Finite Group Databasebeta

← #14292003

Subgroups — #14292003

Order 1920.

332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 96 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#11751108C211yesmaximal, characteristic
2C5×D4×C3⋊C8C211yesmaximal, characteristic
3C3×#65308C211yesmaximal, characteristic
4#11746921C211yesmaximal, characteristic, complemented
5#11745866C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10601647—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91758C2211yescharacteristic
11C22×C5×C3⋊C8—21no—
12C2×C3×#687—21no—
13C3×#4015C2211yescharacteristic
14#91116—21no—
15#91091—21no—
16C4⋊(C3⋊#168)C2211yescharacteristic
17C5×#830—21no—
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3942—21no—
21C3×C4⋊#168C2211yescharacteristic
22#90974—21no—
23#90974—21no—
24#71038—51nomaximal, Hall
25C5×C8×D4—31no—
26#65308D311yescharacteristic
27#65296—31no—
28#64970—31no—
29#64706—31no—
30#64702—31no—
31#64677—31no—
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×Dic30—21no—
35C2×C3×Dic10—21no—
36C3×C5×C4⋊C4D411yescharacteristic
37C3×C5×C22⋊C4—21no—
38C3×C42×C5C2311yescharacteristic
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C2×C3⋊#168—21no—
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8—42no—
44C2×C5×C3⋊C8D411yescharacteristic
45C2×C5×C3⋊C8D411yescharacteristic
46C3×#687—42no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C2×C3×#168—21no—
50C3×#461—51no—
51#5093—51no—
52D4×C3⋊C8D511yescharacteristic
53#5007—51no—
54#4547—51no—
55#4486—51no—
56#4480—51no—
57C22×C5×C8—61no—
58C4×C5×D4C2×D311yescharacteristic
59C2×#687—21no—
60#4015—31no—
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C22⋊C8—61no—
64C4×C5×C8—31no—
65#3964—61no—
66#3948—61no—
67#3948—61no—
68#3942—21no—
69#3939—61no—
70C4⋊#168—31no—
71C4⋊#168C2×D311yescharacteristic
72#1679—151noSylow
73C23×C3×C5—21no—
74C3×C5×D4—21no—
75C3×C5×D4SD1612yes—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5#4111yescharacteristic
82C2×Dic15—41no—
83Dic30—41no—
84Dic30—41no—
85C2×C3×Dic5—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3⋊#168—41no—
89C3×#168—41no—
90C5×C3⋊C8—21no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—41no—
93C2×C3×SD16—101no—
94C3×C4⋊Q8—51no—
95C3×C4×D4C2×D511yescharacteristic
96C22×C3⋊C8—21no—
97#869—51no—
98C3×C4⋊C8—51no—
99C3×#103—101no—
100#832—101no—
101#830—21no—
102#810—101no—
103#810—101no—
104#807—101no—
105C4⋊(C3⋊C8)—51no—
106C4⋊(C3⋊C8)C2×D511yescharacteristic
107C4×C3⋊C8C2×D511yescharacteristic
108C2×C5×D4#6711yescharacteristic
109C22×C4×C5—21no—
110C2×Dic10—21no—
111C2×Dic10—61no—
112C2×C5×C8—31no—
113C2×C5×C8—31no—
114C2×C5×C8—61no—
115C2×C5×C8—122no—
116C5×C4⋊C4#6711yescharacteristic
117C5×C22⋊C4—21no—
118C42×C5C22×D311yescharacteristic
119#687—42no—
120C4⋊Dic5—21no—
121C4⋊Dic5—21no—
122C4⋊Dic5—61no—
123C4⋊Dic5—61no—
124C2×#168—21no—
125C2×#168—61no—
126#487—151no—
127#474—151no—
128#461—51no—
129C8×D4—31no—
130#334—151no—
131#332—151no—
132#332—151no—
133C22×C3×C5—22no—
134C22×C3×C5—41no—
135C22×C3×C5—41no—
136C22×C3×C5#12111yescharacteristic
137C3×C4×C5—21no—
138C3×C4×C5—41no—
139C3×C4×C5C2×SD1611yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143Dic15—81no—
144C3×Dic5—81no—
145C2×C3×Q8—101no—
146C2×C3×D4D2011yescharacteristic
147C22×C3×C4—21no—
148C2×Dic6—101no—
149C3×SD16—202no—
150C2×C3×C8—101no—
151C3×C4⋊C4—101no—
152C3×C4⋊C4—101no—
153C3×C4⋊C4D2011yescharacteristic
154C3×C22⋊C4—21no—
155C3×C42C22×D511yescharacteristic
156C4⋊Dic3—101no—
157C4⋊Dic3—101no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—42no—
160C2×C3⋊C8—101no—
161C2×C3⋊C8C22⋊D511yescharacteristic
162C2×C3⋊C8C22⋊D511yescharacteristic
163C23×C5—21no—
164C5×D4—21no—
165C5×D4#21412yes—
166C2×C4×C5—21no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5D3×D411yescharacteristic
170C2×C4×C5#23711yescharacteristic
171C2×C4×C5C2×#6711yescharacteristic
172C2×Dic5—41no—
173C2×Dic5—121no—
174Dic10—41no—
175Dic10—41no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—61no—
179C5×C8—61no—
180C5×C8—121no—
181#168—41no—
182#168—121no—
183C2×SD16—101no—
184C22×C8—61no—
185C4⋊Q8—51no—
186C4⋊Q8—151no—
187C4×D4D3×D511yescharacteristic
188#107—301no—
189C4⋊C8—31no—
190C4⋊C8—51no—
191C4⋊C8—151no—
192#103—101no—
193#103—301no—
194#103—301no—
195#102—301no—
196C22⋊C8—61no—
197C4×C8—31no—
198C2×C3×C5—42no—
199C2×C3×C5#46311yescharacteristic
200C2×C3×C5#46511yescharacteristic
201C2×C3×C5#47311yescharacteristic
202C23×C3—21no—
203C3×Q8—201no—
204C3×Q8—201no—
205C3×D4—21no—
206C3×D4#67712yes—
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—201no—
211C2×C3×C4C2×D2011yescharacteristic
212C2×C3×C4#70911yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C2×Dic3—201no—
215Dic6—201no—
216Dic6—201no—
217C3×C8—201no—
218C3⋊C8—21no—
219C3⋊C8—21no—
220C3⋊C8—41no—
221C3⋊C8—201no—
222C22×C5—22no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5#93911yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5#91411yescharacteristic
229C4×C5#91611yescharacteristic
230C4×C5C2×#21411yescharacteristic
231C4×C5#95011yescharacteristic
232Dic5—81no—
233Dic5—241no—
234C2×Q8—101no—
235C2×Q8—301no—
236C2×D4#120211yescharacteristic
237C22×C4—21no—
238SD16—202no—
239C2×C8—31no—
240C2×C8—31no—
241C2×C8—61no—
242C2×C8—101no—
243C2×C8—122no—
244C2×C8—301no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—301no—
248C4⋊C4—301no—
249C4⋊C4#120211yescharacteristic
250C22⋊C4—21no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3#407611yescharacteristic
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—401no—
260C3×C4C2×#67711yescharacteristic
261C3×C4#405011yescharacteristic
262C3×C4#407811yescharacteristic
263C3×C4#409611yescharacteristic
264Dic3—401no—
265C2×C5—42no—
266C2×C5#504111yescharacteristic
267C2×C5#516511yescharacteristic
268C2×C5#520411yescharacteristic
269C23—21no—
270Q8—201no—
271Q8—201no—
272Q8—601no—
273Q8—601no—
274D4—21no—
275D4#665712yes—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—201no—
280C2×C4—601no—
281C2×C4#677911yescharacteristic
282C2×C4C2×#120211yescharacteristic
283C2×C4D3×C22⋊D511yescharacteristic
284C8—61no—
285C8—61no—
286C8—121no—
287C8—201no—
288C8—601no—
289C2×C3—42no—
290C2×C3#6530511yescharacteristic
291C2×C3#6540311yescharacteristic
292C2×C3#6543211yescharacteristic
293C5#7103811yescharacteristic, complemented, Sylow
294C22—22no—
295C22—41no—
296C22—41no—
297C22#9156911yescharacteristic
298C4—21no—
299C4—41no—
300C4—401no—
301C4—1201no—
302C4C2×#665711yescharacteristic
303C4#9131111yescharacteristic
304C4#9149511yescharacteristic
305C4#9149611yescharacteristic
306C3#1060164711yescharacteristic, complemented, Sylow
307C2—42no—
308C2#1174853911yescharacteristic
309C2#1174908011yescharacteristic
310C2#1174945411yescharacteristic
subgroupG/H
centerC22#91569
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#121
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1679
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #11746921C2semidirect
5. #11745866C2semidirect
6. #11745859C2semidirect
7. #11745855C2semidirect
252. C3×C5#1679semidirect
293. C5#71038semidirect
306. C3#10601647semidirect

Maximal subgroups

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

subgroupindex
#117511082
C5×D4×C3⋊C82
C3×#653082
#117469212
#117458662
#117458592
#117458552
#106016473
#710385