Finite Group Databasebeta

← C2×#11756457 #14481210

Subgroups — C2×#11756457 #14481210

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756457C2116yesmaximal, direct product factor
3C2×#91787C214yesmaximal
4C2×#91786C212yesmaximal
5C2×#91779C214yesmaximal, complemented
6C2×#91776C212yesmaximal, complemented
7C2×#91761C211yesmaximal, characteristic
8C2×#91758C211yesmaximal, characteristic, complemented
9C2×#66031—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×Dic30C2212yes—
12C3×C5×#125C2218yescomplemented
13C2×C3×C5×C4⋊C4C2212yes—
14C2×C3×C5×C4⋊C4C2214yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6714C2212yes—
17C2×#6714C2214yes—
18C2×C4⋊Dic15C2214yes—
19C2×C4⋊Dic15C2214yes—
20C2×#6712C2212yes—
21C2×#6712C2214yes—
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2214yes—
24#91787C22132yes—
25#91786C22116yes—
26#91779C22132yescomplemented
27#91776C22116yescomplemented
28#91761C2218yes—
29#91758C2218yescomplemented
30C2×#5698—51nomaximal, Hall
31C2×C5×#125D311yescharacteristic, complemented
32#66031—316no—
33C2×#4044—34no—
34C2×#4043—32no—
35C2×#4036—34no—
36C2×#4033—32no—
37C2×#4018—31no—
38C2×#4015—31no—
39C23×D15C2311yescharacteristic
40C22×C3×C4×C5C2314yes—
41C22×C3×C4×C5C2312yes—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15C2312yes—
44C22×Dic15C2314yes—
45C22×Dic15C2311yescharacteristic
46C2×C4×D15—24no—
47C2×C4×D15C2314yes—
48C2×Dic30—28no—
49C2×Dic30C2318yes—
50C3×C5×C4⋊C4C2318yes—
51C3×C5×C4⋊C4C23116yes—
52C3×C42×C5C2314yes—
53#6714C2318yes—
54#6714C23116yes—
55C4⋊Dic15C23116yes—
56C4⋊Dic15C23116yes—
57#6712C2318yes—
58#6712C23116yes—
59C4×Dic15C2314yes—
60C4×Dic15C23116yes—
61C2×C3×#125D511yescharacteristic, complemented
62#5698—516no—
63C2×#898—54no—
64C2×#897—52no—
65C2×#890—54no—
66C2×#887—52no—
67C2×#872—51no—
68C2×#869—51no—
69C22×C4×D5—31no—
70C22×Dic10—32no—
71C5×#125C2×D318yescomplemented
72C2×C5×C4⋊C4C2×D312yes—
73C2×C5×C4⋊C4C2×D314yes—
74C2×C42×C5C2×D311yescharacteristic
75C2×#685—32no—
76C2×#685—34no—
77C2×C4⋊Dic5—34no—
78C2×C4⋊Dic5—34no—
79C2×#683—32no—
80C2×#683—34no—
81C2×C4×Dic5—31no—
82C2×C4×Dic5—34no—
83#4044—332no—
84#4043—316no—
85#4036—332no—
86#4033—316no—
87#4018—38no—
88#4015—38no—
89C2×#541—151noSylow
90C23×C3×C5C2411yescharacteristic
91C22×D15—22no—
92C22×D15—24no—
93C22×D15C2412yes—
94C2×C3×C4×C5—28no—
95C2×C3×C4×C5—24no—
96C2×C3×C4×C5#4114yes—
97C2×C3×C4×C5C2418yes—
98C2×C3×C4×C5C2414yes—
99C2×C3×C4×C5C2412yes—
100C2×Dic15—28no—
101C2×Dic15—22no—
102C2×Dic15—24no—
103C2×Dic15C2414yes—
104C2×Dic15C2418yes—
105C2×Dic15C2412yes—
106C4×D15—28no—
107Dic30—216no—
108C22×C4×D3—51no—
109C22×Dic6—52no—
110C3×#125C2×D518yescomplemented
111C2×C3×C4⋊C4C2×D512yes—
112C2×C3×C4⋊C4C2×D514yes—
113C2×C3×C42C2×D511yescharacteristic
114C2×(C2×D3)⋊C4—52no—
115C2×(C2×D3)⋊C4—54no—
116C2×C4⋊Dic3—54no—
117C2×C4⋊Dic3—54no—
118C2×Dic3⋊C4—52no—
119C2×Dic3⋊C4—54no—
120C2×C4×Dic3—51no—
121C2×C4×Dic3—54no—
122#898—532no—
123#897—516no—
124#890—532no—
125#887—516no—
126#872—58no—
127#869—58no—
128C23×D5—31no—
129C22×C4×C5C22×D312yes—
130C22×C4×C5C22×D314yes—
131C22×C4×C5C22×D311yescharacteristic
132C22×Dic5—34no—
133C22×Dic5—31no—
134C22×Dic5—32no—
135C2×C4×D5—34no—
136C2×C4×D5—64no—
137C2×Dic10—38no—
138C2×Dic10—68no—
139C5×C4⋊C4C22×D318yes—
140C5×C4⋊C4C22×D3116yes—
141C42×C5C22×D314yes—
142#685—38no—
143#685—316no—
144C4⋊Dic5—316no—
145C4⋊Dic5—316no—
146#683—38no—
147#683—316no—
148C4×Dic5—34no—
149C4×Dic5—316no—
150#541—1516no—
151C2×C4⋊Q8—151no—
152C2×#126—154no—
153C2×#125—154no—
154C2×#125D1511yescharacteristic, complemented
155C2×C22⋊Q8—152no—
156C2×C4×Q8—152no—
157C2×#117—151no—
158C22×C3×C5C2×#4112yes—
159C22×C3×C52−1+414yes—
160C22×C3×C5C2511yescharacteristic
161C2×D15—22no—
162C2×D15—24no—
163C2×D15—44no—
164C3×C4×C5—28no—
165C3×C4×C5—24no—
166C3×C4×C5C2×#4114yes—
167Dic15—28no—
168Dic15—22no—
169Dic15—24no—
170C23×D3—51no—
171C22×C3×C4C22×D514yes—
172C22×C3×C4C22×D512yes—
173C22×C3×C4C22×D511yescharacteristic
174C22×Dic3—52no—
175C22×Dic3—54no—
176C22×Dic3—51no—
177C2×C4×D3—54no—
178C2×C4×D3—104no—
179C2×Dic6—58no—
180C2×Dic6—108no—
181C3×C4⋊C4C22×D518yes—
182C3×C4⋊C4C22×D5116yes—
183C3×C42C22×D514yes—
184(C2×D3)⋊C4—58no—
185(C2×D3)⋊C4—516no—
186C4⋊Dic3—516no—
187C4⋊Dic3—516no—
188Dic3⋊C4—58no—
189Dic3⋊C4—516no—
190C4×Dic3—54no—
191C4×Dic3—516no—
192C23×C5C23×D311yescharacteristic
193C22×D5—32no—
194C22×D5—62no—
195C22×D5—64no—
196C2×C4×C5—24no—
197C2×C4×C5—28no—
198C2×C4×C5#23914yes—
199C2×C4×C5C23×D318yes—
200C2×C4×C5C23×D314yes—
201C2×C4×C5C23×D312yes—
202C2×Dic5—34no—
203C2×Dic5—38no—
204C2×Dic5—32no—
205C2×Dic5—68no—
206C2×Dic5—62no—
207C2×Dic5—64no—
208C4×D5—68no—
209Dic10—616no—
210C22×Q8—152no—
211C23×C4—151no—
212C4⋊Q8—158no—
213#126—1532no—
214#125—1532no—
215#125C2×D1518yescomplemented
216C22⋊Q8—1516no—
217C4×Q8—1516no—
218#117—158no—
219C2×C4⋊C4—152no—
220C2×C4⋊C4—154no—
221C2×C4⋊C4—154no—
222C2×C4⋊C4—154no—
223C2×C4⋊C4C2×D1512yes—
224C2×C4⋊C4C2×D1514yes—
225C2×C22⋊C4—152no—
226C2×C22⋊C4—154no—
227C2×C42—151no—
228C2×C42—154no—
229C2×C42C2×D1511yescharacteristic
230C2×C3×C5#54114yescomplemented
231C2×C3×C5C22×#4111yescharacteristic
232C2×C3×C5C2×2−1+412yes—
233D15—42no—
234C23×C3C23×D511yescharacteristic
235C22×D3—52no—
236C22×D3—102no—
237C22×D3—104no—
238C2×C3×C4—28no—
239C2×C3×C4—24no—
240C2×C3×C4#71314yes—
241C2×C3×C4C23×D518yes—
242C2×C3×C4C23×D514yes—
243C2×C3×C4C23×D512yes—
244C2×Dic3—54no—
245C2×Dic3—58no—
246C2×Dic3—52no—
247C2×Dic3—108no—
248C2×Dic3—102no—
249C2×Dic3—104no—
250C4×D3—108no—
251Dic6—1016no—
252C22×C5C2×#23912yes—
253C22×C5#101014yes—
254C22×C5C24×D311yescharacteristic
255C2×D5—62no—
256C2×D5—64no—
257C2×D5—124no—
258C4×C5—28no—
259C4×C5—24no—
260C4×C5C2×#23914yes—
261Dic5—68no—
262Dic5—62no—
263Dic5—64no—
264C24—151no—
265C2×Q8—158no—
266C2×Q8—308no—
267C22×C4—152no—
268C22×C4—154no—
269C22×C4—151no—
270C22×C4—154no—
271C22×C4—304no—
272C22×C4C22×D1514yes—
273C22×C4C22×D1512yes—
274C22×C4C22×D1511yescharacteristic
275C4⋊C4—158no—
276C4⋊C4—1516no—
277C4⋊C4—1516no—
278C4⋊C4—1516no—
279C4⋊C4C22×D1518yes—
280C4⋊C4C22×D15116yes—
281C22⋊C4—158no—
282C22⋊C4—1516no—
283C42—154no—
284C42—1516no—
285C42C22×D1514yes—
286C3×C5C2×#54111yescharacteristic, complemented, Hall
287C22×C3C2×#71312yes—
288C22×C3#415014yes—
289C22×C3C24×D511yescharacteristic
290C2×D3—102no—
291C2×D3—104no—
292C2×D3—204no—
293C3×C4—28no—
294C3×C4—24no—
295C3×C4C2×#71314yes—
296Dic3—108no—
297Dic3—102no—
298Dic3—104no—
299C2×C5#569814yescomplemented
300C2×C5C22×#23911yescharacteristic
301C2×C5C2×#101012yes—
302D5—122no—
303C23—152no—
304C23—302no—
305C23—304no—
306C23C23×D1511yescharacteristic
307Q8—3016no—
308C2×C4—28no—
309C2×C4—24no—
310C2×C4—154no—
311C2×C4—158no—
312C2×C4—152no—
313C2×C4—302no—
314C2×C4—308no—
315C2×C4—304no—
316C2×C4—308no—
317C2×C4#682114yes—
318C2×C4C23×D1518yes—
319C2×C4C23×D1514yes—
320C2×C4C23×D1512yes—
321C2×C3#6603114yescomplemented
322C2×C3C22×#71311yescharacteristic
323C2×C3C2×#415012yes—
324D3—202no—
325C5C2×#569811yescharacteristic, complemented, Sylow
326C22—302no—
327C22—304no—
328C22—604no—
329C22C2×#682112yes—
330C22#9210114yes—
331C22C24×D1511yescharacteristic
332C4—28no—
333C4—24no—
334C4—302no—
335C4—308no—
336C4—304no—
337C4C2×#682114yes—
338C3C2×#6603111yescharacteristic, complemented, Sylow
339C2—602no—
340C2#1175645714yesdirect product factor
341C2C22×#682111yescharacteristic
342C2C2×#9210112yes—
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×#125D15
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. #11756457C2direct (N × H)
5. C2×#91779C2semidirect
6. C2×#91776C2semidirect
8. C2×#91758C2semidirect
12. C3×C5×#125C22semidirect
26. #91779C22semidirect
27. #91776C22semidirect
29. #91758C22semidirect
31. C2×C5×#125D3semidirect
61. C2×C3×#125D5semidirect
71. C5×#125C2×D3semidirect
110. C3×#125C2×D5semidirect
154. C2×#125D15semidirect
215. #125C2×D15semidirect
230. C2×C3×C5#541semidirect
286. C3×C5C2×#541semidirect
299. C2×C5#5698semidirect
321. C2×C3#66031semidirect
325. C5C2×#5698semidirect
338. C3C2×#66031semidirect
340. C2#11756457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1252
#117564572
C2×#917872
C2×#917862
C2×#917792
C2×#917762
C2×#917612
C2×#917582
C2×#660313
C2×#56985