Finite Group Databasebeta

← #14284749

Subgroups — #14284749

Order 1920.

404 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752506C211yesmaximal, characteristic
2C3×#65122C211yesmaximal, characteristic
3#11746869C211yesmaximal, characteristic
4#11746303C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10599212—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91388C412yes—
13#91360—21no—
14#91359—21no—
15#91358C412yes—
16#91333—21no—
17Dic5×Dic6—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#3952—21no—
22C3×C8×Dic5—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90955—21no—
25Dic5×C3⋊C8—21no—
26#70777—51nomaximal, Hall
27#66062—31no—
28#65122—31no—
29#65122D311yescharacteristic
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×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15C2×C412yes—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3C2×C412yes—
46C2×C5×C3⋊C8—21no—
47C3×C4×Dic5C2×C411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C2×C3×#168—21no—
51Dic3⋊Dic5—22no—
52#6669—22no—
53#6665—22no—
54Dic3×Dic5—22no—
55#5470—51no—
56C3×#431—51no—
57#4925—51no—
58#4486—51no—
59#4486D511yescharacteristic, complemented
60#4482—51no—
61#4482—51no—
62C5×C4⋊Q8—31no—
63#4092—61no—
64Q8×Dic5—61no—
65#4043—61no—
66#4038—32no—
67#4036—32no—
68#4033—61no—
69C42×D5C2×D311yescharacteristic
70#4015—31no—
71C5×C4⋊C8—31no—
72C5×C4⋊C8C2×D311yescharacteristic
73#3952—21no—
74#3952—61no—
75C8×Dic5—21no—
76C8×Dic5—61no—
77C4⋊#168—31no—
78C4⋊#168C2×D311yescharacteristic
79#1544—151noSylow
80C22×C3×D5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—22no—
85Dic30—41no—
86Dic30—41no—
87C2×C5×Dic3—22no—
88C5×Dic6—41no—
89C5×Dic6—41no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—22no—
98C3×C5×C8—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C2×C3×C42—51no—
103#926—52no—
104#924—101no—
105#924—101no—
106#870—52no—
107#869—51no—
108#869C2×D511yescharacteristic
109C4×Dic6—101no—
110C4×Dic6—101no—
111C3×C4⋊C8—51no—
112C3×C4⋊C8C2×D511yescharacteristic
113C3×C22⋊C8—101no—
114C3×C4×C8—101no—
115#830—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—101no—
119C2×C5×Q8—61no—
120C2×C4×D5C4×D311yescharacteristic
121C2×C4×D5D1211yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130C4⋊Dic5—32no—
131C4⋊Dic5—61no—
132C4⋊Dic5—62no—
133#683—62no—
134C4×Dic5—62no—
135C4×Dic5C4×D311yescharacteristic
136C4×Dic5D1211yescharacteristic
137C4×Dic5#6711yescharacteristic
138C2×#168—21no—
139C2×#168—61no—
140#533—151no—
141#431—51no—
142#431—151no—
143#332—31no—
144#332—151no—
145#332—151no—
146#332—151no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×C3×D5—21no—
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C3×C4×C5—21no—
152C3×C4×C5#13511yescharacteristic
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156Dic15—42no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5#10112yes—
160C5×Dic3—42no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C2×Dic6—21no—
165C2×Dic6—101no—
166C2×C3×C8—21no—
167C2×C3×C8—101no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42C22×D511yescharacteristic
172#217—102no—
173C4⋊Dic3—21no—
174C4⋊Dic3—52no—
175C4⋊Dic3—101no—
176C4⋊Dic3C4×D512yes—
177Dic3⋊C4—102no—
178Dic3⋊C4—102no—
179C4×Dic3—102no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—101no—
182C22×D5(C2×D3)⋊C411yescharacteristic
183C5×Q8—121no—
184C5×Q8—121no—
185C2×C4×C5—62no—
186C2×C4×C5C2×C4×D311yescharacteristic
187C2×C4×C5C2×D1211yescharacteristic
188C2×C4×C5C2×#6711yescharacteristic
189C2×Dic5—62no—
190C2×Dic5(C2×D3)⋊C411yescharacteristic
191C2×Dic5(C2×D3)⋊C411yescharacteristic
192C2×Dic5(C2×D3)⋊C411yescharacteristic
193C4×D5—21no—
194C4×D5—21no—
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—22no—
198Dic10—121no—
199Dic10—121no—
200C5×C8—41no—
201C5×C8—121no—
202#168—41no—
203#168—121no—
204C4⋊Q8—31no—
205C4⋊Q8—151no—
206#125—152no—
207C22⋊Q8—301no—
208C22⋊Q8—301no—
209C4×Q8—301no—
210C4×Q8—301no—
211#117—152no—
212C2×C42—51no—
213C4⋊C8—31no—
214C4⋊C8—51no—
215C4⋊C8—151no—
216C4⋊C8D3×D511yescharacteristic
217C22⋊C8—101no—
218C22⋊C8—301no—
219C4×C8—101no—
220C4×C8—301no—
221C2×C3×C5C2×#10111yescharacteristic
222C2×C3×C5#41611yescharacteristic
223C2×C3×C5#41611yescharacteristic
224C3×D5—41no—
225C23×C3—51no—
226C2×C3×C4—51no—
227C2×C3×C4—51no—
228C2×C3×C4—51no—
229C2×C3×C4—102no—
230C2×C3×C4—101no—
231C2×C3×C4—101no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—102no—
239Dic6—41no—
240Dic6—41no—
241Dic6—201no—
242Dic6—201no—
243C3×C8—41no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5C2×(C2×D3)⋊C411yescharacteristic
248C2×D5—21no—
249C2×D5—21no—
250C2×D5—21no—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5#90411yescharacteristic
254C4×C5#90411yescharacteristic
255C4×C5#95011yescharacteristic
256C4×C5#95011yescharacteristic
257Dic5—21no—
258Dic5—21no—
259Dic5—122no—
260Dic5#82412yes—
261C2×Q8—61no—
262C2×Q8—301no—
263C22×C4—51no—
264C22×C4—51no—
265C22×C4—51no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—101no—
269C2×C8—301no—
270C4⋊C4—32no—
271C4⋊C4—61no—
272C4⋊C4—152no—
273C4⋊C4—302no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C22⋊C4—302no—
277C42—51no—
278C42—51no—
279C42—51no—
280C42—302no—
281C42C2×D3×D511yescharacteristic
282C3×C5#154411yescharacteristic, complemented, Hall
283C22×C3—101no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3D5×C22⋊C411yescharacteristic
287C3×C4—21no—
288C3×C4—52no—
289C3×C4—101no—
290C3×C4—101no—
291C3×C4#405811yescharacteristic
292C3×C4#406211yescharacteristic
293C3×C4#406211yescharacteristic
294C3×C4#406511yescharacteristic
295Dic3—42no—
296Dic3—202no—
297C2×C5#500211yescharacteristic
298C2×C5#511311yescharacteristic
299C2×C5C2×#82411yescharacteristic
300D5—41no—
301C23—51no—
302Q8—121no—
303Q8—121no—
304Q8—601no—
305Q8—601no—
306C2×C4—51no—
307C2×C4—51no—
308C2×C4—51no—
309C2×C4—62no—
310C2×C4—102no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—302no—
316C2×C4C4×D3×D511yescharacteristic
317C2×C4D5×D1211yescharacteristic
318C2×C4D5×#6711yescharacteristic
319C8—41no—
320C8—121no—
321C8—201no—
322C8—601no—
323C2×C3—201no—
324C2×C3D5×#10111yescharacteristic
325C2×C3#6506111yescharacteristic
326C2×C3#6509311yescharacteristic
327C5#7077711yescharacteristic, complemented, Sylow
328C22—101no—
329C22—101no—
330C22—101no—
331C22D5×(C2×D3)⋊C411yescharacteristic
332C4—21no—
333C4—52no—
334C4—101no—
335C4—101no—
336C4—122no—
337C4—602no—
338C4#9126911yescharacteristic
339C4#9127011yescharacteristic
340C4#9149211yescharacteristic
341C4#9151611yescharacteristic
342C3#1059921211yescharacteristic, complemented, Sylow
343C2—201no—
344C2#1174750111yescharacteristic
345C2#1174813511yescharacteristic
346C2D5×#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#1544
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. #11746303C2semidirect
5. C5×#4486C2semidirect
6. #11745860C2semidirect
7. #11745857C2semidirect
59. #4486D5semidirect
282. C3×C5#1544semidirect
327. C5#70777semidirect
342. C3#10599212semidirect

Maximal subgroups

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

subgroupindex
#117525062
C3×#651222
#117468692
#117463032
C5×#44862
#117458602
#117458572
#105992123
#707775