Finite Group Databasebeta

← C3×#10604479 #14281930

Subgroups — C3×#10604479 #14281930

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65934C211yesmaximal, characteristic
2C3×C4×#704C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊#170C211yesmaximal, characteristic, complemented
4C3×D4⋊#170C212yesmaximal, complemented
5C3×#64872C212yesmaximal, complemented
6#10604479C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#704—21no—
8C22×C3×#170—21no—
9C3×C5×#121C411yescharacteristic
10C3×#4082C411yescharacteristic
11C3×#4081—21no—
12C3×D4×Dic5—21no—
13C3×D4×Dic5C2211yescharacteristic
14C3×#4070C411yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4036C411yescharacteristic
17C3×#4033C2211yescharacteristic
18C3×#4025—21no—
19C3×#4023—21no—
20C3×#4002—21no—
21C3×C4⋊#170—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170C2212yes—
24C3×#1483—51nomaximal, Hall
25#65934C2×C311yescharacteristic
26C4×#704C2×C311yescharacteristic, complemented
27C2×C4⋊#170C2×C311yescharacteristic, complemented
28D4⋊#170C2×C312yescomplemented
29#64872C2×C312yescomplemented
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4C2×C411yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×Dic5—21no—
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×C3×Dic10C2×C411yescharacteristic
37C3×#704—24no—
38C2×C3×#170—22no—
39C2×C3×#170—22no—
40C2×C3×#170—42no—
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C22⋊Dic5—21no—
44C3×C22⋊Dic5—21no—
45C3×C22⋊Dic5—21no—
46C3×C22⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×#683—21no—
50C3×#683—21no—
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5C2311yescharacteristic
57C3×#529—51no—
58C2×C3×C4⋊C8—51no—
59C3×C4×M16—51no—
60C3×Q8⋊C8—52no—
61C3×D4⋊C8—52no—
62C2×#704—21no—
63C22×#170—21no—
64C5×#121C3×C411yescharacteristic
65#4082C3×C411yescharacteristic
66#4081—21no—
67D4×Dic5—21no—
68D4×Dic5C22×C311yescharacteristic
69#4070C3×C411yescharacteristic
70C2×C4×Dic5C22×C311yescharacteristic
71#4036C3×C411yescharacteristic
72#4033C22×C311yescharacteristic
73#4025—21no—
74#4023—21no—
75#4002—21no—
76C4⋊#170—21no—
77C4⋊#170C22×C312yes—
78C4×#170C22×C312yes—
79#1483—51noSylow
80C23×C3×C5—21no—
81C23×C3×C5C22⋊C411yescharacteristic
82C3×C5×D4—22no—
83C3×C5×D4—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—41no—
94C2×C3×Dic5—41no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×D411yescharacteristic
99C3×Dic10—22no—
100C3×#170—24no—
101C3×#170—42no—
102C2×C3×M16—101no—
103C22×C3×C8—101no—
104C3×#126—101no—
105C3×#125—51no—
106C3×#124—51no—
107C3×#123—101no—
108C3×C22⋊Q8—51no—
109C3×#121AGL(1,𝔽5)11yescharacteristic
110C3×C4×Q8—51no—
111C3×C4×D4—51no—
112C3×C4×D4—101no—
113C3×#117—101no—
114C2×C3×C42—51no—
115C3×C4⋊C8—52no—
116C3×C4⋊C8—101no—
117C3×#97—101no—
118C3×C4×C8—52no—
119C2×C5×D4—21no—
120C2×C5×D4C2×C3×C411yescharacteristic
121C22×C4×C5C2×C3×C411yescharacteristic
122C22×Dic5—21no—
123C22×Dic5C3×D411yescharacteristic
124C22×Dic5C3×D411yescharacteristic
125C2×Dic10C2×C3×C411yescharacteristic
126#704—24no—
127C2×#170—22no—
128C2×#170—22no—
129C2×#170—42no—
130C5×C4⋊C4C2×C3×C411yescharacteristic
131C5×C22⋊C4—21no—
132C22⋊Dic5—21no—
133C22⋊Dic5—21no—
134C22⋊Dic5—21no—
135C22⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5C2×C3×C411yescharacteristic
138#683—21no—
139#683—21no—
140#683—21no—
141C4×Dic5—21no—
142C4×Dic5C2×C3×C411yescharacteristic
143C4×Dic5C3×D411yescharacteristic
144C4×Dic5C3×D411yescharacteristic
145C4×Dic5C23×C311yescharacteristic
146#529—51no—
147C2×C4⋊C8—51no—
148C4×M16—51no—
149Q8⋊C8—52no—
150D4⋊C8—52no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5#10412yes—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5#13112yes—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C3×Dic5AGL(1,ℤ/8)11yescharacteristic
167C3×Dic5#13711yescharacteristic
168C2×C3×Q8—51no—
169C2×C3×D4—21no—
170C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—101no—
174C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
175C3×M16—104no—
176C2×C3×C8—102no—
177C2×C3×C8—102no—
178C2×C3×C8—202no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
185C3×C22⋊C4—21no—
186C3×C22⋊C4—101no—
187C3×C22⋊C4—101no—
188C3×C22⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—101no—
195C23×C5—21no—
196C23×C5C3×C22⋊C411yescharacteristic
197C5×D4—22no—
198C5×D4—42no—
199C2×C4×C5—22no—
200C2×C4×C5—21no—
201C2×C4×C5C3×C22⋊C411yescharacteristic
202C2×C4×C5C22×C3×C411yescharacteristic
203C2×Dic5—22no—
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—21no—
208C2×Dic5—41no—
209C2×Dic5—41no—
210C2×Dic5C3×C22⋊C411yescharacteristic
211C2×Dic5C3×C22⋊C411yescharacteristic
212C2×Dic5C2×C3×D411yescharacteristic
213C2×Dic5C2×C3×D411yescharacteristic
214Dic10—22no—
215#170—24no—
216#170—42no—
217C2×M16—101no—
218C22×C8—101no—
219#126—101no—
220#125—51no—
221#124—51no—
222#123—101no—
223C22⋊Q8—51no—
224#121C3×AGL(1,𝔽5)11yescharacteristic
225C4×Q8—51no—
226C4×D4—51no—
227C4×D4—101no—
228#117—101no—
229C2×C42—51no—
230C4⋊C8—52no—
231C4⋊C8—101no—
232#97—101no—
233C4×C8—52no—
234C2×C3×C5—22no—
235C2×C3×C5—81no—
236C2×C3×C5#40811yescharacteristic
237C2×C3×C5#41711yescharacteristic
238C2×C3×C5C2×#10411yescharacteristic
239C23×C3—21no—
240C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
241C3×Q8—102no—
242C3×D4—22no—
243C3×D4—42no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—51no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—102no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
258C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
259C3×C8—104no—
260C3×C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5C3×#10412yes—
267C22×C5C2×C3×C22⋊C411yescharacteristic
268C4×C5—21no—
269C4×C5—41no—
270C4×C5C3×#13112yes—
271Dic5—21no—
272Dic5—21no—
273Dic5—21no—
274Dic5—41no—
275Dic5—41no—
276Dic5C3×AGL(1,ℤ/8)11yescharacteristic
277Dic5C3×#13711yescharacteristic
278C2×Q8—51no—
279C2×D4—21no—
280C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—101no—
284C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
285M16—104no—
286C2×C8—102no—
287C2×C8—102no—
288C2×C8—202no—
289C4⋊C4—51no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—101no—
297C22⋊C4—101no—
298C22⋊C4—101no—
299C22⋊C4—101no—
300C42—51no—
301C42—51no—
302C42—51no—
303C42—51no—
304C42—101no—
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3#400812yes—
312C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—51no—
316C3×C4—51no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4—101no—
320C3×C4—201no—
321C3×C4—201no—
322C3×C4#413112yes—
323C2×C5—22no—
324C2×C5—81no—
325C2×C5C3×#40811yescharacteristic
326C2×C5C3×#41711yescharacteristic
327C2×C5C2×C3×#10411yescharacteristic
328C23—21no—
329C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
330Q8—102no—
331D4—22no—
332D4—42no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—51no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—102no—
342C2×C4—101no—
343C2×C4—101no—
344C2×C4—201no—
345C2×C4—201no—
346C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
347C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
348C8—104no—
349C8—202no—
350C2×C3—22no—
351C2×C3—81no—
352C2×C3C2×#400811yescharacteristic
353C2×C3#6577511yescharacteristic
354C2×C3#6579311yescharacteristic
355C5C3×#148311yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C3×#400812yes—
362C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
363C4—21no—
364C4—41no—
365C4—51no—
366C4—51no—
367C4—101no—
368C4—101no—
369C4—101no—
370C4—201no—
371C4—201no—
372C4C3×#413112yes—
373C3#1060447911yescharacteristic, direct product factor, Sylow
374C2—22no—
375C2—81no—
376C2C2×C3×#400811yescharacteristic
377C2C3×#6577511yescharacteristic
378C2C3×#6579311yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
Fitting, prime radicalC3×C5×#121C4
socleC22×C3×C5C2×C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×#121AGL(1,𝔽5)
hypocenterC5C3×#1483
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
2. C3×C4×#704C2semidirect
3. C2×C3×C4⋊#170C2semidirect
4. C3×D4⋊#170C2semidirect
5. C3×#64872C2semidirect
6. #10604479C3direct (N × H)
26. C4×#704C2×C3semidirect
27. C2×C4⋊#170C2×C3semidirect
28. D4⋊#170C2×C3semidirect
29. #64872C2×C3semidirect
305. C3×C5#1483semidirect
355. C5C3×#1483semidirect
373. C3#10604479direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659342
C3×C4×#7042
C2×C3×C4⋊#1702
C3×D4⋊#1702
C3×#648722
#106044793
C3×#14835