×#9139511yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×#91311C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#91291C2semidirect
3. C2×#91283C2semidirect
4. C2×#91089C2semidirect
5. C2×C5×#803C2semidirect
6. C2×C3×#3937C2semidirect
7. C2×#90993C2semidirect
8. #11747017C2direct (N × H)
17. C2×#6662C4semidirect
18. C2×#6658C4semidirect
19. #91311C4semidirect
21. C2×#6657C4semidirect
22. C2×#6653C4semidirect
26. #91291C22semidirect
29. #91283C22semidirect
31. #91089C22semidirect
32. C5×#803C22semidirect
33. C3×#3937C22semidirect
34. #90993C22semidirect
42. C2×#3937D3semidirect
78. #6662C2×C4semidirect
79. #6658C2×C4semidirect
80. #6657C2×C4semidirect
81. #6653C2×C4semidirect
92. C2×#803D5semidirect
118. #3937C2×D3semidirect
179. #803C2×D5semidirect
349. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
463. C2×C5#4823semidirect
505. C2×C3#65006semidirect
508. C5C2×#4823semidirect
524. C3C2×#65006semidirect
529. C2#11747017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#913112
C2×#912912
C2×#912832
C2×#910892
C2×C5×#8032
C2×C3×#39372
C2×#909932
#117470172
C2×#650063
C2×#48235