Finite Group Databasebeta

← #13086951

Subgroups — #13086951

Order 1440.

444 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4×C3⋊D15C211yesmaximal, characteristic
2C2×#67141C211yesmaximal, characteristic, complemented
3C5×#3750C211yesmaximal, characteristic, complemented
4C32×#683C211yesmaximal, characteristic, complemented
5#10623774C211yesmaximal, characteristic, complemented
6#10623772C211yesmaximal, characteristic
7#10623772C211yesmaximal, characteristic
8#91377—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C4×C3⋊D15—22no—
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67141—22no—
18#64105—51nomaximal, Hall
19C2×C4×D15—34no—
20C2×#1204—34no—
21C5×Dic3⋊C4—34no—
22C3×#683D314yescomplemented
23#6669—34no—
24#6667—34no—
25#6667—34no—
26C22×C32×C5C2311yescharacteristic
27C2×C3⋊D15—21no—
28C2×C3⋊D15—21no—
29C2×C3⋊D15Q812yescomplemented
30C32×C4×C5—21no—
31C3⋊Dic15D412yes—
32C5×C3⋊Dic3—21no—
33C5×C3⋊Dic3—21no—
34C32×Dic5—21no—
35C32×Dic5—21no—
36#4042—91noHall
37C2×C4×C3⋊D3—51no—
38C2×#634—51no—
39C32×C4⋊C4—51no—
40#3752—51no—
41#3752—51no—
42#3750—51no—
43#3750D511yescharacteristic, complemented
44C22×D15—34no—
45C2×C3×C4×C5C2×D314yes—
46C2×Dic15—34no—
47C4×D15—68no—
48C2×C5×Dic3—34no—
49C2×C5×Dic3—34no—
50C2×C3×Dic5C2×D314yes—
51C2×C3×Dic5C2×D314yes—
52#1204—68no—
53#896—154no—
54C2×C32×C5C2×D411yescharacteristic
55C2×C32×C5C2×Q811yescharacteristic
56C2×C32×C5#4111yescharacteristic
57C3⋊D15—22no—
58C2×C4×D5—91no—
59C2×Dic10—91no—
60C5×C4⋊C4—91no—
61#685—91no—
62#685—91no—
63#683—91no—
64#683C3⋊D311yescharacteristic, complemented
65C22×C3⋊D3—51no—
66C2×C32×C4—51no—
67C2×C32×C4—51no—
68C2×C32×C4C2×D511yescharacteristic
69C2×C3⋊Dic3—51no—
70C2×C3⋊Dic3C2×D511yescharacteristic
71C2×C3⋊Dic3C2×D511yescharacteristic
72C4×C3⋊D3—102no—
73#634—102no—
74C22×C3×C5C22×D314yes—
75C2×D15—38no—
76C2×D15—64no—
77C2×D15—64no—
78C3×C4×C5—24no—
79Dic15—38no—
80C3×Dic5—24no—
81C3×Dic5—24no—
82C5×Dic3—64no—
83C5×Dic3—64no—
84C2×C4×D3—154no—
85C2×Dic6—154no—
86C3×C4⋊C4—54no—
87(C2×D3)⋊C4—154no—
88(C2×D3)⋊C4—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—182no—
101C22×C32C22×D511yescharacteristic
102C2×C3⋊D3—52no—
103C2×C3⋊D3—101no—
104C2×C3⋊D3—101no—
105C32×C4—21no—
106C32×C4—101no—
107C32×C4—101no—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C3⋊Dic3—52no—
111C22⋊Q8—451noSylow
112C2×C3×C5#23514yes—
113C2×C3×C5D3×D414yes—
114C2×C3×C5D3×Q814yes—
115D15—68no—
116C22×D3—154no—
117C2×C3×C4—54no—
118C2×C3×C4—54no—
119C2×C3×C4D3×D514yes—
120C2×Dic3—34no—
121C2×Dic3—34no—
122C2×Dic3—154no—
123C4×D3—308no—
124Dic6—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—21no—
134Dic5—92no—
135C2×C32#70911yescharacteristic
136C2×C32D4×D511yescharacteristic
137C2×C32Q8×D511yescharacteristic
138C3⋊D3—102no—
139C2×Q8—451no—
140C22×C4—451no—
141C4⋊C4—51no—
142C4⋊C4—91no—
143C4⋊C4—451no—
144C22⋊C4—451no—
145C22⋊C4—451no—
146C3×C5#89614yescomplemented
147C22×C3C2×D3×D514yes—
148C2×D3—158no—
149C2×D3—304no—
150C2×D3—304no—
151C3×C4—24no—
152C3×C4—104no—
153C3×C4—104no—
154Dic3—64no—
155Dic3—64no—
156Dic3—158no—
157C2×C5#382811yescharacteristic
158C2×C5D4×C3⋊D311yescharacteristic
159C2×C5Q8×C3⋊D311yescharacteristic
160D5—182no—
161C32#404211yescharacteristic, complemented, Sylow
162C23—451no—
163Q8—902no—
164C2×C4—51no—
165C2×C4—51no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—451no—
169C2×C4—902no—
170C2×C4D5×C3⋊D311yescharacteristic
171C2×C3D15⋊Q814yes—
172C2×C3#677114yes—
173C2×C3#679014yes—
174D3—308no—
175C5#6410511yescharacteristic, complemented, Sylow
176C22—452no—
177C22—901no—
178C22—901no—
179C22C2×D5×C3⋊D311yescharacteristic
180C4—21no—
181C4—101no—
182C4—101no—
183C4—181no—
184C4—181no—
185C4—452no—
186C3#9137714yescomplemented
187C2—902no—
188C2#1062415311yescharacteristic
189C2#1062415411yescharacteristic
190C2#1062417311yescharacteristic
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
2. C2×#67141C2semidirect
3. C5×#3750C2semidirect
4. C32×#683C2semidirect
5. #10623774C2semidirect
22. C3×#683D3semidirect
29. C2×C3⋊D15Q8semidirect
43. #3750D5semidirect
64. #683C3⋊D3semidirect
91. C32×C5C22⋊Q8semidirect
146. C3×C5#896semidirect
161. C32#4042semidirect
175. C5#64105semidirect
186. C3#91377semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C2×#671412
C5×#37502
C32×#6832
#106237742
#106237722
#913773
#641055