Finite Group Databasebeta

← C3×#10599950 #14313456

Subgroups — C3×#10599950 #14313456

Order 1920.

572 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66008C211yesmaximal, characteristic
2C3×D5×#99C212yesmaximal, complemented
3C3×C5×#354C211yesmaximal, characteristic, complemented
4C3×#64761C211yesmaximal, characteristic, complemented
5C3×#64694C212yesmaximal, complemented
6#10599950C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic, complemented
8C2×C3×D4×D5C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4093C411yescharacteristic, complemented
11C3×#4086C2211yescharacteristic
12C3×#4030—22no—
13C3×#4028—22no—
14C3×D5×C22⋊C4—22no—
15C3×#4020C411yescharacteristic, complemented
16C3×#4018C411yescharacteristic, complemented
17C3×C5×#99C2212yes—
18C3×#3966C2212yes—
19C3×#3938—22no—
20C3×#2127—51nomaximal, Hall
21#66008C2×C311yescharacteristic
22D5×#99C2×C312yescomplemented
23C5×#354C2×C311yescharacteristic, complemented
24#64761C2×C311yescharacteristic, complemented
25#64694C2×C312yescomplemented
26C23×C3×D5D412yes—
27C2×C3×C5×Q8C2×C411yescharacteristic, complemented
28C2×C3×C5×D4C2311yescharacteristic
29C2×C3×C22⋊D5—22no—
30C2×C3×C22⋊D5D412yes—
31C3×#713—42no—
32C3×D4×D5—42no—
33C2×C3×D20—21no—
34C2×C3×D20—22no—
35C2×C3×D20C2×C411yescharacteristic
36C2×C3×D20C2×C411yescharacteristic, complemented
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—42no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4—22no—
42C3×C42×C5C2×C411yescharacteristic, complemented
43C3×C22⋊Dic5—22no—
44C3×#685—22no—
45C3×#685—21no—
46C3×#685—42no—
47C3×#683—21no—
48C3×C4×Dic5C2×C411yescharacteristic, complemented
49C3×#535—51no—
50C2×C3×#99—52no—
51C3×#354—51no—
52C3×#354D511yescharacteristic, complemented
53C3×#353—52no—
54C2×#713C3×C411yescharacteristic, complemented
55C2×D4×D5C22×C311yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4093C3×C411yescharacteristic, complemented
58#4086C22×C311yescharacteristic
59#4030—22no—
60#4028—22no—
61D5×C22⋊C4—22no—
62#4020C3×C411yescharacteristic, complemented
63#4018C3×C411yescharacteristic, complemented
64C5×#99C22×C312yes—
65#3966C22×C312yes—
66#3938—22no—
67#2127—51noSylow
68C23×C3×C5C2×D412yes—
69C22×C3×D5—22no—
70C22×C3×D5—22no—
71C22×C3×D5—21no—
72C22×C3×D5—82no—
73C22×C3×D5C22⋊C412yes—
74C22×C3×D5C22⋊C411yescharacteristic
75C3×C5×Q8—41no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5C22×C411yescharacteristic
81C3×C22⋊D5—42no—
82C3×C22⋊D5—82no—
83C2×C3×Dic5—21no—
84C2×C3×Dic5—42no—
85C2×C3×Dic5C22⋊C411yescharacteristic
86C3×D20—41no—
87C3×D20—41no—
88C3×D20—42no—
89C3×D20—82no—
90C3×C4×D5—22no—
91C3×C4×D5—42no—
92C3×C4×D5—84no—
93C2×C3×#41—51no—
94C22×C3×D4—51no—
95C3×#127—51no—
96C3×#127—51no—
97C3×#124—51no—
98C3×#124C2×D511yescharacteristic
99C3×#121—102no—
100C3×#120—102no—
101C3×#117—51no—
102C2×C3×C22⋊C4—102no—
103C3×#99—52no—
104C3×#99—102no—
105C3×#99C2×D512yes—
106C23×D5C3×D412yes—
107C2×C5×Q8C2×C3×C411yescharacteristic, complemented
108C2×C5×D4C23×C311yescharacteristic
109C2×C22⋊D5—22no—
110C2×C22⋊D5C3×D412yes—
111#713—42no—
112D4×D5—42no—
113C2×D20—21no—
114C2×D20—22no—
115C2×D20C2×C3×C411yescharacteristic
116C2×D20C2×C3×C411yescharacteristic, complemented
117C2×C4×D5—21no—
118C2×C4×D5—42no—
119C2×C4×D5C2×C3×C411yescharacteristic
120C5×C22⋊C4—22no—
121C5×C22⋊C4—22no—
122C42×C5C2×C3×C411yescharacteristic, complemented
123C22⋊Dic5—22no—
124#685—21no—
125#685—22no—
126#685—42no—
127#683—21no—
128C4×Dic5C2×C3×C411yescharacteristic, complemented
129#535—51no—
130C2×#99—52no—
131#354—51no—
132#354C3×D511yescharacteristic, complemented
133#353—52no—
134C22×C3×C5—22no—
135C22×C3×C5—42no—
136C22×C3×C5C2×C22⋊C411yescharacteristic
137C2×C3×D5—22no—
138C2×C3×D5—41no—
139C2×C3×D5—44no—
140C2×C3×D5—42no—
141C2×C3×D5—42no—
142C2×C3×D5—41no—
143C2×C3×D5—82no—
144C2×C3×D5#9912yes—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147C3×C4×C5—41no—
148C3×C4×C5—82no—
149C3×Dic5—21no—
150C3×Dic5—41no—
151C3×Dic5—82no—
152C24×C3—52no—
153C3×#41—202no—
154C2×C3×Q8C4×D511yescharacteristic, complemented
155C2×C3×D4—52no—
156C2×C3×D4—51no—
157C2×C3×D4—51no—
158C2×C3×D4—101no—
159C2×C3×D4—102no—
160C2×C3×D4—102no—
161C2×C3×D4—202no—
162C2×C3×D4C22×D511yescharacteristic
163C22×C3×C4—51no—
164C22×C3×C4—101no—
165C22×C3×C4—202no—
166C3×C4⋊C4—101no—
167C3×C22⋊C4—22no—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—101no—
170C3×C22⋊C4—102no—
171C3×C22⋊C4—102no—
172C3×C22⋊C4—202no—
173C3×C42—51no—
174C3×C42C4×D511yescharacteristic, complemented
175C23×C5C2×C3×D412yes—
176C22×D5—22no—
177C22×D5—22no—
178C22×D5—21no—
179C22×D5—82no—
180C22×D5C3×C22⋊C412yes—
181C22×D5C3×C22⋊C411yescharacteristic
182C5×Q8—41no—
183C5×D4—41no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—42no—
187C2×C4×C5C22×C3×C411yescharacteristic
188C22⋊D5—42no—
189C22⋊D5—82no—
190C2×Dic5—21no—
191C2×Dic5—42no—
192C2×Dic5C3×C22⋊C411yescharacteristic
193D20—41no—
194D20—41no—
195D20—42no—
196D20—82no—
197C4×D5—22no—
198C4×D5—42no—
199C4×D5—84no—
200C2×#41—51no—
201C22×D4—51no—
202#127—51no—
203#127—51no—
204#124—51no—
205#124C2×C3×D511yescharacteristic
206#121—102no—
207#120—102no—
208#117—51no—
209C2×C22⋊C4—102no—
210#99—52no—
211#99—102no—
212#99C2×C3×D512yes—
213C2×C3×C5—21no—
214C2×C3×C5—42no—
215C2×C3×C5C2×#9911yescharacteristic
216C3×D5—22no—
217C3×D5—42no—
218C3×D5—81no—
219C23×C3—51no—
220C23×C3—52no—
221C23×C3—102no—
222C23×C3—102no—
223C23×C3—101no—
224C23×C3—402no—
225C23×C3D4×D512yes—
226C3×Q8—41no—
227C3×D4—41no—
228C3×D4—201no—
229C3×D4—201no—
230C3×D4—202no—
231C3×D4—202no—
232C3×D4—402no—
233C3×D4—402no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—42no—
237C2×C3×C4—51no—
238C2×C3×C4—102no—
239C2×C3×C4—101no—
240C2×C3×C4—202no—
241C2×C3×C4—202no—
242C2×C3×C4—404no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C22×C5—22no—
245C22×C5—42no—
246C22×C5C2×C3×C22⋊C411yescharacteristic
247C2×D5—22no—
248C2×D5—41no—
249C2×D5—44no—
250C2×D5—42no—
251C2×D5—42no—
252C2×D5—41no—
253C2×D5—82no—
254C2×D5C3×#9912yes—
255C4×C5—21no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—82no—
259Dic5—21no—
260Dic5—41no—
261Dic5—82no—
262C24—52no—
263#41—202no—
264C2×Q8C3×C4×D511yescharacteristic, complemented
265C2×D4—52no—
266C2×D4—51no—
267C2×D4—51no—
268C2×D4—101no—
269C2×D4—102no—
270C2×D4—102no—
271C2×D4—202no—
272C2×D4C22×C3×D511yescharacteristic
273C22×C4—51no—
274C22×C4—101no—
275C22×C4—202no—
276C4⋊C4—101no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—101no—
280C22⋊C4—102no—
281C22⋊C4—102no—
282C22⋊C4—202no—
283C42—51no—
284C42C3×C4×D511yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—22no—
287C22×C3—42no—
288C22×C3—52no—
289C22×C3—102no—
290C22×C3—201no—
291C22×C3—202no—
292C22×C3—202no—
293C22×C3—204no—
294C22×C3—201no—
295C22×C3—402no—
296C22×C3D5×C22⋊C411yescharacteristic
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—82no—
301C3×C4—101no—
302C3×C4—201no—
303C3×C4—402no—
304C2×C5—21no—
305C2×C5—42no—
306C2×C5C2×C3×#9911yescharacteristic
307D5—22no—
308D5—42no—
309D5—81no—
310C23—51no—
311C23—52no—
312C23—102no—
313C23—102no—
314C23—101no—
315C23—402no—
316C23C3×D4×D512yes—
317Q8—41no—
318D4—41no—
319D4—201no—
320D4—201no—
321D4—202no—
322D4—202no—
323D4—402no—
324D4—402no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—51no—
329C2×C4—102no—
330C2×C4—101no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4—404no—
334C2×C4C2×C3×C4×D511yescharacteristic
335C2×C3—21no—
336C2×C3—42no—
337C2×C3—102no—
338C2×C3—202no—
339C2×C3—401no—
340C2×C3D5×#9911yescharacteristic
341C5C3×#212711yescharacteristic, complemented, Sylow
342C22—22no—
343C22—42no—
344C22—52no—
345C22—102no—
346C22—201no—
347C22—202no—
348C22—202no—
349C22—204no—
350C22—201no—
351C22—402no—
352C22C3×D5×C22⋊C411yescharacteristic
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4—101no—
358C4—201no—
359C4—402no—
360C3#1059995011yescharacteristic, direct product factor, Sylow
361C2—21no—
362C2—42no—
363C2—102no—
364C2—202no—
365C2—401no—
366C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#354C2
socleC2×C3×C5C2×#99
prime radicalC3×#66008C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#354D5
hypocenterC5C3×#2127
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
2. C3×D5×#99C2semidirect
3. C3×C5×#354C2semidirect
4. C3×#64761C2semidirect
5. C3×#64694C2semidirect
6. #10599950C3direct (N × H)
7. C2×C3×#713C4semidirect
10. C3×#4093C4semidirect
15. C3×#4020C4semidirect
16. C3×#4018C4semidirect
22. D5×#99C2×C3semidirect
23. C5×#354C2×C3semidirect
24. #64761C2×C3semidirect
25. #64694C2×C3semidirect
27. C2×C3×C5×Q8C2×C4semidirect
36. C2×C3×D20C2×C4semidirect
42. C3×C42×C5C2×C4semidirect
48. C3×C4×Dic5C2×C4semidirect
52. C3×#354D5semidirect
54. C2×#713C3×C4semidirect
57. #4093C3×C4semidirect
62. #4020C3×C4semidirect
63. #4018C3×C4semidirect
107. C2×C5×Q8C2×C3×C4semidirect
116. C2×D20C2×C3×C4semidirect
122. C42×C5C2×C3×C4semidirect
128. C4×Dic5C2×C3×C4semidirect
132. #354C3×D5semidirect
154. C2×C3×Q8C4×D5semidirect
174. C3×C42C4×D5semidirect
264. C2×Q8C3×C4×D5semidirect
284. C42C3×C4×D5semidirect
285. C3×C5#2127semidirect
341. C5C3×#2127semidirect
360. C3#10599950direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660082
C3×D5×#992
C3×C5×#3542
C3×#647612
C3×#646942
#105999503
C3×#21275