Finite Group Databasebeta

← C3×#10604473 #14283929

Subgroups — C3×#10604473 #14283929

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 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×#4002C211yesmaximal, characteristic, complemented
4C3×#64921C212yesmaximal, complemented
5C3×#64870C212yesmaximal, complemented
6#10604473C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#704—21no—
8C22×C3×#170—21no—
9C3×C5×#121C411yescharacteristic
10C3×#4082C2211yescharacteristic
11C3×#4081—21no—
12C3×D4×Dic5—21no—
13C3×D4×Dic5C411yescharacteristic
14C3×#4070C411yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4036C2211yescharacteristic
17C3×#4033C411yescharacteristic
18C3×#4025—21no—
19C3×#4023—21no—
20C3×#4002—21no—
21C3×#4002C2212yes—
22C3×#4002C2212yes—
23C3×C4×#170—21no—
24C3×#1524—51nomaximal, Hall
25#65934C2×C311yescharacteristic
26C4×#704C2×C311yescharacteristic, complemented
27C2×#4002C2×C311yescharacteristic, complemented
28#64921C2×C312yescomplemented
29#64870C2×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—24no—
39C2×C3×#170—22no—
40C2×C3×#170—22no—
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—
58C3×C4×M16—51no—
59C2×C3×#97—51no—
60C3×#330—52no—
61C3×#329—52no—
62C2×#704—21no—
63C22×#170—21no—
64C5×#121C3×C411yescharacteristic
65#4082C22×C311yescharacteristic
66#4081—21no—
67D4×Dic5—21no—
68D4×Dic5C3×C411yescharacteristic
69#4070C3×C411yescharacteristic
70C2×C4×Dic5C22×C311yescharacteristic
71#4036C22×C311yescharacteristic
72#4033C3×C411yescharacteristic
73#4025—21no—
74#4023—21no—
75#4002—21no—
76#4002C22×C312yes—
77#4002C22×C312yes—
78C4×#170—21no—
79#1524—51noSylow
80C23×C3×C5—21no—
81C23×C3×C5C22⋊C411yescharacteristic
82C3×C5×D4—41no—
83C3×C5×D4—42no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—42no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C3×Dic10—41no—
98C3×#170—24no—
99C3×#170—24no—
100C2×C3×M16—101no—
101C22×C3×C8—101no—
102C3×#126—101no—
103C3×#125—51no—
104C3×#124—51no—
105C3×#123—101no—
106C3×C22⋊Q8—51no—
107C3×#121AGL(1,𝔽5)11yescharacteristic
108C3×C4×Q8—51no—
109C3×C4×D4—51no—
110C3×C4×D4—101no—
111C3×#117—101no—
112C2×C3×C42—51no—
113C3×#97—52no—
114C3×#97—52no—
115C3×#97—101no—
116C3×C4×C8—101no—
117C2×C5×D4—21no—
118C2×C5×D4C2×C3×C411yescharacteristic
119C22×C4×C5C2×C3×C411yescharacteristic
120C22×Dic5—21no—
121C22×Dic5C3×D411yescharacteristic
122C22×Dic5C3×D411yescharacteristic
123C2×Dic10C2×C3×C411yescharacteristic
124#704—24no—
125C2×#170—24no—
126C2×#170—22no—
127C2×#170—22no—
128C5×C4⋊C4C2×C3×C411yescharacteristic
129C5×C22⋊C4—21no—
130C22⋊Dic5—21no—
131C22⋊Dic5—21no—
132C22⋊Dic5—21no—
133C22⋊Dic5—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5C2×C3×C411yescharacteristic
136#683—21no—
137#683—21no—
138#683—21no—
139C4×Dic5—21no—
140C4×Dic5C2×C3×C411yescharacteristic
141C4×Dic5C3×D411yescharacteristic
142C4×Dic5C3×D411yescharacteristic
143C4×Dic5C23×C311yescharacteristic
144#529—51no—
145C4×M16—51no—
146C2×#97—51no—
147#330—52no—
148#329—52no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#10412yes—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5#10412yes—
165C2×C3×Q8—51no—
166C2×C3×D4—21no—
167C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—101no—
171C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
172C3×M16—104no—
173C2×C3×C8—102no—
174C2×C3×C8—102no—
175C2×C3×C8—104no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C22⋊C4—101no—
186C3×C22⋊C4—101no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42—51no—
191C3×C42—101no—
192C23×C5—21no—
193C23×C5C3×C22⋊C411yescharacteristic
194C5×D4—41no—
195C5×D4—42no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5C3×C22⋊C411yescharacteristic
199C2×C4×C5C22×C3×C411yescharacteristic
200C2×Dic5—22no—
201C2×Dic5—22no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—42no—
205C2×Dic5C3×C22⋊C411yescharacteristic
206C2×Dic5C3×C22⋊C411yescharacteristic
207C2×Dic5C2×C3×D411yescharacteristic
208C2×Dic5C2×C3×D411yescharacteristic
209Dic10—41no—
210#170—24no—
211#170—24no—
212C2×M16—101no—
213C22×C8—101no—
214#126—101no—
215#125—51no—
216#124—51no—
217#123—101no—
218C22⋊Q8—51no—
219#121C3×AGL(1,𝔽5)11yescharacteristic
220C4×Q8—51no—
221C4×D4—51no—
222C4×D4—101no—
223#117—101no—
224C2×C42—51no—
225#97—52no—
226#97—52no—
227#97—101no—
228C4×C8—101no—
229C2×C3×C5—22no—
230C2×C3×C5—81no—
231C2×C3×C5#41311yescharacteristic
232C2×C3×C5C2×#10411yescharacteristic
233C2×C3×C5C2×#10411yescharacteristic
234C23×C3—21no—
235C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
236C3×Q8—201no—
237C3×D4—41no—
238C3×D4—42no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—102no—
246C2×C3×C4—102no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—202no—
250C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
251C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
252C3×C8—104no—
253C3×C8—104no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—41no—
259C22×C5C3×#10412yes—
260C22×C5C2×C3×C22⋊C411yescharacteristic
261C4×C5—21no—
262C4×C5—21no—
263C4×C5—41no—
264Dic5—21no—
265Dic5—21no—
266Dic5—21no—
267Dic5—41no—
268Dic5—41no—
269Dic5C3×#10412yes—
270C2×Q8—51no—
271C2×D4—21no—
272C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—101no—
276C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
277M16—104no—
278C2×C8—102no—
279C2×C8—102no—
280C2×C8—104no—
281C4⋊C4—51no—
282C4⋊C4—101no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—101no—
289C22⋊C4—101no—
290C22⋊C4—101no—
291C22⋊C4—101no—
292C42—51no—
293C42—51no—
294C42—51no—
295C42—51no—
296C42—101no—
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3#400812yes—
304C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—52no—
309C3×C4—101no—
310C3×C4—101no—
311C3×C4—101no—
312C3×C4—201no—
313C3×C4—201no—
314C2×C5—22no—
315C2×C5—81no—
316C2×C5C3×#41311yescharacteristic
317C2×C5C2×C3×#10411yescharacteristic
318C2×C5C2×C3×#10411yescharacteristic
319C23—21no—
320C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
321Q8—201no—
322D4—41no—
323D4—42no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—51no—
329C2×C4—51no—
330C2×C4—102no—
331C2×C4—102no—
332C2×C4—101no—
333C2×C4—101no—
334C2×C4—202no—
335C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
336C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
337C8—104no—
338C8—104no—
339C2×C3—22no—
340C2×C3—81no—
341C2×C3C2×#400811yescharacteristic
342C2×C3#6577711yescharacteristic
343C2×C3D5⋊#10411yescharacteristic
344C5C3×#152411yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22C3×#400812yes—
351C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—52no—
356C4—101no—
357C4—101no—
358C4—101no—
359C4—201no—
360C4—201no—
361C3#1060447311yescharacteristic, direct product factor, Sylow
362C2—22no—
363C2—81no—
364C2C2×C3×#400811yescharacteristic
365C2C3×#6577711yescharacteristic
366C2C3×D5⋊#10411yescharacteristic
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×#1524
LCSG ▷ C2×C4×C5 ▷ C22×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×#4002C2semidirect
4. C3×#64921C2semidirect
5. C3×#64870C2semidirect
6. #10604473C3direct (N × H)
26. C4×#704C2×C3semidirect
27. C2×#4002C2×C3semidirect
28. #64921C2×C3semidirect
29. #64870C2×C3semidirect
297. C3×C5#1524semidirect
344. C5C3×#1524semidirect
361. C3#10604473direct (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×#40022
C3×#649212
C3×#648702
#106044733
C3×#15245