Finite Group Databasebeta

← C2×#11747165 #14431730

Subgroups — C2×#11747165 #14431730

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#91450C211yesmaximal, characteristic
3C2×#91093C211yesmaximal, characteristic, complemented
4C2×C5×#808C211yesmaximal, characteristic, complemented
5C2×#90986C211yesmaximal, characteristic, complemented
6C2×#90968C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747165C218yesmaximal, direct product factor
9C2×#65152—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C22×C3×C4×D5—21no—
12C22×C3×C4×D5C2211yescharacteristic
13C22×#1202—21no—
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×#683—21no—
20C3×D5×C4⋊C4—22no—
21C3×D5×C4⋊C4C2214yescomplemented
22C2×#6667—21no—
23#91450—22no—
24#91450C2214yes—
25#91093C2214yescomplemented
26C5×#808C2214yescomplemented
27#90986C2214yescomplemented
28#90968C2214yescomplemented
29#90955C2214yescomplemented
30C2×#4968—51nomaximal, Hall
31C2×#4041—31no—
32C2×D5×C4⋊C4D311yescharacteristic, complemented
33C2×C5×#106—31no—
34C2×#3953—31no—
35C2×#3952—31no—
36C2×#3941—31no—
37C2×#3940—31no—
38#65152—38no—
39C23×D15—21no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×D60—22no—
44C2×D60—22no—
45C2×D60—21no—
46C2×D60C2312yes—
47C22×C5×Dic3—21no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5D411yescharacteristic
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—22no—
52C2×C3×C4×D5—24no—
53C2×C3×C4×D5—44no—
54C2×C3×C4×D5D412yes—
55C2×C3×C4×D5C2312yes—
56C2×#1202—24no—
57C2×#1202—44no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4C2312yes—
60C2×C3⋊#168—22no—
61C2×C3⋊#168C2312yes—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2312yes—
64C2×C5×C3⋊C8—22no—
65C2×C5×C3⋊C8C2312yes—
66C3×C4⋊Dic5—21no—
67C3×C4⋊Dic5C2312yes—
68C3×#683—24no—
69#6667—24no—
70C22×C3×C4⋊C4—51no—
71C2×#930—51no—
72C2×#830—51no—
73#4968—58no—
74C2×#809—51no—
75C2×#809—51no—
76C2×#808—51no—
77C2×#808D511yescharacteristic, complemented
78C22×D20—31no—
79C22×D20—61no—
80C22×C4×D5—21no—
81C22×C4×D5C2×D311yescharacteristic
82C22×C5×C8—31no—
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#685—61no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C2×#683—21no—
88C22×#168—31no—
89#4041—34no—
90#4041—62no—
91D5×C4⋊C4—22no—
92D5×C4⋊C4C2×D314yescomplemented
93C5×#106—34no—
94#3953—34no—
95#3952—34no—
96#3941—34no—
97#3940—34no—
98C2×#481—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×D15—22no—
101C22×D15—42no—
102C22×D15—42no—
103C22×D15—42no—
104C22×C3×D5—22no—
105C22×C3×D5—22no—
106C22×C3×D5SD1614yes—
107C22×C3×D5C2×D412yes—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4112yes—
112C2×C3×C4×C5#4112yes—
113C2×C3×C4×C5C2411yescharacteristic
114D60—22no—
115D60—22no—
116D60—42no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—42no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—42no—
122C2×C3×Dic5C2×D412yes—
123C3×C4×D5—24no—
124C3×C4×D5—22no—
125C3×C4×D5—22no—
126C3×C4×D5—48no—
127#1202—48no—
128C3⋊#168—22no—
129C5×C3⋊C8—22no—
130C23×C3×C4—51no—
131C23×C3×C4—101no—
132C22×#67—101no—
133C22×D12—51no—
134C2×C3×C4⋊C4—51no—
135C2×C3×C4⋊C4—54no—
136C2×C3×C4⋊C4—102no—
137C2×C3×C4⋊C4—101no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139#930—54no—
140#930—102no—
141C2×(C2×D3)⋊C4—101no—
142C2×C4⋊Dic3C2×D511yescharacteristic
143C22×C3⋊C8—51no—
144C22×C3⋊C8C2×D511yescharacteristic
145#830—54no—
146#809—54no—
147#809—54no—
148#808—54no—
149#808C2×D514yescomplemented
150C23×D5—61no—
151C23×D5#6711yescharacteristic
152C22×C4×C5—21no—
153C22×C4×C5—61no—
154C22×C4×C5C22×D311yescharacteristic
155C22×Dic5—21no—
156C22×Dic5#6711yescharacteristic
157C2×D20—32no—
158C2×D20—62no—
159C2×D20—62no—
160C2×D20—64no—
161C2×D20—61no—
162C2×D20—124no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—24no—
166C2×C4×D5—44no—
167C2×C4×D5#6712yes—
168C2×C4×D5C22×D312yes—
169C2×C5×C8—32no—
170C2×C5×C8—62no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—32no—
173C5×C4⋊C4—61no—
174C5×C4⋊C4C22×D312yes—
175#685—64no—
176C4⋊Dic5—21no—
177C4⋊Dic5C22×D312yes—
178#683—24no—
179C2×#168—32no—
180C2×#168—62no—
181C2×#121—151no—
182C22×C4⋊C4—51no—
183#481—158no—
184C2×#106—31no—
185C2×#106—151no—
186C2×#102—151no—
187C2×#102—151no—
188C2×C22⋊C8—151no—
189C22×C3×C5#12312yes—
190C22×C3×C5C2×SD1612yes—
191C22×C3×C5AGL(1,ℤ/8)12yes—
192C22×C3×C5C22×D411yescharacteristic
193C2×D15—42no—
194C2×D15—42no—
195C2×D15—42no—
196C2×D15—84no—
197C2×C3×D5—22no—
198C2×C3×D5—22no—
199C2×C3×D5—28no—
200C2×C3×D5C2×SD1614yes—
201C3×C4×C5—42no—
202C3×C4×C5#12312yes—
203C3×C4×C5C2×#4111yescharacteristic
204C3×C4×C5C2×#4111yescharacteristic
205C3×Dic5—22no—
206C3×Dic5—42no—
207C5×Dic3—42no—
208C24×C3—51no—
209C23×D3—101no—
210C22×C3×C4—21no—
211C22×C3×C4—51no—
212C22×C3×C4—52no—
213C22×C3×C4—52no—
214C22×C3×C4—104no—
215C22×C3×C4—102no—
216C22×C3×C4—102no—
217C22×C3×C4—101no—
218C22×C3×C4—204no—
219C22×C3×C4C22×D511yescharacteristic
220C2×#67—104no—
221C2×#67—204no—
222C22×Dic3—21no—
223C2×D12—52no—
224C2×D12—102no—
225C2×D12—102no—
226C2×D12—101no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—52no—
229C3×C4⋊C4—104no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4C22×D512yes—
232(C2×D3)⋊C4—104no—
233C4⋊Dic3—21no—
234C4⋊Dic3C22×D512yes—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—52no—
237C2×C3⋊C8—102no—
238C2×C3⋊C8C22×D512yes—
239C23×C5C2×#6711yescharacteristic
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—62no—
243C22×D5—122no—
244C22×D5—122no—
245C22×D5—122no—
246C22×D5#21514yes—
247C22×D5C2×#6712yes—
248C2×C4×C5—22no—
249C2×C4×C5—42no—
250C2×C4×C5—62no—
251C2×C4×C5—122no—
252C2×C4×C5#23512yes—
253C2×C4×C5#23512yes—
254C2×C4×C5C2×#6711yescharacteristic
255C2×C4×C5C23×D311yescharacteristic
256C2×Dic5—22no—
257C2×Dic5—22no—
258C2×Dic5—42no—
259C2×Dic5C2×#6712yes—
260D20—62no—
261D20—62no—
262D20—128no—
263D20—122no—
264C4×D5—24no—
265C4×D5—22no—
266C4×D5—22no—
267C4×D5—48no—
268C5×C8—62no—
269#168—62no—
270C22×D4—151no—
271C22×D4—301no—
272C23×C4—51no—
273C23×C4—101no—
274C22×C8—31no—
275C22×C8—151no—
276#121—154no—
277#121—302no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—51no—
280C2×C4⋊C4—54no—
281C2×C4⋊C4—102no—
282C2×C4⋊C4—101no—
283C2×C4⋊C4D3×D511yescharacteristic
284C2×C22⋊C4—301no—
285#106—34no—
286#106—154no—
287#102—154no—
288#102—154no—
289C22⋊C8—154no—
290C2×C3×C5#48114yescomplemented
291C2×C3×C5C2×#12311yescharacteristic
292C2×C3×C5C22×SD1611yescharacteristic
293C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
294D15—82no—
295C3×D5—24no—
296C23×C3—52no—
297C23×C3—54no—
298C23×C3—102no—
299C23×C3—102no—
300C23×C3D4×D511yescharacteristic
301C22×D3—102no—
302C22×D3—202no—
303C22×D3—202no—
304C22×D3—202no—
305C2×C3×C4—22no—
306C2×C3×C4—42no—
307C2×C3×C4—52no—
308C2×C3×C4—102no—
309C2×C3×C4—102no—
310C2×C3×C4—102no—
311C2×C3×C4—104no—
312C2×C3×C4—102no—
313C2×C3×C4—208no—
314C2×C3×C4—202no—
315C2×C3×C4#70912yes—
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4#71312yes—
318C2×C3×C4C23×D511yescharacteristic
319#67—208no—
320C2×Dic3—22no—
321C2×Dic3—42no—
322D12—102no—
323D12—102no—
324D12—202no—
325C3⋊C8—22no—
326C3⋊C8—102no—
327C22×C5#92912yes—
328C22×C5#93212yes—
329C22×C5C2×#21512yes—
330C22×C5C22×#6711yescharacteristic
331C2×D5—28no—
332C2×D5—22no—
333C2×D5—22no—
334C2×D5—122no—
335C2×D5—122no—
336C2×D5—122no—
337C2×D5—244no—
338C2×D5C2×#21514yes—
339C4×C5—42no—
340C4×C5—122no—
341C4×C5#92912yes—
342C4×C5C2×#23511yescharacteristic
343C4×C5C2×#23511yescharacteristic
344Dic5—22no—
345Dic5—42no—
346C24—51no—
347C24—301no—
348C2×D4—152no—
349C2×D4—304no—
350C2×D4—302no—
351C2×D4—302no—
352C2×D4—301no—
353C2×D4—604no—
354C22×C4—21no—
355C22×C4—51no—
356C22×C4—52no—
357C22×C4—52no—
358C22×C4—61no—
359C22×C4—104no—
360C22×C4—102no—
361C22×C4—102no—
362C22×C4—101no—
363C22×C4—204no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—32no—
366C2×C8—62no—
367C2×C8—152no—
368C2×C8—302no—
369C4⋊C4—21no—
370C4⋊C4—32no—
371C4⋊C4—52no—
372C4⋊C4—61no—
373C4⋊C4—104no—
374C4⋊C4—101no—
375C4⋊C4C2×D3×D512yes—
376C22⋊C4—304no—
377C3×C5C2×#48111yescharacteristic, complemented, Hall
378C22×C3—54no—
379C22×C3—102no—
380C22×C3—102no—
381C22×C3—108no—
382C22×C3#404012yes—
383C22×C3D5×SD1612yes—
384C22×C3#406012yes—
385C22×C3C2×D4×D511yescharacteristic
386C2×D3—202no—
387C2×D3—202no—
388C2×D3—202no—
389C2×D3—404no—
390C3×C4—42no—
391C3×C4—102no—
392C3×C4—202no—
393C3×C4#404012yes—
394C3×C4C2×#70911yescharacteristic
395C3×C4C2×#71311yescharacteristic
396Dic3—42no—
397C2×C5#496814yescomplemented
398C2×C5C2×#92911yescharacteristic
399C2×C5C2×#93211yescharacteristic
400C2×C5C22×#21511yescharacteristic
401D5—24no—
402D5—242no—
403C23—54no—
404C23—52no—
405C23—102no—
406C23—102no—
407C23—302no—
408C23—602no—
409C23—602no—
410C23—602no—
411C23D5×#6711yescharacteristic
412D4—302no—
413D4—302no—
414D4—608no—
415D4—602no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—52no—
419C2×C4—62no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—104no—
424C2×C4—102no—
425C2×C4—122no—
426C2×C4—208no—
427C2×C4—202no—
428C2×C4#677112yes—
429C2×C4#677312yes—
430C2×C4D5×#6711yescharacteristic
431C2×C4C22×D3×D511yescharacteristic
432C8—62no—
433C8—302no—
434C2×C3—104no—
435C2×C3#6515214yescomplemented
436C2×C3C2×#404011yescharacteristic
437C2×C3C2×D5×SD1611yescharacteristic
438C2×C3C2×#406011yescharacteristic
439D3—402no—
440C5C2×#496811yescharacteristic, complemented, Sylow
441C22—54no—
442C22—108no—
443C22—102no—
444C22—102no—
445C22—602no—
446C22—602no—
447C22—602no—
448C22—1204no—
449C22#9134812yes—
450C22#9149112yes—
451C22D5×#21512yes—
452C22C2×D5×#6711yescharacteristic
453C4—42no—
454C4—102no—
455C4—122no—
456C4—202no—
457C4#9134812yes—
458C4C2×#677111yescharacteristic
459C4C2×#677311yescharacteristic
460C3C2×#6515211yescharacteristic, complemented, Sylow
461C2—104no—
462C2—1202no—
463C2#1174716514yesdirect product factor
464C2C2×#9134811yescharacteristic
465C2C2×#9149111yescharacteristic
466C2C2×D5×#21511yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×#91450C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#481
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×D5×C4⋊C4C2semidirect
3. C2×#91093C2semidirect
4. C2×C5×#808C2semidirect
5. C2×#90986C2semidirect
6. C2×#90968C2semidirect
7. C2×#90955C2semidirect
8. #11747165C2direct (N × H)
21. C3×D5×C4⋊C4C22semidirect
25. #91093C22semidirect
26. C5×#808C22semidirect
27. #90986C22semidirect
28. #90968C22semidirect
29. #90955C22semidirect
32. C2×D5×C4⋊C4D3semidirect
77. C2×#808D5semidirect
92. D5×C4⋊C4C2×D3semidirect
149. #808C2×D5semidirect
290. C2×C3×C5#481semidirect
377. C3×C5C2×#481semidirect
397. C2×C5#4968semidirect
435. C2×C3#65152semidirect
440. C5C2×#4968semidirect
460. C3C2×#65152semidirect
463. C2#11747165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#914502
C2×#910932
C2×C5×#8082
C2×#909862
C2×#909682
C2×#909552
#117471652
C2×#651523
C2×#49685