Finite Group Databasebeta

← C5×#85363 #14511101

Subgroups — C5×#85363 #14511101

Order 1920.

386 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 76 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×#520⋊C3C211yesmaximal, characteristic
2C5×#5426C211yesmaximal, characteristic
3C5×#5424C211yesmaximal, characteristic
4C5×#5391C212yesmaximal, complemented
5C5×#5389C212yesmaximal, complemented
6C5×#3083—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C5×#890—41nomaximal
9C4×C5×SL(2,𝔽3)C2212yes—
10C5×#859C2211yescharacteristic
11C5×#859C2212yes—
12C5×#859C2211yescharacteristic
13#85363C511yesmaximal, characteristic, direct product factor, Hall
14C5×#544—31no—
15C5×#520D311yescharacteristic
16C5×#479—32no—
17C5×#478—32no—
18C5×#477—32no—
19C5×#474—32no—
20C5×#428—31no—
21C2×C5×#107—31no—
22C5×#424—31no—
23C5×#417—31no—
24C5×#416—31no—
25C5×#41⋊C3Q812yescomplemented
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C3×C5×C4⋊C4—41no—
28C5×C4⋊Dic3—42no—
29C5×C4⋊Dic3—41no—
30C5×Dic3⋊C4—42no—
31C4×C5×Dic3—41no—
32#520⋊C3C2×C511yescharacteristic
33#5426C2×C511yescharacteristic
34#5424C2×C511yescharacteristic
35#5391C2×C512yescomplemented
36#5389C2×C512yescomplemented
37C2×C5×#41C2×D311yescharacteristic
38C2×C5×M16—31no—
39C22×C5×C8—31no—
40C5×C4⋊Q8—32no—
41C5×C4⋊Q8—61no—
42C5×#125—32no—
43C5×#125—61no—
44C5×C22⋊Q8—62no—
45C4×C5×Q8C2×D312yes—
46C4×C5×D4—32no—
47C5×#117—31no—
48C5×#117—31no—
49C2×C5×C4⋊C4—31no—
50C2×C5×C4⋊C4—31no—
51C5×#107—32no—
52C5×#107—32no—
53C5×#107—32no—
54C5×#106—32no—
55C5×C4⋊C8—32no—
56C5×C4⋊C8—32no—
57C5×#103—31no—
58C5×#103—31no—
59C5×#103—32no—
60C5×#102—31no—
61C5×#102—31no—
62C5×#102—32no—
63#3083—31noSylow
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5—42no—
66C2×C5×Dic3—41no—
67C2×C5×Dic3—41no—
68C2×C5×Dic3—42no—
69C5×SL(2,𝔽3)C2×Q811yescharacteristic
70C2×#41⋊C3C22×C511yescharacteristic
71#890—41no—
72C4×SL(2,𝔽3)C22×C512yes—
73#859C22×C511yescharacteristic
74#859C22×C512yes—
75#859C22×C511yescharacteristic
76C5×#41—32no—
77C5×#41Dic612yes—
78C2×C5×Q8—62no—
79C2×C5×Q8C22×D311yescharacteristic
80C2×C5×D4—31no—
81C22×C4×C5—31no—
82C22×C4×C5—61no—
83C22×C4×C5—61no—
84C5×M16—62no—
85C2×C5×C8—31no—
86C2×C5×C8—31no—
87C2×C5×C8—32no—
88C2×C5×C8—62no—
89C5×C4⋊C4—32no—
90C5×C4⋊C4—31no—
91C5×C4⋊C4—32no—
92C5×C4⋊C4—31no—
93C5×C4⋊C4—31no—
94C5×C4⋊C4—62no—
95C5×C4⋊C4—61no—
96C5×C4⋊C4—62no—
97C5×C4⋊C4—62no—
98C5×C4⋊C4S411yescharacteristic
99C5×C22⋊C4—32no—
100C5×C22⋊C4—61no—
101C42×C5—32no—
102C42×C5—61no—
103#544—31no—
104#520C5×D311yescharacteristic
105#479—32no—
106#478—32no—
107#477—32no—
108#474—32no—
109#428—31no—
110C2×#107—31no—
111#424—31no—
112#417—31no—
113#416—31no—
114C22×C3×C5—41no—
115C3×C4×C5—42no—
116C3×C4×C5—82no—
117C5×Dic3—82no—
118C5×Dic3—81no—
119C5×Dic3—81no—
120#41⋊C3C5×Q812yescomplemented
121C2×SL(2,𝔽3)C23×C511yescharacteristic
122C3×C4⋊C4—41no—
123C4⋊Dic3—42no—
124C4⋊Dic3—41no—
125Dic3⋊C4—42no—
126C4×Dic3—41no—
127C23×C5—31no—
128C5×Q8—31no—
129C5×Q8—242no—
130C5×Q8C2×Dic611yescharacteristic
131C5×D4—32no—
132C5×D4—61no—
133C2×C4×C5—31no—
134C2×C4×C5—32no—
135C2×C4×C5—32no—
136C2×C4×C5—32no—
137C2×C4×C5—61no—
138C2×C4×C5—61no—
139C2×C4×C5—62no—
140C2×C4×C5—241no—
141C2×C4×C5—241no—
142C2×C4×C5C2×S412yes—
143C2×C4×C5C2×S411yescharacteristic
144C5×C8—61no—
145C5×C8—61no—
146C5×C8—62no—
147C2×#41C2×C5×D311yescharacteristic
148C2×M16—31no—
149C22×C8—31no—
150C4⋊Q8—32no—
151C4⋊Q8—61no—
152#125—32no—
153#125—61no—
154C22⋊Q8—62no—
155C4×Q8C2×C5×D312yes—
156C4×D4—32no—
157#117—31no—
158#117—31no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—31no—
161#107—32no—
162#107—32no—
163#107—32no—
164#106—32no—
165C4⋊C8—32no—
166C4⋊C8—32no—
167#103—31no—
168#103—31no—
169#103—32no—
170#102—31no—
171#102—31no—
172#102—32no—
173C2×C3×C5—41no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C4—41no—
177C2×C3×C4—42no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—42no—
181SL(2,𝔽3)C2×C5×Q811yescharacteristic
182C22×C5—32no—
183C22×C5—61no—
184C22×C5—61no—
185C22×C5C22×S411yescharacteristic
186C4×C5—22no—
187C4×C5—31no—
188C4×C5—31no—
189C4×C5—62no—
190C4×C5—122no—
191C4×C5—121no—
192C4×C5—121no—
193C4×C5A4⋊Q812yes—
194#41—32no—
195#41C5×Dic612yes—
196C2×Q8—62no—
197C2×Q8C22×C5×D311yescharacteristic
198C2×D4—31no—
199C22×C4—31no—
200C22×C4—61no—
201C22×C4—61no—
202M16—62no—
203C2×C8—32no—
204C2×C8—31no—
205C2×C8—31no—
206C2×C8—62no—
207C4⋊C4—32no—
208C4⋊C4—31no—
209C4⋊C4—31no—
210C4⋊C4—32no—
211C4⋊C4—31no—
212C4⋊C4—62no—
213C4⋊C4—61no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4C5×S411yescharacteristic
217C22⋊C4—32no—
218C22⋊C4—61no—
219C42—32no—
220C42—61no—
221C3×C5—41noHall
222C22×C3—41no—
223C3×C4—42no—
224C3×C4—82no—
225Dic3—82no—
226Dic3—81no—
227Dic3—81no—
228C2×C5—62no—
229C2×C5C2×A4⋊Q811yescharacteristic
230C2×C5#592511yescharacteristic
231C2×C5#592711yescharacteristic
232C23—31no—
233Q8—31no—
234Q8—242no—
235Q8C2×C5×Dic611yescharacteristic
236D4—32no—
237D4—61no—
238C2×C4—31no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—32no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—62no—
245C2×C4—241no—
246C2×C4—241no—
247C2×C4C2×C5×S412yes—
248C2×C4C2×C5×S411yescharacteristic
249C8—61no—
250C8—61no—
251C8—62no—
252C2×C3—41no—
253C2×C3—41no—
254C2×C3—41no—
255C5#8536311yescharacteristic, direct product factor, Sylow
256C22—32no—
257C22—61no—
258C22—61no—
259C22C22×C5×S411yescharacteristic
260C4—22no—
261C4—31no—
262C4—31no—
263C4—62no—
264C4—122no—
265C4—121no—
266C4—121no—
267C4C5×A4⋊Q812yes—
268C3—41noSylow
269C2—62no—
270C2C2×C5×A4⋊Q811yescharacteristic
271C2C5×#592511yescharacteristic
272C2C5×#592711yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC5×#520D3
prime radicalC2×C5×#41⋊C3C22
hypercenterC5×C4⋊C4S4
hypocenterSL(2,𝔽3)C2×C5×Q8
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
4. C5×#5391C2semidirect
5. C5×#5389C2semidirect
13. #85363C5direct (N × H)
25. C5×#41⋊C3Q8semidirect
35. #5391C2×C5semidirect
36. #5389C2×C5semidirect
120. #41⋊C3C5×Q8semidirect
255. C5#85363direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#520⋊C32
C5×#54262
C5×#54242
C5×#53912
C5×#53892
C5×#30833
C5×#8904
#853635