Finite Group Databasebeta

← #13086871

Subgroups — #13086871

Order 1440.

444 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 118 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×Dic10C211yesmaximal, characteristic, complemented
2C2×#67137C211yesmaximal, characteristic
3#10623908C211yesmaximal, characteristic
4C5×#3750C211yesmaximal, characteristic, complemented
5#10623774C211yesmaximal, characteristic, complemented
6#10623773C211yesmaximal, characteristic, complemented
7#10623772C211yesmaximal, characteristic
8#91411—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C32×Dic5C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C32×Dic10—22no—
17#67137—22no—
18#64155—51nomaximal, Hall
19C2×C3×Dic10D314yescomplemented
20C2×#1200—34no—
21#6714—34no—
22C5×Dic3⋊C4—34no—
23#6669—34no—
24#6668—34no—
25#6667—34no—
26C22×C32×C5C2311yescharacteristic
27C2×C3⋊D15—21no—
28C2×C3⋊D15—21no—
29C2×C3⋊D15Q812yescomplemented
30C32×C4×C5—21no—
31C3⋊Dic15—21no—
32C5×C3⋊Dic3—21no—
33C5×C3⋊Dic3—21no—
34C32×Dic5—21no—
35C32×Dic5D412yes—
36#4042—91noHall
37C2×C32×Q8—51no—
38C2×C4×C3⋊D3—51no—
39#3752—51no—
40#3752—51no—
41C4⋊(C3⋊Dic3)—51no—
42#3750—51no—
43#3750D511yescharacteristic, complemented
44C22×D15—34no—
45C2×C3×C4×C5C2×D314yes—
46C2×Dic15—34no—
47C2×C5×Dic3—34no—
48C2×C5×Dic3—34no—
49C2×C3×Dic5C2×D314yes—
50C2×C3×Dic5C2×D314yes—
51C3×Dic10—28no—
52#1200—68no—
53#946—154no—
54C2×C32×C5C2×D411yescharacteristic
55C2×C32×C5C2×Q811yescharacteristic
56C2×C32×C5#4111yescharacteristic
57C3⋊D15—22no—
58C2×C4×D5—91no—
59C2×Dic10C3⋊D311yescharacteristic, complemented
60C5×C4⋊C4—91no—
61#685—91no—
62#685—91no—
63#683—91no—
64#683—91no—
65C22×C3⋊D3—51no—
66C32×Q8—102no—
67C2×C32×C4—51no—
68C2×C32×C4—51no—
69C2×C32×C4C2×D511yescharacteristic
70C2×C3⋊Dic3—51no—
71C2×C3⋊Dic3C2×D511yescharacteristic
72C2×C3⋊Dic3C2×D511yescharacteristic
73C4×C3⋊D3—102no—
74C22×C3×C5C22×D314yes—
75C2×D15—38no—
76C2×D15—64no—
77C2×D15—64no—
78C3×C4×C5—24no—
79Dic15—64no—
80C3×Dic5—24no—
81C3×Dic5#6718yes—
82C5×Dic3—64no—
83C5×Dic3—64no—
84C2×C3×Q8—54no—
85C2×C4×D3—154no—
86(C2×D3)⋊C4—154no—
87(C2×D3)⋊C4—154no—
88C4⋊Dic3—154no—
89Dic3⋊C4—34no—
90Dic3⋊C4—154no—
91C32×C5C22⋊Q811yescharacteristic, complemented, Hall
92C22×D5—91no—
93C2×C4×C5—91no—
94C2×C4×C5—91no—
95C2×C4×C5C2×C3⋊D311yescharacteristic
96C2×Dic5—91no—
97C2×Dic5C2×C3⋊D311yescharacteristic
98C2×Dic5C2×C3⋊D311yescharacteristic
99C4×D5—182no—
100Dic10—22no—
101C22×C32C22×D511yescharacteristic
102C2×C3⋊D3—52no—
103C2×C3⋊D3—101no—
104C2×C3⋊D3—101no—
105C32×C4—21no—
106C32×C4—52no—
107C32×C4—101no—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C3⋊Dic3—101no—
111C22⋊Q8—451noSylow
112C2×C3×C5D3×Q814yes—
113C2×C3×C5#23914yes—
114C2×C3×C5C2×#6714yes—
115D15—68no—
116C22×D3—154no—
117C3×Q8—108no—
118C2×C3×C4—54no—
119C2×C3×C4—54no—
120C2×C3×C4D3×D514yes—
121C2×Dic3—34no—
122C2×Dic3—34no—
123C2×Dic3—154no—
124C4×D3—308no—
125C22×C5C22×C3⋊D311yescharacteristic
126C2×D5—92no—
127C2×D5—181no—
128C2×D5—181no—
129C4×C5—21no—
130C4×C5—181no—
131C4×C5—181no—
132Dic5—21no—
133Dic5—181no—
134Dic5#63812yes—
135C2×C32#70911yescharacteristic
136C2×C32D4×D511yescharacteristic
137C2×C32Q8×D511yescharacteristic
138C3⋊D3—102no—
139C2×Q8—51no—
140C22×C4—451no—
141C4⋊C4—91no—
142C4⋊C4—451no—
143C4⋊C4—451no—
144C22⋊C4—451no—
145C22⋊C4—451no—
146C3×C5#94614yescomplemented
147C22×C3C2×D3×D514yes—
148C2×D3—158no—
149C2×D3—304no—
150C2×D3—304no—
151C3×C4—24no—
152C3×C4—58no—
153C3×C4—104no—
154Dic3—64no—
155Dic3—64no—
156Dic3—304no—
157C2×C5Q8×C3⋊D311yescharacteristic
158C2×C5#383211yescharacteristic
159C2×C5C2×#63811yescharacteristic
160D5—182no—
161C32#404211yescharacteristic, complemented, Sylow
162C23—451no—
163Q8—102no—
164C2×C4—51no—
165C2×C4—51no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—451no—
169C2×C4—902no—
170C2×C4D5×C3⋊D311yescharacteristic
171C2×C3#676914yes—
172C2×C3D15⋊Q814yes—
173C2×C3D5×#6714yes—
174D3—308no—
175C5#6415511yescharacteristic, complemented, Sylow
176C22—452no—
177C22—901no—
178C22—901no—
179C22C2×D5×C3⋊D311yescharacteristic
180C4—21no—
181C4—52no—
182C4—101no—
183C4—181no—
184C4—181no—
185C4—901no—
186C3#9141114yescomplemented
187C2—902no—
188C2#1062415211yescharacteristic
189C2#1062415311yescharacteristic
190C2D5×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC22×C3⋊D15C22
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
1. C2×C32×Dic10C2semidirect
4. C5×#3750C2semidirect
5. #10623774C2semidirect
6. #10623773C2semidirect
19. C2×C3×Dic10D3semidirect
29. C2×C3⋊D15Q8semidirect
43. #3750D5semidirect
59. C2×Dic10C3⋊D3semidirect
91. C32×C5C22⋊Q8semidirect
146. C3×C5#946semidirect
161. C32#4042semidirect
175. C5#64155semidirect
186. C3#91411semidirect

Maximal subgroups

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

subgroupindex
C2×C32×Dic102
C2×#671372
#106239082
C5×#37502
#106237742
#106237732
#106237722
#914113
#641555