Finite Group Databasebeta

← C5×#2889⋊C3 #14510958

Subgroups — C5×#2889⋊C3 #14510958

Order 1920.

368 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×C5×2−1+4⋊C3C211yesmaximal, characteristic
2C5×#568⋊C3C212yesmaximal, complemented
3C5×#2889C311yesmaximal, characteristic, complemented, Hall
4C5×2−1+4⋊C3—22no—
5C2×C5×#41⋊C3C2211yescharacteristic
6C22×C5×SL(2,𝔽3)C412yes—
7C5×#131⋊C3—22no—
8C3×C5×#100—41nomaximal
9#2889⋊C3C511yesmaximal, characteristic, direct product factor, Hall
10C2×C5×2−1+4C2×C311yescharacteristic
11C5×#568C2×C312yescomplemented
12C5×#413—31no—
13C5×#413—31no—
14C2×C5×#101—32no—
15C2×C3×C5×D4—41no—
16C5×#41⋊C3D412yes—
17C2×C5×SL(2,𝔽3)—22no—
18C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
19C3×C5×M16—42no—
20C2×2−1+4⋊C3C2×C511yescharacteristic
21#568⋊C3C2×C512yescomplemented
22C5×2−1+4—22no—
23C5×2−1+4—62no—
24C2×C5×#41—31no—
25C2×C5×#41—32no—
26C2×C5×#41C22×C311yescharacteristic
27C22×C5×Q8—31no—
28C22×C5×Q8C3×C412yes—
29C5×#131—22no—
30C5×#131—62no—
31C2×C5×M16—32no—
32C2×C5×M16—32no—
33C5×#101—32no—
34C5×#101—32no—
35C5×#100—31no—
36C5×#100A411yescharacteristic
37#2889C3×C511yescharacteristic, complemented, Sylow
38C23×C3×C5—42no—
39C3×C5×D4—82no—
40C2×C3×C4×C5—41no—
41C5×SL(2,𝔽3)C22⋊C411yescharacteristic
42C3×C5×C8—82no—
432−1+4⋊C3—22no—
44C2×#41⋊C3C22×C511yescharacteristic
45C22×SL(2,𝔽3)C4×C512yes—
46#131⋊C3—22no—
47C3×#100—41no—
48C5×#41—32no—
49C5×#41—62no—
50C5×#41—62no—
51C5×#41—64no—
52C5×#41—64no—
53C5×#41C3×D412yes—
54C2×C5×Q8—22no—
55C2×C5×Q8—31no—
56C2×C5×Q8—32no—
57C2×C5×Q8—62no—
58C2×C5×Q8—62no—
59C2×C5×Q8—62no—
60C2×C5×Q8C2×C3×C411yescharacteristic
61C2×C5×D4—31no—
62C2×C5×D4—32no—
63C2×C5×D4C2×A411yescharacteristic
64C22×C4×C5—31no—
65C22×C4×C5—32no—
66C22×C4×C5—32no—
67C5×M16—32no—
68C5×M16—62no—
69C5×M16—62no—
70C5×M16C2×A412yes—
71C2×C5×C8—62no—
72C2×C5×C8—62no—
73C2×2−1+4C2×C3×C511yescharacteristic
74#568C2×C3×C512yescomplemented
75#413—31no—
76#413—31no—
77C2×#101—32no—
78C22×C3×C5—41no—
79C22×C3×C5—82no—
80C22×C3×C5—162no—
81C3×C4×C5—42no—
82C2×C3×D4—41no—
83#41⋊C3C5×D412yes—
84C2×SL(2,𝔽3)—22no—
85C2×SL(2,𝔽3)C2×C4×C511yescharacteristic
86C3×M16—42no—
87C23×C5—31no—
88C23×C5C4×A412yes—
89C5×Q8—31no—
90C5×Q8—62no—
91C5×Q8—62no—
92C5×Q8—62no—
93C5×Q8C3×C22⋊C411yescharacteristic
94C5×D4—22no—
95C5×D4—32no—
96C5×D4—32no—
97C5×D4—64no—
98C2×C4×C5—31no—
99C2×C4×C5—32no—
100C2×C4×C5—32no—
101C2×C4×C5—32no—
102C2×C4×C5—62no—
103C2×C4×C5—62no—
104C2×C4×C5—64no—
105C2×C4×C5C22×A411yescharacteristic
106C5×C8—22no—
107C5×C8—62no—
1082−1+4—22no—
1092−1+4—62no—
110C2×#41—31no—
111C2×#41—32no—
112C2×#41C22×C3×C511yescharacteristic
113C22×Q8—31no—
114C22×Q8C3×C4×C512yes—
115#131—22no—
116#131—62no—
117C2×M16—32no—
118C2×M16—32no—
119#101—32no—
120#101—32no—
121#100—31no—
122#100C5×A411yescharacteristic
123C2×C3×C5—41no—
124C2×C3×C5—81no—
125C2×C3×C5—162no—
126C23×C3—42no—
127C3×D4—82no—
128C2×C3×C4—41no—
129SL(2,𝔽3)C5×C22⋊C411yescharacteristic
130C3×C8—82no—
131C22×C5—22no—
132C22×C5—32no—
133C22×C5—42no—
134C22×C5—121no—
135C22×C5C2×C4×A411yescharacteristic
136C4×C5—31no—
137C4×C5—31no—
138C4×C5—62no—
139C4×C5D4×A412yes—
140#41—32no—
141#41—62no—
142#41—62no—
143#41—64no—
144#41—64no—
145#41C3×C5×D412yes—
146C2×Q8—22no—
147C2×Q8—31no—
148C2×Q8—32no—
149C2×Q8—62no—
150C2×Q8—62no—
151C2×Q8—62no—
152C2×Q8C2×C3×C4×C511yescharacteristic
153C2×D4—31no—
154C2×D4—32no—
155C2×D4C2×C5×A411yescharacteristic
156C22×C4—31no—
157C22×C4—32no—
158C22×C4—32no—
159M16—32no—
160M16—62no—
161M16—62no—
162M16C2×C5×A412yes—
163C2×C8—62no—
164C2×C8—62no—
165C3×C5—41noHall
166C22×C3—41no—
167C22×C3—82no—
168C22×C3—162no—
169C3×C4—42no—
170C2×C5—21no—
171C2×C5—42no—
172C2×C5—62no—
173C2×C5A4×C22⋊C411yescharacteristic
174C23—31no—
175C23C4×C5×A412yes—
176Q8—31no—
177Q8—62no—
178Q8—62no—
179Q8—62no—
180Q8C3×C5×C22⋊C411yescharacteristic
181D4—22no—
182D4—32no—
183D4—32no—
184D4—64no—
185C2×C4—31no—
186C2×C4—32no—
187C2×C4—32no—
188C2×C4—32no—
189C2×C4—62no—
190C2×C4—62no—
191C2×C4—64no—
192C2×C4C22×C5×A411yescharacteristic
193C8—22no—
194C8—62no—
195C2×C3—41no—
196C2×C3—81no—
197C2×C3—162no—
198C5#2889⋊C311yescharacteristic, direct product factor, Sylow
199C22—22no—
200C22—32no—
201C22—42no—
202C22—121no—
203C22C2×C4×C5×A411yescharacteristic
204C4—31no—
205C4—31no—
206C4—62no—
207C4C5×D4×A412yes—
208C3—41noSylow
209C2—21no—
210C2—42no—
211C2—62no—
212C2C5×A4×C22⋊C411yescharacteristic
subgroupG/H
center, socleC2×C5A4×C22⋊C4
commutatorC2×Q8C2×C3×C4×C5
FrattiniC2×C4C22×C5×A4
FittingC5×#2889C3
prime radicalC2×C5×2−1+4⋊C3C2
cosocleC2×#41C22×C3×C5
hypercenterC5×#100A4
hypocenterQ8C3×C5×C22⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#100

Complements

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

NH ≅ G/Ntype
2. C5×#568⋊C3C2semidirect
3. C5×#2889C3semidirect
9. #2889⋊C3C5direct (N × H)
11. C5×#568C2×C3semidirect
21. #568⋊C3C2×C5semidirect
37. #2889C3×C5semidirect
74. #568C2×C3×C5semidirect
198. C5#2889⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×2−1+4⋊C32
C5×#568⋊C32
C5×#28893
C3×C5×#1004
#2889⋊C35