Finite Group Databasebeta

← C2×#11747195 #14431732

Subgroups — C2×#11747195 #14431732

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×#4041C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#91092C211yesmaximal, characteristic, complemented
4C2×C5×#808C211yesmaximal, characteristic, complemented
5C2×#90965C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747195C218yesmaximal, direct product factor
9C2×#65152—31nomaximal, Hall
10C22×C3×D20—21no—
11C22×C3×D20C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×D5×Dic3—21no—
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C3×#685—21no—
20C3×#4041—22no—
21C3×#4041C2214yes—
22C2×#6668—21no—
23D5×C4⋊Dic3—22no—
24D5×C4⋊Dic3C2214yescomplemented
25#91092C2214yescomplemented
26C5×#808C2214yescomplemented
27#90965C2214yescomplemented
28#90964C2214yescomplemented
29#90955C2214yescomplemented
30C2×#5034—51nomaximal, Hall
31C2×#4041D311yescharacteristic
32C2×D5×C4⋊C4—31no—
33C2×C5×#106—31no—
34C2×#3953—31no—
35C2×#3952—31no—
36C2×#3941—31no—
37C2×#3940—31no—
38#65152—38no—
39C23×C3×D5—21no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×C5×Dic3—21no—
45C22×C3×Dic5D411yescharacteristic
46C2×C3×D20—22no—
47C2×C3×D20—22no—
48C2×C3×D20—24no—
49C2×C3×D20—21no—
50C2×C3×D20—44no—
51C2×C3×D20C2312yes—
52C2×C3×C4×D5—22no—
53C2×C3×C4×D5—22no—
54C2×C3×C4×D5D412yes—
55C2×C3×C4×D5C2312yes—
56C2×D5×Dic3—24no—
57C2×D5×Dic3—44no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4C2312yes—
60C4⋊Dic15—21no—
61C4⋊Dic15C2312yes—
62C2×C3⋊#168—22no—
63C2×C3⋊#168C2312yes—
64C5×C4⋊Dic3—21no—
65C5×C4⋊Dic3C2312yes—
66C2×C5×C3⋊C8—22no—
67C2×C5×C3⋊C8C2312yes—
68C3×#685—24no—
69#6668—24no—
70C2×C3×#121—51no—
71C22×C4⋊Dic3—51no—
72C2×#832—51no—
73C2×#832—51no—
74C2×#830—51no—
75#5034—58no—
76C2×#808—51no—
77C2×#808D511yescharacteristic, complemented
78C22×D20—21no—
79C22×D20C2×D311yescharacteristic
80C22×C4×D5—61no—
81C22×C4×D5C2×D311yescharacteristic
82C22×C5×C8—31no—
83C2×C5×C4⋊C4—31no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#685—21no—
86C2×C4⋊Dic5—31no—
87C2×#683—61no—
88C22×#168—31no—
89#4041—22no—
90#4041C2×D314yes—
91D5×C4⋊C4—34no—
92D5×C4⋊C4—62no—
93C5×#106—34no—
94#3953—34no—
95#3952—34no—
96#3941—34no—
97#3940—34no—
98C2×#481—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5—22no—
103C22×C3×D5—42no—
104C22×C3×D5—42no—
105C22×C3×D5—42no—
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
114C2×Dic15—22no—
115C2×Dic15—42no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—42no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5C2×D412yes—
120C3×D20—22no—
121C3×D20—22no—
122C3×D20—48no—
123C3×D20—42no—
124C3×C4×D5—24no—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127D5×Dic3—48no—
128C3⋊#168—22no—
129C5×C3⋊C8—22no—
130C22×C3×D4—51no—
131C22×C3×D4—101no—
132C23×C3×C4—51no—
133C23×Dic3—101no—
134C3×#121—54no—
135C3×#121—102no—
136C2×C3×C4⋊C4C2×D511yescharacteristic
137C2×C3×C22⋊C4—101no—
138C2×C4⋊Dic3—51no—
139C2×C4⋊Dic3—54no—
140C2×C4⋊Dic3—102no—
141C2×C4⋊Dic3—101no—
142C2×C4⋊Dic3C2×D511yescharacteristic
143C22×C3⋊C8—51no—
144C22×C3⋊C8C2×D511yescharacteristic
145#832—54no—
146#832—54no—
147#830—54no—
148#808—54no—
149#808C2×D514yescomplemented
150C23×D5—21no—
151C23×D5#6711yescharacteristic
152C22×C4×C5—21no—
153C22×C4×C5—61no—
154C22×C4×C5C22×D311yescharacteristic
155C22×Dic5—61no—
156C22×Dic5#6711yescharacteristic
157C2×D20—22no—
158C2×D20—22no—
159C2×D20—24no—
160C2×D20—21no—
161C2×D20—44no—
162C2×D20C22×D312yes—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—64no—
166C2×C4×D5—124no—
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—24no—
176C4⋊Dic5—32no—
177C4⋊Dic5—61no—
178#683—64no—
179C2×#168—32no—
180C2×#168—62no—
181C2×#121—51no—
182C22×C4⋊C4—151no—
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×C3×D5—22no—
194C2×C3×D5—22no—
195C2×C3×D5—28no—
196C2×C3×D5—42no—
197C2×C3×D5—42no—
198C2×C3×D5—42no—
199C2×C3×D5—84no—
200C2×C3×D5C2×SD1614yes—
201C3×C4×C5—42no—
202C3×C4×C5#12312yes—
203C3×C4×C5C2×#4111yescharacteristic
204C3×C4×C5C2×#4111yescharacteristic
205Dic15—42no—
206C3×Dic5—22no—
207C5×Dic3—42no—
208C24×C3—51no—
209C24×C3—101no—
210C2×C3×D4—52no—
211C2×C3×D4—104no—
212C2×C3×D4—102no—
213C2×C3×D4—101no—
214C2×C3×D4—102no—
215C2×C3×D4—204no—
216C22×C3×C4—21no—
217C22×C3×C4—51no—
218C22×C3×C4—52no—
219C22×C3×C4—52no—
220C22×C3×C4—102no—
221C22×C3×C4—102no—
222C22×C3×C4C22×D511yescharacteristic
223C22×Dic3—21no—
224C22×Dic3—104no—
225C22×Dic3—101no—
226C22×Dic3—204no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4C22×D512yes—
229C3×C22⋊C4—104no—
230C4⋊Dic3—21no—
231C4⋊Dic3—52no—
232C4⋊Dic3—104no—
233C4⋊Dic3—101no—
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—22no—
243C22×D5—42no—
244C22×D5—42no—
245C22×D5—42no—
246C22×D5#21414yes—
247C22×D5C2×#6712yes—
248C2×C4×C5—22no—
249C2×C4×C5—42no—
250C2×C4×C5—62no—
251C2×C4×C5—122no—
252C2×C4×C5#23712yes—
253C2×C4×C5#23712yes—
254C2×C4×C5C2×#6711yescharacteristic
255C2×C4×C5C23×D311yescharacteristic
256C2×Dic5—22no—
257C2×Dic5—62no—
258C2×Dic5—122no—
259C2×Dic5C2×#6712yes—
260D20—22no—
261D20—22no—
262D20—48no—
263D20—42no—
264C4×D5—24no—
265C4×D5—22no—
266C4×D5—22no—
267C4×D5—128no—
268C5×C8—62no—
269#168—62no—
270C22×D4—51no—
271C22×D4—101no—
272C23×C4—51no—
273C23×C4—301no—
274C22×C8—31no—
275C22×C8—151no—
276#121—54no—
277#121—102no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—154no—
280C2×C4⋊C4—151no—
281C2×C4⋊C4—302no—
282C2×C4⋊C4—301no—
283C2×C4⋊C4D3×D511yescharacteristic
284C2×C22⋊C4—101no—
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
294C3×D5—24no—
295C3×D5—82no—
296C23×C3—52no—
297C23×C3—54no—
298C23×C3—102no—
299C23×C3—102no—
300C23×C3—102no—
301C23×C3—202no—
302C23×C3—202no—
303C23×C3—202no—
304C23×C3D4×D511yescharacteristic
305C3×D4—102no—
306C3×D4—102no—
307C3×D4—208no—
308C3×D4—202no—
309C2×C3×C4—22no—
310C2×C3×C4—42no—
311C2×C3×C4—52no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
315C2×C3×C4—104no—
316C2×C3×C4#70912yes—
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4#71312yes—
319C2×C3×C4C23×D511yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—42no—
322C2×Dic3—102no—
323C2×Dic3—208no—
324C2×Dic3—202no—
325C3⋊C8—22no—
326C3⋊C8—102no—
327C22×C5C2×#21412yes—
328C22×C5#93512yes—
329C22×C5#94912yes—
330C22×C5C22×#6711yescharacteristic
331C2×D5—22no—
332C2×D5—28no—
333C2×D5—22no—
334C2×D5—42no—
335C2×D5—42no—
336C2×D5—42no—
337C2×D5—84no—
338C2×D5C2×#21414yes—
339C4×C5—42no—
340C4×C5—122no—
341C4×C5#93512yes—
342C4×C5C2×#23711yescharacteristic
343C4×C5C2×#23711yescharacteristic
344Dic5—22no—
345Dic5—122no—
346C24—51no—
347C24—101no—
348C2×D4—52no—
349C2×D4—104no—
350C2×D4—102no—
351C2×D4—102no—
352C2×D4—101no—
353C2×D4—204no—
354C22×C4—21no—
355C22×C4—51no—
356C22×C4—52no—
357C22×C4—52no—
358C22×C4—61no—
359C22×C4—102no—
360C22×C4—102no—
361C22×C4—304no—
362C22×C4—301no—
363C22×C4—604no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—32no—
366C2×C8—62no—
367C2×C8—152no—
368C2×C8—302no—
369C4⋊C4—21no—
370C4⋊C4—32no—
371C4⋊C4—61no—
372C4⋊C4—152no—
373C4⋊C4—304no—
374C4⋊C4—301no—
375C4⋊C4C2×D3×D512yes—
376C22⋊C4—104no—
377C3×C5C2×#48111yescharacteristic, complemented, Hall
378C22×C3—54no—
379C22×C3—102no—
380C22×C3—102no—
381C22×C3—108no—
382C22×C3—202no—
383C22×C3—202no—
384C22×C3—202no—
385C22×C3—404no—
386C22×C3#404012yes—
387C22×C3D5×SD1612yes—
388C22×C3#406012yes—
389C22×C3C2×D4×D511yescharacteristic
390C3×C4—42no—
391C3×C4—102no—
392C3×C4#404012yes—
393C3×C4C2×#70911yescharacteristic
394C3×C4C2×#71311yescharacteristic
395Dic3—42no—
396Dic3—202no—
397C2×C5#503414yescomplemented
398C2×C5C22×#21411yescharacteristic
399C2×C5C2×#93511yescharacteristic
400C2×C5C2×#94911yescharacteristic
401D5—24no—
402D5—82no—
403C23—54no—
404C23—52no—
405C23—102no—
406C23—102no—
407C23—102no—
408C23—202no—
409C23—202no—
410C23—202no—
411C23D5×#6711yescharacteristic
412D4—102no—
413D4—102no—
414D4—208no—
415D4—202no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—52no—
419C2×C4—62no—
420C2×C4—102no—
421C2×C4—104no—
422C2×C4—102no—
423C2×C4—102no—
424C2×C4—122no—
425C2×C4—302no—
426C2×C4—608no—
427C2×C4—602no—
428C2×C4#676512yes—
429C2×C4#676612yes—
430C2×C4D5×#6711yescharacteristic
431C2×C4C22×D3×D511yescharacteristic
432C8—62no—
433C8—302no—
434C2×C3—104no—
435C2×C3—402no—
436C2×C3#6515214yescomplemented
437C2×C3C2×#404011yescharacteristic
438C2×C3C2×D5×SD1611yescharacteristic
439C2×C3C2×#406011yescharacteristic
440C5C2×#503411yescharacteristic, complemented, Sylow
441C22—54no—
442C22—102no—
443C22—102no—
444C22—108no—
445C22—202no—
446C22—202no—
447C22—202no—
448C22—404no—
449C22#9140712yes—
450C22D5×#21412yes—
451C22#9150212yes—
452C22C2×D5×#6711yescharacteristic
453C4—42no—
454C4—102no—
455C4—122no—
456C4—602no—
457C4#9140712yes—
458C4C2×#676511yescharacteristic
459C4C2×#676611yescharacteristic
460C3C2×#6515211yescharacteristic, complemented, Sylow
461C2—104no—
462C2—402no—
463C2#1174719514yesdirect product factor
464C2C2×#9140711yescharacteristic
465C2C2×D5×#21411yescharacteristic
466C2C2×#9150211yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4041C2
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
2. C2×D5×C4⋊Dic3C2semidirect
3. C2×#91092C2semidirect
4. C2×C5×#808C2semidirect
5. C2×#90965C2semidirect
6. C2×#90964C2semidirect
7. C2×#90955C2semidirect
8. #11747195C2direct (N × H)
24. D5×C4⋊Dic3C22semidirect
25. #91092C22semidirect
26. C5×#808C22semidirect
27. #90965C22semidirect
28. #90964C22semidirect
29. #90955C22semidirect
77. C2×#808D5semidirect
149. #808C2×D5semidirect
290. C2×C3×C5#481semidirect
377. C3×C5C2×#481semidirect
397. C2×C5#5034semidirect
436. C2×C3#65152semidirect
440. C5C2×#5034semidirect
460. C3C2×#65152semidirect
463. C2#11747195direct (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×D5×C4⋊Dic32
C2×#910922
C2×C5×#8082
C2×#909652
C2×#909642
C2×#909552
#117471952
C2×#651523
C2×#50345