Finite Group Databasebeta

← #14291996

Subgroups — #14291996

Order 1920.

332 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×C8×D12C211yesmaximal, characteristic
2C3×#64970C211yesmaximal, characteristic, complemented
3#11747070C211yesmaximal, characteristic
4#11746900C211yesmaximal, characteristic
5#11746278C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10601647—31nomaximal, Hall
9C2×C5×D3×C8—21no—
10C4×C5×D12C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6656—21no—
14C3×C4×C5×C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C4⋊(C3⋊#168)C2211yescharacteristic
17C5×(C2×D3)⋊C8—21no—
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3948—21no—
20C3×#3948—21no—
21#90989—21no—
22#90970—21no—
23#90966—21no—
24#71232—51nomaximal, Hall
25C5×C8×D4—31no—
26#65308—31no—
27#65296—31no—
28#64970D311yescharacteristic, complemented
29#64706—31no—
30#64702—31no—
31#64677—31no—
32C2×C5×D12D411yescharacteristic
33C2×C4×C5×D3—21no—
34C2×C3×Dic10—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8D411yescharacteristic
37C2×C3×C5×C8D411yescharacteristic
38C3×C42×C5C2311yescharacteristic
39C2×C3⋊#168—21no—
40C2×C3⋊#168—21no—
41C5×(C2×D3)⋊C4—21no—
42C5×C4⋊Dic3D411yescharacteristic
43C2×C5×C3⋊C8—21no—
44C5×D3×C8—42no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49#6656—42no—
50C3×#487—51no—
51#5087—51no—
52#5083—51no—
53C8×D12D511yescharacteristic
54#4547—51no—
55#4547—51no—
56#4457—51no—
57C22×C5×C8—61no—
58C4×C5×D4—31no—
59C2×#687—61no—
60#4015C2×D311yescharacteristic
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C22⋊C8—61no—
64C4×C5×C8C2×D311yescharacteristic
65#3964—61no—
66#3948—21no—
67#3948—21no—
68#3942—61no—
69#3939—61no—
70C4⋊#168—31no—
71C4⋊#168—31no—
72#1679—151noSylow
73C22×C5×D3—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×C5×Dic3—21no—
78C5×D12—21no—
79C5×D12SD1612yes—
80C4×C5×D3—41no—
81C4×C5×D3—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—41no—
84C3×Dic10—41no—
85C3×Dic10—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8—21no—
89C3×C5×C8—21no—
90C3⋊#168—41no—
91C3⋊#168—41no—
92C5×C3⋊C8—41no—
93C3×C4⋊Q8—51no—
94C3×C4⋊Q8—51no—
95C2×#215—101no—
96C2×D3×C8—21no—
97C4×D12C2×D511yescharacteristic
98C3×#103—101no—
99C3×#103—101no—
100C3×C4×C8C2×D511yescharacteristic
101#835—101no—
102(C2×D3)⋊C8—21no—
103#809—101no—
104#807—101no—
105C4⋊(C3⋊C8)—51no—
106C4⋊(C3⋊C8)—51no—
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108C2×C5×D4—31no—
109C22×C4×C5—61no—
110C2×Dic10—21no—
111C2×Dic10—21no—
112C2×C5×C8—61no—
113C2×C5×C8—122no—
114C2×C5×C8#6711yescharacteristic
115C2×C5×C8#6711yescharacteristic
116C5×C4⋊C4—31no—
117C5×C22⋊C4—61no—
118C42×C5C22×D311yescharacteristic
119#687—122no—
120C4⋊Dic5—21no—
121C4⋊Dic5—21no—
122C4⋊Dic5—21no—
123C4⋊Dic5—21no—
124C2×#168—61no—
125C2×#168—61no—
126#487—51no—
127#474—151no—
128#461—151no—
129C8×D4—31no—
130#334—151no—
131#332—151no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×C5×D3—22no—
135C2×C5×D3—41no—
136C2×C5×D3—41no—
137C3×C4×C5—21no—
138C3×C4×C5C2×SD1611yescharacteristic
139C3×C4×C5#13511yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C3×Dic5—81no—
143C3×Dic5—81no—
144C5×Dic3—41no—
145C2×C3×Q8—101no—
146C2×C3×Q8—101no—
147C2×D12D2011yescharacteristic
148C2×C4×D3—21no—
149C2×C3×C8C22⋊D511yescharacteristic
150C2×C3×C8C22⋊D511yescharacteristic
151C3×C4⋊C4—101no—
152C3×C4⋊C4—101no—
153C3×C4⋊C4—101no—
154C3×C4⋊C4—101no—
155C3×C42C22×D511yescharacteristic
156#215—202no—
157(C2×D3)⋊C4—21no—
158C4⋊Dic3D2011yescharacteristic
159C2×C3⋊C8—21no—
160C2×C3⋊C8—101no—
161C2×C3⋊C8—101no—
162D3×C8—42no—
163C23×C5—61no—
164C5×D4—32no—
165C5×D4—61no—
166C2×C4×C5—61no—
167C2×C4×C5—121no—
168C2×C4×C5—121no—
169C2×C4×C5D3×D411yescharacteristic
170C2×C4×C5#23711yescharacteristic
171C2×C4×C5C2×#6711yescharacteristic
172C2×Dic5—41no—
173C2×Dic5—41no—
174Dic10—41no—
175Dic10—41no—
176Dic10—41no—
177Dic10—41no—
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—121no—
181#168—121no—
182#168—121no—
183C2×SD16—301no—
184C22×C8—61no—
185C4⋊Q8—51no—
186C4⋊Q8—51no—
187C4×D4—31no—
188#107—301no—
189C4⋊C8—31no—
190C4⋊C8—151no—
191C4⋊C8—151no—
192#103—101no—
193#103—101no—
194#103—301no—
195#102—301no—
196C22⋊C8—61no—
197C4×C8D3×D511yescharacteristic
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201C5×D3—42no—
202C22×D3—21no—
203C3×Q8—201no—
204C3×Q8—201no—
205C3×Q8—201no—
206C3×Q8—201no—
207C2×C3×C4—201no—
208C2×C3×C4—201no—
209C2×C3×C4C2×D2011yescharacteristic
210C2×C3×C4#70911yescharacteristic
211C2×C3×C4C2×C22⋊D511yescharacteristic
212C2×Dic3—21no—
213D12—21no—
214D12#67712yes—
215C4×D3—41no—
216C4×D3—41no—
217C3×C8—21no—
218C3×C8—21no—
219C3⋊C8—41no—
220C3⋊C8—201no—
221C3⋊C8—201no—
222C22×C5—62no—
223C22×C5—121no—
224C22×C5—121no—
225C22×C5#93811yescharacteristic
226C4×C5—21no—
227C4×C5—121no—
228C4×C5D3×SD1611yescharacteristic
229C4×C5#91611yescharacteristic
230C4×C5#94911yescharacteristic
231C4×C5#95011yescharacteristic
232Dic5—81no—
233Dic5—81no—
234C2×Q8—101no—
235C2×Q8—101no—
236C2×D4—31no—
237C22×C4—61no—
238SD16—602no—
239C2×C8—61no—
240C2×C8—122no—
241C2×C8—301no—
242C2×C8—301no—
243C2×C8#120111yescharacteristic
244C2×C8#120111yescharacteristic
245C4⋊C4—31no—
246C4⋊C4—101no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4—101no—
250C22⋊C4—61no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3#407611yescharacteristic
254C2×D3—22no—
255C2×D3—41no—
256C2×D3—41no—
257C3×C4—21no—
258C3×C4—401no—
259C3×C4—401no—
260C3×C4C2×#67711yescharacteristic
261C3×C4#405011yescharacteristic
262C3×C4#407811yescharacteristic
263C3×C4#409611yescharacteristic
264Dic3—41no—
265C2×C5—122no—
266C2×C5#505711yescharacteristic
267C2×C5#517111yescharacteristic
268C2×C5#519211yescharacteristic
269C23—61no—
270Q8—201no—
271Q8—201no—
272Q8—201no—
273Q8—201no—
274D4—32no—
275D4—61no—
276C2×C4—61no—
277C2×C4—121no—
278C2×C4—121no—
279C2×C4—201no—
280C2×C4—201no—
281C2×C4#676511yescharacteristic
282C2×C4D3×D2011yescharacteristic
283C2×C4C2×#120111yescharacteristic
284C8—21no—
285C8—21no—
286C8—121no—
287C8—601no—
288C8—601no—
289C2×C3#6530511yescharacteristic
290C2×C3#6540311yescharacteristic
291C2×C3#6543211yescharacteristic
292D3—42no—
293C5#7123211yescharacteristic, complemented, Sylow
294C22—62no—
295C22—121no—
296C22—121no—
297C22#9145611yescharacteristic
298C4—21no—
299C4—121no—
300C4—401no—
301C4—401no—
302C4D3×#67711yescharacteristic
303C4#9127211yescharacteristic
304C4#9129711yescharacteristic
305C4#9129911yescharacteristic
306C3#1060164711yescharacteristic, complemented, Sylow
307C2—122no—
308C2#1174703411yescharacteristic
309C2#1174791211yescharacteristic
310C2#1174809411yescharacteristic
subgroupG/H
centerC22#91456
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#121
prime radicalC2×C5×D12D4
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
2. C3×#64970C2semidirect
5. #11746278C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
28. #64970D3semidirect
252. C3×C5#1679semidirect
293. C5#71232semidirect
306. C3#10601647semidirect

Maximal subgroups

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

subgroupindex
C5×C8×D122
C3×#649702
#117470702
#117469002
#117462782
#117458562
#117458552
#106016473
#712325