Finite Group Databasebeta

← C2×#11755131 #14482875

Subgroups — C2×#11755131 #14482875

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×#6821C211yesmaximal, characteristic, complemented
2C22×C5×D3×Q8C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4#11755131C2116yesmaximal, direct product factor
5C2×#91460C213yesmaximal, complemented
6C2×C4×#1203C213yesmaximal, complemented
7C2×#91383C213yesmaximal, complemented
8C2×#91375C213yesmaximal, complemented
9C2×#66151—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—28no—
12C2×#6821C2218yescomplemented
13C22×D60C2213yes—
14C22×C4×D15C2213yes—
15C2×C5×D3×Q8—28no—
16C2×C5×D3×Q8C2218yescomplemented
17C22×C4×C5×D3C2213yes—
18C22×C5×Dic6C2213yes—
19C22×#1203C2213yes—
20C3×Q8×Dic5C2218yescomplemented
21C2×C3×C4⋊Dic5C2213yes—
22C2×C3×C4×Dic5C2213yes—
23C2×#6668C2213yes—
24C2×#6667C2213yes—
25C2×#6667C2216yes—
26C2×(C2×D3)⋊Dic5C2211yescharacteristic
27#91460C22124yescomplemented
28C4×#1203C22124yescomplemented
29#91383C22124yescomplemented
30#91375C22124yescomplemented
31C2×#5576—51nomaximal, Hall
32C23×C5×Q8—31no—
33C22×#713—31no—
34#66151—316no—
35C2×#4093—33no—
36C2×#4092—33no—
37C2×Q8×Dic5D311yescharacteristic, complemented
38C2×#4076—33no—
39C2×C4×C22⋊D5—33no—
40C23×D15C2313yes—
41C23×C5×D3C2311yescharacteristic
42C2×C3×C5×Q8D418yescomplemented
43C2×C3×C5×Q8C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×Dic15C2311yescharacteristic
46#6821—232no—
47C2×D60—212no—
48C2×D60C23112yes—
49C2×C4×D15—212no—
50C2×C4×D15C23112yes—
51C22×C5×Dic3C2313yes—
52C5×D3×Q8—232no—
53C2×C4×C5×D3—212no—
54C2×C4×C5×D3C23112yes—
55C2×C5×Dic6—212no—
56C2×C5×Dic6C23112yes—
57C22×C3×Dic5C2313yes—
58C22×C3×Dic5C2311yescharacteristic
59C2×#1203—212no—
60C2×#1203C23112yes—
61C3×C4⋊Dic5C23112yes—
62C3×C4×Dic5C23112yes—
63#6668C23112yes—
64#6667C23112yes—
65#6667C23124yes—
66(C2×D3)⋊Dic5C2314yes—
67C22×#239—51no—
68C22×D3×Q8D511yescharacteristic, complemented
69C2×C3×C4×Q8—51no—
70#5576—516no—
71C2×#897—53no—
72C2×#895—53no—
73C2×#875—53no—
74C2×C4×D12—53no—
75C22×C5×Q8—38no—
76C22×C5×Q8—33no—
77C22×C5×Q8—68no—
78C22×C5×Q8C2×D311yescharacteristic
79C23×C4×C5—33no—
80C22×C22⋊D5—33no—
81C2×#713—38no—
82C2×#713—68no—
83C22×D20—33no—
84C22×C4×D5—33no—
85C2×C22⋊Dic5—31no—
86#4093—324no—
87#4092—324no—
88Q8×Dic5C2×D318yescomplemented
89#4076—324no—
90C4×C22⋊D5—324no—
91C2×#685—33no—
92C2×#685—36no—
93C2×C4⋊Dic5C2×D313yes—
94C2×#683—33no—
95C2×C4×Dic5C2×D313yes—
96C2×#548—151noSylow
97C23×C3×C5C2411yescharacteristic
98C22×D15—26no—
99C22×D15—26no—
100C22×D15—26no—
101C22×D15C2416yes—
102C22×C5×D3—22no—
103C22×C5×D3—22no—
104C22×C5×D3#4114yescomplemented
105C22×C5×D3C2412yes—
106C3×C5×Q8C2×D4116yescomplemented
107C2×C3×C4×C5C2×D4112yes—
108C2×C3×C4×C5C2416yes—
109C2×Dic15—22no—
110C2×Dic15C2412yes—
111D60—224no—
112C4×D15—224no—
113C2×C5×Dic3—26no—
114C2×C5×Dic3C2416yes—
115C4×C5×D3—224no—
116C5×Dic6—224no—
117C2×C3×Dic5—26no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5C2412yes—
120C2×C3×Dic5C2416yes—
121#1203—224no—
122C22×C3×Q8C2×D511yescharacteristic
123C2×#239—58no—
124C2×#239—108no—
125C2×D3×Q8—28no—
126C2×D3×Q8C2×D518yescomplemented
127C22×D12—53no—
128C22×D12—53no—
129C22×C4×D3—53no—
130C22×C4×D3C2×D513yes—
131C22×Dic6C2×D513yes—
132C3×C4×Q8—58no—
133C2×C3×C4⋊C4—53no—
134C2×C3×C42—53no—
135C2×(C2×D3)⋊C4—51no—
136C2×(C2×D3)⋊C4—53no—
137C2×(C2×D3)⋊C4—56no—
138C2×C4⋊Dic3—53no—
139#897—524no—
140#895—524no—
141#875—524no—
142C4×D12—524no—
143C24×C5—31no—
144C23×D5—33no—
145C2×C5×Q8—312no—
146C2×C5×Q8—632no—
147C2×C5×Q8—612no—
148C2×C5×Q8D1218yescomplemented
149C2×C5×Q8C22×D314yes—
150C22×C4×C5—33no—
151C22×C4×C5—312no—
152C22×C4×C5—612no—
153C22×C4×C5C22×D313yes—
154C2×C22⋊D5—312no—
155C2×C22⋊D5—612no—
156C22×Dic5—31no—
157C22×Dic5C22×D311yescharacteristic
158C22×Dic5C22×D313yes—
159#713—632no—
160C2×D20—312no—
161C2×D20—612no—
162C2×C4×D5—312no—
163C2×C4×D5—612no—
164C22⋊Dic5—34no—
165#685—312no—
166#685—324no—
167C4⋊Dic5C22×D3112yes—
168#683—312no—
169C4×Dic5C22×D3112yes—
170C22×#41—151no—
171C23×Q8—31no—
172#548—1516no—
173C2×#124—153no—
174C2×C22⋊Q8—153no—
175C2×#121—153no—
176C2×C4×Q8—51no—
177C2×C4×D4—153no—
178C22×C3×C5C22×D412yes—
179C22×C3×C5C2×#4112yes—
180C22×C3×C52−1+412yes—
181C22×C3×C5C2511yescharacteristic
182C2×D15—26no—
183C2×D15—26no—
184C2×D15—26no—
185C2×D15—412no—
186C2×C5×D3—28no—
187C2×C5×D3—22no—
188C2×C5×D3—22no—
189C2×C5×D3C2×#4114yescomplemented
190C3×C4×C5C22×D4112yes—
191Dic15—22no—
192C3×Dic5—26no—
193C3×Dic5—22no—
194C5×Dic3—26no—
195C23×D3—53no—
196C23×D3C22×D511yescharacteristic
197C2×C3×Q8C22⋊D518yescomplemented
198C2×C3×Q8C22×D514yes—
199C22×C3×C4—53no—
200C22×C3×C4—51no—
201C22×C3×C4C22×D513yes—
202C22×Dic3—51no—
203C22×Dic3C22×D513yes—
204#239—1032no—
205D3×Q8—232no—
206C2×D12—512no—
207C2×D12—512no—
208C2×D12—1012no—
209C2×D12—1012no—
210C2×C4×D3—212no—
211C2×C4×D3—512no—
212C2×C4×D3—1012no—
213C2×C4×D3C22×D5112yes—
214C2×Dic6—212no—
215C2×Dic6C22×D5112yes—
216C3×C4⋊C4—512no—
217C3×C42—512no—
218(C2×D3)⋊C4—54no—
219(C2×D3)⋊C4—512no—
220(C2×D3)⋊C4—524no—
221C4⋊Dic3—512no—
222C23×C5—34no—
223C23×C5—32no—
224C23×C5—62no—
225C23×C5—62no—
226C23×C5C23×D311yescharacteristic
227C22×D5—36no—
228C22×D5—66no—
229C22×D5—66no—
230C22×D5—66no—
231C5×Q8—624no—
232C5×Q8C2×D12116yescomplemented
233C2×C4×C5—36no—
234C2×C4×C5—66no—
235C2×C4×C5—624no—
236C2×C4×C5C2×D12112yes—
237C2×C4×C5C23×D316yes—
238C22⋊D5—624no—
239C2×Dic5—22no—
240C2×Dic5—26no—
241C2×Dic5—32no—
242C2×Dic5—62no—
243C2×Dic5C23×D312yes—
244C2×Dic5C23×D316yes—
245D20—624no—
246C4×D5—624no—
247C2×#41—158no—
248C2×#41—308no—
249C22×Q8—38no—
250C22×Q8—33no—
251C22×Q8—68no—
252C22×Q8D3×D511yescharacteristic
253C22×D4—153no—
254C22×D4—153no—
255C23×C4—33no—
256C23×C4—153no—
257#124—1524no—
258C22⋊Q8—1524no—
259#121—1524no—
260C4×Q8—58no—
261C4×D4—1524no—
262C2×C4⋊C4—53no—
263C2×C4⋊C4—153no—
264C2×C22⋊C4—153no—
265C2×C22⋊C4—156no—
266C2×C22⋊C4—151no—
267C2×C42—53no—
268C2×C3×C5#54814yescomplemented
269C2×C3×C5C23×D411yescharacteristic
270C2×C3×C5C22×#4111yescharacteristic
271C2×C3×C5C2×2−1+411yescharacteristic
272D15—46no—
273C5×D3—24no—
274C23×C3C23×D511yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—56no—
278C22×D3—106no—
279C22×D3—106no—
280C22×D3—106no—
281C22×D3#71314yescomplemented
282C22×D3C23×D512yes—
283C3×Q8C2×C22⋊D5116yescomplemented
284C2×C3×C4—56no—
285C2×C3×C4—52no—
286C2×C3×C4—106no—
287C2×C3×C4—102no—
288C2×C3×C4C2×C22⋊D5112yes—
289C2×C3×C4C23×D516yes—
290C2×Dic3—26no—
291C2×Dic3—52no—
292C2×Dic3—102no—
293C2×Dic3C23×D516yes—
294D12—1024no—
295D12—1024no—
296C4×D3—224no—
297C4×D3—1024no—
298Dic6—224no—
299C22×C5—34no—
300C22×C5—62no—
301C22×C5—62no—
302C22×C5—68no—
303C22×C5C22×D1212yes—
304C22×C5#100712yes—
305C22×C5D3×#4112yes—
306C22×C5C24×D311yescharacteristic
307C2×D5—66no—
308C2×D5—66no—
309C2×D5—66no—
310C2×D5—1212no—
311C4×C5—66no—
312C4×C5C22×D12112yes—
313Dic5—22no—
314Dic5—26no—
315Dic5—62no—
316C24—31no—
317C24—153no—
318#41—3032no—
319C2×Q8—312no—
320C2×Q8—632no—
321C2×Q8—612no—
322C2×Q8#120318yescomplemented
323C2×Q8C2×D3×D514yes—
324C2×D4—1512no—
325C2×D4—1512no—
326C2×D4—3012no—
327C2×D4—3012no—
328C22×C4—33no—
329C22×C4—312no—
330C22×C4—51no—
331C22×C4—53no—
332C22×C4—612no—
333C22×C4—151no—
334C22×C4—1512no—
335C22×C4—3012no—
336C22×C4C2×D3×D513yes—
337C4⋊C4—512no—
338C4⋊C4—1512no—
339C22⋊C4—1512no—
340C22⋊C4—1524no—
341C22⋊C4—154no—
342C42—512no—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3C2×#71312yes—
345C22×C3#414712yes—
346C22×C3C22×C22⋊D512yes—
347C22×C3C24×D511yescharacteristic
348C2×D3—28no—
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—106no—
352C2×D3—106no—
353C2×D3—106no—
354C2×D3—2012no—
355C2×D3C2×#71314yescomplemented
356C3×C4—106no—
357C3×C4—102no—
358C3×C4C22×C22⋊D5112yes—
359Dic3—26no—
360Dic3—102no—
361C2×C5—64no—
362C2×C5#557614yescomplemented
363C2×C5C23×D1211yescharacteristic
364C2×C5C2×#100711yescharacteristic
365C2×C5C2×D3×#4111yescharacteristic
366D5—126no—
367C23—34no—
368C23—32no—
369C23—62no—
370C23—62no—
371C23—156no—
372C23—306no—
373C23—306no—
374C23—306no—
375C23C22×D3×D511yescharacteristic
376Q8—624no—
377Q8C2×#1203116yescomplemented
378D4—3024no—
379D4—3024no—
380C2×C4—36no—
381C2×C4—52no—
382C2×C4—56no—
383C2×C4—66no—
384C2×C4—624no—
385C2×C4—102no—
386C2×C4—106no—
387C2×C4—152no—
388C2×C4—302no—
389C2×C4—3024no—
390C2×C4C2×#1203112yes—
391C2×C4C22×D3×D516yes—
392C2×C3#6615114yescomplemented
393C2×C3C22×#71311yescharacteristic
394C2×C3C2×#414711yescharacteristic
395C2×C3C23×C22⋊D511yescharacteristic
396D3—24no—
397D3—206no—
398C5C2×#557611yescharacteristic, complemented, Sylow
399C22—34no—
400C22—62no—
401C22—68no—
402C22—62no—
403C22—306no—
404C22—306no—
405C22—306no—
406C22—6012no—
407C22#9202912yes—
408C22D3×#71312yes—
409C22C22×#120312yes—
410C22C23×D3×D511yescharacteristic
411C4—66no—
412C4—102no—
413C4—106no—
414C4—302no—
415C4C22×#1203112yes—
416C3C2×#6615111yescharacteristic, complemented, Sylow
417C2—64no—
418C2—606no—
419C2#1175513114yesdirect product factor
420C2C2×#9202911yescharacteristic
421C2C2×D3×#71311yescharacteristic
422C2C23×#120311yescharacteristic
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×#6821C2semidirect
2. C22×C5×D3×Q8C2semidirect
3. C2×C3×Q8×Dic5C2semidirect
4. #11755131C2direct (N × H)
5. C2×#91460C2semidirect
6. C2×C4×#1203C2semidirect
7. C2×#91383C2semidirect
8. C2×#91375C2semidirect
12. C2×#6821C22semidirect
16. C2×C5×D3×Q8C22semidirect
20. C3×Q8×Dic5C22semidirect
27. #91460C22semidirect
28. C4×#1203C22semidirect
29. #91383C22semidirect
30. #91375C22semidirect
37. C2×Q8×Dic5D3semidirect
42. C2×C3×C5×Q8D4semidirect
68. C22×D3×Q8D5semidirect
88. Q8×Dic5C2×D3semidirect
104. C22×C5×D3#41semidirect
106. C3×C5×Q8C2×D4semidirect
126. C2×D3×Q8C2×D5semidirect
148. C2×C5×Q8D12semidirect
189. C2×C5×D3C2×#41semidirect
197. C2×C3×Q8C22⋊D5semidirect
232. C5×Q8C2×D12semidirect
268. C2×C3×C5#548semidirect
281. C22×D3#713semidirect
283. C3×Q8C2×C22⋊D5semidirect
322. C2×Q8#1203semidirect
343. C3×C5C2×#548semidirect
355. C2×D3C2×#713semidirect
362. C2×C5#5576semidirect
377. Q8C2×#1203semidirect
392. C2×C3#66151semidirect
398. C5C2×#5576semidirect
416. C3C2×#66151semidirect
419. C2#11755131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×C5×D3×Q82
C2×C3×Q8×Dic52
#117551312
C2×#914602
C2×C4×#12032
C2×#913832
C2×#913752
C2×#661513
C2×#55765