Finite Group Databasebeta

← C5×#85337 #14511075

Subgroups — C5×#85337 #14511075

Order 1920.

434 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5426C212yesmaximal
3C5×#5391C212yesmaximal, complemented
4C5×#5386C212yesmaximal, complemented
5C5×#3079—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7C5×#869—41nomaximal
8C4×C5×SL(2,𝔽3)C2211yescharacteristic
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10C5×#859C2214yes—
11#85337C511yesmaximal, characteristic, direct product factor, Hall
12C2×C5×C4⋊Q8—31no—
13C4×C5×#41D311yescharacteristic
14C5×#477—32no—
15C5×#476—32no—
16C5×#475—32no—
17C5×#474—32no—
18C5×#428—32no—
19C5×#423—31no—
20C5×#417—32no—
21C2×C5×Dic6—42no—
22C5×#41⋊C3Q812yescomplemented
23C2×C5×SL(2,𝔽3)C2311yescharacteristic
24C3×C42×C5—41no—
25C5×C4⋊Dic3—42no—
26C5×C4⋊Dic3—42no—
27C4×#41⋊C3C2×C511yescharacteristic
28#5426C2×C512yes—
29#5391C2×C512yescomplemented
30#5386C2×C512yescomplemented
31C2×C5×#41C2×D311yescharacteristic
32C22×C5×Q8—61no—
33C2×C5×M16—32no—
34C5×C4⋊Q8—32no—
35C5×C4⋊Q8—32no—
36C5×C4⋊Q8—61no—
37C5×C4⋊Q8—61no—
38C4×C5×Q8C2×D311yescharacteristic
39C4×C5×Q8C2×D311yescharacteristic
40C4×C5×D4—31no—
41C4×C5×D4—31no—
42C5×#117—31no—
43C2×C5×C4⋊C4—32no—
44C2×C5×C4⋊C4—61no—
45C2×C42×C5—31no—
46C5×#107—34no—
47C5×#106—34no—
48C5×C4⋊C8—32no—
49C5×C4⋊C8—32no—
50C5×#103—34no—
51C5×#102—34no—
52#3079—31noSylow
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—41no—
56C2×C5×Dic3—44no—
57C5×Dic6—84no—
58C5×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
59C2×#41⋊C3C22×C511yescharacteristic
60#869—41no—
61C4×SL(2,𝔽3)C22×C511yescharacteristic
62C4×SL(2,𝔽3)C22×C511yescharacteristic
63#859C22×C514yes—
64C5×#41—32no—
65C5×#41Dic612yescomplemented
66C2×C5×Q8—62no—
67C2×C5×Q8—62no—
68C2×C5×Q8—124no—
69C2×C5×Q8C22×D311yescharacteristic
70C2×C5×D4—31no—
71C22×C4×C5—31no—
72C22×C4×C5—31no—
73C22×C4×C5—31no—
74C22×C4×C5—62no—
75C5×M16—64no—
76C2×C5×C8—34no—
77C5×C4⋊C4—31no—
78C5×C4⋊C4—31no—
79C5×C4⋊C4—34no—
80C5×C4⋊C4—62no—
81C5×C4⋊C4—62no—
82C5×C4⋊C4—62no—
83C5×C22⋊C4—61no—
84C42×C5—31no—
85C42×C5—31no—
86C42×C5—31no—
87C42×C5S411yescharacteristic
88C2×C4⋊Q8—31no—
89C4×#41C5×D311yescharacteristic
90#477—32no—
91#476—32no—
92#475—32no—
93#474—32no—
94#428—32no—
95#423—31no—
96#417—32no—
97C22×C3×C5—41no—
98C3×C4×C5—42no—
99C3×C4×C5—42no—
100C3×C4×C5—42no—
101C5×Dic3—84no—
102C2×Dic6—42no—
103#41⋊C3C5×Q812yescomplemented
104C2×SL(2,𝔽3)C23×C511yescharacteristic
105C3×C42—41no—
106C4⋊Dic3—42no—
107C4⋊Dic3—42no—
108C23×C5—31no—
109C5×Q8—31no—
110C5×Q8—124no—
111C5×Q8—124no—
112C5×Q8C2×Dic611yescharacteristic
113C5×D4—32no—
114C5×D4—61no—
115C2×C4×C5—31no—
116C2×C4×C5—32no—
117C2×C4×C5—32no—
118C2×C4×C5—31no—
119C2×C4×C5—31no—
120C2×C4×C5—62no—
121C2×C4×C5—62no—
122C2×C4×C5—64no—
123C2×C4×C5—124no—
124C2×C4×C5C2×S411yescharacteristic
125C2×C4×C5C2×S411yescharacteristic
126C2×C4×C5C2×S411yescharacteristic
127C5×C8—64no—
128C2×#41C2×C5×D311yescharacteristic
129C22×Q8—61no—
130C2×M16—32no—
131C4⋊Q8—32no—
132C4⋊Q8—32no—
133C4⋊Q8—61no—
134C4⋊Q8—61no—
135C4×Q8C2×C5×D311yescharacteristic
136C4×Q8C2×C5×D311yescharacteristic
137C4×D4—31no—
138C4×D4—31no—
139#117—31no—
140C2×C4⋊C4—32no—
141C2×C4⋊C4—61no—
142C2×C42—31no—
143#107—34no—
144#106—34no—
145C4⋊C8—32no—
146C4⋊C8—32no—
147#103—34no—
148#102—34no—
149C2×C3×C5—41no—
150C2×C3×C5—41no—
151C2×C3×C5—41no—
152C2×C3×C4—41no—
153C2×C3×C4—41no—
154C2×C3×C4—41no—
155C2×Dic3—44no—
156Dic6—84no—
157SL(2,𝔽3)C2×C5×Q811yescharacteristic, complemented
158C22×C5—32no—
159C22×C5—61no—
160C22×C5—61no—
161C22×C5C22×S411yescharacteristic
162C4×C5—31no—
163C4×C5—31no—
164C4×C5—61no—
165C4×C5—61no—
166C4×C5—124no—
167C4×C5A4⋊Q812yes—
168C4×C5#98412yes—
169C4×C5#98612yes—
170#41—32no—
171#41C5×Dic612yescomplemented
172C2×Q8—62no—
173C2×Q8—62no—
174C2×Q8—124no—
175C2×Q8C22×C5×D311yescharacteristic
176C2×D4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—62no—
181M16—64no—
182C2×C8—34no—
183C4⋊C4—31no—
184C4⋊C4—31no—
185C4⋊C4—34no—
186C4⋊C4—62no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C22⋊C4—61no—
190C42—31no—
191C42—31no—
192C42—31no—
193C42C5×S411yescharacteristic
194C3×C5—41noHall
195C22×C3—41no—
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—42no—
199Dic3—84no—
200C2×C5—62no—
201C2×C5C2×A4⋊Q811yescharacteristic
202C2×C5C2×#98411yescharacteristic
203C2×C5C2×#98611yescharacteristic
204C23—31no—
205Q8—31no—
206Q8—124no—
207Q8—124no—
208Q8C2×C5×Dic611yescharacteristic
209D4—32no—
210D4—61no—
211C2×C4—31no—
212C2×C4—32no—
213C2×C4—32no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—64no—
219C2×C4—124no—
220C2×C4C2×C5×S411yescharacteristic
221C2×C4C2×C5×S411yescharacteristic
222C2×C4C2×C5×S411yescharacteristic
223C8—64no—
224C2×C3—41no—
225C2×C3—41no—
226C2×C3—41no—
227C5#8533711yescharacteristic, direct product factor, Sylow
228C22—32no—
229C22—61no—
230C22—61no—
231C22C22×C5×S411yescharacteristic
232C4—31no—
233C4—31no—
234C4—61no—
235C4—61no—
236C4—124no—
237C4C5×A4⋊Q812yes—
238C4C5×#98412yes—
239C4C5×#98612yes—
240C3—41noSylow
241C2—62no—
242C2C2×C5×A4⋊Q811yescharacteristic
243C2C2×C5×#98411yescharacteristic
244C2C2×C5×#98611yescharacteristic
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)C2×C5×Q8
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×#5386C2semidirect
11. #85337C5direct (N × H)
22. C5×#41⋊C3Q8semidirect
29. #5391C2×C5semidirect
30. #5386C2×C5semidirect
58. C5×SL(2,𝔽3)C2×Q8semidirect
65. C5×#41Dic6semidirect
103. #41⋊C3C5×Q8semidirect
157. SL(2,𝔽3)C2×C5×Q8semidirect
171. #41C5×Dic6semidirect
227. C5#85337direct (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×#54262
C5×#53912
C5×#53862
C5×#30793
C5×#8694
#853375