Finite Group Databasebeta

← C3×#65935 #11755612

Subgroups — C3×#65935 #11755612

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#121C211yesmaximal, characteristic, complemented
2C3×#4085C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4C3×#4085C211yesmaximal, characteristic, complemented
5C3×#4081C211yesmaximal, characteristic, complemented
6C3×D4×Dic5C211yesmaximal, characteristic, complemented
7C3×D4×Dic5C211yesmaximal, characteristic, complemented
8C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
9C2×C3×#683C211yesmaximal, characteristic, complemented
10C3×#4044C211yesmaximal, characteristic, complemented
11C3×#4035C211yesmaximal, characteristic, complemented
12C3×#4029C211yesmaximal, characteristic, complemented
13C3×#4027C211yesmaximal, characteristic, complemented
14C3×#4025C211yesmaximal, characteristic, complemented
15C3×#4023C211yesmaximal, characteristic, complemented
16#65935C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic
20C22×C3×C4×C5C2211yescharacteristic
21C2×C3×C22⋊D5C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C22×C3×Dic5C2211yescharacteristic
25C22×C3×Dic5C2211yescharacteristic
26C22×C3×Dic5C2211yescharacteristic
27C22×C3×Dic5C2211yescharacteristic
28C2×C3×C4×D5C2211yescharacteristic
29C3×C5×C4⋊C4C2211yescharacteristic
30C3×C5×C22⋊C4C2211yescharacteristic
31C3×C5×C22⋊C4C2211yescharacteristic
32C3×C22⋊Dic5C2211yescharacteristic
33C3×C22⋊Dic5C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×C22⋊Dic5C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×C4⋊Dic5C2211yescharacteristic
41C3×C4⋊Dic5C2211yescharacteristic
42C3×#683C2211yescharacteristic
43C3×#683C2211yescharacteristic
44C3×#683C2211yescharacteristic
45C3×#683C2211yescharacteristic
46C3×#683C2211yescharacteristic
47C3×#683C2211yescharacteristic
48C3×#683C2211yescharacteristic
49C3×C4×Dic5C2211yescharacteristic
50C3×C4×Dic5C2211yescharacteristic
51C3×C4×Dic5C2211yescharacteristic
52C3×#553—51nomaximal, Hall
53C5×#121C2×C311yescharacteristic, complemented
54#4085C2×C311yescharacteristic, complemented
55#4085C2×C311yescharacteristic, complemented
56#4085C2×C311yescharacteristic, complemented
57#4081C2×C311yescharacteristic, complemented
58D4×Dic5C2×C311yescharacteristic, complemented
59D4×Dic5C2×C311yescharacteristic, complemented
60C4×C22⋊D5C2×C311yescharacteristic, complemented
61C2×#683C2×C311yescharacteristic, complemented
62#4044C2×C311yescharacteristic, complemented
63#4035C2×C311yescharacteristic, complemented
64#4029C2×C311yescharacteristic, complemented
65#4027C2×C311yescharacteristic, complemented
66#4025C2×C311yescharacteristic, complemented
67#4023C2×C311yescharacteristic, complemented
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C23×C3×C5C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C3×C5×D4—22no—
73C3×C5×D4—22no—
74C3×C5×D4—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C3×C22⋊D5—22no—
81C3×C22⋊D5—22no—
82C3×C22⋊D5—41no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C3×C4×D5—41no—
95C3×#126—51no—
96C3×#126—51no—
97C3×#125—51no—
98C3×#123—51no—
99C3×#123—51no—
100C3×#121—51no—
101C3×#121—51no—
102C3×#121—51no—
103C3×#121D511yescharacteristic, complemented
104C3×C4×D4—51no—
105C3×C4×D4—51no—
106C3×C4×D4—51no—
107C3×C4×D4—51no—
108C3×#117—51no—
109C2×C3×C4⋊C4—51no—
110C2×C5×D4C22×C311yescharacteristic
111C2×C5×D4C22×C311yescharacteristic
112C2×C5×D4C22×C311yescharacteristic
113C22×C4×C5C22×C311yescharacteristic
114C2×C22⋊D5C22×C311yescharacteristic
115C2×C22⋊D5C22×C311yescharacteristic
116C2×C22⋊D5C22×C311yescharacteristic
117C22×Dic5C22×C311yescharacteristic
118C22×Dic5C22×C311yescharacteristic
119C22×Dic5C22×C311yescharacteristic
120C22×Dic5C22×C311yescharacteristic
121C2×C4×D5C22×C311yescharacteristic
122C5×C4⋊C4C22×C311yescharacteristic
123C5×C22⋊C4C22×C311yescharacteristic
124C5×C22⋊C4C22×C311yescharacteristic
125C22⋊Dic5C22×C311yescharacteristic
126C22⋊Dic5C22×C311yescharacteristic
127C22⋊Dic5C22×C311yescharacteristic
128C22⋊Dic5C22×C311yescharacteristic
129C22⋊Dic5C22×C311yescharacteristic
130#685C22×C311yescharacteristic
131#685C22×C311yescharacteristic
132#685C22×C311yescharacteristic
133C4⋊Dic5C22×C311yescharacteristic
134C4⋊Dic5C22×C311yescharacteristic
135#683C22×C311yescharacteristic
136#683C22×C311yescharacteristic
137#683C22×C311yescharacteristic
138#683C22×C311yescharacteristic
139#683C22×C311yescharacteristic
140#683C22×C311yescharacteristic
141#683C22×C311yescharacteristic
142C4×Dic5C22×C311yescharacteristic
143C4×Dic5C22×C311yescharacteristic
144C4×Dic5C22×C311yescharacteristic
145#553—51noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5#4112yes—
155C22×C3×C5C2411yescharacteristic
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5#4112yes—
170C2×C3×D4—51no—
171C2×C3×D4—51no—
172C2×C3×D4—51no—
173C2×C3×D4C2×D511yescharacteristic
174C2×C3×D4C2×D511yescharacteristic
175C2×C3×D4C2×D511yescharacteristic
176C22×C3×C4—51no—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4C2×D511yescharacteristic
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4C2×D511yescharacteristic
192C3×C22⋊C4—51no—
193C3×C22⋊C4—51no—
194C3×C22⋊C4—51no—
195C3×C22⋊C4—51no—
196C3×C22⋊C4—51no—
197C3×C22⋊C4—51no—
198C3×C22⋊C4—51no—
199C3×C22⋊C4—51no—
200C3×C22⋊C4C2×D511yescharacteristic
201C3×C22⋊C4C2×D511yescharacteristic
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—51no—
205C23×C5C23×C311yescharacteristic
206C23×C5C23×C311yescharacteristic
207C23×C5C23×C311yescharacteristic
208C22×D5C23×C311yescharacteristic
209C5×D4—22no—
210C5×D4—22no—
211C5×D4—41no—
212C2×C4×C5—41no—
213C2×C4×C5C23×C311yescharacteristic
214C2×C4×C5C23×C311yescharacteristic
215C2×C4×C5C23×C311yescharacteristic
216C2×C4×C5C23×C311yescharacteristic
217C22⋊D5—22no—
218C22⋊D5—22no—
219C22⋊D5—41no—
220C2×Dic5—22no—
221C2×Dic5—22no—
222C2×Dic5—41no—
223C2×Dic5—41no—
224C2×Dic5C23×C311yescharacteristic
225C2×Dic5C23×C311yescharacteristic
226C2×Dic5C23×C311yescharacteristic
227C2×Dic5C23×C311yescharacteristic
228C2×Dic5C23×C311yescharacteristic
229C2×Dic5C23×C311yescharacteristic
230C2×Dic5C23×C311yescharacteristic
231C4×D5—41no—
232#126—51no—
233#126—51no—
234#125—51no—
235#123—51no—
236#123—51no—
237#121—51no—
238#121—51no—
239#121—51no—
240#121C3×D511yescharacteristic, complemented
241C4×D4—51no—
242C4×D4—51no—
243C4×D4—51no—
244C4×D4—51no—
245#117—51no—
246C2×C4⋊C4—51no—
247C2×C3×C5—22no—
248C2×C3×C5—41no—
249C2×C3×C5—41no—
250C2×C3×C5C2×#4111yescharacteristic
251C2×C3×C5C2×#4111yescharacteristic
252C2×C3×C5H(5,𝔽2)11yescharacteristic
253C3×D5—41no—
254C23×C3—51no—
255C23×C3C22×D511yescharacteristic
256C23×C3C22×D511yescharacteristic
257C23×C3C22×D511yescharacteristic
258C3×D4—22no—
259C3×D4—22no—
260C3×D4—41no—
261C3×D4—102no—
262C3×D4—102no—
263C3×D4—201no—
264C2×C3×C4—41no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—51no—
270C2×C3×C4—51no—
271C2×C3×C4—51no—
272C2×C3×C4—102no—
273C2×C3×C4—102no—
274C2×C3×C4—201no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4C22×D511yescharacteristic
278C2×C3×C4C22×D511yescharacteristic
279C2×C3×C4C22×D511yescharacteristic
280C2×C3×C4C22×D511yescharacteristic
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5C3×#4112yes—
290C22×C5C24×C311yescharacteristic
291C2×D5—21no—
292C2×D5—21no—
293C2×D5—21no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—21no—
298Dic5—21no—
299Dic5—21no—
300Dic5—21no—
301Dic5—21no—
302Dic5—21no—
303Dic5—21no—
304Dic5C3×#4112yes—
305C2×D4—51no—
306C2×D4—51no—
307C2×D4—51no—
308C2×D4C2×C3×D511yescharacteristic
309C2×D4C2×C3×D511yescharacteristic
310C2×D4C2×C3×D511yescharacteristic
311C22×C4—51no—
312C22×C4—51no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4C2×C3×D511yescharacteristic
317C4⋊C4—51no—
318C4⋊C4—51no—
319C4⋊C4—51no—
320C4⋊C4—51no—
321C4⋊C4—51no—
322C4⋊C4—51no—
323C4⋊C4—51no—
324C4⋊C4—51no—
325C4⋊C4—51no—
326C4⋊C4C2×C3×D511yescharacteristic
327C22⋊C4—51no—
328C22⋊C4—51no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—51no—
332C22⋊C4—51no—
333C22⋊C4—51no—
334C22⋊C4—51no—
335C22⋊C4C2×C3×D511yescharacteristic
336C22⋊C4C2×C3×D511yescharacteristic
337C42—51no—
338C42—51no—
339C42—51no—
340C3×C5#55311yescharacteristic, complemented, Hall
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—101no—
350C22×C3—101no—
351C22×C3—101no—
352C22×C3#71112yes—
353C22×C3C23×D511yescharacteristic
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—52no—
359C3×C4—101no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363C3×C4—101no—
364C3×C4—101no—
365C2×C5—22no—
366C2×C5—41no—
367C2×C5—41no—
368C2×C5C2×C3×#4111yescharacteristic
369C2×C5C2×C3×#4111yescharacteristic
370C2×C5C3×H(5,𝔽2)11yescharacteristic
371D5—41no—
372C23—51no—
373C23C22×C3×D511yescharacteristic
374C23C22×C3×D511yescharacteristic
375C23C22×C3×D511yescharacteristic
376D4—22no—
377D4—22no—
378D4—41no—
379D4—102no—
380D4—102no—
381D4—201no—
382C2×C4—41no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—201no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4C22×C3×D511yescharacteristic
396C2×C4C22×C3×D511yescharacteristic
397C2×C4C22×C3×D511yescharacteristic
398C2×C4C22×C3×D511yescharacteristic
399C2×C3—22no—
400C2×C3—41no—
401C2×C3—41no—
402C2×C3—201no—
403C2×C3C2×#71111yescharacteristic
404C2×C3#414411yescharacteristic
405C2×C3D5×#4111yescharacteristic
406C5C3×#55311yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—101no—
416C22—101no—
417C22—101no—
418C22C3×#71112yes—
419C22C23×C3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—52no—
425C4—101no—
426C4—101no—
427C4—101no—
428C4—101no—
429C4—101no—
430C4—101no—
431C3#6593511yescharacteristic, direct product factor, Sylow
432C2—22no—
433C2—41no—
434C2—41no—
435C2—201no—
436C2C2×C3×#71111yescharacteristic
437C2C3×#414411yescharacteristic
438C2C3×D5×#4111yescharacteristic
subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#121C2
socleC22×C3×C5C24
hypercenterC3×#121D5
hypocenterC5C3×#553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C3×C5×#121C2semidirect
2. C3×#4085C2semidirect
3. C3×#4085C2semidirect
4. C3×#4085C2semidirect
5. C3×#4081C2semidirect
6. C3×D4×Dic5C2semidirect
7. C3×D4×Dic5C2semidirect
8. C3×C4×C22⋊D5C2semidirect
9. C2×C3×#683C2semidirect
10. C3×#4044C2semidirect
11. C3×#4035C2semidirect
12. C3×#4029C2semidirect
13. C3×#4027C2semidirect
14. C3×#4025C2semidirect
15. C3×#4023C2semidirect
16. #65935C3direct (N × H)
53. C5×#121C2×C3semidirect
54. #4085C2×C3semidirect
55. #4085C2×C3semidirect
56. #4085C2×C3semidirect
57. #4081C2×C3semidirect
58. D4×Dic5C2×C3semidirect
59. D4×Dic5C2×C3semidirect
60. C4×C22⋊D5C2×C3semidirect
61. C2×#683C2×C3semidirect
62. #4044C2×C3semidirect
63. #4035C2×C3semidirect
64. #4029C2×C3semidirect
65. #4027C2×C3semidirect
66. #4025C2×C3semidirect
67. #4023C2×C3semidirect
103. C3×#121D5semidirect
240. #121C3×D5semidirect
340. C3×C5#553semidirect
406. C5C3×#553semidirect
431. C3#65935direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#1212
C3×#40852
C3×#40812
C3×D4×Dic52
C3×C4×C22⋊D52
C2×C3×#6832
C3×#40442
C3×#40352
C3×#40292
C3×#40272
C3×#40252
C3×#40232
#659353
C3×#5535