Finite Group Databasebeta

← C2×#11755244 #14482872

Subgroups — C2×#11755244 #14482872

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#239C211yesmaximal, characteristic, complemented
2C22×C3×Q8×D5C211yesmaximal, characteristic, complemented
3C2×Q8×Dic15C211yesmaximal, characteristic, complemented
4#11755244C2116yesmaximal, direct product factor
5C2×#91449C213yesmaximal, complemented
6C2×C4×#1201C213yesmaximal, complemented
7C2×#91370C213yesmaximal, complemented
8C2×#91369C213yesmaximal, complemented
9C2×#66165—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C5×#239—28no—
12C2×C5×#239C2218yescomplemented
13C22×C5×D12C2213yes—
14C22×C4×C5×D3C2213yes—
15C2×C3×Q8×D5—28no—
16C2×C3×Q8×D5C2218yescomplemented
17C22×C3×C4×D5C2213yes—
18C22×C3×Dic10C2213yes—
19C22×#1201C2213yes—
20Q8×Dic15C2218yescomplemented
21C2×C4⋊Dic15C2213yes—
22C2×C4×Dic15C2213yes—
23C2×#6669C2213yes—
24C2×(C2×D3)⋊Dic5C2216yes—
25C2×(C2×D3)⋊Dic5C2213yes—
26C2×#6665C2211yescharacteristic
27#91449C22124yescomplemented
28C4×#1201C22124yescomplemented
29#91370C22124yescomplemented
30#91369C22124yescomplemented
31C2×#5817—51nomaximal, Hall
32C22×C5×#41—31no—
33C22×Q8×D5D311yescharacteristic, complemented
34#66165—316no—
35C2×Q8×Dic5—31no—
36C2×#4084—33no—
37C2×#4082—33no—
38C2×C4×C22⋊D5—33no—
39C2×#4070—33no—
40C23×C5×D3C2313yes—
41C23×C3×D5C2311yescharacteristic
42C2×C3×C5×Q8D418yescomplemented
43C2×C3×C5×Q8C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×Dic15C2313yes—
46C22×Dic15C2311yescharacteristic
47C22×C5×Dic3C2311yescharacteristic
48C5×#239—232no—
49C2×C5×D12—212no—
50C2×C5×D12C23112yes—
51C2×C4×C5×D3—212no—
52C2×C4×C5×D3C23112yes—
53C22×C3×Dic5C2313yes—
54C3×Q8×D5—232no—
55C2×C3×C4×D5—212no—
56C2×C3×C4×D5C23112yes—
57C2×C3×Dic10—212no—
58C2×C3×Dic10C23112yes—
59C2×#1201—212no—
60C2×#1201C23112yes—
61C4⋊Dic15C23112yes—
62C4×Dic15C23112yes—
63#6669C23112yes—
64(C2×D3)⋊Dic5C23112yes—
65(C2×D3)⋊Dic5C23124yes—
66#6665C2314yes—
67C23×C3×Q8—51no—
68C22×#239D511yescharacteristic, complemented
69#5817—516no—
70C2×#947—53no—
71C2×#946—53no—
72C2×Q8×Dic3—51no—
73C2×#930—53no—
74C2×C4×#67—53no—
75C2×C5×#41—38no—
76C2×C5×#41—68no—
77C22×C5×Q8C2×D311yescharacteristic
78C22×C5×D4—33no—
79C23×C4×C5—33no—
80C22×C22⋊D5—33no—
81C2×Q8×D5—28no—
82C2×Q8×D5C2×D318yescomplemented
83C22×C4×D5C2×D313yes—
84C22×Dic10C2×D313yes—
85C2×C22⋊Dic5—36no—
86C2×C22⋊Dic5—33no—
87Q8×Dic5—38no—
88#4084—324no—
89#4082—324no—
90C4×C22⋊D5—324no—
91C2×#685—31no—
92C2×C4⋊Dic5—33no—
93#4070—324no—
94C2×#683—33no—
95C2×C4×Dic5—33no—
96C2×#548—151noSylow
97C23×C3×C5C2411yescharacteristic
98C22×C5×D3—26no—
99C22×C5×D3—26no—
100C22×C5×D3—26no—
101C22×C5×D3C2416yes—
102C22×C3×D5—22no—
103C22×C3×D5—22no—
104C22×C3×D5#4114yescomplemented
105C22×C3×D5C2412yes—
106C3×C5×Q8C2×D4116yescomplemented
107C2×C3×C4×C5C2×D4112yes—
108C2×C3×C4×C5C2416yes—
109C2×Dic15—26no—
110C2×Dic15—22no—
111C2×Dic15C2412yes—
112C2×Dic15C2416yes—
113C2×C5×Dic3—22no—
114C2×C5×Dic3C2412yes—
115C5×D12—224no—
116C4×C5×D3—224no—
117C2×C3×Dic5—26no—
118C2×C3×Dic5C2416yes—
119C3×C4×D5—224no—
120C3×Dic10—224no—
121#1201—224no—
122C22×C3×Q8—58no—
123C22×C3×Q8—53no—
124C22×C3×Q8—108no—
125C22×C3×Q8C2×D511yescharacteristic
126C23×C3×C4—53no—
127C22×#67—53no—
128C2×#239—28no—
129C2×#239C2×D518yescomplemented
130C22×D12C2×D513yes—
131C22×C4×D3C2×D513yes—
132C2×#217—51no—
133#947—524no—
134#946—524no—
135Q8×Dic3—58no—
136#930—524no—
137C4×#67—524no—
138C2×(C2×D3)⋊C4—53no—
139C2×(C2×D3)⋊C4—56no—
140C2×C4⋊Dic3—53no—
141C2×Dic3⋊C4—53no—
142C2×C4×Dic3—53no—
143C24×C5—33no—
144C23×D5C22×D311yescharacteristic
145C5×#41—632no—
146C2×C5×Q8#6718yescomplemented
147C2×C5×Q8C22×D314yes—
148C2×C5×D4—312no—
149C2×C5×D4—612no—
150C22×C4×C5—31no—
151C22×C4×C5—312no—
152C22×C4×C5—612no—
153C22×C4×C5C22×D313yes—
154C2×C22⋊D5—312no—
155C2×C22⋊D5—612no—
156C22×Dic5—31no—
157C22×Dic5—33no—
158C22×Dic5C22×D313yes—
159Q8×D5—232no—
160C2×C4×D5—212no—
161C2×C4×D5C22×D3112yes—
162C2×Dic10—212no—
163C2×Dic10C22×D3112yes—
164C22⋊Dic5—324no—
165C22⋊Dic5—312no—
166#685—34no—
167C4⋊Dic5—312no—
168#683—312no—
169C4×Dic5—312no—
170C22×#41—31no—
171C23×Q8—51no—
172#548—1516no—
173C2×#124—153no—
174C2×C22⋊Q8—153no—
175C2×#121—153no—
176C2×C4×Q8—151no—
177C2×C4×D4—153no—
178C22×C3×C5C22×D412yes—
179C22×C3×C5C2×#4112yes—
180C22×C3×C52−1+412yes—
181C22×C3×C5C2511yescharacteristic
182C2×C5×D3—26no—
183C2×C5×D3—26no—
184C2×C5×D3—26no—
185C2×C5×D3—412no—
186C2×C3×D5—28no—
187C2×C3×D5—22no—
188C2×C3×D5—22no—
189C2×C3×D5C2×#4114yescomplemented
190C3×C4×C5C22×D4112yes—
191Dic15—26no—
192Dic15—22no—
193C3×Dic5—26no—
194C5×Dic3—22no—
195C24×C3—51no—
196C23×D3C22×D513yes—
197C2×C3×Q8—512no—
198C2×C3×Q8—1032no—
199C2×C3×Q8—1012no—
200C2×C3×Q8C22⋊D518yescomplemented
201C2×C3×Q8C22×D514yes—
202C22×C3×C4—53no—
203C22×C3×C4—512no—
204C22×C3×C4—1012no—
205C22×C3×C4C22×D513yes—
206C2×#67—512no—
207C2×#67—1012no—
208C22×Dic3—51no—
209C22×Dic3—53no—
210C22×Dic3C22×D511yescharacteristic
211#239—232no—
212C2×D12—212no—
213C2×D12C22×D5112yes—
214C2×C4×D3—212no—
215C2×C4×D3C22×D5112yes—
216#217—54no—
217(C2×D3)⋊C4—512no—
218(C2×D3)⋊C4—524no—
219C4⋊Dic3—512no—
220Dic3⋊C4—512no—
221C4×Dic3—512no—
222C23×C5—36no—
223C23×C5—66no—
224C23×C5—66no—
225C23×C5—66no—
226C23×C5C23×D311yescharacteristic
227C22×D5—22no—
228C22×D5—22no—
229C22×D5#23914yescomplemented
230C22×D5C23×D312yes—
231C5×Q8C2×#67116yescomplemented
232C5×D4—624no—
233C2×C4×C5—32no—
234C2×C4×C5—62no—
235C2×C4×C5—624no—
236C2×C4×C5C2×#67112yes—
237C2×C4×C5C23×D316yes—
238C22⋊D5—624no—
239C2×Dic5—26no—
240C2×Dic5—32no—
241C2×Dic5—36no—
242C2×Dic5—66no—
243C2×Dic5—62no—
244C2×Dic5C23×D316yes—
245C4×D5—224no—
246Dic10—224no—
247C2×#41—38no—
248C2×#41—68no—
249C22×Q8—58no—
250C22×Q8—53no—
251C22×Q8—108no—
252C22×Q8D3×D511yescharacteristic
253C22×D4—33no—
254C22×D4—153no—
255C23×C4—33no—
256C23×C4—53no—
257#124—1524no—
258C22⋊Q8—1524no—
259#121—1524no—
260C4×Q8—158no—
261C4×D4—1524no—
262C2×C4⋊C4—153no—
263C2×C4⋊C4—153no—
264C2×C22⋊C4—151no—
265C2×C22⋊C4—153no—
266C2×C22⋊C4—156no—
267C2×C42—153no—
268C2×C3×C5#54814yescomplemented
269C2×C3×C5C23×D411yescharacteristic
270C2×C3×C5C22×#4111yescharacteristic
271C2×C3×C5C2×2−1+411yescharacteristic
272C3×D5—24no—
273C5×D3—46no—
274C23×C3—54no—
275C23×C3—52no—
276C23×C3—102no—
277C23×C3—102no—
278C23×C3C23×D511yescharacteristic
279C22×D3—26no—
280C22×D3—26no—
281C22×D3—26no—
282C22×D3C23×D516yes—
283C3×Q8—1024no—
284C3×Q8C2×C22⋊D5116yescomplemented
285C2×C3×C4—56no—
286C2×C3×C4—106no—
287C2×C3×C4—1024no—
288C2×C3×C4C2×C22⋊D5112yes—
289C2×C3×C4C23×D516yes—
290#67—1024no—
291C2×Dic3—22no—
292C2×Dic3—52no—
293C2×Dic3—56no—
294C2×Dic3—106no—
295C2×Dic3—102no—
296C2×Dic3C23×D512yes—
297D12—224no—
298C4×D3—224no—
299C22×C5—66no—
300C22×C5—66no—
301C22×C5—66no—
302C22×C5—1212no—
303C22×C5C2×#23912yes—
304C22×C5#100712yes—
305C22×C5C22×#6712yes—
306C22×C5C24×D311yescharacteristic
307C2×D5—22no—
308C2×D5—22no—
309C2×D5—28no—
310C2×D5C2×#23914yescomplemented
311C4×C5—62no—
312C4×C5C22×#67112yes—
313Dic5—26no—
314Dic5—66no—
315Dic5—62no—
316C24—33no—
317C24—51no—
318#41—632no—
319C2×Q8—512no—
320C2×Q8—1032no—
321C2×Q8—1012no—
322C2×Q8#120118yescomplemented
323C2×Q8C2×D3×D514yes—
324C2×D4—312no—
325C2×D4—612no—
326C2×D4—1512no—
327C2×D4—3012no—
328C22×C4—31no—
329C22×C4—312no—
330C22×C4—53no—
331C22×C4—512no—
332C22×C4—612no—
333C22×C4—1012no—
334C22×C4—151no—
335C22×C4—153no—
336C22×C4C2×D3×D513yes—
337C4⋊C4—1512no—
338C4⋊C4—1512no—
339C22⋊C4—154no—
340C22⋊C4—1512no—
341C22⋊C4—1524no—
342C42—1512no—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3—54no—
345C22×C3—108no—
346C22×C3—102no—
347C22×C3—102no—
348C22×C3D5×#4112yes—
349C22×C3#415012yes—
350C22×C3C22×C22⋊D512yes—
351C22×C3C24×D511yescharacteristic
352C2×D3—26no—
353C2×D3—26no—
354C2×D3—26no—
355C2×D3—412no—
356C3×C4—106no—
357C3×C4C22×C22⋊D5112yes—
358Dic3—22no—
359Dic3—106no—
360Dic3—102no—
361C2×C5—126no—
362C2×C5#581714yescomplemented
363C2×C5C22×#23911yescharacteristic
364C2×C5C2×#100711yescharacteristic
365C2×C5C23×#6711yescharacteristic
366D5—24no—
367C23—36no—
368C23—54no—
369C23—52no—
370C23—66no—
371C23—66no—
372C23—66no—
373C23—102no—
374C23—102no—
375C23C22×D3×D511yescharacteristic
376Q8—1024no—
377Q8C2×#1201116yescomplemented
378D4—624no—
379D4—3024no—
380C2×C4—32no—
381C2×C4—56no—
382C2×C4—62no—
383C2×C4—624no—
384C2×C4—106no—
385C2×C4—1024no—
386C2×C4—152no—
387C2×C4—156no—
388C2×C4—302no—
389C2×C4—306no—
390C2×C4C2×#1201112yes—
391C2×C4C22×D3×D516yes—
392C2×C3—104no—
393C2×C3#6616514yescomplemented
394C2×C3C2×D5×#4111yescharacteristic
395C2×C3C2×#415011yescharacteristic
396C2×C3C23×C22⋊D511yescharacteristic
397D3—46no—
398C5C2×#581711yescharacteristic, complemented, Sylow
399C22—54no—
400C22—66no—
401C22—66no—
402C22—66no—
403C22—102no—
404C22—108no—
405C22—102no—
406C22—1212no—
407C22#9203012yes—
408C22D5×#23912yes—
409C22C22×#120112yes—
410C22C23×D3×D511yescharacteristic
411C4—62no—
412C4—106no—
413C4—302no—
414C4—306no—
415C4C22×#1201112yes—
416C3C2×#6616511yescharacteristic, complemented, Sylow
417C2—104no—
418C2—126no—
419C2#1175524414yesdirect product factor
420C2C2×#9203011yescharacteristic
421C2C2×D5×#23911yescharacteristic
422C2C23×#120111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#239C2semidirect
2. C22×C3×Q8×D5C2semidirect
3. C2×Q8×Dic15C2semidirect
4. #11755244C2direct (N × H)
5. C2×#91449C2semidirect
6. C2×C4×#1201C2semidirect
7. C2×#91370C2semidirect
8. C2×#91369C2semidirect
12. C2×C5×#239C22semidirect
16. C2×C3×Q8×D5C22semidirect
20. Q8×Dic15C22semidirect
27. #91449C22semidirect
28. C4×#1201C22semidirect
29. #91370C22semidirect
30. #91369C22semidirect
33. C22×Q8×D5D3semidirect
42. C2×C3×C5×Q8D4semidirect
68. C22×#239D5semidirect
82. C2×Q8×D5C2×D3semidirect
104. C22×C3×D5#41semidirect
106. C3×C5×Q8C2×D4semidirect
129. C2×#239C2×D5semidirect
146. C2×C5×Q8#67semidirect
189. C2×C3×D5C2×#41semidirect
200. C2×C3×Q8C22⋊D5semidirect
229. C22×D5#239semidirect
231. C5×Q8C2×#67semidirect
268. C2×C3×C5#548semidirect
284. C3×Q8C2×C22⋊D5semidirect
310. C2×D5C2×#239semidirect
322. C2×Q8#1201semidirect
343. C3×C5C2×#548semidirect
362. C2×C5#5817semidirect
377. Q8C2×#1201semidirect
393. C2×C3#66165semidirect
398. C5C2×#5817semidirect
416. C3C2×#66165semidirect
419. C2#11755244direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2392
C22×C3×Q8×D52
C2×Q8×Dic152
#117552442
C2×#914492
C2×C4×#12012
C2×#913702
C2×#913692
C2×#661653
C2×#58175