Finite Group Databasebeta

← C3×#10604440 #14282171

Subgroups — C3×#10604440 #14282171

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#713C211yesmaximal, characteristic
2C3×#65683C211yesmaximal, characteristic, complemented
3C3×#65680C211yesmaximal, characteristic, complemented
4C3×Q8⋊#170C212yesmaximal, complemented
5C3×#64871C212yesmaximal, complemented
6#10604440C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic
8C3×C4×C5×Q8C411yescharacteristic
9C3×Q8×Dic5C2211yescharacteristic
10C3×#4039—21no—
11C3×#4039C2211yescharacteristic
12C3×#4038—21no—
13C3×#4038C411yescharacteristic
14C3×C4×D20—21no—
15C3×C4×D20C411yescharacteristic
16C3×C42×D5—21no—
17C3×C42×D5C2211yescharacteristic
18C3×#4003—21no—
19C3×#4003—21no—
20C3×#4002—21no—
21C3×C4⋊#170—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170C2212yes—
24C3×#1488—51nomaximal, Hall
25C4×#713C2×C311yescharacteristic
26#65683C2×C311yescharacteristic, complemented
27#65680C2×C311yescharacteristic, complemented
28Q8⋊#170C2×C312yescomplemented
29#64871C2×C312yescomplemented
30C2×C3×C5×Q8C2×C411yescharacteristic
31C3×#713—22no—
32C3×#713—22no—
33C2×C3×D20—21no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×#170—22no—
42C2×C3×#170—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2×C411yescharacteristic
47C3×#685—21no—
48C3×#685—21no—
49C3×#685—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×C4×Dic5—21no—
53C3×C4×Dic5—21no—
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5C2311yescharacteristic
57C3×C4×#41—51no—
58C3×#432—51no—
59C3×#431—51no—
60C3×Q8⋊C8—52no—
61C3×D4⋊C8—52no—
62C2×#713C3×C411yescharacteristic
63C4×C5×Q8C3×C411yescharacteristic
64Q8×Dic5C22×C311yescharacteristic
65#4039—21no—
66#4039C22×C311yescharacteristic
67#4038—21no—
68#4038C3×C411yescharacteristic
69C4×D20—21no—
70C4×D20C3×C411yescharacteristic
71C42×D5—21no—
72C42×D5C22×C311yescharacteristic
73#4003—21no—
74#4003—21no—
75#4002—21no—
76C4⋊#170—21no—
77C4⋊#170C22×C312yes—
78C4×#170C22×C312yes—
79#1488—51noSylow
80C22×C3×D5—21no—
81C22×C3×D5C22⋊C411yescharacteristic
82C3×C5×Q8—21no—
83C3×C5×Q8M1612yes—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×Dic5—21no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×D20—24no—
94C3×D20—21no—
95C3×D20M1612yes—
96C3×C4×D5—24no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C4×D5—22no—
100C3×C4×D5—41no—
101C3×C4×D5—42no—
102C3×C4×D5—42no—
103C3×#170—42no—
104C3×#170—42no—
105C2×C3×#41—51no—
106C3×C4×Q8—51no—
107C3×C4×Q8AGL(1,𝔽5)11yescharacteristic
108C3×C4×D4—51no—
109C3×C4×D4—51no—
110C3×C4×D4—101no—
111C3×C4×D4—101no—
112C3×#117—51no—
113C3×#117—101no—
114C2×C3×C42—51no—
115C2×C3×C42—101no—
116C3×C4⋊C8—52no—
117C3×C4⋊C8—101no—
118C3×C22⋊C8—101no—
119C3×C22⋊C8—101no—
120C3×#97—101no—
121C3×C4×C8—52no—
122C2×C5×Q8C2×C3×C411yescharacteristic
123#713—22no—
124#713—22no—
125C2×D20—21no—
126C2×D20C2×C3×C411yescharacteristic
127C2×C4×D5—21no—
128C2×C4×D5—21no—
129C2×C4×D5—21no—
130C2×C4×D5C2×C3×C411yescharacteristic
131C2×C4×D5C3×D411yescharacteristic
132C2×C4×D5C3×D411yescharacteristic
133C2×#170—22no—
134C2×#170—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4C2×C3×C411yescharacteristic
137C42×C5—21no—
138C42×C5C2×C3×C411yescharacteristic
139#685—21no—
140#685—21no—
141#685—21no—
142C4⋊Dic5—21no—
143C4⋊Dic5C2×C3×C411yescharacteristic
144C4×Dic5—21no—
145C4×Dic5—21no—
146C4×Dic5C3×D411yescharacteristic
147C4×Dic5C3×D411yescharacteristic
148C4×Dic5C23×C311yescharacteristic
149C4×#41—51no—
150#432—51no—
151#431—51no—
152Q8⋊C8—52no—
153D4⋊C8—52no—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×C3×D5—21no—
156C2×C3×D5—22no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C3×C4×C5—22no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5C2×M1611yescharacteristic
166C3×C4×C5C2×M1611yescharacteristic
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5—41no—
170C3×Dic5#13512yes—
171C3×#41—102no—
172C3×#41—102no—
173C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
174C2×C3×D4—51no—
175C2×C3×D4—101no—
176C22×C3×C4—51no—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—101no—
180C22×C3×C4—101no—
181C22×C3×C4—101no—
182C2×C3×C8—102no—
183C2×C3×C8—102no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
188C3×C22⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C22⋊C4—101no—
191C3×C42—21no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—51no—
195C3×C42—101no—
196C3×C42—101no—
197C3×C42C2×AGL(1,𝔽5)11yescharacteristic
198C22×D5—21no—
199C22×D5C3×C22⋊C411yescharacteristic
200C5×Q8—21no—
201C5×Q8C3×M1612yes—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5C3×C22⋊C411yescharacteristic
205C2×C4×C5C3×C22⋊C411yescharacteristic
206C2×C4×C5C22×C3×C411yescharacteristic
207C2×Dic5—21no—
208C2×Dic5C3×C22⋊C411yescharacteristic
209C2×Dic5C2×C3×D411yescharacteristic
210C2×Dic5C2×C3×D411yescharacteristic
211D20—24no—
212D20—21no—
213D20C3×M1612yes—
214C4×D5—24no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—22no—
218C4×D5—41no—
219C4×D5—42no—
220C4×D5—42no—
221#170—42no—
222#170—42no—
223C2×#41—51no—
224C4×Q8—51no—
225C4×Q8C3×AGL(1,𝔽5)11yescharacteristic
226C4×D4—51no—
227C4×D4—51no—
228C4×D4—101no—
229C4×D4—101no—
230#117—51no—
231#117—101no—
232C2×C42—51no—
233C2×C42—101no—
234C4⋊C8—52no—
235C4⋊C8—101no—
236C22⋊C8—101no—
237C22⋊C8—101no—
238#97—101no—
239C4×C8—52no—
240C2×C3×C5#40711yescharacteristic
241C2×C3×C5#41611yescharacteristic
242C2×C3×C5#42111yescharacteristic
243C3×D5—41no—
244C3×D5—42no—
245C23×C3—51no—
246C23×C3—101no—
247C3×Q8—21no—
248C3×Q8#70012yes—
249C3×D4—52no—
250C3×D4—104no—
251C3×D4—101no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—102no—
258C2×C3×C4—104no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—201no—
263C2×C3×C4—202no—
264C2×C3×C4—202no—
265C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
266C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
268C3×C8—202no—
269C3×C8—202no—
270C22×C5C2×C3×C22⋊C411yescharacteristic
271C2×D5—21no—
272C2×D5—22no—
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—41no—
276C2×D5—41no—
277C4×C5—22no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—41no—
281C4×C5C2×C3×M1611yescharacteristic
282C4×C5C2×C3×M1611yescharacteristic
283Dic5—21no—
284Dic5—21no—
285Dic5—41no—
286Dic5C3×#13512yes—
287#41—102no—
288#41—102no—
289C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
290C2×D4—51no—
291C2×D4—101no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—101no—
296C22×C4—101no—
297C22×C4—101no—
298C2×C8—102no—
299C2×C8—102no—
300C4⋊C4—21no—
301C4⋊C4—51no—
302C4⋊C4—101no—
303C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
304C22⋊C4—101no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C42—21no—
308C42—51no—
309C42—51no—
310C42—51no—
311C42—101no—
312C42—101no—
313C42C2×C3×AGL(1,𝔽5)11yescharacteristic
314C3×C5#148811yescharacteristic, complemented, Hall
315C22×C3—101no—
316C22×C3—102no—
317C22×C3—101no—
318C22×C3—101no—
319C22×C3—201no—
320C22×C3—201no—
321C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
322C3×C4—21no—
323C3×C4—22no—
324C3×C4—21no—
325C3×C4—41no—
326C3×C4—52no—
327C3×C4—101no—
328C3×C4—101no—
329C3×C4—201no—
330C3×C4C2×#70011yescharacteristic
331C3×C4D5⋊M1611yescharacteristic
332C2×C5C3×#40711yescharacteristic
333C2×C5C3×#41611yescharacteristic
334C2×C5C3×#42111yescharacteristic
335D5—41no—
336D5—42no—
337C23—51no—
338C23—101no—
339Q8—21no—
340Q8C3×#70012yes—
341D4—52no—
342D4—104no—
343D4—101no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—102no—
350C2×C4—104no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—201no—
355C2×C4—202no—
356C2×C4—202no—
357C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
358C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
359C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
360C8—202no—
361C8—202no—
362C2×C3—201no—
363C2×C3—202no—
364C2×C3#6575611yescharacteristic
365C2×C3#6578411yescharacteristic
366C2×C3#6579411yescharacteristic
367C5C3×#148811yescharacteristic, complemented, Sylow
368C22—102no—
369C22—101no—
370C22—101no—
371C22—101no—
372C22—201no—
373C22—201no—
374C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
375C4—22no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—52no—
380C4—101no—
381C4—101no—
382C4—201no—
383C4C2×C3×#70011yescharacteristic
384C4C3×D5⋊M1611yescharacteristic
385C3#1060444011yescharacteristic, direct product factor, Sylow
386C2—201no—
387C2—202no—
388C2C3×#6575611yescharacteristic
389C2C3×#6578411yescharacteristic
390C2C3×#6579411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#713C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4×Q8AGL(1,𝔽5)
hypocenterC5C3×#1488
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65683C2semidirect
3. C3×#65680C2semidirect
4. C3×Q8⋊#170C2semidirect
5. C3×#64871C2semidirect
6. #10604440C3direct (N × H)
26. #65683C2×C3semidirect
27. #65680C2×C3semidirect
28. Q8⋊#170C2×C3semidirect
29. #64871C2×C3semidirect
314. C3×C5#1488semidirect
367. C5C3×#1488semidirect
385. C3#10604440direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×#7132
C3×#656832
C3×#656802
C3×Q8⋊#1702
C3×#648712
#106044403
C3×#14885