Finite Group Databasebeta

← C3×#65999 #11755676

Subgroups — C3×#65999 #11755676

Order 960.

436 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#123C211yesmaximal, characteristic, complemented
2C3×#4085C211yesmaximal, characteristic
3C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C3×#4075C211yesmaximal, characteristic, complemented
5C2×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#4044C211yesmaximal, characteristic, complemented
7C3×#4043C211yesmaximal, characteristic, complemented
8C3×#4036C211yesmaximal, characteristic, complemented
9C3×#4035C211yesmaximal, characteristic, complemented
10C3×#4032C211yesmaximal, characteristic, complemented
11C3×#4029C211yesmaximal, characteristic, complemented
12C3×#4027C211yesmaximal, characteristic, complemented
13C3×#4025C211yesmaximal, characteristic, complemented
14C3×#4024C211yesmaximal, characteristic, complemented
15C3×#4024C211yesmaximal, characteristic, complemented
16#65999C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×C3×C4×C5C2211yescharacteristic
19C2×C3×C22⋊D5C2211yescharacteristic
20C2×C3×C22⋊D5C2211yescharacteristic
21C22×C3×Dic5C2211yescharacteristic
22C22×C3×Dic5C2211yescharacteristic
23C22×C3×Dic5C2211yescharacteristic
24C2×C3×C4×D5C2211yescharacteristic
25C2×C3×Dic10C2211yescharacteristic
26C3×C5×C4⋊C4C2211yescharacteristic
27C3×C5×C4⋊C4C2211yescharacteristic
28C3×C5×C22⋊C4C2211yescharacteristic
29C3×C5×C22⋊C4C2211yescharacteristic
30C3×C5×C22⋊C4C2211yescharacteristic
31C3×C22⋊Dic5C2211yescharacteristic
32C3×C22⋊Dic5C2211yescharacteristic
33C3×C22⋊Dic5C2211yescharacteristic
34C3×#685C2211yescharacteristic
35C3×#685C2211yescharacteristic
36C3×#685C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×C4⋊Dic5C2211yescharacteristic
39C3×C4⋊Dic5C2211yescharacteristic
40C3×C4⋊Dic5C2211yescharacteristic
41C3×C4⋊Dic5C2211yescharacteristic
42C3×C4⋊Dic5C2211yescharacteristic
43C3×C4⋊Dic5C2211yescharacteristic
44C3×#683C2211yescharacteristic
45C3×#683C2211yescharacteristic
46C3×#683C2211yescharacteristic
47C3×#683C2211yescharacteristic
48C3×#683C2211yescharacteristic
49C3×#683C2211yescharacteristic
50C3×C4×Dic5C2211yescharacteristic
51C3×C4×Dic5C2211yescharacteristic
52C3×#539—51nomaximal, Hall
53C5×#123C2×C311yescharacteristic, complemented
54#4085C2×C311yescharacteristic
55D4×Dic5C2×C311yescharacteristic, complemented
56#4075C2×C311yescharacteristic, complemented
57C2×C4⋊Dic5C2×C311yescharacteristic, complemented
58#4044C2×C311yescharacteristic, complemented
59#4043C2×C311yescharacteristic, complemented
60#4036C2×C311yescharacteristic, complemented
61#4035C2×C311yescharacteristic, complemented
62#4032C2×C311yescharacteristic, complemented
63#4029C2×C311yescharacteristic, complemented
64#4027C2×C311yescharacteristic, complemented
65#4025C2×C311yescharacteristic, complemented
66#4024C2×C311yescharacteristic, complemented
67#4024C2×C311yescharacteristic, complemented
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C3×C5×D4—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C3×C22⋊D5—22no—
79C3×C22⋊D5—41no—
80C2×C3×Dic5—41no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C3×C4×D5—41no—
91C3×Dic10—41no—
92C3×#126—51no—
93C3×#126—51no—
94C3×#125—51no—
95C3×#125—51no—
96C3×#123—51no—
97C3×#123—51no—
98C3×#123—51no—
99C3×#123D511yescharacteristic, complemented
100C3×C22⋊Q8—51no—
101C3×C22⋊Q8—51no—
102C3×C22⋊Q8—51no—
103C3×#121—51no—
104C3×C4×D4—51no—
105C3×C4×D4—51no—
106C2×C3×C4⋊C4—51no—
107C2×C5×D4C22×C311yescharacteristic
108C22×C4×C5C22×C311yescharacteristic
109C2×C22⋊D5C22×C311yescharacteristic
110C2×C22⋊D5C22×C311yescharacteristic
111C22×Dic5C22×C311yescharacteristic
112C22×Dic5C22×C311yescharacteristic
113C22×Dic5C22×C311yescharacteristic
114C2×C4×D5C22×C311yescharacteristic
115C2×Dic10C22×C311yescharacteristic
116C5×C4⋊C4C22×C311yescharacteristic
117C5×C4⋊C4C22×C311yescharacteristic
118C5×C22⋊C4C22×C311yescharacteristic
119C5×C22⋊C4C22×C311yescharacteristic
120C5×C22⋊C4C22×C311yescharacteristic
121C22⋊Dic5C22×C311yescharacteristic
122C22⋊Dic5C22×C311yescharacteristic
123C22⋊Dic5C22×C311yescharacteristic
124#685C22×C311yescharacteristic
125#685C22×C311yescharacteristic
126#685C22×C311yescharacteristic
127#685C22×C311yescharacteristic
128C4⋊Dic5C22×C311yescharacteristic
129C4⋊Dic5C22×C311yescharacteristic
130C4⋊Dic5C22×C311yescharacteristic
131C4⋊Dic5C22×C311yescharacteristic
132C4⋊Dic5C22×C311yescharacteristic
133C4⋊Dic5C22×C311yescharacteristic
134#683C22×C311yescharacteristic
135#683C22×C311yescharacteristic
136#683C22×C311yescharacteristic
137#683C22×C311yescharacteristic
138#683C22×C311yescharacteristic
139#683C22×C311yescharacteristic
140C4×Dic5C22×C311yescharacteristic
141C4×Dic5C22×C311yescharacteristic
142#539—51noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5#4112yes—
149C22×C3×C5C2411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C2×C3×Q8—51no—
166C2×C3×D4—51no—
167C2×C3×D4—51no—
168C2×C3×D4C2×D511yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4C2×D511yescharacteristic
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4C2×D511yescharacteristic
187C3×C4⋊C4C2×D511yescharacteristic
188C3×C22⋊C4—51no—
189C3×C22⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193C3×C22⋊C4—51no—
194C3×C22⋊C4—51no—
195C3×C22⋊C4C2×D511yescharacteristic
196C3×C22⋊C4C2×D511yescharacteristic
197C3×C22⋊C4C2×D511yescharacteristic
198C3×C42—51no—
199C3×C42—51no—
200C23×C5C23×C311yescharacteristic
201C23×C5C23×C311yescharacteristic
202C22×D5C23×C311yescharacteristic
203C5×D4—22no—
204C2×C4×C5—22no—
205C2×C4×C5C23×C311yescharacteristic
206C2×C4×C5C23×C311yescharacteristic
207C2×C4×C5C23×C311yescharacteristic
208C2×C4×C5C23×C311yescharacteristic
209C2×C4×C5C23×C311yescharacteristic
210C22⋊D5—22no—
211C22⋊D5—41no—
212C2×Dic5—41no—
213C2×Dic5—41no—
214C2×Dic5—41no—
215C2×Dic5C23×C311yescharacteristic
216C2×Dic5C23×C311yescharacteristic
217C2×Dic5C23×C311yescharacteristic
218C2×Dic5C23×C311yescharacteristic
219C2×Dic5C23×C311yescharacteristic
220C2×Dic5C23×C311yescharacteristic
221C2×Dic5C23×C311yescharacteristic
222C4×D5—41no—
223Dic10—41no—
224#126—51no—
225#126—51no—
226#125—51no—
227#125—51no—
228#123—51no—
229#123—51no—
230#123—51no—
231#123C3×D511yescharacteristic, complemented
232C22⋊Q8—51no—
233C22⋊Q8—51no—
234C22⋊Q8—51no—
235#121—51no—
236C4×D4—51no—
237C4×D4—51no—
238C2×C4⋊C4—51no—
239C2×C3×C5—22no—
240C2×C3×C5—41no—
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5H(5,𝔽2)11yescharacteristic
243C2×C3×C52−1+411yescharacteristic
244C3×D5—41no—
245C23×C3—51no—
246C23×C3C22×D511yescharacteristic
247C23×C3C22×D511yescharacteristic
248C3×Q8—201no—
249C3×D4—22no—
250C3×D4—102no—
251C3×D4—201no—
252C2×C3×C4—22no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—201no—
261C2×C3×C4—201no—
262C2×C3×C4—201no—
263C2×C3×C4—201no—
264C2×C3×C4C22×D511yescharacteristic
265C2×C3×C4C22×D511yescharacteristic
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268C2×C3×C4C22×D511yescharacteristic
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5C3×#4112yes—
275C22×C5C24×C311yescharacteristic
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287Dic5—21no—
288Dic5—21no—
289Dic5—21no—
290Dic5—21no—
291C2×Q8—51no—
292C2×D4—51no—
293C2×D4—51no—
294C2×D4C2×C3×D511yescharacteristic
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4C2×C3×D511yescharacteristic
300C4⋊C4—51no—
301C4⋊C4—51no—
302C4⋊C4—51no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—51no—
306C4⋊C4—51no—
307C4⋊C4—51no—
308C4⋊C4—51no—
309C4⋊C4—51no—
310C4⋊C4—51no—
311C4⋊C4—51no—
312C4⋊C4C2×C3×D511yescharacteristic
313C4⋊C4C2×C3×D511yescharacteristic
314C22⋊C4—51no—
315C22⋊C4—51no—
316C22⋊C4—51no—
317C22⋊C4—51no—
318C22⋊C4—51no—
319C22⋊C4—51no—
320C22⋊C4—51no—
321C22⋊C4C2×C3×D511yescharacteristic
322C22⋊C4C2×C3×D511yescharacteristic
323C22⋊C4C2×C3×D511yescharacteristic
324C42—51no—
325C42—51no—
326C3×C5#53911yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—101no—
333C22×C3—101no—
334C22×C3—101no—
335C22×C3#71112yes—
336C22×C3C23×D511yescharacteristic
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—101no—
343C3×C4—101no—
344C3×C4—101no—
345C3×C4—101no—
346C3×C4—101no—
347C3×C4—101no—
348C3×C4—101no—
349C2×C5—22no—
350C2×C5—41no—
351C2×C5C2×C3×#4111yescharacteristic
352C2×C5C3×H(5,𝔽2)11yescharacteristic
353C2×C5C3×2−1+411yescharacteristic
354D5—41no—
355C23—51no—
356C23C22×C3×D511yescharacteristic
357C23C22×C3×D511yescharacteristic
358Q8—201no—
359D4—22no—
360D4—102no—
361D4—201no—
362C2×C4—22no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—51no—
370C2×C4—201no—
371C2×C4—201no—
372C2×C4—201no—
373C2×C4—201no—
374C2×C4C22×C3×D511yescharacteristic
375C2×C4C22×C3×D511yescharacteristic
376C2×C4C22×C3×D511yescharacteristic
377C2×C4C22×C3×D511yescharacteristic
378C2×C4C22×C3×D511yescharacteristic
379C2×C3—22no—
380C2×C3—41no—
381C2×C3—201no—
382C2×C3C2×#71111yescharacteristic
383C2×C3#414911yescharacteristic
384C2×C3#415011yescharacteristic
385C5C3×#53911yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—101no—
392C22—101no—
393C22—101no—
394C22C3×#71112yes—
395C22C23×C3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—101no—
402C4—101no—
403C4—101no—
404C4—101no—
405C4—101no—
406C4—101no—
407C4—101no—
408C3#6599911yescharacteristic, direct product factor, Sylow
409C2—22no—
410C2—41no—
411C2—201no—
412C2C2×C3×#71111yescharacteristic
413C2C3×#414911yescharacteristic
414C2C3×#415011yescharacteristic
subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#123C2
socleC22×C3×C5C24
prime radicalC3×#4085C2
hypercenterC3×#123D5
hypocenterC5C3×#539
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. C3×C5×#123C2semidirect
3. C3×D4×Dic5C2semidirect
4. C3×#4075C2semidirect
5. C2×C3×C4⋊Dic5C2semidirect
6. C3×#4044C2semidirect
7. C3×#4043C2semidirect
8. C3×#4036C2semidirect
9. C3×#4035C2semidirect
10. C3×#4032C2semidirect
11. C3×#4029C2semidirect
12. C3×#4027C2semidirect
13. C3×#4025C2semidirect
14. C3×#4024C2semidirect
15. C3×#4024C2semidirect
16. #65999C3direct (N × H)
53. C5×#123C2×C3semidirect
55. D4×Dic5C2×C3semidirect
56. #4075C2×C3semidirect
57. C2×C4⋊Dic5C2×C3semidirect
58. #4044C2×C3semidirect
59. #4043C2×C3semidirect
60. #4036C2×C3semidirect
61. #4035C2×C3semidirect
62. #4032C2×C3semidirect
63. #4029C2×C3semidirect
64. #4027C2×C3semidirect
65. #4025C2×C3semidirect
66. #4024C2×C3semidirect
67. #4024C2×C3semidirect
99. C3×#123D5semidirect
231. #123C3×D5semidirect
326. C3×C5#539semidirect
385. C5C3×#539semidirect
408. C3#65999direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#1232
C3×#40852
C3×D4×Dic52
C3×#40752
C2×C3×C4⋊Dic52
C3×#40442
C3×#40432
C3×#40362
C3×#40352
C3×#40322
C3×#40292
C3×#40272
C3×#40252
C3×#40242
#659993
C3×#5395