Finite Group Databasebeta

← C3×#10599156 #14284075

Subgroups — C3×#10599156 #14284075

Order 1920.

424 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×D5×#125C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic
3C3×#64994C211yesmaximal, characteristic
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6C3×#64685C211yesmaximal, characteristic, complemented
7C3×#64685C211yesmaximal, characteristic, complemented
8#10599156C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#125C2211yescharacteristic
10C2×C3×#676—21no—
11C3×D5×C4⋊C4—21no—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C411yescharacteristic
14C3×D5×C4⋊C4C411yescharacteristic
15C3×#4036C411yescharacteristic
16C3×#4036C411yescharacteristic
17C3×#4035—21no—
18C3×#4035—21no—
19C3×C42×D5C2211yescharacteristic
20C3×#4016C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23C3×#3952—21no—
24C3×#3946—21no—
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic
27C3×#3935C2211yescharacteristic
28C3×#1528—51nomaximal, Hall
29D5×#125C2×C311yescharacteristic
30#64996C2×C311yescharacteristic
31#64994C2×C311yescharacteristic
32C5×#330C2×C311yescharacteristic, complemented
33#64763C2×C311yescharacteristic, complemented
34#64685C2×C311yescharacteristic, complemented
35#64685C2×C311yescharacteristic, complemented
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5C2311yescharacteristic
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#676—24no—
64C2×C3×#125—51no—
65C3×#432—51no—
66C3×C4×M16—51no—
67C3×#330—51no—
68C3×#330—51no—
69C3×#330—51no—
70C3×#330D511yescharacteristic, complemented
71C5×#125C22×C311yescharacteristic
72C2×#676—21no—
73D5×C4⋊C4—21no—
74D5×C4⋊C4—21no—
75D5×C4⋊C4C3×C411yescharacteristic
76D5×C4⋊C4C3×C411yescharacteristic
77#4036C3×C411yescharacteristic
78#4036C3×C411yescharacteristic
79#4035—21no—
80#4035—21no—
81C42×D5C22×C311yescharacteristic
82#4016C22×C311yescharacteristic
83C5×#97C22×C311yescharacteristic
84C5×#97C22×C311yescharacteristic
85#3952—21no—
86#3946—21no—
87C8×Dic5—21no—
88#3935C22×C311yescharacteristic
89#3935C22×C311yescharacteristic
90#1528—51noSylow
91C22×C3×D5C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C3×C4×D5—22no—
103C3×C4×D5—22no—
104C3×C4×D5—41no—
105C3×C4×D5—42no—
106C3×C4×D5—42no—
107C3×C5×C8—22no—
108C3×C5×C8—41no—
109C3×#168—22no—
110C3×#168—41no—
111C2×C3×M16—101no—
112C3×#125—51no—
113C3×#125—51no—
114C3×#125—51no—
115C3×#125—101no—
116C3×#125—101no—
117C3×#125C2×D511yescharacteristic
118C2×C3×C4⋊C4—51no—
119C2×C3×C4⋊C4—51no—
120C2×C3×C4⋊C4—101no—
121C2×C3×C4⋊C4—101no—
122C2×C3×C42—51no—
123C3×C4⋊C8—101no—
124C3×C22⋊C8—101no—
125C3×#97—51no—
126C3×#97—51no—
127C3×#97C2×D511yescharacteristic
128C3×#97C2×D511yescharacteristic
129C3×C4×C8—101no—
130C2×C4×D5—21no—
131C2×C4×D5—21no—
132C2×C4×D5C2×C3×C411yescharacteristic
133C2×C4×D5C3×D411yescharacteristic
134C2×C4×D5C3×D411yescharacteristic
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C2×C3×C411yescharacteristic
140C5×C4⋊C4C2×C3×C411yescharacteristic
141C42×C5C23×C311yescharacteristic
142C4⋊Dic5—21no—
143C4⋊Dic5—21no—
144C4⋊Dic5C2×C3×C411yescharacteristic
145C4⋊Dic5C2×C3×C411yescharacteristic
146#683—21no—
147#683—21no—
148#683—21no—
149#683—21no—
150#683—21no—
151#683—21no—
152C4×Dic5C2×C3×C411yescharacteristic
153C4×Dic5C3×D411yescharacteristic
154C4×Dic5C3×D411yescharacteristic
155C2×#168—21no—
156C2×#168—21no—
157#676—24no—
158C2×#125—51no—
159#432—51no—
160C4×M16—51no—
161#330—51no—
162#330—51no—
163#330—51no—
164#330C3×D511yescharacteristic, complemented
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5#10412yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C3×Dic5—21no—
175C3×Dic5—21no—
176C3×Dic5—41no—
177C3×Dic5—41no—
178C3×Dic5#10112yes—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4—101no—
183C22×C3×C4—101no—
184C3×M16—104no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—101no—
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—51no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4C4×D511yescharacteristic
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42C22×D511yescharacteristic
207C22×D5C3×C22⋊C411yescharacteristic
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5C22×C3×C411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C2×Dic5—21no—
214C2×Dic5—21no—
215C2×Dic5C3×C22⋊C411yescharacteristic
216C2×Dic5C3×C22⋊C411yescharacteristic
217C2×Dic5C3×C22⋊C411yescharacteristic
218C4×D5—22no—
219C4×D5—22no—
220C4×D5—41no—
221C4×D5—42no—
222C4×D5—42no—
223C5×C8—22no—
224C5×C8—41no—
225#168—22no—
226#168—41no—
227C2×M16—101no—
228#125—51no—
229#125—51no—
230#125—51no—
231#125—101no—
232#125—101no—
233#125C2×C3×D511yescharacteristic
234C2×C4⋊C4—51no—
235C2×C4⋊C4—51no—
236C2×C4⋊C4—101no—
237C2×C4⋊C4—101no—
238C2×C42—51no—
239C4⋊C8—101no—
240C22⋊C8—101no—
241#97—51no—
242#97—51no—
243#97C2×C3×D511yescharacteristic
244#97C2×C3×D511yescharacteristic
245C4×C8—101no—
246C2×C3×C5C2×#10111yescharacteristic
247C2×C3×C5C2×#10411yescharacteristic
248C2×C3×C5#42111yescharacteristic
249C3×D5—22no—
250C23×C3—51no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—102no—
257C2×C3×C4—102no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—201no—
261C2×C3×C4—202no—
262C2×C3×C4—202no—
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C3×C8—22no—
267C3×C8—41no—
268C3×C8—102no—
269C3×C8—201no—
270C22×C5C2×C3×C22⋊C411yescharacteristic
271C2×D5—21no—
272C2×D5—21no—
273C2×D5C3×#10412yes—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—41no—
278C4×C5—41no—
279Dic5—21no—
280Dic5—21no—
281Dic5—41no—
282Dic5—41no—
283Dic5C3×#10112yes—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—101no—
288C22×C4—101no—
289M16—104no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—101no—
293C2×C8—101no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—51no—
297C4⋊C4—51no—
298C4⋊C4—101no—
299C4⋊C4—101no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4—101no—
303C4⋊C4—101no—
304C4⋊C4—101no—
305C4⋊C4—101no—
306C4⋊C4C3×C4×D511yescharacteristic
307C4⋊C4C3×C4×D511yescharacteristic
308C42—51no—
309C42—51no—
310C42—51no—
311C42C22×C3×D511yescharacteristic
312C3×C5#152811yescharacteristic, complemented, Hall
313C22×C3—52no—
314C22×C3—101no—
315C22×C3—101no—
316C22×C3D5×C22⋊C411yescharacteristic
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—52no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—201no—
326C3×C4—201no—
327C2×C5C2×C3×#10111yescharacteristic
328C2×C5C2×C3×#10411yescharacteristic
329C2×C5C3×#42111yescharacteristic
330D5—22no—
331C23—51no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—102no—
338C2×C4—102no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—201no—
342C2×C4—202no—
343C2×C4—202no—
344C2×C4C2×C3×C4×D511yescharacteristic
345C2×C4C3×D4×D511yescharacteristic
346C2×C4C3×D4×D511yescharacteristic
347C8—22no—
348C8—41no—
349C8—102no—
350C8—201no—
351C2×C3—102no—
352C2×C3D5×#10111yescharacteristic
353C2×C3D5×#10411yescharacteristic
354C2×C3#6511011yescharacteristic
355C5C3×#152811yescharacteristic, complemented, Sylow
356C22—52no—
357C22—101no—
358C22—101no—
359C22C3×D5×C22⋊C411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—52no—
366C4—101no—
367C4—101no—
368C4—201no—
369C4—201no—
370C3#1059915611yescharacteristic, direct product factor, Sylow
371C2—102no—
372C2C3×D5×#10111yescharacteristic
373C2C3×D5×#10411yescharacteristic
374C2C3×#6511011yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#330D5
hypocenterC5C3×#1528
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
4. C3×C5×#330C2semidirect
5. C3×#64763C2semidirect
6. C3×#64685C2semidirect
7. C3×#64685C2semidirect
8. #10599156C3direct (N × H)
32. C5×#330C2×C3semidirect
33. #64763C2×C3semidirect
34. #64685C2×C3semidirect
35. #64685C2×C3semidirect
70. C3×#330D5semidirect
164. #330C3×D5semidirect
312. C3×C5#1528semidirect
355. C5C3×#1528semidirect
370. C3#10599156direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1252
C3×#649962
C3×#649942
C3×C5×#3302
C3×#647632
C3×#646852
#105991563
C3×#15285