Finite Group Databasebeta

← C3×C5×#2191 #14275225

Subgroups — C3×C5×#2191 #14275225

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#575C211yesmaximal, characteristic
2C3×C5×#510C212yesmaximal, complemented
3C3×C5×#470C211yesmaximal, characteristic, complemented
4C3×C5×#360C212yesmaximal, complemented
5C3×C5×#349C211yesmaximal, characteristic, complemented
6C5×#2191C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41—21no—
8C3×C5×#137—22no—
9C3×C5×AGL(1,ℤ/8)—22no—
10C3×C5×#135—21no—
11C3×C5×#135C2212yes—
12C2×C3×C5×Q16C2211yescharacteristic, complemented
13C2×C3×C5×M16C2211yescharacteristic
14C3×C5×C22⋊Q8—21no—
15C3×C5×Q32—22no—
16C3×C5×SD32—22no—
17C3×C5×M32C2212yescomplemented
18C3×C5×#106C2211yescharacteristic, complemented
19C3×C5×#103—21no—
20C3×#2191C511yesmaximal, characteristic, direct product factor, Hall
21C5×#575C2×C311yescharacteristic
22C5×#510C2×C312yescomplemented
23C5×#470C2×C311yescharacteristic, complemented
24C5×#360C2×C312yescomplemented
25C5×#349C2×C311yescharacteristic, complemented
26C3×C5×#41—22no—
27C3×C5×#41—22no—
28C3×C5×#41—41no—
29C3×C5×#41—41no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×Q8—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—41no—
34C22×C3×C4×C5—41no—
35C22×C3×C4×C5D411yescharacteristic
36C3×C5×Q16—21no—
37C3×C5×Q16—22no—
38C3×C5×Q16D412yes—
39C3×C5×SD16—22no—
40C3×C5×SD16—22no—
41C3×C5×D8—21no—
42C3×C5×D8D412yes—
43C3×C5×M16—22no—
44C2×C3×C5×C8D411yescharacteristic
45C2×C3×C5×C8C2311yescharacteristic
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—41no—
48C3×C5×C22⋊C4—41no—
49C3×C5×C16—22no—
50C3×#575C2×C511yescharacteristic
51C3×#510C2×C512yescomplemented
52C3×#470C2×C511yescharacteristic, complemented
53C3×#360C2×C512yescomplemented
54C3×#349C2×C511yescharacteristic, complemented
55C2×C5×#41—21no—
56C5×#137—22no—
57C5×AGL(1,ℤ/8)—22no—
58C5×#135—21no—
59C5×#135C22×C312yes—
60C2×C5×Q16C22×C311yescharacteristic, complemented
61C2×C5×M16C22×C311yescharacteristic
62C5×C22⋊Q8—21no—
63C5×Q32—22no—
64C5×SD32—22no—
65C5×M32C22×C312yescomplemented
66C5×#106C22×C311yescharacteristic, complemented
67C5×#103—21no—
68#2191C3×C511yescharacteristic, direct product factor, Sylow
69C23×C3×C5—41no—
70C23×C3×C5D811yescharacteristic
71C3×C5×Q8—22no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C3×C5×Q8—41no—
75C3×C5×D4—22no—
76C3×C5×D4—41no—
77C3×C5×D4—42no—
78C3×C5×D4—42no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5D811yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×C3×#41—21no—
91C3×#137—22no—
92C3×AGL(1,ℤ/8)—22no—
93C3×#135—21no—
94C3×#135C22×C512yes—
95C2×C3×Q16C22×C511yescharacteristic, complemented
96C2×C3×M16C22×C511yescharacteristic
97C3×C22⋊Q8—21no—
98C3×Q32—22no—
99C3×SD32—22no—
100C3×M32C22×C512yescomplemented
101C3×#106C22×C511yescharacteristic, complemented
102C3×#103—21no—
103C5×#41—22no—
104C5×#41—22no—
105C5×#41—41no—
106C5×#41—41no—
107C2×C5×Q8—21no—
108C2×C5×Q8—21no—
109C2×C5×D4—21no—
110C2×C5×D4—41no—
111C22×C4×C5—41no—
112C22×C4×C5C3×D411yescharacteristic
113C5×Q16—21no—
114C5×Q16—22no—
115C5×Q16C3×D412yes—
116C5×SD16—22no—
117C5×SD16—22no—
118C5×D8—21no—
119C5×D8C3×D412yes—
120C5×M16—22no—
121C2×C5×C8C3×D411yescharacteristic
122C2×C5×C8C23×C311yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—41no—
125C5×C22⋊C4—41no—
126C5×C16—22no—
127#575C2×C3×C511yescharacteristic
128#510C2×C3×C512yescomplemented
129#470C2×C3×C511yescharacteristic, complemented
130#360C2×C3×C512yescomplemented
131#349C2×C3×C511yescharacteristic, complemented
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5—42no—
135C22×C3×C5—82no—
136C22×C3×C5C2×D811yescharacteristic
137C3×C4×C5—21no—
138C3×C4×C5—42no—
139C3×C4×C5—81no—
140C3×C4×C5—81no—
141C3×C4×C5#12011yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×#41—22no—
144C3×#41—22no—
145C3×#41—41no—
146C3×#41—41no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×D4—21no—
150C2×C3×D4—41no—
151C22×C3×C4—41no—
152C22×C3×C4C5×D411yescharacteristic
153C3×Q16—21no—
154C3×Q16—22no—
155C3×Q16C5×D412yes—
156C3×SD16—22no—
157C3×SD16—22no—
158C3×D8—21no—
159C3×D8C5×D412yes—
160C3×M16—22no—
161C2×C3×C8C5×D411yescharacteristic
162C2×C3×C8C23×C511yescharacteristic
163C3×C4⋊C4—21no—
164C3×C4⋊C4—41no—
165C3×C22⋊C4—41no—
166C3×C16—22no—
167C23×C5—41no—
168C23×C5C3×D811yescharacteristic
169C5×Q8—22no—
170C5×Q8—41no—
171C5×Q8—41no—
172C5×Q8—41no—
173C5×D4—22no—
174C5×D4—41no—
175C5×D4—42no—
176C5×D4—42no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—42no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5C3×D811yescharacteristic
185C2×C4×C5C2×C3×D411yescharacteristic
186C5×C8—21no—
187C5×C8C2×C3×D412yes—
188C2×#41—21no—
189#137—22no—
190AGL(1,ℤ/8)—22no—
191#135—21no—
192#135C22×C3×C512yes—
193C2×Q16C22×C3×C511yescharacteristic, complemented
194C2×M16C22×C3×C511yescharacteristic
195C22⋊Q8—21no—
196Q32—22no—
197SD32—22no—
198M32C22×C3×C512yescomplemented
199#106C22×C3×C511yescharacteristic, complemented
200#103—21no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5—82no—
204C2×C3×C5#44711yescharacteristic
205C23×C3—41no—
206C23×C3C5×D811yescharacteristic
207C3×Q8—22no—
208C3×Q8—41no—
209C3×Q8—41no—
210C3×Q8—41no—
211C3×D4—22no—
212C3×D4—41no—
213C3×D4—42no—
214C3×D4—42no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—42no—
218C2×C3×C4—41no—
219C2×C3×C4—42no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4C5×D811yescharacteristic
223C2×C3×C4C2×C5×D411yescharacteristic
224C3×C8—21no—
225C3×C8C2×C5×D412yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5C2×C3×D811yescharacteristic
231C4×C5—21no—
232C4×C5—42no—
233C4×C5—81no—
234C4×C5—81no—
235C4×C5C3×#12011yescharacteristic
236C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×D4—21no—
244C2×D4—41no—
245C22×C4—41no—
246C22×C4C3×C5×D411yescharacteristic
247Q16—21no—
248Q16—22no—
249Q16C3×C5×D412yes—
250SD16—22no—
251SD16—22no—
252D8—21no—
253D8C3×C5×D412yes—
254M16—22no—
255C2×C8C3×C5×D411yescharacteristic
256C2×C8C23×C3×C511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—41no—
259C22⋊C4—41no—
260C16—22no—
261C3×C5#219111yescharacteristic, direct product factor, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—42no—
265C22×C3—82no—
266C22×C3C2×C5×D811yescharacteristic
267C3×C4—21no—
268C3×C4—42no—
269C3×C4—81no—
270C3×C4—81no—
271C3×C4C5×#12011yescharacteristic
272C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
273C2×C5—21no—
274C2×C5—41no—
275C2×C5—82no—
276C2×C5C3×#44711yescharacteristic
277C23—41no—
278C23C3×C5×D811yescharacteristic
279Q8—22no—
280Q8—41no—
281Q8—41no—
282Q8—41no—
283D4—22no—
284D4—41no—
285D4—42no—
286D4—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C3×C5×D811yescharacteristic
295C2×C4C2×C3×C5×D411yescharacteristic
296C8—21no—
297C8C2×C3×C5×D412yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—82no—
301C2×C3C5×#44711yescharacteristic
302C5C3×#219111yescharacteristic, direct product factor, Sylow
303C22—21no—
304C22—41no—
305C22—42no—
306C22—82no—
307C22C2×C3×C5×D811yescharacteristic
308C4—21no—
309C4—42no—
310C4—81no—
311C4—81no—
312C4C3×C5×#12011yescharacteristic
313C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
314C3C5×#219111yescharacteristic, direct product factor, Sylow
315C2—21no—
316C2—41no—
317C2—82no—
318C2C3×C5×#44711yescharacteristic
subgroupG/H
center, socleC2×C3×C5#447
commutator, Frattini, cosocleC2×C8C23×C3×C5
prime radicalC3×C5×#575C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#510C2semidirect
3. C3×C5×#470C2semidirect
4. C3×C5×#360C2semidirect
5. C3×C5×#349C2semidirect
6. C5×#2191C3direct (N × H)
12. C2×C3×C5×Q16C22semidirect
17. C3×C5×M32C22semidirect
18. C3×C5×#106C22semidirect
20. C3×#2191C5direct (N × H)
22. C5×#510C2×C3semidirect
23. C5×#470C2×C3semidirect
24. C5×#360C2×C3semidirect
25. C5×#349C2×C3semidirect
51. C3×#510C2×C5semidirect
52. C3×#470C2×C5semidirect
53. C3×#360C2×C5semidirect
54. C3×#349C2×C5semidirect
60. C2×C5×Q16C22×C3semidirect
65. C5×M32C22×C3semidirect
66. C5×#106C22×C3semidirect
68. #2191C3×C5direct (N × H)
95. C2×C3×Q16C22×C5semidirect
100. C3×M32C22×C5semidirect
101. C3×#106C22×C5semidirect
128. #510C2×C3×C5semidirect
129. #470C2×C3×C5semidirect
130. #360C2×C3×C5semidirect
131. #349C2×C3×C5semidirect
193. C2×Q16C22×C3×C5semidirect
198. M32C22×C3×C5semidirect
199. #106C22×C3×C5semidirect
261. C3×C5#2191direct (N × H)
302. C5C3×#2191direct (N × H)
314. C3C5×#2191direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5752
C3×C5×#5102
C3×C5×#4702
C3×C5×#3602
C3×C5×#3492
C5×#21913
C3×#21915