Finite Group Databasebeta

← C2×#11755140 #14479034

Subgroups — C2×#11755140 #14479034

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
4#11755140C2116yesmaximal, direct product factor
5C2×#91358C213yesmaximal
6C2×#91357C213yesmaximal
7C2×#91331C213yesmaximal, complemented
8C2×Dic3×Dic10C213yesmaximal, complemented
9C2×#65906—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C3×Q8×D5C4116yescomplemented
12C2×C3×Q8×D5C2218yes—
13C22×C3×C4×D5C2213yes—
14C22×C3×Dic10C2213yes—
15Q8×Dic15C2218yescomplemented
16C2×C4⋊Dic15C2213yes—
17C2×C4×Dic15C2213yes—
18C5×Q8×Dic3C2218yescomplemented
19C2×C5×C4⋊Dic3C2213yes—
20C2×C4×C5×Dic3C2213yes—
21C2×#6668C2213yes—
22C2×#6668C2213yes—
23C2×#6665C2211yescharacteristic
24C2×#6665C2213yes—
25C2×Dic3×Dic5C2216yes—
26#91358C22124yes—
27#91357C22124yes—
28#91331C22124yescomplemented
29Dic3×Dic10C22124yescomplemented
30C2×#5812—51nomaximal, Hall
31C22×Q8×D5D311yescharacteristic
32C2×C4×C5×Q8—31no—
33C2×Q8×Dic5—31no—
34#65906—316no—
35C2×#4038—33no—
36C2×#4033—33no—
37C2×#4018—33no—
38C2×C4×Dic10—33no—
39C23×C3×D5C2311yescharacteristic
40C2×C3×C5×Q8C2×C418yes—
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2311yescharacteristic
46C22×C5×Dic3C2313yes—
47C22×C3×Dic5C2313yes—
48C3×Q8×D5C2×C4164yescomplemented
49C2×C3×C4×D5C2×C4124yes—
50C2×C3×C4×D5C23112yes—
51C2×C3×Dic10C2×C4124yes—
52C2×C3×Dic10C23112yes—
53C4⋊Dic15C23112yes—
54C4×Dic15C23112yes—
55C5×C4⋊Dic3C23112yes—
56C4×C5×Dic3C23112yes—
57#6668C23112yes—
58#6668C23112yes—
59#6665C2314yes—
60#6665C23112yes—
61Dic3×Dic5C23124yes—
62C23×C3×Q8—51no—
63#5812—516no—
64C2×Q8×Dic3—51no—
65C2×Q8×Dic3—53no—
66C2×Q8×Dic3—53no—
67C2×Q8×Dic3D511yescharacteristic, complemented
68C2×#926—53no—
69C2×#926—53no—
70C22×C5×Q8C2×D311yescharacteristic
71C2×Q8×D5Dic3116yescomplemented
72C2×Q8×D5C2×D318yes—
73C22×C4×D5C2×D313yes—
74C22×Dic10C2×D313yes—
75C4×C5×Q8—38no—
76C2×C5×C4⋊C4—33no—
77C2×C42×C5—33no—
78Q8×Dic5—38no—
79C2×#685—31no—
80C2×#685—33no—
81C2×C4⋊Dic5—33no—
82C2×#683—33no—
83C2×#683—33no—
84C2×C4×Dic5—33no—
85C2×C4×Dic5—36no—
86#4038—324no—
87#4033—324no—
88#4018—324no—
89C4×Dic10—324no—
90C2×#519—151noSylow
91C23×C3×C5C2411yescharacteristic
92C22×C3×D5—22no—
93C22×C3×D5—22no—
94C22×C3×D5C22×C414yes—
95C22×C3×D5C2412yes—
96C3×C5×Q8C22×C4116yes—
97C2×C3×C4×C5C22×C4112yes—
98C2×C3×C4×C5C2416yes—
99C2×Dic15—26no—
100C2×Dic15—22no—
101C2×Dic15C2416yes—
102C2×Dic15C2412yes—
103C2×C5×Dic3—22no—
104C2×C5×Dic3—26no—
105C2×C5×Dic3C2416yes—
106C2×C5×Dic3C2412yes—
107C2×C3×Dic5C22×C4112yes—
108C2×C3×Dic5C2416yes—
109C3×C4×D5C22×C4148yes—
110C3×Dic10C22×C4148yes—
111C22×C3×Q8—516no—
112C22×C3×Q8—58no—
113C22×C3×Q8—53no—
114C22×C3×Q8C2×D511yescharacteristic
115C23×C3×C4—53no—
116C2×#217—53no—
117C2×#217—51no—
118Q8×Dic3—58no—
119Q8×Dic3—524no—
120Q8×Dic3—524no—
121Q8×Dic3C2×D518yescomplemented
122#926—524no—
123#926—524no—
124C2×C4⋊Dic3—53no—
125C2×C4⋊Dic3—53no—
126C2×C4⋊Dic3—53no—
127C2×C4⋊Dic3C2×D513yes—
128C2×C4×Dic3—53no—
129C2×C4×Dic3—56no—
130C2×C4×Dic3C2×D513yes—
131C23×D5C22×D311yescharacteristic
132C2×C5×Q8C2×Dic318yes—
133C2×C5×Q8C22×D314yes—
134C22×C4×C5—31no—
135C22×C4×C5—33no—
136C22×C4×C5C22×D313yes—
137C22×Dic5—31no—
138C22×Dic5—33no—
139C22×Dic5C22×D313yes—
140Q8×D5C2×Dic3164yescomplemented
141C2×C4×D5C2×Dic3124yes—
142C2×C4×D5C22×D3112yes—
143C2×Dic10C2×Dic3124yes—
144C2×Dic10C22×D3112yes—
145C5×C4⋊C4—312no—
146C42×C5—312no—
147#685—34no—
148#685—312no—
149C4⋊Dic5—312no—
150#683—312no—
151#683—312no—
152C4×Dic5—312no—
153C4×Dic5—324no—
154C23×Q8—51no—
155#519—1516no—
156C2×C4×Q8—31no—
157C2×C4×Q8—153no—
158C2×C4×Q8—153no—
159C2×C4×Q8—151no—
160C2×#117—153no—
161C2×#117—153no—
162C22×C3×C5C23×C412yes—
163C22×C3×C52−1+412yes—
164C22×C3×C52−1+412yes—
165C22×C3×C5C2511yescharacteristic
166C2×C3×D5—28no—
167C2×C3×D5—22no—
168C2×C3×D5—22no—
169C2×C3×D5C23×C414yes—
170C3×C4×C5C23×C4112yes—
171Dic15—26no—
172Dic15—22no—
173C3×Dic5C23×C4112yes—
174C5×Dic3—22no—
175C5×Dic3—26no—
176C24×C3—51no—
177C2×C3×Q8—564no—
178C2×C3×Q8—524no—
179C2×C3×Q8—512no—
180C2×C3×Q8C4×D518yes—
181C2×C3×Q8C22×D514yes—
182C22×C3×C4—53no—
183C22×C3×C4—524no—
184C22×C3×C4—512no—
185C22×C3×C4C22×D513yes—
186C22×Dic3—53no—
187C22×Dic3—51no—
188C22×Dic3C22×D513yes—
189C22×Dic3C22×D511yescharacteristic
190#217—512no—
191#217—54no—
192C4⋊Dic3—512no—
193C4⋊Dic3—512no—
194C4⋊Dic3—512no—
195C4⋊Dic3C22×D5112yes—
196C4×Dic3—512no—
197C4×Dic3—524no—
198C4×Dic3C22×D5112yes—
199C23×C5C23×D311yescharacteristic
200C22×D5—22no—
201C22×D5—22no—
202C22×D5C22×Dic314yes—
203C22×D5C23×D312yes—
204C5×Q8C22×Dic3116yes—
205C2×C4×C5—36no—
206C2×C4×C5—32no—
207C2×C4×C5—62no—
208C2×C4×C5—66no—
209C2×C4×C5C22×Dic3112yes—
210C2×C4×C5C23×D316yes—
211C2×Dic5—32no—
212C2×Dic5—36no—
213C2×Dic5—66no—
214C2×Dic5—62no—
215C2×Dic5C22×Dic3112yes—
216C2×Dic5C23×D316yes—
217C4×D5C22×Dic3148yes—
218Dic10C22×Dic3148yes—
219C22×Q8—516no—
220C22×Q8—58no—
221C22×Q8—53no—
222C22×Q8D3×D511yescharacteristic
223C23×C4—53no—
224C4×Q8—38no—
225C4×Q8—1524no—
226C4×Q8—1524no—
227C4×Q8—158no—
228#117—1524no—
229#117—1524no—
230C2×C4⋊C4—33no—
231C2×C4⋊C4—153no—
232C2×C4⋊C4—153no—
233C2×C4⋊C4—153no—
234C2×C22⋊C4—151no—
235C2×C22⋊C4—153no—
236C2×C42—33no—
237C2×C42—156no—
238C2×C42—153no—
239C2×C3×C5#51914yescomplemented
240C2×C3×C5C24×C411yescharacteristic
241C2×C3×C5C2×2−1+411yescharacteristic
242C2×C3×C5C2×2−1+411yescharacteristic
243C3×D5—24no—
244C23×C3—54no—
245C23×C3—52no—
246C23×C3—102no—
247C23×C3—102no—
248C23×C3C23×D511yescharacteristic
249C3×Q8—548no—
250C3×Q8C2×C4×D5116yes—
251C2×C3×C4—512no—
252C2×C3×C4—56no—
253C2×C3×C4—548no—
254C2×C3×C4C2×C4×D5112yes—
255C2×C3×C4C23×D516yes—
256C2×Dic3—22no—
257C2×Dic3—26no—
258C2×Dic3—56no—
259C2×Dic3—52no—
260C2×Dic3—106no—
261C2×Dic3—102no—
262C2×Dic3C23×D516yes—
263C2×Dic3C23×D512yes—
264C22×C5#100712yes—
265C22×C5#100712yes—
266C22×C5C23×Dic312yes—
267C22×C5C24×D311yescharacteristic
268C2×D5—22no—
269C2×D5—22no—
270C2×D5—28no—
271C2×D5C23×Dic314yes—
272C4×C5—62no—
273C4×C5—66no—
274C4×C5C23×Dic3112yes—
275Dic5—66no—
276Dic5—62no—
277Dic5C23×Dic3112yes—
278C24—51no—
279C2×Q8—564no—
280C2×Q8—524no—
281C2×Q8—512no—
282C2×Q8D5×Dic318yes—
283C2×Q8C2×D3×D514yes—
284C22×C4—31no—
285C22×C4—33no—
286C22×C4—53no—
287C22×C4—524no—
288C22×C4—512no—
289C22×C4—153no—
290C22×C4—151no—
291C22×C4C2×D3×D513yes—
292C4⋊C4—312no—
293C4⋊C4—1512no—
294C4⋊C4—1512no—
295C4⋊C4—1512no—
296C22⋊C4—154no—
297C22⋊C4—1512no—
298C42—312no—
299C42—1524no—
300C42—1512no—
301C3×C5C2×#51911yescharacteristic, complemented, Hall
302C22×C3—54no—
303C22×C3—108no—
304C22×C3—102no—
305C22×C3—102no—
306C22×C3C22×C4×D512yes—
307C22×C3#414712yes—
308C22×C3#415012yes—
309C22×C3C24×D511yescharacteristic
310C3×C4—512no—
311C3×C4C22×C4×D5112yes—
312Dic3—22no—
313Dic3—26no—
314Dic3—106no—
315Dic3—102no—
316C2×C5#581214yescomplemented
317C2×C5C2×#100711yescharacteristic
318C2×C5C2×#100711yescharacteristic
319C2×C5C24×Dic311yescharacteristic
320D5—24no—
321C23—54no—
322C23—52no—
323C23—102no—
324C23—102no—
325C23C22×D3×D511yescharacteristic
326Q8—548no—
327Q8C2×D5×Dic3116yes—
328C2×C4—32no—
329C2×C4—36no—
330C2×C4—512no—
331C2×C4—56no—
332C2×C4—548no—
333C2×C4—62no—
334C2×C4—66no—
335C2×C4—156no—
336C2×C4—152no—
337C2×C4—306no—
338C2×C4—302no—
339C2×C4C2×D5×Dic3112yes—
340C2×C4C22×D3×D516yes—
341C2×C3—104no—
342C2×C3#6590614yescomplemented
343C2×C3C23×C4×D511yescharacteristic
344C2×C3C2×#414711yescharacteristic
345C2×C3C2×#415011yescharacteristic
346C5C2×#581211yescharacteristic, complemented, Sylow
347C22—54no—
348C22—108no—
349C22—102no—
350C22—102no—
351C22#9202912yes—
352C22#9203012yes—
353C22C22×D5×Dic312yes—
354C22C23×D3×D511yescharacteristic
355C4—512no—
356C4—62no—
357C4—66no—
358C4—306no—
359C4—302no—
360C4C22×D5×Dic3112yes—
361C3C2×#6590611yescharacteristic, complemented, Sylow
362C2—104no—
363C2#1175514014yesdirect product factor
364C2C2×#9202911yescharacteristic
365C2C2×#9203011yescharacteristic
366C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC22×C3×C5C25
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×C5×Q8×Dic3C2semidirect
4. #11755140C2direct (N × H)
7. C2×#91331C2semidirect
8. C2×Dic3×Dic10C2semidirect
11. C2×C3×Q8×D5C4semidirect
15. Q8×Dic15C22semidirect
18. C5×Q8×Dic3C22semidirect
28. #91331C22semidirect
29. Dic3×Dic10C22semidirect
48. C3×Q8×D5C2×C4semidirect
67. C2×Q8×Dic3D5semidirect
71. C2×Q8×D5Dic3semidirect
121. Q8×Dic3C2×D5semidirect
140. Q8×D5C2×Dic3semidirect
239. C2×C3×C5#519semidirect
301. C3×C5C2×#519semidirect
316. C2×C5#5812semidirect
342. C2×C3#65906semidirect
346. C5C2×#5812semidirect
361. C3C2×#65906semidirect
363. C2#11755140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C2×Q8×Dic152
C2×C5×Q8×Dic32
#117551402
C2×#913582
C2×#913572
C2×#913312
C2×Dic3×Dic102
C2×#659063
C2×#58125