Finite Group Databasebeta

← C3×C5×#2133 #14275167

Subgroups — C3×C5×#2133 #14275167

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#536C211yesmaximal, characteristic
2C2×C3×C5×#101C212yesmaximal, complemented
3C3×C5×#356C212yesmaximal, complemented
4C3×C5×#355C212yesmaximal, complemented
5C5×#2133C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C411yescharacteristic
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×C5×M16—22no—
9C3×C5×C4⋊Q8C411yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#124C411yescharacteristic
12C3×C5×#124C2211yescharacteristic
13C3×C5×#123—22no—
14C3×C5×C22⋊Q8—22no—
15C3×C5×#117C411yescharacteristic
16C3×C5×#101—22no—
17C3×C5×#101C2214yes—
18C3×#2133C511yesmaximal, characteristic, direct product factor, Hall
19C5×#536C2×C311yescharacteristic
20C2×C5×#101C2×C312yescomplemented
21C5×#356C2×C312yescomplemented
22C5×#355C2×C312yescomplemented
23C3×C5×#41—42no—
24C2×C3×C5×Q8—42no—
25C2×C3×C5×Q8C2×C411yescharacteristic
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×Q8D412yes—
28C2×C3×C5×Q8C2311yescharacteristic
29C2×C3×C5×D4—21no—
30C2×C3×C5×D4C2×C411yescharacteristic
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D412yes—
34C3×C5×M16—24no—
35C3×C5×M16—42no—
36C2×C3×C5×C8—42no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C22⋊C4—21no—
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—22no—
43C3×C42×C5C2×C411yescharacteristic
44C3×C42×C5C2×C411yescharacteristic
45C3×#536C2×C511yescharacteristic
46C2×C3×#101C2×C512yescomplemented
47C3×#356C2×C512yescomplemented
48C3×#355C2×C512yescomplemented
49C2×C5×#41C3×C411yescharacteristic
50C22×C5×Q8C22×C311yescharacteristic
51C2×C5×M16—22no—
52C5×C4⋊Q8C3×C411yescharacteristic
53C5×C4⋊Q8C22×C311yescharacteristic
54C5×#124C3×C411yescharacteristic
55C5×#124C22×C311yescharacteristic
56C5×#123—22no—
57C5×C22⋊Q8—22no—
58C5×#117C3×C411yescharacteristic
59C5×#101—22no—
60C5×#101C22×C314yes—
61#2133C3×C511yescharacteristic, direct product factor, Sylow
62C23×C3×C5—21no—
63C23×C3×C5C22⋊C411yescharacteristic
64C3×C5×Q8—41no—
65C3×C5×Q8—42no—
66C3×C5×Q8—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C3×C5×D4—42no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—42no—
77C2×C3×C4×C5C22⋊C412yes—
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×C3×C4×C5C2×D412yes—
81C3×C5×C8—44no—
82C2×C3×#41C4×C511yescharacteristic
83C22×C3×Q8C22×C511yescharacteristic
84C2×C3×M16—22no—
85C3×C4⋊Q8C4×C511yescharacteristic
86C3×C4⋊Q8C22×C511yescharacteristic
87C3×#124C4×C511yescharacteristic
88C3×#124C22×C511yescharacteristic
89C3×#123—22no—
90C3×C22⋊Q8—22no—
91C3×#117C4×C511yescharacteristic
92C3×#101—22no—
93C3×#101C22×C514yes—
94C5×#41—42no—
95C2×C5×Q8—42no—
96C2×C5×Q8C2×C3×C411yescharacteristic
97C2×C5×Q8C2×C3×C411yescharacteristic
98C2×C5×Q8C3×D412yes—
99C2×C5×Q8C23×C311yescharacteristic
100C2×C5×D4—21no—
101C2×C5×D4C2×C3×C411yescharacteristic
102C22×C4×C5—21no—
103C22×C4×C5C2×C3×C411yescharacteristic
104C22×C4×C5C3×D412yes—
105C5×M16—24no—
106C5×M16—42no—
107C2×C5×C8—42no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—22no—
111C5×C22⋊C4—21no—
112C5×C22⋊C4—22no—
113C5×C22⋊C4—22no—
114C42×C5C2×C3×C411yescharacteristic
115C42×C5C2×C3×C411yescharacteristic
116#536C2×C3×C511yescharacteristic
117C2×#101C2×C3×C512yescomplemented
118#356C2×C3×C512yescomplemented
119#355C2×C3×C512yescomplemented
120C22×C3×C5—41no—
121C22×C3×C5—42no—
122C22×C3×C5—41no—
123C22×C3×C5#9912yes—
124C22×C3×C5C2×C22⋊C411yescharacteristic
125C3×C4×C5—22no—
126C3×C4×C5—21no—
127C3×C4×C5—22no—
128C3×C4×C5—21no—
129C3×C4×C5—41no—
130C3×C4×C5—41no—
131C3×C4×C5—41no—
132C3×#41—42no—
133C2×C3×Q8—42no—
134C2×C3×Q8C2×C4×C511yescharacteristic
135C2×C3×Q8C2×C4×C511yescharacteristic
136C2×C3×Q8C5×D412yes—
137C2×C3×Q8C23×C511yescharacteristic
138C2×C3×D4—21no—
139C2×C3×D4C2×C4×C511yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4C2×C4×C511yescharacteristic
142C22×C3×C4C5×D412yes—
143C3×M16—24no—
144C3×M16—42no—
145C2×C3×C8—42no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C22⋊C4—21no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C42C2×C4×C511yescharacteristic
153C3×C42C2×C4×C511yescharacteristic
154C23×C5—21no—
155C23×C5C3×C22⋊C411yescharacteristic
156C5×Q8—41no—
157C5×Q8—42no—
158C5×Q8—41no—
159C5×Q8—41no—
160C5×D4—41no—
161C5×D4—42no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—42no—
169C2×C4×C5C3×C22⋊C412yes—
170C2×C4×C5C3×C22⋊C411yescharacteristic
171C2×C4×C5C22×C3×C411yescharacteristic
172C2×C4×C5C2×C3×D412yes—
173C5×C8—44no—
174C2×#41C3×C4×C511yescharacteristic
175C22×Q8C22×C3×C511yescharacteristic
176C2×M16—22no—
177C4⋊Q8C3×C4×C511yescharacteristic
178C4⋊Q8C22×C3×C511yescharacteristic
179#124C3×C4×C511yescharacteristic
180#124C22×C3×C511yescharacteristic
181#123—22no—
182C22⋊Q8—22no—
183#117C3×C4×C511yescharacteristic
184#101—22no—
185#101C22×C3×C514yes—
186C2×C3×C5—21no—
187C2×C3×C5—22no—
188C2×C3×C5—81no—
189C2×C3×C5C2×#9911yescharacteristic
190C23×C3—21no—
191C23×C3C5×C22⋊C411yescharacteristic
192C3×Q8—41no—
193C3×Q8—42no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×D4—41no—
197C3×D4—42no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—42no—
205C2×C3×C4C5×C22⋊C412yes—
206C2×C3×C4C5×C22⋊C411yescharacteristic
207C2×C3×C4C22×C4×C511yescharacteristic
208C2×C3×C4C2×C5×D412yes—
209C3×C8—44no—
210C22×C5—41no—
211C22×C5—42no—
212C22×C5—41no—
213C22×C5C3×#9912yes—
214C22×C5C2×C3×C22⋊C411yescharacteristic
215C4×C5—22no—
216C4×C5—21no—
217C4×C5—22no—
218C4×C5—21no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—41no—
222#41—42no—
223C2×Q8—42no—
224C2×Q8C2×C3×C4×C511yescharacteristic
225C2×Q8C2×C3×C4×C511yescharacteristic
226C2×Q8C3×C5×D412yes—
227C2×Q8C23×C3×C511yescharacteristic
228C2×D4—21no—
229C2×D4C2×C3×C4×C511yescharacteristic
230C22×C4—21no—
231C22×C4C2×C3×C4×C511yescharacteristic
232C22×C4C3×C5×D412yes—
233M16—24no—
234M16—42no—
235C2×C8—42no—
236C4⋊C4—21no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C22⋊C4—21no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C42C2×C3×C4×C511yescharacteristic
243C42C2×C3×C4×C511yescharacteristic
244C3×C5#213311yescharacteristic, direct product factor, Hall
245C22×C3—41no—
246C22×C3—42no—
247C22×C3—41no—
248C22×C3C5×#9912yes—
249C22×C3C2×C5×C22⋊C411yescharacteristic
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—41no—
255C3×C4—41no—
256C3×C4—41no—
257C2×C5—21no—
258C2×C5—22no—
259C2×C5—81no—
260C2×C5C2×C3×#9911yescharacteristic
261C23—21no—
262C23C3×C5×C22⋊C411yescharacteristic
263Q8—41no—
264Q8—42no—
265Q8—41no—
266Q8—41no—
267D4—41no—
268D4—42no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4C3×C5×C22⋊C412yes—
277C2×C4C3×C5×C22⋊C411yescharacteristic
278C2×C4C22×C3×C4×C511yescharacteristic
279C2×C4C2×C3×C5×D412yes—
280C8—44no—
281C2×C3—21no—
282C2×C3—22no—
283C2×C3—81no—
284C2×C3C2×C5×#9911yescharacteristic
285C5C3×#213311yescharacteristic, direct product factor, Sylow
286C22—41no—
287C22—42no—
288C22—41no—
289C22C3×C5×#9912yes—
290C22C2×C3×C5×C22⋊C411yescharacteristic
291C4—22no—
292C4—21no—
293C4—22no—
294C4—21no—
295C4—41no—
296C4—41no—
297C4—41no—
298C3C5×#213311yescharacteristic, direct product factor, Sylow
299C2—21no—
300C2—22no—
301C2—81no—
302C2C2×C3×C5×#9911yescharacteristic
subgroupG/H
center, socleC2×C3×C5C2×#99
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC2×Q8C23×C3×C5
prime radicalC2×C3×C5×#41C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C23×C3×C5 ◁ C22×C3×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#101C2semidirect
3. C3×C5×#356C2semidirect
4. C3×C5×#355C2semidirect
5. C5×#2133C3direct (N × H)
18. C3×#2133C5direct (N × H)
20. C2×C5×#101C2×C3semidirect
21. C5×#356C2×C3semidirect
22. C5×#355C2×C3semidirect
46. C2×C3×#101C2×C5semidirect
47. C3×#356C2×C5semidirect
48. C3×#355C2×C5semidirect
61. #2133C3×C5direct (N × H)
117. C2×#101C2×C3×C5semidirect
118. #356C2×C3×C5semidirect
119. #355C2×C3×C5semidirect
244. C3×C5#2133direct (N × H)
285. C5C3×#2133direct (N × H)
298. C3C5×#2133direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5362
C2×C3×C5×#1012
C3×C5×#3562
C3×C5×#3552
C5×#21333
C3×#21335