Finite Group Databasebeta

← C3×C5×#939 #13087943

Subgroups — C3×C5×#939 #13087943

Order 1440.

430 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×C5×#67C211yesmaximal, characteristic, complemented
3C2×C3×C5×#67C211yesmaximal, characteristic, complemented
4C22×C3×C5×Dic3C211yesmaximal, characteristic, complemented
5C3×C5×#217C211yesmaximal, characteristic, complemented
6C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C3×C5×#121—31nomaximal
9C5×#939C311yesmaximal, characteristic, direct product factor
10C23×C32×C5C2211yescharacteristic
11C23×C32×C5C2211yescharacteristic
12C22×C3×C5×D3C2211yescharacteristic
13C32×C5×D4—22no—
14C2×C32×C4×C5C2211yescharacteristic
15C3×C5×#67—22no—
16C3×C5×#67—22no—
17C2×C3×C5×Dic3—22no—
18C2×C3×C5×Dic3C2211yescharacteristic
19C2×C3×C5×Dic3C2211yescharacteristic
20C2×C3×C5×Dic3C2211yescharacteristic
21C3×#939C511yesmaximal, characteristic, direct product factor, Hall
22C2×C3×C5×D4—21no—
23C2×C3×C5×D4—31no—
24C2×C3×C5×D4—31no—
25C2×C3×C5×D4D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C311yescharacteristic, complemented
27C22×C3×C4×C5—31no—
28C2×C5×#67C2×C311yescharacteristic, complemented
29C2×C5×#67C2×C311yescharacteristic, complemented
30C22×C5×Dic3C2×C311yescharacteristic, complemented
31C3×C5×C4⋊C4—31no—
32C3×C5×C22⋊C4—31no—
33C3×C5×C22⋊C4—31no—
34C5×#217C2×C311yescharacteristic, complemented
35C5×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
36C5×Dic3⋊C4C2×C311yescharacteristic, complemented
37C22×C32×C5—21no—
38C22×C32×C5—21no—
39C22×C32×C5—21no—
40C22×C32×C5—21no—
41C22×C32×C5—21no—
42C22×C32×C5D412yescomplemented
43C22×C32×C5C2311yescharacteristic
44C2×C3×C5×D3—21no—
45C2×C3×C5×D3—21no—
46C2×C3×C5×D3—21no—
47C32×C4×C5—21no—
48C3×C5×Dic3—21no—
49C3×C5×Dic3—21no—
50C3×C5×Dic3D412yescomplemented
51C5×#121—31noHall
52C2×C32×D4C2×C511yescharacteristic, complemented
53C2×C3×#67C2×C511yescharacteristic, complemented
54C2×C3×#67C2×C511yescharacteristic, complemented
55C22×C3×Dic3C2×C511yescharacteristic, complemented
56C3×#217C2×C511yescharacteristic, complemented
57C3×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
58C3×Dic3⋊C4C2×C511yescharacteristic, complemented
59C23×C3×C5—21no—
60C23×C3×C5—21no—
61C23×C3×C5—31no—
62C23×C3×C5C2×D311yescharacteristic
63C23×C3×C5C2×D311yescharacteristic
64C23×C3×C5C22×C311yescharacteristic
65C23×C3×C5C22×C311yescharacteristic
66C22×C5×D3C22×C311yescharacteristic
67C3×C5×D4—24no—
68C3×C5×D4—22no—
69C3×C5×D4—22no—
70C3×C5×D4—62no—
71C3×C5×D4—62no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—31no—
74C2×C3×C4×C5—31no—
75C2×C3×C4×C5—31no—
76C2×C3×C4×C5—62no—
77C2×C3×C4×C5C2×D311yescharacteristic
78C2×C3×C4×C5C22×C311yescharacteristic
79C5×#67—22no—
80C5×#67—22no—
81C2×C5×Dic3—22no—
82C2×C5×Dic3C22×C311yescharacteristic
83C2×C5×Dic3C22×C311yescharacteristic
84C2×C5×Dic3C22×C311yescharacteristic
85C3×#121—31no—
86#939C3×C511yescharacteristic, direct product factor
87C2×C32×C5—22no—
88C2×C32×C5—41no—
89C2×C32×C5C2×D411yescharacteristic
90C2×C32×C5C2×D411yescharacteristic
91C2×C32×C5#4111yescharacteristic
92C3×C5×D3—41no—
93C2×C5×D4—31no—
94C2×C5×D4—31no—
95C2×C5×D4C3×D311yescharacteristic, complemented
96C22×C4×C5—31no—
97C5×C4⋊C4—31no—
98C5×C22⋊C4—31no—
99C5×C22⋊C4—31no—
100C23×C32C22×C511yescharacteristic
101C23×C32C22×C511yescharacteristic
102C22×C3×D3C22×C511yescharacteristic
103C32×D4—22no—
104C2×C32×C4C22×C511yescharacteristic
105C3×#67—22no—
106C3×#67—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3C22×C511yescharacteristic
109C2×C3×Dic3C22×C511yescharacteristic
110C2×C3×Dic3C22×C511yescharacteristic
111C22×C3×C5—21no—
112C22×C3×C5—21no—
113C22×C3×C5—21no—
114C22×C3×C5—21no—
115C22×C3×C5—22no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5—21no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5—22no—
123C22×C3×C5—21no—
124C22×C3×C5—41no—
125C22×C3×C5—41no—
126C22×C3×C5—41no—
127C22×C3×C5—41no—
128C22×C3×C5—61no—
129C22×C3×C5—61no—
130C22×C3×C5—61no—
131C22×C3×C5#6712yescomplemented
132C22×C3×C5C3×D412yescomplemented
133C22×C3×C5C22×D311yescharacteristic
134C22×C3×C5C23×C311yescharacteristic
135C2×C5×D3—21no—
136C2×C5×D3—21no—
137C2×C5×D3—21no—
138C3×C4×C5—22no—
139C3×C4×C5—21no—
140C3×C4×C5—21no—
141C3×C4×C5—32no—
142C3×C4×C5—61no—
143C3×C4×C5—61no—
144C5×Dic3—21no—
145C5×Dic3—21no—
146C5×Dic3C3×D412yescomplemented
147C2×C3×D4—21no—
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C2×C3×D4C5×D311yescharacteristic, complemented
151C2×C3×D4C2×C3×C511yescharacteristic, complemented
152C22×C3×C4—31no—
153C2×#67C2×C3×C511yescharacteristic, complemented
154C2×#67C2×C3×C511yescharacteristic, complemented
155C22×Dic3C2×C3×C511yescharacteristic, complemented
156C3×C4⋊C4—31no—
157C3×C22⋊C4—31no—
158C3×C22⋊C4—31no—
159#217C2×C3×C511yescharacteristic, complemented
160(C2×D3)⋊C4C2×C3×C511yescharacteristic, complemented
161Dic3⋊C4C2×C3×C511yescharacteristic, complemented
162C32×C5#12111yescharacteristic, complemented, Hall
163C23×C5—31no—
164C23×C5C2×C3×D311yescharacteristic
165C23×C5C2×C3×D311yescharacteristic
166C5×D4—22no—
167C5×D4—62no—
168C5×D4—62no—
169C2×C4×C5—31no—
170C2×C4×C5—31no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5C2×C3×D311yescharacteristic
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32C5×D412yescomplemented
180C22×C32C23×C511yescharacteristic
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3—21no—
184C32×C4—21no—
185C3×Dic3—21no—
186C3×Dic3—21no—
187C3×Dic3C5×D412yescomplemented
188#121—31noSylow
189C2×C3×C5—22no—
190C2×C3×C5—22no—
191C2×C3×C5—21no—
192C2×C3×C5—21no—
193C2×C3×C5—21no—
194C2×C3×C5—42no—
195C2×C3×C5—42no—
196C2×C3×C5—41no—
197C2×C3×C5—41no—
198C2×C3×C5—121no—
199C2×C3×C5D3×D411yescharacteristic
200C2×C3×C5#23711yescharacteristic
201C2×C3×C5C2×#6711yescharacteristic
202C2×C3×C5C2×C3×D411yescharacteristic
203C2×C3×C5C2×C3×D411yescharacteristic
204C2×C3×C5C3×#4111yescharacteristic
205C5×D3—41no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—31no—
209C23×C3C2×C5×D311yescharacteristic
210C23×C3C2×C5×D311yescharacteristic
211C23×C3C22×C3×C511yescharacteristic
212C23×C3C22×C3×C511yescharacteristic
213C22×D3C22×C3×C511yescharacteristic
214C3×D4—24no—
215C3×D4—22no—
216C3×D4—22no—
217C3×D4—62no—
218C3×D4—62no—
219C2×C3×C4—21no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—62no—
224C2×C3×C4C2×C5×D311yescharacteristic
225C2×C3×C4C22×C3×C511yescharacteristic
226#67—22no—
227#67—22no—
228C2×Dic3—22no—
229C2×Dic3C22×C3×C511yescharacteristic
230C2×Dic3C22×C3×C511yescharacteristic
231C2×Dic3C22×C3×C511yescharacteristic
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—61no—
238C22×C5—61no—
239C22×C5—61no—
240C22×C5C3×#6712yescomplemented
241C22×C5C22×C3×D311yescharacteristic
242C4×C5—21no—
243C4×C5—32no—
244C4×C5—61no—
245C4×C5—61no—
246C2×C32—22no—
247C2×C32—41no—
248C2×C32C2×C5×D411yescharacteristic
249C2×C32C2×C5×D411yescharacteristic
250C2×C32C5×#4111yescharacteristic
251C3×D3—41no—
252C2×D4—31no—
253C2×D4—31no—
254C2×D4C3×C5×D311yescharacteristic, complemented
255C22×C4—31no—
256C4⋊C4—31no—
257C22⋊C4—31no—
258C22⋊C4—31no—
259C3×C5—21no—
260C3×C5#93911yescharacteristic, direct product factor
261C3×C5C3×#12111yescharacteristic, complemented
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—61no—
280C22×C3—61no—
281C22×C3—61no—
282C22×C3C5×#6712yescomplemented
283C22×C3C3×C5×D412yescomplemented
284C22×C3C22×C5×D311yescharacteristic
285C22×C3C23×C3×C511yescharacteristic
286C2×D3—21no—
287C2×D3—21no—
288C2×D3—21no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—32no—
293C3×C4—61no—
294C3×C4—61no—
295Dic3—21no—
296Dic3—21no—
297Dic3C3×C5×D412yescomplemented
298C2×C5—22no—
299C2×C5—41no—
300C2×C5—121no—
301C2×C5C3×D3×D411yescharacteristic
302C2×C5C3×#23711yescharacteristic
303C2×C5C2×C3×#6711yescharacteristic
304C32C5×#12111yescharacteristic, complemented, Sylow
305C23—31no—
306C23C2×C3×C5×D311yescharacteristic
307C23C2×C3×C5×D311yescharacteristic
308D4—22no—
309D4—62no—
310D4—62no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—62no—
315C2×C4C2×C3×C5×D311yescharacteristic
316C2×C3—22no—
317C2×C3—22no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—42no—
322C2×C3—42no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—121no—
326C2×C3C5×D3×D411yescharacteristic
327C2×C3C5×#23711yescharacteristic
328C2×C3C2×C5×#6711yescharacteristic
329C2×C3C2×C3×C5×D411yescharacteristic
330C2×C3C2×C3×C5×D411yescharacteristic
331C2×C3C3×C5×#4111yescharacteristic
332D3—41no—
333C5C3×#93911yescharacteristic, direct product factor, Sylow
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—61no—
340C22—61no—
341C22—61no—
342C22C3×C5×#6712yescomplemented
343C22C22×C3×C5×D311yescharacteristic
344C4—21no—
345C4—32no—
346C4—61no—
347C4—61no—
348C3—21no—
349C3C5×#93911yescharacteristic, direct product factor
350C3C3×C5×#12111yescharacteristic, complemented
351C2—22no—
352C2—41no—
353C2—121no—
354C2C3×C5×D3×D411yescharacteristic
355C2C3×C5×#23711yescharacteristic
356C2C2×C3×C5×#6711yescharacteristic
subgroupG/H
centerC22×C3×C5C22×D3
commutator, cosocleC22×C3C23×C3×C5
FrattiniC22C22×C3×C5×D3
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C3×C5×D4D3
hypocenterC3C3×C5×#121
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C2×C3×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×C3×C5×#67C2semidirect
3. C2×C3×C5×#67C2semidirect
4. C22×C3×C5×Dic3C2semidirect
5. C3×C5×#217C2semidirect
6. C3×C5×(C2×D3)⋊C4C2semidirect
7. C3×C5×Dic3⋊C4C2semidirect
9. C5×#939C3direct (N × H)
21. C3×#939C5direct (N × H)
25. C2×C3×C5×D4D3semidirect
26. C2×C3×C5×D4C2×C3semidirect
28. C2×C5×#67C2×C3semidirect
29. C2×C5×#67C2×C3semidirect
30. C22×C5×Dic3C2×C3semidirect
34. C5×#217C2×C3semidirect
35. C5×(C2×D3)⋊C4C2×C3semidirect
36. C5×Dic3⋊C4C2×C3semidirect
42. C22×C32×C5D4semidirect
50. C3×C5×Dic3D4semidirect
52. C2×C32×D4C2×C5semidirect
53. C2×C3×#67C2×C5semidirect
54. C2×C3×#67C2×C5semidirect
55. C22×C3×Dic3C2×C5semidirect
56. C3×#217C2×C5semidirect
57. C3×(C2×D3)⋊C4C2×C5semidirect
58. C3×Dic3⋊C4C2×C5semidirect
86. #939C3×C5direct (N × H)
95. C2×C5×D4C3×D3semidirect
131. C22×C3×C5#67semidirect
132. C22×C3×C5C3×D4semidirect
146. C5×Dic3C3×D4semidirect
150. C2×C3×D4C5×D3semidirect
151. C2×C3×D4C2×C3×C5semidirect
153. C2×#67C2×C3×C5semidirect
154. C2×#67C2×C3×C5semidirect
155. C22×Dic3C2×C3×C5semidirect
159. #217C2×C3×C5semidirect
160. (C2×D3)⋊C4C2×C3×C5semidirect
161. Dic3⋊C4C2×C3×C5semidirect
162. C32×C5#121semidirect
179. C22×C32C5×D4semidirect
187. C3×Dic3C5×D4semidirect
240. C22×C5C3×#67semidirect
254. C2×D4C3×C5×D3semidirect
260. C3×C5#939direct (N × H)
261. C3×C5C3×#121semidirect
282. C22×C3C5×#67semidirect
283. C22×C3C3×C5×D4semidirect
297. Dic3C3×C5×D4semidirect
304. C32C5×#121semidirect
333. C5C3×#939direct (N × H)
342. C22C3×C5×#67semidirect
349. C3C5×#939direct (N × H)
350. C3C3×C5×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×C3×C5×#672
C22×C3×C5×Dic32
C3×C5×#2172
C3×C5×(C2×D3)⋊C42
C3×C5×Dic3⋊C42
C3×C5×#1213
C5×#9393
C3×#9395