Finite Group Databasebeta

← C3×#10602276 #14316056

Subgroups — C3×#10602276 #14316056

Order 1920.

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

normal subgroups only

This group has 452 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
1C2×C3×D5×Q16C211yesmaximal, characteristic, complemented
2C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
3C3×#65446C211yesmaximal, characteristic
4C2×C3×#3959C211yesmaximal, characteristic, complemented
5C3×#64784C211yesmaximal, characteristic, complemented
6C3×#64727C211yesmaximal, characteristic, complemented
7C3×#64723C211yesmaximal, characteristic, complemented
8#10602276C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×C3×C5×D8C2211yescharacteristic
12C2×C3×#689—21no—
13C3×#4084—21no—
14C3×D5×Q16—22no—
15C3×D5×Q16—22no—
16C2×C3×Dic20C2211yescharacteristic
17C2×C3×C8×D5C2211yescharacteristic
18C3×C5×SD32—22no—
19C2×C3×C5×C16C2211yescharacteristic
20C3×#3964—21no—
21C3×#3959—22no—
22C3×#3950C2211yescharacteristic
23C2×C3×#672C2211yescharacteristic
24C3×#2185—51nomaximal, Hall
25C2×D5×Q16C2×C311yescharacteristic, complemented
26C2×C5×SD32C2×C311yescharacteristic, complemented
27#65446C2×C311yescharacteristic
28C2×#3959C2×C311yescharacteristic, complemented
29#64784C2×C311yescharacteristic, complemented
30#64727C2×C311yescharacteristic, complemented
31#64723C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C22⋊D5—41no—
35C3×Q8×D5—24no—
36C3×Q8×D5—42no—
37C2×C3×C4×D5—41no—
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10—21no—
40C2×C3×Dic10—41no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C3×C5×D8—21no—
44C3×C5×D8—21no—
45C2×C3×C5×C8C2311yescharacteristic
46C3×C22⋊Dic5—41no—
47C3×#689—24no—
48C3×C4⋊Dic5—21no—
49C2×C3×#168D411yescharacteristic
50C3×Dic20—21no—
51C3×Dic20D412yescomplemented
52C3×C8×D5—21no—
53C3×C8×D5—21no—
54C3×C5×C16—21no—
55C3×#672—21no—
56C22×C3×Q16—51no—
57C2×C3×SD32—51no—
58C2×C3×SD32D511yescharacteristic, complemented
59C3×#466—51no—
60C3×#358—51no—
61C3×#358—51no—
62C3×C22⋊C16—51no—
63C2×Q8×D5—21no—
64C2×C5×Q16C22×C311yescharacteristic
65C2×C5×D8C22×C311yescharacteristic
66C2×#689—21no—
67#4084—21no—
68D5×Q16—22no—
69D5×Q16—22no—
70C2×Dic20C22×C311yescharacteristic
71C2×C8×D5C22×C311yescharacteristic
72C5×SD32—22no—
73C2×C5×C16C22×C311yescharacteristic
74#3964—21no—
75#3959—22no—
76#3950C22×C311yescharacteristic
77C2×#672C22×C311yescharacteristic
78#2185—51noSylow
79C23×C3×C5—41no—
80C22×C3×D5D811yescharacteristic
81C3×C5×Q8—22no—
82C3×C5×Q8—41no—
83C3×C5×D4—41no—
84C3×C5×D4—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C3×C22⋊D5—82no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5D811yescharacteristic
91C3×C4×D5—21no—
92C3×C4×D5—21no—
93C3×C4×D5—44no—
94C3×Dic10—22no—
95C3×Dic10—44no—
96C3×Dic10—41no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C22×C3×Q8—101no—
101C2×C3×Q16—51no—
102C2×C3×Q16—101no—
103C2×C3×Q16—102no—
104C2×C3×Q16—102no—
105C2×C3×Q16C2×D511yescharacteristic
106C2×C3×D8C2×D511yescharacteristic
107C22×C3×C8—51no—
108C3×#121—101no—
109C3×SD32—22no—
110C3×SD32—102no—
111C2×C3×C16—51no—
112C2×C3×C16C2×D511yescharacteristic
113C3×#107—51no—
114C3×#102—101no—
115C2×C5×Q8—21no—
116C2×C5×D4—21no—
117C2×C22⋊D5—41no—
118Q8×D5—24no—
119Q8×D5—42no—
120C2×C4×D5—41no—
121C2×C4×D5C3×D411yescharacteristic
122C2×Dic10—21no—
123C2×Dic10—41no—
124C5×Q16—21no—
125C5×Q16C3×D412yescomplemented
126C5×D8—21no—
127C5×D8—21no—
128C2×C5×C8C23×C311yescharacteristic
129C22⋊Dic5—41no—
130#689—24no—
131C4⋊Dic5—21no—
132C2×#168C3×D411yescharacteristic
133Dic20—21no—
134Dic20C3×D412yescomplemented
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—21no—
138#672—21no—
139C22×Q16—51no—
140C2×SD32—51no—
141C2×SD32C3×D511yescharacteristic, complemented
142#466—51no—
143#358—51no—
144#358—51no—
145C22⋊C16—51no—
146C22×C3×C5—81no—
147C22×C3×C5—81no—
148C22×C3×C5—81no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5SD3212yescomplemented
153C3×C4×C5—42no—
154C3×C4×C5#12011yescharacteristic
155C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
156C3×Dic5—21no—
157C3×Dic5—42no—
158C3×Dic5—81no—
159C2×C3×Q8—21no—
160C2×C3×Q8—104no—
161C2×C3×Q8—101no—
162C2×C3×Q8—201no—
163C2×C3×Q8—202no—
164C2×C3×D4—21no—
165C2×C3×D4—201no—
166C22×C3×C4—51no—
167C22×C3×C4—201no—
168C3×Q16—21no—
169C3×Q16—52no—
170C3×Q16—104no—
171C3×Q16—101no—
172C3×Q16C22⋊D512yescomplemented
173C3×D8—21no—
174C3×D8—21no—
175C2×C3×C8—51no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C2×C3×C8C22×D511yescharacteristic
179C3×C4⋊C4—101no—
180C3×C22⋊C4—201no—
181C3×C16—21no—
182C3×C16—101no—
183C23×C5—41no—
184C22×D5C3×D811yescharacteristic
185C5×Q8—22no—
186C5×Q8—41no—
187C5×D4—41no—
188C5×D4—41no—
189C2×C4×C5—41no—
190C2×C4×C5C2×C3×D411yescharacteristic
191C22⋊D5—82no—
192C2×Dic5—41no—
193C2×Dic5—41no—
194C2×Dic5C3×D811yescharacteristic
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—44no—
198Dic10—22no—
199Dic10—44no—
200Dic10—41no—
201C5×C8C2×C3×D411yescharacteristic
202C5×C8C2×C3×D411yescharacteristic
203#168—21no—
204C22×Q8—101no—
205C2×Q16—51no—
206C2×Q16—101no—
207C2×Q16—102no—
208C2×Q16—102no—
209C2×Q16C2×C3×D511yescharacteristic
210C2×D8C2×C3×D511yescharacteristic
211C22×C8—51no—
212#121—101no—
213SD32—22no—
214SD32—102no—
215C2×C16—51no—
216C2×C16C2×C3×D511yescharacteristic
217#107—51no—
218#102—101no—
219C2×C3×C5—161no—
220C2×C3×C5#44711yescharacteristic
221C2×C3×C5C2×SD3211yescharacteristic
222C2×C3×C5#51011yescharacteristic
223C3×D5—22no—
224C23×C3—41no—
225C23×C3—51no—
226C3×Q8—22no—
227C3×Q8—41no—
228C3×Q8—102no—
229C3×Q8—204no—
230C3×Q8—201no—
231C3×D4—41no—
232C3×D4—41no—
233C3×D4—402no—
234C2×C3×C4—41no—
235C2×C3×C4—51no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—204no—
239C2×C3×C4—201no—
240C2×C3×C4—201no—
241C2×C3×C4D4×D511yescharacteristic
242C3×C8—101no—
243C3×C8D4×D511yescharacteristic
244C3×C8C2×C22⋊D511yescharacteristic
245C22×C5—81no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5C2×C3×D811yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5C3×SD3212yescomplemented
252C4×C5—42no—
253C4×C5C3×#12011yescharacteristic
254C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
255Dic5—21no—
256Dic5—42no—
257Dic5—81no—
258C2×Q8—21no—
259C2×Q8—104no—
260C2×Q8—101no—
261C2×Q8—201no—
262C2×Q8—202no—
263C2×D4—21no—
264C2×D4—201no—
265C22×C4—51no—
266C22×C4—201no—
267Q16—21no—
268Q16—52no—
269Q16—104no—
270Q16—101no—
271Q16C3×C22⋊D512yescomplemented
272D8—21no—
273D8—21no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C22×C3×D511yescharacteristic
278C4⋊C4—101no—
279C22⋊C4—201no—
280C16—21no—
281C16—101no—
282C3×C5#218511yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—81no—
287C22×C3—101no—
288C22×C3—101no—
289C22×C3D5×D811yescharacteristic
290C3×C4—42no—
291C3×C4—101no—
292C3×C4—202no—
293C3×C4—401no—
294C3×C4#405711yescharacteristic
295C3×C4#408311yescharacteristic
296C2×C5—161no—
297C2×C5C3×#44711yescharacteristic
298C2×C5C2×C3×SD3211yescharacteristic
299C2×C5C3×#51011yescharacteristic
300D5—22no—
301C23—41no—
302C23—51no—
303Q8—22no—
304Q8—41no—
305Q8—102no—
306Q8—204no—
307Q8—201no—
308D4—41no—
309D4—41no—
310D4—402no—
311C2×C4—41no—
312C2×C4—51no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—204no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4C3×D4×D511yescharacteristic
319C8—101no—
320C8C3×D4×D511yescharacteristic
321C8C2×C3×C22⋊D511yescharacteristic
322C2×C3—102no—
323C2×C3—161no—
324C2×C3D5×SD3211yescharacteristic
325C2×C3#6520411yescharacteristic
326C2×C3#6544511yescharacteristic
327C5C3×#218511yescharacteristic, complemented, Sylow
328C22—52no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—101no—
333C22—101no—
334C22C3×D5×D811yescharacteristic
335C4—42no—
336C4—101no—
337C4—202no—
338C4—401no—
339C4C3×#405711yescharacteristic
340C4C3×#408311yescharacteristic
341C3#1060227611yescharacteristic, direct product factor, Sylow
342C2—102no—
343C2—161no—
344C2C3×D5×SD3211yescharacteristic
345C2C3×#6520411yescharacteristic
346C2C3×#6544511yescharacteristic
subgroupG/H
centerC22×C3D5×D8
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×SD32C2
socleC22×C3×C5C2×D8
prime radicalC3×#65446C2
hypercenterC2×C3×SD32D5
hypocenterC5C3×#2185
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×SD32

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×Q16C2semidirect
2. C2×C3×C5×SD32C2semidirect
4. C2×C3×#3959C2semidirect
5. C3×#64784C2semidirect
6. C3×#64727C2semidirect
7. C3×#64723C2semidirect
8. #10602276C3direct (N × H)
25. C2×D5×Q16C2×C3semidirect
26. C2×C5×SD32C2×C3semidirect
28. C2×#3959C2×C3semidirect
29. #64784C2×C3semidirect
30. #64727C2×C3semidirect
31. #64723C2×C3semidirect
42. C3×C5×Q16D4semidirect
51. C3×Dic20D4semidirect
58. C2×C3×SD32D5semidirect
125. C5×Q16C3×D4semidirect
134. Dic20C3×D4semidirect
141. C2×SD32C3×D5semidirect
152. C2×C3×D5SD32semidirect
172. C3×Q16C22⋊D5semidirect
251. C2×D5C3×SD32semidirect
271. Q16C3×C22⋊D5semidirect
282. C3×C5#2185semidirect
327. C5C3×#2185semidirect
341. C3#10602276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
C2×C3×C5×SD322
C3×#654462
C2×C3×#39592
C3×#647842
C3×#647272
C3×#647232
#106022763
C3×#21855