Finite Group Databasebeta

← C5×#85338 #14511076

Subgroups — C5×#85338 #14511076

Order 1920.

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

normal subgroups only

This group has 394 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2C5×#5425C212yesmaximal
3C5×#5391C211yesmaximal, characteristic, complemented
4C5×C4⋊#226C211yesmaximal, characteristic, complemented
5C5×#5388C212yesmaximal, complemented
6C5×#3116—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×C5×#226C2212yes—
9C5×#870—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12C5×#859C2212yes—
13#85338C511yesmaximal, characteristic, direct product factor, Hall
14C5×#533—31no—
15C4×C5×#41D311yescharacteristic
16C5×#485—32no—
17C5×#477—31no—
18C5×#476—31no—
19C5×#462—31no—
20C5×#461—31no—
21C5×#452—32no—
22C5×#441—32no—
23C5×#440—32no—
24C5×#432—31no—
25C5×#41⋊C3—21no—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5×#226—22no—
28C3×C42×C5—41no—
29C5×C4⋊Dic3—41no—
30C5×C4⋊Dic3—41no—
31C5×Dic3⋊C4—42no—
32C5×Dic3⋊C4—42no—
33C4×#41⋊C3C2×C511yescharacteristic
34#5425C2×C512yes—
35#5391C2×C511yescharacteristic, complemented
36C4⋊#226C2×C511yescharacteristic, complemented
37#5388C2×C512yescomplemented
38C2×C5×#41C2×D311yescharacteristic
39C2×C5×Q16—32no—
40C2×C5×SD16—32no—
41C5×C4⋊Q8—31no—
42C5×C4⋊Q8—31no—
43C5×#125—61no—
44C5×C22⋊Q8—32no—
45C5×C22⋊Q8—61no—
46C4×C5×Q8—32no—
47C4×C5×Q8—61no—
48C4×C5×Q8C2×D311yescharacteristic
49C4×C5×Q8C2×D311yescharacteristic
50C4×C5×D4—31no—
51C4×C5×D4—31no—
52C5×#117—31no—
53C5×#117—61no—
54C2×C42×C5—31no—
55C5×#107—32no—
56C5×#106—32no—
57C5×C4⋊C8—31no—
58C5×C4⋊C8—31no—
59C5×#103—32no—
60C5×#103—32no—
61C5×#103—32no—
62C5×#102—32no—
63C5×C22⋊C8—32no—
64C5×#97—32no—
65#3116—31noSylow
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—41no—
69C2×C5×Dic3—42no—
70C2×C5×Dic3—42no—
71C5×SL(2,𝔽3)#4111yescharacteristic
72C2×#41⋊C3C22×C511yescharacteristic
73C2×#226C22×C512yes—
74#870—41no—
75C4×SL(2,𝔽3)C22×C511yescharacteristic
76C4×SL(2,𝔽3)C22×C511yescharacteristic
77#859C22×C512yes—
78C5×#41—21no—
79C5×#41—61no—
80C2×C5×Q8—32no—
81C2×C5×Q8—61no—
82C2×C5×Q8C22×D311yescharacteristic
83C2×C5×D4—31no—
84C22×C4×C5—31no—
85C22×C4×C5—31no—
86C22×C4×C5—31no—
87C5×Q16—62no—
88C5×Q16—62no—
89C5×SD16—64no—
90C2×C5×C8—32no—
91C2×C5×C8—32no—
92C5×C4⋊C4—31no—
93C5×C4⋊C4—31no—
94C5×C4⋊C4—32no—
95C5×C4⋊C4—61no—
96C5×C4⋊C4—61no—
97C5×C4⋊C4—61no—
98C5×C4⋊C4—62no—
99C5×C4⋊C4—62no—
100C5×C22⋊C4—61no—
101C5×C22⋊C4—62no—
102C42×C5—31no—
103C42×C5—31no—
104C42×C5—31no—
105C42×C5—62no—
106C42×C5S411yescharacteristic
107#533—31no—
108C4×#41C5×D311yescharacteristic
109#485—32no—
110#477—31no—
111#476—31no—
112#462—31no—
113#461—31no—
114#452—32no—
115#441—32no—
116#440—32no—
117#432—31no—
118C22×C3×C5—41no—
119C3×C4×C5—42no—
120C3×C4×C5—81no—
121C3×C4×C5—81no—
122C5×Dic3—82no—
123C5×Dic3—82no—
124#41⋊C3—21no—
125C2×SL(2,𝔽3)C23×C511yescharacteristic
126#226—22no—
127C3×C42—41no—
128C4⋊Dic3—41no—
129C4⋊Dic3—41no—
130Dic3⋊C4—42no—
131Dic3⋊C4—42no—
132C23×C5—31no—
133C5×Q8—31no—
134C5×Q8—62no—
135C5×Q8—62no—
136C5×Q8—122no—
137C5×Q8#23511yescharacteristic
138C5×D4—32no—
139C5×D4—61no—
140C2×C4×C5—31no—
141C2×C4×C5—31no—
142C2×C4×C5—31no—
143C2×C4×C5—61no—
144C2×C4×C5—61no—
145C2×C4×C5—62no—
146C2×C4×C5—62no—
147C2×C4×C5—62no—
148C2×C4×C5—121no—
149C2×C4×C5C2×S411yescharacteristic
150C2×C4×C5C2×S411yescharacteristic
151C2×C4×C5C2×S411yescharacteristic
152C5×C8—62no—
153C5×C8—62no—
154C2×#41C2×C5×D311yescharacteristic
155C2×Q16—32no—
156C2×SD16—32no—
157C4⋊Q8—31no—
158C4⋊Q8—31no—
159#125—61no—
160C22⋊Q8—32no—
161C22⋊Q8—61no—
162C4×Q8—32no—
163C4×Q8—61no—
164C4×Q8C2×C5×D311yescharacteristic
165C4×Q8C2×C5×D311yescharacteristic
166C4×D4—31no—
167C4×D4—31no—
168#117—31no—
169#117—61no—
170C2×C42—31no—
171#107—32no—
172#106—32no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175#103—32no—
176#103—32no—
177#103—32no—
178#102—32no—
179C22⋊C8—32no—
180#97—32no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×Dic3—42no—
188C2×Dic3—42no—
189SL(2,𝔽3)C5×#4111yescharacteristic
190C22×C5—61no—
191C22×C5—61no—
192C22×C5—61no—
193C22×C5C22×S411yescharacteristic
194C4×C5—21no—
195C4×C5—21no—
196C4×C5—31no—
197C4×C5—31no—
198C4×C5—61no—
199C4×C5—61no—
200C4×C5—122no—
201C4×C5—122no—
202C4×C5#98412yes—
203#41—21no—
204#41—61no—
205C2×Q8—32no—
206C2×Q8—61no—
207C2×Q8C22×C5×D311yescharacteristic
208C2×D4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—31no—
212Q16—62no—
213Q16—62no—
214SD16—64no—
215C2×C8—32no—
216C2×C8—32no—
217C4⋊C4—31no—
218C4⋊C4—31no—
219C4⋊C4—32no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—62no—
224C4⋊C4—62no—
225C22⋊C4—61no—
226C22⋊C4—62no—
227C42—31no—
228C42—31no—
229C42—31no—
230C42—62no—
231C42C5×S411yescharacteristic
232C3×C5—41noHall
233C22×C3—41no—
234C3×C4—42no—
235C3×C4—81no—
236C3×C4—81no—
237Dic3—82no—
238Dic3—82no—
239C2×C5—121no—
240C2×C5#591211yescharacteristic
241C2×C5C2×#98411yescharacteristic
242C2×C5#592311yescharacteristic
243C23—31no—
244Q8—31no—
245Q8—62no—
246Q8—62no—
247Q8—122no—
248Q8C5×#23511yescharacteristic
249D4—32no—
250D4—61no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—61no—
255C2×C4—61no—
256C2×C4—62no—
257C2×C4—62no—
258C2×C4—62no—
259C2×C4—121no—
260C2×C4C2×C5×S411yescharacteristic
261C2×C4C2×C5×S411yescharacteristic
262C2×C4C2×C5×S411yescharacteristic
263C8—62no—
264C8—62no—
265C2×C3—41no—
266C2×C3—41no—
267C2×C3—41no—
268C5#8533811yescharacteristic, direct product factor, Sylow
269C22—61no—
270C22—61no—
271C22—61no—
272C22C22×C5×S411yescharacteristic
273C4—21no—
274C4—21no—
275C4—31no—
276C4—31no—
277C4—61no—
278C4—61no—
279C4—122no—
280C4—122no—
281C4C5×#98412yes—
282C3—41noSylow
283C2—121no—
284C2C5×#591211yescharacteristic
285C2C2×C5×#98411yescharacteristic
286C2C5×#592311yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC4×C5×#41D3
prime radicalC2×C5×#41⋊C3C22
hypercenterC42×C5S4
hypocenterSL(2,𝔽3)C5×#41
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C42×C5

Complements

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

NH ≅ G/Ntype
3. C5×#5391C2semidirect
4. C5×C4⋊#226C2semidirect
5. C5×#5388C2semidirect
13. #85338C5direct (N × H)
35. #5391C2×C5semidirect
36. C4⋊#226C2×C5semidirect
37. #5388C2×C5semidirect
268. C5#85338direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
C5×#54252
C5×#53912
C5×C4⋊#2262
C5×#53882
C5×#31163
C5×#8704
#853385