Finite Group Databasebeta

← #14438719

Subgroups — #14438719

Order 1920.

784 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 156 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#11756484C211yesmaximal, characteristic
2#11752631C211yesmaximal, characteristic, complemented
3C5×#5082C211yesmaximal, characteristic, complemented
4C3×#65371C211yesmaximal, characteristic, complemented
5#11749205C214yesmaximal, complemented
6#11749190C214yesmaximal, complemented
7#11746915C211yesmaximal, characteristic, complemented
8#11746911C211yesmaximal, characteristic, complemented
9#11746844C211yesmaximal, characteristic, complemented
10#10613471—31nomaximal, Hall
11C2×#6821C2212yes—
12C3×C5×C4⋊Q8C2211yescharacteristic
13#91836C2212yes—
14#91784—22no—
15#91782—22no—
16#91763C2211yescharacteristic
17C42×D15C2211yescharacteristic
18C5×#870C2211yescharacteristic
19C3×#4016C2211yescharacteristic
20#91437C2212yes—
21#91404—22no—
22#91384C2212yes—
23#91382—22no—
24C2×#6651C2212yes—
25C5×#835C2214yes—
26C5×#803C2211yescharacteristic
27C3×#3967C2214yes—
28C3×#3935C2211yescharacteristic
29#90969C2214yes—
30#90968C2214yes—
31#90951C2212yes—
32#81740—51nomaximal, Hall
33#66059—31no—
34D5×#125—31no—
35C5×#491—31no—
36#65371D311yescharacteristic, complemented
37#65356—31no—
38#65092—34no—
39#65089—34no—
40#65002—31no—
41#64996—31no—
42C2×C3×C5×Q8C2312yes—
43#6821—28no—
44C2×D60—22no—
45C2×D60—22no—
46C2×D60C2312yes—
47C2×C4×D15—22no—
48C2×C4×D15D412yes—
49C2×C4×D15C2311yescharacteristic
50C2×#1200—22no—
51C3×C5×C4⋊C4—22no—
52C3×C42×C5C2311yescharacteristic
53#6714—24no—
54C4×Dic15D412yes—
55C4×Dic15C2311yescharacteristic
56C5×C4⋊Dic3C2312yes—
57C5×Dic3⋊C4—22no—
58C2×C5×C3⋊C8C2312yes—
59C3×C4⋊Dic5C2312yes—
60C3×#683—22no—
61C2×C3×#168C2312yes—
62Dic3⋊Dic5—22no—
63#6669—22no—
64#6668—22no—
65#6651—24no—
66#5725—51no—
67D3×#125—51no—
68C3×#491—51no—
69#5082D511yescharacteristic, complemented
70#5067—51no—
71#4803—54no—
72#4800—54no—
73#4713—51no—
74#4707—51no—
75C2×#713—32no—
76C5×C4⋊Q8C2×D311yescharacteristic
77C5×#125—31no—
78#4093—32no—
79C2×#676—32no—
80#4041—62no—
81#4039—62no—
82D5×C4⋊C4—32no—
83D5×C4⋊C4—62no—
84#4036—32no—
85#4035—62no—
86#4020—31no—
87C42×D5—31no—
88#4016C2×D311yescharacteristic
89C5×#103—34no—
90C5×#97—31no—
91#3967C2×D314yes—
92#3953—34no—
93C8×Dic5—32no—
94#3941—34no—
95#3935C2×D311yescharacteristic
96#3142—151noSylow
97C22×D15—22no—
98C22×D15C2×D411yescharacteristic
99C3×C5×Q8—24no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C2×D412yes—
102C2×C3×C4×C5C2411yescharacteristic
103C2×Dic15C2×D412yes—
104C2×Dic15C2×D411yescharacteristic
105D60—24no—
106D60—44no—
107D60—44no—
108C4×D15—42no—
109C4×D15—44no—
110C4×D15#4114yes—
111C2×C5×Dic3—22no—
112C2×C3×Dic5—22no—
113#1200—44no—
114C3×#168—22no—
115C5×C3⋊C8—22no—
116C2×#239—52no—
117C3×C4⋊Q8C2×D511yescharacteristic
118C3×#125—51no—
119#947—52no—
120C2×ΓL(1,𝔽25)—52no—
121#895—102no—
122#893—102no—
123D3×C4⋊C4—52no—
124D3×C4⋊C4—102no—
125#890—52no—
126#889—102no—
127#874—51no—
128C42×D3—51no—
129#870C2×D511yescharacteristic
130C3×#103—54no—
131C3×#97—51no—
132#835C2×D514yes—
133#821—54no—
134C8×Dic3—52no—
135#809—54no—
136#803C2×D511yescharacteristic
137C2×C5×Q8C22×D312yes—
138#713—68no—
139C2×D20—32no—
140C2×D20—62no—
141C2×D20—62no—
142C2×C4×D5—31no—
143C2×C4×D5—32no—
144C2×C4×D5—62no—
145C2×C4×D5—62no—
146C2×C5×C8—32no—
147C5×C4⋊C4—22no—
148C5×C4⋊C4—32no—
149C5×C4⋊C4—62no—
150C42×C5C22×D311yescharacteristic
151#685—64no—
152C4⋊Dic5—62no—
153C4⋊Dic5C22×D312yes—
154#683—22no—
155#683—62no—
156#683—62no—
157C4×Dic5—32no—
158C4×Dic5—31no—
159C2×#168C22×D312yes—
160#676—64no—
161#532—151no—
162C2×#125—151no—
163#491—31no—
164#491—51no—
165#490—151no—
166#490—151no—
167#488—154no—
168#417—154no—
169C4×M16—151no—
170C22×C3×C5C22×D411yescharacteristic
171C2×D15—22no—
172C2×D15—42no—
173C2×D15—44no—
174C2×D15#12412yes—
175C3×C4×C5—22no—
176C3×C4×C5—42no—
177C3×C4×C5C2×#4112yes—
178Dic15—22no—
179Dic15#12412yes—
180C3×Dic5—42no—
181C5×Dic3—42no—
182C2×C3×Q8C22×D512yes—
183#239—108no—
184C2×D12—52no—
185C2×D12—102no—
186C2×D12—102no—
187C2×C4×D3—51no—
188C2×C4×D3—52no—
189C2×C4×D3—102no—
190C2×C4×D3—102no—
191C2×C3×C8—52no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—52no—
194C3×C4⋊C4—102no—
195C3×C42C22×D511yescharacteristic
196(C2×D3)⋊C4—104no—
197C4⋊Dic3—102no—
198C4⋊Dic3C22×D512yes—
199Dic3⋊C4—22no—
200Dic3⋊C4—102no—
201Dic3⋊C4—102no—
202C4×Dic3—52no—
203C4×Dic3—51no—
204C2×C3⋊C8C22×D512yes—
205ΓL(1,𝔽25)—104no—
206C22×D5—31no—
207C22×D5—62no—
208C5×Q8—24no—
209C2×C4×C5—22no—
210C2×C4×C5—62no—
211C2×C4×C5D3×D412yes—
212C2×C4×C5C23×D311yescharacteristic
213C2×Dic5—22no—
214C2×Dic5—31no—
215C2×Dic5—32no—
216D20—64no—
217D20—124no—
218D20—124no—
219C4×D5—34no—
220C4×D5—124no—
221C4×D5—124no—
222C4×D5—122no—
223C5×C8—62no—
224#168—22no—
225C2×#41—152no—
226C2×M16—152no—
227C4⋊Q8D3×D511yescharacteristic
228#127—151no—
229#125—31no—
230#125—51no—
231#125—152no—
232#125—302no—
233#124—152no—
234#121—302no—
235C4×D4—302no—
236C2×C4⋊C4—152no—
237C2×C4⋊C4—302no—
238C2×C42—151no—
239#103—34no—
240#103—54no—
241#102—154no—
242#102—154no—
243#97—31no—
244#97—51no—
245C4×C8—152no—
246C2×C3×C5C2×#12411yescharacteristic
247C2×C3×C5#57512yes—
248D15—22no—
249D15—82no—
250C22×D3—51no—
251C22×D3—102no—
252C3×Q8—24no—
253C2×C3×C4—22no—
254C2×C3×C4—102no—
255C2×C3×C4D4×D512yes—
256C2×C3×C4C23×D511yescharacteristic
257C2×Dic3—22no—
258C2×Dic3—51no—
259C2×Dic3—52no—
260D12—104no—
261D12—204no—
262D12—204no—
263C4×D3—54no—
264C4×D3—204no—
265C4×D3—204no—
266C4×D3—202no—
267C3×C8—102no—
268C3⋊C8—22no—
269C22×C5C2×D3×D411yescharacteristic
270C2×D5—32no—
271C2×D5—62no—
272C2×D5—122no—
273C2×D5—124no—
274C4×C5—22no—
275C4×C5—42no—
276C4×C5—122no—
277C4×C5D3×#4112yes—
278Dic5—32no—
279Dic5—42no—
280Dic5—62no—
281#41—308no—
282C2×Q8C2×D3×D512yes—
283C2×D4—152no—
284C2×D4—302no—
285C2×D4—302no—
286C22×C4—151no—
287C22×C4—152no—
288C22×C4—302no—
289C22×C4—302no—
290M16—304no—
291C2×C8—32no—
292C2×C8—52no—
293C4⋊C4—22no—
294C4⋊C4—32no—
295C4⋊C4—52no—
296C4⋊C4—62no—
297C4⋊C4—102no—
298C4⋊C4—302no—
299C4⋊C4—302no—
300C4⋊C4—302no—
301C22⋊C4—304no—
302C42—152no—
303C42—151no—
304C42C2×D3×D511yescharacteristic
305C3×C5#314211yescharacteristic, complemented, Hall
306C22×C3C2×D4×D511yescharacteristic
307C2×D3—52no—
308C2×D3—102no—
309C2×D3—204no—
310C2×D3—202no—
311C3×C4—22no—
312C3×C4—42no—
313C3×C4—202no—
314C3×C4D5×#4112yes—
315Dic3—42no—
316Dic3—52no—
317Dic3—102no—
318C2×C5D3×#12411yescharacteristic
319C2×C5#577712yes—
320D5—62no—
321D5—242no—
322C23—151no—
323C23—302no—
324Q8—24no—
325D4—304no—
326D4—604no—
327D4—604no—
328C2×C4—22no—
329C2×C4—62no—
330C2×C4—102no—
331C2×C4—151no—
332C2×C4—154no—
333C2×C4—152no—
334C2×C4—602no—
335C2×C4—604no—
336C2×C4—604no—
337C2×C4#679012yes—
338C2×C4C22×D3×D511yescharacteristic
339C8—62no—
340C8—102no—
341C2×C3D5×#12411yescharacteristic
342C2×C3#6611112yes—
343D3—102no—
344D3—402no—
345C5#8174011yescharacteristic, complemented, Sylow
346C22—152no—
347C22—302no—
348C22—602no—
349C22—604no—
350C22C2×#679011yescharacteristic
351C4—22no—
352C4—42no—
353C4—122no—
354C4—152no—
355C4—202no—
356C4—302no—
357C4#9202412yes—
358C3#1061347111yescharacteristic, complemented, Sylow
359C2—302no—
360C2—1202no—
361C2#1175483111yescharacteristic
362C2#1175509612yes—
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11756484C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11752631C2semidirect
3. C5×#5082C2semidirect
4. C3×#65371C2semidirect
5. #11749205C2semidirect
6. #11749190C2semidirect
7. #11746915C2semidirect
8. #11746911C2semidirect
9. #11746844C2semidirect
36. #65371D3semidirect
69. #5082D5semidirect
305. C3×C5#3142semidirect
345. C5#81740semidirect
358. C3#10613471semidirect

Maximal subgroups

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

subgroupindex
#117564842
#117526312
C5×#50822
C3×#653712
#117492052
#117491902
#117469152
#117469112
#117468442
#106134713
#817405