Finite Group Databasebeta

← #2513×C151 #34065845

Subgroups — #2513×C151 #34065845

Order 19328.

440 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#397×C151C212yesmaximal, complemented
2#397×C151C212yesmaximal, complemented
3#390×C151C211yesmaximal, characteristic
4#390×C151C211yesmaximal, characteristic
5#390×C151C211yesmaximal, characteristic
6#389×C151C211yesmaximal, characteristic, complemented
7#388×C151C212yesmaximal, complemented
8#388×C151C212yesmaximal, complemented
9#382×C151C211yesmaximal, characteristic, complemented
10C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
11C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
12C22×D4×C151C2211yescharacteristic
13C2×C4⋊C4×C151C2211yescharacteristic
14C2×C4⋊C4×C151C2211yescharacteristic
15C2×C4⋊C4×C151C2211yescharacteristic
16C2×C4⋊C4×C151C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C2×C4⋊C4×C151C2212yes—
19C2×C22⋊C4×C151C2212yes—
20C2×C22⋊C4×C151C2212yes—
21C2×C22⋊C4×C151C2212yes—
22C2×C22⋊C4×C151C2212yes—
23C2×C22⋊C4×C151C2212yes—
24C2×C22⋊C4×C151C2212yes—
25C2×C42×C151C2211yescharacteristic
26C2×C42×C151C2211yescharacteristic
27C2×C42×C151C2211yescharacteristic
28C2×C42×C151C2212yes—
29#95×C151C2211yescharacteristic
30#95×C151C2211yescharacteristic
31#95×C151C2212yes—
32#95×C151C2212yes—
33#95×C151C2212yes—
34#95×C151C2212yes—
35C24×C151C2312yes—
36C2×D4×C151—22no—
37C2×D4×C151—22no—
38C2×D4×C151—22no—
39C22×C4×C151C2311yescharacteristic
40C22×C4×C151C2311yescharacteristic
41C22×C4×C151C2311yescharacteristic
42C22×C4×C151C2312yes—
43C22×C4×C151C2312yes—
44C22×C4×C151C2311yescharacteristic
45C22×C4×C151C2312yes—
46C22×C4×C151C2311yescharacteristic
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C4⋊C4×C151—22no—
50C4⋊C4×C151—22no—
51C4⋊C4×C151—22no—
52C4⋊C4×C151—22no—
53C4⋊C4×C151—22no—
54C4⋊C4×C151—42no—
55C22⋊C4×C151—24no—
56C22⋊C4×C151—24no—
57C22⋊C4×C151—42no—
58C22⋊C4×C151—42no—
59C22⋊C4×C151—42no—
60C22⋊C4×C151—42no—
61C42×C151—22no—
62C42×C151—22no—
63C42×C151—22no—
64C42×C151—42no—
65C23×C151—22no—
66C23×C151—22no—
67C23×C151—22no—
68C23×C151—22no—
69C23×C151—22no—
70C23×C151—22no—
71C23×C151—22no—
72C23×C151C2411yescharacteristic
73D4×C151—44no—
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—21no—
99C2×C4×C151#4112yes—
100C2×C4×C151#4112yes—
101C2×C4×C151#4112yes—
102C2×C4×C151#4112yes—
103C2×C4×C151#4112yes—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—42no—
108C22×C151—42no—
109C22×C151—42no—
110C22×C151—42no—
111C22×C151C2×#4111yescharacteristic
112C22×C151C2×#4111yescharacteristic
113C22×C151C2×#4111yescharacteristic
114C22×C151C2×#4111yescharacteristic
115C22×C151C2×#4111yescharacteristic
116C22×C151H(5,𝔽2)11yescharacteristic
117C22×C151H(5,𝔽2)11yescharacteristic
118C4×C151—22no—
119C4×C151—22no—
120C4×C151—41no—
121C4×C151—42no—
122C4×C151—41no—
123C4×C151—41no—
124C4×C151—41no—
125C4×C151—42no—
126C4×C151—42no—
127C4×C151#12614yes—
128C2×C151—82no—
129C2×C151C2×#12611yescharacteristic
130C2×C151#52911yescharacteristic
131C2×C151#54011yescharacteristic
132C2×C151#55311yescharacteristic
133C2×C151#55511yescharacteristic
134C2×C151#55911yescharacteristic
135C2×C151#55911yescharacteristic
136C151#251311yescharacteristic, direct product factor, Sylow
137#2513C15111yesmaximal, characteristic, direct product factor, Sylow
138#397C2×C15112yescomplemented
139#397C2×C15112yescomplemented
140#390C2×C15111yescharacteristic
141#390C2×C15111yescharacteristic
142#390C2×C15111yescharacteristic
143#389C2×C15111yescharacteristic, complemented
144#388C2×C15112yescomplemented
145#388C2×C15112yescomplemented
146#382C2×C15111yescharacteristic, complemented
147C4×C4⋊C4C2×C15111yescharacteristic, complemented
148C4×C4⋊C4C2×C15111yescharacteristic, complemented
149C22×D4C22×C15111yescharacteristic
150C2×C4⋊C4C22×C15111yescharacteristic
151C2×C4⋊C4C22×C15111yescharacteristic
152C2×C4⋊C4C22×C15111yescharacteristic
153C2×C4⋊C4C22×C15111yescharacteristic
154C2×C4⋊C4C22×C15111yescharacteristic
155C2×C4⋊C4C22×C15112yes—
156C2×C22⋊C4C22×C15112yes—
157C2×C22⋊C4C22×C15112yes—
158C2×C22⋊C4C22×C15112yes—
159C2×C22⋊C4C22×C15112yes—
160C2×C22⋊C4C22×C15112yes—
161C2×C22⋊C4C22×C15112yes—
162C2×C42C22×C15111yescharacteristic
163C2×C42C22×C15111yescharacteristic
164C2×C42C22×C15111yescharacteristic
165C2×C42C22×C15112yes—
166#95C22×C15111yescharacteristic
167#95C22×C15111yescharacteristic
168#95C22×C15112yes—
169#95C22×C15112yes—
170#95C22×C15112yes—
171#95C22×C15112yes—
172C24C23×C15112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—22no—
176C22×C4C23×C15111yescharacteristic
177C22×C4C23×C15111yescharacteristic
178C22×C4C23×C15111yescharacteristic
179C22×C4C23×C15112yes—
180C22×C4C23×C15112yes—
181C22×C4C23×C15111yescharacteristic
182C22×C4C23×C15112yes—
183C22×C4C23×C15111yescharacteristic
184C22×C4C23×C15111yescharacteristic
185C22×C4C23×C15111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C22⋊C4—24no—
193C22⋊C4—24no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—42no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23C24×C15111yescharacteristic
210D4—44no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4#41×C15112yes—
237C2×C4#41×C15112yes—
238C2×C4#41×C15112yes—
239C2×C4#41×C15112yes—
240C2×C4#41×C15112yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×#41×C15111yescharacteristic
249C22C2×#41×C15111yescharacteristic
250C22C2×#41×C15111yescharacteristic
251C22C2×#41×C15111yescharacteristic
252C22C2×#41×C15111yescharacteristic
253C22H(5,𝔽2)×C15111yescharacteristic
254C22H(5,𝔽2)×C15111yescharacteristic
255C4—22no—
256C4—22no—
257C4—41no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—42no—
263C4—42no—
264C4#126×C15114yes—
265C2—82no—
266C2C2×#126×C15111yescharacteristic
267C2#529×C15111yescharacteristic
268C2#540×C15111yescharacteristic
269C2#553×C15111yescharacteristic
270C2#555×C15111yescharacteristic
271C2#559×C15111yescharacteristic
272C2#559×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC22×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #397×C151C2semidirect
2. #397×C151C2semidirect
6. #389×C151C2semidirect
7. #388×C151C2semidirect
8. #388×C151C2semidirect
9. #382×C151C2semidirect
10. C4×C4⋊C4×C151C2semidirect
11. C4×C4⋊C4×C151C2semidirect
136. C151#2513direct (N × H)
137. #2513C151direct (N × H)
138. #397C2×C151semidirect
139. #397C2×C151semidirect
143. #389C2×C151semidirect
144. #388C2×C151semidirect
145. #388C2×C151semidirect
146. #382C2×C151semidirect
147. C4×C4⋊C4C2×C151semidirect
148. C4×C4⋊C4C2×C151semidirect

Maximal subgroups

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

subgroupindex
#397×C1512
#390×C1512
#389×C1512
#388×C1512
#382×C1512
C4×C4⋊C4×C1512
#2513151