Finite Group Databasebeta

← C3×#10600492 #14287961

Subgroups — C3×#10600492 #14287961

Order 1920.

616 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 106 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×#65827C211yesmaximal, characteristic
2C3×C5×#393C211yesmaximal, characteristic, complemented
3C3×#65516C212yesmaximal, complemented
4C3×#64745C211yesmaximal, characteristic, complemented
5C3×#64671C212yesmaximal, complemented
6#10600492C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×Q8C2211yescharacteristic, complemented
8C22×C3×C22⋊D5—21no—
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×#688—22no—
12C3×#4076—21no—
13C3×#4076C2212yes—
14C3×#4032—22no—
15C3×#4028—22no—
16C3×C5×#95—21no—
17C3×C5×#95C2211yescharacteristic, complemented
18C3×#3967—22no—
19C3×C22⋊#168C2212yescomplemented
20C3×#1601—51nomaximal, Hall
21#65827C2×C311yescharacteristic
22C5×#393C2×C311yescharacteristic, complemented
23#65516C2×C312yescomplemented
24#64745C2×C311yescharacteristic, complemented
25#64671C2×C312yescomplemented
26C24×C3×C5D411yescharacteristic
27C23×C3×D5—21no—
28C2×C3×C5×Q8—22no—
29C2×C3×C5×Q8—42no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C2×C3×C22⋊D5—22no—
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—42no—
37C2×C3×C22⋊D5—42no—
38C22×C3×Dic5—21no—
39C2×C3×D20—21no—
40C2×C3×D20D412yes—
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—42no—
43C3×#688—44no—
44C3×#685—22no—
45C3×#685—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D412yes—
48C2×C3×#168—22no—
49C3×#534—51no—
50C3×#448—52no—
51C3×#393D511yescharacteristic, complemented
52C3×#327—52no—
53C3×#323—51no—
54C22×C5×Q8C22×C311yescharacteristic, complemented
55C22×C22⋊D5—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4C22×C311yescharacteristic
58C2×#688—22no—
59#4076—21no—
60#4076C22×C312yes—
61#4032—22no—
62#4028—22no—
63C5×#95—21no—
64C5×#95C22×C311yescharacteristic, complemented
65#3967—22no—
66C22⋊#168C22×C312yescomplemented
67#1601—51noSylow
68C23×C3×C5—21no—
69C23×C3×C5—21no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5SD1612yescomplemented
73C23×C3×C5C2×D411yescharacteristic
74C22×C3×D5—22no—
75C22×C3×D5—42no—
76C22×C3×D5—81no—
77C22×C3×D5—81no—
78C3×C5×Q8—24no—
79C3×C5×Q8—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D412yes—
90C3×C22⋊D5—44no—
91C3×C22⋊D5—42no—
92C3×C22⋊D5—42no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—42no—
95C3×D20—42no—
96C3×D20—81no—
97C3×#168—42no—
98C22×C3×Q8C2×D511yescharacteristic, complemented
99C22×C3×D4—101no—
100C2×C3×SD16—102no—
101C3×#123—102no—
102C3×#121—52no—
103C3×#121—101no—
104C3×#120—102no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4C2×D511yescharacteristic
107C3×#103—102no—
108C3×C22⋊C8—52no—
109C3×#95—21no—
110C3×#95C2×D511yescharacteristic, complemented
111C24×C5C3×D411yescharacteristic
112C23×D5—21no—
113C2×C5×Q8—22no—
114C2×C5×Q8—42no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5C3×D411yescharacteristic
118C22×C4×C5C23×C311yescharacteristic
119C2×C22⋊D5—22no—
120C2×C22⋊D5—22no—
121C2×C22⋊D5—42no—
122C2×C22⋊D5—42no—
123C22×Dic5—21no—
124C2×D20—21no—
125C2×D20C3×D412yes—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—42no—
128#688—44no—
129#685—22no—
130#685—22no—
131C4⋊Dic5—21no—
132C4⋊Dic5C3×D412yes—
133C2×#168—22no—
134#534—51no—
135#448—52no—
136#393C3×D511yescharacteristic, complemented
137#327—52no—
138#323—51no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—22no—
142C22×C3×C5—42no—
143C22×C3×C5—41no—
144C22×C3×C5—41no—
145C22×C3×C5—81no—
146C22×C3×C5#12011yescharacteristic
147C22×C3×C5C2×SD1611yescharacteristic
148C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C3×D5—42no—
150C2×C3×D5—42no—
151C2×C3×D5—42no—
152C2×C3×D5—84no—
153C3×C4×C5—22no—
154C3×C4×C5—41no—
155C3×C4×C5—42no—
156C3×C4×C5—81no—
157C3×Dic5—42no—
158C24×C3—101no—
159C24×C3C22⋊D511yescharacteristic
160C2×C3×Q8—22no—
161C2×C3×Q8—42no—
162C2×C3×D4—52no—
163C2×C3×D4—101no—
164C2×C3×D4—102no—
165C2×C3×D4—102no—
166C2×C3×D4—202no—
167C2×C3×D4—202no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—101no—
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22×D511yescharacteristic
173C3×SD16—204no—
174C2×C3×C8—102no—
175C3×C4⋊C4—52no—
176C3×C4⋊C4—101no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—42no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—102no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5C3×SD1612yescomplemented
186C23×C5C2×C3×D411yescharacteristic
187C22×D5—22no—
188C22×D5—42no—
189C22×D5—81no—
190C22×D5—81no—
191C5×Q8—24no—
192C5×Q8—42no—
193C2×C4×C5—22no—
194C2×C4×C5—21no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5C2×C3×D412yes—
203C22⋊D5—44no—
204C22⋊D5—42no—
205C22⋊D5—42no—
206C2×Dic5—22no—
207C2×Dic5—42no—
208D20—42no—
209D20—81no—
210#168—42no—
211C22×Q8C2×C3×D511yescharacteristic, complemented
212C22×D4—101no—
213C2×SD16—102no—
214#123—102no—
215#121—52no—
216#121—101no—
217#120—102no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×C3×D511yescharacteristic
220#103—102no—
221C22⋊C8—52no—
222#95—21no—
223#95C2×C3×D511yescharacteristic, complemented
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5—42no—
227C2×C3×C5#45011yescharacteristic
228C2×C3×C5#45511yescharacteristic
229C2×C3×C5B(4,𝔽2)11yescharacteristic
230C3×D5—82no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—102no—
236C23×C3—202no—
237C23×C3—401no—
238C23×C3—401no—
239C23×C3#68812yescomplemented
240C23×C3C2×C22⋊D511yescharacteristic
241C3×Q8—24no—
242C3×Q8—42no—
243C3×D4—202no—
244C3×D4—204no—
245C3×D4—202no—
246C3×D4—202no—
247C3×D4—401no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—102no—
258C2×C3×C4—202no—
259C2×C3×C4D4×D512yes—
260C3×C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—22no—
264C22×C5—42no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5C3×#12011yescharacteristic
269C22×C5C2×C3×SD1611yescharacteristic
270C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
271C2×D5—42no—
272C2×D5—42no—
273C2×D5—42no—
274C2×D5—84no—
275C4×C5—22no—
276C4×C5—41no—
277C4×C5—42no—
278C4×C5—81no—
279Dic5—42no—
280C24—101no—
281C24C3×C22⋊D511yescharacteristic
282C2×Q8—22no—
283C2×Q8—42no—
284C2×D4—52no—
285C2×D4—101no—
286C2×D4—102no—
287C2×D4—102no—
288C2×D4—202no—
289C2×D4—202no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—101no—
293C22×C4C3×C22⋊D511yescharacteristic
294C22×C4C22×C3×D511yescharacteristic
295SD16—204no—
296C2×C8—102no—
297C4⋊C4—52no—
298C4⋊C4—101no—
299C22⋊C4—22no—
300C22⋊C4—42no—
301C22⋊C4—102no—
302C22⋊C4—102no—
303C3×C5#160111yescharacteristic, complemented, Hall
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—22no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—81no—
311C22×C3—202no—
312C22×C3—202no—
313C22×C3—202no—
314C22×C3—404no—
315C22×C3#408311yescharacteristic
316C22×C3C2×#68811yescharacteristic
317C22×C3#409511yescharacteristic
318C3×C4—22no—
319C3×C4—42no—
320C3×C4—41no—
321C3×C4—81no—
322C3×C4—202no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—42no—
326C2×C5C3×#45011yescharacteristic
327C2×C5C3×#45511yescharacteristic
328C2×C5C3×B(4,𝔽2)11yescharacteristic
329D5—82no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—102no—
335C23—202no—
336C23—401no—
337C23—401no—
338C23C3×#68812yescomplemented
339C23C2×C3×C22⋊D511yescharacteristic
340Q8—24no—
341Q8—42no—
342D4—202no—
343D4—204no—
344D4—202no—
345D4—202no—
346D4—401no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—102no—
357C2×C4—202no—
358C2×C4C3×D4×D512yes—
359C8—202no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—402no—
364C2×C3#6532111yescharacteristic
365C2×C3#6533511yescharacteristic
366C2×C3#6535011yescharacteristic
367C5C3×#160111yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—22no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—202no—
376C22—202no—
377C22—202no—
378C22—404no—
379C22C3×#408311yescharacteristic
380C22C2×C3×#68811yescharacteristic
381C22C3×#409511yescharacteristic
382C4—22no—
383C4—42no—
384C4—41no—
385C4—81no—
386C4—202no—
387C3#1060049211yescharacteristic, direct product factor, Sylow
388C2—21no—
389C2—21no—
390C2—42no—
391C2—402no—
392C2C3×#6532111yescharacteristic
393C2C3×#6533511yescharacteristic
394C2C3×#6535011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#393C2
socleC22×C3×C5#120
prime radicalC3×#65827C2
hypercenterC3×#393D5
hypocenterC5C3×#1601
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#393

Complements

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

NH ≅ G/Ntype
2. C3×C5×#393C2semidirect
3. C3×#65516C2semidirect
4. C3×#64745C2semidirect
5. C3×#64671C2semidirect
6. #10600492C3direct (N × H)
7. C22×C3×C5×Q8C22semidirect
17. C3×C5×#95C22semidirect
19. C3×C22⋊#168C22semidirect
22. C5×#393C2×C3semidirect
23. #65516C2×C3semidirect
24. #64745C2×C3semidirect
25. #64671C2×C3semidirect
51. C3×#393D5semidirect
54. C22×C5×Q8C22×C3semidirect
64. C5×#95C22×C3semidirect
66. C22⋊#168C22×C3semidirect
72. C23×C3×C5SD16semidirect
98. C22×C3×Q8C2×D5semidirect
110. C3×#95C2×D5semidirect
136. #393C3×D5semidirect
185. C23×C5C3×SD16semidirect
211. C22×Q8C2×C3×D5semidirect
223. #95C2×C3×D5semidirect
239. C23×C3#688semidirect
303. C3×C5#1601semidirect
338. C23C3×#688semidirect
367. C5C3×#1601semidirect
387. C3#10600492direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658272
C3×C5×#3932
C3×#655162
C3×#647452
C3×#646712
#106004923
C3×#16015