Finite Group Databasebeta

← C2×#11755254 #14483021

Subgroups — C2×#11755254 #14483021

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×C5×#239C211yesmaximal, characteristic, complemented
2C22×C3×#713C211yesmaximal, characteristic, complemented
3C2×Q8×Dic15C211yesmaximal, characteristic, complemented
4#11755254C2116yesmaximal, direct product factor
5C2×#91463C213yesmaximal, complemented
6C2×#91456C213yesmaximal, complemented
7C2×#91449C213yesmaximal, complemented
8C2×C4×#1201C213yesmaximal, complemented
9C2×#66168—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C5×#239—28no—
12C2×C5×#239C2218yescomplemented
13C22×C5×D12C2213yes—
14C22×C4×C5×D3C2213yes—
15C2×C3×#713—28no—
16C2×C3×#713C2218yescomplemented
17C22×C3×D20C2213yes—
18C22×C3×C4×D5C2213yes—
19C22×#1201C2213yes—
20C22×#1201C2216yes—
21Q8×Dic15C2218yescomplemented
22C2×C4⋊Dic15C2213yes—
23C2×C4×Dic15C2213yes—
24C2×#6669C2211yescharacteristic
25C2×(C2×D3)⋊Dic5C2213yes—
26C2×#6665C2213yes—
27#91463C22124yescomplemented
28#91456C22124yescomplemented
29#91449C22124yescomplemented
30C4×#1201C22124yescomplemented
31C2×#5834—51nomaximal, Hall
32C22×C5×#41—31no—
33C22×#713D311yescharacteristic, complemented
34#66168—316no—
35C2×Q8×Dic5—31no—
36C2×#4086—33no—
37C2×#4084—33no—
38C2×#4076—33no—
39C2×C4×C22⋊D5—33no—
40C23×C5×D3C2313yes—
41C23×C3×D5C2313yes—
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×Dic5C2311yescharacteristic
54C3×#713—232no—
55C2×C3×D20—212no—
56C2×C3×D20C23112yes—
57C2×C3×C4×D5—212no—
58C2×C3×C4×D5C23112yes—
59C2×#1201—212no—
60C2×#1201—412no—
61C2×#1201C23112yes—
62C2×#1201C23124yes—
63C4⋊Dic15C23112yes—
64C4×Dic15C23112yes—
65#6669C2314yes—
66(C2×D3)⋊Dic5C23112yes—
67#6665C23112yes—
68C22×C3×#41—51no—
69C22×#239D511yescharacteristic, complemented
70#5834—516no—
71C2×Q8×Dic3—51no—
72C2×#940—53no—
73C2×#938—53no—
74C2×#930—53no—
75C2×C4×#67—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—28no—
84C2×#713C2×D318yescomplemented
85C22×D20C2×D313yes—
86C22×C4×D5C2×D313yes—
87C2×C22⋊Dic5—33no—
88Q8×Dic5—38no—
89#4086—324no—
90#4084—324no—
91#4076—324no—
92C4×C22⋊D5—324no—
93C2×#685—33no—
94C2×C4⋊Dic5—33no—
95C2×#683—31no—
96C2×C4×Dic5—33no—
97C2×#550—151noSylow
98C23×C3×C5C2411yescharacteristic
99C22×C5×D3—26no—
100C22×C5×D3—26no—
101C22×C5×D3—26no—
102C22×C5×D3C2416yes—
103C22×C3×D5—26no—
104C22×C3×D5—26no—
105C22×C3×D5—26no—
106C22×C3×D5C2416yes—
107C3×C5×Q8C2×D4116yescomplemented
108C2×C3×C4×C5C2×D4112yes—
109C2×C3×C4×C5C2416yes—
110C2×Dic15—26no—
111C2×Dic15#4114yescomplemented
112C2×Dic15C2416yes—
113C2×Dic15C2412yes—
114C2×C5×Dic3—22no—
115C2×C5×Dic3C2412yes—
116C5×D12—224no—
117C4×C5×D3—224no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5C2412yes—
120C3×D20—224no—
121C3×C4×D5—224no—
122#1201—224no—
123#1201—424no—
124C2×C3×#41—58no—
125C2×C3×#41—108no—
126C22×C3×Q8C2×D511yescharacteristic
127C22×C3×D4—53no—
128C23×C3×C4—53no—
129C22×#67—53no—
130C22×#67—56no—
131C2×#239—28no—
132C2×#239C2×D518yescomplemented
133C22×D12C2×D513yes—
134C22×C4×D3C2×D513yes—
135C2×#217—53no—
136Q8×Dic3—58no—
137#940—524no—
138#938—524no—
139#930—524no—
140C4×#67—524no—
141C2×(C2×D3)⋊C4—53no—
142C2×C4⋊Dic3—53no—
143C2×Dic3⋊C4—51no—
144C2×C4×Dic3—53no—
145C24×C5—33no—
146C23×D5C22×D313yes—
147C5×#41—632no—
148C2×C5×Q8#6718yescomplemented
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×Dic5—33no—
162C22×Dic5C22×D311yescharacteristic
163#713—232no—
164C2×D20—212no—
165C2×D20C22×D3112yes—
166C2×C4×D5—212no—
167C2×C4×D5C22×D3112yes—
168C22⋊Dic5—312no—
169#685—312no—
170C4⋊Dic5—312no—
171#683—34no—
172C4×Dic5—312no—
173C22×#41—31no—
174C22×#41—51no—
175#550—1516no—
176C2×#127—153no—
177C2×#121—153no—
178C2×#121—153no—
179C2×C4×Q8—151no—
180C2×C4×D4—153no—
181C22×C3×C5C22×D412yes—
182C22×C3×C5C2×#4112yes—
183C22×C3×C5H(5,𝔽2)12yes—
184C22×C3×C5C2511yescharacteristic
185C2×C5×D3—26no—
186C2×C5×D3—26no—
187C2×C5×D3—26no—
188C2×C5×D3—412no—
189C2×C3×D5—26no—
190C2×C3×D5—26no—
191C2×C3×D5—26no—
192C2×C3×D5—412no—
193C3×C4×C5C22×D4112yes—
194Dic15—26no—
195Dic15C2×#4114yescomplemented
196C3×Dic5—22no—
197C5×Dic3—22no—
198C24×C3—53no—
199C23×D3C22×D513yes—
200C3×#41—1032no—
201C2×C3×Q8C22⋊D518yescomplemented
202C2×C3×Q8C22×D514yes—
203C2×C3×D4—512no—
204C2×C3×D4—1012no—
205C22×C3×C4—51no—
206C22×C3×C4—512no—
207C22×C3×C4—1012no—
208C22×C3×C4C22×D513yes—
209C2×#67—512no—
210C2×#67—524no—
211C2×#67—1012no—
212C2×#67—2012no—
213C22×Dic3—51no—
214C22×Dic3—53no—
215C22×Dic3C22×D511yescharacteristic
216#239—232no—
217C2×D12—212no—
218C2×D12C22×D5112yes—
219C2×C4×D3—212no—
220C2×C4×D3C22×D5112yes—
221#217—512no—
222(C2×D3)⋊C4—512no—
223C4⋊Dic3—512no—
224Dic3⋊C4—54no—
225C4×Dic3—512no—
226C23×C5—36no—
227C23×C5—66no—
228C23×C5—66no—
229C23×C5—66no—
230C23×C5C23×D311yescharacteristic
231C22×D5—26no—
232C22×D5—26no—
233C22×D5—26no—
234C22×D5C23×D316yes—
235C5×Q8C2×#67116yescomplemented
236C5×D4—624no—
237C2×C4×C5—32no—
238C2×C4×C5—62no—
239C2×C4×C5—624no—
240C2×C4×C5C2×#67112yes—
241C2×C4×C5C23×D316yes—
242C22⋊D5—624no—
243C22⋊D5—1224no—
244C2×Dic5—22no—
245C2×Dic5—34no—
246C2×Dic5—32no—
247C2×Dic5—36no—
248C2×Dic5—66no—
249C2×Dic5C23×D312yes—
250D20—224no—
251C4×D5—224no—
252C2×#41—38no—
253C2×#41—58no—
254C2×#41—68no—
255C2×#41—108no—
256C22×Q8D3×D511yescharacteristic
257C22×D4—33no—
258C22×D4—53no—
259C22×D4—153no—
260C22×D4—156no—
261C23×C4—33no—
262C23×C4—53no—
263#127—1524no—
264#121—1524no—
265#121—1524no—
266C4×Q8—158no—
267C4×D4—1524no—
268C2×C4⋊C4—151no—
269C2×C4⋊C4—153no—
270C2×C22⋊C4—153no—
271C2×C22⋊C4—153no—
272C2×C42—153no—
273C2×C3×C5#55014yescomplemented
274C2×C3×C5C23×D411yescharacteristic
275C2×C3×C5C22×#4111yescharacteristic
276C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
277C3×D5—46no—
278C5×D3—46no—
279C23×C3—56no—
280C23×C3—106no—
281C23×C3—106no—
282C23×C3—106no—
283C23×C3C23×D511yescharacteristic
284C22×D3—26no—
285C22×D3—26no—
286C22×D3—26no—
287C22×D3C23×D516yes—
288C3×Q8C2×C22⋊D5116yescomplemented
289C3×D4—1024no—
290C2×C3×C4—52no—
291C2×C3×C4—102no—
292C2×C3×C4—1024no—
293C2×C3×C4C2×C22⋊D5112yes—
294C2×C3×C4C23×D516yes—
295#67—1024no—
296#67—2024no—
297C2×Dic3—22no—
298C2×Dic3—54no—
299C2×Dic3—52no—
300C2×Dic3—56no—
301C2×Dic3—106no—
302C2×Dic3C23×D512yes—
303D12—224no—
304C4×D3—224no—
305C22×C5—66no—
306C22×C5—66no—
307C22×C5—66no—
308C22×C5—1212no—
309C22×C5D3×#4112yes—
310C22×C5#100912yes—
311C22×C5C22×#6712yes—
312C22×C5C24×D311yescharacteristic
313C2×D5—26no—
314C2×D5—26no—
315C2×D5—26no—
316C2×D5—412no—
317C4×C5—62no—
318C4×C5C22×#67112yes—
319Dic5—22no—
320Dic5—34no—
321Dic5—66no—
322C24—33no—
323C24—53no—
324#41—632no—
325#41—1032no—
326C2×Q8#120118yescomplemented
327C2×Q8C2×D3×D514yes—
328C2×D4—312no—
329C2×D4—512no—
330C2×D4—612no—
331C2×D4—1012no—
332C2×D4—1512no—
333C2×D4—1524no—
334C2×D4—3012no—
335C2×D4—6012no—
336C22×C4—31no—
337C22×C4—312no—
338C22×C4—51no—
339C22×C4—512no—
340C22×C4—612no—
341C22×C4—1012no—
342C22×C4—151no—
343C22×C4—153no—
344C22×C4C2×D3×D513yes—
345C4⋊C4—154no—
346C4⋊C4—1512no—
347C22⋊C4—1512no—
348C22⋊C4—1512no—
349C42—1512no—
350C3×C5C2×#55011yescharacteristic, complemented, Hall
351C22×C3—106no—
352C22×C3—106no—
353C22×C3—106no—
354C22×C3—2012no—
355C22×C3D5×#4112yes—
356C22×C3#414912yes—
357C22×C3C22×C22⋊D512yes—
358C22×C3C24×D511yescharacteristic
359C2×D3—26no—
360C2×D3—26no—
361C2×D3—26no—
362C2×D3—412no—
363C3×C4—102no—
364C3×C4C22×C22⋊D5112yes—
365Dic3—22no—
366Dic3—54no—
367Dic3—106no—
368C2×C5—126no—
369C2×C5#583414yescomplemented
370C2×C5C2×D3×#4111yescharacteristic
371C2×C5C2×#100911yescharacteristic
372C2×C5C23×#6711yescharacteristic
373D5—46no—
374C23—36no—
375C23—56no—
376C23—66no—
377C23—66no—
378C23—66no—
379C23—106no—
380C23—106no—
381C23—106no—
382C23C22×D3×D511yescharacteristic
383Q8C2×#1201116yescomplemented
384D4—624no—
385D4—1024no—
386D4—3024no—
387D4—6024no—
388C2×C4—32no—
389C2×C4—52no—
390C2×C4—62no—
391C2×C4—624no—
392C2×C4—102no—
393C2×C4—1024no—
394C2×C4—154no—
395C2×C4—152no—
396C2×C4—156no—
397C2×C4—306no—
398C2×C4C2×#1201112yes—
399C2×C4C22×D3×D516yes—
400C2×C3—206no—
401C2×C3#6616814yescomplemented
402C2×C3C2×D5×#4111yescharacteristic
403C2×C3C2×#414911yescharacteristic
404C2×C3C23×C22⋊D511yescharacteristic
405D3—46no—
406C5C2×#583411yescharacteristic, complemented, Sylow
407C22—66no—
408C22—66no—
409C22—66no—
410C22—106no—
411C22—106no—
412C22—106no—
413C22—1212no—
414C22—2012no—
415C22#9203412yes—
416C22#9203512yes—
417C22C22×#120112yes—
418C22C23×D3×D511yescharacteristic
419C4—62no—
420C4—102no—
421C4—154no—
422C4—306no—
423C4C22×#1201112yes—
424C3C2×#6616811yescharacteristic, complemented, Sylow
425C2—126no—
426C2—206no—
427C2#1175525414yesdirect product factor
428C2C2×#9203411yescharacteristic
429C2C2×#9203511yescharacteristic
430C2C23×#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×#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×C5×#239C2semidirect
2. C22×C3×#713C2semidirect
3. C2×Q8×Dic15C2semidirect
4. #11755254C2direct (N × H)
5. C2×#91463C2semidirect
6. C2×#91456C2semidirect
7. C2×#91449C2semidirect
8. C2×C4×#1201C2semidirect
12. C2×C5×#239C22semidirect
16. C2×C3×#713C22semidirect
21. Q8×Dic15C22semidirect
27. #91463C22semidirect
28. #91456C22semidirect
29. #91449C22semidirect
30. C4×#1201C22semidirect
33. C22×#713D3semidirect
42. C2×C3×C5×Q8D4semidirect
69. C22×#239D5semidirect
84. C2×#713C2×D3semidirect
107. C3×C5×Q8C2×D4semidirect
111. C2×Dic15#41semidirect
132. C2×#239C2×D5semidirect
148. C2×C5×Q8#67semidirect
195. Dic15C2×#41semidirect
201. C2×C3×Q8C22⋊D5semidirect
235. C5×Q8C2×#67semidirect
273. C2×C3×C5#550semidirect
288. C3×Q8C2×C22⋊D5semidirect
326. C2×Q8#1201semidirect
350. C3×C5C2×#550semidirect
369. C2×C5#5834semidirect
383. Q8C2×#1201semidirect
401. C2×C3#66168semidirect
406. C5C2×#5834semidirect
424. C3C2×#66168semidirect
427. C2#11755254direct (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×#7132
C2×Q8×Dic152
#117552542
C2×#914632
C2×#914562
C2×#914492
C2×C4×#12012
C2×#661683
C2×#58345