Finite Group Databasebeta

← #13086883

Subgroups — #13086883

Order 1440.

444 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 110 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×#634C211yesmaximal, characteristic, complemented
2C2×#67137C211yesmaximal, characteristic
3#10623908C211yesmaximal, characteristic
4C32×#683C211yesmaximal, characteristic, complemented
5#10623775C211yesmaximal, characteristic, complemented
6#10623774C211yesmaximal, characteristic, complemented
7#10623772C211yesmaximal, characteristic
8#91424—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C5×#634—22no—
15C2×C32×Dic5C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67137—22no—
18#64105—51nomaximal, Hall
19C2×C5×Dic6—34no—
20C2×#1200—34no—
21#6714—34no—
22C3×#683D314yescomplemented
23Dic3⋊Dic5—34no—
24#6669—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⋊Dic3D412yes—
34C32×Dic5—21no—
35C32×Dic5—21no—
36#4092—91noHall
37C2×C4×C3⋊D3—51no—
38C2×#634D511yescharacteristic, complemented
39C32×C4⋊C4—51no—
40#3752—51no—
41#3752—51no—
42#3750—51no—
43#3750—51no—
44C22×D15—34no—
45C2×C3×C4×C5C2×D314yes—
46C2×Dic15—34no—
47C2×C5×Dic3—34no—
48C2×C5×Dic3—34no—
49C5×Dic6—68no—
50C2×C3×Dic5C2×D314yes—
51C2×C3×Dic5C2×D314yes—
52#1200—68no—
53#896—154no—
54C2×C32×C5C2×D411yescharacteristic
55C2×C32×C5C2×Q811yescharacteristic
56C2×C32×C5#4111yescharacteristic
57C3⋊D15—22no—
58C2×C5×Q8—91no—
59C2×C4×D5—91no—
60#685—91no—
61#685—91no—
62C4⋊Dic5—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—22no—
74C22×C3×C5C22×D314yes—
75C2×D15—38no—
76C2×D15—64no—
77C2×D15—64no—
78C3×C4×C5—24no—
79Dic15—64no—
80C3×Dic5—24no—
81C3×Dic5—24no—
82C5×Dic3—38no—
83C5×Dic3—64no—
84C2×C4×D3—154no—
85C2×Dic6—34no—
86C3×C4⋊C4—54no—
87(C2×D3)⋊C4—154no—
88(C2×D3)⋊C4—154no—
89Dic3⋊C4—154no—
90Dic3⋊C4—154no—
91C32×C5C22⋊Q811yescharacteristic, complemented, Hall
92C22×D5—91no—
93C5×Q8—182no—
94C2×C4×C5—91no—
95C2×C4×C5—91no—
96C2×C4×C5C2×C3⋊D311yescharacteristic
97C2×Dic5—91no—
98C2×Dic5C2×C3⋊D311yescharacteristic
99C2×Dic5C2×C3⋊D311yescharacteristic
100C4×D5—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—101no—
110C3⋊Dic3C22⋊D512yes—
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—68no—
125C22×C5C22×C3⋊D311yescharacteristic
126C2×D5—92no—
127C2×D5—181no—
128C2×D5—181no—
129C4×C5—21no—
130C4×C5—92no—
131C4×C5—181no—
132Dic5—21no—
133Dic5—21no—
134Dic5—181no—
135C2×C32Q8×D511yescharacteristic
136C2×C32#71311yescharacteristic
137C2×C32C2×C22⋊D511yescharacteristic
138C3⋊D3—102no—
139C2×Q8—91no—
140C22×C4—451no—
141C4⋊C4—51no—
142C4⋊C4—451no—
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—38no—
155Dic3—64no—
156Dic3—304no—
157C2×C5#382811yescharacteristic
158C2×C5D4×C3⋊D311yescharacteristic
159C2×C5Q8×C3⋊D311yescharacteristic
160D5—182no—
161C32#409211yescharacteristic, complemented, Sylow
162C23—451no—
163Q8—182no—
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#677314yes—
173C2×C3D3×C22⋊D514yes—
174D3—308no—
175C5#6410511yescharacteristic, complemented, Sylow
176C22—452no—
177C22—901no—
178C22—901no—
179C22C2×D5×C3⋊D311yescharacteristic
180C4—21no—
181C4—92no—
182C4—101no—
183C4—101no—
184C4—181no—
185C4—901no—
186C3#9142414yescomplemented
187C2—902no—
188C2#1062415311yescharacteristic
189C2#1062415611yescharacteristic
190C2C3⋊D3×C22⋊D511yescharacteristic
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×C5×#634C2semidirect
4. C32×#683C2semidirect
5. #10623775C2semidirect
6. #10623774C2semidirect
22. C3×#683D3semidirect
29. C2×C3⋊D15Q8semidirect
38. C2×#634D5semidirect
64. #683C3⋊D3semidirect
91. C32×C5C22⋊Q8semidirect
146. C3×C5#896semidirect
161. C32#4092semidirect
175. C5#64105semidirect
186. C3#91424semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6342
C2×#671372
#106239082
C32×#6832
#106237752
#106237742
#106237722
#914243
#641055