Finite Group Databasebeta

← #14437966

Subgroups — #14437966

Order 1920.

768 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752631C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic
3D15×#97C211yesmaximal, characteristic
4C5×#4703C211yesmaximal, characteristic, complemented
5C3×#64992C211yesmaximal, characteristic, complemented
6#11748040C214yesmaximal, complemented
7#11747609C214yesmaximal
8#11746928C211yesmaximal, characteristic, complemented
9#11746925C211yesmaximal, characteristic, complemented
10D5×#491—31nomaximal, Hall
11C2×D15⋊Q8C2212yes—
12C2×C8×D15C2212yes—
13C42×D15C2211yescharacteristic
14C5×#870C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C3×#4016C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18#91470—22no—
19#91437—22no—
20#91437C2212yes—
21#91404—22no—
22#91385C2212yes—
23#91384C2212yes—
24#91382—22no—
25C3×C5×#97C2211yescharacteristic
26#91099C2212yes—
27#91087C2211yescharacteristic
28C5×#816C2214yes—
29C3×#3948C2214yes—
30#90972C2214yes—
31#90970C2214yes—
32D3×#491—51nomaximal, Hall
33D5×C4⋊Q8—31no—
34D5×#125—31no—
35C5×#491—31no—
36#65371—31no—
37#65358—31no—
38D5×#103—34no—
39#65086—34no—
40D5×#97—31no—
41#64992D311yescharacteristic, complemented
42C2×C4×D15D412yes—
43C2×C4×D15C2311yescharacteristic
44C2×C5×Dic6C2312yes—
45C2×C3×Dic10C2312yes—
46C2×#1204—22no—
47C2×#1200—22no—
48C2×#1200—22no—
49D15⋊Q8—28no—
50C2×C3×C5×C8C2312yes—
51C3×C42×C5C2311yescharacteristic
52C4×Dic15D412yes—
53C4×Dic15C2311yescharacteristic
54C2×C3⋊#168C2312yes—
55C8×D15—24no—
56C5×C4⋊Dic3—22no—
57C5×C4⋊Dic3C2312yes—
58C5×Dic3⋊C4—22no—
59C3×C4⋊Dic5—22no—
60C3×C4⋊Dic5C2312yes—
61C3×#683—22no—
62Dic3⋊Dic5—22no—
63#6669—24no—
64#6669—22no—
65#6668—22no—
66D3×C4⋊Q8—51no—
67D3×#125—51no—
68C3×#491—51no—
69#5082—51no—
70#5069—51no—
71D3×#103—54no—
72#4797—54no—
73D3×#97—51no—
74#4703D511yescharacteristic, complemented
75C2×Q8×D5—32no—
76C5×C4⋊Q8—31no—
77C5×#125—31no—
78#4090—32no—
79C2×C8×D5—32no—
80D5×C4⋊C4—32no—
81D5×C4⋊C4—62no—
82D5×C4⋊C4—62no—
83#4036—32no—
84#4035—62no—
85#4034—62no—
86C42×D5—31no—
87#4016C2×D311yescharacteristic
88#4015C2×D311yescharacteristic
89C5×#103—34no—
90C5×#97C2×D311yescharacteristic
91#3967—34no—
92#3948C2×D314yes—
93#3947—32no—
94#3942—34no—
95#3935—31no—
96C2×#491—151noSylow
97C22×D15C2×D411yescharacteristic
98C2×C3×C4×C5C2×D412yes—
99C2×C3×C4×C5C2411yescharacteristic
100C2×Dic15C2×D412yes—
101C2×Dic15C2×D411yescharacteristic
102C4×D15—24no—
103C4×D15#4114yes—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C5×Dic6—24no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C3×Dic10—24no—
110#1204—44no—
111#1200—44no—
112#1200—44no—
113C3×C5×C8—22no—
114C3⋊#168—22no—
115C2×D3×Q8—52no—
116C3×C4⋊Q8—51no—
117C3×#125—51no—
118#944—52no—
119C2×D3×C8—52no—
120D3×C4⋊C4—52no—
121D3×C4⋊C4—102no—
122D3×C4⋊C4—102no—
123#890—52no—
124#889—102no—
125#888—102no—
126C42×D3—51no—
127#870C2×D511yescharacteristic
128#869C2×D511yescharacteristic
129C3×#103—54no—
130C3×#97C2×D511yescharacteristic
131#835—54no—
132#816C2×D514yes—
133#815—52no—
134#810—54no—
135#803—51no—
136C2×C5×Q8—32no—
137Q8×D5—68no—
138C2×C4×D5—31no—
139C2×C4×D5—32no—
140C2×C4×D5—62no—
141C2×C4×D5—62no—
142C2×Dic10—62no—
143C2×Dic10C22×D312yes—
144C2×C5×C8C22×D312yes—
145C5×C4⋊C4—32no—
146C5×C4⋊C4—62no—
147C5×C4⋊C4—62no—
148C42×C5C22×D311yescharacteristic
149C4⋊Dic5—22no—
150C4⋊Dic5—62no—
151C4⋊Dic5C22×D312yes—
152#683—22no—
153#683—62no—
154#683—64no—
155#683—62no—
156C4×Dic5—32no—
157C4×Dic5—31no—
158C2×#168—32no—
159C8×D5—64no—
160C2×C4⋊Q8—151no—
161C2×#125—151no—
162#491—31no—
163#491—51no—
164#491—154no—
165#491—151no—
166#491—151no—
167C2×#103—154no—
168C2×#97—151no—
169C22×C3×C5C22×D411yescharacteristic
170C2×D15#12412yes—
171C2×D15#13714yes—
172C3×C4×C5—22no—
173C3×C4×C5C2×#4112yes—
174Dic15—22no—
175Dic15#12412yes—
176C3×Dic5—42no—
177C3×Dic5—42no—
178C5×Dic3—42no—
179C5×Dic3—42no—
180C2×C3×Q8—52no—
181D3×Q8—108no—
182C2×C4×D3—51no—
183C2×C4×D3—52no—
184C2×C4×D3—102no—
185C2×C4×D3—102no—
186C2×Dic6—102no—
187C2×Dic6C22×D512yes—
188C2×C3×C8C22×D512yes—
189C3×C4⋊C4—52no—
190C3×C4⋊C4—102no—
191C3×C4⋊C4—102no—
192C3×C42C22×D511yescharacteristic
193C4⋊Dic3—22no—
194C4⋊Dic3—102no—
195C4⋊Dic3C22×D512yes—
196Dic3⋊C4—22no—
197Dic3⋊C4—104no—
198Dic3⋊C4—102no—
199Dic3⋊C4—102no—
200C4×Dic3—52no—
201C4×Dic3—51no—
202C2×C3⋊C8—52no—
203D3×C8—104no—
204C22×D5—31no—
205C5×Q8—64no—
206C2×C4×C5—62no—
207C2×C4×C5—62no—
208C2×C4×C5D3×D412yes—
209C2×C4×C5C23×D311yescharacteristic
210C2×Dic5—22no—
211C2×Dic5—22no—
212C2×Dic5—31no—
213C2×Dic5—32no—
214C4×D5—34no—
215C4×D5—64no—
216C4×D5—124no—
217C4×D5—124no—
218Dic10—24no—
219Dic10—124no—
220C5×C8—22no—
221#168—62no—
222C22×Q8—152no—
223C22×C8—152no—
224C4⋊Q8—31no—
225C4⋊Q8—51no—
226C4⋊Q8—152no—
227C4⋊Q8—302no—
228#125—31no—
229#125—51no—
230#125—152no—
231#125—302no—
232C2×C4⋊C4—152no—
233C2×C4⋊C4—302no—
234C2×C4⋊C4—302no—
235C2×C42—151no—
236#103—34no—
237#103—54no—
238#103—154no—
239#103—154no—
240#97—152no—
241#97—151no—
242#97D3×D511yescharacteristic
243C2×C3×C5C2×#12411yescharacteristic
244C2×C3×C5C2×#13712yes—
245D15#49114yescomplemented
246C22×D3—51no—
247C3×Q8—104no—
248C2×C3×C4—102no—
249C2×C3×C4—102no—
250C2×C3×C4D4×D512yes—
251C2×C3×C4C23×D511yescharacteristic
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—51no—
255C2×Dic3—52no—
256C4×D3—54no—
257C4×D3—104no—
258C4×D3—204no—
259C4×D3—204no—
260Dic6—24no—
261Dic6—204no—
262C3×C8—22no—
263C3⋊C8—102no—
264C22×C5C2×D3×D411yescharacteristic
265C2×D5—32no—
266C2×D5—34no—
267C4×C5—22no—
268C4×C5—122no—
269C4×C5—122no—
270C4×C5D3×#4112yes—
271Dic5—32no—
272Dic5—42no—
273Dic5—42no—
274Dic5—62no—
275C2×Q8—32no—
276C2×Q8—52no—
277C2×Q8—302no—
278C2×Q8—308no—
279C22×C4—151no—
280C22×C4—152no—
281C22×C4—302no—
282C22×C4—302no—
283C2×C8—152no—
284C2×C8—304no—
285C2×C8C2×D3×D512yes—
286C4⋊C4—32no—
287C4⋊C4—52no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C4⋊C4—102no—
291C4⋊C4—102no—
292C4⋊C4—302no—
293C4⋊C4—302no—
294C4⋊C4—302no—
295C4⋊C4—304no—
296C42—152no—
297C42—151no—
298C42C2×D3×D511yescharacteristic
299C3×C5C2×#49111yescharacteristic, complemented, Hall
300C22×C3C2×D4×D511yescharacteristic
301C2×D3—54no—
302C2×D3—52no—
303C3×C4—22no—
304C3×C4—202no—
305C3×C4—202no—
306C3×C4D5×#4112yes—
307Dic3—42no—
308Dic3—42no—
309Dic3—52no—
310Dic3—102no—
311C2×C5D3×#12411yescharacteristic
312C2×C5D3×#13712yes—
313D5—34no—
314C23—151no—
315Q8—64no—
316Q8—104no—
317Q8—604no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—151no—
323C2×C4—154no—
324C2×C4—152no—
325C2×C4—304no—
326C2×C4—604no—
327C2×C4—604no—
328C2×C4#677712yes—
329C2×C4C22×D3×D511yescharacteristic
330C8—22no—
331C8—302no—
332C2×C3D5×#12411yescharacteristic
333C2×C3D5×#13712yes—
334D3—54no—
335C5D3×#49111yescharacteristic, complemented, Sylow
336C22—152no—
337C22—154no—
338C22C2×#677711yescharacteristic
339C4—22no—
340C4—122no—
341C4—122no—
342C4—152no—
343C4—202no—
344C4—202no—
345C4—302no—
346C4#9201612yes—
347C3D5×#49111yescharacteristic, complemented, Sylow
348C2—154no—
349C2#1175275111yescharacteristic
350C2#1175403412yes—
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#97D3×D5
hypocenterC3×C5C2×#491
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C5×#4703C2semidirect
5. C3×#64992C2semidirect
6. #11748040C2semidirect
8. #11746928C2semidirect
9. #11746925C2semidirect
41. #64992D3semidirect
74. #4703D5semidirect
245. D15#491semidirect
299. C3×C5C2×#491semidirect
335. C5D3×#491semidirect
347. C3D5×#491semidirect

Maximal subgroups

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

subgroupindex
#117526312
#117525622
D15×#972
C5×#47032
C3×#649922
#117480402
#117476092
#117469282
#117469252
D5×#4913
D3×#4915