Finite Group Databasebeta

← #14307125

Subgroups — #14307125

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756229C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic
3C4×#6710C211yesmaximal, characteristic
4#11746344C214yesmaximal
5#10600286—31nomaximal, Hall
6C2×C3×C5×C4⋊C4—21no—
7C2×C3×C42×C5C2212yes—
8C2×C3×C42×C5C2211yescharacteristic
9#91815C2212yes—
10#91813—21no—
11#91813—21no—
12C2×#6710C2212yes—
13#91759C412yescomplemented
14#91758C411yescharacteristic, complemented
15#91758C411yescharacteristic, complemented
16C4×Dic30—21no—
17C4×Dic30—21no—
18C3×C5×#95—21no—
19#91087—21no—
20C4×C3⋊#168—21no—
21#69493—51nomaximal, Hall
22#65804—31no—
23C4×C5×C4⋊C4D311yescharacteristic
24C4×#681—31no—
25#64743—34no—
26C22×C3×C4×C5—22no—
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×Dic30—21no—
31C2×Dic30—21no—
32C3×C5×C4⋊C4—24no—
33C3×C42×C5—24no—
34C3×C42×C5C2×C411yescharacteristic
35C3×C42×C5C2×C411yescharacteristic
36C3×C42×C5D411yescharacteristic
37C3×C42×C5D411yescharacteristic
38#6719—22no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15C2×C412yes—
42C4⋊Dic15C2×C412yes—
43#6712—22no—
44#6712—22no—
45C4×Dic15—22no—
46#6710—22no—
47#6710Q814yescomplemented
48C2×C3⋊#168—22no—
49#5470—51no—
50C3×C4×C4⋊C4D511yescharacteristic
51C4×#208—51no—
52#4523—54no—
53C2×C5×C4⋊C4—21no—
54C2×C42×C5C2×D312yes—
55C2×C42×C5C2×D311yescharacteristic
56#4072—32no—
57#4070—61no—
58#4070—61no—
59C2×#681—32no—
60#4016—32no—
61#4015—31no—
62#4015—31no—
63C4×Dic10—61no—
64C4×Dic10—61no—
65C5×#95—21no—
66#3935—61no—
67C4×#168—61no—
68#1986—151noSylow
69C23×C3×C5C2×D411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—24no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—42no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5C2×Q812yes—
82C2×C3×C4×C5#4112yes—
83C2×Dic15—22no—
84C2×Dic15—22no—
85Dic30—42no—
86Dic30—42no—
87C3⋊#168—24no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C42C2×D512yes—
90C2×C3×C42C2×D511yescharacteristic
91#926—52no—
92#924—101no—
93#924—101no—
94C2×#208—52no—
95#870—52no—
96#869—51no—
97#869—51no—
98C4×Dic6—101no—
99C4×Dic6—101no—
100C3×#95—21no—
101#803—101no—
102C4×C3⋊C8—101no—
103C22×C4×C5—22no—
104C22×C4×C5#6711yescharacteristic
105C22×C4×C5#6711yescharacteristic
106C22×C4×C5C22×D311yescharacteristic
107C2×Dic10—61no—
108C2×Dic10—61no—
109C5×C4⋊C4—24no—
110C42×C5—24no—
111C42×C5C4×D311yescharacteristic
112C42×C5C4×D311yescharacteristic
113C42×C5D1211yescharacteristic
114C42×C5D1211yescharacteristic
115C22⋊Dic5—62no—
116C4⋊Dic5—32no—
117C4⋊Dic5—32no—
118C4⋊Dic5—61no—
119C4⋊Dic5—61no—
120#683—62no—
121#683—62no—
122C4×Dic5—62no—
123#681—34no—
124#681—62no—
125C2×#168—62no—
126#533—151no—
127C4×M16—151no—
128C4×C4⋊C4D1511yescharacteristic
129#339—154no—
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12411yescharacteristic
134C22×C3×C5C4⋊Q811yescharacteristic
135C3×C4×C5—21no—
136C3×C4×C5—21no—
137C3×C4×C5—21no—
138C3×C4×C5—44no—
139C3×C4×C5#10412yes—
140C3×C4×C5C4×Q812yes—
141C3×C4×C5C22⋊Q812yes—
142Dic15—42no—
143Dic15—42no—
144C22×C3×C4—22no—
145C22×C3×C4C22⋊D511yescharacteristic
146C22×C3×C4C22⋊D511yescharacteristic
147C22×C3×C4C22×D511yescharacteristic
148C2×Dic6—101no—
149C2×Dic6—101no—
150C3×C4⋊C4—24no—
151C3×C42—24no—
152C3×C42C4×D511yescharacteristic
153C3×C42C4×D511yescharacteristic
154C3×C42D2011yescharacteristic
155C3×C42D2011yescharacteristic
156#217—102no—
157C4⋊Dic3—52no—
158C4⋊Dic3—52no—
159C4⋊Dic3—101no—
160C4⋊Dic3—101no—
161Dic3⋊C4—102no—
162Dic3⋊C4—102no—
163C4×Dic3—102no—
164#208—54no—
165#208—102no—
166C2×C3⋊C8—102no—
167C23×C5C2×#6711yescharacteristic
168C2×C4×C5—22no—
169C2×C4×C5—24no—
170C2×C4×C5—41no—
171C2×C4×C5—42no—
172C2×C4×C5—42no—
173C2×C4×C5(C2×D3)⋊C411yescharacteristic
174C2×C4×C5(C2×D3)⋊C411yescharacteristic
175C2×C4×C5(C2×D3)⋊C411yescharacteristic
176C2×C4×C5(C2×D3)⋊C411yescharacteristic
177C2×C4×C5C2×C4×D311yescharacteristic
178C2×C4×C5C2×D1211yescharacteristic
179C2×C4×C5#23712yes—
180C2×C4×C5D3×Q812yes—
181C2×Dic5—62no—
182C2×Dic5—62no—
183Dic10—122no—
184Dic10—122no—
185#168—64no—
186C2×M16—152no—
187C4⋊Q8—151no—
188C4⋊Q8—151no—
189#125—152no—
190C22⋊Q8—301no—
191C22⋊Q8—301no—
192C4×Q8—301no—
193C4×Q8—301no—
194#117—152no—
195C2×C4⋊C4—21no—
196C2×C42C2×D1512yes—
197C2×C42C2×D1511yescharacteristic
198#97—301no—
199C4×C8—301no—
200#95—21no—
201C2×C3×C5—21no—
202C2×C3×C5—21no—
203C2×C3×C5#39111yescharacteristic
204C2×C3×C5C2×#10411yescharacteristic
205C2×C3×C5#42111yescharacteristic
206C23×C3C2×C22⋊D511yescharacteristic
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4—41no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4#68511yescharacteristic
213C2×C3×C4#68511yescharacteristic
214C2×C3×C4#68511yescharacteristic
215C2×C3×C4#68511yescharacteristic
216C2×C3×C4C2×C4×D511yescharacteristic
217C2×C3×C4C2×D2011yescharacteristic
218C2×C3×C4#71112yes—
219C2×C3×C4Q8×D512yes—
220C2×Dic3—102no—
221C2×Dic3—102no—
222Dic6—202no—
223Dic6—202no—
224C3⋊C8—104no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5C2×(C2×D3)⋊C411yescharacteristic
228C22×C5#93611yescharacteristic
229C22×C5#94411yescharacteristic
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—44no—
234C4×C5#80512yes—
235C4×C5#88712yes—
236C4×C5#89712yes—
237Dic5—122no—
238Dic5—122no—
239C2×Q8—301no—
240C2×Q8—301no—
241C22×C4—22no—
242C22×C4#122011yescharacteristic
243C22×C4#122011yescharacteristic
244C22×C4C22×D1511yescharacteristic
245M16—154no—
246M16—302no—
247C2×C8—302no—
248C4⋊C4—24no—
249C4⋊C4—152no—
250C4⋊C4—152no—
251C4⋊C4—302no—
252C4⋊C4—302no—
253C4⋊C4—301no—
254C4⋊C4—301no—
255C22⋊C4—302no—
256C42—24no—
257C42—302no—
258C42C4×D1511yescharacteristic
259C42C4×D1511yescharacteristic
260C42D6011yescharacteristic
261C42D6011yescharacteristic
262C3×C5#198611yescharacteristic, complemented, Hall
263C22×C3—21no—
264C22×C3—21no—
265C22×C3C2×#68511yescharacteristic
266C22×C3#408211yescharacteristic
267C22×C3#409011yescharacteristic
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—44no—
272C3×C4#393712yes—
273C3×C4#403312yes—
274C3×C4#404312yes—
275Dic3—202no—
276Dic3—202no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5C2×#80511yescharacteristic
280C2×C5#497311yescharacteristic
281C2×C5#500511yescharacteristic
282C23C2×#122011yescharacteristic
283Q8—602no—
284Q8—602no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—302no—
291C2×C4—302no—
292C2×C4#671411yescharacteristic
293C2×C4#671411yescharacteristic
294C2×C4#671411yescharacteristic
295C2×C4#671411yescharacteristic
296C2×C4C2×C4×D1511yescharacteristic
297C2×C4C2×D6011yescharacteristic
298C2×C4#681912yes—
299C2×C4Q8×D1512yes—
300C8—304no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3C2×#393711yescharacteristic
304C2×C3#6526311yescharacteristic
305C2×C3#6529411yescharacteristic
306C5#6949311yescharacteristic, complemented, Sylow
307C22—21no—
308C22—21no—
309C22C2×#671411yescharacteristic
310C22#9182511yescharacteristic
311C22#9183311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—44no—
316C4—602no—
317C4—602no—
318C4#9108912yes—
319C4#9177612yes—
320C4#9178612yes—
321C3#1060028611yescharacteristic, complemented, Sylow
322C2—21no—
323C2—21no—
324C2C2×#9108911yescharacteristic
325C2#1175107411yescharacteristic
326C2#1175110611yescharacteristic
subgroupG/H
centerC2×C4C2×D60
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×C4⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC4×C4⋊C4D15
hypocenterC3×C5#1986
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #91759C4semidirect
14. #91758C4semidirect
15. #91758C4semidirect
47. #6710Q8semidirect
262. C3×C5#1986semidirect
306. C5#69493semidirect
321. C3#10600286semidirect

Maximal subgroups

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

subgroupindex
#117562292
C3×C4×C5×C4⋊C42
C4×#67102
#117463442
#106002863
#694935