Finite Group Databasebeta

← #14291981

Subgroups — #14291981

Order 1920.

332 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11750947C211yesmaximal, characteristic
2#11750942C211yesmaximal, characteristic
3C8×D60C211yesmaximal, characteristic
4#11750782C211yesmaximal, characteristic, complemented
5C3×C5×#334C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10599332—31nomaximal, Hall
9C2×#6706—21no—
10C2×C8×D15—21no—
11C4×D60C2211yescharacteristic
12#91758C2211yescharacteristic
13#91758C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17#91105—21no—
18#91104—21no—
19#91102—21no—
20#91100—21no—
21#91100—21no—
22#91100—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24#68539—51nomaximal, Hall
25#65135—31no—
26#65130—31no—
27C8×D20—31no—
28#64970—31no—
29C5×#334D311yescharacteristic, complemented
30#64706—31no—
31#64702—31no—
32C2×D60D411yescharacteristic
33C2×C4×D15—21no—
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48#6706—42no—
49C8×D15—42no—
50#4846—51no—
51#4841—51no—
52C8×D12—51no—
53#4681—51no—
54C3×#334D511yescharacteristic, complemented
55#4486—51no—
56#4482—51no—
57C2×#677—61no—
58C2×C8×D5—61no—
59C4×D20—31no—
60#4015—31no—
61#4015—31no—
62C5×C4⋊C8C2×D311yescharacteristic
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8C2×D311yescharacteristic
65#3953—61no—
66#3952—61no—
67#3950—61no—
68#3948—61no—
69#3948—61no—
70#3948—61no—
71C4⋊#168—31no—
72#1679—151noSylow
73C22×D15—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—21no—
78C2×Dic15—41no—
79C2×Dic15—41no—
80D60—21no—
81D60SD1612yes—
82C4×D15—41no—
83C4×D15—41no—
84Dic30—41no—
85Dic30—41no—
86Dic30—41no—
87Dic30—41no—
88C3×C5×C8—21no—
89C3×C5×C8—21no—
90C3×C5×C8—41no—
91C3×C5×C8—41no—
92C3⋊#168—41no—
93C2×#204—101no—
94C2×D3×C8—101no—
95C4×D12—51no—
96#869—51no—
97#869—51no—
98C3×C4⋊C8C2×D511yescharacteristic
99C3×C4⋊C8C2×D511yescharacteristic
100C3×C4×C8C2×D511yescharacteristic
101#821—101no—
102(C2×D3)⋊C8—101no—
103#818—101no—
104#816—101no—
105#816—101no—
106#816—101no—
107C4⋊(C3⋊C8)—51no—
108C2×D20—31no—
109C2×C4×D5—61no—
110C2×Dic10—61no—
111C2×Dic10—61no—
112C2×C5×C8—21no—
113C2×C5×C8—21no—
114C2×C5×C8D1211yescharacteristic
115C2×C5×C8D1211yescharacteristic
116C42×C5C22×D311yescharacteristic
117#685—61no—
118C4⋊Dic5—31no—
119C4⋊Dic5—61no—
120C4⋊Dic5—61no—
121C4⋊Dic5—61no—
122C4⋊Dic5—61no—
123C2×#168—61no—
124#677—122no—
125C8×D5—122no—
126#487—151no—
127#474—151no—
128#461—151no—
129C8×D4—151no—
130#334D1511yescharacteristic, complemented
131#332—151no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×D15—22no—
135C2×D15—41no—
136C2×D15—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—41no—
143Dic15—81no—
144Dic15—81no—
145C2×D12—51no—
146C2×C4×D3—101no—
147C2×Dic6—101no—
148C2×Dic6—101no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8D2011yescharacteristic
152C2×C3×C8D2011yescharacteristic
153C3×C42C22×D511yescharacteristic
154(C2×D3)⋊C4—101no—
155C4⋊Dic3—51no—
156C4⋊Dic3—101no—
157C4⋊Dic3—101no—
158C4⋊Dic3—101no—
159C4⋊Dic3—101no—
160C2×C3⋊C8—101no—
161#204—202no—
162D3×C8—202no—
163C22×D5—61no—
164C2×C4×C5C2×D1211yescharacteristic
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5#23911yescharacteristic
167C2×Dic5—61no—
168C2×Dic5—121no—
169C2×Dic5—121no—
170D20—32no—
171D20—61no—
172C4×D5—121no—
173C4×D5—121no—
174Dic10—121no—
175Dic10—121no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—41no—
181C5×C8—41no—
182#168—121no—
183C2×SD16—301no—
184C22×C8—301no—
185C4⋊Q8—151no—
186C4⋊Q8—151no—
187C4×D4—151no—
188#107—301no—
189C4⋊C8—151no—
190C4⋊C8C2×D1511yescharacteristic
191C4⋊C8C2×D1511yescharacteristic
192#103—301no—
193#103—301no—
194#103—301no—
195#102—301no—
196C22⋊C8—301no—
197C4×C8C2×D1511yescharacteristic
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201D15—42no—
202C22×D3—101no—
203C2×C3×C4C2×D2011yescharacteristic
204C2×C3×C4D4×D511yescharacteristic
205C2×C3×C4#71311yescharacteristic
206C2×Dic3—101no—
207C2×Dic3—201no—
208C2×Dic3—201no—
209D12—52no—
210D12—101no—
211C4×D3—201no—
212C4×D3—201no—
213Dic6—201no—
214Dic6—201no—
215Dic6—201no—
216Dic6—201no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—41no—
220C3×C8—41no—
221C3⋊C8—201no—
222C22×C5#89511yescharacteristic
223C2×D5—62no—
224C2×D5—121no—
225C2×D5—121no—
226C4×C5—21no—
227C4×C5#90411yescharacteristic
228C4×C5#90811yescharacteristic
229C4×C5D3×SD1611yescharacteristic
230C4×C5#91611yescharacteristic
231Dic5—121no—
232Dic5—241no—
233Dic5—241no—
234C2×Q8—301no—
235C2×Q8—301no—
236C2×D4—151no—
237C22×C4—301no—
238SD16—602no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—301no—
242C2×C8—602no—
243C2×C8D6011yescharacteristic
244C2×C8D6011yescharacteristic
245C4⋊C4—151no—
246C4⋊C4—301no—
247C4⋊C4—301no—
248C4⋊C4—301no—
249C4⋊C4—301no—
250C22⋊C4—301no—
251C42C22×D1511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3#404111yescharacteristic
254C2×D3—102no—
255C2×D3—201no—
256C2×D3—201no—
257C3×C4—21no—
258C3×C4#405011yescharacteristic
259C3×C4#405411yescharacteristic
260C3×C4D5×SD1611yescharacteristic
261C3×C4#406211yescharacteristic
262Dic3—201no—
263Dic3—401no—
264Dic3—401no—
265C2×C5#484411yescharacteristic
266C2×C5#486411yescharacteristic
267C2×C5#489611yescharacteristic
268D5—122no—
269C23—301no—
270Q8—601no—
271Q8—601no—
272Q8—601no—
273Q8—601no—
274D4—152no—
275D4—301no—
276C2×C4—301no—
277C2×C4—601no—
278C2×C4—601no—
279C2×C4—601no—
280C2×C4—601no—
281C2×C4C2×D6011yescharacteristic
282C2×C4D4×D1511yescharacteristic
283C2×C4#682111yescharacteristic
284C8—21no—
285C8—21no—
286C8—41no—
287C8—41no—
288C8—601no—
289C2×C3#6513311yescharacteristic
290C2×C3#6515311yescharacteristic
291C2×C3#6518511yescharacteristic
292D3—202no—
293C5#6853911yescharacteristic, complemented, Sylow
294C22—302no—
295C22—601no—
296C22—601no—
297C22#9178411yescharacteristic
298C4—21no—
299C4—601no—
300C4—1201no—
301C4—1201no—
302C4#9179311yescharacteristic
303C4#9179711yescharacteristic
304C4SD16×D1511yescharacteristic
305C4#9180511yescharacteristic
306C3#1059933211yescharacteristic, complemented, Sylow
307C2—602no—
308C2#1175094511yescharacteristic
309C2#1175096511yescharacteristic
310C2#1175099711yescharacteristic
subgroupG/H
centerC22#91784
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#334C2
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenter#334D15
hypocenterC3×C5#1679
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
4. #11750782C2semidirect
5. C3×C5×#334C2semidirect
6. #11746307C2semidirect
7. #11746303C2semidirect
29. C5×#334D3semidirect
54. C3×#334D5semidirect
130. #334D15semidirect
252. C3×C5#1679semidirect
293. C5#68539semidirect
306. C3#10599332semidirect

Maximal subgroups

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

subgroupindex
#117509472
#117509422
C8×D602
#117507822
C3×C5×#3342
#117463072
#117463032
#105993323
#685395