Finite Group Databasebeta

← C2×#11747442 #14427717

Subgroups — C2×#11747442 #14427717

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4041C211yesmaximal, characteristic, complemented
2C2×#91450C211yesmaximal, characteristic, complemented
3C22×#6653C211yesmaximal, characteristic, complemented
4C22×D5×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#91093C211yesmaximal, characteristic, complemented
6C2×C5×#807C211yesmaximal, characteristic, complemented
7C2×#90964C211yesmaximal, characteristic, complemented
8#11747442C218yesmaximal, direct product factor
9C2×#65172—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C22×C3×D20—21no—
12C22×C3×D20C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1202—21no—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C3×#685—21no—
20C3×#4041—22no—
21C3×#4041C2214yescomplemented
22C2×#6667—21no—
23#91450—22no—
24#91450C2214yescomplemented
25C2×#6653—24no—
26C2×#6653C2214yescomplemented
27C2×D5×C3⋊C8—24no—
28C2×D5×C3⋊C8C2214yescomplemented
29#91093C2214yescomplemented
30C5×#807C2214yescomplemented
31#90964C2214yescomplemented
32C2×#5038—51nomaximal, Hall
33C22×D40—31no—
34C22×C8×D5—31no—
35C2×#4041—31no—
36C2×#4041D311yescharacteristic, complemented
37C2×C5×#107—31no—
38C2×#3941—31no—
39C2×#3941—31no—
40#65172—38no—
41C23×D15—21no—
42C23×C3×D5—21no—
43C23×C3×D5D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×D60—22no—
47C2×D60—22no—
48C2×D60—21no—
49C2×D60C2312yes—
50C22×C5×Dic3—21no—
51C22×C3×Dic5D411yescharacteristic
52C2×C3×D20—22no—
53C2×C3×D20—22no—
54C2×C3×D20—24no—
55C2×C3×D20—21no—
56C2×C3×D20—44no—
57C2×C3×D20C2312yes—
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5C2312yes—
62C2×#1202—24no—
63C2×#1202—44no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C2×C3⋊#168—22no—
67C2×C3⋊#168C2312yes—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3C2312yes—
70C2×C5×C3⋊C8D414yescomplemented
71C2×C5×C3⋊C8C2312yes—
72C3×#685—24no—
73#6667—24no—
74#6653—28no—
75D5×C3⋊C8—28no—
76C2×C3×#121—51no—
77C22×#213—51no—
78C2×#930—51no—
79C23×C3⋊C8—51no—
80C2×#832—51no—
81#5038—58no—
82C2×#809—51no—
83C2×#807D511yescharacteristic, complemented
84C22×D20—21no—
85C22×D20—31no—
86C22×D20—61no—
87C22×D20C2×D311yescharacteristic
88C22×C4×D5C2×D311yescharacteristic
89C22×C5×C8—31no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4C2×D311yescharacteristic
92C2×#685—21no—
93C2×#685—61no—
94C22×#168—31no—
95C2×D40—34no—
96C2×D40—64no—
97C2×C8×D5—34no—
98C2×C8×D5—64no—
99#4041—22no—
100#4041—34no—
101#4041—62no—
102#4041C2×D314yescomplemented
103C5×#107—34no—
104#3941—34no—
105#3941—34no—
106C2×#466—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—22no—
109C22×D15—42no—
110C22×D15—42no—
111C22×D15—42no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—42no—
116C22×C3×D5—42no—
117C22×C3×D5—42no—
118C22×C3×D5D814yescomplemented
119C22×C3×D5C2×D412yes—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—42no—
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5#4112yes—
125C2×C3×C4×C5C2411yescharacteristic
126D60—22no—
127D60—22no—
128D60—42no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—42no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5C2×D412yes—
133C3×D20—22no—
134C3×D20—22no—
135C3×D20—48no—
136C3×D20—42no—
137C3×C4×D5—24no—
138C3×C4×D5—22no—
139C3×C4×D5—22no—
140#1202—48no—
141C3⋊#168—22no—
142C5×C3⋊C8C2×D414yescomplemented
143C22×C3×D4—51no—
144C22×C3×D4—101no—
145C23×C3×C4—51no—
146C22×#67—101no—
147C22×D12—51no—
148C3×#121—54no—
149C3×#121—102no—
150C2×C3×C4⋊C4C2×D511yescharacteristic
151C2×C3×C22⋊C4—101no—
152C2×#213—54no—
153C2×#213—104no—
154#930—54no—
155#930—102no—
156C2×(C2×D3)⋊C4—101no—
157C2×C4⋊Dic3C2×D511yescharacteristic
158C22×C3⋊C8—51no—
159C22×C3⋊C8—54no—
160C22×C3⋊C8—104no—
161C22×C3⋊C8C2×D511yescharacteristic
162#832—54no—
163#809—54no—
164#807C2×D514yescomplemented
165C23×D5—21no—
166C23×D5—61no—
167C23×D5#6711yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—61no—
170C22×C4×C5C22×D311yescharacteristic
171C22×Dic5#6711yescharacteristic
172C2×D20—22no—
173C2×D20—22no—
174C2×D20—24no—
175C2×D20—21no—
176C2×D20—32no—
177C2×D20—44no—
178C2×D20—62no—
179C2×D20—62no—
180C2×D20—64no—
181C2×D20—61no—
182C2×D20—124no—
183C2×D20C22×D312yes—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5#6712yes—
187C2×C4×D5C22×D312yes—
188C2×C5×C8—34no—
189C2×C5×C8—32no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—61no—
193C5×C4⋊C4C22×D312yes—
194#685—24no—
195#685—64no—
196C2×#168—32no—
197C2×#168—62no—
198D40—68no—
199C8×D5—68no—
200C22×D8—151no—
201C23×C8—151no—
202C2×#121—51no—
203C2×#121—151no—
204#466—158no—
205C2×#107—31no—
206C2×#102—151no—
207C2×#102—151no—
208C22×C3×C5#12112yes—
209C22×C3×C5C2×D812yes—
210C22×C3×C5#13512yes—
211C22×C3×C5C22×D411yescharacteristic
212C2×D15—42no—
213C2×D15—42no—
214C2×D15—42no—
215C2×D15—84no—
216C2×C3×D5—22no—
217C2×C3×D5—22no—
218C2×C3×D5—28no—
219C2×C3×D5—42no—
220C2×C3×D5—42no—
221C2×C3×D5—42no—
222C2×C3×D5—84no—
223C2×C3×D5C2×D814yescomplemented
224C3×C4×C5—42no—
225C3×C4×C5#12112yes—
226C3×C4×C5C22×D411yescharacteristic
227C3×C4×C5C2×#4111yescharacteristic
228C3×Dic5—22no—
229C5×Dic3—42no—
230C24×C3—51no—
231C24×C3—101no—
232C23×D3—101no—
233C2×C3×D4—52no—
234C2×C3×D4—104no—
235C2×C3×D4—102no—
236C2×C3×D4—101no—
237C2×C3×D4—102no—
238C2×C3×D4—204no—
239C22×C3×C4—21no—
240C22×C3×C4—51no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—102no—
244C22×C3×C4—102no—
245C22×C3×C4C22×D511yescharacteristic
246C2×#67—104no—
247C2×#67—204no—
248C22×Dic3—21no—
249C2×D12—52no—
250C2×D12—102no—
251C2×D12—102no—
252C2×D12—101no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4C22×D512yes—
255C3×C22⋊C4—104no—
256#213—108no—
257(C2×D3)⋊C4—104no—
258C4⋊Dic3—21no—
259C4⋊Dic3C22×D512yes—
260C2×C3⋊C8—52no—
261C2×C3⋊C8—102no—
262C2×C3⋊C8—108no—
263C2×C3⋊C8D2014yescomplemented
264C2×C3⋊C8C22×D512yes—
265C23×C5C2×#6711yescharacteristic
266C22×D5—22no—
267C22×D5—22no—
268C22×D5—22no—
269C22×D5—42no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—62no—
273C22×D5—122no—
274C22×D5—122no—
275C22×D5—122no—
276C22×D5#21314yescomplemented
277C22×D5C2×#6712yes—
278C2×C4×C5—22no—
279C2×C4×C5—42no—
280C2×C4×C5—62no—
281C2×C4×C5—122no—
282C2×C4×C5D3×D412yes—
283C2×C4×C5#23712yes—
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—22no—
287C2×Dic5C2×#6712yes—
288D20—22no—
289D20—22no—
290D20—48no—
291D20—42no—
292D20—62no—
293D20—62no—
294D20—128no—
295D20—122no—
296C4×D5—24no—
297C4×D5—22no—
298C4×D5—22no—
299C5×C8—34no—
300#168—62no—
301C22×D4—51no—
302C22×D4—101no—
303C22×D4—151no—
304C22×D4—301no—
305C23×C4—51no—
306C2×D8—154no—
307C2×D8—304no—
308C22×C8—31no—
309C22×C8—154no—
310C22×C8—151no—
311C22×C8—304no—
312#121—54no—
313#121—102no—
314#121—154no—
315#121—302no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—101no—
319C2×C22⋊C4—301no—
320#107—34no—
321#102—154no—
322#102—154no—
323C2×C3×C5#46614yescomplemented
324C2×C3×C5C2×#12111yescharacteristic
325C2×C3×C5C22×D811yescharacteristic
326C2×C3×C5C2×#13511yescharacteristic
327D15—82no—
328C3×D5—24no—
329C3×D5—82no—
330C23×C3—52no—
331C23×C3—54no—
332C23×C3—102no—
333C23×C3—102no—
334C23×C3—102no—
335C23×C3—202no—
336C23×C3—202no—
337C23×C3—202no—
338C23×C3D4×D511yescharacteristic
339C22×D3—102no—
340C22×D3—202no—
341C22×D3—202no—
342C22×D3—202no—
343C3×D4—102no—
344C3×D4—102no—
345C3×D4—208no—
346C3×D4—202no—
347C2×C3×C4—22no—
348C2×C3×C4—42no—
349C2×C3×C4—52no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—104no—
354C2×C3×C4C2×D2012yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4#71312yes—
357C2×C3×C4C23×D511yescharacteristic
358#67—208no—
359C2×Dic3—22no—
360C2×Dic3—42no—
361D12—102no—
362D12—102no—
363D12—202no—
364C3⋊C8—102no—
365C3⋊C8C2×D2014yescomplemented
366C22×C5C2×#21312yes—
367C22×C5#93912yes—
368C22×C5#95012yes—
369C22×C5C22×#6711yescharacteristic
370C2×D5—22no—
371C2×D5—28no—
372C2×D5—22no—
373C2×D5—42no—
374C2×D5—42no—
375C2×D5—42no—
376C2×D5—84no—
377C2×D5—122no—
378C2×D5—122no—
379C2×D5—122no—
380C2×D5—244no—
381C2×D5C2×#21314yescomplemented
382C4×C5—42no—
383C4×C5—122no—
384C4×C5#93912yes—
385C4×C5C2×D3×D411yescharacteristic
386C4×C5C2×#23711yescharacteristic
387Dic5—22no—
388C24—51no—
389C24—101no—
390C24—301no—
391C2×D4—52no—
392C2×D4—104no—
393C2×D4—102no—
394C2×D4—102no—
395C2×D4—101no—
396C2×D4—152no—
397C2×D4—204no—
398C2×D4—304no—
399C2×D4—302no—
400C2×D4—302no—
401C2×D4—301no—
402C2×D4—604no—
403C22×C4—21no—
404C22×C4—51no—
405C22×C4—52no—
406C22×C4—52no—
407C22×C4—61no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4C2×D3×D511yescharacteristic
411D8—308no—
412C2×C8—34no—
413C2×C8—32no—
414C2×C8—152no—
415C2×C8—308no—
416C2×C8—302no—
417C4⋊C4—21no—
418C4⋊C4—32no—
419C4⋊C4—61no—
420C4⋊C4C2×D3×D512yes—
421C22⋊C4—104no—
422C22⋊C4—304no—
423C3×C5C2×#46611yescharacteristic, complemented, Hall
424C22×C3—54no—
425C22×C3—102no—
426C22×C3—102no—
427C22×C3—108no—
428C22×C3—202no—
429C22×C3—202no—
430C22×C3—202no—
431C22×C3—404no—
432C22×C3#404112yes—
433C22×C3D5×D812yes—
434C22×C3#406512yes—
435C22×C3C2×D4×D511yescharacteristic
436C2×D3—202no—
437C2×D3—202no—
438C2×D3—202no—
439C2×D3—404no—
440C3×C4—42no—
441C3×C4—102no—
442C3×C4#404112yes—
443C3×C4C22×D2011yescharacteristic
444C3×C4C2×#71311yescharacteristic
445Dic3—42no—
446C2×C5#503814yescomplemented
447C2×C5C22×#21311yescharacteristic
448C2×C5C2×#93911yescharacteristic
449C2×C5C2×#95011yescharacteristic
450D5—24no—
451D5—82no—
452D5—242no—
453C23—54no—
454C23—52no—
455C23—102no—
456C23—102no—
457C23—102no—
458C23—202no—
459C23—202no—
460C23—202no—
461C23—302no—
462C23—602no—
463C23—602no—
464C23—602no—
465C23D5×#6711yescharacteristic
466D4—102no—
467D4—102no—
468D4—208no—
469D4—202no—
470D4—302no—
471D4—302no—
472D4—608no—
473D4—602no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—52no—
477C2×C4—62no—
478C2×C4—102no—
479C2×C4—104no—
480C2×C4—102no—
481C2×C4—102no—
482C2×C4—122no—
483C2×C4#676612yes—
484C2×C4D3×D2012yes—
485C2×C4D5×#6711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—34no—
488C8—302no—
489C2×C3—104no—
490C2×C3—402no—
491C2×C3#6517214yescomplemented
492C2×C3C2×#404111yescharacteristic
493C2×C3C2×D5×D811yescharacteristic
494C2×C3C2×#406511yescharacteristic
495D3—402no—
496C5C2×#503811yescharacteristic, complemented, Sylow
497C22—54no—
498C22—102no—
499C22—102no—
500C22—108no—
501C22—202no—
502C22—202no—
503C22—202no—
504C22—404no—
505C22—602no—
506C22—602no—
507C22—602no—
508C22—1204no—
509C22#9140912yes—
510C22D5×#21312yes—
511C22#9151612yes—
512C22C2×D5×#6711yescharacteristic
513C4—42no—
514C4—102no—
515C4—122no—
516C4#9140912yes—
517C4C2×#676611yescharacteristic
518C4C2×D3×D2011yescharacteristic
519C3C2×#6517211yescharacteristic, complemented, Sylow
520C2—104no—
521C2—402no—
522C2—1202no—
523C2#1174744214yesdirect product factor
524C2C2×#9140911yescharacteristic
525C2C2×D5×#21311yescharacteristic
526C2C2×#9151611yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#466
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4041C2semidirect
2. C2×#91450C2semidirect
3. C22×#6653C2semidirect
4. C22×D5×C3⋊C8C2semidirect
5. C2×#91093C2semidirect
6. C2×C5×#807C2semidirect
7. C2×#90964C2semidirect
8. #11747442C2direct (N × H)
21. C3×#4041C22semidirect
24. #91450C22semidirect
26. C2×#6653C22semidirect
28. C2×D5×C3⋊C8C22semidirect
29. #91093C22semidirect
30. C5×#807C22semidirect
31. #90964C22semidirect
36. C2×#4041D3semidirect
70. C2×C5×C3⋊C8D4semidirect
83. C2×#807D5semidirect
102. #4041C2×D3semidirect
118. C22×C3×D5D8semidirect
142. C5×C3⋊C8C2×D4semidirect
164. #807C2×D5semidirect
223. C2×C3×D5C2×D8semidirect
263. C2×C3⋊C8D20semidirect
276. C22×D5#213semidirect
323. C2×C3×C5#466semidirect
365. C3⋊C8C2×D20semidirect
381. C2×D5C2×#213semidirect
423. C3×C5C2×#466semidirect
446. C2×C5#5038semidirect
491. C2×C3#65172semidirect
496. C5C2×#5038semidirect
519. C3C2×#65172semidirect
523. C2#11747442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40412
C2×#914502
C22×#66532
C22×D5×C3⋊C82
C2×#910932
C2×C5×#8072
C2×#909642
#117474422
C2×#651723
C2×#50385