Finite Group Databasebeta

← C3×#10602539 #14283920

Subgroups — C3×#10602539 #14283920

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×C5×#529C211yesmaximal, characteristic
2C3×C4×#681C211yesmaximal, characteristic, complemented
3C2×C3×#3935C211yesmaximal, characteristic, complemented
4C3×#64763C212yesmaximal, complemented
5C3×#64760C212yesmaximal, complemented
6#10602539C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×#126—21no—
8C3×C5×#125C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×C5×#123—21no—
11C3×C5×C22⋊Q8C411yescharacteristic
12C3×C5×#121C411yescharacteristic
13C3×C4×C5×Q8C411yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4C411yescharacteristic
16C3×C5×#117—21no—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×#681—21no—
19C22×C3×#168—21no—
20C3×#3935—21no—
21C3×#3935C2212yes—
22C3×#3935C2212yes—
23C3×C4×#168—21no—
24C3×#1524—51nomaximal, Hall
25C5×#529C2×C311yescharacteristic
26C4×#681C2×C311yescharacteristic, complemented
27C2×#3935C2×C311yescharacteristic, complemented
28#64763C2×C312yescomplemented
29#64760C2×C312yescomplemented
30C2×C3×C5×Q8C2×C411yescharacteristic
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C5×C4⋊C4C2×C411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×C42×C5C2×C411yescharacteristic
50C3×C42×C5D411yescharacteristic
51C3×C42×C5D411yescharacteristic
52C3×C42×C5C2311yescharacteristic
53C3×#681—24no—
54C2×C3×#168—24no—
55C2×C3×#168—22no—
56C2×C3×#168—22no—
57C3×#529D511yescharacteristic
58C3×C4×M16—51no—
59C2×C3×#97—51no—
60C3×#330—52no—
61C3×#329—52no—
62C5×#126—21no—
63C5×#125C22×C311yescharacteristic
64C5×#124C22×C311yescharacteristic
65C5×#123—21no—
66C5×C22⋊Q8C3×C411yescharacteristic
67C5×#121C3×C411yescharacteristic
68C4×C5×Q8C3×C411yescharacteristic
69C4×C5×D4—21no—
70C4×C5×D4C3×C411yescharacteristic
71C5×#117—21no—
72C2×C42×C5C22×C311yescharacteristic
73C2×#681—21no—
74C22×#168—21no—
75#3935—21no—
76#3935C22×C312yes—
77#3935C22×C312yes—
78C4×#168—21no—
79#1524—51noSylow
80C23×C3×C5—21no—
81C23×C3×C5C22⋊C411yescharacteristic
82C3×C5×Q8—41no—
83C3×C5×D4—41no—
84C3×C5×D4—42no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C3×#168—24no—
99C3×#168—24no—
100C2×C3×M16—101no—
101C22×C3×C8—101no—
102C3×#126—21no—
103C3×#125C2×D511yescharacteristic
104C3×#124C2×D511yescharacteristic
105C3×#123—21no—
106C3×C22⋊Q8Dic511yescharacteristic
107C3×#121Dic511yescharacteristic
108C3×C4×Q8Dic511yescharacteristic
109C3×C4×D4—21no—
110C3×C4×D4Dic511yescharacteristic
111C3×#117—21no—
112C2×C3×C42C2×D511yescharacteristic
113C3×#97—52no—
114C3×#97—52no—
115C3×#97—101no—
116C3×C4×C8—101no—
117C2×C5×Q8C2×C3×C411yescharacteristic
118C2×C5×D4—21no—
119C2×C5×D4C2×C3×C411yescharacteristic
120C22×C4×C5—21no—
121C22×C4×C5C2×C3×C411yescharacteristic
122C22×C4×C5C3×D411yescharacteristic
123C22×C4×C5C3×D411yescharacteristic
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C2×C3×C411yescharacteristic
129C5×C4⋊C4C2×C3×C411yescharacteristic
130C5×C22⋊C4—21no—
131C5×C22⋊C4—21no—
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C42×C5—21no—
136C42×C5C2×C3×C411yescharacteristic
137C42×C5C3×D411yescharacteristic
138C42×C5C3×D411yescharacteristic
139C42×C5C23×C311yescharacteristic
140#681—24no—
141C2×#168—24no—
142C2×#168—22no—
143C2×#168—22no—
144#529C3×D511yescharacteristic
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—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×C4×C5—41no—
164C3×C4×C5#10412yes—
165C2×C3×Q8C2×Dic511yescharacteristic
166C2×C3×D4—21no—
167C2×C3×D4C2×Dic511yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4C2×Dic511yescharacteristic
170C22×C3×C4C22⋊D511yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C3×M16—104no—
173C2×C3×C8—104no—
174C2×C3×C8—102no—
175C2×C3×C8—102no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C2×Dic511yescharacteristic
181C3×C4⋊C4C2×Dic511yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C42—21no—
188C3×C42C2×Dic511yescharacteristic
189C3×C42C22⋊D511yescharacteristic
190C3×C42C22⋊D511yescharacteristic
191C3×C42C22×D511yescharacteristic
192C23×C5—21no—
193C23×C5C3×C22⋊C411yescharacteristic
194C5×Q8—41no—
195C5×D4—41no—
196C5×D4—42no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—41no—
203C2×C4×C5—42no—
204C2×C4×C5C3×C22⋊C411yescharacteristic
205C2×C4×C5C3×C22⋊C411yescharacteristic
206C2×C4×C5C3×C22⋊C411yescharacteristic
207C2×C4×C5C22×C3×C411yescharacteristic
208C2×C4×C5C2×C3×D411yescharacteristic
209C2×C4×C5C2×C3×D411yescharacteristic
210#168—24no—
211#168—24no—
212C2×M16—101no—
213C22×C8—101no—
214#126—21no—
215#125C2×C3×D511yescharacteristic
216#124C2×C3×D511yescharacteristic
217#123—21no—
218C22⋊Q8C3×Dic511yescharacteristic
219#121C3×Dic511yescharacteristic
220C4×Q8C3×Dic511yescharacteristic
221C4×D4—21no—
222C4×D4C3×Dic511yescharacteristic
223#117—21no—
224C2×C42C2×C3×D511yescharacteristic
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⋊Dic511yescharacteristic
236C3×Q8—41no—
237C3×D4—41no—
238C3×D4—42no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4C22⋊Dic511yescharacteristic
247C2×C3×C4C22⋊Dic511yescharacteristic
248C2×C3×C4C22⋊Dic511yescharacteristic
249C2×C3×C4C22×Dic511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
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—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—41no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5C3×#10412yes—
270C2×Q8C2×C3×Dic511yescharacteristic
271C2×D4—21no—
272C2×D4C2×C3×Dic511yescharacteristic
273C22×C4—21no—
274C22×C4C2×C3×Dic511yescharacteristic
275C22×C4C3×C22⋊D511yescharacteristic
276C22×C4C3×C22⋊D511yescharacteristic
277M16—104no—
278C2×C8—104no—
279C2×C8—102no—
280C2×C8—102no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4C2×C3×Dic511yescharacteristic
286C4⋊C4C2×C3×Dic511yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C42—21no—
293C42C2×C3×Dic511yescharacteristic
294C42C3×C22⋊D511yescharacteristic
295C42C3×C22⋊D511yescharacteristic
296C42C22×C3×D511yescharacteristic
297C3×C5#152411yescharacteristic, complemented, Hall
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3#396912yes—
304C22×C3C2×C22⋊Dic511yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4#396912yes—
314C2×C5—22no—
315C2×C5—81no—
316C2×C5C3×#41311yescharacteristic
317C2×C5C2×C3×#10411yescharacteristic
318C2×C5C2×C3×#10411yescharacteristic
319C23—21no—
320C23C3×C22⋊Dic511yescharacteristic
321Q8—41no—
322D4—41no—
323D4—42no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4C3×C22⋊Dic511yescharacteristic
332C2×C4C3×C22⋊Dic511yescharacteristic
333C2×C4C3×C22⋊Dic511yescharacteristic
334C2×C4C22×C3×Dic511yescharacteristic
335C2×C4C2×C3×C22⋊D511yescharacteristic
336C2×C4C2×C3×C22⋊D511yescharacteristic
337C8—104no—
338C8—104no—
339C2×C3—22no—
340C2×C3—81no—
341C2×C3C2×#396911yescharacteristic
342C2×C3C2×#396911yescharacteristic
343C2×C3#6552611yescharacteristic
344C5C3×#152411yescharacteristic, complemented, Sylow
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22C3×#396912yes—
351C22C2×C3×C22⋊Dic511yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C3×#396912yes—
361C3#1060253911yescharacteristic, direct product factor, Sylow
362C2—22no—
363C2—81no—
364C2C2×C3×#396911yescharacteristic
365C2C2×C3×#396911yescharacteristic
366C2C3×#6552611yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊Dic5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#529C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×C5×#121C4
cosocleC42×C5C23×C3
hypercenterC3×#529D5
hypocenterC5C3×#1524
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#529

Complements

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

NH ≅ G/Ntype
2. C3×C4×#681C2semidirect
3. C2×C3×#3935C2semidirect
4. C3×#64763C2semidirect
5. C3×#64760C2semidirect
6. #10602539C3direct (N × H)
26. C4×#681C2×C3semidirect
27. C2×#3935C2×C3semidirect
28. #64763C2×C3semidirect
29. #64760C2×C3semidirect
297. C3×C5#1524semidirect
344. C5C3×#1524semidirect
361. C3#10602539direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5292
C3×C4×#6812
C2×C3×#39352
C3×#647632
C3×#647602
#106025393
C3×#15245