Finite Group Databasebeta

← #13085890

Subgroups — #13085890

Order 1440.

358 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 88 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×#67137C211yesmaximal, characteristic
2#10623828C211yesmaximal, characteristic, complemented
3#10623813C212yesmaximal
4C5×Dic32C211yesmaximal, characteristic, complemented
5C3×#6668C212yesmaximal, complemented
6#91403—32nomaximal
7C22×C3⋊D15C2211yescharacteristic
8C2×C5×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic15C2212yes—
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12#67137C414yescomplemented
13#63849—51nomaximal, Hall
14C2×#1200—32no—
15C2×#1200—61no—
16#6714—32no—
17C4×C5×Dic3—32no—
18C3×#683—32no—
19#6668D312yescomplemented
20#6667—32no—
21Dic3×Dic5—32no—
22C22×C32×C5C2311yescharacteristic
23C2×C3⋊D15—22no—
24C2×C3⋊D15C2×C412yes—
25C5×C3⋊Dic3C2×C412yes—
26C3×Dic15—22no—
27C3×C5×Dic3—22no—
28C32×Dic5C2×C412yes—
29#4018—91noHall
30C2×C4×C3⋊D3—51no—
31C3×C4⋊Dic3—52no—
32#3722—52no—
33Dic32—51no—
34Dic32D511yescharacteristic, complemented
35C22×D15—32no—
36C22×D15—61no—
37C2×C3×C4×C5—32no—
38C2×Dic15C2×D312yes—
39C2×C5×Dic3—32no—
40C2×C5×Dic3—61no—
41C2×C5×Dic3C2×D312yes—
42C2×C3×Dic5—21no—
43C2×C3×Dic5—32no—
44C2×C3×Dic5C2×D312yes—
45#1200—38no—
46#1200—64no—
47#892—152no—
48C2×C32×C5C22×C411yescharacteristic
49C2×C32×C5#4112yes—
50C3⋊D15—22no—
51C2×C4×D5—91no—
52C42×C5—91no—
53#685—92no—
54#683—32no—
55C4×Dic5—91no—
56C22×C3⋊D3—51no—
57C2×C32×C4—51no—
58C2×C3⋊Dic3C2×D511yescharacteristic
59C4×C3⋊D3—54no—
60C2×C3×Dic3—52no—
61C2×C3×Dic3C2×D512yes—
62C22×C3×C5—21no—
63C22×C3×C5C22×D312yes—
64C2×D15—34no—
65C2×D15—62no—
66C2×D15—64no—
67C2×D15—62no—
68C2×D15—62no—
69C3×C4×C5—62no—
70Dic15—22no—
71C3×Dic5—22no—
72C3×Dic5—62no—
73C3×Dic5C4×D314yes—
74C5×Dic3—22no—
75C5×Dic3—34no—
76C5×Dic3—62no—
77C2×C4×D3—152no—
78C2×C4×D3—301no—
79C3×C4⋊C4—152no—
80(C2×D3)⋊C4—152no—
81(C2×D3)⋊C4—152no—
82C4⋊Dic3—52no—
83C4×Dic3—32no—
84C4×Dic3—152no—
85C32×C5#11711yescharacteristic, complemented, Hall
86C22×D5—91no—
87C2×C4×C5—32no—
88C2×C4×C5—91no—
89C2×Dic5—32no—
90C2×Dic5D3211yescharacteristic
91C4×D5—94no—
92C22×C32C22×D511yescharacteristic
93C2×C3⋊D3—52no—
94C2×C3⋊D3—102no—
95C32×C4—52no—
96C3⋊Dic3C4×D512yes—
97C3×Dic3—22no—
98C3×Dic3—102no—
99#117—451noSylow
100C2×C3×C5—22no—
101C2×C3×C5—21no—
102C2×C3×C5C2×C4×D312yes—
103C2×C3×C5#23712yes—
104C2×C3×C5#23912yes—
105D15—64no—
106D15—64no—
107C22×D3—152no—
108C22×D3—301no—
109C2×C3×C4—32no—
110C2×C3×C4—52no—
111C2×C3×C4—101no—
112C2×C3×C4—152no—
113C2×Dic3—32no—
114C2×Dic3—52no—
115C2×Dic3—61no—
116C2×Dic3D3×D512yes—
117C4×D3—158no—
118C4×D3—304no—
119C22×C5C2×D3211yescharacteristic
120C2×D5—92no—
121C2×D5—182no—
122C4×C5—62no—
123C4×C5—92no—
124Dic5—62no—
125Dic5#62412yes—
126C2×C32C2×C4×D511yescharacteristic
127C2×C32#70912yes—
128C3⋊D3—102no—
129C22×C4—451no—
130C4⋊C4—152no—
131C22⋊C4—452no—
132C42—91no—
133C42—451no—
134C3×C5—21no—
135C3×C5#89212yescomplemented
136C22×C3—21no—
137C22×C3C2×D3×D512yes—
138C2×D3—154no—
139C2×D3—302no—
140C2×D3—304no—
141C2×D3—302no—
142C2×D3—302no—
143C3×C4—54no—
144C3×C4—62no—
145C3×C4—102no—
146C3×C4—302no—
147Dic3—22no—
148Dic3—34no—
149Dic3—62no—
150Dic3—102no—
151C2×C5#379612yes—
152C2×C5C2×#62411yescharacteristic
153D5—182no—
154C32#401811yescharacteristic, complemented, Sylow
155C23—451no—
156C2×C4—32no—
157C2×C4—51no—
158C2×C4—91no—
159C2×C4—152no—
160C2×C4—454no—
161C2×C3—21no—
162C2×C3—22no—
163C2×C3#676912yes—
164C2×C3C4×D3×D512yes—
165C2×C3#677912yes—
166D3—304no—
167D3—304no—
168C5#6384911yescharacteristic, complemented, Sylow
169C22—452no—
170C22—902no—
171C22D32×D511yescharacteristic
172C4—52no—
173C4—62no—
174C4—92no—
175C4—302no—
176C3—21no—
177C3#9140312yescomplemented
178C2—902no—
179C2D5×#62411yescharacteristic
180C2#1062405512yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C3⋊D15C22
hypocenterC32×C5#117
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #10623828C2semidirect
4. C5×Dic32C2semidirect
5. C3×#6668C2semidirect
12. #67137C4semidirect
19. #6668D3semidirect
34. Dic32D5semidirect
85. C32×C5#117semidirect
135. C3×C5#892semidirect
154. C32#4018semidirect
168. C5#63849semidirect
177. C3#91403semidirect

Maximal subgroups

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

subgroupindex
C2×#671372
#106238282
#106238132
C5×Dic322
C3×#66682
#914033
#638495