Finite Group Databasebeta

← C3×C5×#1482 #14274516

Subgroups — C3×C5×#1482 #14274516

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#529C211yesmaximal, characteristic
2C3×C5×#431C211yesmaximal, characteristic, complemented
3C3×C5×#431C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C212yesmaximal, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1482C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#126—21no—
8C3×C5×#125C411yescharacteristic
9C3×C5×#124C411yescharacteristic
10C3×C5×#123—21no—
11C3×C5×C22⋊Q8C411yescharacteristic
12C3×C5×#121C411yescharacteristic
13C3×C4×C5×Q8C2211yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C2×C3×C42×C5C2211yescharacteristic
18C3×C5×C4⋊C8—21no—
19C3×C5×C4⋊C8C2212yes—
20C3×C5×C22⋊C8—21no—
21C3×C5×C22⋊C8—21no—
22C3×C4×C5×C8—21no—
23C3×C4×C5×C8C2212yes—
24C3×#1482C511yesmaximal, characteristic, direct product factor, Hall
25C5×#529C2×C311yescharacteristic
26C5×#431C2×C311yescharacteristic, complemented
27C5×#431C2×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—22no—
38C2×C3×C5×C8—22no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C5×C22⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5—21no—
51C3×C42×C5C2×C411yescharacteristic
52C3×C42×C5D411yescharacteristic
53C3×C42×C5D411yescharacteristic
54C3×C42×C5C2311yescharacteristic
55C3×#529C2×C511yescharacteristic
56C3×#431C2×C511yescharacteristic, complemented
57C3×#431C2×C511yescharacteristic, complemented
58C3×Q8⋊C8C2×C512yescomplemented
59C3×D4⋊C8C2×C512yescomplemented
60C5×#126—21no—
61C5×#125C3×C411yescharacteristic
62C5×#124C3×C411yescharacteristic
63C5×#123—21no—
64C5×C22⋊Q8C3×C411yescharacteristic
65C5×#121C3×C411yescharacteristic
66C4×C5×Q8C22×C311yescharacteristic
67C4×C5×D4—21no—
68C4×C5×D4C22×C311yescharacteristic
69C5×#117—21no—
70C2×C42×C5C22×C311yescharacteristic
71C5×C4⋊C8—21no—
72C5×C4⋊C8C22×C312yes—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C4×C5×C8—21no—
76C4×C5×C8C22×C312yes—
77#1482C3×C511yescharacteristic, direct product factor, Sylow
78C23×C3×C5—21no—
79C23×C3×C5C22⋊C411yescharacteristic
80C3×C5×Q8—22no—
81C3×C5×D4—22no—
82C3×C5×D4—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C3×C5×C8—42no—
97C3×C5×C8—42no—
98C3×#126—21no—
99C3×#125C4×C511yescharacteristic
100C3×#124C4×C511yescharacteristic
101C3×#123—21no—
102C3×C22⋊Q8C4×C511yescharacteristic
103C3×#121C4×C511yescharacteristic
104C3×C4×Q8C22×C511yescharacteristic
105C3×C4×D4—21no—
106C3×C4×D4C22×C511yescharacteristic
107C3×#117—21no—
108C2×C3×C42C22×C511yescharacteristic
109C3×C4⋊C8—21no—
110C3×C4⋊C8C22×C512yes—
111C3×C22⋊C8—21no—
112C3×C22⋊C8—21no—
113C3×C4×C8—21no—
114C3×C4×C8C22×C512yes—
115C2×C5×Q8C2×C3×C411yescharacteristic
116C2×C5×D4—21no—
117C2×C5×D4C2×C3×C411yescharacteristic
118C22×C4×C5—21no—
119C22×C4×C5C2×C3×C411yescharacteristic
120C22×C4×C5C3×D411yescharacteristic
121C22×C4×C5C3×D411yescharacteristic
122C2×C5×C8—22no—
123C2×C5×C8—22no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C2×C3×C411yescharacteristic
129C5×C4⋊C4C2×C3×C411yescharacteristic
130C5×C22⋊C4—21no—
131C5×C22⋊C4—21no—
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C42×C5—21no—
136C42×C5C2×C3×C411yescharacteristic
137C42×C5C3×D411yescharacteristic
138C42×C5C3×D411yescharacteristic
139C42×C5C23×C311yescharacteristic
140#529C2×C3×C511yescharacteristic
141#431C2×C3×C511yescharacteristic, complemented
142#431C2×C3×C511yescharacteristic, complemented
143Q8⋊C8C2×C3×C512yescomplemented
144D4⋊C8C2×C3×C512yescomplemented
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13112yes—
160C3×C4×C5#13512yes—
161C2×C3×Q8C2×C4×C511yescharacteristic
162C2×C3×D4—21no—
163C2×C3×D4C2×C4×C511yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4C2×C4×C511yescharacteristic
166C22×C3×C4C5×D411yescharacteristic
167C22×C3×C4C5×D411yescharacteristic
168C2×C3×C8—22no—
169C2×C3×C8—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C2×C4×C511yescharacteristic
175C3×C4⋊C4C2×C4×C511yescharacteristic
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C42—21no—
182C3×C42C2×C4×C511yescharacteristic
183C3×C42C5×D411yescharacteristic
184C3×C42C5×D411yescharacteristic
185C3×C42C23×C511yescharacteristic
186C23×C5—21no—
187C23×C5C3×C22⋊C411yescharacteristic
188C5×Q8—22no—
189C5×D4—22no—
190C5×D4—42no—
191C2×C4×C5—22no—
192C2×C4×C5—22no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5C3×C22⋊C411yescharacteristic
199C2×C4×C5C3×C22⋊C411yescharacteristic
200C2×C4×C5C3×C22⋊C411yescharacteristic
201C2×C4×C5C22×C3×C411yescharacteristic
202C2×C4×C5C2×C3×D411yescharacteristic
203C2×C4×C5C2×C3×D411yescharacteristic
204C5×C8—42no—
205C5×C8—42no—
206#126—21no—
207#125C3×C4×C511yescharacteristic
208#124C3×C4×C511yescharacteristic
209#123—21no—
210C22⋊Q8C3×C4×C511yescharacteristic
211#121C3×C4×C511yescharacteristic
212C4×Q8C22×C3×C511yescharacteristic
213C4×D4—21no—
214C4×D4C22×C3×C511yescharacteristic
215#117—21no—
216C2×C42C22×C3×C511yescharacteristic
217C4⋊C8—21no—
218C4⋊C8C22×C3×C512yes—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C4×C8—21no—
222C4×C8C22×C3×C512yes—
223C2×C3×C5—41no—
224C2×C3×C5—81no—
225C2×C3×C5#40811yescharacteristic
226C2×C3×C5#41611yescharacteristic
227C2×C3×C5#42111yescharacteristic
228C23×C3—21no—
229C23×C3C5×C22⋊C411yescharacteristic
230C3×Q8—22no—
231C3×D4—22no—
232C3×D4—42no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—42no—
240C2×C3×C4C5×C22⋊C411yescharacteristic
241C2×C3×C4C5×C22⋊C411yescharacteristic
242C2×C3×C4C5×C22⋊C411yescharacteristic
243C2×C3×C4C22×C4×C511yescharacteristic
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246C3×C8—42no—
247C3×C8—42no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5C2×C3×C22⋊C411yescharacteristic
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—41no—
260C4×C5—41no—
261C4×C5—41no—
262C4×C5C3×#13112yes—
263C4×C5C3×#13512yes—
264C2×Q8C2×C3×C4×C511yescharacteristic
265C2×D4—21no—
266C2×D4C2×C3×C4×C511yescharacteristic
267C22×C4—21no—
268C22×C4C2×C3×C4×C511yescharacteristic
269C22×C4C3×C5×D411yescharacteristic
270C22×C4C3×C5×D411yescharacteristic
271C2×C8—22no—
272C2×C8—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4C2×C3×C4×C511yescharacteristic
278C4⋊C4C2×C3×C4×C511yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42C2×C3×C4×C511yescharacteristic
286C42C3×C5×D411yescharacteristic
287C42C3×C5×D411yescharacteristic
288C42C23×C3×C511yescharacteristic
289C3×C5#148211yescharacteristic, direct product factor, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3C2×C5×C22⋊C411yescharacteristic
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4C5×#13112yes—
305C3×C4C5×#13512yes—
306C2×C5—41no—
307C2×C5—81no—
308C2×C5C3×#40811yescharacteristic
309C2×C5C3×#41611yescharacteristic
310C2×C5C3×#42111yescharacteristic
311C23—21no—
312C23C3×C5×C22⋊C411yescharacteristic
313Q8—22no—
314D4—22no—
315D4—42no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4C3×C5×C22⋊C411yescharacteristic
324C2×C4C3×C5×C22⋊C411yescharacteristic
325C2×C4C3×C5×C22⋊C411yescharacteristic
326C2×C4C22×C3×C4×C511yescharacteristic
327C2×C4C2×C3×C5×D411yescharacteristic
328C2×C4C2×C3×C5×D411yescharacteristic
329C8—42no—
330C8—42no—
331C2×C3—41no—
332C2×C3—81no—
333C2×C3C5×#40811yescharacteristic
334C2×C3C5×#41611yescharacteristic
335C2×C3C5×#42111yescharacteristic
336C5C3×#148211yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22C2×C3×C5×C22⋊C411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4C3×C5×#13112yes—
352C4C3×C5×#13512yes—
353C3C5×#148211yescharacteristic, direct product factor, Sylow
354C2—41no—
355C2—81no—
356C2C3×C5×#40811yescharacteristic
357C2C3×C5×#41611yescharacteristic
358C2C3×C5×#42111yescharacteristic
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×#431C2semidirect
3. C3×C5×#431C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1482C3direct (N × H)
24. C3×#1482C5direct (N × H)
26. C5×#431C2×C3semidirect
27. C5×#431C2×C3semidirect
28. C5×Q8⋊C8C2×C3semidirect
29. C5×D4⋊C8C2×C3semidirect
56. C3×#431C2×C5semidirect
57. C3×#431C2×C5semidirect
58. C3×Q8⋊C8C2×C5semidirect
59. C3×D4⋊C8C2×C5semidirect
77. #1482C3×C5direct (N × H)
141. #431C2×C3×C5semidirect
142. #431C2×C3×C5semidirect
143. Q8⋊C8C2×C3×C5semidirect
144. D4⋊C8C2×C3×C5semidirect
289. C3×C5#1482direct (N × H)
336. C5C3×#1482direct (N × H)
353. C3C5×#1482direct (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×#4312
C3×C5×Q8⋊C82
C3×C5×D4⋊C82
C5×#14823
C3×#14825