Finite Group Databasebeta

← C3×C5×#1495 #14274529

Subgroups — C3×C5×#1495 #14274529

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 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×#423C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C212yesmaximal, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1495C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×M16—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⋊C8—21no—
20C3×C5×C4⋊C8—21no—
21C3×C5×C4⋊C8C2212yes—
22C3×C5×C22⋊C8—21no—
23C3×C4×C5×C8C2212yes—
24C3×#1495C511yesmaximal, characteristic, direct product factor, Hall
25C5×#529C2×C311yescharacteristic
26C5×#431C2×C311yescharacteristic, complemented
27C5×#423C2×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
37C3×C5×M16—42no—
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×#431C2×C511yescharacteristic, complemented
58C3×#423C2×C511yescharacteristic, complemented
59C3×Q8⋊C8C2×C512yescomplemented
60C3×D4⋊C8C2×C512yescomplemented
61C2×C5×M16—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⋊C8—21no—
74C5×C4⋊C8—21no—
75C5×C4⋊C8C22×C312yes—
76C5×C22⋊C8—21no—
77C4×C5×C8C22×C312yes—
78#1495C3×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—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C3×C5×C8—42no—
100C3×C5×C8—42no—
101C2×C3×M16—21no—
102C3×#126—21no—
103C3×#125C4×C511yescharacteristic
104C3×#124C4×C511yescharacteristic
105C3×#123—21no—
106C3×C22⋊Q8C4×C511yescharacteristic
107C3×#121C4×C511yescharacteristic
108C3×C4×Q8C22×C511yescharacteristic
109C3×C4×D4—21no—
110C3×C4×D4C22×C511yescharacteristic
111C3×#117—21no—
112C2×C3×C42C22×C511yescharacteristic
113C3×C4⋊C8—21no—
114C3×C4⋊C8—21no—
115C3×C4⋊C8C22×C512yes—
116C3×C22⋊C8—21no—
117C3×C4×C8C22×C512yes—
118C2×C5×Q8C2×C3×C411yescharacteristic
119C2×C5×D4—21no—
120C2×C5×D4C2×C3×C411yescharacteristic
121C22×C4×C5—21no—
122C22×C4×C5C2×C3×C411yescharacteristic
123C22×C4×C5C3×D411yescharacteristic
124C22×C4×C5C3×D411yescharacteristic
125C5×M16—42no—
126C2×C5×C8—22no—
127C2×C5×C8—22no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C2×C3×C411yescharacteristic
133C5×C4⋊C4C2×C3×C411yescharacteristic
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—21no—
137C5×C22⋊C4—21no—
138C5×C22⋊C4—21no—
139C42×C5—21no—
140C42×C5C2×C3×C411yescharacteristic
141C42×C5C3×D411yescharacteristic
142C42×C5C3×D411yescharacteristic
143C42×C5C23×C311yescharacteristic
144#529C2×C3×C511yescharacteristic
145#431C2×C3×C511yescharacteristic, complemented
146#423C2×C3×C511yescharacteristic, complemented
147Q8⋊C8C2×C3×C512yescomplemented
148D4⋊C8C2×C3×C512yescomplemented
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×C4×C5#13112yes—
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C2×C3×Q8C2×C4×C511yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4C2×C4×C511yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4C2×C4×C511yescharacteristic
171C22×C3×C4C5×D411yescharacteristic
172C22×C3×C4C5×D411yescharacteristic
173C3×M16—42no—
174C2×C3×C8—22no—
175C2×C3×C8—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C2×C4×C511yescharacteristic
181C3×C4⋊C4C2×C4×C511yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C42—21no—
188C3×C42C2×C4×C511yescharacteristic
189C3×C42C5×D411yescharacteristic
190C3×C42C5×D411yescharacteristic
191C3×C42C23×C511yescharacteristic
192C23×C5—21no—
193C23×C5C3×C22⋊C411yescharacteristic
194C5×Q8—22no—
195C5×D4—22no—
196C5×D4—42no—
197C2×C4×C5—22no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5C3×C22⋊C411yescharacteristic
207C2×C4×C5C3×C22⋊C411yescharacteristic
208C2×C4×C5C3×C22⋊C411yescharacteristic
209C2×C4×C5C22×C3×C411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C5×C8—42no—
213C5×C8—42no—
214C2×M16—21no—
215#126—21no—
216#125C3×C4×C511yescharacteristic
217#124C3×C4×C511yescharacteristic
218#123—21no—
219C22⋊Q8C3×C4×C511yescharacteristic
220#121C3×C4×C511yescharacteristic
221C4×Q8C22×C3×C511yescharacteristic
222C4×D4—21no—
223C4×D4C22×C3×C511yescharacteristic
224#117—21no—
225C2×C42C22×C3×C511yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8C22×C3×C512yes—
229C22⋊C8—21no—
230C4×C8C22×C3×C512yes—
231C2×C3×C5—41no—
232C2×C3×C5—81no—
233C2×C3×C5#40811yescharacteristic
234C2×C3×C5#41711yescharacteristic
235C2×C3×C5#42111yescharacteristic
236C23×C3—21no—
237C23×C3C5×C22⋊C411yescharacteristic
238C3×Q8—22no—
239C3×D4—22no—
240C3×D4—42no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4C5×C22⋊C411yescharacteristic
251C2×C3×C4C5×C22⋊C411yescharacteristic
252C2×C3×C4C5×C22⋊C411yescharacteristic
253C2×C3×C4C22×C4×C511yescharacteristic
254C2×C3×C4C2×C5×D411yescharacteristic
255C2×C3×C4C2×C5×D411yescharacteristic
256C3×C8—42no—
257C3×C8—42no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C2×C3×C22⋊C411yescharacteristic
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5C3×#13112yes—
273C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
274C4×C5C3×#13711yescharacteristic
275C2×Q8C2×C3×C4×C511yescharacteristic
276C2×D4—21no—
277C2×D4C2×C3×C4×C511yescharacteristic
278C22×C4—21no—
279C22×C4C2×C3×C4×C511yescharacteristic
280C22×C4C3×C5×D411yescharacteristic
281C22×C4C3×C5×D411yescharacteristic
282M16—42no—
283C2×C8—22no—
284C2×C8—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4C2×C3×C4×C511yescharacteristic
290C4⋊C4C2×C3×C4×C511yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C42—21no—
297C42C2×C3×C4×C511yescharacteristic
298C42C3×C5×D411yescharacteristic
299C42C3×C5×D411yescharacteristic
300C42C23×C3×C511yescharacteristic
301C3×C5#149511yescharacteristic, direct product factor, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3C2×C5×C22⋊C411yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4C5×#13112yes—
317C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
318C3×C4C5×#13711yescharacteristic
319C2×C5—41no—
320C2×C5—81no—
321C2×C5C3×#40811yescharacteristic
322C2×C5C3×#41711yescharacteristic
323C2×C5C3×#42111yescharacteristic
324C23—21no—
325C23C3×C5×C22⋊C411yescharacteristic
326Q8—22no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C3×C5×C22⋊C411yescharacteristic
339C2×C4C3×C5×C22⋊C411yescharacteristic
340C2×C4C3×C5×C22⋊C411yescharacteristic
341C2×C4C22×C3×C4×C511yescharacteristic
342C2×C4C2×C3×C5×D411yescharacteristic
343C2×C4C2×C3×C5×D411yescharacteristic
344C8—42no—
345C8—42no—
346C2×C3—41no—
347C2×C3—81no—
348C2×C3C5×#40811yescharacteristic
349C2×C3C5×#41711yescharacteristic
350C2×C3C5×#42111yescharacteristic
351C5C3×#149511yescharacteristic, direct product factor, Sylow
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×C3×C5×C22⋊C411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C3×C5×#13112yes—
367C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
368C4C3×C5×#13711yescharacteristic
369C3C5×#149511yescharacteristic, direct product factor, Sylow
370C2—41no—
371C2—81no—
372C2C3×C5×#40811yescharacteristic
373C2C3×C5×#41711yescharacteristic
374C2C3×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×#423C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1495C3direct (N × H)
24. C3×#1495C5direct (N × H)
26. C5×#431C2×C3semidirect
27. C5×#423C2×C3semidirect
28. C5×Q8⋊C8C2×C3semidirect
29. C5×D4⋊C8C2×C3semidirect
57. C3×#431C2×C5semidirect
58. C3×#423C2×C5semidirect
59. C3×Q8⋊C8C2×C5semidirect
60. C3×D4⋊C8C2×C5semidirect
78. #1495C3×C5direct (N × H)
145. #431C2×C3×C5semidirect
146. #423C2×C3×C5semidirect
147. Q8⋊C8C2×C3×C5semidirect
148. D4⋊C8C2×C3×C5semidirect
301. C3×C5#1495direct (N × H)
351. C5C3×#1495direct (N × H)
369. C3C5×#1495direct (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×#4232
C3×C5×Q8⋊C82
C3×C5×D4⋊C82
C5×#14953
C3×#14955