Finite Group Databasebeta

← #10615319⋊C3 #14512262

Subgroups — #10615319⋊C3 #14512262

Order 1920.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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×C4⋊(#41⋊C3)C211yesmaximal, characteristic
2#65904⋊C3C211yesmaximal, characteristic, complemented
3SL(2,𝔽3)×#168C211yesmaximal, characteristic, complemented
4#10615319C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3—21no—
6C4×C5×SL(2,𝔽3)C2211yescharacteristic
7Dic5×SL(2,𝔽3)—21no—
8C3×#3940—41nomaximal
9#3392⋊C3—51nomaximal, Hall
10C5×#550C2×C311yescharacteristic
11#65904C2×C311yescharacteristic
12#65365—31no—
13#65364—31no—
14Q8×#168C2×C311yescharacteristic
15#65308—31no—
16C4×#687—31no—
17C5×#41⋊C3—41no—
18C2×C5×SL(2,𝔽3)D411yescharacteristic
19C3×C5×C4⋊C4—41no—
20C3×C4⋊Dic5—41no—
21C2×C3×#168—41no—
22#557⋊C3—51no—
23C4⋊(#41⋊C3)D511yescharacteristic
24C8×SL(2,𝔽3)—51no—
25C2×C5×#41—21no—
26C5×#127—31no—
27C5×#121—61no—
28C4×C5×Q8C22×C311yescharacteristic
29C4×C5×D4—31no—
30Q8×Dic5—21no—
31C2×#687—32no—
32C2×#687—31no—
33#4036—61no—
34#4015—31no—
35C4×Dic10—31no—
36#3964—31no—
37#3942—31no—
38#3940A411yescharacteristic
39C4⋊#168—31no—
40C4×#168—31no—
41#3392—51noSylow
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5—81no—
44C2×C3×Dic5—81no—
45C5×SL(2,𝔽3)SD1611yescharacteristic, complemented
46C3×#168—42no—
47C2×#41⋊C3—21no—
48C4×SL(2,𝔽3)—101no—
49C4×SL(2,𝔽3)C2×D511yescharacteristic
50C3×#106—201no—
51C5×#41—41no—
52C5×#41—121no—
53C2×C5×Q8C3×D411yescharacteristic
54C2×C5×D4—31no—
55C2×C5×D4—61no—
56C2×C5×D4—61no—
57C22×C4×C5—61no—
58C2×Dic10—31no—
59C5×C4⋊C4—31no—
60C5×C4⋊C4C2×A411yescharacteristic
61C5×C22⋊C4—61no—
62C42×C5—31no—
63#687—62no—
64#687—122no—
65C4⋊Dic5—61no—
66C4⋊Dic5—61no—
67C4⋊Dic5C2×A411yescharacteristic
68#683—61no—
69C4×Dic5—61no—
70C2×#168—31no—
71C2×#168C2×A411yescharacteristic
72#557—51no—
73#550C3×D511yescharacteristic
74#492—151no—
75#461—151no—
76#460—151no—
77C8×Q8—51no—
78C4×SD16—151no—
79C22×C3×C5—41no—
80C3×C4×C5—41no—
81C3×C4×C5—41no—
82C3×C4×C5—161no—
83C3×Dic5—161no—
84#41⋊C3—41no—
85C2×SL(2,𝔽3)C22⋊D511yescharacteristic
86C2×C3×C8—201no—
87C3×C4⋊C4—41no—
88C3×C4⋊C4—201no—
89C23×C5—61no—
90C5×Q8—31no—
91C5×Q8C3×SD1611yescharacteristic
92C5×D4—61no—
93C5×D4—61no—
94C5×D4—121no—
95C5×D4—121no—
96C5×D4—241no—
97C2×C4×C5—21no—
98C2×C4×C5—31no—
99C2×C4×C5—31no—
100C2×C4×C5—121no—
101C2×C4×C5—121no—
102C2×C4×C5C22×A411yescharacteristic
103C2×Dic5—21no—
104C2×Dic5—61no—
105Dic10—61no—
106Dic10—61no—
107#168—61no—
108#168#41⋊C312yescomplemented
109C2×#41—21no—
110C2×SD16—151no—
111C2×SD16—152no—
112C4⋊Q8—151no—
113#127—31no—
114#125—301no—
115#121—61no—
116C4×Q8—101no—
117C4×Q8—151no—
118C4×Q8C2×C3×D511yescharacteristic
119C4×D4—31no—
120#106—51no—
121C4⋊C8—151no—
122#103—151no—
123#102—151no—
124C4×C8—151no—
125C2×C3×C5—41no—
126C2×C3×C5—41no—
127C2×C3×C5—41no—
128C2×C3×C4—41no—
129C2×C3×C4—81no—
130C2×C3×C4—401no—
131SL(2,𝔽3)#68711yescharacteristic, complemented
132C3×C8—202no—
133C22×C5—121no—
134C22×C5—121no—
135C22×C5—121no—
136C22×C5D4×A411yescharacteristic
137C4×C5—31no—
138C4×C5—31no—
139C4×C5—41no—
140C4×C5—61no—
141C4×C5C2×#41⋊C311yescharacteristic
142C4×C5#99411yescharacteristic
143Dic5—41no—
144Dic5—121no—
145#41—41no—
146#41—121no—
147C2×Q8—151no—
148C2×Q8C3×C22⋊D511yescharacteristic
149C2×D4—31no—
150C2×D4—61no—
151C2×D4—61no—
152C22×C4—61no—
153SD16—302no—
154SD16—602no—
155C2×C8—51no—
156C2×C8—151no—
157C4⋊C4—31no—
158C4⋊C4—51no—
159C4⋊C4—301no—
160C4⋊C4—301no—
161C4⋊C4—301no—
162C4⋊C4D5×A411yescharacteristic
163C22⋊C4—61no—
164C42—31no—
165C42—301no—
166C3×C5—41noHall
167C22×C3—41no—
168C3×C4—41no—
169C3×C4—41no—
170C3×C4—161no—
171C3×C4—801no—
172C2×C5—241no—
173C2×C5C4⋊(#41⋊C3)11yescharacteristic
174C2×C5A4×SD1611yescharacteristic
175C2×C5#577⋊C311yescharacteristic
176C23—61no—
177Q8—31no—
178Q8—301no—
179Q8—301no—
180Q8C3×#68711yescharacteristic
181D4—61no—
182D4—61no—
183D4—121no—
184D4—121no—
185D4—241no—
186C2×C4—21no—
187C2×C4—31no—
188C2×C4—31no—
189C2×C4—101no—
190C2×C4—121no—
191C2×C4—121no—
192C2×C4—301no—
193C2×C4C2×D5×A411yescharacteristic
194C8—52no—
195C8—301no—
196C2×C3—41no—
197C2×C3—41no—
198C2×C3—41no—
199C5#3392⋊C311yescharacteristic, complemented, Sylow
200C22—121no—
201C22—121no—
202C22—121no—
203C22A4×C22⋊D511yescharacteristic
204C4—31no—
205C4—31no—
206C4—41no—
207C4—61no—
208C4—201no—
209C4—601no—
210C4C5⋊#99411yescharacteristic
211C4D5×#41⋊C311yescharacteristic
212C3—41noSylow
213C2—241no—
214C2A4×#68711yescharacteristic
215C2#66168⋊C311yescharacteristic
216C2#66170⋊C311yescharacteristic
subgroupG/H
centerC22A4×C22⋊D5
commutator, cosocleC4×C5×Q8C22×C3
FrattiniC2×C4C2×D5×A4
FittingC5×#550C2×C3
socleC22×C5D4×A4
prime radicalC5×C4⋊(#41⋊C3)C2
hypercenterC4⋊C4D5×A4
hypocenterC5×Q8C3×SD16
LCSG ▷ C4×C5×Q8 ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #65904⋊C3C2semidirect
3. SL(2,𝔽3)×#168C2semidirect
4. #10615319C3semidirect
45. C5×SL(2,𝔽3)SD16semidirect
108. #168#41⋊C3semidirect
131. SL(2,𝔽3)#687semidirect
199. C5#3392⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×C4⋊(#41⋊C3)2
#65904⋊C32
SL(2,𝔽3)×#1682
#106153193
C3×#39404
#3392⋊C35