Finite Group Databasebeta

← C3×#10599945 #14313497

Subgroups — C3×#10599945 #14313497

Order 1920.

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

normal subgroups only

This group has 540 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×#66049C211yesmaximal, characteristic
2C3×#65029C212yesmaximal, complemented
3C3×C5×#353C211yesmaximal, characteristic, complemented
4C3×#64765C211yesmaximal, characteristic, complemented
5C3×#64694C212yesmaximal, complemented
6#10599945C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#711C2211yescharacteristic
8C2×C3×D4×D5C411yescharacteristic, complemented
9C3×C5×#127C2211yescharacteristic
10C3×#4086C2211yescharacteristic
11C3×#4085—22no—
12C3×#4083—22no—
13C3×#4082C411yescharacteristic, complemented
14C3×#4023—22no—
15C3×#4021C411yescharacteristic, complemented
16C3×#4018C411yescharacteristic, complemented
17C3×C5×#99C2212yescomplemented
18C3×#3966C2212yescomplemented
19C3×#3938—22no—
20C3×#2128—51nomaximal, Hall
21#66049C2×C311yescharacteristic
22#65029C2×C312yescomplemented
23C5×#353C2×C311yescharacteristic, complemented
24#64765C2×C311yescharacteristic, complemented
25#64694C2×C312yescomplemented
26C23×C3×D5—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C5×D4C2311yescharacteristic
30C2×C3×C22⋊D5—22no—
31C2×C3×C22⋊D5—21no—
32C2×C3×C22⋊D5D412yes—
33C22×C3×Dic5D412yes—
34C3×#711—42no—
35C3×D4×D5—42no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×Dic10C2×C411yescharacteristic
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2×C411yescharacteristic
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—22no—
43C3×#685—21no—
44C3×#685—22no—
45C3×#683—21no—
46C3×#683—42no—
47C3×C4×Dic5—42no—
48C3×C4×Dic5C2×C411yescharacteristic
49C3×#535—51no—
50C3×#410—52no—
51C3×#353—51no—
52C3×#353—52no—
53C3×#353D511yescharacteristic, complemented
54C2×#711C22×C311yescharacteristic
55C2×D4×D5C3×C411yescharacteristic, complemented
56C5×#127C22×C311yescharacteristic
57#4086C22×C311yescharacteristic
58#4085—22no—
59#4083—22no—
60#4082C3×C411yescharacteristic, complemented
61#4023—22no—
62#4021C3×C411yescharacteristic, complemented
63#4018C3×C411yescharacteristic, complemented
64C5×#99C22×C312yescomplemented
65#3966C22×C312yescomplemented
66#3938—22no—
67#2128—51noSylow
68C23×C3×C5—21no—
69C23×C3×C5C2×D412yes—
70C22×C3×D5—21no—
71C22×C3×D5—42no—
72C22×C3×D5—82no—
73C22×C3×D5C22⋊C411yescharacteristic
74C3×C5×D4—41no—
75C3×C5×D4—41no—
76C3×C5×D4—82no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5C22×C411yescharacteristic
80C3×C22⋊D5—42no—
81C3×C22⋊D5—42no—
82C3×C22⋊D5—82no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—42no—
87C2×C3×Dic5C22⋊C412yes—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C3×D20—41no—
90C3×C4×D5—22no—
91C3×Dic10—41no—
92C2×C3×#41—51no—
93C22×C3×D4—51no—
94C3×#127—51no—
95C3×#127C2×D511yescharacteristic
96C3×#124—51no—
97C3×#124—51no—
98C3×#121—102no—
99C3×#120—102no—
100C3×#117—51no—
101C3×#117—102no—
102C3×#99—52no—
103C3×#99—102no—
104C3×#99C2×D512yescomplemented
105C23×D5—21no—
106C2×C5×D4—22no—
107C2×C5×D4C2×C3×C411yescharacteristic
108C2×C5×D4C23×C311yescharacteristic
109C2×C22⋊D5—22no—
110C2×C22⋊D5—21no—
111C2×C22⋊D5C3×D412yes—
112C22×Dic5C3×D412yes—
113#711—42no—
114D4×D5—42no—
115C2×D20C2×C3×C411yescharacteristic
116C2×C4×D5C2×C3×C411yescharacteristic
117C2×Dic10C2×C3×C411yescharacteristic
118C5×C22⋊C4—22no—
119C42×C5C2×C3×C411yescharacteristic
120C22⋊Dic5—22no—
121C22⋊Dic5—22no—
122#685—21no—
123#685—22no—
124#683—21no—
125#683—42no—
126C4×Dic5—42no—
127C4×Dic5C2×C3×C411yescharacteristic
128#535—51no—
129#410—52no—
130#353—51no—
131#353—52no—
132#353C3×D511yescharacteristic, complemented
133C22×C3×C5—22no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—41no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C2×C3×D5—21no—
139C2×C3×D5—41no—
140C2×C3×D5—42no—
141C2×C3×D5—41no—
142C2×C3×D5—84no—
143C3×C4×C5—21no—
144C3×C4×C5—41no—
145C3×C4×C5—82no—
146C3×Dic5—22no—
147C3×Dic5—41no—
148C3×Dic5—82no—
149C3×Dic5#9912yes—
150C24×C3—101no—
151C3×#41—202no—
152C2×C3×Q8—51no—
153C2×C3×D4—22no—
154C2×C3×D4—52no—
155C2×C3×D4—51no—
156C2×C3×D4—101no—
157C2×C3×D4—102no—
158C2×C3×D4—202no—
159C2×C3×D4C4×D511yescharacteristic
160C2×C3×D4C22×D511yescharacteristic
161C22×C3×C4—52no—
162C22×C3×C4—51no—
163C3×C4⋊C4—101no—
164C3×C4⋊C4—202no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—102no—
167C3×C22⋊C4—101no—
168C3×C22⋊C4—102no—
169C3×C22⋊C4—102no—
170C3×C42—51no—
171C3×C42—202no—
172C3×C42C4×D511yescharacteristic
173C23×C5—21no—
174C23×C5C2×C3×D412yes—
175C22×D5—21no—
176C22×D5—42no—
177C22×D5—82no—
178C22×D5C3×C22⋊C411yescharacteristic
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—82no—
182C2×C4×C5—21no—
183C2×C4×C5—42no—
184C2×C4×C5C22×C3×C411yescharacteristic
185C22⋊D5—42no—
186C22⋊D5—42no—
187C22⋊D5—82no—
188C2×Dic5—22no—
189C2×Dic5—22no—
190C2×Dic5—21no—
191C2×Dic5—42no—
192C2×Dic5C3×C22⋊C412yes—
193C2×Dic5C3×C22⋊C411yescharacteristic
194D20—41no—
195C4×D5—22no—
196Dic10—41no—
197C2×#41—51no—
198C22×D4—51no—
199#127—51no—
200#127C2×C3×D511yescharacteristic
201#124—51no—
202#124—51no—
203#121—102no—
204#120—102no—
205#117—51no—
206#117—102no—
207#99—52no—
208#99—102no—
209#99C2×C3×D512yescomplemented
210C2×C3×C5—21no—
211C2×C3×C5—42no—
212C2×C3×C5—81no—
213C2×C3×C5C2×#9911yescharacteristic
214C3×D5—41no—
215C3×D5—81no—
216C23×C3—21no—
217C23×C3—51no—
218C23×C3—101no—
219C23×C3—202no—
220C23×C3—402no—
221C23×C3D4×D512yes—
222C3×Q8—201no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—82no—
226C3×D4—201no—
227C3×D4—202no—
228C3×D4—202no—
229C3×D4—402no—
230C2×C3×C4—21no—
231C2×C3×C4—42no—
232C2×C3×C4—51no—
233C2×C3×C4—52no—
234C2×C3×C4—102no—
235C2×C3×C4—102no—
236C2×C3×C4—102no—
237C2×C3×C4—101no—
238C2×C3×C4—202no—
239C2×C3×C4C2×C4×D511yescharacteristic
240C22×C5—22no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—41no—
244C22×C5C2×C3×C22⋊C411yescharacteristic
245C2×D5—21no—
246C2×D5—41no—
247C2×D5—42no—
248C2×D5—41no—
249C2×D5—84no—
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—82no—
253Dic5—22no—
254Dic5—41no—
255Dic5—82no—
256Dic5C3×#9912yes—
257C24—101no—
258#41—202no—
259C2×Q8—51no—
260C2×D4—22no—
261C2×D4—52no—
262C2×D4—51no—
263C2×D4—101no—
264C2×D4—102no—
265C2×D4—202no—
266C2×D4C3×C4×D511yescharacteristic
267C2×D4C22×C3×D511yescharacteristic
268C22×C4—52no—
269C22×C4—51no—
270C4⋊C4—101no—
271C4⋊C4—202no—
272C22⋊C4—22no—
273C22⋊C4—102no—
274C22⋊C4—101no—
275C22⋊C4—102no—
276C22⋊C4—102no—
277C42—51no—
278C42—202no—
279C42C3×C4×D511yescharacteristic
280C3×C5#212811yescharacteristic, complemented, Hall
281C22×C3—22no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3—101no—
286C22×C3—201no—
287C22×C3—202no—
288C22×C3—201no—
289C22×C3—404no—
290C22×C3D5×C22⋊C411yescharacteristic
291C3×C4—21no—
292C3×C4—41no—
293C3×C4—52no—
294C3×C4—82no—
295C3×C4—102no—
296C3×C4—201no—
297C3×C4—402no—
298C2×C5—21no—
299C2×C5—42no—
300C2×C5—81no—
301C2×C5C2×C3×#9911yescharacteristic
302D5—41no—
303D5—81no—
304C23—21no—
305C23—51no—
306C23—101no—
307C23—202no—
308C23—402no—
309C23C3×D4×D512yes—
310Q8—201no—
311D4—41no—
312D4—41no—
313D4—82no—
314D4—201no—
315D4—202no—
316D4—202no—
317D4—402no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—51no—
321C2×C4—52no—
322C2×C4—102no—
323C2×C4—102no—
324C2×C4—102no—
325C2×C4—101no—
326C2×C4—202no—
327C2×C4C2×C3×C4×D511yescharacteristic
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—81no—
331C2×C3—201no—
332C2×C3—401no—
333C2×C3D5×#9911yescharacteristic
334C5C3×#212811yescharacteristic, complemented, Sylow
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—101no—
340C22—201no—
341C22—202no—
342C22—201no—
343C22—404no—
344C22C3×D5×C22⋊C411yescharacteristic
345C4—21no—
346C4—41no—
347C4—52no—
348C4—82no—
349C4—102no—
350C4—201no—
351C4—402no—
352C3#1059994511yescharacteristic, direct product factor, Sylow
353C2—21no—
354C2—42no—
355C2—81no—
356C2—201no—
357C2—401no—
358C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#353C2
socleC2×C3×C5C2×#99
prime radicalC3×#66049C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#353D5
hypocenterC5C3×#2128
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#353

Complements

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

NH ≅ G/Ntype
2. C3×#65029C2semidirect
3. C3×C5×#353C2semidirect
4. C3×#64765C2semidirect
5. C3×#64694C2semidirect
6. #10599945C3direct (N × H)
8. C2×C3×D4×D5C4semidirect
13. C3×#4082C4semidirect
15. C3×#4021C4semidirect
16. C3×#4018C4semidirect
17. C3×C5×#99C22semidirect
18. C3×#3966C22semidirect
22. #65029C2×C3semidirect
23. C5×#353C2×C3semidirect
24. #64765C2×C3semidirect
25. #64694C2×C3semidirect
53. C3×#353D5semidirect
55. C2×D4×D5C3×C4semidirect
60. #4082C3×C4semidirect
62. #4021C3×C4semidirect
63. #4018C3×C4semidirect
64. C5×#99C22×C3semidirect
65. #3966C22×C3semidirect
104. C3×#99C2×D5semidirect
132. #353C3×D5semidirect
209. #99C2×C3×D5semidirect
280. C3×C5#2128semidirect
334. C5C3×#2128semidirect
352. C3#10599945direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660492
C3×#650292
C3×C5×#3532
C3×#647652
C3×#646942
#105999453
C3×#21285