Finite Group Databasebeta

← #72230513

Subgroups — #72230513

Order 2400.

380 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×D3×C5⋊D5C211yesmaximal, characteristic
2#11925152C211yesmaximal, characteristic, complemented
3#11925126C212yesmaximal, complemented
4C5×#6650C212yesmaximal, complemented
5C3×#87769C211yesmaximal, characteristic, complemented
6#11716936—31nomaximal, Hall
7C2×D3×C5⋊D5C411yescharacteristic
8C4×C3⋊(C5⋊D5)C2211yescharacteristic
9C4×C52×D3C2211yescharacteristic
10C3×C4×C5⋊D5C2211yescharacteristic
11#10597113C411yescharacteristic
12D3×#1039C411yescharacteristic
13Dic3×C5⋊D5C411yescharacteristic
14C5×C3⋊#168C2212yescomplemented
15C3×C5×#168C2212yescomplemented
16#91246—52nomaximal
17C2×C4×C5⋊D5—31no—
18C5×#681—32no—
19#87769—31no—
20#87769D311yescharacteristic, complemented
21#87767—32no—
22C2×C3⋊(C5⋊D5)C2×C411yescharacteristic
23C2×C52×D3C2×C411yescharacteristic
24C2×C3×C5⋊D5C2×C411yescharacteristic
25D3×C5⋊D5—22no—
26C3×C4×C52C2311yescharacteristic
27C3⋊#1039C2×C411yescharacteristic
28C52×Dic3C2×C411yescharacteristic
29C3×#1039C2×C411yescharacteristic
30C4×D3×D5—52no—
31C4×D3×D5—102no—
32C8×D15—52no—
33C5×ΓL(1,𝔽25)—52no—
34C3×#676—52no—
35#6650D512yescomplemented
36#6649—52no—
37#6648—52no—
38C22×C5⋊D5—31no—
39C2×C4×C52—31no—
40C2×#1039—31no—
41C4×C5⋊D5—31no—
42C4×C5⋊D5—31no—
43C4×C5⋊D5—31no—
44C4×C5⋊D5C2×D311yescharacteristic
45C5×#168—32no—
46C5×#168C2×D312yescomplemented
47D5×M16—152no—
48C2×C3×C52C22×C411yescharacteristic
49C3⋊(C5⋊D5)M1612yescomplemented
50C52×D3—21no—
51C3×C5⋊D5—21no—
52C2×D3×D5—52no—
53C2×D3×D5—102no—
54C4×D15—52no—
55C4×D15—102no—
56C4×C5×D3—22no—
57C4×C5×D3C2×D512yes—
58C3×C4×D5—52no—
59C3×C4×D5—102no—
60#1200—52no—
61#1200—102no—
62D3×Dic5—52no—
63D3×Dic5—102no—
64D5×Dic3—52no—
65D5×Dic3—102no—
66C3×C5×C8—52no—
67C3⋊#168C2×D512yescomplemented
68C3×#168C2×D512yescomplemented
69C5×C3⋊C8—52no—
70C22×C52—31no—
71C2×C5⋊D5—31no—
72C2×C5⋊D5—62no—
73C2×C5⋊D5C4×D311yescharacteristic
74C4×C52—31no—
75C4×C52C22×D311yescharacteristic
76#1039—31no—
77#1039C4×D311yescharacteristic
78D3×M16—251noHall
79C2×C4×D5—152no—
80C2×C4×D5—302no—
81C5×M16—152no—
82#681—32no—
83#676—52no—
84#676—152no—
85C8×D5—152no—
86C8×D5—152no—
87C3×C52C2×M1611yescharacteristic, complemented, Hall
88C2×D15—52no—
89C2×D15—102no—
90C2×C5×D3—22no—
91C2×C5×D3C4×D512yes—
92C2×C3×D5—52no—
93C2×C3×D5—102no—
94D3×D5—104no—
95D3×D5—104no—
96D3×D5—104no—
97C3×C4×C5—22no—
98C3×C4×C5C22×D512yes—
99Dic15—52no—
100Dic15—102no—
101C3×Dic5—52no—
102C3×Dic5—102no—
103C5×Dic3—22no—
104C5×Dic3C4×D512yes—
105C2×C52—61no—
106C2×C52C2×C4×D311yescharacteristic
107C5⋊D5—21no—
108C5⋊D5—32no—
109C2×C4×D3—251no—
110C3×M16—251no—
111#208—251no—
112ΓL(1,𝔽25)—52no—
113D3×C8—252no—
114C22×D5—152no—
115C22×D5—302no—
116C2×C4×C5—32no—
117C2×C4×C5—62no—
118C2×Dic5—152no—
119C2×Dic5—302no—
120C4×D5—52no—
121C4×D5—102no—
122C4×D5—152no—
123C4×D5—152no—
124C4×D5—152no—
125C4×D5—302no—
126C4×D5—302no—
127C4×D5—302no—
128C5×C8—52no—
129C5×C8—152no—
130#168—32no—
131#168D3×D512yescomplemented
132C2×M16—751noSylow
133C2×C3×C5—22no—
134C2×C3×C5C2×C4×D512yes—
135D15—54no—
136D15—104no—
137C3×D5—102no—
138C3×D5—102no—
139C3×D5—102no—
140C5×D3—22no—
141C5×D3—22no—
142C5×D3—22no—
143C52D3×M1611yescharacteristic, complemented, Sylow
144C22×D3—251no—
145C2×C3×C4—251no—
146C2×Dic3—251no—
147C4×D3—251no—
148C4×D3—251no—
149C4×D3—251no—
150C4×D3D5211yescharacteristic
151C3×C8—52no—
152C3⋊C8—52no—
153C22×C5—32no—
154C22×C5—62no—
155C2×D5—52no—
156C2×D5—102no—
157C2×D5—152no—
158C2×D5—302no—
159C2×D5—304no—
160C2×D5—304no—
161C2×D5—304no—
162C4×C5—22no—
163C4×C5—32no—
164C4×C5—62no—
165C4×C5C2×D3×D512yes—
166Dic5—52no—
167Dic5—102no—
168Dic5—152no—
169Dic5—302no—
170C22×C4—751no—
171M16—152no—
172M16—251no—
173M16—751no—
174C2×C8—752no—
175C3×C5—22no—
176C3×C5D5×M1612yescomplemented
177C22×C3—251no—
178C2×D3—251no—
179C2×D3—502no—
180C2×D3#603611yescharacteristic
181C3×C4—251no—
182C3×C4C2×D5211yescharacteristic
183Dic3—251no—
184Dic3#603611yescharacteristic
185C2×C5—22no—
186C2×C5—62no—
187C2×C5—62no—
188C2×C5—62no—
189C2×C5C4×D3×D512yes—
190D5—102no—
191D5—102no—
192D5—102no—
193D5—154no—
194D5—304no—
195C23—751no—
196C2×C4—31no—
197C2×C4—251no—
198C2×C4—751no—
199C2×C4—751no—
200C2×C4—751no—
201C2×C4—751no—
202C8—52no—
203C8—152no—
204C2×C3—501no—
205C2×C3C2×#603611yescharacteristic
206D3—21no—
207D3—252no—
208C5—22no—
209C5#9124612yescomplemented
210C22—31no—
211C22—251no—
212C22—751no—
213C22—1502no—
214C4—31no—
215C4—251no—
216C4—751no—
217C4D3×D5211yescharacteristic
218C3#1171693611yescharacteristic, complemented, Sylow
219C2—61no—
220C2—501no—
221C2—752no—
222C2D3×#603611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4D3×D52
commutator, socleC2×C3×C52C22×C4
Fitting, cosocleC3×C4×C52C23
prime radicalC2×D3×C5⋊D5C4
hypocenterC3×C52C2×M16
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #11925152C2semidirect
3. #11925126C2semidirect
4. C5×#6650C2semidirect
5. C3×#87769C2semidirect
14. C5×C3⋊#168C22semidirect
15. C3×C5×#168C22semidirect
20. #87769D3semidirect
35. #6650D5semidirect
46. C5×#168C2×D3semidirect
49. C3⋊(C5⋊D5)M16semidirect
67. C3⋊#168C2×D5semidirect
68. C3×#168C2×D5semidirect
87. C3×C52C2×M16semidirect
131. #168D3×D5semidirect
143. C52D3×M16semidirect
176. C3×C5D5×M16semidirect
209. C5#91246semidirect
218. C3#11716936semidirect

Maximal subgroups

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

subgroupindex
C4×D3×C5⋊D52
#119251522
#119251262
C5×#66502
C3×#877692
#117169363
#912465