Finite Group Databasebeta

← C3×#10599154 #14283917

Subgroups — C3×#10599154 #14283917

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66025C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic, complemented
3C3×D5×#97C211yesmaximal, characteristic, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6C3×#64684C211yesmaximal, characteristic, complemented
7C3×#64684C211yesmaximal, characteristic, complemented
8#10599154C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#125C2211yescharacteristic
10C2×C3×#676—21no—
11C2×C3×C8×D5—21no—
12C3×#4044—21no—
13C3×#4043C411yescharacteristic
14C3×#4041C411yescharacteristic
15C3×#4040—21no—
16C3×#4039—21no—
17C3×#4039C411yescharacteristic
18C3×#4038—21no—
19C3×#4033C411yescharacteristic
20C3×#4021C2211yescharacteristic
21C3×C42×D5C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23C3×C5×#97C2211yescharacteristic
24C3×#3947—21no—
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic
27C3×#3935C2211yescharacteristic
28C3×#1524—51nomaximal, Hall
29#66025C2×C311yescharacteristic
30#64996C2×C311yescharacteristic, complemented
31D5×#97C2×C311yescharacteristic, complemented
32C5×#330C2×C311yescharacteristic, complemented
33#64763C2×C311yescharacteristic, complemented
34#64684C2×C311yescharacteristic, complemented
35#64684C2×C311yescharacteristic, complemented
36C2×C3×D20—21no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×Dic10C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5C2311yescharacteristic
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#676—24no—
64C3×C8×D5—24no—
65C3×#529—51no—
66C3×C4×M16—51no—
67C2×C3×#97—51no—
68C3×#330—51no—
69C3×#330D511yescharacteristic, complemented
70C3×#329—51no—
71C3×#329—51no—
72C5×#125C22×C311yescharacteristic
73C2×#676—21no—
74C2×C8×D5—21no—
75#4044—21no—
76#4043C3×C411yescharacteristic
77#4041C3×C411yescharacteristic
78#4040—21no—
79#4039—21no—
80#4039C3×C411yescharacteristic
81#4038—21no—
82#4033C3×C411yescharacteristic
83#4021C22×C311yescharacteristic
84C42×D5C22×C311yescharacteristic
85C5×#97C22×C311yescharacteristic
86C5×#97C22×C311yescharacteristic
87#3947—21no—
88C8×Dic5—21no—
89#3935C22×C311yescharacteristic
90#3935C22×C311yescharacteristic
91#1524—51noSylow
92C22×C3×D5—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C3×D20—41no—
104C3×D20—42no—
105C3×C4×D5—22no—
106C3×C4×D5—22no—
107C3×C4×D5—41no—
108C3×C4×D5—42no—
109C3×Dic10—41no—
110C3×C5×C8—22no—
111C3×C5×C8—22no—
112C3×#168—22no—
113C3×#168—22no—
114C2×C3×M16—101no—
115C22×C3×C8—101no—
116C3×#126—101no—
117C3×#125C2×D511yescharacteristic
118C3×#124—51no—
119C3×#123—101no—
120C3×C22⋊Q8—51no—
121C3×#121—51no—
122C3×C4×Q8—51no—
123C3×C4×D4—51no—
124C3×C4×D4—101no—
125C3×#117—101no—
126C2×C3×C42—51no—
127C3×#97—51no—
128C3×#97—51no—
129C3×#97—101no—
130C3×#97C2×D511yescharacteristic
131C3×#97C2×D511yescharacteristic
132C3×C4×C8—101no—
133C2×D20—21no—
134C2×D20C2×C3×C411yescharacteristic
135C2×C4×D5—21no—
136C2×C4×D5C2×C3×C411yescharacteristic
137C2×C4×D5C3×D411yescharacteristic
138C2×C4×D5C3×D411yescharacteristic
139C2×Dic10C2×C3×C411yescharacteristic
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4C2×C3×C411yescharacteristic
145C5×C4⋊C4C2×C3×C411yescharacteristic
146C42×C5C23×C311yescharacteristic
147#685—21no—
148#685—21no—
149#685—21no—
150#685—21no—
151#685—21no—
152C4⋊Dic5—21no—
153#683—21no—
154C4×Dic5—21no—
155C4×Dic5C2×C3×C411yescharacteristic
156C4×Dic5C3×D411yescharacteristic
157C4×Dic5C3×D411yescharacteristic
158C2×#168—21no—
159C2×#168—21no—
160#676—24no—
161C8×D5—24no—
162#529—51no—
163C4×M16—51no—
164C2×#97—51no—
165#330—51no—
166#330C3×D511yescharacteristic, complemented
167#329—51no—
168#329—51no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×Dic5—21no—
182C3×Dic5—21no—
183C3×Dic5—41no—
184C3×Dic5#10412yes—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C22×C3×C4—101no—
192C3×M16—104no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—104no—
196C2×C3×C8—101no—
197C2×C3×C8—101no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C4⋊C4C4×D511yescharacteristic
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42—51no—
212C3×C42—101no—
213C3×C42C22×D511yescharacteristic
214C22×D5—21no—
215C22×D5C3×C22⋊C411yescharacteristic
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5C22×C3×C411yescharacteristic
219C2×C4×C5C2×C3×D411yescharacteristic
220C2×C4×C5C2×C3×D411yescharacteristic
221C2×Dic5—21no—
222C2×Dic5C3×C22⋊C411yescharacteristic
223C2×Dic5C3×C22⋊C411yescharacteristic
224C2×Dic5C3×C22⋊C411yescharacteristic
225D20—41no—
226D20—42no—
227C4×D5—22no—
228C4×D5—22no—
229C4×D5—41no—
230C4×D5—42no—
231Dic10—41no—
232C5×C8—22no—
233C5×C8—22no—
234#168—22no—
235#168—22no—
236C2×M16—101no—
237C22×C8—101no—
238#126—101no—
239#125C2×C3×D511yescharacteristic
240#124—51no—
241#123—101no—
242C22⋊Q8—51no—
243#121—51no—
244C4×Q8—51no—
245C4×D4—51no—
246C4×D4—101no—
247#117—101no—
248C2×C42—51no—
249#97—51no—
250#97—51no—
251#97—101no—
252#97C2×C3×D511yescharacteristic
253#97C2×C3×D511yescharacteristic
254C4×C8—101no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C3×D5—22no—
259C3×D5—81no—
260C23×C3—51no—
261C23×C3—101no—
262C3×Q8—201no—
263C3×D4—201no—
264C3×D4—202no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—51no—
270C2×C3×C4—102no—
271C2×C3×C4—102no—
272C2×C3×C4—101no—
273C2×C3×C4—201no—
274C2×C3×C4—202no—
275C2×C3×C4C2×C4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C3×C8—22no—
279C3×C8—22no—
280C3×C8—102no—
281C3×C8—102no—
282C22×C5C2×C3×C22⋊C411yescharacteristic
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—41no—
286C2×D5—41no—
287C2×D5—41no—
288C2×D5C3×#10412yes—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—41no—
293C4×C5—41no—
294Dic5—21no—
295Dic5—21no—
296Dic5—41no—
297Dic5C3×#10412yes—
298C2×Q8—51no—
299C2×D4—51no—
300C2×D4—101no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—101no—
305M16—104no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—104no—
309C2×C8—101no—
310C2×C8—101no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—101no—
314C4⋊C4—101no—
315C4⋊C4C3×C4×D511yescharacteristic
316C4⋊C4C3×C4×D511yescharacteristic
317C22⋊C4—101no—
318C22⋊C4—101no—
319C22⋊C4—101no—
320C22⋊C4—101no—
321C22⋊C4—101no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42—101no—
326C42C22×C3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—52no—
329C22×C3—101no—
330C22×C3—101no—
331C22×C3—201no—
332C22×C3—201no—
333C22×C3—201no—
334C22×C3D5×C22⋊C411yescharacteristic
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—52no—
341C3×C4—101no—
342C3×C4—101no—
343C3×C4—201no—
344C2×C5C3×#41311yescharacteristic
345C2×C5C2×C3×#10411yescharacteristic
346C2×C5C2×C3×#10411yescharacteristic
347D5—22no—
348D5—81no—
349C23—51no—
350C23—101no—
351Q8—201no—
352D4—201no—
353D4—202no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—102no—
360C2×C4—102no—
361C2×C4—101no—
362C2×C4—201no—
363C2×C4—202no—
364C2×C4C2×C3×C4×D511yescharacteristic
365C2×C4C3×D4×D511yescharacteristic
366C2×C4C3×D4×D511yescharacteristic
367C8—22no—
368C8—22no—
369C8—102no—
370C8—102no—
371C2×C3—102no—
372C2×C3—401no—
373C2×C3#6504011yescharacteristic
374C2×C3D5×#10411yescharacteristic
375C2×C3D5×#10411yescharacteristic
376C5C3×#152411yescharacteristic, complemented, Sylow
377C22—52no—
378C22—101no—
379C22—101no—
380C22—201no—
381C22—201no—
382C22—201no—
383C22C3×D5×C22⋊C411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—52no—
390C4—101no—
391C4—101no—
392C4—201no—
393C3#1059915411yescharacteristic, direct product factor, Sylow
394C2—102no—
395C2—401no—
396C2C3×#6504011yescharacteristic
397C2C3×D5×#10411yescharacteristic
398C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4041C4
cosocleC42×C5C23×C3
hypercenterC3×#330D5
hypocenterC5C3×#1524
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
2. C3×#64996C2semidirect
3. C3×D5×#97C2semidirect
4. C3×C5×#330C2semidirect
5. C3×#64763C2semidirect
6. C3×#64684C2semidirect
7. C3×#64684C2semidirect
8. #10599154C3direct (N × H)
30. #64996C2×C3semidirect
31. D5×#97C2×C3semidirect
32. C5×#330C2×C3semidirect
33. #64763C2×C3semidirect
34. #64684C2×C3semidirect
35. #64684C2×C3semidirect
69. C3×#330D5semidirect
166. #330C3×D5semidirect
327. C3×C5#1524semidirect
376. C5C3×#1524semidirect
393. C3#10599154direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660252
C3×#649962
C3×D5×#972
C3×C5×#3302
C3×#647632
C3×#646842
#105991543
C3×#15245