Finite Group Databasebeta

← C3×C5×#1494 #14274528

Subgroups — C3×C5×#1494 #14274528

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#529C211yesmaximal, characteristic
2C3×C5×#432C211yesmaximal, characteristic, complemented
3C2×C3×C4×C5×C8C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C212yesmaximal, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1494C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C8—21no—
8C3×C5×#126—21no—
9C3×C5×#125C411yescharacteristic
10C3×C5×#124C411yescharacteristic
11C3×C5×#123—21no—
12C3×C5×C22⋊Q8C411yescharacteristic
13C3×C5×#121C411yescharacteristic
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C3×C5×#117—21no—
18C2×C3×C42×C5C2211yescharacteristic
19C3×C5×C4⋊C8C2212yes—
20C3×C5×C22⋊C8—21no—
21C3×C5×#97—21no—
22C3×C4×C5×C8—21no—
23C3×C4×C5×C8C2212yes—
24C3×#1494C511yesmaximal, characteristic, direct product factor, Hall
25C5×#529C2×C311yescharacteristic
26C5×#432C2×C311yescharacteristic, complemented
27C2×C4×C5×C8C2×C311yescharacteristic, complemented
28C5×Q8⋊C8C2×C312yescomplemented
29C5×D4⋊C8C2×C312yescomplemented
30C2×C3×C5×Q8C2×C411yescharacteristic
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C2×C3×C5×C8—24no—
38C2×C3×C5×C8—22no—
39C2×C3×C5×C8—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C5×C22⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2×C411yescharacteristic
53C3×C42×C5D411yescharacteristic
54C3×C42×C5D411yescharacteristic
55C3×C42×C5C2311yescharacteristic
56C3×#529C2×C511yescharacteristic
57C3×#432C2×C511yescharacteristic, complemented
58C2×C3×C4×C8C2×C511yescharacteristic, complemented
59C3×Q8⋊C8C2×C512yescomplemented
60C3×D4⋊C8C2×C512yescomplemented
61C22×C5×C8—21no—
62C5×#126—21no—
63C5×#125C3×C411yescharacteristic
64C5×#124C3×C411yescharacteristic
65C5×#123—21no—
66C5×C22⋊Q8C3×C411yescharacteristic
67C5×#121C3×C411yescharacteristic
68C4×C5×Q8C22×C311yescharacteristic
69C4×C5×D4—21no—
70C4×C5×D4C22×C311yescharacteristic
71C5×#117—21no—
72C2×C42×C5C22×C311yescharacteristic
73C5×C4⋊C8C22×C312yes—
74C5×C22⋊C8—21no—
75C5×#97—21no—
76C4×C5×C8—21no—
77C4×C5×C8C22×C312yes—
78#1494C3×C511yescharacteristic, direct product factor, Sylow
79C23×C3×C5—21no—
80C23×C3×C5C22⋊C411yescharacteristic
81C3×C5×Q8—22no—
82C3×C5×D4—22no—
83C3×C5×D4—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C3×C5×C8—24no—
98C3×C5×C8—42no—
99C22×C3×C8—21no—
100C3×#126—21no—
101C3×#125C4×C511yescharacteristic
102C3×#124C4×C511yescharacteristic
103C3×#123—21no—
104C3×C22⋊Q8C4×C511yescharacteristic
105C3×#121C4×C511yescharacteristic
106C3×C4×Q8C22×C511yescharacteristic
107C3×C4×D4—21no—
108C3×C4×D4C22×C511yescharacteristic
109C3×#117—21no—
110C2×C3×C42C22×C511yescharacteristic
111C3×C4⋊C8C22×C512yes—
112C3×C22⋊C8—21no—
113C3×#97—21no—
114C3×C4×C8—21no—
115C3×C4×C8C22×C512yes—
116C2×C5×Q8C2×C3×C411yescharacteristic
117C2×C5×D4—21no—
118C2×C5×D4C2×C3×C411yescharacteristic
119C22×C4×C5—21no—
120C22×C4×C5C2×C3×C411yescharacteristic
121C22×C4×C5C3×D411yescharacteristic
122C22×C4×C5C3×D411yescharacteristic
123C2×C5×C8—24no—
124C2×C5×C8—22no—
125C2×C5×C8—22no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4C2×C3×C411yescharacteristic
131C5×C4⋊C4C2×C3×C411yescharacteristic
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—21no—
137C42×C5—21no—
138C42×C5C2×C3×C411yescharacteristic
139C42×C5C3×D411yescharacteristic
140C42×C5C3×D411yescharacteristic
141C42×C5C23×C311yescharacteristic
142#529C2×C3×C511yescharacteristic
143#432C2×C3×C511yescharacteristic, complemented
144C2×C4×C8C2×C3×C511yescharacteristic, complemented
145Q8⋊C8C2×C3×C512yescomplemented
146D4⋊C8C2×C3×C512yescomplemented
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5#10412yes—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5—41no—
161C3×C4×C5#13112yes—
162C3×C4×C5#13512yes—
163C2×C3×Q8C2×C4×C511yescharacteristic
164C2×C3×D4—21no—
165C2×C3×D4C2×C4×C511yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4C2×C4×C511yescharacteristic
168C22×C3×C4C5×D411yescharacteristic
169C22×C3×C4C5×D411yescharacteristic
170C2×C3×C8—24no—
171C2×C3×C8—22no—
172C2×C3×C8—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C2×C4×C511yescharacteristic
178C3×C4⋊C4C2×C4×C511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C42—21no—
185C3×C42C2×C4×C511yescharacteristic
186C3×C42C5×D411yescharacteristic
187C3×C42C5×D411yescharacteristic
188C3×C42C23×C511yescharacteristic
189C23×C5—21no—
190C23×C5C3×C22⋊C411yescharacteristic
191C5×Q8—22no—
192C5×D4—22no—
193C5×D4—42no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—22no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—42no—
201C2×C4×C5C3×C22⋊C411yescharacteristic
202C2×C4×C5C3×C22⋊C411yescharacteristic
203C2×C4×C5C3×C22⋊C411yescharacteristic
204C2×C4×C5C22×C3×C411yescharacteristic
205C2×C4×C5C2×C3×D411yescharacteristic
206C2×C4×C5C2×C3×D411yescharacteristic
207C5×C8—24no—
208C5×C8—42no—
209C22×C8—21no—
210#126—21no—
211#125C3×C4×C511yescharacteristic
212#124C3×C4×C511yescharacteristic
213#123—21no—
214C22⋊Q8C3×C4×C511yescharacteristic
215#121C3×C4×C511yescharacteristic
216C4×Q8C22×C3×C511yescharacteristic
217C4×D4—21no—
218C4×D4C22×C3×C511yescharacteristic
219#117—21no—
220C2×C42C22×C3×C511yescharacteristic
221C4⋊C8C22×C3×C512yes—
222C22⋊C8—21no—
223#97—21no—
224C4×C8—21no—
225C4×C8C22×C3×C512yes—
226C2×C3×C5—22no—
227C2×C3×C5—81no—
228C2×C3×C5#40811yescharacteristic
229C2×C3×C5#41611yescharacteristic
230C2×C3×C5C2×#10411yescharacteristic
231C23×C3—21no—
232C23×C3C5×C22⋊C411yescharacteristic
233C3×Q8—22no—
234C3×D4—22no—
235C3×D4—42no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—42no—
243C2×C3×C4C5×C22⋊C411yescharacteristic
244C2×C3×C4C5×C22⋊C411yescharacteristic
245C2×C3×C4C5×C22⋊C411yescharacteristic
246C2×C3×C4C22×C4×C511yescharacteristic
247C2×C3×C4C2×C5×D411yescharacteristic
248C2×C3×C4C2×C5×D411yescharacteristic
249C3×C8—24no—
250C3×C8—42no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5C3×#10412yes—
257C22×C5C2×C3×C22⋊C411yescharacteristic
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5—41no—
263C4×C5—41no—
264C4×C5—41no—
265C4×C5C3×#13112yes—
266C4×C5C3×#13512yes—
267C2×Q8C2×C3×C4×C511yescharacteristic
268C2×D4—21no—
269C2×D4C2×C3×C4×C511yescharacteristic
270C22×C4—21no—
271C22×C4C2×C3×C4×C511yescharacteristic
272C22×C4C3×C5×D411yescharacteristic
273C22×C4C3×C5×D411yescharacteristic
274C2×C8—24no—
275C2×C8—22no—
276C2×C8—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C2×C3×C4×C511yescharacteristic
282C4⋊C4C2×C3×C4×C511yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C42—21no—
289C42C2×C3×C4×C511yescharacteristic
290C42C3×C5×D411yescharacteristic
291C42C3×C5×D411yescharacteristic
292C42C23×C3×C511yescharacteristic
293C3×C5#149411yescharacteristic, direct product factor, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3C5×#10412yes—
300C22×C3C2×C5×C22⋊C411yescharacteristic
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4C5×#13112yes—
309C3×C4C5×#13512yes—
310C2×C5—22no—
311C2×C5—81no—
312C2×C5C3×#40811yescharacteristic
313C2×C5C3×#41611yescharacteristic
314C2×C5C2×C3×#10411yescharacteristic
315C23—21no—
316C23C3×C5×C22⋊C411yescharacteristic
317Q8—22no—
318D4—22no—
319D4—42no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4C3×C5×C22⋊C411yescharacteristic
328C2×C4C3×C5×C22⋊C411yescharacteristic
329C2×C4C3×C5×C22⋊C411yescharacteristic
330C2×C4C22×C3×C4×C511yescharacteristic
331C2×C4C2×C3×C5×D411yescharacteristic
332C2×C4C2×C3×C5×D411yescharacteristic
333C8—24no—
334C8—42no—
335C2×C3—22no—
336C2×C3—81no—
337C2×C3C5×#40811yescharacteristic
338C2×C3C5×#41611yescharacteristic
339C2×C3C2×C5×#10411yescharacteristic
340C5C3×#149411yescharacteristic, direct product factor, Sylow
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C3×C5×#10412yes—
347C22C2×C3×C5×C22⋊C411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4C3×C5×#13112yes—
356C4C3×C5×#13512yes—
357C3C5×#149411yescharacteristic, direct product factor, Sylow
358C2—22no—
359C2—81no—
360C2C3×C5×#40811yescharacteristic
361C2C3×C5×#41611yescharacteristic
362C2C2×C3×C5×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC42C23×C3×C5
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×C5×#121C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#432C2semidirect
3. C2×C3×C4×C5×C8C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1494C3direct (N × H)
24. C3×#1494C5direct (N × H)
26. C5×#432C2×C3semidirect
27. C2×C4×C5×C8C2×C3semidirect
28. C5×Q8⋊C8C2×C3semidirect
29. C5×D4⋊C8C2×C3semidirect
57. C3×#432C2×C5semidirect
58. C2×C3×C4×C8C2×C5semidirect
59. C3×Q8⋊C8C2×C5semidirect
60. C3×D4⋊C8C2×C5semidirect
78. #1494C3×C5direct (N × H)
143. #432C2×C3×C5semidirect
144. C2×C4×C8C2×C3×C5semidirect
145. Q8⋊C8C2×C3×C5semidirect
146. D4⋊C8C2×C3×C5semidirect
293. C3×C5#1494direct (N × H)
340. C5C3×#1494direct (N × H)
357. C3C5×#1494direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5292
C3×C5×#4322
C2×C3×C4×C5×C82
C3×C5×Q8⋊C82
C3×C5×D4⋊C82
C5×#14943
C3×#14945