Finite Group Databasebeta

← C3×#10604441 #14282234

Subgroups — C3×#10604441 #14282234

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#713C211yesmaximal, characteristic
2C3×#65681C211yesmaximal, characteristic, complemented
3C3×C4×#700C211yesmaximal, characteristic, complemented
4C3×Q8⋊#170C212yesmaximal, complemented
5C3×#64871C212yesmaximal, complemented
6#10604441C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C411yescharacteristic
8C2×C3×#700—21no—
9C2×C3×#700—21no—
10C3×C4×C5×Q8C411yescharacteristic
11C3×Q8×Dic5C2211yescharacteristic
12C3×#4039—21no—
13C3×#4039C2211yescharacteristic
14C3×#4038—21no—
15C3×#4038C411yescharacteristic
16C3×C4×D20—21no—
17C3×C4×D20C411yescharacteristic
18C3×C42×D5—21no—
19C3×C42×D5C2211yescharacteristic
20C3×#4002—21no—
21C3×C4⋊#170—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170C2212yes—
24C3×#1489—51nomaximal, Hall
25C4×#713C2×C311yescharacteristic
26#65681C2×C311yescharacteristic, complemented
27C4×#700C2×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×#700—24no—
44C3×#700—42no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2×C411yescharacteristic
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×C4×Dic5—21no—
55C3×C4×Dic5—21no—
56C3×C4×Dic5D411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5C2311yescharacteristic
59C3×C4×#41—51no—
60C3×#423—51no—
61C3×C4×M16—51no—
62C3×Q8⋊C8—52no—
63C3×D4⋊C8—52no—
64C2×#713C3×C411yescharacteristic
65C2×#700—21no—
66C2×#700—21no—
67C4×C5×Q8C3×C411yescharacteristic
68Q8×Dic5C22×C311yescharacteristic
69#4039—21no—
70#4039C22×C311yescharacteristic
71#4038—21no—
72#4038C3×C411yescharacteristic
73C4×D20—21no—
74C4×D20C3×C411yescharacteristic
75C42×D5—21no—
76C42×D5C22×C311yescharacteristic
77#4002—21no—
78C4⋊#170—21no—
79C4⋊#170C22×C312yes—
80C4×#170C22×C312yes—
81#1489—51noSylow
82C22×C3×D5—21no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×Q8—21no—
85C3×C5×Q8M1612yescomplemented
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×Dic5—21no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C3×D20—24no—
96C3×D20—21no—
97C3×D20M1612yescomplemented
98C3×C4×D5—24no—
99C3×C4×D5—22no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×C4×D5—21no—
104C3×C4×D5—42no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×#170—24no—
108C3×#170—42no—
109C2×C3×#41—51no—
110C2×C3×M16—101no—
111C2×C3×M16—101no—
112C3×C4×Q8—51no—
113C3×C4×Q8AGL(1,𝔽5)11yescharacteristic
114C3×C4×D4—51no—
115C3×C4×D4—51no—
116C3×C4×D4—101no—
117C3×C4×D4—101no—
118C3×#117—51no—
119C3×#117—101no—
120C2×C3×C42—51no—
121C2×C3×C42—101no—
122C3×C4⋊C8—52no—
123C3×C4⋊C8—101no—
124C3×#97—101no—
125C3×C4×C8—52no—
126C2×C5×Q8C2×C3×C411yescharacteristic
127#713—22no—
128#713—22no—
129C2×D20—21no—
130C2×D20C2×C3×C411yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—21no—
133C2×C4×D5—21no—
134C2×C4×D5C2×C3×C411yescharacteristic
135C2×C4×D5C3×D411yescharacteristic
136C2×C4×D5C3×D411yescharacteristic
137C2×#170—22no—
138C2×#170—22no—
139#700—24no—
140#700—42no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4C2×C3×C411yescharacteristic
143C42×C5—21no—
144C42×C5C2×C3×C411yescharacteristic
145#685—21no—
146#685—21no—
147#685—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5C2×C3×C411yescharacteristic
150C4×Dic5—21no—
151C4×Dic5—21no—
152C4×Dic5C3×D411yescharacteristic
153C4×Dic5C3×D411yescharacteristic
154C4×Dic5C23×C311yescharacteristic
155C4×#41—51no—
156#423—51no—
157C4×M16—51no—
158Q8⋊C8—52no—
159D4⋊C8—52no—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C2×C3×D5—21no—
162C2×C3×D5—22no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C3×C4×C5—22no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5#10412yes—
171C3×C4×C5C2×M1611yescharacteristic
172C3×C4×C5C2×M1611yescharacteristic
173C3×Dic5—21no—
174C3×Dic5—21no—
175C3×Dic5—41no—
176C3×Dic5AGL(1,ℤ/8)11yescharacteristic
177C3×Dic5#13711yescharacteristic
178C3×#41—102no—
179C3×#41—102no—
180C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
181C2×C3×D4—51no—
182C2×C3×D4—101no—
183C22×C3×C4—51no—
184C22×C3×C4—51no—
185C22×C3×C4—51no—
186C22×C3×C4—101no—
187C22×C3×C4—101no—
188C22×C3×C4—101no—
189C3×M16—104no—
190C3×M16—202no—
191C2×C3×C8—102no—
192C2×C3×C8—102no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
197C3×C22⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C22⋊C4—101no—
200C3×C42—21no—
201C3×C42—51no—
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—101no—
205C3×C42—101no—
206C3×C42C2×AGL(1,𝔽5)11yescharacteristic
207C22×D5—21no—
208C22×D5C3×C22⋊C411yescharacteristic
209C5×Q8—21no—
210C5×Q8C3×M1612yescomplemented
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5C3×C22⋊C411yescharacteristic
214C2×C4×C5C3×C22⋊C411yescharacteristic
215C2×C4×C5C22×C3×C411yescharacteristic
216C2×Dic5—21no—
217C2×Dic5C3×C22⋊C411yescharacteristic
218C2×Dic5C2×C3×D411yescharacteristic
219C2×Dic5C2×C3×D411yescharacteristic
220D20—24no—
221D20—21no—
222D20C3×M1612yescomplemented
223C4×D5—24no—
224C4×D5—22no—
225C4×D5—21no—
226C4×D5—21no—
227C4×D5—21no—
228C4×D5—21no—
229C4×D5—42no—
230C4×D5—41no—
231C4×D5—41no—
232#170—24no—
233#170—42no—
234C2×#41—51no—
235C2×M16—101no—
236C2×M16—101no—
237C4×Q8—51no—
238C4×Q8C3×AGL(1,𝔽5)11yescharacteristic
239C4×D4—51no—
240C4×D4—51no—
241C4×D4—101no—
242C4×D4—101no—
243#117—51no—
244#117—101no—
245C2×C42—51no—
246C2×C42—101no—
247C4⋊C8—52no—
248C4⋊C8—101no—
249#97—101no—
250C4×C8—52no—
251C2×C3×C5#40711yescharacteristic
252C2×C3×C5#41711yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C3×D5—41no—
255C3×D5—42no—
256C23×C3—51no—
257C23×C3—101no—
258C3×Q8—21no—
259C3×Q8#70012yescomplemented
260C3×D4—52no—
261C3×D4—104no—
262C3×D4—101no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—101no—
269C2×C3×C4—101no—
270C2×C3×C4—104no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—102no—
274C2×C3×C4—101no—
275C2×C3×C4—201no—
276C2×C3×C4—201no—
277C2×C3×C4—202no—
278C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
279C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
280C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
281C3×C8—104no—
282C3×C8—202no—
283C22×C5C2×C3×C22⋊C411yescharacteristic
284C2×D5—21no—
285C2×D5—22no—
286C2×D5—21no—
287C2×D5—21no—
288C2×D5—41no—
289C2×D5—41no—
290C4×C5—22no—
291C4×C5—21no—
292C4×C5—41no—
293C4×C5C3×#10412yes—
294C4×C5C2×C3×M1611yescharacteristic
295C4×C5C2×C3×M1611yescharacteristic
296Dic5—21no—
297Dic5—21no—
298Dic5—41no—
299Dic5C3×AGL(1,ℤ/8)11yescharacteristic
300Dic5C3×#13711yescharacteristic
301#41—102no—
302#41—102no—
303C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
304C2×D4—51no—
305C2×D4—101no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—51no—
309C22×C4—101no—
310C22×C4—101no—
311C22×C4—101no—
312M16—104no—
313M16—202no—
314C2×C8—102no—
315C2×C8—102no—
316C4⋊C4—21no—
317C4⋊C4—51no—
318C4⋊C4—101no—
319C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
320C22⋊C4—101no—
321C22⋊C4—101no—
322C22⋊C4—101no—
323C42—21no—
324C42—51no—
325C42—51no—
326C42—51no—
327C42—101no—
328C42—101no—
329C42C2×C3×AGL(1,𝔽5)11yescharacteristic
330C3×C5#148911yescharacteristic, complemented, Hall
331C22×C3—101no—
332C22×C3—102no—
333C22×C3—101no—
334C22×C3—101no—
335C22×C3—201no—
336C22×C3—201no—
337C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
338C3×C4—21no—
339C3×C4—22no—
340C3×C4—41no—
341C3×C4—51no—
342C3×C4—51no—
343C3×C4—101no—
344C3×C4—101no—
345C3×C4—201no—
346C3×C4#401012yes—
347C3×C4C2×#70011yescharacteristic
348C3×C4D5⋊M1611yescharacteristic
349C2×C5C3×#40711yescharacteristic
350C2×C5C3×#41711yescharacteristic
351C2×C5C2×C3×#10411yescharacteristic
352D5—41no—
353D5—42no—
354C23—51no—
355C23—101no—
356Q8—21no—
357Q8C3×#70012yescomplemented
358D4—52no—
359D4—104no—
360D4—101no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—104no—
369C2×C4—101no—
370C2×C4—101no—
371C2×C4—102no—
372C2×C4—101no—
373C2×C4—201no—
374C2×C4—201no—
375C2×C4—202no—
376C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
377C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
378C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
379C8—104no—
380C8—202no—
381C2×C3—201no—
382C2×C3—202no—
383C2×C3#6575611yescharacteristic
384C2×C3C2×#401011yescharacteristic
385C2×C3#6579311yescharacteristic
386C5C3×#148911yescharacteristic, complemented, Sylow
387C22—102no—
388C22—101no—
389C22—101no—
390C22—101no—
391C22—201no—
392C22—201no—
393C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
394C4—22no—
395C4—21no—
396C4—41no—
397C4—51no—
398C4—51no—
399C4—101no—
400C4—101no—
401C4—201no—
402C4C3×#401012yes—
403C4C2×C3×#70011yescharacteristic
404C4C3×D5⋊M1611yescharacteristic
405C3#1060444111yescharacteristic, direct product factor, Sylow
406C2—201no—
407C2—202no—
408C2C3×#6575611yescharacteristic
409C2C2×C3×#401011yescharacteristic
410C2C3×#6579311yescharacteristic
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×#1489
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×#65681C2semidirect
3. C3×C4×#700C2semidirect
4. C3×Q8⋊#170C2semidirect
5. C3×#64871C2semidirect
6. #10604441C3direct (N × H)
26. #65681C2×C3semidirect
27. C4×#700C2×C3semidirect
28. Q8⋊#170C2×C3semidirect
29. #64871C2×C3semidirect
85. C3×C5×Q8M16semidirect
97. C3×D20M16semidirect
210. C5×Q8C3×M16semidirect
222. D20C3×M16semidirect
259. C3×Q8#700semidirect
330. C3×C5#1489semidirect
357. Q8C3×#700semidirect
386. C5C3×#1489semidirect
405. C3#10604441direct (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×#656812
C3×C4×#7002
C3×Q8⋊#1702
C3×#648712
#106044413
C3×#14895