Finite Group Databasebeta

← C2×#11755245 #14483022

Subgroups — C2×#11755245 #14483022

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6821C211yesmaximal, characteristic, complemented
2C22×C5×#239C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4#11755245C2116yesmaximal, direct product factor
5C2×#91466C213yesmaximal, complemented
6C2×#91460C213yesmaximal, complemented
7C2×#91451C213yesmaximal, complemented
8C2×C4×#1203C213yesmaximal, complemented
9C2×#66168—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—28no—
12C2×#6821C2218yescomplemented
13C22×D60C2213yes—
14C22×C4×D15C2213yes—
15C2×C5×#239—28no—
16C2×C5×#239C2218yescomplemented
17C22×C5×D12C2213yes—
18C22×C4×C5×D3C2213yes—
19C22×#1203C2213yes—
20C22×#1203C2216yes—
21C3×Q8×Dic5C2218yescomplemented
22C2×C3×C4⋊Dic5C2213yes—
23C2×C3×C4×Dic5C2213yes—
24C2×#6668C2211yescharacteristic
25C2×#6667C2213yes—
26C2×(C2×D3)⋊Dic5C2213yes—
27#91466C22124yescomplemented
28#91460C22124yescomplemented
29#91451C22124yescomplemented
30C4×#1203C22124yescomplemented
31C2×#5577—51nomaximal, Hall
32C22×C5×#41—31no—
33C22×#713—31no—
34#66168—316no—
35C2×Q8×Dic5D311yescharacteristic, complemented
36C2×#4086—33no—
37C2×#4084—33no—
38C2×#4076—33no—
39C2×C4×C22⋊D5—33no—
40C23×D15C2313yes—
41C23×C5×D3C2313yes—
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×Dic3C2311yescharacteristic
52C5×#239—232no—
53C2×C5×D12—212no—
54C2×C5×D12C23112yes—
55C2×C4×C5×D3—212no—
56C2×C4×C5×D3C23112yes—
57C22×C3×Dic5C2313yes—
58C22×C3×Dic5C2311yescharacteristic
59C2×#1203—212no—
60C2×#1203—412no—
61C2×#1203C23112yes—
62C2×#1203C23124yes—
63C3×C4⋊Dic5C23112yes—
64C3×C4×Dic5C23112yes—
65#6668C2314yes—
66#6667C23112yes—
67(C2×D3)⋊Dic5C23112yes—
68C22×#239—51no—
69C22×#239D511yescharacteristic, complemented
70C2×C3×C4×Q8—51no—
71#5577—516no—
72C2×#895—53no—
73C2×#895—53no—
74C2×#874—53no—
75C2×C4×D12—53no—
76C2×C5×#41—38no—
77C2×C5×#41—68no—
78C22×C5×Q8C2×D311yescharacteristic
79C22×C5×D4—33no—
80C23×C4×C5—33no—
81C22×C22⋊D5—33no—
82C22×C22⋊D5—36no—
83C2×#713—38no—
84C2×#713—68no—
85C22×D20—33no—
86C22×C4×D5—33no—
87C2×C22⋊Dic5—33no—
88Q8×Dic5C2×D318yescomplemented
89#4086—324no—
90#4084—324no—
91#4076—324no—
92C4×C22⋊D5—324no—
93C2×#685—33no—
94C2×C4⋊Dic5C2×D313yes—
95C2×#683—31no—
96C2×C4×Dic5C2×D313yes—
97C2×#550—151noSylow
98C23×C3×C5C2411yescharacteristic
99C22×D15—26no—
100C22×D15—26no—
101C22×D15—26no—
102C22×D15C2416yes—
103C22×C5×D3—26no—
104C22×C5×D3—26no—
105C22×C5×D3—26no—
106C22×C5×D3C2416yes—
107C3×C5×Q8C2×D4116yescomplemented
108C2×C3×C4×C5C2×D4112yes—
109C2×C3×C4×C5C2416yes—
110C2×Dic15—22no—
111C2×Dic15C2412yes—
112D60—224no—
113C4×D15—224no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3C2412yes—
116C5×D12—224no—
117C4×C5×D3—224no—
118C2×C3×Dic5—26no—
119C2×C3×Dic5#4114yescomplemented
120C2×C3×Dic5C2416yes—
121C2×C3×Dic5C2412yes—
122#1203—224no—
123#1203—424no—
124C22×C3×Q8C2×D511yescharacteristic
125C2×#239—28no—
126C2×#239—58no—
127C2×#239—108no—
128C2×#239C2×D518yescomplemented
129C22×D12—53no—
130C22×D12—53no—
131C22×D12—56no—
132C22×D12C2×D513yes—
133C22×C4×D3—53no—
134C22×C4×D3C2×D513yes—
135C3×C4×Q8—58no—
136C2×C3×C4⋊C4—53no—
137C2×C3×C42—53no—
138C2×(C2×D3)⋊C4—53no—
139C2×(C2×D3)⋊C4—53no—
140C2×C4⋊Dic3—51no—
141#895—524no—
142#895—524no—
143#874—524no—
144C4×D12—524no—
145C24×C5—33no—
146C23×D5—33no—
147C5×#41—632no—
148C2×C5×Q8D1218yescomplemented
149C2×C5×Q8C22×D314yes—
150C2×C5×D4—312no—
151C2×C5×D4—612no—
152C22×C4×C5—31no—
153C22×C4×C5—312no—
154C22×C4×C5—612no—
155C22×C4×C5C22×D313yes—
156C2×C22⋊D5—312no—
157C2×C22⋊D5—324no—
158C2×C22⋊D5—612no—
159C2×C22⋊D5—1212no—
160C22×Dic5—31no—
161C22×Dic5C22×D313yes—
162C22×Dic5C22×D311yescharacteristic
163#713—632no—
164C2×D20—312no—
165C2×D20—612no—
166C2×C4×D5—312no—
167C2×C4×D5—612no—
168C22⋊Dic5—312no—
169#685—312no—
170C4⋊Dic5C22×D3112yes—
171#683—34no—
172C4×Dic5C22×D3112yes—
173C22×#41—31no—
174C22×#41—151no—
175#550—1516no—
176C2×#127—153no—
177C2×#121—153no—
178C2×#121—153no—
179C2×C4×Q8—51no—
180C2×C4×D4—153no—
181C22×C3×C5C22×D412yes—
182C22×C3×C5C2×#4112yes—
183C22×C3×C5H(5,𝔽2)12yes—
184C22×C3×C5C2511yescharacteristic
185C2×D15—26no—
186C2×D15—26no—
187C2×D15—26no—
188C2×D15—412no—
189C2×C5×D3—26no—
190C2×C5×D3—26no—
191C2×C5×D3—26no—
192C2×C5×D3—412no—
193C3×C4×C5C22×D4112yes—
194Dic15—22no—
195C3×Dic5—26no—
196C3×Dic5C2×#4114yescomplemented
197C5×Dic3—22no—
198C23×D3—53no—
199C23×D3C22×D513yes—
200C2×C3×Q8C22⋊D518yescomplemented
201C2×C3×Q8C22×D514yes—
202C22×C3×C4—51no—
203C22×C3×C4—53no—
204C22×C3×C4C22×D513yes—
205C22×Dic3—51no—
206C22×Dic3C22×D511yescharacteristic
207#239—232no—
208#239—1032no—
209C2×D12—212no—
210C2×D12—512no—
211C2×D12—512no—
212C2×D12—524no—
213C2×D12—1012no—
214C2×D12—1012no—
215C2×D12—2012no—
216C2×D12C22×D5112yes—
217C2×C4×D3—212no—
218C2×C4×D3—512no—
219C2×C4×D3—1012no—
220C2×C4×D3C22×D5112yes—
221C3×C4⋊C4—512no—
222C3×C42—512no—
223(C2×D3)⋊C4—512no—
224(C2×D3)⋊C4—512no—
225C4⋊Dic3—54no—
226C23×C5—36no—
227C23×C5—66no—
228C23×C5—66no—
229C23×C5—66no—
230C23×C5C23×D311yescharacteristic
231C22×D5—36no—
232C22×D5—66no—
233C22×D5—66no—
234C22×D5—66no—
235C5×Q8C2×D12116yescomplemented
236C5×D4—624no—
237C2×C4×C5—32no—
238C2×C4×C5—62no—
239C2×C4×C5—624no—
240C2×C4×C5C2×D12112yes—
241C2×C4×C5C23×D316yes—
242C22⋊D5—624no—
243C22⋊D5—1224no—
244C2×Dic5—26no—
245C2×Dic5—32no—
246C2×Dic5—62no—
247C2×Dic5#23914yescomplemented
248C2×Dic5C23×D316yes—
249C2×Dic5C23×D312yes—
250D20—624no—
251C4×D5—624no—
252C2×#41—38no—
253C2×#41—68no—
254C2×#41—158no—
255C2×#41—308no—
256C22×Q8D3×D511yescharacteristic
257C22×D4—33no—
258C22×D4—153no—
259C22×D4—156no—
260C22×D4—153no—
261C23×C4—33no—
262C23×C4—153no—
263#127—1524no—
264#121—1524no—
265#121—1524no—
266C4×Q8—58no—
267C4×D4—1524no—
268C2×C4⋊C4—53no—
269C2×C4⋊C4—151no—
270C2×C22⋊C4—153no—
271C2×C22⋊C4—153no—
272C2×C42—53no—
273C2×C3×C5#55014yescomplemented
274C2×C3×C5C23×D411yescharacteristic
275C2×C3×C5C22×#4111yescharacteristic
276C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
277D15—46no—
278C5×D3—46no—
279C23×C3C23×D511yescharacteristic
280C22×D3—26no—
281C22×D3—26no—
282C22×D3—26no—
283C22×D3—56no—
284C22×D3—106no—
285C22×D3—106no—
286C22×D3—106no—
287C22×D3C23×D516yes—
288C3×Q8C2×C22⋊D5116yescomplemented
289C2×C3×C4—54no—
290C2×C3×C4—52no—
291C2×C3×C4—56no—
292C2×C3×C4—106no—
293C2×C3×C4C2×C22⋊D5112yes—
294C2×C3×C4C23×D516yes—
295C2×Dic3—22no—
296C2×Dic3—52no—
297C2×Dic3—102no—
298C2×Dic3C23×D512yes—
299D12—224no—
300D12—1024no—
301D12—1024no—
302D12—2024no—
303C4×D3—224no—
304C4×D3—1024no—
305C22×C5—66no—
306C22×C5—66no—
307C22×C5—66no—
308C22×C5—1212no—
309C22×C5C22×D1212yes—
310C22×C5C2×#23912yes—
311C22×C5#100912yes—
312C22×C5C24×D311yescharacteristic
313C2×D5—66no—
314C2×D5—66no—
315C2×D5—66no—
316C2×D5—1212no—
317C4×C5—62no—
318C4×C5C22×D12112yes—
319Dic5—26no—
320Dic5—62no—
321Dic5C2×#23914yescomplemented
322C24—33no—
323C24—153no—
324#41—632no—
325#41—3032no—
326C2×Q8#120318yescomplemented
327C2×Q8C2×D3×D514yes—
328C2×D4—312no—
329C2×D4—612no—
330C2×D4—1512no—
331C2×D4—1524no—
332C2×D4—1512no—
333C2×D4—3012no—
334C2×D4—3012no—
335C2×D4—6012no—
336C22×C4—31no—
337C22×C4—312no—
338C22×C4—51no—
339C22×C4—53no—
340C22×C4—612no—
341C22×C4—151no—
342C22×C4—1512no—
343C22×C4—3012no—
344C22×C4C2×D3×D513yes—
345C4⋊C4—512no—
346C4⋊C4—154no—
347C22⋊C4—1512no—
348C22⋊C4—1512no—
349C42—512no—
350C3×C5C2×#55011yescharacteristic, complemented, Hall
351C22×C3D5×#4112yes—
352C22×C3#414912yes—
353C22×C3C22×C22⋊D512yes—
354C22×C3C24×D511yescharacteristic
355C2×D3—26no—
356C2×D3—26no—
357C2×D3—26no—
358C2×D3—412no—
359C2×D3—106no—
360C2×D3—106no—
361C2×D3—106no—
362C2×D3—2012no—
363C3×C4—54no—
364C3×C4—106no—
365C3×C4C22×C22⋊D5112yes—
366Dic3—22no—
367Dic3—102no—
368C2×C5—126no—
369C2×C5#557714yescomplemented
370C2×C5C23×D1211yescharacteristic
371C2×C5C22×#23911yescharacteristic
372C2×C5C2×#100911yescharacteristic
373D5—126no—
374C23—36no—
375C23—66no—
376C23—66no—
377C23—66no—
378C23—156no—
379C23—306no—
380C23—306no—
381C23—306no—
382C23C22×D3×D511yescharacteristic
383Q8C2×#1203116yescomplemented
384D4—624no—
385D4—3024no—
386D4—3024no—
387D4—6024no—
388C2×C4—32no—
389C2×C4—54no—
390C2×C4—52no—
391C2×C4—56no—
392C2×C4—62no—
393C2×C4—624no—
394C2×C4—106no—
395C2×C4—152no—
396C2×C4—302no—
397C2×C4—3024no—
398C2×C4C2×#1203112yes—
399C2×C4C22×D3×D516yes—
400C2×C3#6616814yescomplemented
401C2×C3C2×D5×#4111yescharacteristic
402C2×C3C2×#414911yescharacteristic
403C2×C3C23×C22⋊D511yescharacteristic
404D3—46no—
405D3—206no—
406C5C2×#557711yescharacteristic, complemented, Sylow
407C22—66no—
408C22—66no—
409C22—66no—
410C22—1212no—
411C22—306no—
412C22—306no—
413C22—306no—
414C22—6012no—
415C22D5×#23912yes—
416C22#9203512yes—
417C22C22×#120312yes—
418C22C23×D3×D511yescharacteristic
419C4—54no—
420C4—62no—
421C4—106no—
422C4—302no—
423C4C22×#1203112yes—
424C3C2×#6616811yescharacteristic, complemented, Sylow
425C2—126no—
426C2—606no—
427C2#1175524514yesdirect product factor
428C2C2×D5×#23911yescharacteristic
429C2C2×#9203511yescharacteristic
430C2C23×#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×#550
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×#239C2semidirect
3. C2×C3×Q8×Dic5C2semidirect
4. #11755245C2direct (N × H)
5. C2×#91466C2semidirect
6. C2×#91460C2semidirect
7. C2×#91451C2semidirect
8. C2×C4×#1203C2semidirect
12. C2×#6821C22semidirect
16. C2×C5×#239C22semidirect
21. C3×Q8×Dic5C22semidirect
27. #91466C22semidirect
28. #91460C22semidirect
29. #91451C22semidirect
30. C4×#1203C22semidirect
35. C2×Q8×Dic5D3semidirect
42. C2×C3×C5×Q8D4semidirect
69. C22×#239D5semidirect
88. Q8×Dic5C2×D3semidirect
107. C3×C5×Q8C2×D4semidirect
119. C2×C3×Dic5#41semidirect
128. C2×#239C2×D5semidirect
148. C2×C5×Q8D12semidirect
196. C3×Dic5C2×#41semidirect
200. C2×C3×Q8C22⋊D5semidirect
235. C5×Q8C2×D12semidirect
247. C2×Dic5#239semidirect
273. C2×C3×C5#550semidirect
288. C3×Q8C2×C22⋊D5semidirect
321. Dic5C2×#239semidirect
326. C2×Q8#1203semidirect
350. C3×C5C2×#550semidirect
369. C2×C5#5577semidirect
383. Q8C2×#1203semidirect
400. C2×C3#66168semidirect
406. C5C2×#5577semidirect
424. C3C2×#66168semidirect
427. C2#11755245direct (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×#2392
C2×C3×Q8×Dic52
#117552452
C2×#914662
C2×#914602
C2×#914512
C2×C4×#12032
C2×#661683
C2×#55775