Finite Group Databasebeta

← #14438718

Subgroups — #14438718

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66059C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic, complemented
3#11751183C211yesmaximal, characteristic, complemented
4C5×#5082C211yesmaximal, characteristic, complemented
5#11749331C214yesmaximal, complemented
6#11749198C214yesmaximal, complemented
7#11747003C211yesmaximal, characteristic, complemented
8#11746897C211yesmaximal, characteristic, complemented
9#11746892C211yesmaximal, characteristic, complemented
10#10613471—31nomaximal, Hall
11C2×C3×#713C2212yes—
12C3×C5×C4⋊Q8C2211yescharacteristic
13#91759C2211yescharacteristic
14C5×#870C2211yescharacteristic
15C3×#4093C2212yes—
16C3×#4041—22no—
17C3×#4039—22no—
18C3×#4020C2211yescharacteristic
19C3×C42×D5C2211yescharacteristic
20D5×C4⋊Dic3C2212yes—
21D5×Dic3⋊C4—22no—
22#91388C2212yes—
23#91378—22no—
24C2×#6649C2212yes—
25#91119C2214yes—
26#91087C2211yescharacteristic
27C5×#835C2214yes—
28C5×#803C2211yescharacteristic
29#90965C2214yes—
30#90964C2214yes—
31Dic5×C3⋊C8C2212yes—
32#83284—51nomaximal, Hall
33#66059D311yescharacteristic
34D5×#125—31no—
35C5×#491—31no—
36#65371—31no—
37#65356—31no—
38#65092—34no—
39#65089—34no—
40#65002—31no—
41#64996—31no—
42C2×C3×C5×Q8C2312yes—
43C3×#713—28no—
44C2×C3×D20—22no—
45C2×C3×D20—22no—
46C2×C3×D20C2312yes—
47C2×C3×C4×D5—22no—
48C2×C3×C4×D5D412yes—
49C2×C3×C4×D5C2311yescharacteristic
50C2×D5×Dic3—22no—
51C3×C5×C4⋊C4—22no—
52C3×C42×C5C2311yescharacteristic
53C4⋊Dic15C2312yes—
54#6712—22no—
55C2×C3⋊#168C2312yes—
56C5×C4⋊Dic3C2312yes—
57C5×Dic3⋊C4—22no—
58C2×C5×C3⋊C8C2312yes—
59C3×#685—24no—
60C3×C4×Dic5D412yes—
61C3×C4×Dic5C2311yescharacteristic
62Dic3⋊Dic5—22no—
63#6669—22no—
64#6668—22no—
65#6649—24no—
66C3×#532—51no—
67C2×#870—51no—
68#5232—54no—
69#5082—51no—
70#5082D511yescharacteristic, complemented
71#5071—51no—
72#5071—51no—
73#5056—54no—
74C4×#208—51no—
75C2×#713C2×D312yes—
76C5×C4⋊Q8C2×D311yescharacteristic
77C5×#125—31no—
78#4093C2×D312yes—
79C2×#676—32no—
80#4041—22no—
81#4039—22no—
82D5×C4⋊C4—32no—
83D5×C4⋊C4—62no—
84#4036—32no—
85#4035—62no—
86#4020C2×D311yescharacteristic
87C42×D5C2×D311yescharacteristic
88#4016—31no—
89C5×#103—34no—
90C5×#97—31no—
91#3967—34no—
92#3953—34no—
93C8×Dic5—32no—
94#3941—34no—
95#3935—31no—
96#3142—151noSylow
97C22×C3×D5—22no—
98C22×C3×D5C2×D411yescharacteristic
99C3×C5×Q8—24no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C2×D412yes—
102C2×C3×C4×C5C2411yescharacteristic
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C2×C3×Dic5C2×D412yes—
106C2×C3×Dic5C2×D411yescharacteristic
107C3×D20—24no—
108C3×D20—44no—
109C3×D20—44no—
110C3×C4×D5—42no—
111C3×C4×D5—44no—
112C3×C4×D5#4114yes—
113D5×Dic3—44no—
114C3⋊#168—22no—
115C5×C3⋊C8—22no—
116C2×C3×#41—52no—
117C3×C4⋊Q8C2×D511yescharacteristic
118C3×#127—51no—
119C3×#124—52no—
120C3×#121—102no—
121C3×C4×D4—102no—
122C2×C3×C42—51no—
123C2×C4⋊Dic3—52no—
124C2×Dic3⋊C4—102no—
125C2×#208—52no—
126#870—51no—
127#870—52no—
128#870—102no—
129#870C2×D511yescharacteristic
130#835—54no—
131#835C2×D514yes—
132#832—54no—
133#832—54no—
134#803—51no—
135#803C2×D511yescharacteristic
136C4×C3⋊C8—52no—
137C2×C5×Q8C22×D312yes—
138#713—28no—
139C2×D20—22no—
140C2×D20—22no—
141C2×D20C22×D312yes—
142C2×C4×D5—22no—
143C2×C4×D5—62no—
144C2×C4×D5#6712yes—
145C2×C4×D5C22×D311yescharacteristic
146C2×C5×C8—32no—
147C5×C4⋊C4—22no—
148C5×C4⋊C4—32no—
149C5×C4⋊C4—62no—
150C42×C5C22×D311yescharacteristic
151#685—24no—
152C4⋊Dic5—32no—
153C4⋊Dic5—62no—
154#683—62no—
155#683—62no—
156#683—62no—
157C4×Dic5#6712yes—
158C4×Dic5C22×D311yescharacteristic
159C2×#168—32no—
160#676—64no—
161#532—51no—
162C2×#125—151no—
163#491—31no—
164#491—151no—
165#490—151no—
166#490—151no—
167#488—154no—
168#417—154no—
169C4×M16—151no—
170C22×C3×C5C22×D411yescharacteristic
171C2×C3×D5—22no—
172C2×C3×D5—42no—
173C2×C3×D5—44no—
174C2×C3×D5#12412yes—
175C3×C4×C5—22no—
176C3×C4×C5—42no—
177C3×C4×C5C2×#4112yes—
178Dic15—42no—
179C3×Dic5—22no—
180C3×Dic5#12412yes—
181C5×Dic3—42no—
182C3×#41—108no—
183C2×C3×Q8C22×D512yes—
184C2×C3×D4—52no—
185C2×C3×D4—102no—
186C2×C3×D4—102no—
187C22×C3×C4—51no—
188C22×C3×C4—52no—
189C22×C3×C4—102no—
190C22×Dic3—102no—
191C3×C4⋊C4—22no—
192C3×C22⋊C4—104no—
193C3×C42—52no—
194C3×C42—51no—
195C3×C42C22×D511yescharacteristic
196C4⋊Dic3—52no—
197C4⋊Dic3—102no—
198C4⋊Dic3C22×D512yes—
199Dic3⋊C4—22no—
200Dic3⋊C4—102no—
201Dic3⋊C4—102no—
202Dic3⋊C4—102no—
203#208—104no—
204C2×C3⋊C8—52no—
205C2×C3⋊C8C22×D512yes—
206C22×D5—22no—
207C22×D5C2×#6711yescharacteristic
208C5×Q8—24no—
209C2×C4×C5—22no—
210C2×C4×C5—62no—
211C2×C4×C5C2×#6712yes—
212C2×C4×C5C23×D311yescharacteristic
213C2×Dic5—62no—
214C2×Dic5C2×#6712yes—
215C2×Dic5C2×#6711yescharacteristic
216D20—24no—
217D20—44no—
218D20—44no—
219C4×D5—42no—
220C4×D5—44no—
221C4×D5—124no—
222C4×D5#23714yes—
223C5×C8—62no—
224#168—62no—
225C2×#41—52no—
226C2×M16—152no—
227C4⋊Q8D3×D511yescharacteristic
228#127—51no—
229#125—31no—
230#125—152no—
231#125—151no—
232#125—302no—
233#124—52no—
234#121—102no—
235C4×D4—102no—
236C2×C4⋊C4—152no—
237C2×C4⋊C4—302no—
238C2×C42—51no—
239#103—34no—
240#103—154no—
241#102—154no—
242#102—154no—
243#97—31no—
244#97—151no—
245C4×C8—152no—
246C2×C3×C5C2×#12411yescharacteristic
247C2×C3×C5#57512yes—
248C3×D5—22no—
249C3×D5—82no—
250C23×C3—51no—
251C23×C3—102no—
252C3×Q8—24no—
253C3×D4—104no—
254C3×D4—204no—
255C3×D4—204no—
256C2×C3×C4—22no—
257C2×C3×C4—51no—
258C2×C3×C4—54no—
259C2×C3×C4—52no—
260C2×C3×C4—202no—
261C2×C3×C4—204no—
262C2×C3×C4D4×D512yes—
263C2×C3×C4C23×D511yescharacteristic
264C2×Dic3—22no—
265C2×Dic3—102no—
266C2×Dic3—204no—
267C3⋊C8—22no—
268C3⋊C8—102no—
269C22×C5C22×#6711yescharacteristic
270C2×D5—22no—
271C2×D5—42no—
272C2×D5—44no—
273C2×D5#93612yes—
274C4×C5—22no—
275C4×C5—42no—
276C4×C5—122no—
277C4×C5C2×#23712yes—
278Dic5—22no—
279Dic5—122no—
280Dic5#93612yes—
281#41—108no—
282C2×Q8C2×D3×D512yes—
283C2×D4—52no—
284C2×D4—102no—
285C2×D4—102no—
286C22×C4—51no—
287C22×C4—52no—
288C22×C4—102no—
289C22×C4—302no—
290M16—304no—
291C2×C8—32no—
292C2×C8—152no—
293C4⋊C4—22no—
294C4⋊C4—32no—
295C4⋊C4—62no—
296C4⋊C4—152no—
297C4⋊C4—302no—
298C4⋊C4—302no—
299C4⋊C4—302no—
300C4⋊C4—302no—
301C22⋊C4—104no—
302C42—52no—
303C42—51no—
304C42C2×D3×D511yescharacteristic
305C3×C5#314211yescharacteristic, complemented, Hall
306C22×C3—52no—
307C22×C3—102no—
308C22×C3—204no—
309C22×C3—202no—
310C22×C3C2×D4×D511yescharacteristic
311C3×C4—22no—
312C3×C4—42no—
313C3×C4—52no—
314C3×C4—102no—
315C3×C4D5×#4112yes—
316Dic3—42no—
317Dic3—202no—
318C2×C5C2×#93611yescharacteristic
319C2×C5#582212yes—
320D5—22no—
321D5—82no—
322C23—51no—
323C23—102no—
324Q8—24no—
325D4—104no—
326D4—204no—
327D4—204no—
328C2×C4—22no—
329C2×C4—51no—
330C2×C4—54no—
331C2×C4—52no—
332C2×C4—62no—
333C2×C4—202no—
334C2×C4—204no—
335C2×C4—302no—
336C2×C4—604no—
337C2×C4D5×#6712yes—
338C2×C4C22×D3×D511yescharacteristic
339C8—62no—
340C8—302no—
341C2×C3—102no—
342C2×C3—402no—
343C2×C3D5×#12411yescharacteristic
344C2×C3#6611112yes—
345C5#8328411yescharacteristic, complemented, Sylow
346C22—52no—
347C22—102no—
348C22—202no—
349C22—204no—
350C22C2×D5×#6711yescharacteristic
351C4—22no—
352C4—42no—
353C4—52no—
354C4—102no—
355C4—122no—
356C4—602no—
357C4D5×#23712yes—
358C3#1061347111yescharacteristic, complemented, Sylow
359C2—102no—
360C2—402no—
361C2D5×#93611yescharacteristic
362C2#1175508412yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC3×#66059C2
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. D5×#870C2semidirect
3. #11751183C2semidirect
4. C5×#5082C2semidirect
5. #11749331C2semidirect
6. #11749198C2semidirect
7. #11747003C2semidirect
8. #11746897C2semidirect
9. #11746892C2semidirect
70. #5082D5semidirect
305. C3×C5#3142semidirect
345. C5#83284semidirect
358. C3#10613471semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
D5×#8702
#117511832
C5×#50822
#117493312
#117491982
#117470032
#117468972
#117468922
#106134713
#832845