Finite Group Databasebeta

← #14437987

Subgroups — #14437987

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
1D15×#125C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic
3C5×#5069C211yesmaximal, characteristic, complemented
4C3×#65358C211yesmaximal, characteristic, complemented
5#11747490C214yesmaximal
6#11747429C214yesmaximal, complemented
7#11746983C211yesmaximal, characteristic
8#11746931C211yesmaximal, characteristic, complemented
9#11746922C211yesmaximal, characteristic, complemented
10D5×#491—31nomaximal, Hall
11C2×D15⋊Q8C2212yes—
12C3×C5×#125C2211yescharacteristic
13C4⋊C4×D15—22no—
14C4⋊C4×D15C2212yes—
15#91779C2212yes—
16#91778—22no—
17C42×D15C2211yescharacteristic
18#91759C2211yescharacteristic
19C5×#869C2211yescharacteristic
20C3×#4015C2211yescharacteristic
21#91470—22no—
22#91437—22no—
23#91385C2212yes—
24C2×#6648C2212yes—
25C5×#810C2214yes—
26C5×#803C2211yescharacteristic
27C3×#3942C2214yes—
28C3×#3935C2211yescharacteristic
29#90973C2214yes—
30#90971C2214yes—
31#90954C2212yes—
32D3×#491—51nomaximal, Hall
33D5×C4⋊Q8—31no—
34D5×#125—31no—
35C5×#491—31no—
36#65371—31no—
37#65358D311yescharacteristic, complemented
38D5×#103—34no—
39#65086—34no—
40D5×#97—31no—
41#64992—31no—
42C2×C4×D15—22no—
43C2×C4×D15D412yes—
44C2×C4×D15C2311yescharacteristic
45C2×C5×Dic6C2312yes—
46C2×C3×Dic10C2312yes—
47C2×#1204—22no—
48C2×#1200—22no—
49D15⋊Q8—28no—
50C3×C5×C4⋊C4—22no—
51C3×C5×C4⋊C4C2312yes—
52C3×C42×C5C2311yescharacteristic
53C4⋊Dic15—22no—
54C4⋊Dic15C2312yes—
55#6712—22no—
56#6712—22no—
57#6712—22no—
58C4×Dic15D412yes—
59C4×Dic15C2311yescharacteristic
60C5×C4⋊Dic3—22no—
61C2×C5×C3⋊C8C2312yes—
62C3×C4⋊Dic5—22no—
63C2×C3×#168C2312yes—
64#6669—24no—
65#6648—24no—
66D3×C4⋊Q8—51no—
67D3×#125—51no—
68C3×#491—51no—
69#5082—51no—
70#5069D511yescharacteristic, complemented
71D3×#103—54no—
72#4797—54no—
73D3×#97—51no—
74#4703—51no—
75C2×Q8×D5—32no—
76C5×C4⋊Q8—31no—
77C5×#125C2×D311yescharacteristic
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#4016—31no—
88#4015C2×D311yescharacteristic
89C5×#103—34no—
90C5×#97—31no—
91#3967—34no—
92#3948—34no—
93#3947—32no—
94#3942C2×D314yes—
95#3935C2×D311yescharacteristic
96C2×#491—151noSylow
97C22×D15C2×D411yescharacteristic
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D412yes—
100C2×C3×C4×C5C2411yescharacteristic
101C2×Dic15—22no—
102C2×Dic15C2×D412yes—
103C2×Dic15C2×D411yescharacteristic
104C4×D15—24no—
105C4×D15—44no—
106C4×D15#4114yes—
107C2×C5×Dic3—22no—
108C5×Dic6—24no—
109C2×C3×Dic5—22no—
110C3×Dic10—24no—
111#1204—44no—
112#1200—44no—
113C3×#168—22no—
114C5×C3⋊C8—22no—
115C2×D3×Q8—52no—
116C3×C4⋊Q8—51no—
117C3×#125C2×D511yescharacteristic
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#870—51no—
128#869C2×D511yescharacteristic
129C3×#103—54no—
130C3×#97—51no—
131#835—54no—
132#816—54no—
133#815—52no—
134#810C2×D514yes—
135#803C2×D511yescharacteristic
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×C8—32no—
145C5×C4⋊C4—22no—
146C5×C4⋊C4—62no—
147C5×C4⋊C4C22×D312yes—
148C42×C5C22×D311yescharacteristic
149C4⋊Dic5—22no—
150C4⋊Dic5—32no—
151C4⋊Dic5—62no—
152#683—64no—
153#683—62no—
154#683—62no—
155#683—62no—
156C4×Dic5—32no—
157C4×Dic5—31no—
158C2×#168C22×D312yes—
159C8×D5—64no—
160C2×C4⋊Q8—151no—
161C2×#125—151no—
162#491—31no—
163#491—51no—
164#491—151no—
165#491—151no—
166#491—154no—
167C2×#103—154no—
168C2×#97—151no—
169C22×C3×C5C22×D411yescharacteristic
170C2×D15#12412yes—
171C2×D15#13714yes—
172C3×C4×C5—22no—
173C3×C4×C5—42no—
174C3×C4×C5C2×#4112yes—
175Dic15—22no—
176Dic15—42no—
177Dic15#12412yes—
178C3×Dic5—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×C8—52no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—102no—
191C3×C4⋊C4C22×D512yes—
192C3×C42C22×D511yescharacteristic
193C4⋊Dic3—22no—
194C4⋊Dic3—52no—
195C4⋊Dic3—102no—
196Dic3⋊C4—104no—
197Dic3⋊C4—102no—
198Dic3⋊C4—102no—
199Dic3⋊C4—102no—
200C4×Dic3—52no—
201C4×Dic3—51no—
202C2×C3⋊C8C22×D512yes—
203D3×C8—104no—
204C22×D5—31no—
205C5×Q8—64no—
206C2×C4×C5—22no—
207C2×C4×C5—62no—
208C2×C4×C5D3×D412yes—
209C2×C4×C5C23×D311yescharacteristic
210C2×Dic5—22no—
211C2×Dic5—31no—
212C2×Dic5—32no—
213C2×Dic5—62no—
214C4×D5—34no—
215C4×D5—64no—
216C4×D5—124no—
217C4×D5—124no—
218Dic10—24no—
219Dic10—124no—
220C5×C8—62no—
221#168—22no—
222C22×Q8—152no—
223C22×C8—152no—
224C4⋊Q8—31no—
225C4⋊Q8—51no—
226C4⋊Q8—152no—
227C4⋊Q8—302no—
228#125—152no—
229#125—151no—
230#125—302no—
231#125D3×D511yescharacteristic
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—31no—
241#97—51no—
242#97—152no—
243C2×C3×C5C2×#12411yescharacteristic
244C2×C3×C5C2×#13712yes—
245D15#49114yescomplemented
246C22×D3—51no—
247C3×Q8—104no—
248C2×C3×C4—22no—
249C2×C3×C4—102no—
250C2×C3×C4D4×D512yes—
251C2×C3×C4C23×D511yescharacteristic
252C2×Dic3—22no—
253C2×Dic3—51no—
254C2×Dic3—52no—
255C2×Dic3—102no—
256C4×D3—54no—
257C4×D3—104no—
258C4×D3—204no—
259C4×D3—204no—
260Dic6—24no—
261Dic6—204no—
262C3×C8—102no—
263C3⋊C8—22no—
264C22×C5C2×D3×D411yescharacteristic
265C2×D5—32no—
266C2×D5—34no—
267C4×C5—22no—
268C4×C5—42no—
269C4×C5—122no—
270C4×C5D3×#4112yes—
271Dic5—32no—
272Dic5—42no—
273Dic5—62no—
274Dic5—122no—
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—32no—
284C2×C8—52no—
285C2×C8—304no—
286C4⋊C4—22no—
287C4⋊C4—62no—
288C4⋊C4—102no—
289C4⋊C4—152no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—302no—
293C4⋊C4—304no—
294C4⋊C4—302no—
295C4⋊C4C2×D3×D512yes—
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—42no—
305C3×C4—202no—
306C3×C4D5×#4112yes—
307Dic3—42no—
308Dic3—52no—
309Dic3—102no—
310Dic3—202no—
311C2×C5D3×#12411yescharacteristic
312C2×C5D3×#13712yes—
313D5—34no—
314C23—151no—
315Q8—64no—
316Q8—104no—
317Q8—604no—
318C2×C4—22no—
319C2×C4—62no—
320C2×C4—102no—
321C2×C4—151no—
322C2×C4—154no—
323C2×C4—152no—
324C2×C4—304no—
325C2×C4—302no—
326C2×C4—604no—
327C2×C4—604no—
328C2×C4#679012yes—
329C2×C4C22×D3×D511yescharacteristic
330C8—62no—
331C8—102no—
332C2×C3D5×#12411yescharacteristic
333C2×C3D5×#13712yes—
334D3—54no—
335C5D3×#49111yescharacteristic, complemented, Sylow
336C22—152no—
337C22—154no—
338C22C2×#679011yescharacteristic
339C4—22no—
340C4—42no—
341C4—122no—
342C4—152no—
343C4—202no—
344C4—302no—
345C4—602no—
346C4#9203412yes—
347C3D5×#49111yescharacteristic, complemented, Sylow
348C2—154no—
349C2#1175528511yescharacteristic
350C2#1175534212yes—
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#125D3×D5
hypocenterC3×C5C2×#491
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C5×#5069C2semidirect
4. C3×#65358C2semidirect
6. #11747429C2semidirect
8. #11746931C2semidirect
9. #11746922C2semidirect
37. #65358D3semidirect
70. #5069D5semidirect
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
D15×#1252
#117525622
C5×#50692
C3×#653582
#117474902
#117474292
#117469832
#117469312
#117469222
D5×#4913
D3×#4915