Finite Group Databasebeta

← C5×#3416⋊C3 #14511005

Subgroups — C5×#3416⋊C3 #14511005

Order 1920.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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×#578⋊C3C211yesmaximal, characteristic, complemented
2C5×#576⋊C3C211yesmaximal, characteristic, complemented
3C5×#504⋊C3C211yesmaximal, characteristic, complemented
4C5×#3416C311yesmaximal, characteristic, complemented, Hall
5C5×2−1+4⋊C3—21no—
6C5×#994—21no—
7C5×#131⋊C3C2211yescharacteristic
8C3×C5×SD32—41nomaximal
9#3416⋊C3C511yesmaximal, characteristic, direct product factor, Hall
10C5×#578C2×C311yescharacteristic
11C5×#576C2×C311yescharacteristic, complemented
12C5×#510—31no—
13C5×#509—31no—
14C5×#508—31no—
15C2×C5×SD32—31no—
16C5×#504C2×C311yescharacteristic, complemented
17C5×#41⋊C3—41no—
18C5×#41⋊C3D411yescharacteristic
19C2×C5×SL(2,𝔽3)—41no—
20C3×C5×Q16—41no—
21C3×C5×D8—41no—
22C3×C5×C16—41no—
23#578⋊C3C2×C511yescharacteristic, complemented
24#576⋊C3C2×C511yescharacteristic, complemented
25#504⋊C3C2×C511yescharacteristic, complemented
26C5×2−1+4—21no—
27C5×H(5,𝔽2)—21no—
28C5×#137—61no—
29C5×AGL(1,ℤ/8)—61no—
30C5×#135—31no—
31C5×#135—31no—
32C2×C5×Q16—31no—
33C2×C5×D8—31no—
34C5×#131C22×C311yescharacteristic
35C5×Q32—31no—
36C5×SD32—32no—
37C5×SD32—31no—
38C5×SD32A411yescharacteristic
39C5×D16—31no—
40C5×M32—31no—
41C2×C5×C16—31no—
42#3416C3×C511yescharacteristic, complemented, Sylow
43C3×C5×Q8—81no—
44C3×C5×D4—81no—
45C5×SL(2,𝔽3)D811yescharacteristic
46C3×C5×C8—41no—
472−1+4⋊C3—21no—
48#994—21no—
49#131⋊C3C22×C511yescharacteristic
50C3×SD32—41no—
51C5×#41—41no—
52C5×#41—61no—
53C5×#41—61no—
54C5×#41—121no—
55C5×#41C3×D411yescharacteristic
56C2×C5×Q8—41no—
57C2×C5×Q8—61no—
58C2×C5×D4—61no—
59C2×C5×D4—121no—
60C5×Q16—31no—
61C5×Q16—61no—
62C5×Q16C2×A411yescharacteristic
63C5×SD16—61no—
64C5×SD16—61no—
65C5×D8—31no—
66C5×D8—61no—
67C5×D8C2×A411yescharacteristic
68C5×M16—31no—
69C2×C5×C8—31no—
70C5×C16—31no—
71C5×C16C2×A411yescharacteristic
72#578C2×C3×C511yescharacteristic
73#576C2×C3×C511yescharacteristic, complemented
74#510—31no—
75#509—31no—
76#508—31no—
77C2×SD32—31no—
78#504C2×C3×C511yescharacteristic, complemented
79C22×C3×C5—161no—
80C3×C4×C5—41no—
81C3×C4×C5—161no—
82#41⋊C3—41no—
83#41⋊C3C5×D411yescharacteristic
84C2×SL(2,𝔽3)—41no—
85C3×Q16—41no—
86C3×D8—41no—
87C3×C16—41no—
88C23×C5—121no—
89C5×Q8—21no—
90C5×Q8—61no—
91C5×Q8—121no—
92C5×Q8C3×D811yescharacteristic
93C5×D4—21no—
94C5×D4—31no—
95C5×D4—61no—
96C5×D4—121no—
97C5×D4—121no—
98C5×D4—121no—
99C2×C4×C5—31no—
100C2×C4×C5—121no—
101C2×C4×C5—121no—
102C2×C4×C5—121no—
103C5×C8—31no—
104C5×C8C22×A411yescharacteristic
1052−1+4—21no—
106H(5,𝔽2)—21no—
107#137—61no—
108AGL(1,ℤ/8)—61no—
109#135—31no—
110#135—31no—
111C2×Q16—31no—
112C2×D8—31no—
113#131C22×C3×C511yescharacteristic
114Q32—31no—
115SD32—32no—
116SD32—31no—
117SD32C5×A411yescharacteristic
118D16—31no—
119M32—31no—
120C2×C16—31no—
121C2×C3×C5—41no—
122C2×C3×C5—321no—
123C3×Q8—81no—
124C3×D4—81no—
125SL(2,𝔽3)C5×D811yescharacteristic
126C3×C8—41no—
127C22×C5—31no—
128C22×C5—41no—
129C22×C5—121no—
130C22×C5—481no—
131C4×C5—31no—
132C4×C5—41no—
133C4×C5—121no—
134C4×C5D4×A411yescharacteristic
135#41—41no—
136#41—61no—
137#41—61no—
138#41—121no—
139#41C3×C5×D411yescharacteristic
140C2×Q8—41no—
141C2×Q8—61no—
142C2×D4—61no—
143C2×D4—121no—
144Q16—31no—
145Q16—61no—
146Q16C2×C5×A411yescharacteristic
147SD16—61no—
148SD16—61no—
149D8—31no—
150D8—61no—
151D8C2×C5×A411yescharacteristic
152M16—31no—
153C2×C8—31no—
154C16—31no—
155C16C2×C5×A411yescharacteristic
156C3×C5—41noHall
157C22×C3—161no—
158C3×C4—41no—
159C3×C4—161no—
160C2×C5—61no—
161C2×C5—81no—
162C2×C5—241no—
163C2×C5A4×D811yescharacteristic
164C23—121no—
165Q8—21no—
166Q8—61no—
167Q8—121no—
168Q8C3×C5×D811yescharacteristic
169D4—21no—
170D4—31no—
171D4—61no—
172D4—121no—
173D4—121no—
174D4—121no—
175C2×C4—31no—
176C2×C4—121no—
177C2×C4—121no—
178C2×C4—121no—
179C8—31no—
180C8C22×C5×A411yescharacteristic
181C2×C3—41no—
182C2×C3—321no—
183C5#3416⋊C311yescharacteristic, direct product factor, Sylow
184C22—31no—
185C22—41no—
186C22—121no—
187C22—481no—
188C4—31no—
189C4—41no—
190C4—121no—
191C4C5×D4×A411yescharacteristic
192C3—41noSylow
193C2—61no—
194C2—81no—
195C2—241no—
196C2C5×A4×D811yescharacteristic
subgroupG/H
center, socleC2×C5A4×D8
commutator, cosocle#131C22×C3×C5
FrattiniC8C22×C5×A4
FittingC5×#3416C3
hypercenterC5×SD32A4
hypocenterQ8C3×C5×D8
LCSG ▷ #131 ▷ #41 ▷ Q8
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×SD32

Complements

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

NH ≅ G/Ntype
1. C5×#578⋊C3C2semidirect
2. C5×#576⋊C3C2semidirect
3. C5×#504⋊C3C2semidirect
4. C5×#3416C3semidirect
9. #3416⋊C3C5direct (N × H)
11. C5×#576C2×C3semidirect
16. C5×#504C2×C3semidirect
23. #578⋊C3C2×C5semidirect
24. #576⋊C3C2×C5semidirect
25. #504⋊C3C2×C5semidirect
42. #3416C3×C5semidirect
73. #576C2×C3×C5semidirect
78. #504C2×C3×C5semidirect
183. C5#3416⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#578⋊C32
C5×#576⋊C32
C5×#504⋊C32
C5×#34163
C3×C5×SD324
#3416⋊C35