Finite Group Databasebeta

← #14293703

Subgroups — #14293703

Order 1920.

396 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 100 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×#4680C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic
3#11747079C211yesmaximal, characteristic
4#11747079C211yesmaximal, characteristic
5#11746962C211yesmaximal, characteristic, complemented
6#11746924C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10602128—31nomaximal, Hall
9C5×#869C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6655—22no—
14C2×#6655—22no—
15C3×C4×C5×C8C2211yescharacteristic
16C4×C3⋊#168C2211yescharacteristic
17C4×C3⋊#168C2211yescharacteristic
18C5×#817—22no—
19C3×#3953—22no—
20#90989—22no—
21#90970—22no—
22#71184—51nomaximal, Hall
23C5×#498—31no—
24#65382—31no—
25#65374—31no—
26#65374—31no—
27#65367—31no—
28#64983D311yescharacteristic
29#64674—31no—
30C2×C5×Dic6—21no—
31C2×C5×Dic6—21no—
32C2×C3×D20—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8D412yes—
37C3×C42×C5C2311yescharacteristic
38C2×C3⋊#168D412yes—
39C2×C3⋊#168D412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46#6655—44no—
47#6655—44no—
48C3×#486—51no—
49#5079—51no—
50#5078—51no—
51#5076—51no—
52#5076—51no—
53#4680D511yescharacteristic, complemented
54#4454—51no—
55C5×C4⋊Q8—31no—
56C5×C4⋊Q8—31no—
57C2×#688—62no—
58C2×#688—62no—
59#4020C2×D311yescharacteristic
60#4015C2×D311yescharacteristic
61C5×#106—62no—
62C4×C5×C8C2×D311yescharacteristic
63#3953—22no—
64#3942—62no—
65#3939—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1714—151noSylow
69C22×C3×D5—41no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C5×Dic3—41no—
74C2×C5×Dic3—41no—
75C5×Dic6—42no—
76C5×Dic6—42no—
77C2×C3×Dic5—41no—
78C3×D20—42no—
79C3×D20—42no—
80C3×D20—42no—
81C3×Dic10—42no—
82C3×C5×C8—22no—
83C3⋊#168—22no—
84C3⋊#168SD1614yescomplemented
85C3×C4⋊Q8—51no—
86C3×#127—51no—
87C2×#214—102no—
88C2×#214—102no—
89#869C2×D511yescharacteristic
90#869C2×D511yescharacteristic
91C3×#102—102no—
92C3×C4×C8C2×D511yescharacteristic
93#835—102no—
94#817—22no—
95#807—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8—51no—
98C2×C5×Q8—61no—
99C2×C5×Q8—61no—
100C2×D20—21no—
101C2×D20—21no—
102C2×D20—21no—
103C2×Dic10—21no—
104C2×C5×C8#6712yes—
105C5×C4⋊C4—61no—
106C5×C4⋊C4—61no—
107C5×C4⋊C4—61no—
108C5×C4⋊C4—61no—
109C42×C5C22×D311yescharacteristic
110#688—124no—
111#688—124no—
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C2×#168—32no—
115C2×#168—32no—
116#500—151no—
117#498—31no—
118#492—151no—
119#492—151no—
120#487—151no—
121#486—51no—
122#322—151no—
123C22×C3×C5#12711yescharacteristic
124C2×C3×D5—81no—
125C2×C3×D5—81no—
126C2×C3×D5—81no—
127C3×C4×C5C2×SD1612yes—
128C3×C4×C5AGL(1,ℤ/8)12yes—
129C3×C4×C5#13712yes—
130C3×Dic5—81no—
131C5×Dic3—81no—
132C5×Dic3—81no—
133C2×C3×Q8—101no—
134C2×C3×D4—101no—
135C2×C3×D4—101no—
136C2×C3×D4—101no—
137C2×Dic6—21no—
138C2×Dic6—21no—
139C2×C3×C8C22⋊D512yes—
140C3×C4⋊C4—101no—
141C3×C4⋊C4—101no—
142C3×C42C22×D511yescharacteristic
143#214—204no—
144#214—204no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C2×C3⋊C8—52no—
150C2×C3⋊C8—52no—
151C22×D5—41no—
152C5×Q8—122no—
153C5×Q8—122no—
154C2×C4×C5—121no—
155C2×C4×C5—121no—
156C2×C4×C5D3×D411yescharacteristic
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5C2×#6711yescharacteristic
159C2×Dic5—41no—
160D20—42no—
161D20—42no—
162D20—42no—
163Dic10—42no—
164C5×C8—22no—
165#168—34no—
166#168—62no—
167C2×SD16—302no—
168C2×SD16—302no—
169C4⋊Q8—31no—
170C4⋊Q8—31no—
171C4⋊Q8—51no—
172#127—51no—
173#107—302no—
174#106—62no—
175#103—302no—
176#102—102no—
177C4×C8—151no—
178C4×C8—151no—
179C4×C8D3×D511yescharacteristic
180C2×C3×C5#49211yescharacteristic
181C2×C3×C5#49611yescharacteristic
182C2×C3×C5#49711yescharacteristic
183C3×D5—161no—
184C23×C3—201no—
185C3×Q8—202no—
186C3×D4—202no—
187C3×D4—202no—
188C3×D4—202no—
189C2×C3×C4—201no—
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4D4×D511yescharacteristic
192C2×C3×C4C2×C22⋊D511yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—41no—
195Dic6—42no—
196Dic6—42no—
197C3×C8—22no—
198C3⋊C8—54no—
199C3⋊C8—102no—
200C22×C5#94011yescharacteristic
201C2×D5—81no—
202C2×D5—81no—
203C2×D5—81no—
204C4×C5—241no—
205C4×C5—241no—
206C4×C5#91112yes—
207C4×C5D3×SD1612yes—
208C4×C5#95112yes—
209Dic5—81no—
210C2×Q8—61no—
211C2×Q8—61no—
212C2×Q8—101no—
213C2×D4—101no—
214C2×D4—101no—
215C2×D4—101no—
216SD16—604no—
217SD16—604no—
218C2×C8—152no—
219C2×C8—152no—
220C2×C8#120112yes—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—101no—
226C4⋊C4—101no—
227C42C2×D3×D511yescharacteristic
228C3×C5#171411yescharacteristic, complemented, Hall
229C22×C3—401no—
230C22×C3—401no—
231C22×C3—401no—
232C22×C3#408611yescharacteristic
233C3×C4—401no—
234C3×C4D5×SD1612yes—
235C3×C4#406012yes—
236C3×C4#408812yes—
237Dic3—81no—
238Dic3—81no—
239C2×C5#506011yescharacteristic
240C2×C5#515411yescharacteristic
241C2×C5#517511yescharacteristic
242D5—161no—
243C23—201no—
244Q8—122no—
245Q8—122no—
246Q8—202no—
247D4—202no—
248D4—202no—
249D4—202no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—201no—
253C2×C4#677711yescharacteristic
254C2×C4#677711yescharacteristic
255C2×C4C2×#120111yescharacteristic
256C8—22no—
257C8—154no—
258C8—302no—
259C2×C3—801no—
260C2×C3#6537511yescharacteristic
261C2×C3#6546411yescharacteristic
262C2×C3#6546511yescharacteristic
263C5#7118411yescharacteristic, complemented, Sylow
264C22—401no—
265C22—401no—
266C22—401no—
267C22#9146311yescharacteristic
268C4—241no—
269C4—241no—
270C4—401no—
271C4#9125512yes—
272C4#9125812yes—
273C4#9130712yes—
274C3#1060212811yescharacteristic, complemented, Sylow
275C2—801no—
276C2#1174708011yescharacteristic
277C2#1174801011yescharacteristic
278C2#1174801511yescharacteristic
subgroupG/H
centerC22#91463
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radicalC3×#4020C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1714
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
1. C5×#4680C2semidirect
5. #11746962C2semidirect
6. #11746924C2semidirect
7. #11746275C2semidirect
53. #4680D5semidirect
84. C3⋊#168SD16semidirect
228. C3×C5#1714semidirect
263. C5#71184semidirect
274. C3#10602128semidirect

Maximal subgroups

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

subgroupindex
C5×#46802
C3×#649832
#117470792
#117469622
#117469242
#117462752
#106021283
#711845