Finite Group Databasebeta

← #14285261

Subgroups — #14285261

Order 1920.

456 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
1D5×#869C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3#11746871C211yesmaximal, characteristic
4#11746307C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10599221—31nomaximal, Hall
9C2×D5×Dic6—21no—
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91468—21no—
14#91468C412yes—
15D5×C4⋊Dic3—21no—
16D5×C4⋊Dic3C412yes—
17#91376—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3952—21no—
22C3×#3947—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90955—21no—
25#90952—21no—
26#70822—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65124—31no—
29#65124D311yescharacteristic
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×Dic30—21no—
35C2×C5×Dic6—21no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×#1204—22no—
40C2×D5×Dic3—22no—
41D5×Dic6—42no—
42D5×Dic6—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15C2×C412yes—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3C2×C412yes—
50C2×C5×C3⋊C8—21no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C2×C3×#168—21no—
55#6668—22no—
56#6668—22no—
57C2×#869—51no—
58C3×#432—51no—
59#4926—51no—
60#4486—51no—
61#4486—51no—
62#4486—51no—
63#4486D511yescharacteristic, complemented
64C2×Q8×D5—61no—
65C5×C4⋊Q8—31no—
66#4090—61no—
67D5×C4⋊C4—32no—
68D5×C4⋊C4—61no—
69#4034—32no—
70#4034—61no—
71C42×D5C2×D311yescharacteristic
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—21no—
76#3952—61no—
77#3947—21no—
78#3947—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1556—151noSylow
82C22×C3×D5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—41no—
88Dic30—41no—
89C2×C5×Dic3—22no—
90C5×Dic6—41no—
91C5×Dic6—41no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C3×C4×D5—22no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C4×D5—21no—
100#1204—44no—
101D5×Dic3—44no—
102C3×C5×C8—41no—
103C3⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C22×Dic6—101no—
107C2×C3×C42—51no—
108C2×C4⋊Dic3—52no—
109C2×C4⋊Dic3—101no—
110#869—51no—
111#869—52no—
112#869—101no—
113#869—101no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C22⋊C8—101no—
118C3×#97—101no—
119#830—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122#803—101no—
123C2×C5×Q8—61no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×C4×D5—62no—
127C2×C4×D5C4×D311yescharacteristic
128C2×C4×D5D1211yescharacteristic
129C2×C4×D5#6711yescharacteristic
130C2×Dic10—61no—
131C2×Dic10—62no—
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—32no—
135C5×C4⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C4×Dic5C4×D311yescharacteristic
142C4×Dic5D1211yescharacteristic
143C4×Dic5#6711yescharacteristic
144C2×#168—21no—
145C2×#168—61no—
146C2×C4⋊Q8—151no—
147#432—51no—
148#432—151no—
149#332—31no—
150#332—151no—
151#332—151no—
152#332—151no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5#10112yes—
157C3×C4×C5—21no—
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—42no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C5×Dic3—42no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×Dic3—102no—
171C2×Dic6—21no—
172C2×Dic6—102no—
173C2×Dic6—101no—
174C2×Dic6—202no—
175C2×Dic6—202no—
176C2×C3×C8—21no—
177C2×C3×C8—101no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181C3×C42C22×D511yescharacteristic
182C4⋊Dic3—21no—
183C4⋊Dic3—52no—
184C4⋊Dic3—102no—
185C4⋊Dic3—102no—
186C4⋊Dic3—101no—
187C4⋊Dic3C4×D512yes—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—101no—
190C22×D5(C2×D3)⋊C411yescharacteristic
191C5×Q8—121no—
192C5×Q8—121no—
193C2×C4×C5—62no—
194C2×C4×C5C2×C4×D311yescharacteristic
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—62no—
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201C4×D5—22no—
202C4×D5—21no—
203C4×D5—21no—
204C4×D5—21no—
205C4×D5—21no—
206C4×D5—124no—
207Dic10—124no—
208Dic10—121no—
209Dic10—121no—
210C5×C8—41no—
211C5×C8—121no—
212#168—41no—
213#168—121no—
214C22×Q8—301no—
215C4⋊Q8—31no—
216C4⋊Q8—152no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C4⋊Q8—301no—
220C2×C4⋊C4—152no—
221C2×C4⋊C4—301no—
222C2×C42—51no—
223C4⋊C8—31no—
224C4⋊C8—51no—
225C4⋊C8—151no—
226C4⋊C8D3×D511yescharacteristic
227C22⋊C8—101no—
228C22⋊C8—301no—
229#97—101no—
230#97—301no—
231C2×C3×C5C2×#10111yescharacteristic
232C2×C3×C5#41811yescharacteristic
233C2×C3×C5#41911yescharacteristic
234C3×D5—22no—
235C23×C3—51no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—51no—
239C2×C3×C4—102no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4C2×C4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—22no—
248C2×Dic3—102no—
249C2×Dic3—204no—
250Dic6—41no—
251Dic6—41no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255C3×C8—41no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5C2×(C2×D3)⋊C411yescharacteristic
260C2×D5—21no—
261C2×D5—21no—
262C2×D5#82412yes—
263C4×C5—21no—
264C4×C5—122no—
265C4×C5#90811yescharacteristic
266C4×C5#90811yescharacteristic
267C4×C5#95111yescharacteristic
268C4×C5#95111yescharacteristic
269Dic5—21no—
270Dic5—21no—
271Dic5—21no—
272Dic5—122no—
273C2×Q8—61no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—602no—
277C2×Q8—602no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—101no—
285C2×C8—301no—
286C4⋊C4—32no—
287C4⋊C4—61no—
288C4⋊C4—152no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C42—51no—
293C42—51no—
294C42—51no—
295C42C2×D3×D511yescharacteristic
296C3×C5#155611yescharacteristic, complemented, Hall
297C22×C3—52no—
298C22×C3—101no—
299C22×C3—101no—
300C22×C3D5×C22⋊C411yescharacteristic
301C3×C4—21no—
302C3×C4—101no—
303C3×C4—101no—
304C3×C4—101no—
305C3×C4#405711yescharacteristic
306C3×C4#406011yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4#406411yescharacteristic
309Dic3—42no—
310Dic3—202no—
311C2×C5#500411yescharacteristic
312C2×C5#513111yescharacteristic
313C2×C5C2×#82411yescharacteristic
314D5—22no—
315C23—51no—
316Q8—121no—
317Q8—121no—
318Q8—604no—
319Q8—601no—
320Q8—601no—
321C2×C4—51no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—62no—
325C2×C4—102no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—302no—
331C2×C4—604no—
332C2×C4C4×D3×D511yescharacteristic
333C2×C4D5×D1211yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C8—41no—
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3—102no—
340C2×C3D5×#10111yescharacteristic
341C2×C3#6505911yescharacteristic
342C2×C3#6509111yescharacteristic
343C5#7082211yescharacteristic, complemented, Sylow
344C22—52no—
345C22—101no—
346C22—101no—
347C22D5×(C2×D3)⋊C411yescharacteristic
348C4—21no—
349C4—101no—
350C4—101no—
351C4—101no—
352C4—122no—
353C4—602no—
354C4#9124911yescharacteristic
355C4#9125011yescharacteristic
356C4#9148411yescharacteristic
357C4#9150811yescharacteristic
358C3#1059922111yescharacteristic, complemented, Sylow
359C2—102no—
360C2#1174748711yescharacteristic
361C2#1174810511yescharacteristic
362C2D5×#82411yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #11746307C2semidirect
5. C5×#4486C2semidirect
6. #11745859C2semidirect
7. #11745857C2semidirect
63. #4486D5semidirect
296. C3×C5#1556semidirect
343. C5#70822semidirect
358. C3#10599221semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
C3×#651242
#117468712
#117463072
C5×#44862
#117458592
#117458572
#105992213
#708225