Finite Group Databasebeta

← #13086945

Subgroups — #13086945

Order 1440.

444 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 128 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×C32×C4×D5C211yesmaximal, characteristic
2C2×#67141C211yesmaximal, characteristic, complemented
3#10623906C211yesmaximal, characteristic, complemented
4C5×#3750C211yesmaximal, characteristic, complemented
5#10623773C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic
7#10623770C211yesmaximal, characteristic
8#91349—34nomaximal
9C22×C32×D5C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C32×C4×D5—22no—
17#67141—22no—
18#64133—51nomaximal, Hall
19C2×C3×C4×D5D314yes—
20C2×#1204—34no—
21#6712—34no—
22C5×Dic3⋊C4—34no—
23#6668—34no—
24#6665—34no—
25#6665—34no—
26C22×C32×C5C2311yescharacteristic
27C2×C32×D5—21no—
28C2×C32×D5—21no—
29C2×C32×D5Q812yescomplemented
30C32×C4×C5—21no—
31C3⋊Dic15—21no—
32C3⋊Dic15—21no—
33C5×C3⋊Dic3—21no—
34C5×C3⋊Dic3—21no—
35C32×Dic5D412yes—
36#4042—91noHall
37C22×C32×C4—51no—
38C2×#634—51no—
39#3757—51no—
40#3757—51no—
41C4⋊(C3⋊Dic3)—51no—
42#3750—51no—
43#3750D511yescharacteristic, complemented
44C22×C3×D5C2×D314yes—
45C2×C3×C4×C5C2×D314yes—
46C2×Dic15—34no—
47C2×Dic15—34no—
48C2×C5×Dic3—34no—
49C2×C5×Dic3—34no—
50C2×C3×Dic5C2×D314yes—
51C3×C4×D5—28no—
52#1204—68no—
53#924—154no—
54C2×C32×C5C2×D411yescharacteristic
55C2×C32×C5C2×Q811yescharacteristic
56C2×C32×C5#4111yescharacteristic
57C32×D5—22no—
58C2×C4×D5C3⋊D311yescharacteristic
59C2×Dic10—91no—
60C5×C4⋊C4—91no—
61#685—91no—
62#685—91no—
63#683—91no—
64#683—91no—
65C23×C32—51no—
66C2×C32×C4—51no—
67C2×C32×C4—102no—
68C2×C32×C4C2×D511yescharacteristic
69C2×C3⋊Dic3—51no—
70C2×C3⋊Dic3—51no—
71C2×C3⋊Dic3C2×D511yescharacteristic
72C2×C3⋊Dic3C2×D511yescharacteristic
73#634—102no—
74C22×C3×C5C22×D314yes—
75C2×C3×D5—24no—
76C2×C3×D5—24no—
77C2×C3×D5Dic618yescomplemented
78C3×C4×C5—24no—
79Dic15—64no—
80Dic15—64no—
81C3×Dic5#6718yes—
82C5×Dic3—64no—
83C5×Dic3—64no—
84C22×C3×C4—54no—
85C2×Dic6—154no—
86#217—154no—
87#217—154no—
88C4⋊Dic3—154no—
89Dic3⋊C4—34no—
90Dic3⋊C4—154no—
91C32×C5C22⋊Q811yescharacteristic, complemented, Hall
92C22×D5C2×C3⋊D311yescharacteristic
93C2×C4×C5—91no—
94C2×C4×C5—91no—
95C2×C4×C5C2×C3⋊D311yescharacteristic
96C2×Dic5—91no—
97C2×Dic5—91no—
98C2×Dic5C2×C3⋊D311yescharacteristic
99C4×D5—22no—
100Dic10—182no—
101C22×C32—52no—
102C22×C32—101no—
103C22×C32—101no—
104C22×C32C22×D511yescharacteristic
105C32×C4—21no—
106C32×C4—52no—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C3⋊Dic3—101no—
110C3⋊Dic3—101no—
111C22⋊Q8—451noSylow
112C2×C3×C5C2×Dic614yes—
113C2×C3×C5#23514yes—
114C2×C3×C5C2×#6714yes—
115C3×D5—28no—
116C23×C3—54no—
117C2×C3×C4—54no—
118C2×C3×C4—108no—
119C2×C3×C4D3×D514yes—
120C2×Dic3—34no—
121C2×Dic3—34no—
122C2×Dic3—154no—
123C2×Dic3—154no—
124Dic6—308no—
125C22×C5C22×C3⋊D311yescharacteristic
126C2×D5—21no—
127C2×D5—21no—
128C2×D5#63412yescomplemented
129C4×C5—21no—
130C4×C5—181no—
131C4×C5—181no—
132Dic5—181no—
133Dic5—181no—
134Dic5#63812yes—
135C2×C32—102no—
136C2×C32#70911yescharacteristic
137C2×C32D4×D511yescharacteristic
138C2×C32Q8×D511yescharacteristic
139C2×Q8—451no—
140C22×C4—51no—
141C4⋊C4—91no—
142C4⋊C4—451no—
143C4⋊C4—451no—
144C22⋊C4—451no—
145C22⋊C4—451no—
146C3×C5#92414yescomplemented
147C22×C3—58no—
148C22×C3—104no—
149C22×C3—104no—
150C22×C3C2×D3×D514yes—
151C3×C4—24no—
152C3×C4—58no—
153Dic3—64no—
154Dic3—64no—
155Dic3—304no—
156Dic3—304no—
157C2×C5C2×#63411yescharacteristic
158C2×C5#382811yescharacteristic
159C2×C5C2×#63811yescharacteristic
160D5—22no—
161C32#404211yescharacteristic, complemented, Sylow
162C23—51no—
163Q8—902no—
164C2×C4—51no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—102no—
168C2×C4—451no—
169C2×C4—451no—
170C2×C4D5×C3⋊D311yescharacteristic
171C2×C3—108no—
172C2×C3D5×Dic614yes—
173C2×C3#677114yes—
174C2×C3D5×#6714yes—
175C5#6413311yescharacteristic, complemented, Sylow
176C22—52no—
177C22—101no—
178C22—101no—
179C22C2×D5×C3⋊D311yescharacteristic
180C4—21no—
181C4—52no—
182C4—181no—
183C4—181no—
184C4—901no—
185C4—901no—
186C3#9134914yescomplemented
187C2—102no—
188C2D5×#63411yescharacteristic
189C2#1062415411yescharacteristic
190C2D5×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC22×C32×D5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C22⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#67141C2semidirect
3. #10623906C2semidirect
4. C5×#3750C2semidirect
5. #10623773C2semidirect
29. C2×C32×D5Q8semidirect
43. #3750D5semidirect
77. C2×C3×D5Dic6semidirect
91. C32×C5C22⋊Q8semidirect
128. C2×D5#634semidirect
146. C3×C5#924semidirect
161. C32#4042semidirect
175. C5#64133semidirect
186. C3#91349semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D52
C2×#671412
#106239062
C5×#37502
#106237732
#106237702
#913493
#641335