Finite Group Databasebeta

← C3×#10601869 #14316098

Subgroups — C3×#10601869 #14316098

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4050C211yesmaximal, characteristic, complemented
2C3×C5×#466C211yesmaximal, characteristic, complemented
3C2×C3×#3959C211yesmaximal, characteristic, complemented
4C2×C3×#3958C211yesmaximal, characteristic, complemented
5C3×C22⋊#672C211yesmaximal, characteristic, complemented
6C3×#64712C211yesmaximal, characteristic, complemented
7C3×#64711C211yesmaximal, characteristic, complemented
8#10601869C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C3×C5×#121—21no—
13C2×C3×Dic20C2211yescharacteristic
14C3×#4050—22no—
15C3×#4050—22no—
16C2×C3×D40C2211yescharacteristic
17C2×C3×#677—21no—
18C3×C5×#107C2211yescharacteristic
19C3×C5×#102—21no—
20C3×#3959—22no—
21C3×#3958—22no—
22C2×C3×#672C2211yescharacteristic
23C2×C3×#672C2211yescharacteristic
24C3×#2186—51nomaximal, Hall
25C2×#4050C2×C311yescharacteristic, complemented
26C5×#466C2×C311yescharacteristic, complemented
27C2×#3959C2×C311yescharacteristic, complemented
28C2×#3958C2×C311yescharacteristic, complemented
29C22⋊#672C2×C311yescharacteristic, complemented
30#64712C2×C311yescharacteristic, complemented
31#64711C2×C311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—41no—
34C22×C3×C4×C5D411yescharacteristic
35C2×C3×C22⋊D5—41no—
36C3×#709—24no—
37C3×#709—42no—
38C2×C3×D20—21no—
39C2×C3×C4×D5—41no—
40C2×C3×Dic10—21no—
41C3×C5×D8—21no—
42C3×C5×D8—21no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8D411yescharacteristic
46C2×C3×C5×C8C2311yescharacteristic
47C3×C5×C4⋊C4—21no—
48C3×C5×C22⋊C4—41no—
49C3×Dic20—21no—
50C3×Dic20D412yescomplemented
51C3×D40—21no—
52C3×D40D412yescomplemented
53C3×#677—24no—
54C3×#672—21no—
55C3×#672—21no—
56C2×C3×#135—51no—
57C2×C3×SD32—51no—
58C2×C3×D16—51no—
59C3×#466D511yescharacteristic, complemented
60C3×#358—51no—
61C3×#357—51no—
62C3×C22⋊C16—51no—
63C2×#709—21no—
64C2×C5×D8C22×C311yescharacteristic
65C22×C5×C8C22×C311yescharacteristic
66C5×#121—21no—
67C2×Dic20C22×C311yescharacteristic
68#4050—22no—
69#4050—22no—
70C2×D40C22×C311yescharacteristic
71C2×#677—21no—
72C5×#107C22×C311yescharacteristic
73C5×#102—21no—
74#3959—22no—
75#3958—22no—
76C2×#672C22×C311yescharacteristic
77C2×#672C22×C311yescharacteristic
78#2186—51noSylow
79C23×C3×C5—41no—
80C23×C3×C5D811yescharacteristic
81C22×C3×D5—41no—
82C3×C5×D4—41no—
83C3×C5×D4—41no—
84C3×C5×D4—82no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5D811yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C3×C22⋊D5—44no—
91C2×C3×Dic5—41no—
92C3×D20—22no—
93C3×D20—41no—
94C3×C4×D5—44no—
95C3×Dic10—22no—
96C3×Dic10—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×C3×#41—101no—
101C3×#135—102no—
102C3×#135—102no—
103C2×C3×Q16—51no—
104C2×C3×SD16—101no—
105C2×C3×D8—51no—
106C2×C3×D8C2×D511yescharacteristic
107C22×C3×C8C2×D511yescharacteristic
108C3×#121—21no—
109C3×SD32—102no—
110C3×D16—102no—
111C2×C3×C16—51no—
112C2×C3×C16—51no—
113C3×#107C2×D511yescharacteristic
114C3×#102—21no—
115C2×C5×D4—21no—
116C2×C5×D4—41no—
117C22×C4×C5C3×D411yescharacteristic
118C2×C22⋊D5—41no—
119#709—24no—
120#709—42no—
121C2×D20—21no—
122C2×C4×D5—41no—
123C2×Dic10—21no—
124C5×D8—21no—
125C5×D8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C2×C5×C8C3×D411yescharacteristic
129C2×C5×C8C23×C311yescharacteristic
130C5×C4⋊C4—21no—
131C5×C22⋊C4—41no—
132Dic20—21no—
133Dic20C3×D412yescomplemented
134D40—21no—
135D40C3×D412yescomplemented
136#677—24no—
137#672—21no—
138#672—21no—
139C2×#135—51no—
140C2×SD32—51no—
141C2×D16—51no—
142#466C3×D511yescharacteristic, complemented
143#358—51no—
144#357—51no—
145C22⋊C16—51no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5—81no—
152C22×C3×C5C2×D811yescharacteristic
153C2×C3×D5—42no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—21no—
157C3×C4×C5—81no—
158C3×C4×C5#12011yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×Dic5—42no—
161C3×#41—104no—
162C3×#41—202no—
163C2×C3×Q8—101no—
164C2×C3×D4—21no—
165C2×C3×D4—41no—
166C2×C3×D4—101no—
167C2×C3×D4—201no—
168C22×C3×C4—201no—
169C22×C3×C4C22⋊D511yescharacteristic
170C3×Q16—52no—
171C3×Q16—101no—
172C3×SD16—104no—
173C3×D8—21no—
174C3×D8—21no—
175C3×D8—52no—
176C3×D8—101no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8C22⋊D511yescharacteristic
180C2×C3×C8C22×D511yescharacteristic
181C3×C4⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C16—101no—
184C3×C16—101no—
185C23×C5—41no—
186C23×C5C3×D811yescharacteristic
187C22×D5—41no—
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—82no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5C3×D811yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C22⋊D5—44no—
197C2×Dic5—41no—
198D20—22no—
199D20—41no—
200C4×D5—44no—
201Dic10—22no—
202Dic10—41no—
203C5×C8—21no—
204C5×C8C2×C3×D411yescharacteristic
205C5×C8C2×C3×D411yescharacteristic
206C2×#41—101no—
207#135—102no—
208#135—102no—
209C2×Q16—51no—
210C2×SD16—101no—
211C2×D8—51no—
212C2×D8C2×C3×D511yescharacteristic
213C22×C8C2×C3×D511yescharacteristic
214#121—21no—
215SD32—102no—
216D16—102no—
217C2×C16—51no—
218C2×C16—51no—
219#107C2×C3×D511yescharacteristic
220#102—21no—
221C2×C3×C5—41no—
222C2×C3×C5—161no—
223C2×C3×C5#44711yescharacteristic
224C2×C3×C5#50811yescharacteristic
225C2×C3×C5#50911yescharacteristic
226C3×D5—82no—
227C23×C3—41no—
228C23×C3—201no—
229C23×C3#68611yescharacteristic
230C3×Q8—102no—
231C3×Q8—201no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—82no—
235C3×D4—102no—
236C3×D4—204no—
237C3×D4—201no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—204no—
242C2×C3×C4—201no—
243C2×C3×C4#68611yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C3×C8—21no—
246C3×C8D4×D511yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—81no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5C2×C3×D811yescharacteristic
255C2×D5—42no—
256C2×D5—81no—
257C2×D5—81no—
258C4×C5—21no—
259C4×C5—81no—
260C4×C5C3×#12011yescharacteristic
261C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
262Dic5—42no—
263#41—104no—
264#41—202no—
265C2×Q8—101no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—101no—
269C2×D4—201no—
270C22×C4—201no—
271C22×C4C3×C22⋊D511yescharacteristic
272Q16—52no—
273Q16—101no—
274SD16—104no—
275D8—21no—
276D8—21no—
277D8—52no—
278D8—101no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C3×C22⋊D511yescharacteristic
282C2×C8C22×C3×D511yescharacteristic
283C4⋊C4—21no—
284C22⋊C4—41no—
285C16—101no—
286C16—101no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—81no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3—202no—
295C22×C3—401no—
296C22×C3—401no—
297C22×C3C2×#68611yescharacteristic
298C3×C4—21no—
299C3×C4—81no—
300C3×C4—202no—
301C3×C4#408311yescharacteristic
302C3×C4#409511yescharacteristic
303C2×C5—41no—
304C2×C5—161no—
305C2×C5C3×#44711yescharacteristic
306C2×C5C3×#50811yescharacteristic
307C2×C5C3×#50911yescharacteristic
308D5—82no—
309C23—41no—
310C23—201no—
311C23C3×#68611yescharacteristic
312Q8—102no—
313Q8—201no—
314D4—41no—
315D4—41no—
316D4—82no—
317D4—102no—
318D4—204no—
319D4—201no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—204no—
324C2×C4—201no—
325C2×C4C3×#68611yescharacteristic
326C2×C4C2×C3×C22⋊D511yescharacteristic
327C8—21no—
328C8C3×D4×D511yescharacteristic
329C8C3×D4×D511yescharacteristic
330C2×C3—41no—
331C2×C3—161no—
332C2×C3—402no—
333C2×C3#6532511yescharacteristic
334C2×C3#6543611yescharacteristic
335C2×C3#6548311yescharacteristic
336C5C3×#218611yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—202no—
344C22—401no—
345C22—401no—
346C22C2×C3×#68611yescharacteristic
347C4—21no—
348C4—81no—
349C4—202no—
350C4C3×#408311yescharacteristic
351C4C3×#409511yescharacteristic
352C3#1060186911yescharacteristic, direct product factor, Sylow
353C2—41no—
354C2—161no—
355C2—402no—
356C2C3×#6532511yescharacteristic
357C2C3×#6543611yescharacteristic
358C2C3×#6548311yescharacteristic
subgroupG/H
centerC22×C3C2×#686
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#466C2
socleC22×C3×C5C2×D8
hypercenterC3×#466D5
hypocenterC5C3×#2186
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×#466

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4050C2semidirect
2. C3×C5×#466C2semidirect
3. C2×C3×#3959C2semidirect
4. C2×C3×#3958C2semidirect
5. C3×C22⋊#672C2semidirect
6. C3×#64712C2semidirect
7. C3×#64711C2semidirect
8. #10601869C3direct (N × H)
25. C2×#4050C2×C3semidirect
26. C5×#466C2×C3semidirect
27. C2×#3959C2×C3semidirect
28. C2×#3958C2×C3semidirect
29. C22⋊#672C2×C3semidirect
30. #64712C2×C3semidirect
31. #64711C2×C3semidirect
50. C3×Dic20D4semidirect
52. C3×D40D4semidirect
59. C3×#466D5semidirect
133. Dic20C3×D4semidirect
135. D40C3×D4semidirect
142. #466C3×D5semidirect
287. C3×C5#2186semidirect
336. C5C3×#2186semidirect
352. C3#10601869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40502
C3×C5×#4662
C2×C3×#39592
C2×C3×#39582
C3×C22⋊#6722
C3×#647122
C3×#647112
#106018693
C3×#21865