Finite Group Databasebeta

← C5×#85426 #14511164

Subgroups — C5×#85426 #14511164

Order 1920.

378 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 72 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×Q8×SL(2,𝔽3)C211yesmaximal, characteristic
2C5×#5389C212yesmaximal
3C5×#5388C212yesmaximal
4C4×C5×#226C211yesmaximal, characteristic
5C5×#5386C211yesmaximal, characteristic
6C5×#3387—31nomaximal, Hall
7C2×C5×#226C2211yescharacteristic
8C5×#944—41nomaximal
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10C4×C5×SL(2,𝔽3)C2212yes—
11C5×#859C2212yes—
12C5×#859C2211yescharacteristic
13#85426C511yesmaximal, characteristic, direct product factor, Hall
14C5×Q82D311yescharacteristic
15C5×#557—31no—
16C5×#501—32no—
17C5×#498—31no—
18C5×#479—32no—
19C5×#477—31no—
20C5×#475—32no—
21C5×#475—31no—
22C5×#446—31no—
23C5×#441—32no—
24C4×C5×Q16—31no—
25C2×C3×C5×Q8—41no—
26C2×C5×Dic6—41no—
27C2×C5×SL(2,𝔽3)C2311yescharacteristic
28C5×#226Q812yescomplemented
29C5×Dic3⋊C4—42no—
30C5×Dic3⋊C4—42no—
31C4×C5×Dic3—41no—
32Q8×SL(2,𝔽3)C2×C511yescharacteristic
33#5389C2×C512yes—
34#5388C2×C512yes—
35C4×#226C2×C511yescharacteristic
36#5386C2×C511yescharacteristic
37C2×C5×Q16—31no—
38C5×C4⋊Q8—32no—
39C5×C4⋊Q8—31no—
40C5×C4⋊Q8—31no—
41C5×C4⋊Q8—61no—
42C5×#125—32no—
43C5×#125—62no—
44C4×C5×Q8—31no—
45C4×C5×Q8—31no—
46C4×C5×Q8—32no—
47C4×C5×Q8—61no—
48C4×C5×Q8C2×D311yescharacteristic
49C4×C5×Q8C2×D312yes—
50C5×#107—31no—
51C5×#107—32no—
52C5×#106—32no—
53C5×#106—32no—
54C5×#106—32no—
55C5×C4⋊C8—31no—
56C5×C4⋊C8—32no—
57C5×#103—31no—
58C5×#103—32no—
59C5×#103—31no—
60C5×#103—32no—
61C5×#97—32no—
62C4×C5×C8—31no—
63#3387—31noSylow
64C3×C5×Q8—82no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—42no—
67C2×C5×Dic3—41no—
68C2×C5×Dic3—41no—
69C2×C5×Dic3—42no—
70C5×Dic6—82no—
71C5×SL(2,𝔽3)C2×Q811yescharacteristic
72C2×#226C22×C511yescharacteristic
73#944—41no—
74C4×SL(2,𝔽3)C22×C511yescharacteristic
75C4×SL(2,𝔽3)C22×C512yes—
76#859C22×C512yes—
77#859C22×C511yescharacteristic
78C2×C5×Q8—31no—
79C2×C5×Q8—61no—
80C2×C5×Q8—61no—
81C2×C5×Q8S411yescharacteristic
82C2×C5×Q8C22×D311yescharacteristic
83C5×Q16—32no—
84C5×Q16—32no—
85C2×C5×C8—31no—
86C2×C5×C8—31no—
87C2×C5×C8—32no—
88C5×C4⋊C4—32no—
89C5×C4⋊C4—31no—
90C5×C4⋊C4—31no—
91C5×C4⋊C4—32no—
92C5×C4⋊C4—31no—
93C5×C4⋊C4—32no—
94C5×C4⋊C4—61no—
95C5×C4⋊C4—62no—
96C5×C4⋊C4—61no—
97C5×C4⋊C4—62no—
98C5×C4⋊C4—62no—
99C42×C5—32no—
100C42×C5—31no—
101C42×C5—62no—
102C42×C5—61no—
103Q82C5×D311yescharacteristic
104#557—31no—
105#501—32no—
106#498—31no—
107#479—32no—
108#477—31no—
109#475—32no—
110#475—31no—
111#446—31no—
112#441—32no—
113C4×Q16—31no—
114C22×C3×C5—41no—
115C3×C4×C5—42no—
116C3×C4×C5—82no—
117C5×Dic3—42no—
118C5×Dic3—42no—
119C5×Dic3—82no—
120C2×C3×Q8—41no—
121C2×Dic6—41no—
122C2×SL(2,𝔽3)C23×C511yescharacteristic
123#226C5×Q812yescomplemented
124Dic3⋊C4—42no—
125Dic3⋊C4—42no—
126C4×Dic3—41no—
127C5×Q8—22no—
128C5×Q8—31no—
129C5×Q8—32no—
130C5×Q8—61no—
131C5×Q8—122no—
132C5×Q8—241no—
133C5×Q8D3×Q811yescharacteristic
134C2×C4×C5—31no—
135C2×C4×C5—32no—
136C2×C4×C5—31no—
137C2×C4×C5—61no—
138C2×C4×C5—61no—
139C2×C4×C5—62no—
140C2×C4×C5C2×S412yes—
141C2×C4×C5C2×S411yescharacteristic
142C5×C8—32no—
143C5×C8—61no—
144C5×C8—62no—
145C2×Q16—31no—
146C4⋊Q8—32no—
147C4⋊Q8—31no—
148C4⋊Q8—31no—
149C4⋊Q8—61no—
150#125—32no—
151#125—62no—
152C4×Q8—31no—
153C4×Q8—31no—
154C4×Q8—32no—
155C4×Q8—61no—
156C4×Q8C2×C5×D311yescharacteristic
157C4×Q8C2×C5×D312yes—
158#107—31no—
159#107—32no—
160#106—32no—
161#106—32no—
162#106—32no—
163C4⋊C8—31no—
164C4⋊C8—32no—
165#103—31no—
166#103—32no—
167#103—31no—
168#103—32no—
169#97—32no—
170C4×C8—31no—
171C2×C3×C5—41no—
172C2×C3×C5—41no—
173C2×C3×C5—41no—
174C3×Q8—82no—
175C2×C3×C4—41no—
176C2×C3×C4—42no—
177C2×Dic3—41no—
178C2×Dic3—41no—
179C2×Dic3—42no—
180Dic6—82no—
181SL(2,𝔽3)C2×C5×Q811yescharacteristic
182C22×C5C22×S411yescharacteristic
183C4×C5—22no—
184C4×C5—31no—
185C4×C5—31no—
186C4×C5—62no—
187C4×C5—62no—
188C4×C5—61no—
189C4×C5—122no—
190C4×C5—121no—
191C4×C5#98312yes—
192C2×Q8—31no—
193C2×Q8—61no—
194C2×Q8—61no—
195C2×Q8C5×S411yescharacteristic
196C2×Q8C22×C5×D311yescharacteristic
197Q16—32no—
198Q16—32no—
199C2×C8—31no—
200C2×C8—31no—
201C2×C8—32no—
202C4⋊C4—32no—
203C4⋊C4—31no—
204C4⋊C4—31no—
205C4⋊C4—32no—
206C4⋊C4—32no—
207C4⋊C4—31no—
208C4⋊C4—61no—
209C4⋊C4—62no—
210C4⋊C4—61no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C42—31no—
214C42—32no—
215C42—62no—
216C42—61no—
217C3×C5—41noHall
218C22×C3—41no—
219C3×C4—42no—
220C3×C4—82no—
221Dic3—42no—
222Dic3—42no—
223Dic3—82no—
224C2×C5C2×#98311yescharacteristic
225C2×C5Q8×S411yescharacteristic
226C2×C5#592411yescharacteristic
227Q8—22no—
228Q8—31no—
229Q8—32no—
230Q8—61no—
231Q8—122no—
232Q8—241no—
233Q8C5×D3×Q811yescharacteristic
234C2×C4—31no—
235C2×C4—32no—
236C2×C4—31no—
237C2×C4—61no—
238C2×C4—61no—
239C2×C4—62no—
240C2×C4C2×C5×S412yes—
241C2×C4C2×C5×S411yescharacteristic
242C8—32no—
243C8—61no—
244C8—62no—
245C2×C3—41no—
246C2×C3—41no—
247C2×C3—41no—
248C5#8542611yescharacteristic, direct product factor, Sylow
249C22C22×C5×S411yescharacteristic
250C4—22no—
251C4—31no—
252C4—31no—
253C4—62no—
254C4—62no—
255C4—61no—
256C4—122no—
257C4—121no—
258C4C5×#98312yes—
259C3—41noSylow
260C2C2×C5×#98311yescharacteristic
261C2C5×Q8×S411yescharacteristic
262C2C5×#592411yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC5×Q82D3
prime radicalC2×C5×SL(2,𝔽3)C23
hypercenterC2×C5×Q8S4
hypocenterSL(2,𝔽3)C2×C5×Q8
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C2×C5×Q8

Complements

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

NH ≅ G/Ntype
13. #85426C5direct (N × H)
28. C5×#226Q8semidirect
123. #226C5×Q8semidirect
248. C5#85426direct (N × H)

Maximal subgroups

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

subgroupindex
C5×Q8×SL(2,𝔽3)2
C5×#53892
C5×#53882
C4×C5×#2262
C5×#53862
C5×#33873
C5×#9444
#854265