Finite Group Databasebeta

← C2×#11748952 #14431717

Subgroups — C2×#11748952 #14431717

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×#4084C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#91116C211yesmaximal, characteristic, complemented
4C2×C5×#832C211yesmaximal, characteristic, complemented
5#11748952C218yesmaximal, direct product factor
6C2×#90987C211yesmaximal, characteristic, complemented
7C2×#90986C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65066—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×C3×C22⋊D5—21no—
12C22×C3×C4×D5C2211yescharacteristic
13C22×D5×Dic3—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×C22⋊Dic5—21no—
19C3×#4084—22no—
20C3×#4084C2214yes—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×#6668—21no—
23D5×C4⋊Dic3—22no—
24D5×C4⋊Dic3C2214yescomplemented
25#91116C2214yescomplemented
26C5×#832C2214yescomplemented
27#90987C2214yescomplemented
28#90986C2214yescomplemented
29#90955C2214yescomplemented
30C2×#5034—51nomaximal, Hall
31C2×#4084D311yescharacteristic
32C2×D5×C4⋊C4—31no—
33C2×C5×#102—31no—
34C2×#3964—31no—
35C2×#3952—31no—
36C2×#3949—31no—
37C2×#3940—31no—
38#65066—38no—
39C24×C3×C5—21no—
40C23×C3×D5D411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C22×C5×Dic3—21no—
48C2×C3×C22⋊D5—24no—
49C2×C3×C22⋊D5—44no—
50C22×C3×Dic5—21no—
51C22×C3×Dic5D411yescharacteristic
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—
58C4⋊Dic15—21no—
59C4⋊Dic15C2312yes—
60C2×C3⋊#168—22no—
61C2×C3⋊#168C2312yes—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2312yes—
64C2×C5×C3⋊C8—22no—
65C2×C5×C3⋊C8C2312yes—
66C3×C22⋊Dic5—24no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5C2312yes—
69#6668—24no—
70C2×C3×#121—51no—
71C22×C4⋊Dic3—51no—
72C2×#832—51no—
73C2×#832D511yescharacteristic, complemented
74C2×#830—51no—
75#5034—58no—
76C2×#808—51no—
77C2×#808—51no—
78C22×C5×D4C2×D311yescharacteristic
79C22×C22⋊D5—21no—
80C22×C4×D5—61no—
81C22×C4×D5C2×D311yescharacteristic
82C22×C5×C8—31no—
83C2×C5×C4⋊C4—31no—
84C2×C22⋊Dic5—21no—
85#4084—22no—
86#4084C2×D314yes—
87C2×C4⋊Dic5—31no—
88C2×C4⋊Dic5C2×D311yescharacteristic
89C2×#683—61no—
90C22×#168—31no—
91D5×C4⋊C4—34no—
92D5×C4⋊C4—62no—
93C5×#102—34no—
94#3964—34no—
95#3952—34no—
96#3949—34no—
97#3940—34no—
98C2×#481—151noSylow
99C23×C3×C5—22no—
100C23×C3×C5—42no—
101C23×C3×C5—42no—
102C23×C3×C5—42no—
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—22no—
105C22×C3×D5—22no—
106C22×C3×D5SD1614yes—
107C22×C3×D5C2×D412yes—
108C3×C5×D4—22no—
109C3×C5×D4—22no—
110C3×C5×D4—42no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4112yes—
113C2×C3×C4×C5#4112yes—
114C2×C3×C4×C5C2411yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—42no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—42no—
119C3×C22⋊D5—48no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—42no—
123C2×C3×Dic5C2×D412yes—
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—101no—
131C22×C3×D4C2×D511yescharacteristic
132C23×C3×C4—51no—
133C23×Dic3—101no—
134C3×#121—54no—
135C3×#121—102no—
136C2×C3×C4⋊C4—51no—
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#832C2×D514yescomplemented
147#830—54no—
148#808—54no—
149#808—54no—
150C24×C5—21no—
151C23×D5#6711yescharacteristic
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C2×C5×D4—21no—
155C2×C5×D4C22×D312yes—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C2×C22⋊D5—24no—
159C2×C22⋊D5—44no—
160C22×Dic5—21no—
161C22×Dic5—61no—
162C22×Dic5#6711yescharacteristic
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—32no—
172C5×C4⋊C4—61no—
173C22⋊Dic5—24no—
174C4⋊Dic5—21no—
175C4⋊Dic5—32no—
176C4⋊Dic5—61no—
177C4⋊Dic5C22×D312yes—
178#683—64no—
179C2×#168—32no—
180C2×#168—62no—
181C2×#121—51no—
182C22×C4⋊C4—151no—
183#481—158no—
184C2×#106—151no—
185C2×#106—151no—
186C2×#102—31no—
187C2×#102—151no—
188C2×C22⋊C8—151no—
189C22×C3×C5—42no—
190C22×C3×C5—42no—
191C22×C3×C5—42no—
192C22×C3×C5—84no—
193C22×C3×C5#12312yes—
194C22×C3×C5C2×SD1612yes—
195C22×C3×C5AGL(1,ℤ/8)12yes—
196C22×C3×C5C22×D411yescharacteristic
197C2×C3×D5—22no—
198C2×C3×D5—22no—
199C2×C3×D5—28no—
200C2×C3×D5C2×SD1614yes—
201C3×C4×C5#12312yes—
202C3×C4×C5C2×#4111yescharacteristic
203C3×C4×C5C2×#4111yescharacteristic
204Dic15—42no—
205C3×Dic5—22no—
206C3×Dic5—42no—
207C5×Dic3—42no—
208C24×C3—21no—
209C24×C3—51no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—104no—
214C2×C3×D4—204no—
215C2×C3×D4C22×D512yes—
216C22×C3×C4—51no—
217C22×C3×C4—52no—
218C22×C3×C4—52no—
219C22×C3×C4—102no—
220C22×C3×C4—102no—
221C22×C3×C4—101no—
222C22×C3×C4C22×D511yescharacteristic
223C22×Dic3—21no—
224C22×Dic3—104no—
225C22×Dic3—101no—
226C22×Dic3—204no—
227C3×C4⋊C4—52no—
228C3×C4⋊C4—101no—
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×C5—22no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5C2×#6711yescharacteristic
244C22×D5—22no—
245C22×D5—22no—
246C22×D5#21414yes—
247C22×D5C2×#6712yes—
248C5×D4—22no—
249C5×D4—22no—
250C5×D4—42no—
251C2×C4×C5—62no—
252C2×C4×C5—122no—
253C2×C4×C5#23712yes—
254C2×C4×C5#23712yes—
255C2×C4×C5C2×#6711yescharacteristic
256C2×C4×C5C23×D311yescharacteristic
257C22⋊D5—48no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—42no—
261C2×Dic5—62no—
262C2×Dic5—122no—
263C2×Dic5C2×#6712yes—
264C4×D5—24no—
265C4×D5—22no—
266C4×D5—22no—
267C4×D5—128no—
268C5×C8—62no—
269#168—62no—
270C22×D4—101no—
271C22×D4D3×D511yescharacteristic
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—51no—
280C2×C4⋊C4—154no—
281C2×C4⋊C4—151no—
282C2×C4⋊C4—302no—
283C2×C4⋊C4—301no—
284C2×C22⋊C4—101no—
285#106—154no—
286#106—154no—
287#102—34no—
288#102—154no—
289C22⋊C8—154no—
290C2×C3×C5—82no—
291C2×C3×C5#48114yescomplemented
292C2×C3×C5C2×#12311yescharacteristic
293C2×C3×C5C22×SD1611yescharacteristic
294C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
295C3×D5—24no—
296C23×C3—22no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—42no—
300C23×C3—52no—
301C23×C3—54no—
302C23×C3—102no—
303C23×C3—102no—
304C23×C3D4×D511yescharacteristic
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—42no—
308C3×D4—208no—
309C2×C3×C4—52no—
310C2×C3×C4—102no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—104no—
314C2×C3×C4—102no—
315C2×C3×C4—202no—
316C2×C3×C4#70912yes—
317C2×C3×C4D4×D511yescharacteristic
318C2×C3×C4#71112yes—
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×C5—42no—
328C22×C5—42no—
329C22×C5—42no—
330C22×C5—84no—
331C22×C5C2×#21412yes—
332C22×C5#93512yes—
333C22×C5#94912yes—
334C22×C5C22×#6711yescharacteristic
335C2×D5—22no—
336C2×D5—28no—
337C2×D5—22no—
338C2×D5C2×#21414yes—
339C4×C5—122no—
340C4×C5#93512yes—
341C4×C5C2×#23711yescharacteristic
342C4×C5C2×#23711yescharacteristic
343Dic5—22no—
344Dic5—42no—
345Dic5—122no—
346C24—21no—
347C24—51no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—104no—
352C2×D4—204no—
353C2×D4C2×D3×D512yes—
354C22×C4—51no—
355C22×C4—52no—
356C22×C4—52no—
357C22×C4—61no—
358C22×C4—102no—
359C22×C4—102no—
360C22×C4—101no—
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—32no—
370C4⋊C4—52no—
371C4⋊C4—61no—
372C4⋊C4—101no—
373C4⋊C4—152no—
374C4⋊C4—304no—
375C4⋊C4—301no—
376C22⋊C4—104no—
377C3×C5C2×#48111yescharacteristic, complemented, Hall
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—54no—
382C22×C3—84no—
383C22×C3—102no—
384C22×C3—102no—
385C22×C3—108no—
386C22×C3#402912yes—
387C22×C3#405712yes—
388C22×C3D5×SD1612yes—
389C22×C3C2×D4×D511yescharacteristic
390C3×C4—102no—
391C3×C4—202no—
392C3×C4#402912yes—
393C3×C4C2×#70911yescharacteristic
394C3×C4C2×#71111yescharacteristic
395Dic3—42no—
396Dic3—202no—
397C2×C5—82no—
398C2×C5#503414yescomplemented
399C2×C5C22×#21411yescharacteristic
400C2×C5C2×#93511yescharacteristic
401C2×C5C2×#94911yescharacteristic
402D5—24no—
403C23—22no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—54no—
408C23—52no—
409C23—102no—
410C23—102no—
411C23D5×#6711yescharacteristic
412D4—22no—
413D4—22no—
414D4—42no—
415D4—208no—
416C2×C4—52no—
417C2×C4—62no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—104no—
422C2×C4—102no—
423C2×C4—122no—
424C2×C4—202no—
425C2×C4—302no—
426C2×C4—608no—
427C2×C4—602no—
428C2×C4#677912yes—
429C2×C4#678012yes—
430C2×C4D5×#6711yescharacteristic
431C2×C4C22×D3×D511yescharacteristic
432C8—62no—
433C8—302no—
434C2×C3—82no—
435C2×C3—104no—
436C2×C3#6506614yescomplemented
437C2×C3C2×#402911yescharacteristic
438C2×C3C2×#405711yescharacteristic
439C2×C3C2×D5×SD1611yescharacteristic
440C5C2×#503411yescharacteristic, complemented, Sylow
441C22—42no—
442C22—42no—
443C22—42no—
444C22—54no—
445C22—84no—
446C22—108no—
447C22—102no—
448C22—102no—
449C22#9147812yes—
450C22D5×#21412yes—
451C22#9154812yes—
452C22C2×D5×#6711yescharacteristic
453C4—102no—
454C4—122no—
455C4—202no—
456C4—602no—
457C4#9154812yes—
458C4C2×#677911yescharacteristic
459C4C2×#678011yescharacteristic
460C3C2×#6506611yescharacteristic, complemented, Sylow
461C2—82no—
462C2—104no—
463C2#1174895214yesdirect product factor
464C2C2×#9147811yescharacteristic
465C2C2×D5×#21411yescharacteristic
466C2C2×#9154811yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4084C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#481
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D5×C4⋊Dic3C2semidirect
3. C2×#91116C2semidirect
4. C2×C5×#832C2semidirect
5. #11748952C2direct (N × H)
6. C2×#90987C2semidirect
7. C2×#90986C2semidirect
8. C2×#90955C2semidirect
24. D5×C4⋊Dic3C22semidirect
25. #91116C22semidirect
26. C5×#832C22semidirect
27. #90987C22semidirect
28. #90986C22semidirect
29. #90955C22semidirect
73. C2×#832D5semidirect
146. #832C2×D5semidirect
291. C2×C3×C5#481semidirect
377. C3×C5C2×#481semidirect
398. C2×C5#5034semidirect
436. C2×C3#65066semidirect
440. C5C2×#5034semidirect
460. C3C2×#65066semidirect
463. C2#11748952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40842
C2×D5×C4⋊Dic32
C2×#911162
C2×C5×#8322
#117489522
C2×#909872
C2×#909862
C2×#909552
C2×#650663
C2×#50345