Finite Group Databasebeta

← C5×#85361 #14511099

Subgroups — C5×#85361 #14511099

Order 1920.

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

normal subgroups only

This group has 398 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×#5389C212yesmaximal, complemented
5C5×#5386C212yesmaximal, complemented
6C5×#3084—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C5×#888—41nomaximal
9C4×C5×SL(2,𝔽3)C2212yes—
10C5×#859C2211yescharacteristic
11C5×#859C2212yes—
12C5×#859C2211yescharacteristic
13#85361C511yesmaximal, characteristic, direct product factor, Hall
14C5×#544—31no—
15C5×#520D311yescharacteristic
16C5×#479—32no—
17C5×#478—32no—
18C5×#476—32no—
19C5×#475—32no—
20C5×#428—31no—
21C2×C5×#106—31no—
22C5×#424—31no—
23C5×#417—31no—
24C5×#416—31no—
25C2×C5×Dic6—42no—
26C5×#41⋊C3Q812yescomplemented
27C2×C5×SL(2,𝔽3)C2311yescharacteristic
28C3×C5×C4⋊C4—41no—
29C5×C4⋊Dic3—41no—
30C5×Dic3⋊C4—42no—
31C4×C5×Dic3—41no—
32#520⋊C3C2×C511yescharacteristic
33#5426C2×C511yescharacteristic
34#5424C2×C511yescharacteristic
35#5389C2×C512yescomplemented
36#5386C2×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×#106—32no—
53C5×#106—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#3084—31noSylow
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5—42no—
66C2×C5×Dic3—41no—
67C2×C5×Dic3—41no—
68C2×C5×Dic3—42no—
69C5×Dic6—84no—
70C5×SL(2,𝔽3)C2×Q811yescharacteristic
71C2×#41⋊C3C22×C511yescharacteristic
72#888—41no—
73C4×SL(2,𝔽3)C22×C512yes—
74#859C22×C511yescharacteristic
75#859C22×C512yes—
76#859C22×C511yescharacteristic
77C5×#41—32no—
78C5×#41Dic612yescomplemented
79C2×C5×Q8—62no—
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—31no—
83C22×C4×C5—61no—
84C22×C4×C5—61no—
85C5×M16—62no—
86C2×C5×C8—31no—
87C2×C5×C8—31no—
88C2×C5×C8—32no—
89C2×C5×C8—62no—
90C5×C4⋊C4—32no—
91C5×C4⋊C4—31no—
92C5×C4⋊C4—32no—
93C5×C4⋊C4—31no—
94C5×C4⋊C4—31no—
95C5×C4⋊C4—62no—
96C5×C4⋊C4—62no—
97C5×C4⋊C4—61no—
98C5×C4⋊C4—62no—
99C5×C4⋊C4S411yescharacteristic
100C5×C22⋊C4—32no—
101C5×C22⋊C4—61no—
102C42×C5—32no—
103C42×C5—61no—
104#544—31no—
105#520C5×D311yescharacteristic
106#479—32no—
107#478—32no—
108#476—32no—
109#475—32no—
110#428—31no—
111C2×#106—31no—
112#424—31no—
113#417—31no—
114#416—31no—
115C22×C3×C5—41no—
116C3×C4×C5—42no—
117C3×C4×C5—82no—
118C5×Dic3—42no—
119C5×Dic3—42no—
120C5×Dic3—82no—
121C2×Dic6—42no—
122#41⋊C3C5×Q812yescomplemented
123C2×SL(2,𝔽3)C23×C511yescharacteristic
124C3×C4⋊C4—41no—
125C4⋊Dic3—41no—
126Dic3⋊C4—42no—
127C4×Dic3—41no—
128C23×C5—31no—
129C5×Q8—31no—
130C5×Q8—242no—
131C5×Q8C2×Dic611yescharacteristic
132C5×D4—32no—
133C5×D4—61no—
134C2×C4×C5—31no—
135C2×C4×C5—32no—
136C2×C4×C5—32no—
137C2×C4×C5—32no—
138C2×C4×C5—61no—
139C2×C4×C5—61no—
140C2×C4×C5—62no—
141C2×C4×C5—241no—
142C2×C4×C5—241no—
143C2×C4×C5C2×S412yes—
144C2×C4×C5C2×S411yescharacteristic
145C5×C8—61no—
146C5×C8—61no—
147C5×C8—62no—
148C2×#41C2×C5×D311yescharacteristic
149C2×M16—31no—
150C22×C8—31no—
151C4⋊Q8—32no—
152C4⋊Q8—61no—
153#125—32no—
154#125—61no—
155C22⋊Q8—62no—
156C4×Q8C2×C5×D312yes—
157C4×D4—32no—
158#117—31no—
159#117—31no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—31no—
162#107—32no—
163#106—32no—
164#106—32no—
165#106—32no—
166C4⋊C8—32no—
167C4⋊C8—32no—
168#103—31no—
169#103—31no—
170#103—32no—
171#102—31no—
172#102—31no—
173#102—32no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C5—41no—
177C2×C3×C4—41no—
178C2×C3×C4—42no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—42no—
182Dic6—84no—
183SL(2,𝔽3)C2×C5×Q811yescharacteristic
184C22×C5—32no—
185C22×C5—61no—
186C22×C5—61no—
187C22×C5C22×S411yescharacteristic
188C4×C5—22no—
189C4×C5—31no—
190C4×C5—31no—
191C4×C5—62no—
192C4×C5—121no—
193C4×C5—121no—
194C4×C5—122no—
195C4×C5A4⋊Q812yes—
196#41—32no—
197#41C5×Dic612yescomplemented
198C2×Q8—62no—
199C2×Q8C22×C5×D311yescharacteristic
200C2×D4—31no—
201C22×C4—31no—
202C22×C4—61no—
203C22×C4—61no—
204M16—62no—
205C2×C8—31no—
206C2×C8—31no—
207C2×C8—32no—
208C2×C8—62no—
209C4⋊C4—32no—
210C4⋊C4—31no—
211C4⋊C4—32no—
212C4⋊C4—31no—
213C4⋊C4—31no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4—61no—
217C4⋊C4—62no—
218C4⋊C4C5×S411yescharacteristic
219C22⋊C4—32no—
220C22⋊C4—61no—
221C42—32no—
222C42—61no—
223C3×C5—41noHall
224C22×C3—41no—
225C3×C4—42no—
226C3×C4—82no—
227Dic3—42no—
228Dic3—42no—
229Dic3—82no—
230C2×C5—62no—
231C2×C5C2×A4⋊Q811yescharacteristic
232C2×C5#592411yescharacteristic
233C2×C5#592611yescharacteristic
234C23—31no—
235Q8—31no—
236Q8—242no—
237Q8C2×C5×Dic611yescharacteristic
238D4—32no—
239D4—61no—
240C2×C4—31no—
241C2×C4—32no—
242C2×C4—32no—
243C2×C4—32no—
244C2×C4—61no—
245C2×C4—61no—
246C2×C4—62no—
247C2×C4—241no—
248C2×C4—241no—
249C2×C4C2×C5×S412yes—
250C2×C4C2×C5×S411yescharacteristic
251C8—61no—
252C8—61no—
253C8—62no—
254C2×C3—41no—
255C2×C3—41no—
256C2×C3—41no—
257C5#8536111yescharacteristic, direct product factor, Sylow
258C22—32no—
259C22—61no—
260C22—61no—
261C22C22×C5×S411yescharacteristic
262C4—22no—
263C4—31no—
264C4—31no—
265C4—62no—
266C4—121no—
267C4—122no—
268C4—121no—
269C4C5×A4⋊Q812yes—
270C3—41noSylow
271C2—62no—
272C2C2×C5×A4⋊Q811yescharacteristic
273C2C5×#592411yescharacteristic
274C2C5×#592611yescharacteristic
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×#5389C2semidirect
5. C5×#5386C2semidirect
13. #85361C5direct (N × H)
26. C5×#41⋊C3Q8semidirect
35. #5389C2×C5semidirect
36. #5386C2×C5semidirect
78. C5×#41Dic6semidirect
122. #41⋊C3C5×Q8semidirect
197. #41C5×Dic6semidirect
257. C5#85361direct (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×#53892
C5×#53862
C5×#30843
C5×#8884
#853615