Finite Group Databasebeta

← #14438654

Subgroups — #14438654

Order 1920.

784 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 167 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#11756475C211yesmaximal, characteristic
2D15×#125C211yesmaximal, characteristic, complemented
3C3×C5×#490C211yesmaximal, characteristic, complemented
4#11751172C211yesmaximal, characteristic, complemented
5#11751170C211yesmaximal, characteristic, complemented
6#11750872C214yesmaximal, complemented
7#11750869C214yesmaximal, complemented
8#11750808C211yesmaximal, characteristic, complemented
9#11750804C211yesmaximal, characteristic, complemented
10#10613447—31nomaximal, Hall
11C2×#6819C2212yes—
12C3×C5×#127C2211yescharacteristic
13C3×C5×#125C2211yescharacteristic
14#91827—22no—
15#91825C2212yes—
16D4×Dic15—22no—
17C2×#6705C2212yes—
18C4⋊C4×D15—22no—
19C4⋊C4×D15C2212yes—
20#91779C2212yes—
21#91778—22no—
22C42×D15C2211yescharacteristic
23#91759C2211yescharacteristic
24#91758C2211yescharacteristic
25C3×C5×#102C2214yes—
26C3×C5×#97C2211yescharacteristic
27#91116C2214yes—
28#91100C2214yes—
29C8×Dic15C2212yes—
30#91094C2214yes—
31#91087C2211yescharacteristic
32#81716—51nomaximal, Hall
33#66050—31no—
34D5×#125—31no—
35C5×#490D311yescharacteristic, complemented
36#65360—31no—
37#65358—31no—
38#65060—34no—
39#65057—34no—
40#64996—31no—
41#64992—31no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4C2312yes—
44C2×#1220—22no—
45C22×Dic15—22no—
46#6819—28no—
47C2×C4×D15—22no—
48C2×C4×D15D412yes—
49C2×C4×D15C2311yescharacteristic
50C2×Dic30C2312yes—
51C2×C3×C5×C8C2312yes—
52C3×C5×C4⋊C4—22no—
53C3×C5×C4⋊C4C2312yes—
54C3×C42×C5C2311yescharacteristic
55#6719—24no—
56C4⋊Dic15—22no—
57C4⋊Dic15—22no—
58C4⋊Dic15C2312yes—
59#6712—22no—
60#6712—22no—
61#6712—22no—
62C4×Dic15D412yes—
63C4×Dic15C2311yescharacteristic
64C2×C3⋊#168C2312yes—
65#6705—24no—
66#5716—51no—
67D3×#125—51no—
68C3×#490D511yescharacteristic, complemented
69#5071—51no—
70#5069—51no—
71#4771—54no—
72#4768—54no—
73#4707—51no—
74#4703—51no—
75C2×#711—32no—
76C5×#127C2×D311yescharacteristic
77C5×#125C2×D311yescharacteristic
78#4084—62no—
79#4082—32no—
80D4×Dic5—62no—
81C2×#676—32no—
82D5×C4⋊C4—32no—
83D5×C4⋊C4—62no—
84#4036—32no—
85#4035—62no—
86C42×D5—31no—
87#4016—31no—
88#4015—31no—
89C5×#102C2×D314yes—
90C5×#97C2×D311yescharacteristic
91#3964—34no—
92#3948—34no—
93C8×Dic5—32no—
94#3942—34no—
95#3935—31no—
96#3142—151noSylow
97C23×C3×C5—22no—
98C22×D15C2×D411yescharacteristic
99C3×C5×D4—24no—
100C3×C5×D4—44no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5C2×D412yes—
103C2×C3×C4×C5C2411yescharacteristic
104#1220—44no—
105C2×Dic15—22no—
106C2×Dic15—22no—
107C2×Dic15—44no—
108C2×Dic15C2×D412yes—
109C2×Dic15C2×D411yescharacteristic
110C4×D15—42no—
111C4×D15—44no—
112C4×D15#4114yes—
113Dic30—24no—
114C3×C5×C8—22no—
115C3⋊#168—22no—
116C2×#237—52no—
117C3×#127C2×D511yescharacteristic
118C3×#125C2×D511yescharacteristic
119#938—102no—
120#936—52no—
121D4×Dic3—102no—
122C2×ΓL(1,𝔽25)—52no—
123D3×C4⋊C4—52no—
124D3×C4⋊C4—102no—
125#890—52no—
126#889—102no—
127C42×D3—51no—
128#870—51no—
129#869—51no—
130C3×#102C2×D514yes—
131C3×#97C2×D511yescharacteristic
132#832—54no—
133#816—54no—
134C8×Dic3—52no—
135#810—54no—
136#803—51no—
137C2×C5×D4—22no—
138C2×C5×D4C22×D312yes—
139C2×C22⋊D5—62no—
140C22×Dic5—62no—
141#711—68no—
142C2×C4×D5—31no—
143C2×C4×D5—32no—
144C2×C4×D5—62no—
145C2×Dic10—32no—
146C2×C5×C8C22×D312yes—
147C5×C4⋊C4—22no—
148C5×C4⋊C4C22×D312yes—
149C42×C5C22×D311yescharacteristic
150C22⋊Dic5—64no—
151C4⋊Dic5—32no—
152C4⋊Dic5—62no—
153C4⋊Dic5—62no—
154#683—62no—
155#683—62no—
156#683—62no—
157C4×Dic5—32no—
158C4×Dic5—31no—
159C2×#168—32no—
160#676—64no—
161#532—151no—
162C2×#125—151no—
163#491—151no—
164#491—151no—
165#490—151no—
166#490D1511yescharacteristic, complemented
167#488—154no—
168#417—154no—
169C4×M16—151no—
170C22×C3×C5—42no—
171C22×C3×C5—44no—
172C22×C3×C5C22×D411yescharacteristic
173C2×D15—22no—
174C2×D15#12412yes—
175C3×C4×C5—22no—
176C3×C4×C5—42no—
177C3×C4×C5C2×#4112yes—
178Dic15—22no—
179Dic15—42no—
180Dic15—42no—
181Dic15#12412yes—
182C2×C3×D4—22no—
183C2×C3×D4C22×D512yes—
184C2×#67—102no—
185C22×Dic3—102no—
186#237—108no—
187C2×C4×D3—51no—
188C2×C4×D3—52no—
189C2×C4×D3—102no—
190C2×Dic6—52no—
191C2×C3×C8C22×D512yes—
192C3×C4⋊C4—22no—
193C3×C4⋊C4C22×D512yes—
194C3×C42C22×D511yescharacteristic
195#217—104no—
196C4⋊Dic3—52no—
197C4⋊Dic3—102no—
198C4⋊Dic3—102no—
199Dic3⋊C4—102no—
200Dic3⋊C4—102no—
201Dic3⋊C4—102no—
202C4×Dic3—52no—
203C4×Dic3—51no—
204C2×C3⋊C8—52no—
205ΓL(1,𝔽25)—104no—
206C23×C5—22no—
207C22×D5—31no—
208C5×D4—24no—
209C5×D4—44no—
210C2×C4×C5—22no—
211C2×C4×C5D3×D412yes—
212C2×C4×C5C23×D311yescharacteristic
213C22⋊D5—124no—
214C2×Dic5—31no—
215C2×Dic5—32no—
216C2×Dic5—62no—
217C2×Dic5—62no—
218C2×Dic5—124no—
219C4×D5—34no—
220C4×D5—122no—
221C4×D5—124no—
222Dic10—64no—
223C5×C8—22no—
224#168—62no—
225C2×#41—152no—
226C2×M16—152no—
227C4⋊Q8—151no—
228#127C2×D1511yescharacteristic
229#125—152no—
230#125—151no—
231#125—302no—
232#125C2×D1511yescharacteristic
233#124—152no—
234#121—302no—
235C4×D4—302no—
236C2×C4⋊C4—152no—
237C2×C4⋊C4—302no—
238C2×C42—151no—
239#103—154no—
240#103—154no—
241#102—154no—
242#102C2×D1514yes—
243#97—151no—
244#97C2×D1511yescharacteristic
245C4×C8—152no—
246C2×C3×C5—82no—
247C2×C3×C5C2×#12411yescharacteristic
248C2×C3×C5#57512yes—
249D15—22no—
250C23×C3—22no—
251C22×D3—51no—
252C3×D4—24no—
253C3×D4—44no—
254C2×C3×C4—22no—
255C2×C3×C4D4×D512yes—
256C2×C3×C4C23×D511yescharacteristic
257#67—204no—
258C2×Dic3—51no—
259C2×Dic3—52no—
260C2×Dic3—102no—
261C2×Dic3—102no—
262C2×Dic3—204no—
263C4×D3—54no—
264C4×D3—202no—
265C4×D3—204no—
266Dic6—104no—
267C3×C8—22no—
268C3⋊C8—102no—
269C22×C5—42no—
270C22×C5—44no—
271C22×C5C2×D3×D411yescharacteristic
272C2×D5—32no—
273C2×D5—62no—
274C4×C5—22no—
275C4×C5—42no—
276C4×C5D3×#4112yes—
277Dic5—32no—
278Dic5—62no—
279Dic5—122no—
280Dic5—122no—
281#41—308no—
282C2×Q8—152no—
283C2×D4—22no—
284C2×D4—302no—
285C2×D4C22×D1512yes—
286C22×C4—151no—
287C22×C4—152no—
288C22×C4—302no—
289C22×C4—302no—
290M16—304no—
291C2×C8—152no—
292C2×C8C22×D1512yes—
293C4⋊C4—22no—
294C4⋊C4—152no—
295C4⋊C4—302no—
296C4⋊C4—302no—
297C4⋊C4—302no—
298C4⋊C4—302no—
299C4⋊C4—302no—
300C4⋊C4C22×D1512yes—
301C22⋊C4—304no—
302C42—152no—
303C42—151no—
304C42C22×D1511yescharacteristic
305C3×C5#314211yescharacteristic, complemented, Hall
306C22×C3—44no—
307C22×C3—42no—
308C22×C3C2×D4×D511yescharacteristic
309C2×D3—52no—
310C2×D3—102no—
311C3×C4—22no—
312C3×C4—42no—
313C3×C4D5×#4112yes—
314Dic3—52no—
315Dic3—102no—
316Dic3—202no—
317Dic3—202no—
318C2×C5—82no—
319C2×C5D3×#12411yescharacteristic
320C2×C5#577312yes—
321D5—62no—
322C23—22no—
323C23—151no—
324Q8—304no—
325D4—24no—
326D4—44no—
327D4—604no—
328C2×C4—22no—
329C2×C4—151no—
330C2×C4—154no—
331C2×C4—152no—
332C2×C4—302no—
333C2×C4—302no—
334C2×C4—602no—
335C2×C4—604no—
336C2×C4—604no—
337C2×C4D4×D1512yes—
338C2×C4C23×D1511yescharacteristic
339C8—22no—
340C8—302no—
341C2×C3—82no—
342C2×C3D5×#12411yescharacteristic
343C2×C3#6610712yes—
344D3—102no—
345C5#8171611yescharacteristic, complemented, Sylow
346C22—42no—
347C22—44no—
348C22—152no—
349C22—302no—
350C22C2×D4×D1511yescharacteristic
351C4—22no—
352C4—42no—
353C4—152no—
354C4—302no—
355C4—602no—
356C4—602no—
357C4#41×D1512yes—
358C3#1061344711yescharacteristic, complemented, Sylow
359C2—82no—
360C2—302no—
361C2D15×#12411yescharacteristic
362C2#1175653212yes—
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#490C2
socleC22×C3×C5C22×D4
prime radical#11756475C2
hypercenter#490D15
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. D15×#125C2semidirect
3. C3×C5×#490C2semidirect
4. #11751172C2semidirect
5. #11751170C2semidirect
6. #11750872C2semidirect
7. #11750869C2semidirect
8. #11750808C2semidirect
9. #11750804C2semidirect
35. C5×#490D3semidirect
68. C3×#490D5semidirect
166. #490D15semidirect
305. C3×C5#3142semidirect
345. C5#81716semidirect
358. C3#10613447semidirect

Maximal subgroups

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

subgroupindex
#117564752
D15×#1252
C3×C5×#4902
#117511722
#117511702
#117508722
#117508692
#117508082
#117508042
#106134473
#817165