Finite Group Databasebeta

← C3×#10601884 #14316341

Subgroups — C3×#10601884 #14316341

Order 1920.

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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×#66082C211yesmaximal, characteristic
2C3×C5×#470C211yesmaximal, characteristic, complemented
3C3×#65468C212yesmaximal, complemented
4C3×#64773C211yesmaximal, characteristic, complemented
5C3×#64708C212yesmaximal, complemented
6#10601884C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709—21no—
8C2×C3×C5×Q16C2211yescharacteristic, complemented
9C2×C3×C5×M16C2211yescharacteristic
10C3×C5×C22⋊Q8—21no—
11C3×#4055—22no—
12C3×#4054—22no—
13C3×#4050—21no—
14C3×#4050C2212yes—
15C3×C5×#106C2211yescharacteristic, complemented
16C3×C5×#103—21no—
17C3×#3961—22no—
18C3×#3960—22no—
19C3×#3944C2212yescomplemented
20C3×#2191—51nomaximal, Hall
21#66082C2×C311yescharacteristic
22C5×#470C2×C311yescharacteristic, complemented
23#65468C2×C312yescomplemented
24#64773C2×C311yescharacteristic, complemented
25#64708C2×C312yescomplemented
26C2×C3×C5×Q8—21no—
27C22×C3×C4×C5D411yescharacteristic
28C2×C3×C22⋊D5—41no—
29C3×#709—22no—
30C3×#709—22no—
31C3×#709—41no—
32C3×#709—41no—
33C2×C3×D20—21no—
34C2×C3×C4×D5—41no—
35C2×C3×Dic10—21no—
36C3×C5×Q16—22no—
37C3×C5×M16—22no—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8C2311yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—41no—
42C3×C5×C22⋊C4—41no—
43C3×Dic20—21no—
44C3×Dic20D412yes—
45C3×D40—21no—
46C3×D40D412yes—
47C3×#677—22no—
48C3×#677—22no—
49C3×#672—22no—
50C3×#575—51no—
51C3×#510—52no—
52C3×#470D511yescharacteristic, complemented
53C3×#360—52no—
54C3×#349—51no—
55C2×#709—21no—
56C2×C5×Q16C22×C311yescharacteristic, complemented
57C2×C5×M16C22×C311yescharacteristic
58C5×C22⋊Q8—21no—
59#4055—22no—
60#4054—22no—
61#4050—21no—
62#4050C22×C312yes—
63C5×#106C22×C311yescharacteristic, complemented
64C5×#103—21no—
65#3961—22no—
66#3960—22no—
67#3944C22×C312yescomplemented
68#2191—51noSylow
69C23×C3×C5D811yescharacteristic
70C22×C3×D5—41no—
71C3×C5×Q8—41no—
72C3×C5×Q8—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5D811yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C3×C22⋊D5—42no—
80C3×C22⋊D5—42no—
81C2×C3×Dic5—41no—
82C3×D20—22no—
83C3×D20—41no—
84C3×C4×D5—42no—
85C3×C4×D5—42no—
86C3×Dic10—22no—
87C3×Dic10—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×C3×#41—101no—
91C3×#137—102no—
92C3×AGL(1,ℤ/8)—102no—
93C3×#135—52no—
94C3×#135—101no—
95C2×C3×Q16C2×D511yescharacteristic, complemented
96C2×C3×M16C2×D511yescharacteristic
97C3×C22⋊Q8—21no—
98C3×Q32—102no—
99C3×SD32—102no—
100C3×M32—52no—
101C3×#106C2×D511yescharacteristic, complemented
102C3×#103—21no—
103C2×C5×Q8—21no—
104C22×C4×C5C3×D411yescharacteristic
105C2×C22⋊D5—41no—
106#709—22no—
107#709—22no—
108#709—41no—
109#709—41no—
110C2×D20—21no—
111C2×C4×D5—41no—
112C2×Dic10—21no—
113C5×Q16—22no—
114C5×M16—22no—
115C2×C5×C8C3×D411yescharacteristic
116C2×C5×C8C23×C311yescharacteristic
117C5×C4⋊C4—21no—
118C5×C4⋊C4—41no—
119C5×C22⋊C4—41no—
120Dic20—21no—
121Dic20C3×D412yes—
122D40—21no—
123D40C3×D412yes—
124#677—22no—
125#677—22no—
126#672—22no—
127#575—51no—
128#510—52no—
129#470C3×D511yescharacteristic, complemented
130#360—52no—
131#349—51no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×C3×D5—42no—
136C2×C3×D5—82no—
137C3×C4×C5—21no—
138C3×C4×C5—81no—
139C3×C4×C5—81no—
140C3×C4×C5#12011yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C3×Dic5—42no—
143C3×#41—102no—
144C3×#41—102no—
145C3×#41—201no—
146C3×#41—201no—
147C2×C3×Q8—21no—
148C2×C3×Q8—101no—
149C2×C3×D4—101no—
150C2×C3×D4—201no—
151C22×C3×C4—201no—
152C22×C3×C4C22⋊D511yescharacteristic
153C3×Q16—22no—
154C3×Q16—52no—
155C3×Q16—101no—
156C3×SD16—102no—
157C3×SD16—102no—
158C3×D8—52no—
159C3×D8—101no—
160C3×M16—22no—
161C2×C3×C8C22⋊D511yescharacteristic
162C2×C3×C8C22×D511yescharacteristic
163C3×C4⋊C4—21no—
164C3×C4⋊C4—41no—
165C3×C22⋊C4—41no—
166C3×C16—102no—
167C23×C5C3×D811yescharacteristic
168C22×D5—41no—
169C5×Q8—41no—
170C5×Q8—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5C3×D811yescharacteristic
176C2×C4×C5C2×C3×D411yescharacteristic
177C22⋊D5—42no—
178C22⋊D5—42no—
179C2×Dic5—41no—
180D20—22no—
181D20—41no—
182C4×D5—42no—
183C4×D5—42no—
184Dic10—22no—
185Dic10—41no—
186C5×C8—21no—
187C5×C8C2×C3×D412yes—
188C2×#41—101no—
189#137—102no—
190AGL(1,ℤ/8)—102no—
191#135—52no—
192#135—101no—
193C2×Q16C2×C3×D511yescharacteristic, complemented
194C2×M16C2×C3×D511yescharacteristic
195C22⋊Q8—21no—
196Q32—102no—
197SD32—102no—
198M32—52no—
199#106C2×C3×D511yescharacteristic, complemented
200#103—21no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204C3×D5—82no—
205C23×C3—201no—
206C23×C3#68611yescharacteristic
207C3×Q8—41no—
208C3×Q8—41no—
209C3×Q8—102no—
210C3×Q8—201no—
211C3×D4—102no—
212C3×D4—201no—
213C3×D4—202no—
214C3×D4—202no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—202no—
220C2×C3×C4—201no—
221C2×C3×C4—202no—
222C2×C3×C4#68611yescharacteristic
223C2×C3×C4C2×C22⋊D511yescharacteristic
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×C3×D811yescharacteristic
229C2×D5—42no—
230C2×D5—82no—
231C4×C5—21no—
232C4×C5—81no—
233C4×C5—81no—
234C4×C5C3×#12011yescharacteristic
235C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
236Dic5—42no—
237#41—102no—
238#41—102no—
239#41—201no—
240#41—201no—
241C2×Q8—21no—
242C2×Q8—101no—
243C2×D4—101no—
244C2×D4—201no—
245C22×C4—201no—
246C22×C4C3×C22⋊D511yescharacteristic
247Q16—22no—
248Q16—52no—
249Q16—101no—
250SD16—102no—
251SD16—102no—
252D8—52no—
253D8—101no—
254M16—22no—
255C2×C8C3×C22⋊D511yescharacteristic
256C2×C8C22×C3×D511yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—41no—
259C22⋊C4—41no—
260C16—102no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—202no—
265C22×C3—402no—
266C22×C3C2×#68611yescharacteristic
267C3×C4—21no—
268C3×C4—81no—
269C3×C4—81no—
270C3×C4—202no—
271C3×C4#408311yescharacteristic
272C3×C4#409511yescharacteristic
273C2×C5—21no—
274C2×C5—41no—
275C2×C5C3×#44711yescharacteristic
276D5—82no—
277C23—201no—
278C23C3×#68611yescharacteristic
279Q8—41no—
280Q8—41no—
281Q8—102no—
282Q8—201no—
283D4—102no—
284D4—201no—
285D4—202no—
286D4—202no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—202no—
292C2×C4—201no—
293C2×C4—202no—
294C2×C4C3×#68611yescharacteristic
295C2×C4C2×C3×C22⋊D511yescharacteristic
296C8—21no—
297C8C3×D4×D512yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—402no—
301C2×C3#6532511yescharacteristic
302C5C3×#219111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—202no—
306C22—402no—
307C22C2×C3×#68611yescharacteristic
308C4—21no—
309C4—81no—
310C4—81no—
311C4—202no—
312C4C3×#408311yescharacteristic
313C4C3×#409511yescharacteristic
314C3#1060188411yescharacteristic, direct product factor, Sylow
315C2—21no—
316C2—41no—
317C2—402no—
318C2C3×#6532511yescharacteristic
subgroupG/H
centerC2×C3#65325
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#470C2
socleC2×C3×C5#447
prime radicalC3×#66082C2
hypercenterC3×#470D5
hypocenterC5C3×#2191
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×M16 ◁ C3×#470

Complements

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

NH ≅ G/Ntype
2. C3×C5×#470C2semidirect
3. C3×#65468C2semidirect
4. C3×#64773C2semidirect
5. C3×#64708C2semidirect
6. #10601884C3direct (N × H)
8. C2×C3×C5×Q16C22semidirect
15. C3×C5×#106C22semidirect
19. C3×#3944C22semidirect
22. C5×#470C2×C3semidirect
23. #65468C2×C3semidirect
24. #64773C2×C3semidirect
25. #64708C2×C3semidirect
52. C3×#470D5semidirect
56. C2×C5×Q16C22×C3semidirect
63. C5×#106C22×C3semidirect
67. #3944C22×C3semidirect
95. C2×C3×Q16C2×D5semidirect
101. C3×#106C2×D5semidirect
129. #470C3×D5semidirect
193. C2×Q16C2×C3×D5semidirect
199. #106C2×C3×D5semidirect
261. C3×C5#2191semidirect
302. C5C3×#2191semidirect
314. C3#10601884direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660822
C3×C5×#4702
C3×#654682
C3×#647732
C3×#647082
#106018843
C3×#21915