Finite Group Databasebeta

← C3×#10604397 #14284132

Subgroups — C3×#10604397 #14284132

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65891C211yesmaximal, characteristic
2C3×#65683C211yesmaximal, characteristic, complemented
3C3×C4×#700C211yesmaximal, characteristic, complemented
4C3×#64921C212yesmaximal, complemented
5C3×#64870C212yesmaximal, complemented
6#10604397C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#700—21no—
8C3×C4×C5×D4C411yescharacteristic
9C3×#4084C411yescharacteristic
10C3×#4082C2211yescharacteristic
11C3×C4×C22⋊D5—21no—
12C3×#4072—21no—
13C3×#4043C411yescharacteristic
14C3×#4036C2211yescharacteristic
15C3×#4029—21no—
16C3×#4025—21no—
17C3×C42×D5C2211yescharacteristic
18C3×C4×Dic10C411yescharacteristic
19C3×#4003—21no—
20C3×#4002C2212yes—
21C3×#4002C2212yes—
22C3×C4⋊#170—21no—
23C3×C4×#170—21no—
24C3×#1529—51nomaximal, Hall
25#65891C2×C311yescharacteristic
26#65683C2×C311yescharacteristic, complemented
27C4×#700C2×C311yescharacteristic, complemented
28#64921C2×C312yescomplemented
29#64870C2×C312yescomplemented
30C2×C3×C5×D4C2×C411yescharacteristic
31C22×C3×C4×C5—21no—
32C2×C3×C22⋊D5—21no—
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×Dic10C2×C411yescharacteristic
37C2×C3×#170—22no—
38C2×C3×#170—22no—
39C3×#700—24no—
40C3×C5×C4⋊C4C2×C411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2×C411yescharacteristic
43C3×C22⋊Dic5—21no—
44C3×C22⋊Dic5—21no—
45C3×C22⋊Dic5—21no—
46C3×#685—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C411yescharacteristic
50C3×#683—21no—
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5C2311yescharacteristic
56C3×#529—51no—
57C3×#432—51no—
58C3×C4×M16—51no—
59C3×#330—52no—
60C3×#329—52no—
61C2×#700—21no—
62C4×C5×D4C3×C411yescharacteristic
63#4084C3×C411yescharacteristic
64#4082C22×C311yescharacteristic
65C4×C22⋊D5—21no—
66#4072—21no—
67#4043C3×C411yescharacteristic
68#4036C22×C311yescharacteristic
69#4029—21no—
70#4025—21no—
71C42×D5C22×C311yescharacteristic
72C4×Dic10C3×C411yescharacteristic
73#4003—21no—
74#4002C22×C312yes—
75#4002C22×C312yes—
76C4⋊#170—21no—
77C4×#170—21no—
78#1529—51noSylow
79C23×C3×C5—21no—
80C22×C3×D5C22⋊C411yescharacteristic
81C3×C5×D4—41no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C3×C22⋊D5—42no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×C4×D5—22no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C3×Dic10—41no—
97C3×#170—24no—
98C3×#170—42no—
99C2×C3×M16—101no—
100C3×#126—101no—
101C3×#125—51no—
102C3×#124—51no—
103C3×#123—101no—
104C3×C22⋊Q8—51no—
105C3×#121—51no—
106C3×C4×Q8—51no—
107C3×C4×D4—101no—
108C3×C4×D4AGL(1,𝔽5)11yescharacteristic
109C3×#117—101no—
110C2×C3×C42—51no—
111C3×C4⋊C8—101no—
112C3×C22⋊C8—101no—
113C3×#97—52no—
114C3×#97—52no—
115C3×C4×C8—101no—
116C2×C5×D4C2×C3×C411yescharacteristic
117C22×C4×C5—21no—
118C2×C22⋊D5—21no—
119C2×C4×D5C2×C3×C411yescharacteristic
120C2×C4×D5C3×D411yescharacteristic
121C2×C4×D5C3×D411yescharacteristic
122C2×Dic10C2×C3×C411yescharacteristic
123C2×#170—22no—
124C2×#170—22no—
125#700—24no—
126C5×C4⋊C4C2×C3×C411yescharacteristic
127C5×C22⋊C4—21no—
128C42×C5C2×C3×C411yescharacteristic
129C22⋊Dic5—21no—
130C22⋊Dic5—21no—
131C22⋊Dic5—21no—
132#685—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5C2×C3×C411yescharacteristic
136#683—21no—
137#683—21no—
138C4×Dic5—21no—
139C4×Dic5C3×D411yescharacteristic
140C4×Dic5C3×D411yescharacteristic
141C4×Dic5C23×C311yescharacteristic
142#529—51no—
143#432—51no—
144C4×M16—51no—
145#330—52no—
146#329—52no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5#10412yes—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C2×C3×Q8—51no—
164C2×C3×D4—101no—
165C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C3×M16—104no—
171C2×C3×C8—102no—
172C2×C3×C8—102no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C22⋊C4—101no—
183C3×C22⋊C4—101no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—101no—
188C3×C42C2×AGL(1,𝔽5)11yescharacteristic
189C23×C5—21no—
190C22×D5C3×C22⋊C411yescharacteristic
191C5×D4—41no—
192C2×C4×C5—21no—
193C2×C4×C5—42no—
194C2×C4×C5C3×C22⋊C411yescharacteristic
195C2×C4×C5C3×C22⋊C411yescharacteristic
196C2×C4×C5C22×C3×C411yescharacteristic
197C22⋊D5—42no—
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5C3×C22⋊C411yescharacteristic
201C2×Dic5C2×C3×D411yescharacteristic
202C2×Dic5C2×C3×D411yescharacteristic
203C4×D5—22no—
204C4×D5—41no—
205C4×D5—41no—
206Dic10—41no—
207#170—24no—
208#170—42no—
209C2×M16—101no—
210#126—101no—
211#125—51no—
212#124—51no—
213#123—101no—
214C22⋊Q8—51no—
215#121—51no—
216C4×Q8—51no—
217C4×D4—101no—
218C4×D4C3×AGL(1,𝔽5)11yescharacteristic
219#117—101no—
220C2×C42—51no—
221C4⋊C8—101no—
222C22⋊C8—101no—
223#97—52no—
224#97—52no—
225C4×C8—101no—
226C2×C3×C5—81no—
227C2×C3×C5#41311yescharacteristic
228C2×C3×C5C2×#10411yescharacteristic
229C2×C3×C5#42111yescharacteristic
230C3×D5—41no—
231C23×C3—21no—
232C23×C3—51no—
233C3×Q8—201no—
234C3×D4—41no—
235C3×D4—202no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—102no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—201no—
245C2×C3×C4—201no—
246C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
247C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
248C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
249C3×C8—104no—
250C3×C8—202no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5C2×C3×C22⋊C411yescharacteristic
255C2×D5—21no—
256C2×D5—21no—
257C2×D5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—41no—
261C4×C5C3×#10412yes—
262Dic5—21no—
263Dic5—21no—
264Dic5—21no—
265Dic5—41no—
266Dic5—41no—
267C2×Q8—51no—
268C2×D4—101no—
269C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
270C22×C4—21no—
271C22×C4—51no—
272C22×C4—51no—
273C22×C4—51no—
274M16—104no—
275C2×C8—102no—
276C2×C8—102no—
277C4⋊C4—51no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—101no—
285C22⋊C4—101no—
286C22⋊C4—101no—
287C22⋊C4—101no—
288C42—51no—
289C42—51no—
290C42—51no—
291C42—101no—
292C42C2×C3×AGL(1,𝔽5)11yescharacteristic
293C3×C5#152911yescharacteristic, complemented, Hall
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—101no—
298C22×C3—101no—
299C22×C3—101no—
300C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—101no—
305C3×C4—101no—
306C3×C4—101no—
307C3×C4—201no—
308C3×C4—201no—
309C3×C4#400812yes—
310C2×C5—81no—
311C2×C5C3×#41311yescharacteristic
312C2×C5C2×C3×#10411yescharacteristic
313C2×C5C3×#42111yescharacteristic
314D5—41no—
315C23—21no—
316C23—51no—
317Q8—201no—
318D4—41no—
319D4—202no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—51no—
325C2×C4—102no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
331C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
332C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
333C8—104no—
334C8—202no—
335C2×C3—81no—
336C2×C3—201no—
337C2×C3#6576111yescharacteristic
338C2×C3C2×#400811yescharacteristic
339C2×C3#6579511yescharacteristic
340C5C3×#152911yescharacteristic, complemented, Sylow
341C22—41no—
342C22—41no—
343C22—41no—
344C22—101no—
345C22—101no—
346C22—101no—
347C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—101no—
352C4—101no—
353C4—101no—
354C4—201no—
355C4—201no—
356C4C3×#400812yes—
357C3#1060439711yescharacteristic, direct product factor, Sylow
358C2—81no—
359C2—201no—
360C2C3×#6576111yescharacteristic
361C2C2×C3×#400811yescharacteristic
362C2C3×#6579511yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4084C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C3×#1529
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65683C2semidirect
3. C3×C4×#700C2semidirect
4. C3×#64921C2semidirect
5. C3×#64870C2semidirect
6. #10604397C3direct (N × H)
26. #65683C2×C3semidirect
27. C4×#700C2×C3semidirect
28. #64921C2×C3semidirect
29. #64870C2×C3semidirect
293. C3×C5#1529semidirect
340. C5C3×#1529semidirect
357. C3#10604397direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658912
C3×#656832
C3×C4×#7002
C3×#649212
C3×#648702
#106043973
C3×#15295