Finite Group Databasebeta

← C3×C5×#1608 #14274642

Subgroups — C3×C5×#1608 #14274642

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#543C211yesmaximal, characteristic
2C3×C5×#483C212yesmaximal, complemented
3C3×C5×#397C211yesmaximal, characteristic
4C3×C5×#328C212yesmaximal, complemented
5C3×C5×#323C211yesmaximal, characteristic
6C5×#1608C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C22⋊Q8—22no—
8C3×C5×C22⋊Q8—21no—
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8C2212yes—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C3×C5×#106—22no—
16C3×C5×#103—22no—
17C3×C5×C22⋊C8C2212yes—
18C3×C5×#95—21no—
19C3×C5×#95C2211yescharacteristic
20C3×#1608C511yesmaximal, characteristic, direct product factor, Hall
21C5×#543C2×C311yescharacteristic
22C5×#483C2×C312yescomplemented
23C5×#397C2×C311yescharacteristic
24C5×#328C2×C312yescomplemented
25C5×#323C2×C311yescharacteristic
26C24×C3×C5D411yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4D412yes—
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—22no—
43C3×C5×C22⋊C4—22no—
44C3×C5×C22⋊C4—42no—
45C3×#543C2×C511yescharacteristic
46C3×#483C2×C512yescomplemented
47C3×#397C2×C511yescharacteristic
48C3×#328C2×C512yescomplemented
49C3×#323C2×C511yescharacteristic
50C5×C22⋊Q8—22no—
51C5×C22⋊Q8—21no—
52C5×C22⋊Q8—22no—
53C5×C22⋊Q8C22×C312yes—
54C2×C5×C4⋊C4C22×C311yescharacteristic
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4C22×C311yescharacteristic
58C5×#106—22no—
59C5×#103—22no—
60C5×C22⋊C8C22×C312yes—
61C5×#95—21no—
62C5×#95C22×C311yescharacteristic
63#1608C3×C511yescharacteristic, direct product factor, Sylow
64C23×C3×C5—21no—
65C23×C3×C5—21no—
66C23×C3×C5—41no—
67C23×C3×C5—41no—
68C23×C3×C5SD1612yes—
69C23×C3×C5C2×D411yescharacteristic
70C3×C5×Q8—42no—
71C3×C5×Q8—81no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—22no—
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×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—81no—
84C2×C3×C4×C5—81no—
85C2×C3×C4×C5C2×D412yes—
86C3×C5×C8—42no—
87C3×C22⋊Q8—22no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8C22×C512yes—
91C2×C3×C4⋊C4C22×C511yescharacteristic
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4C22×C511yescharacteristic
95C3×#106—22no—
96C3×#103—22no—
97C3×C22⋊C8C22×C512yes—
98C3×#95—21no—
99C3×#95C22×C511yescharacteristic
100C24×C5C3×D411yescharacteristic
101C2×C5×Q8—21no—
102C2×C5×Q8C3×D412yes—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5C3×D411yescharacteristic
108C22×C4×C5C23×C311yescharacteristic
109C2×C5×C8—22no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4C3×D412yes—
115C5×C22⋊C4—22no—
116C5×C22⋊C4—22no—
117C5×C22⋊C4—22no—
118C5×C22⋊C4—42no—
119#543C2×C3×C511yescharacteristic
120#483C2×C3×C512yescomplemented
121#397C2×C3×C511yescharacteristic
122#328C2×C3×C512yescomplemented
123#323C2×C3×C511yescharacteristic
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—22no—
127C22×C3×C5—42no—
128C22×C3×C5—41no—
129C22×C3×C5—41no—
130C22×C3×C5—81no—
131C22×C3×C5#12011yescharacteristic
132C22×C3×C5C2×SD1611yescharacteristic
133C22×C3×C5#13711yescharacteristic
134C3×C4×C5—22no—
135C3×C4×C5—41no—
136C3×C4×C5—42no—
137C3×C4×C5—42no—
138C3×C4×C5—81no—
139C3×C4×C5—81no—
140C24×C3C5×D411yescharacteristic
141C2×C3×Q8—21no—
142C2×C3×Q8C5×D412yes—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4C5×D411yescharacteristic
148C22×C3×C4C23×C511yescharacteristic
149C2×C3×C8—22no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4C5×D412yes—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—42no—
159C23×C5—21no—
160C23×C5—21no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5C3×SD1612yes—
164C23×C5C2×C3×D411yescharacteristic
165C5×Q8—42no—
166C5×Q8—81no—
167C2×C4×C5—22no—
168C2×C4×C5—21no—
169C2×C4×C5—22no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5C2×C3×D412yes—
181C5×C8—42no—
182C22⋊Q8—22no—
183C22⋊Q8—21no—
184C22⋊Q8—22no—
185C22⋊Q8C22×C3×C512yes—
186C2×C4⋊C4C22×C3×C511yescharacteristic
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4C22×C3×C511yescharacteristic
190#106—22no—
191#103—22no—
192C22⋊C8C22×C3×C512yes—
193#95—21no—
194#95C22×C3×C511yescharacteristic
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—42no—
198C2×C3×C5#44811yescharacteristic
199C2×C3×C5#45511yescharacteristic
200C2×C3×C5#45811yescharacteristic
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—41no—
204C23×C3—41no—
205C23×C3C5×SD1612yes—
206C23×C3C2×C5×D411yescharacteristic
207C3×Q8—42no—
208C3×Q8—81no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—81no—
221C2×C3×C4—81no—
222C2×C3×C4C2×C5×D412yes—
223C3×C8—42no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—22no—
227C22×C5—42no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—81no—
231C22×C5C3×#12011yescharacteristic
232C22×C5C2×C3×SD1611yescharacteristic
233C22×C5C3×#13711yescharacteristic
234C4×C5—22no—
235C4×C5—41no—
236C4×C5—42no—
237C4×C5—42no—
238C4×C5—81no—
239C4×C5—81no—
240C24C3×C5×D411yescharacteristic
241C2×Q8—21no—
242C2×Q8C3×C5×D412yes—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C3×C5×D411yescharacteristic
248C22×C4C23×C3×C511yescharacteristic
249C2×C8—22no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4C3×C5×D412yes—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—42no—
259C3×C5#160811yescharacteristic, direct product factor, Hall
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—42no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—81no—
267C22×C3C5×#12011yescharacteristic
268C22×C3C2×C5×SD1611yescharacteristic
269C22×C3C5×#13711yescharacteristic
270C3×C4—22no—
271C3×C4—41no—
272C3×C4—42no—
273C3×C4—42no—
274C3×C4—81no—
275C3×C4—81no—
276C2×C5—21no—
277C2×C5—21no—
278C2×C5—42no—
279C2×C5C3×#44811yescharacteristic
280C2×C5C3×#45511yescharacteristic
281C2×C5C3×#45811yescharacteristic
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23C3×C5×SD1612yes—
287C23C2×C3×C5×D411yescharacteristic
288Q8—42no—
289Q8—81no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C2×C3×C5×D412yes—
304C8—42no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3C5×#44811yescharacteristic
309C2×C3C5×#45511yescharacteristic
310C2×C3C5×#45811yescharacteristic
311C5C3×#160811yescharacteristic, direct product factor, Sylow
312C22—21no—
313C22—21no—
314C22—22no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22C3×C5×#12011yescharacteristic
320C22C2×C3×C5×SD1611yescharacteristic
321C22C3×C5×#13711yescharacteristic
322C4—22no—
323C4—41no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—81no—
328C3C5×#160811yescharacteristic, direct product factor, Sylow
329C2—21no—
330C2—21no—
331C2—42no—
332C2C3×C5×#44811yescharacteristic
333C2C3×C5×#45511yescharacteristic
334C2C3×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC24×C3×C5D4
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
2. C3×C5×#483C2semidirect
4. C3×C5×#328C2semidirect
6. C5×#1608C3direct (N × H)
20. C3×#1608C5direct (N × H)
22. C5×#483C2×C3semidirect
24. C5×#328C2×C3semidirect
46. C3×#483C2×C5semidirect
48. C3×#328C2×C5semidirect
63. #1608C3×C5direct (N × H)
120. #483C2×C3×C5semidirect
122. #328C2×C3×C5semidirect
259. C3×C5#1608direct (N × H)
311. C5C3×#1608direct (N × H)
328. C3C5×#1608direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5432
C3×C5×#4832
C3×C5×#3972
C3×C5×#3282
C3×C5×#3232
C5×#16083
C3×#16085