Finite Group Databasebeta

← #14292822

Subgroups — #14292822

Order 1920.

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

normal subgroups only

This group has 304 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×#65138C211yesmaximal, characteristic
2#11747095C211yesmaximal, characteristic
3#11746960C211yesmaximal, characteristic
4#11746861C211yesmaximal, characteristic
5#11746303C211yesmaximal, characteristic
6C5×#4480C211yesmaximal, characteristic
7#11745856C211yesmaximal, characteristic
8#10599345—31nomaximal, Hall
9#91758C2211yescharacteristic
10C2×C3×Dic20—21no—
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13C2×#6662—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3948—21no—
19#90990—21no—
20#90990—21no—
21#90982—21no—
22#90974—21no—
23#90952—21no—
24#71057—51nomaximal, Hall
25#65138—31no—
26#65138D311yescharacteristic
27#64971—31no—
28#64968—31no—
29C5×#334—31no—
30#64702—31no—
31#64702—31no—
32C2×Dic30—21no—
33C2×C3×Dic10—21no—
34C2×C3×Dic10D411yescharacteristic
35C2×C3×C5×C8—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C2×C3⋊#168—21no—
40C2×C5×C3⋊C8—21no—
41C2×C5×C3⋊C8D411yescharacteristic
42C2×C5×C3⋊C8D411yescharacteristic
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C3×Dic20—42no—
49#6662—42no—
50C3×#462—51no—
51#5078—51no—
52#5031—51no—
53#5024—51no—
54#4547—51no—
55#4482—51no—
56#4480D511yescharacteristic
57C2×Dic20—21no—
58C2×Dic20—61no—
59#4015—31no—
60#4015C2×D311yescharacteristic
61C4×Dic10C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8—31no—
65#3950—61no—
66#3950—61no—
67#3948—21no—
68#3948—61no—
69#3947—61no—
70#3946—61no—
71C4⋊#168—31no—
72#1694—151noSylow
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—41no—
77Dic30—41no—
78Dic30—41no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—41no—
82C3×Dic10—21no—
83C3×Dic10—21no—
84C3×Dic10—41no—
85C3×Dic10—41no—
86C3×C5×C8—41no—
87C3⋊#168—41no—
88C5×C3⋊C8—21no—
89C5×C3⋊C8—41no—
90C5×C3⋊C8Q1612yescomplemented
91C2×C3×Q16—101no—
92C3×C4⋊Q8—51no—
93C3×C4×Q8—51no—
94C2×#216—101no—
95#869—51no—
96C3×C4⋊C8C2×D511yescharacteristic
97C3×#103—101no—
98#810—101no—
99#807—101no—
100#807—101no—
101C4⋊(C3⋊C8)—51no—
102C4⋊(C3⋊C8)—101no—
103C4⋊(C3⋊C8)C2×D511yescharacteristic
104#803—101no—
105C4×C3⋊C8C2×D511yescharacteristic
106C2×Dic10—21no—
107C2×Dic10—61no—
108C2×Dic10#6711yescharacteristic
109C2×C5×C8—21no—
110C2×C5×C8—31no—
111C2×C5×C8—31no—
112C2×C5×C8—61no—
113C42×C5C22×D311yescharacteristic
114C4⋊Dic5—21no—
115C4⋊Dic5—21no—
116C4⋊Dic5—61no—
117C4⋊Dic5—61no—
118C4⋊Dic5#6711yescharacteristic
119#683—21no—
120C4×Dic5—21no—
121C2×#168—61no—
122Dic20—42no—
123Dic20—122no—
124#500—151no—
125#462—51no—
126#462—151no—
127#446—151no—
128#334—31no—
129#332—151no—
130#332—151no—
131C22×C3×C5#12111yescharacteristic
132C3×C4×C5—21no—
133C3×C4×C5C2×Q1611yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C3×C4×C5#13711yescharacteristic
137Dic15—81no—
138C3×Dic5—41no—
139C3×Dic5—41no—
140C3×Dic5—81no—
141C2×C3×Q8—51no—
142C2×C3×Q8—101no—
143C2×Dic6—101no—
144C3×Q16—202no—
145C2×C3×C8—21no—
146C3×C4⋊C4—51no—
147C3×C4⋊C4—101no—
148C3×C4⋊C4—101no—
149C3×C4⋊C4—101no—
150C3×C42—101no—
151C3×C42C22×D511yescharacteristic
152#216—202no—
153C4⋊Dic3—101no—
154C4⋊Dic3—101no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—101no—
157C2×C3⋊C8D2011yescharacteristic
158C2×C3⋊C8D2011yescharacteristic
159C2×C4×C5D3×D411yescharacteristic
160C2×C4×C5#23711yescharacteristic
161C2×C4×C5C2×#6711yescharacteristic
162C2×Dic5—21no—
163C2×Dic5—21no—
164C2×Dic5—41no—
165C2×Dic5—121no—
166Dic10—21no—
167Dic10—21no—
168Dic10—41no—
169Dic10—41no—
170Dic10—121no—
171Dic10—121no—
172C5×C8—32no—
173C5×C8—41no—
174C5×C8—61no—
175C5×C8—121no—
176#168—121no—
177C2×Q16—101no—
178C2×Q16—301no—
179C4⋊Q8—51no—
180C4⋊Q8—151no—
181C4×Q8—51no—
182#107—301no—
183#107—301no—
184C4⋊C8—31no—
185C4⋊C8—151no—
186C4⋊C8—301no—
187C4⋊C8D3×D511yescharacteristic
188#103—101no—
189#103—301no—
190#97—301no—
191C4×C8—31no—
192C2×C3×C5#46211yescharacteristic
193C2×C3×C5#46911yescharacteristic
194C2×C3×C5#47311yescharacteristic
195C3×Q8—101no—
196C3×Q8—101no—
197C3×Q8—201no—
198C3×Q8—201no—
199C2×C3×C4—101no—
200C2×C3×C4—101no—
201C2×C3×C4—201no—
202C2×C3×C4C2×D2011yescharacteristic
203C2×C3×C4D4×D511yescharacteristic
204C2×C3×C4#71311yescharacteristic
205C2×Dic3—201no—
206Dic6—201no—
207Dic6—201no—
208C3×C8—41no—
209C3⋊C8—21no—
210C3⋊C8—41no—
211C3⋊C8—201no—
212C3⋊C8Dic2012yescomplemented
213C22×C5#93911yescharacteristic
214C4×C5—21no—
215C4×C5D3×Q1611yescharacteristic
216C4×C5#91811yescharacteristic
217C4×C5#93211yescharacteristic
218C4×C5#94911yescharacteristic
219Dic5—41no—
220Dic5—41no—
221Dic5—81no—
222Dic5—241no—
223C2×Q8—51no—
224C2×Q8—101no—
225C2×Q8—301no—
226Q16—202no—
227Q16—602no—
228C2×C8—21no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—61no—
232C2×C8—301no—
233C4⋊C4—51no—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—101no—
237C4⋊C4—301no—
238C4⋊C4—301no—
239C42—101no—
240C42C2×D3×D511yescharacteristic
241C3×C5#169411yescharacteristic, complemented, Hall
242C22×C3#404111yescharacteristic
243C3×C4—21no—
244C3×C4—201no—
245C3×C4—201no—
246C3×C4—401no—
247C3×C4C2×Dic2011yescharacteristic
248C3×C4#405511yescharacteristic
249C3×C4#406011yescharacteristic
250C3×C4#406011yescharacteristic
251Dic3—401no—
252C2×C5#503911yescharacteristic
253C2×C5#518211yescharacteristic
254C2×C5#520411yescharacteristic
255Q8—101no—
256Q8—101no—
257Q8—201no—
258Q8—201no—
259Q8—601no—
260Q8—601no—
261C2×C4—101no—
262C2×C4—101no—
263C2×C4—201no—
264C2×C4—601no—
265C2×C4#676611yescharacteristic
266C2×C4D3×D2011yescharacteristic
267C2×C4D5×#6711yescharacteristic
268C8—32no—
269C8—41no—
270C8—61no—
271C8—121no—
272C8—601no—
273C2×C3#6513811yescharacteristic
274C2×C3#6515411yescharacteristic
275C2×C3#6518511yescharacteristic
276C5#7105711yescharacteristic, complemented, Sylow
277C22#9140911yescharacteristic
278C4—21no—
279C4—201no—
280C4—201no—
281C4—401no—
282C4—1201no—
283C4D3×Dic2011yescharacteristic
284C4#9126311yescharacteristic
285C4#9149111yescharacteristic
286C4#9150211yescharacteristic
287C3#1059934511yescharacteristic, complemented, Sylow
288C2#1174746111yescharacteristic
289C2#1174784011yescharacteristic
290C2#1174818211yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1694
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
90. C5×C3⋊C8Q16semidirect
212. C3⋊C8Dic20semidirect
241. C3×C5#1694semidirect
276. C5#71057semidirect
287. C3#10599345semidirect

Maximal subgroups

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

subgroupindex
C3×#651382
#117470952
#117469602
#117468612
#117463032
C5×#44802
#117458562
#105993453
#710575