Finite Group Databasebeta

← C3×#66030 #11755707

Subgroups — C3×#66030 #11755707

Order 960.

384 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#125C211yesmaximal, characteristic, complemented
2C3×#4044C211yesmaximal, characteristic
3C3×#4044C211yesmaximal, characteristic
4C3×#4044C211yesmaximal, characteristic
5C3×#4042C211yesmaximal, characteristic
6C3×#4042C211yesmaximal, characteristic
7C3×#4038C211yesmaximal, characteristic
8C3×#4036C211yesmaximal, characteristic, complemented
9C3×#4035C211yesmaximal, characteristic, complemented
10C3×#4035C211yesmaximal, characteristic, complemented
11C3×#4035C211yesmaximal, characteristic, complemented
12C3×#4034C211yesmaximal, characteristic, complemented
13C3×#4033C211yesmaximal, characteristic, complemented
14C3×#4022C211yesmaximal, characteristic
15C3×C4×Dic10C211yesmaximal, characteristic, complemented
16#66030C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C4×D5C2211yescharacteristic
18C2×C3×Dic10C2211yescharacteristic
19C2×C3×Dic10C2211yescharacteristic
20C3×C5×C4⋊C4C2211yescharacteristic
21C3×C5×C4⋊C4C2211yescharacteristic
22C3×C5×C4⋊C4C2211yescharacteristic
23C3×C5×C4⋊C4C2211yescharacteristic
24C3×C5×C4⋊C4C2211yescharacteristic
25C3×C5×C4⋊C4C2211yescharacteristic
26C3×C42×C5C2211yescharacteristic
27C3×#685C2211yescharacteristic
28C3×#685C2211yescharacteristic
29C3×#685C2211yescharacteristic
30C3×#685C2211yescharacteristic
31C3×#685C2211yescharacteristic
32C3×#685C2211yescharacteristic
33C3×C4⋊Dic5C2211yescharacteristic
34C3×C4⋊Dic5C2211yescharacteristic
35C3×C4⋊Dic5C2211yescharacteristic
36C3×C4⋊Dic5C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×#683C2211yescharacteristic
40C3×#683C2211yescharacteristic
41C3×#683C2211yescharacteristic
42C3×#683C2211yescharacteristic
43C3×#683C2211yescharacteristic
44C3×#683C2211yescharacteristic
45C3×#683C2211yescharacteristic
46C3×#683C2211yescharacteristic
47C3×C4×Dic5C2211yescharacteristic
48C3×C4×Dic5C2211yescharacteristic
49C3×C4×Dic5C2211yescharacteristic
50C3×C4×Dic5C2211yescharacteristic
51C3×C4×Dic5C2211yescharacteristic
52C3×#541—51nomaximal, Hall
53C5×#125C2×C311yescharacteristic, complemented
54#4044C2×C311yescharacteristic
55#4044C2×C311yescharacteristic
56#4044C2×C311yescharacteristic
57#4042C2×C311yescharacteristic
58#4042C2×C311yescharacteristic
59#4038C2×C311yescharacteristic
60#4036C2×C311yescharacteristic, complemented
61#4035C2×C311yescharacteristic, complemented
62#4035C2×C311yescharacteristic, complemented
63#4035C2×C311yescharacteristic, complemented
64#4034C2×C311yescharacteristic, complemented
65#4033C2×C311yescharacteristic, complemented
66#4022C2×C311yescharacteristic
67C4×Dic10C2×C311yescharacteristic, complemented
68C22×C3×D5C2311yescharacteristic
69C2×C3×C4×C5C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×Dic5C2311yescharacteristic
77C2×C3×Dic5C2311yescharacteristic
78C2×C3×Dic5C2311yescharacteristic
79C2×C3×Dic5C2311yescharacteristic
80C2×C3×Dic5C2311yescharacteristic
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C3×C4×D5—22no—
84C3×Dic10—22no—
85C3×Dic10—22no—
86C3×C4⋊Q8—51no—
87C3×#126—51no—
88C3×#126—51no—
89C3×#126—51no—
90C3×#126—51no—
91C3×#125—51no—
92C3×#125—51no—
93C3×#125—51no—
94C3×#125—51no—
95C3×#125D511yescharacteristic, complemented
96C3×C22⋊Q8—51no—
97C3×C22⋊Q8—51no—
98C3×C4×Q8—51no—
99C3×C4×Q8—51no—
100C3×#117—51no—
101C2×C4×D5C22×C311yescharacteristic
102C2×Dic10C22×C311yescharacteristic
103C2×Dic10C22×C311yescharacteristic
104C5×C4⋊C4C22×C311yescharacteristic
105C5×C4⋊C4C22×C311yescharacteristic
106C5×C4⋊C4C22×C311yescharacteristic
107C5×C4⋊C4C22×C311yescharacteristic
108C5×C4⋊C4C22×C311yescharacteristic
109C5×C4⋊C4C22×C311yescharacteristic
110C42×C5C22×C311yescharacteristic
111#685C22×C311yescharacteristic
112#685C22×C311yescharacteristic
113#685C22×C311yescharacteristic
114#685C22×C311yescharacteristic
115#685C22×C311yescharacteristic
116#685C22×C311yescharacteristic
117C4⋊Dic5C22×C311yescharacteristic
118C4⋊Dic5C22×C311yescharacteristic
119C4⋊Dic5C22×C311yescharacteristic
120C4⋊Dic5C22×C311yescharacteristic
121#683C22×C311yescharacteristic
122#683C22×C311yescharacteristic
123#683C22×C311yescharacteristic
124#683C22×C311yescharacteristic
125#683C22×C311yescharacteristic
126#683C22×C311yescharacteristic
127#683C22×C311yescharacteristic
128#683C22×C311yescharacteristic
129#683C22×C311yescharacteristic
130#683C22×C311yescharacteristic
131C4×Dic5C22×C311yescharacteristic
132C4×Dic5C22×C311yescharacteristic
133C4×Dic5C22×C311yescharacteristic
134C4×Dic5C22×C311yescharacteristic
135C4×Dic5C22×C311yescharacteristic
136#541—51noSylow
137C22×C3×C5C2411yescharacteristic
138C2×C3×D5—21no—
139C2×C3×D5—21no—
140C2×C3×D5—21no—
141C3×C4×C5—21no—
142C3×C4×C5—21no—
143C3×C4×C5—21no—
144C3×C4×C5—21no—
145C3×C4×C5—21no—
146C3×C4×C5—21no—
147C3×C4×C5—21no—
148C3×Dic5—21no—
149C3×Dic5—21no—
150C3×Dic5—21no—
151C3×Dic5—21no—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5#4112yes—
155C2×C3×Q8—51no—
156C2×C3×Q8—51no—
157C22×C3×C4—51no—
158C3×C4⋊C4—51no—
159C3×C4⋊C4—51no—
160C3×C4⋊C4—51no—
161C3×C4⋊C4—51no—
162C3×C4⋊C4—51no—
163C3×C4⋊C4—51no—
164C3×C4⋊C4—51no—
165C3×C4⋊C4—51no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—51no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4C2×D511yescharacteristic
173C3×C4⋊C4C2×D511yescharacteristic
174C3×C4⋊C4C2×D511yescharacteristic
175C3×C4⋊C4C2×D511yescharacteristic
176C3×C4⋊C4C2×D511yescharacteristic
177C3×C4⋊C4C2×D511yescharacteristic
178C3×C22⋊C4—51no—
179C3×C22⋊C4—51no—
180C3×C22⋊C4—51no—
181C3×C22⋊C4—51no—
182C3×C22⋊C4—51no—
183C3×C22⋊C4—51no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42C2×D511yescharacteristic
190C22×D5C23×C311yescharacteristic
191C2×C4×C5C23×C311yescharacteristic
192C2×C4×C5C23×C311yescharacteristic
193C2×C4×C5C23×C311yescharacteristic
194C2×C4×C5C23×C311yescharacteristic
195C2×C4×C5C23×C311yescharacteristic
196C2×C4×C5C23×C311yescharacteristic
197C2×C4×C5C23×C311yescharacteristic
198C2×Dic5C23×C311yescharacteristic
199C2×Dic5C23×C311yescharacteristic
200C2×Dic5C23×C311yescharacteristic
201C2×Dic5C23×C311yescharacteristic
202C2×Dic5C23×C311yescharacteristic
203C2×Dic5C23×C311yescharacteristic
204C2×Dic5C23×C311yescharacteristic
205C4×D5—22no—
206Dic10—22no—
207Dic10—22no—
208C4⋊Q8—51no—
209#126—51no—
210#126—51no—
211#126—51no—
212#126—51no—
213#125—51no—
214#125—51no—
215#125—51no—
216#125—51no—
217#125C3×D511yescharacteristic, complemented
218C22⋊Q8—51no—
219C22⋊Q8—51no—
220C4×Q8—51no—
221C4×Q8—51no—
222#117—51no—
223C2×C3×C5C2×#4111yescharacteristic
224C2×C3×C52−1+411yescharacteristic
225C2×C3×C52−1+411yescharacteristic
226C3×D5—41no—
227C23×C3—51no—
228C3×Q8—102no—
229C3×Q8—102no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4C22×D511yescharacteristic
239C2×C3×C4C22×D511yescharacteristic
240C2×C3×C4C22×D511yescharacteristic
241C2×C3×C4C22×D511yescharacteristic
242C2×C3×C4C22×D511yescharacteristic
243C2×C3×C4C22×D511yescharacteristic
244C2×C3×C4C22×D511yescharacteristic
245C22×C5C24×C311yescharacteristic
246C2×D5—21no—
247C2×D5—21no—
248C2×D5—21no—
249C4×C5—21no—
250C4×C5—21no—
251C4×C5—21no—
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—21no—
256Dic5—21no—
257Dic5—21no—
258Dic5—21no—
259Dic5—21no—
260Dic5—21no—
261Dic5—21no—
262Dic5C3×#4112yes—
263C2×Q8—51no—
264C2×Q8—51no—
265C22×C4—51no—
266C4⋊C4—51no—
267C4⋊C4—51no—
268C4⋊C4—51no—
269C4⋊C4—51no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—51no—
273C4⋊C4—51no—
274C4⋊C4—51no—
275C4⋊C4—51no—
276C4⋊C4—51no—
277C4⋊C4—51no—
278C4⋊C4—51no—
279C4⋊C4—51no—
280C4⋊C4C2×C3×D511yescharacteristic
281C4⋊C4C2×C3×D511yescharacteristic
282C4⋊C4C2×C3×D511yescharacteristic
283C4⋊C4C2×C3×D511yescharacteristic
284C4⋊C4C2×C3×D511yescharacteristic
285C4⋊C4C2×C3×D511yescharacteristic
286C22⋊C4—51no—
287C22⋊C4—51no—
288C22⋊C4—51no—
289C22⋊C4—51no—
290C22⋊C4—51no—
291C22⋊C4—51no—
292C42—51no—
293C42—51no—
294C42—51no—
295C42—51no—
296C42—51no—
297C42C2×C3×D511yescharacteristic
298C3×C5#54111yescharacteristic, complemented, Hall
299C22×C3—101no—
300C22×C3—101no—
301C22×C3—101no—
302C22×C3C23×D511yescharacteristic
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—52no—
311C3×C4—101no—
312C3×C4—101no—
313C3×C4—101no—
314C3×C4—101no—
315C3×C4—101no—
316C3×C4—101no—
317C2×C5C2×C3×#4111yescharacteristic
318C2×C5C3×2−1+411yescharacteristic
319C2×C5C3×2−1+411yescharacteristic
320D5—41no—
321C23—51no—
322Q8—102no—
323Q8—102no—
324C2×C4—51no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—51no—
329C2×C4—51no—
330C2×C4—51no—
331C2×C4—102no—
332C2×C4C22×C3×D511yescharacteristic
333C2×C4C22×C3×D511yescharacteristic
334C2×C4C22×C3×D511yescharacteristic
335C2×C4C22×C3×D511yescharacteristic
336C2×C4C22×C3×D511yescharacteristic
337C2×C4C22×C3×D511yescharacteristic
338C2×C4C22×C3×D511yescharacteristic
339C2×C3—201no—
340C2×C3#414711yescharacteristic
341C2×C3D5×#4111yescharacteristic
342C2×C3#415011yescharacteristic
343C5C3×#54111yescharacteristic, complemented, Sylow
344C22—101no—
345C22—101no—
346C22—101no—
347C22C23×C3×D511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—52no—
356C4—101no—
357C4—101no—
358C4—101no—
359C4—101no—
360C4—101no—
361C4—101no—
362C3#6603011yescharacteristic, direct product factor, Sylow
363C2—201no—
364C2C3×#414711yescharacteristic
365C2C3×D5×#4111yescharacteristic
366C2C3×#415011yescharacteristic
subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#125C2
socleC22×C3×C5C24
prime radicalC22×C3×D5C23
hypercenterC3×#125D5
hypocenterC5C3×#541
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
1. C3×C5×#125C2semidirect
8. C3×#4036C2semidirect
9. C3×#4035C2semidirect
10. C3×#4035C2semidirect
11. C3×#4035C2semidirect
12. C3×#4034C2semidirect
13. C3×#4033C2semidirect
15. C3×C4×Dic10C2semidirect
16. #66030C3direct (N × H)
53. C5×#125C2×C3semidirect
60. #4036C2×C3semidirect
61. #4035C2×C3semidirect
62. #4035C2×C3semidirect
63. #4035C2×C3semidirect
64. #4034C2×C3semidirect
65. #4033C2×C3semidirect
67. C4×Dic10C2×C3semidirect
95. C3×#125D5semidirect
217. #125C3×D5semidirect
298. C3×C5#541semidirect
343. C5C3×#541semidirect
362. C3#66030direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#1252
C3×#40442
C3×#40422
C3×#40382
C3×#40362
C3×#40352
C3×#40342
C3×#40332
C3×#40222
C3×C4×Dic102
#660303
C3×#5415