Finite Group Databasebeta

← #14285003

Subgroups — #14285003

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752506C211yesmaximal, characteristic
2C3×#65126C211yesmaximal, characteristic
3D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#11746302C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10599216—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×#676—21no—
12C3×C42×D5C2211yescharacteristic
13#91388—21no—
14#91360C412yes—
15#91359—21no—
16#91358—21no—
17#91333C412yes—
18Dic5×Dic6—21no—
19C2×D5×C3⋊C8—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3946—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90982—21no—
26#70509—51nomaximal, Hall
27#66062—31no—
28#65126D311yescharacteristic
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767—31no—
32#64701—31no—
33#64701—31no—
34C2×Dic30C2×C412yes—
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⋊Dic15—21no—
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—
51C3×#676—42no—
52Dic3⋊Dic5—22no—
53#6669—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56D5×C3⋊C8—42no—
57#5470—51no—
58C3×#423—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4486—51no—
61#4486D511yescharacteristic, complemented
62#4481—51no—
63#4481—51no—
64C5×C4⋊Q8—31no—
65#4092—61no—
66Q8×Dic5—61no—
67C2×#676—21no—
68C2×C8×D5—61no—
69#4043—32no—
70#4038—61no—
71#4036—61no—
72#4033—32no—
73C42×D5C2×D311yescharacteristic
74#4015—31no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77#3946—21no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1550—151noSylow
82C22×C3×D5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—42no—
88C2×C5×Dic3—22no—
89C5×Dic6—41no—
90C5×Dic6—41no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—41no—
97C3×C4×D5SD1612yes—
98C3×C4×D5Q1612yes—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C2×C3×M16—101no—
104C2×C3×C42—51no—
105#926—101no—
106#924—52no—
107#924—101no—
108C22×C3⋊C8—101no—
109#870—101no—
110#869—51no—
111#869C2×D511yescharacteristic
112C4×Dic6—52no—
113C4×Dic6—101no—
114C3×C4⋊C8—51no—
115C3×C4⋊C8—101no—
116C3×C4⋊C8C2×D511yescharacteristic
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—101no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C4×D5C4×D311yescharacteristic
122C2×C4×D5D1211yescharacteristic
123C2×C4×D5#6711yescharacteristic
124C2×Dic10—32no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—61no—
132C4⋊Dic5—61no—
133C4⋊Dic5—62no—
134#683—62no—
135C4×Dic5—62no—
136C4×Dic5C4×D311yescharacteristic
137C4×Dic5D1211yescharacteristic
138C4×Dic5#6711yescharacteristic
139C2×#168—21no—
140C2×#168—61no—
141#676—42no—
142C8×D5—122no—
143#533—151no—
144#423—51no—
145C2×C4⋊C8—151no—
146#333—151no—
147#333—151no—
148#332—31no—
149#332—151no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5#10312yes—
154C3×C4×C5—21no—
155C3×C4×C5C2×SD1611yescharacteristic
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—42no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5#10312yes—
163C5×Dic3—42no—
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C2×Dic6—21no—
168C2×Dic6—52no—
169C3×M16—202no—
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C42—51no—
173C3×C42—51no—
174C3×C42—51no—
175C3×C42C22×D511yescharacteristic
176#217—102no—
177C4⋊Dic3—21no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3C4×D512yes—
181Dic3⋊C4—102no—
182Dic3⋊C4—102no—
183C4×Dic3—102no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—202no—
187C22×D5(C2×D3)⋊C411yescharacteristic
188C5×Q8—121no—
189C5×Q8—121no—
190C2×C4×C5—62no—
191C2×C4×C5C2×C4×D311yescharacteristic
192C2×C4×C5C2×D1211yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—62no—
195C2×Dic5(C2×D3)⋊C411yescharacteristic
196C2×Dic5(C2×D3)⋊C411yescharacteristic
197C2×Dic5(C2×D3)⋊C411yescharacteristic
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—41no—
201C4×D5#21412yes—
202C4×D5#21612yes—
203Dic10—122no—
204C5×C8—41no—
205C5×C8—121no—
206#168—41no—
207#168—121no—
208C2×M16—101no—
209C22×C8—301no—
210C4⋊Q8—31no—
211C4⋊Q8—151no—
212#125—301no—
213C22⋊Q8—152no—
214C22⋊Q8—301no—
215C4×Q8—152no—
216C4×Q8—301no—
217#117—301no—
218C2×C42—51no—
219C4⋊C8—31no—
220C4⋊C8—51no—
221C4⋊C8—101no—
222C4⋊C8—151no—
223C4⋊C8—301no—
224C4⋊C8D3×D511yescharacteristic
225C2×C3×C5#41311yescharacteristic
226C2×C3×C5C2×#10311yescharacteristic
227C2×C3×C5#41711yescharacteristic
228C3×D5—22no—
229C23×C3—51no—
230C2×C3×C4—51no—
231C2×C3×C4—52no—
232C2×C3×C4—52no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4—201no—
238C2×C3×C4C2×C4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×Dic3—22no—
242C2×Dic3—102no—
243Dic6—41no—
244Dic6—41no—
245Dic6—202no—
246C3×C8—41no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5C2×(C2×D3)⋊C411yescharacteristic
251C2×D5—21no—
252C2×D5—21no—
253C2×D5#81012yes—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#90811yescharacteristic
257C4×C5#90911yescharacteristic
258C4×C5C2×#21411yescharacteristic
259C4×C5C2×#21611yescharacteristic
260Dic5—21no—
261Dic5—21no—
262Dic5—122no—
263Dic5#81012yes—
264C2×Q8—61no—
265C2×Q8—152no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269M16—202no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—301no—
274C2×C8—602no—
275C4⋊C4—32no—
276C4⋊C4—61no—
277C4⋊C4—302no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C22⋊C4—302no—
282C42—51no—
283C42—51no—
284C42—51no—
285C42—302no—
286C42C2×D3×D511yescharacteristic
287C3×C5#155011yescharacteristic, complemented, Hall
288C22×C3—52no—
289C22×C3—101no—
290C22×C3—101no—
291C22×C3D5×C22⋊C411yescharacteristic
292C3×C4—21no—
293C3×C4—52no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4#405711yescharacteristic
297C3×C4D5×SD1611yescharacteristic
298C3×C4#406111yescharacteristic
299C3×C4D5×Q1611yescharacteristic
300Dic3—42no—
301Dic3—202no—
302C2×C5C2×#81011yescharacteristic
303C2×C5#513211yescharacteristic
304C2×C5#513311yescharacteristic
305D5—22no—
306C23—51no—
307Q8—121no—
308Q8—121no—
309Q8—602no—
310C2×C4—51no—
311C2×C4—52no—
312C2×C4—52no—
313C2×C4—51no—
314C2×C4—51no—
315C2×C4—62no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—201no—
319C2×C4—302no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4D5×D1211yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3—102no—
328C2×C3#6504011yescharacteristic
329C2×C3#6506011yescharacteristic
330C2×C3D5×#10311yescharacteristic
331C5#7050911yescharacteristic, complemented, Sylow
332C22—52no—
333C22—101no—
334C22—101no—
335C22D5×(C2×D3)⋊C411yescharacteristic
336C4—21no—
337C4—52no—
338C4—101no—
339C4—101no—
340C4—122no—
341C4—602no—
342C4#9125011yescharacteristic
343C4#9126011yescharacteristic
344C4D5×#21411yescharacteristic
345C4D5×#21611yescharacteristic
346C3#1059921611yescharacteristic, complemented, Sylow
347C2—102no—
348C2D5×#81011yescharacteristic
349C2#1174760511yescharacteristic
350C2#1174823111yescharacteristic
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#1550
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. #11746302C2semidirect
5. C5×#4486C2semidirect
6. #11745863C2semidirect
7. #11745857C2semidirect
61. #4486D5semidirect
287. C3×C5#1550semidirect
331. C5#70509semidirect
346. C3#10599216semidirect

Maximal subgroups

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

subgroupindex
#117525062
C3×#651262
D5×C4⋊(C3⋊C8)2
#117463022
C5×#44862
#117458632
#117458572
#105992163
#705095