Finite Group Databasebeta

← #14438006

Subgroups — #14438006

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#11756484C211yesmaximal, characteristic
2#11756447C211yesmaximal, characteristic, complemented
3C3×C5×#491C211yesmaximal, characteristic, complemented
4#11751183C211yesmaximal, characteristic, complemented
5#11751168C211yesmaximal, characteristic, complemented
6#11750905C214yesmaximal, complemented
7#11750895C214yesmaximal, complemented
8#11750814C211yesmaximal, characteristic, complemented
9D15×#97C211yesmaximal, characteristic, complemented
10#10613468—31nomaximal, Hall
11C2×#6821C2212yes—
12C3×C5×C4⋊Q8C2211yescharacteristic
13C3×C5×#125C2211yescharacteristic
14#91836C2212yes—
15C2×C8×D15C2212yes—
16#91785—22no—
17#91784—22no—
18#91782—22no—
19#91781C2212yes—
20#91777C2212yes—
21#91776—22no—
22#91763C2211yescharacteristic
23C42×D15C2211yescharacteristic
24#91759C2211yescharacteristic
25C3×C5×#103C2214yes—
26C3×C5×#97C2211yescharacteristic
27#91119C2214yes—
28#91105C2214yes—
29#91099C2212yes—
30#91093C2214yes—
31#91087C2211yescharacteristic
32#81737—51nomaximal, Hall
33#66059—31no—
34#66022—31no—
35C5×#491D311yescharacteristic, complemented
36#65371—31no—
37#65356—31no—
38#65093—34no—
39#65084—34no—
40#65002—31no—
41D5×#97—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×Dic30—22no—
51C2×C3×C5×C8C2312yes—
52C3×C5×C4⋊C4—22no—
53C3×C5×C4⋊C4—22no—
54C3×C5×C4⋊C4C2312yes—
55C3×C42×C5C2311yescharacteristic
56#6714—22no—
57#6714—24no—
58C4⋊Dic15C2312yes—
59#6712—22no—
60#6712—22no—
61C4×Dic15—22no—
62C4×Dic15D412yes—
63C4×Dic15C2311yescharacteristic
64C2×C3⋊#168C2312yes—
65C8×D15—24no—
66#5725—51no—
67#5688—51no—
68C3×#491D511yescharacteristic, complemented
69#5082—51no—
70#5067—51no—
71#4804—54no—
72#4794—54no—
73#4713—51no—
74D3×#97—51no—
75C2×#713—32no—
76C5×C4⋊Q8C2×D311yescharacteristic
77C5×#125C2×D311yescharacteristic
78#4093—32no—
79C2×C8×D5—32no—
80#4042—62no—
81#4041—62no—
82#4039—62no—
83#4038—32no—
84#4034—32no—
85#4033—62no—
86#4020—31no—
87C42×D5—31no—
88#4016—31no—
89C5×#103C2×D314yes—
90C5×#97C2×D311yescharacteristic
91#3967—34no—
92#3953—34no—
93#3947—32no—
94#3941—34no—
95#3935—31no—
96#3135—151noSylow
97C22×D15—22no—
98C22×D15C2×D411yescharacteristic
99C3×C5×Q8—24no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5C2×D412yes—
103C2×C3×C4×C5C2411yescharacteristic
104C2×Dic15—22no—
105C2×Dic15C2×D412yes—
106C2×Dic15C2×D411yescharacteristic
107D60—24no—
108D60—44no—
109D60—44no—
110C4×D15—42no—
111C4×D15—44no—
112C4×D15#4114yes—
113Dic30—44no—
114C3×C5×C8—22no—
115C3⋊#168—22no—
116C2×#239—52no—
117C3×C4⋊Q8C2×D511yescharacteristic
118C3×#125C2×D511yescharacteristic
119#947—52no—
120C2×D3×C8—52no—
121#896—102no—
122#895—102no—
123#893—102no—
124#892—52no—
125#888—52no—
126#887—102no—
127#874—51no—
128C42×D3—51no—
129#870—51no—
130C3×#103C2×D514yes—
131C3×#97C2×D511yescharacteristic
132#835—54no—
133#821—54no—
134#815—52no—
135#809—54no—
136#803—51no—
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×Dic10—62no—
146C2×C5×C8C22×D312yes—
147C5×C4⋊C4—22no—
148C5×C4⋊C4—22no—
149C5×C4⋊C4C22×D312yes—
150C42×C5C22×D311yescharacteristic
151#685—64no—
152#685—62no—
153C4⋊Dic5—32no—
154#683—62no—
155#683—62no—
156C4×Dic5—32no—
157C4×Dic5—31no—
158C4×Dic5—62no—
159C2×#168—32no—
160C8×D5—64no—
161#533—151no—
162#532—151no—
163#491—151no—
164#491D1511yescharacteristic, complemented
165#490—151no—
166#490—151no—
167#489—154no—
168#416—154no—
169C2×#97—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×C5—42no—
178C3×C4×C5C2×#4112yes—
179Dic15—22no—
180Dic15—42no—
181Dic15#12412yes—
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×Dic6—102no—
191C2×C3×C8C22×D512yes—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4C22×D512yes—
195C3×C42C22×D511yescharacteristic
196(C2×D3)⋊C4—104no—
197(C2×D3)⋊C4—102no—
198C4⋊Dic3—52no—
199Dic3⋊C4—102no—
200Dic3⋊C4—102no—
201C4×Dic3—52no—
202C4×Dic3—51no—
203C4×Dic3—102no—
204C2×C3⋊C8—52no—
205D3×C8—104no—
206C22×D5—31no—
207C22×D5—62no—
208C5×Q8—24no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5D3×D412yes—
212C2×C4×C5C23×D311yescharacteristic
213C2×Dic5—31no—
214C2×Dic5—32no—
215C2×Dic5—62no—
216D20—64no—
217D20—124no—
218D20—124no—
219C4×D5—34no—
220C4×D5—124no—
221C4×D5—122no—
222Dic10—124no—
223C5×C8—22no—
224#168—62no—
225C2×#41—152no—
226C22×C8—152no—
227C4⋊Q8—152no—
228C4⋊Q8C2×D1511yescharacteristic
229#127—151no—
230#125—151no—
231#125C2×D1511yescharacteristic
232#124—152no—
233C22⋊Q8—302no—
234#121—302no—
235C4×Q8—302no—
236C4×D4—302no—
237#117—152no—
238C2×C42—151no—
239#103—154no—
240#103C2×D1514yes—
241#102—154no—
242#102—154no—
243#97—152no—
244#97—151no—
245#97C2×D1511yescharacteristic
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—22no—
255C2×C3×C4D4×D512yes—
256C2×C3×C4C23×D511yescharacteristic
257C2×Dic3—51no—
258C2×Dic3—52no—
259C2×Dic3—102no—
260D12—104no—
261D12—204no—
262D12—204no—
263C4×D3—54no—
264C4×D3—204no—
265C4×D3—202no—
266Dic6—204no—
267C3×C8—22no—
268C3⋊C8—102no—
269C22×C5C2×D3×D411yescharacteristic
270C2×D5—32no—
271C2×D5—62no—
272C2×D5—122no—
273C2×D5—124no—
274C4×C5—22no—
275C4×C5—42no—
276C4×C5—42no—
277C4×C5D3×#4112yes—
278Dic5—32no—
279Dic5—62no—
280Dic5—122no—
281#41—308no—
282C2×Q8—302no—
283C2×Q8C22×D1512yes—
284C2×D4—152no—
285C2×D4—302no—
286C2×D4—302no—
287C22×C4—151no—
288C22×C4—152no—
289C22×C4—302no—
290C2×C8—152no—
291C2×C8—304no—
292C2×C8C22×D1512yes—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—152no—
296C4⋊C4—302no—
297C4⋊C4—302no—
298C4⋊C4C22×D1512yes—
299C22⋊C4—304no—
300C22⋊C4—302no—
301C42—152no—
302C42—151no—
303C42—302no—
304C42C22×D1511yescharacteristic
305C3×C5#313511yescharacteristic, 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—42no—
314C3×C4D5×#4112yes—
315Dic3—52no—
316Dic3—102no—
317Dic3—202no—
318C2×C5D3×#12411yescharacteristic
319C2×C5#577712yes—
320D5—62no—
321D5—242no—
322C23—151no—
323C23—302no—
324Q8—24no—
325Q8—604no—
326D4—304no—
327D4—604no—
328D4—604no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—151no—
332C2×C4—154no—
333C2×C4—152no—
334C2×C4—302no—
335C2×C4—602no—
336C2×C4—604no—
337C2×C4D4×D1512yes—
338C2×C4C23×D1511yescharacteristic
339C8—22no—
340C8—302no—
341C2×C3D5×#12411yescharacteristic
342C2×C3#6611112yes—
343D3—102no—
344D3—402no—
345C5#8173711yescharacteristic, complemented, Sylow
346C22—152no—
347C22—302no—
348C22—602no—
349C22—604no—
350C22C2×D4×D1511yescharacteristic
351C4—22no—
352C4—42no—
353C4—42no—
354C4—152no—
355C4—302no—
356C4—602no—
357C4#41×D1512yes—
358C3#1061346811yescharacteristic, complemented, Sylow
359C2—302no—
360C2—1202no—
361C2D15×#12411yescharacteristic
362C2#1175653612yes—
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#491C2
socleC22×C3×C5C22×D4
prime radical#11756484C2
hypercenter#491D15
hypocenterC3×C5#3135
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #11756447C2semidirect
3. C3×C5×#491C2semidirect
4. #11751183C2semidirect
5. #11751168C2semidirect
6. #11750905C2semidirect
7. #11750895C2semidirect
8. #11750814C2semidirect
9. D15×#97C2semidirect
35. C5×#491D3semidirect
68. C3×#491D5semidirect
164. #491D15semidirect
305. C3×C5#3135semidirect
345. C5#81737semidirect
358. C3#10613468semidirect

Maximal subgroups

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

subgroupindex
#117564842
#117564472
C3×C5×#4912
#117511832
#117511682
#117509052
#117508952
#117508142
D15×#972
#106134683
#817375