Finite Group Databasebeta

← C3×C5×#1602 #14274636

Subgroups — C3×C5×#1602 #14274636

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#543C211yesmaximal, characteristic
2C3×C5×#451C212yesmaximal, complemented
3C3×C5×#393C211yesmaximal, characteristic
4C3×C5×#328C212yesmaximal, complemented
5C3×C5×#323C211yesmaximal, characteristic
6C5×#1602C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×C5×Q16—22no—
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8—22no—
12C3×C5×C22⋊Q8C2212yes—
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C3×C5×#103—22no—
17C3×C5×C22⋊C8C2212yes—
18C3×C5×#95—21no—
19C3×C5×#95C2211yescharacteristic
20C3×#1602C511yesmaximal, characteristic, direct product factor, Hall
21C5×#543C2×C311yescharacteristic
22C5×#451C2×C312yescomplemented
23C5×#393C2×C311yescharacteristic
24C5×#328C2×C312yescomplemented
25C5×#323C2×C311yescharacteristic
26C24×C3×C5D411yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8—22no—
29C2×C3×C5×Q8—42no—
30C2×C3×C5×Q8D412yes—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C3×C5×Q16—44no—
38C2×C3×C5×C8—22no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4D412yes—
43C3×C5×C22⋊C4—22no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—42no—
47C3×#543C2×C511yescharacteristic
48C3×#451C2×C512yescomplemented
49C3×#393C2×C511yescharacteristic
50C3×#328C2×C512yescomplemented
51C3×#323C2×C511yescharacteristic
52C22×C5×Q8C22×C311yescharacteristic
53C2×C5×Q16—22no—
54C5×C22⋊Q8—22no—
55C5×C22⋊Q8—21no—
56C5×C22⋊Q8—22no—
57C5×C22⋊Q8C22×C312yes—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4C22×C311yescharacteristic
61C5×#103—22no—
62C5×C22⋊C8C22×C312yes—
63C5×#95—21no—
64C5×#95C22×C311yescharacteristic
65#1602C3×C511yescharacteristic, direct product factor, Sylow
66C23×C3×C5—21no—
67C23×C3×C5—21no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5Q1612yescomplemented
71C23×C3×C5C2×D411yescharacteristic
72C3×C5×Q8—24no—
73C3×C5×Q8—42no—
74C3×C5×Q8—42no—
75C3×C5×Q8—81no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—81no—
88C2×C3×C4×C5—81no—
89C2×C3×C4×C5C2×D412yes—
90C3×C5×C8—42no—
91C22×C3×Q8C22×C511yescharacteristic
92C2×C3×Q16—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—21no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8C22×C512yes—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4C22×C511yescharacteristic
100C3×#103—22no—
101C3×C22⋊C8C22×C512yes—
102C3×#95—21no—
103C3×#95C22×C511yescharacteristic
104C24×C5C3×D411yescharacteristic
105C2×C5×Q8—21no—
106C2×C5×Q8—22no—
107C2×C5×Q8—42no—
108C2×C5×Q8C3×D412yes—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5C3×D411yescharacteristic
114C22×C4×C5C23×C311yescharacteristic
115C5×Q16—44no—
116C2×C5×C8—22no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4C3×D412yes—
121C5×C22⋊C4—22no—
122C5×C22⋊C4—22no—
123C5×C22⋊C4—22no—
124C5×C22⋊C4—42no—
125#543C2×C3×C511yescharacteristic
126#451C2×C3×C512yescomplemented
127#393C2×C3×C511yescharacteristic
128#328C2×C3×C512yescomplemented
129#323C2×C3×C511yescharacteristic
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5—22no—
133C22×C3×C5—42no—
134C22×C3×C5—41no—
135C22×C3×C5—41no—
136C22×C3×C5—81no—
137C22×C3×C5#12011yescharacteristic
138C22×C3×C5C2×Q1611yescharacteristic
139C22×C3×C5#13711yescharacteristic
140C3×C4×C5—22no—
141C3×C4×C5—41no—
142C3×C4×C5—42no—
143C3×C4×C5—42no—
144C3×C4×C5—42no—
145C3×C4×C5—81no—
146C24×C3C5×D411yescharacteristic
147C2×C3×Q8—21no—
148C2×C3×Q8—22no—
149C2×C3×Q8—42no—
150C2×C3×Q8C5×D412yes—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4C5×D411yescharacteristic
156C22×C3×C4C23×C511yescharacteristic
157C3×Q16—44no—
158C2×C3×C8—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4C5×D412yes—
163C3×C22⋊C4—22no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—42no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5C3×Q1612yescomplemented
172C23×C5C2×C3×D411yescharacteristic
173C5×Q8—24no—
174C5×Q8—42no—
175C5×Q8—42no—
176C5×Q8—81no—
177C2×C4×C5—22no—
178C2×C4×C5—22no—
179C2×C4×C5—21no—
180C2×C4×C5—22no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—81no—
189C2×C4×C5—81no—
190C2×C4×C5C2×C3×D412yes—
191C5×C8—42no—
192C22×Q8C22×C3×C511yescharacteristic
193C2×Q16—22no—
194C22⋊Q8—22no—
195C22⋊Q8—21no—
196C22⋊Q8—22no—
197C22⋊Q8C22×C3×C512yes—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4C22×C3×C511yescharacteristic
201#103—22no—
202C22⋊C8C22×C3×C512yes—
203#95—21no—
204#95C22×C3×C511yescharacteristic
205C2×C3×C5—21no—
206C2×C3×C5—21no—
207C2×C3×C5—42no—
208C2×C3×C5#45111yescharacteristic
209C2×C3×C5#45511yescharacteristic
210C2×C3×C5B(4,𝔽2)11yescharacteristic
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3C5×Q1612yescomplemented
216C23×C3C2×C5×D411yescharacteristic
217C3×Q8—24no—
218C3×Q8—42no—
219C3×Q8—42no—
220C3×Q8—81no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—22no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—81no—
233C2×C3×C4—81no—
234C2×C3×C4C2×C5×D412yes—
235C3×C8—42no—
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—22no—
239C22×C5—42no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—81no—
243C22×C5C3×#12011yescharacteristic
244C22×C5C2×C3×Q1611yescharacteristic
245C22×C5C3×#13711yescharacteristic
246C4×C5—22no—
247C4×C5—41no—
248C4×C5—42no—
249C4×C5—42no—
250C4×C5—42no—
251C4×C5—81no—
252C24C3×C5×D411yescharacteristic
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—42no—
256C2×Q8C3×C5×D412yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C3×C5×D411yescharacteristic
262C22×C4C23×C3×C511yescharacteristic
263Q16—44no—
264C2×C8—22no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4C3×C5×D412yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—42no—
273C3×C5#160211yescharacteristic, direct product factor, Hall
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3—42no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—81no—
281C22×C3C5×#12011yescharacteristic
282C22×C3C2×C5×Q1611yescharacteristic
283C22×C3C5×#13711yescharacteristic
284C3×C4—22no—
285C3×C4—41no—
286C3×C4—42no—
287C3×C4—42no—
288C3×C4—42no—
289C3×C4—81no—
290C2×C5—21no—
291C2×C5—21no—
292C2×C5—42no—
293C2×C5C3×#45111yescharacteristic
294C2×C5C3×#45511yescharacteristic
295C2×C5C3×B(4,𝔽2)11yescharacteristic
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23C3×C5×Q1612yescomplemented
301C23C2×C3×C5×D411yescharacteristic
302Q8—24no—
303Q8—42no—
304Q8—42no—
305Q8—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C2×C3×C5×D412yes—
320C8—42no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—42no—
324C2×C3C5×#45111yescharacteristic
325C2×C3C5×#45511yescharacteristic
326C2×C3C5×B(4,𝔽2)11yescharacteristic
327C5C3×#160211yescharacteristic, direct product factor, Sylow
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22C3×C5×#12011yescharacteristic
336C22C2×C3×C5×Q1611yescharacteristic
337C22C3×C5×#13711yescharacteristic
338C4—22no—
339C4—41no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—81no—
344C3C5×#160211yescharacteristic, direct product factor, Sylow
345C2—21no—
346C2—21no—
347C2—42no—
348C2C3×C5×#45111yescharacteristic
349C2C3×C5×#45511yescharacteristic
350C2C3×C5×B(4,𝔽2)11yescharacteristic
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×#451C2semidirect
4. C3×C5×#328C2semidirect
6. C5×#1602C3direct (N × H)
20. C3×#1602C5direct (N × H)
22. C5×#451C2×C3semidirect
24. C5×#328C2×C3semidirect
48. C3×#451C2×C5semidirect
50. C3×#328C2×C5semidirect
65. #1602C3×C5direct (N × H)
70. C23×C3×C5Q16semidirect
126. #451C2×C3×C5semidirect
128. #328C2×C3×C5semidirect
171. C23×C5C3×Q16semidirect
215. C23×C3C5×Q16semidirect
273. C3×C5#1602direct (N × H)
300. C23C3×C5×Q16semidirect
327. C5C3×#1602direct (N × H)
344. C3C5×#1602direct (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×#4512
C3×C5×#3932
C3×C5×#3282
C3×C5×#3232
C5×#16023
C3×#16025