Finite Group Databasebeta

← #14284672

Subgroups — #14284672

Order 1920.

424 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
3D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4#11746302C211yesmaximal, characteristic, complemented
5C5×#4482C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745858C211yesmaximal, characteristic, complemented
8#10599211—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91388—21no—
13#91360C412yes—
14#91359—21no—
15#91358—21no—
16#91333C412yes—
17Dic5×Dic6—21no—
18C2×D5×C3⋊C8—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3952—21no—
23C3×C8×Dic5—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90982—21no—
26#70776—51nomaximal, Hall
27#66062—31no—
28#65122D311yescharacteristic
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—
51Dic3⋊Dic5—22no—
52#6669—22no—
53#6665—22no—
54Dic3×Dic5—22no—
55D5×C3⋊C8—42no—
56#5470—51no—
57C3×#431—51no—
58C2×C4⋊(C3⋊C8)—51no—
59#4482—51no—
60#4482D511yescharacteristic, complemented
61#4481—51no—
62#4481—51no—
63C5×C4⋊Q8—31no—
64#4092—61no—
65Q8×Dic5—61no—
66C2×C8×D5—61no—
67#4043—32no—
68#4038—61no—
69#4036—61no—
70#4033—32no—
71C42×D5C2×D311yescharacteristic
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—21no—
76#3946—61no—
77C8×Dic5—21no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1542—151noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—22no—
86Dic30—42no—
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—41no—
96C3×C4×D5SD1612yes—
97C3×C4×D5Q1612yes—
98C3×C5×C8—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C2×C3×C42—51no—
103#926—101no—
104#924—52no—
105#924—101no—
106C22×C3⋊C8—101no—
107#870—101no—
108#869—51no—
109#869C2×D511yescharacteristic
110C4×Dic6—52no—
111C4×Dic6—101no—
112C3×C4⋊C8—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C22⋊C8—101no—
115C3×C4×C8—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—61no—
120C2×C4×D5C4×D311yescharacteristic
121C2×C4×D5D1211yescharacteristic
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—32no—
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130C4⋊Dic5—61no—
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—
140C8×D5—122no—
141#533—151no—
142#431—51no—
143C2×C4⋊C8—151no—
144#333—151no—
145#333—151no—
146#332—31no—
147#332—151no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C2×C3×D5#10312yes—
152C3×C4×C5—21no—
153C3×C4×C5C2×SD1611yescharacteristic
154C3×C4×C5C2×Q1611yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157Dic15—42no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5#10312yes—
161C5×Dic3—42no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C2×Dic6—21no—
166C2×Dic6—52no—
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42C22×D511yescharacteristic
173#217—102no—
174C4⋊Dic3—21no—
175C4⋊Dic3—101no—
176C4⋊Dic3—101no—
177C4⋊Dic3C4×D512yes—
178Dic3⋊C4—102no—
179Dic3⋊C4—102no—
180C4×Dic3—102no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—202no—
184C22×D5(C2×D3)⋊C411yescharacteristic
185C5×Q8—121no—
186C5×Q8—121no—
187C2×C4×C5—62no—
188C2×C4×C5C2×C4×D311yescharacteristic
189C2×C4×C5C2×D1211yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×Dic5—62no—
192C2×Dic5(C2×D3)⋊C411yescharacteristic
193C2×Dic5(C2×D3)⋊C411yescharacteristic
194C2×Dic5(C2×D3)⋊C411yescharacteristic
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—41no—
198C4×D5#20412yes—
199C4×D5Dic1212yes—
200Dic10—122no—
201C5×C8—41no—
202C5×C8—121no—
203#168—41no—
204#168—121no—
205C22×C8—301no—
206C4⋊Q8—31no—
207C4⋊Q8—151no—
208#125—301no—
209C22⋊Q8—152no—
210C22⋊Q8—301no—
211C4×Q8—152no—
212C4×Q8—301no—
213#117—301no—
214C2×C42—51no—
215C4⋊C8—31no—
216C4⋊C8—51no—
217C4⋊C8—151no—
218C4⋊C8—301no—
219C4⋊C8D3×D511yescharacteristic
220C22⋊C8—101no—
221C4×C8—101no—
222C2×C3×C5#41311yescharacteristic
223C2×C3×C5C2×#10311yescharacteristic
224C2×C3×C5#41611yescharacteristic
225C3×D5—22no—
226C23×C3—51no—
227C2×C3×C4—51no—
228C2×C3×C4—52no—
229C2×C3×C4—52no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4—201no—
235C2×C3×C4C2×C4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×Dic3—22no—
239C2×Dic3—102no—
240Dic6—41no—
241Dic6—41no—
242Dic6—202no—
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#81612yes—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5C2×#20411yescharacteristic
254C4×C5C2×Dic1211yescharacteristic
255C4×C5#95011yescharacteristic
256C4×C5#95011yescharacteristic
257Dic5—21no—
258Dic5—21no—
259Dic5—122no—
260Dic5#81612yes—
261C2×Q8—61no—
262C2×Q8—152no—
263C22×C4—51no—
264C22×C4—51no—
265C22×C4—51no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—101no—
269C2×C8—301no—
270C2×C8—602no—
271C4⋊C4—32no—
272C4⋊C4—61no—
273C4⋊C4—302no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C22⋊C4—302no—
278C42—51no—
279C42—51no—
280C42—51no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#154211yescharacteristic, complemented, Hall
284C22×C3—52no—
285C22×C3—101no—
286C22×C3—101no—
287C22×C3D5×C22⋊C411yescharacteristic
288C3×C4—21no—
289C3×C4—52no—
290C3×C4—101no—
291C3×C4—101no—
292C3×C4#405811yescharacteristic
293C3×C4D5×SD1611yescharacteristic
294C3×C4#406211yescharacteristic
295C3×C4D5×Q1611yescharacteristic
296Dic3—42no—
297Dic3—202no—
298C2×C5#500211yescharacteristic
299C2×C5C2×#81611yescharacteristic
300C2×C5#513211yescharacteristic
301D5—22no—
302C23—51no—
303Q8—121no—
304Q8—121no—
305Q8—602no—
306C2×C4—51no—
307C2×C4—52no—
308C2×C4—52no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—62no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—201no—
315C2×C4—302no—
316C2×C4C4×D3×D511yescharacteristic
317C2×C4D5×D1211yescharacteristic
318C2×C4D5×#6711yescharacteristic
319C8—41no—
320C8—121no—
321C8—201no—
322C8—601no—
323C2×C3—102no—
324C2×C3#6504011yescharacteristic
325C2×C3#6506111yescharacteristic
326C2×C3D5×#10311yescharacteristic
327C5#7077611yescharacteristic, complemented, Sylow
328C22—52no—
329C22—101no—
330C22—101no—
331C22D5×(C2×D3)⋊C411yescharacteristic
332C4—21no—
333C4—52no—
334C4—101no—
335C4—101no—
336C4—122no—
337C4—602no—
338C4D5×#20411yescharacteristic
339C4D5×Dic1211yescharacteristic
340C4#9149011yescharacteristic
341C4#9151411yescharacteristic
342C3#1059921111yescharacteristic, complemented, Sylow
343C2—102no—
344C2#1174749911yescharacteristic
345C2D5×#81611yescharacteristic
346C2#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#1542
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×#4482C2semidirect
6. #11745863C2semidirect
7. #11745858C2semidirect
60. #4482D5semidirect
283. C3×C5#1542semidirect
327. C5#70776semidirect
342. C3#10599211semidirect

Maximal subgroups

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

subgroupindex
#117525062
C3×#651222
D5×C4⋊(C3⋊C8)2
#117463022
C5×#44822
#117458632
#117458582
#105992113
#707765