Finite Group Databasebeta

← #13085887

Subgroups — #13085887

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×D5×C3⋊Dic3C211yesmaximal, characteristic
2#10623828C211yesmaximal, characteristic, complemented
3#10623815C212yesmaximal, complemented
4C5×Dic32C211yesmaximal, characteristic, complemented
5C3×#6665C212yesmaximal
6#91393—32nomaximal
7C22×C32×D5C2211yescharacteristic
8C2×C3⋊Dic15C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C2×C3×Dic15C2212yes—
11C2×C3×C5×Dic3C2212yes—
12D5×C3⋊Dic3C414yescomplemented
13#63957—51nomaximal, Hall
14C2×D5×Dic3—32no—
15C2×D5×Dic3—61no—
16#6712—32no—
17C4×C5×Dic3—32no—
18C3×#685—32no—
19#6669—32no—
20#6665D312yes—
21Dic3×Dic5—32no—
22C22×C32×C5C2311yescharacteristic
23C2×C32×D5—22no—
24C2×C32×D5C2×C412yes—
25C3⋊Dic15C2×C412yes—
26C5×C3⋊Dic3C2×C412yes—
27C3×Dic15—22no—
28C3×C5×Dic3—22no—
29#4018—91noHall
30C22×C3⋊Dic3—51no—
31C3×#217—52no—
32#3724—52no—
33Dic32—51no—
34Dic32D511yescharacteristic, complemented
35C22×C3×D5—21no—
36C22×C3×D5C2×D312yes—
37C2×C3×C4×C5—32no—
38C2×Dic15—32no—
39C2×Dic15—61no—
40C2×Dic15C2×D312yes—
41C2×C5×Dic3—32no—
42C2×C5×Dic3—61no—
43C2×C5×Dic3C2×D312yes—
44C2×C3×Dic5—32no—
45D5×Dic3—38no—
46D5×Dic3—64no—
47#877—152no—
48C2×C32×C5C22×C411yescharacteristic
49C2×C32×C5#4112yes—
50C32×D5—22no—
51C2×C4×D5—91no—
52C42×C5—91no—
53#685—32no—
54#683—92no—
55C4×Dic5—91no—
56C23×C32—51no—
57C2×C3⋊Dic3—51no—
58C2×C3⋊Dic3—54no—
59C2×C3⋊Dic3C2×D511yescharacteristic
60C2×C3×Dic3—52no—
61C2×C3×Dic3C2×D512yes—
62C22×C3×C5—21no—
63C22×C3×C5C22×D312yes—
64C2×C3×D5—24no—
65C2×C3×D5—22no—
66C2×C3×D5—22no—
67C2×C3×D5—22no—
68C2×C3×D5C4×D314yes—
69C3×C4×C5—62no—
70Dic15—22no—
71Dic15—34no—
72Dic15—62no—
73C3×Dic5—62no—
74C5×Dic3—22no—
75C5×Dic3—34no—
76C5×Dic3—62no—
77C22×Dic3—152no—
78C22×Dic3—301no—
79C3×C22⋊C4—152no—
80#217—52no—
81Dic3⋊C4—152no—
82Dic3⋊C4—152no—
83C4×Dic3—32no—
84C4×Dic3—152no—
85C32×C5#11711yescharacteristic, complemented, Hall
86C22×D5D3211yescharacteristic
87C2×C4×C5—32no—
88C2×C4×C5—91no—
89C2×Dic5—32no—
90C2×Dic5—91no—
91C4×D5—94no—
92C22×C32—52no—
93C22×C32—102no—
94C22×C32C22×D511yescharacteristic
95C3⋊Dic3—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#23712yes—
105C3×D5—24no—
106C3×D5—24no—
107C23×C3—52no—
108C23×C3—101no—
109C2×C3×C4—32no—
110C2×C3×C4—152no—
111C2×Dic3—32no—
112C2×Dic3—52no—
113C2×Dic3—61no—
114C2×Dic3—158no—
115C2×Dic3—152no—
116C2×Dic3—304no—
117C2×Dic3—301no—
118C2×Dic3D3×D512yes—
119C22×C5C2×D3211yescharacteristic
120C2×D5—22no—
121C2×D5#62412yes—
122C4×C5—62no—
123C4×C5—92no—
124Dic5—62no—
125Dic5—92no—
126C2×C32—102no—
127C2×C32C2×C4×D511yescharacteristic
128C2×C32#70912yes—
129C22×C4—451no—
130C4⋊C4—452no—
131C22⋊C4—152no—
132C42—91no—
133C42—451no—
134C3×C5—21no—
135C3×C5#87712yescomplemented
136C22×C3—21no—
137C22×C3—54no—
138C22×C3—102no—
139C22×C3—104no—
140C22×C3—102no—
141C22×C3—102no—
142C22×C3C2×D3×D512yes—
143C3×C4—62no—
144C3×C4—302no—
145Dic3—22no—
146Dic3—34no—
147Dic3—62no—
148Dic3—102no—
149Dic3—154no—
150Dic3—302no—
151C2×C5#380512yes—
152C2×C5C2×#62411yescharacteristic
153D5—22no—
154C32#401811yescharacteristic, complemented, Sylow
155C23—51no—
156C2×C4—32no—
157C2×C4—91no—
158C2×C4—152no—
159C2×C4—454no—
160C2×C4—451no—
161C2×C3—21no—
162C2×C3—22no—
163C2×C3—104no—
164C2×C3—104no—
165C2×C3#676512yes—
166C2×C3C4×D3×D512yes—
167C2×C3#677912yes—
168C5#6395711yescharacteristic, complemented, Sylow
169C22—52no—
170C22—102no—
171C22D32×D511yescharacteristic
172C4—62no—
173C4—92no—
174C4—302no—
175C4—452no—
176C3—21no—
177C3#9139312yescomplemented
178C2—102no—
179C2D5×#62411yescharacteristic
180C2#1062404512yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C32×D5C22
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
3. #10623815C2semidirect
4. C5×Dic32C2semidirect
12. D5×C3⋊Dic3C4semidirect
34. Dic32D5semidirect
85. C32×C5#117semidirect
135. C3×C5#877semidirect
154. C32#4018semidirect
168. C5#63957semidirect
177. C3#91393semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C3⋊Dic32
#106238282
#106238152
C5×Dic322
C3×#66652
#913933
#639575