Finite Group Databasebeta

← #14292012

Subgroups — #14292012

Order 1920.

332 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65135C211yesmaximal, characteristic
2#11747062C211yesmaximal, characteristic
3C3⋊C8×D20C211yesmaximal, characteristic
4#11746920C211yesmaximal, characteristic, complemented
5#11746303C211yesmaximal, characteristic, complemented
6C5×#4480C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599332—31nomaximal, Hall
9#91758C2211yescharacteristic
10C3×C4×D20C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6657—21no—
13C2×D5×C3⋊C8—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3953—21no—
19C3×#3950—21no—
20#90974—21no—
21#90971—21no—
22#90971—21no—
23#90955—21no—
24#71102—51nomaximal, Hall
25#65135D311yescharacteristic
26#65130—31no—
27C8×D20—31no—
28#64970—31no—
29C5×#334—31no—
30#64706—31no—
31#64702—31no—
32C2×Dic30—21no—
33C2×C3×D20D411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168—21no—
41C2×C5×C3⋊C8—21no—
42C2×C5×C3⋊C8D411yescharacteristic
43C2×C5×C3⋊C8D411yescharacteristic
44C3×#685—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D411yescharacteristic
48#6657—42no—
49D5×C3⋊C8—42no—
50C3×#474—51no—
51#5079—51no—
52#5019—51no—
53D4×C3⋊C8—51no—
54#4547—51no—
55#4482—51no—
56#4480D511yescharacteristic, complemented
57C2×#677—61no—
58C2×C8×D5—61no—
59C4×D20C2×D311yescharacteristic
60#4015—31no—
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8—31no—
65#3953—21no—
66#3952—61no—
67#3950—21no—
68#3948—61no—
69#3948—61no—
70#3948—61no—
71C4⋊#168—31no—
72#1679—151noSylow
73C22×C3×D5—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—41no—
78Dic30—41no—
79Dic30—41no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—41no—
82C3×D20—21no—
83C3×D20SD1612yes—
84C3×C4×D5—41no—
85C3×C4×D5—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8—41no—
89C3⋊#168—41no—
90C5×C3⋊C8—21no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—41no—
93C3×C4⋊Q8—51no—
94C3×C4×D4—51no—
95C2×#214—101no—
96C22×C3⋊C8—101no—
97#869—51no—
98C3×#107—101no—
99C3×C4⋊C8C2×D511yescharacteristic
100C3×#102—101no—
101#835—101no—
102#835—101no—
103#830—101no—
104#810—101no—
105C4⋊(C3⋊C8)—51no—
106C4⋊(C3⋊C8)C2×D511yescharacteristic
107C4×C3⋊C8C2×D511yescharacteristic
108C2×D20#6711yescharacteristic
109C2×C4×D5—21no—
110C2×Dic10—21no—
111C2×Dic10—61no—
112C2×C5×C8—21no—
113C2×C5×C8—31no—
114C2×C5×C8—31no—
115C2×C5×C8—61no—
116C42×C5C22×D311yescharacteristic
117#685—21no—
118C4⋊Dic5—21no—
119C4⋊Dic5—21no—
120C4⋊Dic5—61no—
121C4⋊Dic5—61no—
122C4⋊Dic5#6711yescharacteristic
123C2×#168—61no—
124#677—122no—
125C8×D5—122no—
126#487—151no—
127#474—51no—
128#461—151no—
129C8×D4—151no—
130#334—31no—
131#332—151no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×C3×D5—22no—
135C2×C3×D5—41no—
136C2×C3×D5—41no—
137C3×C4×C5—21no—
138C3×C4×C5C2×SD1611yescharacteristic
139C3×C4×C5#13511yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142Dic15—81no—
143C3×Dic5—41no—
144C3×Dic5—81no—
145C2×C3×Q8—101no—
146C2×C3×D4—51no—
147C22×C3×C4—101no—
148C2×Dic6—101no—
149C2×C3×C8—21no—
150C3×C4⋊C4—51no—
151C3×C4⋊C4—101no—
152C3×C4⋊C4—101no—
153C3×C22⋊C4—101no—
154C3×C42C22×D511yescharacteristic
155#214—202no—
156C4⋊Dic3—101no—
157C4⋊Dic3—101no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—101no—
160C2×C3⋊C8—202no—
161C2×C3⋊C8D2011yescharacteristic
162C2×C3⋊C8D2011yescharacteristic
163C22×D5—21no—
164C2×C4×C5D3×D411yescharacteristic
165C2×C4×C5#23711yescharacteristic
166C2×C4×C5C2×#6711yescharacteristic
167C2×Dic5—21no—
168C2×Dic5—41no—
169C2×Dic5—121no—
170D20—21no—
171D20#21512yes—
172C4×D5—41no—
173C4×D5—41no—
174Dic10—41no—
175Dic10—41no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—41no—
179C5×C8—61no—
180C5×C8—61no—
181C5×C8—121no—
182#168—121no—
183C2×SD16—301no—
184C22×C8—301no—
185C4⋊Q8—51no—
186C4⋊Q8—151no—
187C4×D4—51no—
188#107—101no—
189C4⋊C8—31no—
190C4⋊C8—151no—
191C4⋊C8D3×D511yescharacteristic
192#103—301no—
193#103—301no—
194#103—301no—
195#102—101no—
196C22⋊C8—301no—
197C4×C8—31no—
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201C3×D5—42no—
202C23×C3—101no—
203C3×Q8—201no—
204C3×Q8—201no—
205C3×D4—52no—
206C3×D4—101no—
207C2×C3×C4—101no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4C2×D2011yescharacteristic
212C2×C3×C4D4×D511yescharacteristic
213C2×C3×C4#71311yescharacteristic
214C2×Dic3—201no—
215Dic6—201no—
216Dic6—201no—
217C3×C8—41no—
218C3⋊C8—21no—
219C3⋊C8—21no—
220C3⋊C8—41no—
221C3⋊C8—201no—
222C22×C5#93911yescharacteristic
223C2×D5—22no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—21no—
227C4×C5#91111yescharacteristic
228C4×C5#91211yescharacteristic
229C4×C5C2×#21511yescharacteristic
230C4×C5#95011yescharacteristic
231Dic5—41no—
232Dic5—81no—
233Dic5—241no—
234C2×Q8—101no—
235C2×Q8—301no—
236C2×D4—51no—
237C22×C4—101no—
238SD16—602no—
239C2×C8—21no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—61no—
243C2×C8—301no—
244C2×C8—602no—
245C4⋊C4—51no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—301no—
249C4⋊C4—301no—
250C22⋊C4—101no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3—102no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3#404111yescharacteristic
257C3×C4—21no—
258C3×C4—201no—
259C3×C4—401no—
260C3×C4#405011yescharacteristic
261C3×C4#405411yescharacteristic
262C3×C4D5×SD1611yescharacteristic
263C3×C4#406211yescharacteristic
264Dic3—401no—
265C2×C5#504811yescharacteristic
266C2×C5#515311yescharacteristic
267C2×C5#520411yescharacteristic
268D5—42no—
269C23—101no—
270Q8—201no—
271Q8—201no—
272Q8—601no—
273Q8—601no—
274D4—52no—
275D4—101no—
276C2×C4—101no—
277C2×C4—201no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—601no—
281C2×C4#676611yescharacteristic
282C2×C4D3×D2011yescharacteristic
283C2×C4D5×#6711yescharacteristic
284C8—41no—
285C8—61no—
286C8—61no—
287C8—121no—
288C8—601no—
289C2×C3—202no—
290C2×C3#6513311yescharacteristic
291C2×C3#6515311yescharacteristic
292C2×C3#6518511yescharacteristic
293C5#7110211yescharacteristic, complemented, Sylow
294C22—102no—
295C22—201no—
296C22—201no—
297C22#9140911yescharacteristic
298C4—21no—
299C4—201no—
300C4—401no—
301C4—1201no—
302C4#9125411yescharacteristic
303C4#9127311yescharacteristic
304C4#9149211yescharacteristic
305C4D5×#21511yescharacteristic
306C3#1059933211yescharacteristic, complemented, Sylow
307C2—202no—
308C2#1174744311yescharacteristic
309C2#1174775611yescharacteristic
310C2#1174818211yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1679
LCSG ▷ C3×C42×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. #11746920C2semidirect
5. #11746303C2semidirect
6. C5×#4480C2semidirect
7. #11745855C2semidirect
56. #4480D5semidirect
252. C3×C5#1679semidirect
293. C5#71102semidirect
306. C3#10599332semidirect

Maximal subgroups

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

subgroupindex
C3×#651352
#117470622
C3⋊C8×D202
#117469202
#117463032
C5×#44802
#117458552
#105993323
#711025