Finite Group Databasebeta

← C5×#85406 #14511144

Subgroups — C5×#85406 #14511144

Order 1920.

404 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 68 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×C4⋊(#41⋊C3)C211yesmaximal, characteristic
2C5×#5426C212yesmaximal, complemented
3C5×#5425C212yesmaximal, complemented
4C5×#5391C211yesmaximal, characteristic, complemented
5C4×C5×#226C211yesmaximal, characteristic, complemented
6C5×#3333—31nomaximal, Hall
7C2×C5×#41⋊C3C2212yes—
8C2×C5×#226C2211yescharacteristic
9C5×#890—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C5×#859C2211yescharacteristic
12C5×#859C2212yes—
13#85406C511yesmaximal, characteristic, direct product factor, Hall
14C5×#554—31no—
15C5×#550D311yescharacteristic
16C5×#486—31no—
17C5×#480—32no—
18C5×#477—31no—
19C5×#468—32no—
20C5×#460—31no—
21C5×#452—32no—
22C4×C5×Q16—31no—
23C5×#436—31no—
24C5×#417—32no—
25C5×#41⋊C3—22no—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5×#226—21no—
28C3×C5×C4⋊C4—41no—
29C5×C4⋊Dic3—41no—
30C5×C4⋊Dic3—42no—
31C5×Dic3⋊C4—42no—
32C4×C5×Dic3—41no—
33C4⋊(#41⋊C3)C2×C511yescharacteristic
34#5426C2×C512yescomplemented
35#5425C2×C512yescomplemented
36#5391C2×C511yescharacteristic, complemented
37C4×#226C2×C511yescharacteristic, complemented
38C2×C5×#41C2×D312yes—
39C2×C5×Q16—31no—
40C2×C5×SD16—32no—
41C2×C5×M16—32no—
42C5×C4⋊Q8—31no—
43C5×#127—31no—
44C5×#125—61no—
45C5×C22⋊Q8—32no—
46C5×C22⋊Q8—62no—
47C5×#121—32no—
48C4×C5×Q8—31no—
49C4×C5×Q8C2×D311yescharacteristic
50C4×C5×D4—31no—
51C4×C5×D4—61no—
52C2×C5×C4⋊C4—32no—
53C5×#107—31no—
54C5×#107—32no—
55C5×C4⋊C8—31no—
56C5×#103—31no—
57C5×#103—31no—
58C5×#103—32no—
59C5×#102—32no—
60C5×#102—32no—
61C5×#102—32no—
62C5×C22⋊C8—32no—
63C4×C5×C8—31no—
64#3333—31noSylow
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—42no—
67C2×C5×Dic3—41no—
68C2×C5×Dic3—41no—
69C2×C5×Dic3—42no—
70C5×SL(2,𝔽3)#4111yescharacteristic
71C2×#41⋊C3C22×C512yes—
72C2×#226C22×C511yescharacteristic
73#890—41no—
74C4×SL(2,𝔽3)C22×C511yescharacteristic
75#859C22×C511yescharacteristic
76#859C22×C512yes—
77C5×#41—22no—
78C5×#41—62no—
79C2×C5×Q8—31no—
80C2×C5×Q8—61no—
81C2×C5×Q8C22×D311yescharacteristic
82C2×C5×D4—32no—
83C2×C5×D4—31no—
84C2×C5×D4—61no—
85C22×C4×C5—32no—
86C22×C4×C5—62no—
87C5×Q16—61no—
88C5×Q16—61no—
89C5×SD16—122no—
90C5×M16—122no—
91C2×C5×C8—31no—
92C2×C5×C8—32no—
93C2×C5×C8—31no—
94C5×C4⋊C4—31no—
95C5×C4⋊C4—31no—
96C5×C4⋊C4—32no—
97C5×C4⋊C4—61no—
98C5×C4⋊C4—62no—
99C5×C4⋊C4—61no—
100C5×C4⋊C4—62no—
101C5×C4⋊C4S411yescharacteristic
102C5×C22⋊C4—32no—
103C5×C22⋊C4—62no—
104C42×C5—31no—
105C42×C5—61no—
106#554—31no—
107#550C5×D311yescharacteristic
108#486—31no—
109#480—32no—
110#477—31no—
111#468—32no—
112#460—31no—
113#452—32no—
114C4×Q16—31no—
115#436—31no—
116#417—32no—
117C22×C3×C5—41no—
118C3×C4×C5—42no—
119C3×C4×C5—82no—
120C5×Dic3—81no—
121C5×Dic3—81no—
122C5×Dic3—82no—
123#41⋊C3—22no—
124C2×SL(2,𝔽3)C23×C511yescharacteristic
125#226—21no—
126C3×C4⋊C4—41no—
127C4⋊Dic3—41no—
128C4⋊Dic3—42no—
129Dic3⋊C4—42no—
130C4×Dic3—41no—
131C23×C5—32no—
132C5×Q8—31no—
133C5×Q8—61no—
134C5×Q8—61no—
135C5×Q8—241no—
136C5×Q8#23711yescharacteristic
137C5×D4—62no—
138C5×D4—62no—
139C5×D4—62no—
140C5×D4—241no—
141C2×C4×C5—31no—
142C2×C4×C5—31no—
143C2×C4×C5—62no—
144C2×C4×C5—62no—
145C2×C4×C5—61no—
146C2×C4×C5—61no—
147C2×C4×C5—62no—
148C2×C4×C5—242no—
149C2×C4×C5C2×S412yes—
150C2×C4×C5C2×S411yescharacteristic
151C5×C8—61no—
152C5×C8—62no—
153C5×C8—61no—
154C2×#41C2×C5×D312yes—
155C2×Q16—31no—
156C2×SD16—32no—
157C2×M16—32no—
158C4⋊Q8—31no—
159#127—31no—
160#125—61no—
161C22⋊Q8—32no—
162C22⋊Q8—62no—
163#121—32no—
164C4×Q8—31no—
165C4×Q8C2×C5×D311yescharacteristic
166C4×D4—31no—
167C4×D4—61no—
168C2×C4⋊C4—32no—
169#107—31no—
170#107—32no—
171C4⋊C8—31no—
172#103—31no—
173#103—31no—
174#103—32no—
175#102—32no—
176#102—32no—
177#102—32no—
178C22⋊C8—32no—
179C4×C8—31no—
180C2×C3×C5—41no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C4—41no—
184C2×C3×C4—42no—
185C2×Dic3—41no—
186C2×Dic3—42no—
187C2×Dic3—41no—
188SL(2,𝔽3)C5×#4111yescharacteristic
189C22×C5—62no—
190C22×C5—62no—
191C22×C5—62no—
192C22×C5C22×S411yescharacteristic
193C4×C5—22no—
194C4×C5—31no—
195C4×C5—31no—
196C4×C5—61no—
197C4×C5—121no—
198C4×C5—121no—
199C4×C5—122no—
200C4×C5#98412yes—
201#41—22no—
202#41—62no—
203C2×Q8—31no—
204C2×Q8—61no—
205C2×Q8C22×C5×D311yescharacteristic
206C2×D4—32no—
207C2×D4—31no—
208C2×D4—61no—
209C22×C4—32no—
210C22×C4—62no—
211Q16—61no—
212Q16—61no—
213SD16—122no—
214M16—122no—
215C2×C8—31no—
216C2×C8—31no—
217C2×C8—32no—
218C4⋊C4—31no—
219C4⋊C4—31no—
220C4⋊C4—32no—
221C4⋊C4—61no—
222C4⋊C4—62no—
223C4⋊C4—61no—
224C4⋊C4—62no—
225C4⋊C4C5×S411yescharacteristic
226C22⋊C4—32no—
227C22⋊C4—62no—
228C42—31no—
229C42—61no—
230C3×C5—41noHall
231C22×C3—41no—
232C3×C4—42no—
233C3×C4—82no—
234Dic3—81no—
235Dic3—82no—
236Dic3—81no—
237C2×C5—122no—
238C2×C5#591411yescharacteristic
239C2×C5C2×#98411yescharacteristic
240C2×C5#592511yescharacteristic
241C23—32no—
242Q8—31no—
243Q8—61no—
244Q8—61no—
245Q8—241no—
246Q8C5×#23711yescharacteristic
247D4—62no—
248D4—62no—
249D4—62no—
250D4—241no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—62no—
254C2×C4—62no—
255C2×C4—61no—
256C2×C4—61no—
257C2×C4—62no—
258C2×C4—242no—
259C2×C4C2×C5×S412yes—
260C2×C4C2×C5×S411yescharacteristic
261C8—61no—
262C8—62no—
263C8—61no—
264C2×C3—41no—
265C2×C3—41no—
266C2×C3—41no—
267C5#8540611yescharacteristic, direct product factor, Sylow
268C22—62no—
269C22—62no—
270C22—62no—
271C22C22×C5×S411yescharacteristic
272C4—22no—
273C4—31no—
274C4—31no—
275C4—61no—
276C4—121no—
277C4—121no—
278C4—122no—
279C4C5×#98412yes—
280C3—41noSylow
281C2—122no—
282C2C5×#591411yescharacteristic
283C2C2×C5×#98411yescharacteristic
284C2C5×#592511yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC5×#550D3
prime radicalC5×C4⋊(#41⋊C3)C2
hypercenterC5×C4⋊C4S4
hypocenterSL(2,𝔽3)C5×#41
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#5426C2semidirect
3. C5×#5425C2semidirect
4. C5×#5391C2semidirect
5. C4×C5×#226C2semidirect
13. #85406C5direct (N × H)
34. #5426C2×C5semidirect
35. #5425C2×C5semidirect
36. #5391C2×C5semidirect
37. C4×#226C2×C5semidirect
267. C5#85406direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C4⋊(#41⋊C3)2
C5×#54262
C5×#54252
C5×#53912
C4×C5×#2262
C5×#33333
C5×#8904
#854065