Finite Group Databasebeta

← C3×C5×#1611 #14274645

Subgroups — C3×C5×#1611 #14274645

Order 1920.

420 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#544C211yesmaximal, characteristic
2C3×C5×#483C212yesmaximal
3C3×C5×#398C211yesmaximal, characteristic
4C3×C5×#328C212yesmaximal
5C3×C5×#324C211yesmaximal, characteristic
6C5×#1611C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8—22no—
8C3×C5×#125—22no—
9C3×C5×C22⋊Q8—21no—
10C3×C5×C22⋊Q8C2212yes—
11C3×C5×#117—21no—
12C2×C3×C5×C4⋊C4—21no—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C3×C5×#106—22no—
16C3×C5×#103—22no—
17C3×C5×C22⋊C8C2212yes—
18C3×C5×#95—21no—
19C3×C5×#95C2211yescharacteristic
20C3×#1611C511yesmaximal, characteristic, direct product factor, Hall
21C5×#544C2×C311yescharacteristic
22C5×#483C2×C312yes—
23C5×#398C2×C311yescharacteristic
24C5×#328C2×C312yes—
25C5×#324C2×C311yescharacteristic
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D412yes—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×C3×C5×C8—22no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—42no—
42C3×C5×C4⋊C4D412yes—
43C3×C5×C22⋊C4—22no—
44C3×C42×C5—22no—
45C3×#544C2×C511yescharacteristic
46C3×#483C2×C512yes—
47C3×#398C2×C511yescharacteristic
48C3×#328C2×C512yes—
49C3×#324C2×C511yescharacteristic
50C5×C4⋊Q8—22no—
51C5×#125—22no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8C22×C312yes—
54C5×#117—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4C22×C311yescharacteristic
57C2×C5×C4⋊C4C22×C311yescharacteristic
58C5×#106—22no—
59C5×#103—22no—
60C5×C22⋊C8C22×C312yes—
61C5×#95—21no—
62C5×#95C22×C311yescharacteristic
63#1611C3×C511yescharacteristic, direct product factor, Sylow
64C23×C3×C5C2×D411yescharacteristic
65C3×C5×Q8—42no—
66C3×C5×Q8—81no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5SD1612yes—
81C2×C3×C4×C5C2×D412yes—
82C3×C5×C8—42no—
83C3×C4⋊Q8—22no—
84C3×#125—22no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8C22×C512yes—
87C3×#117—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4C22×C511yescharacteristic
90C2×C3×C4⋊C4C22×C511yescharacteristic
91C3×#106—22no—
92C3×#103—22no—
93C3×C22⋊C8C22×C512yes—
94C3×#95—21no—
95C3×#95C22×C511yescharacteristic
96C2×C5×Q8—21no—
97C2×C5×Q8C3×D412yes—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5C3×D411yescharacteristic
101C22×C4×C5C3×D411yescharacteristic
102C22×C4×C5C23×C311yescharacteristic
103C2×C5×C8—22no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—42no—
112C5×C4⋊C4C3×D412yes—
113C5×C22⋊C4—22no—
114C42×C5—22no—
115#544C2×C3×C511yescharacteristic
116#483C2×C3×C512yes—
117#398C2×C3×C511yescharacteristic
118#328C2×C3×C512yes—
119#324C2×C3×C511yescharacteristic
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C2×SD1611yescharacteristic
124C22×C3×C5#13711yescharacteristic
125C3×C4×C5—22no—
126C3×C4×C5—22no—
127C3×C4×C5—42no—
128C3×C4×C5—42no—
129C3×C4×C5—41no—
130C3×C4×C5—42no—
131C3×C4×C5—81no—
132C2×C3×Q8—21no—
133C2×C3×Q8C5×D412yes—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4C5×D411yescharacteristic
137C22×C3×C4C5×D411yescharacteristic
138C22×C3×C4C23×C511yescharacteristic
139C2×C3×C8—22no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—42no—
148C3×C4⋊C4C5×D412yes—
149C3×C22⋊C4—22no—
150C3×C42—22no—
151C23×C5C2×C3×D411yescharacteristic
152C5×Q8—42no—
153C5×Q8—81no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—22no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5C3×SD1612yes—
168C2×C4×C5C2×C3×D412yes—
169C5×C8—42no—
170C4⋊Q8—22no—
171#125—22no—
172C22⋊Q8—21no—
173C22⋊Q8C22×C3×C512yes—
174#117—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C22×C3×C511yescharacteristic
177C2×C4⋊C4C22×C3×C511yescharacteristic
178#106—22no—
179#103—22no—
180C22⋊C8C22×C3×C512yes—
181#95—21no—
182#95C22×C3×C511yescharacteristic
183C2×C3×C5—21no—
184C2×C3×C5—21no—
185C2×C3×C5#44811yescharacteristic
186C2×C3×C5#45611yescharacteristic
187C2×C3×C5#45811yescharacteristic
188C23×C3C2×C5×D411yescharacteristic
189C3×Q8—42no—
190C3×Q8—81no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4C5×SD1612yes—
205C2×C3×C4C2×C5×D412yes—
206C3×C8—42no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5C3×#12011yescharacteristic
210C22×C5C2×C3×SD1611yescharacteristic
211C22×C5C3×#13711yescharacteristic
212C4×C5—22no—
213C4×C5—22no—
214C4×C5—42no—
215C4×C5—42no—
216C4×C5—41no—
217C4×C5—42no—
218C4×C5—81no—
219C2×Q8—21no—
220C2×Q8C3×C5×D412yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C3×C5×D411yescharacteristic
224C22×C4C3×C5×D411yescharacteristic
225C22×C4C23×C3×C511yescharacteristic
226C2×C8—22no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—42no—
235C4⋊C4C3×C5×D412yes—
236C22⋊C4—22no—
237C42—22no—
238C3×C5#161111yescharacteristic, direct product factor, Hall
239C22×C3—21no—
240C22×C3—21no—
241C22×C3C5×#12011yescharacteristic
242C22×C3C2×C5×SD1611yescharacteristic
243C22×C3C5×#13711yescharacteristic
244C3×C4—22no—
245C3×C4—22no—
246C3×C4—42no—
247C3×C4—42no—
248C3×C4—41no—
249C3×C4—42no—
250C3×C4—81no—
251C2×C5—21no—
252C2×C5—21no—
253C2×C5C3×#44811yescharacteristic
254C2×C5C3×#45611yescharacteristic
255C2×C5C3×#45811yescharacteristic
256C23C2×C3×C5×D411yescharacteristic
257Q8—42no—
258Q8—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4C3×C5×SD1612yes—
273C2×C4C2×C3×C5×D412yes—
274C8—42no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3C5×#44811yescharacteristic
278C2×C3C5×#45611yescharacteristic
279C2×C3C5×#45811yescharacteristic
280C5C3×#161111yescharacteristic, direct product factor, Sylow
281C22—21no—
282C22—21no—
283C22C3×C5×#12011yescharacteristic
284C22C2×C3×C5×SD1611yescharacteristic
285C22C3×C5×#13711yescharacteristic
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—41no—
291C4—42no—
292C4—81no—
293C3C5×#161111yescharacteristic, direct product factor, Sylow
294C2—21no—
295C2—21no—
296C2C3×C5×#44811yescharacteristic
297C2C3×C5×#45611yescharacteristic
298C2C3×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC23×C3×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#1611C3direct (N × H)
20. C3×#1611C5direct (N × H)
63. #1611C3×C5direct (N × H)
238. C3×C5#1611direct (N × H)
280. C5C3×#1611direct (N × H)
293. C3C5×#1611direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5442
C3×C5×#4832
C3×C5×#3982
C3×C5×#3282
C3×C5×#3242
C5×#16113
C3×#16115