Finite Group Databasebeta

← C3×#10604483 #14282526

Subgroups — C3×#10604483 #14282526

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65934C211yesmaximal, characteristic
2C3×#65758C211yesmaximal, characteristic, complemented
3C3×#65748C211yesmaximal, characteristic, complemented
4C3×D4⋊#170C212yesmaximal, complemented
5C3×#64872C212yesmaximal, complemented
6#10604483C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#704—21no—
8C3×C5×#121C411yescharacteristic
9C3×#4082C411yescharacteristic
10C3×#4081—21no—
11C3×D4×Dic5—21no—
12C3×D4×Dic5C2211yescharacteristic
13C3×#4070C411yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×#4036C411yescharacteristic
16C3×#4033C2211yescharacteristic
17C3×#4025—21no—
18C3×#4023—21no—
19C3×C22⋊#170—21no—
20C3×#4004—21no—
21C3×C4⋊#170—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170C2212yes—
24C3×#1495—51nomaximal, Hall
25#65934C2×C311yescharacteristic
26#65758C2×C311yescharacteristic, complemented
27#65748C2×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—42no—
38C2×C3×#170—22no—
39C2×C3×#170—22no—
40C3×C5×C4⋊C4C2×C411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C22⋊Dic5—21no—
43C3×C22⋊Dic5—21no—
44C3×C22⋊Dic5—21no—
45C3×C22⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5C2×C411yescharacteristic
48C3×#683—21no—
49C3×#683—21no—
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5C2311yescharacteristic
56C3×#529—51no—
57C3×#431—51no—
58C3×#423—51no—
59C3×Q8⋊C8—52no—
60C3×D4⋊C8—52no—
61C2×#704—21no—
62C5×#121C3×C411yescharacteristic
63#4082C3×C411yescharacteristic
64#4081—21no—
65D4×Dic5—21no—
66D4×Dic5C22×C311yescharacteristic
67#4070C3×C411yescharacteristic
68C2×C4×Dic5C22×C311yescharacteristic
69#4036C3×C411yescharacteristic
70#4033C22×C311yescharacteristic
71#4025—21no—
72#4023—21no—
73C22⋊#170—21no—
74#4004—21no—
75C4⋊#170—21no—
76C4⋊#170C22×C312yes—
77C4×#170C22×C312yes—
78#1495—51noSylow
79C23×C3×C5—21no—
80C23×C3×C5C22⋊C411yescharacteristic
81C3×C5×D4—22no—
82C3×C5×D4—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×Dic5—21no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5—41no—
93C2×C3×Dic5—41no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C3×Dic10—22no—
99C3×#170—42no—
100C3×#170—42no—
101C2×C3×M16—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×C4⋊C8—52no—
114C3×C4⋊C8—101no—
115C3×C4⋊C8—101no—
116C3×C22⋊C8—101no—
117C3×C4×C8—52no—
118C2×C5×D4—21no—
119C2×C5×D4C2×C3×C411yescharacteristic
120C22×C4×C5C2×C3×C411yescharacteristic
121C22×Dic5—21no—
122C22×Dic5C3×D411yescharacteristic
123C22×Dic5C3×D411yescharacteristic
124C2×Dic10C2×C3×C411yescharacteristic
125#704—42no—
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—
145#431—51no—
146#423—51no—
147Q8⋊C8—52no—
148D4⋊C8—52no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5#13112yes—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5AGL(1,ℤ/8)11yescharacteristic
165C3×Dic5#13711yescharacteristic
166C2×C3×Q8—51no—
167C2×C3×D4—21no—
168C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—101no—
172C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
173C3×M16—202no—
174C2×C3×C8—102no—
175C2×C3×C8—102no—
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—22no—
195C5×D4—42no—
196C2×C4×C5—22no—
197C2×C4×C5—21no—
198C2×C4×C5C3×C22⋊C411yescharacteristic
199C2×C4×C5C22×C3×C411yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—41no—
205C2×Dic5—41no—
206C2×Dic5—41no—
207C2×Dic5C3×C22⋊C411yescharacteristic
208C2×Dic5C3×C22⋊C411yescharacteristic
209C2×Dic5C2×C3×D411yescharacteristic
210C2×Dic5C2×C3×D411yescharacteristic
211Dic10—22no—
212#170—42no—
213#170—42no—
214C2×M16—101no—
215#126—101no—
216#125—51no—
217#124—51no—
218#123—101no—
219C22⋊Q8—51no—
220#121C3×AGL(1,𝔽5)11yescharacteristic
221C4×Q8—51no—
222C4×D4—51no—
223C4×D4—101no—
224#117—101no—
225C2×C42—51no—
226C4⋊C8—52no—
227C4⋊C8—101no—
228C4⋊C8—101no—
229C22⋊C8—101no—
230C4×C8—52no—
231C2×C3×C5—41no—
232C2×C3×C5—81no—
233C2×C3×C5#40811yescharacteristic
234C2×C3×C5#41711yescharacteristic
235C2×C3×C5#42111yescharacteristic
236C23×C3—21no—
237C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
238C3×Q8—102no—
239C3×D4—22no—
240C3×D4—42no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—51no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4—201no—
254C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
255C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
256C3×C8—202no—
257C3×C8—202no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C2×C3×C22⋊C411yescharacteristic
265C4×C5—21no—
266C4×C5—41no—
267C4×C5C3×#13112yes—
268Dic5—21no—
269Dic5—21no—
270Dic5—21no—
271Dic5—41no—
272Dic5—41no—
273Dic5C3×AGL(1,ℤ/8)11yescharacteristic
274Dic5C3×#13711yescharacteristic
275C2×Q8—51no—
276C2×D4—21no—
277C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—101no—
281C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
282M16—202no—
283C2×C8—102no—
284C2×C8—102no—
285C4⋊C4—51no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—101no—
293C22⋊C4—101no—
294C22⋊C4—101no—
295C22⋊C4—101no—
296C42—51no—
297C42—51no—
298C42—51no—
299C42—51no—
300C42—101no—
301C3×C5#149511yescharacteristic, complemented, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—51no—
312C3×C4—51no—
313C3×C4—101no—
314C3×C4—101no—
315C3×C4—101no—
316C3×C4—201no—
317C3×C4—201no—
318C3×C4#413112yes—
319C2×C5—41no—
320C2×C5—81no—
321C2×C5C3×#40811yescharacteristic
322C2×C5C3×#41711yescharacteristic
323C2×C5C3×#42111yescharacteristic
324C23—21no—
325C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
326Q8—102no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—51no—
334C2×C4—51no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—201no—
340C2×C4—201no—
341C2×C4—201no—
342C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
343C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
344C8—202no—
345C8—202no—
346C2×C3—41no—
347C2×C3—81no—
348C2×C3#6576911yescharacteristic
349C2×C3#6577511yescharacteristic
350C2×C3#6579311yescharacteristic
351C5C3×#149511yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
359C4—21no—
360C4—41no—
361C4—51no—
362C4—51no—
363C4—101no—
364C4—101no—
365C4—101no—
366C4—201no—
367C4—201no—
368C4C3×#413112yes—
369C3#1060448311yescharacteristic, direct product factor, Sylow
370C2—41no—
371C2—81no—
372C2C3×#6576911yescharacteristic
373C2C3×#6577511yescharacteristic
374C2C3×#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×#1495
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×#65758C2semidirect
3. C3×#65748C2semidirect
4. C3×D4⋊#170C2semidirect
5. C3×#64872C2semidirect
6. #10604483C3direct (N × H)
26. #65758C2×C3semidirect
27. #65748C2×C3semidirect
28. D4⋊#170C2×C3semidirect
29. #64872C2×C3semidirect
301. C3×C5#1495semidirect
351. C5C3×#1495semidirect
369. C3#10604483direct (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×#657582
C3×#657482
C3×D4⋊#1702
C3×#648722
#106044833
C3×#14955