Finite Group Databasebeta

← C3×#10600262 #14282876

Subgroups — C3×#10600262 #14282876

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65811C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#65214C211yesmaximal, characteristic, complemented
4C3×#64671C214yesmaximal, complemented
5#10600262C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×#709—21no—
7C2×C3×C5×C4⋊C4—21no—
8C2×C3×C42×C5—21no—
9C2×C3×C42×C5C2211yescharacteristic
10C3×#4076—21no—
11C3×#4076C2212yes—
12C3×#4021—21no—
13C3×#4020C411yescharacteristic, complemented
14C3×C4×D20—21no—
15C3×C4×D20C412yescomplemented
16C3×#4015C411yescharacteristic, complemented
17C3×C5×#95C2212yes—
18C3×C22⋊#168C2212yes—
19C3×C4⋊#168—21no—
20C3×C4×#168—21no—
21C3×#1502—51nomaximal, Hall
22#65811C2×C311yescharacteristic
23C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
24#65214C2×C311yescharacteristic, complemented
25#64671C2×C314yescomplemented
26C22×C3×C4×C5—22no—
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×C3×C22⋊D5—22no—
31C3×#709—42no—
32C3×#709—42no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×D20C2×C412yes—
36C2×C3×C4×D5—22no—
37C2×C3×Dic10—21no—
38C3×C5×C4⋊C4—24no—
39C3×C42×C5—42no—
40C3×C42×C5C2×C411yescharacteristic
41C3×C42×C5C2×C411yescharacteristic
42C3×C42×C5D411yescharacteristic
43C3×C42×C5D411yescharacteristic
44C3×#685—22no—
45C3×#685—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5C2×C412yes—
48C2×C3×#168—22no—
49C3×#532—51no—
50C3×#431—51no—
51C3×C4×C4⋊C4D511yescharacteristic, complemented
52C3×#327—54no—
53C2×#709—21no—
54C2×C5×C4⋊C4—21no—
55C2×C42×C5—21no—
56C2×C42×C5C22×C311yescharacteristic
57#4076—21no—
58#4076C22×C312yes—
59#4021—21no—
60#4020C3×C411yescharacteristic, complemented
61C4×D20—21no—
62C4×D20C3×C412yescomplemented
63#4015C3×C411yescharacteristic, complemented
64C5×#95C22×C312yes—
65C22⋊#168C22×C312yes—
66C4⋊#168—21no—
67C4×#168—21no—
68#1502—51noSylow
69C23×C3×C5C2×D411yescharacteristic
70C22×C3×D5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—24no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5D812yes—
81C2×C3×C4×C5SD1612yes—
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C3×C22⋊D5—42no—
85C3×C22⋊D5—42no—
86C2×C3×Dic5—22no—
87C3×D20—42no—
88C3×D20—42no—
89C3×D20—42no—
90C3×C4×D5—44no—
91C3×Dic10—42no—
92C3×#168—42no—
93C2×C3×#41—101no—
94C3×C4⋊Q8—51no—
95C3×#127—51no—
96C3×#124—101no—
97C3×#121—52no—
98C3×#121—101no—
99C3×C4×D4—52no—
100C3×C4×D4—101no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C42—21no—
103C2×C3×C42C2×D511yescharacteristic
104C3×C4⋊C8—101no—
105C3×C22⋊C8—52no—
106C3×C4×C8—101no—
107C3×#95C2×D512yes—
108C22×C4×C5—22no—
109C22×C4×C5C3×D411yescharacteristic
110C22×C4×C5C3×D411yescharacteristic
111C22×C4×C5C23×C311yescharacteristic
112C2×C22⋊D5—22no—
113#709—42no—
114#709—42no—
115C2×D20—21no—
116C2×D20—21no—
117C2×D20C2×C3×C412yes—
118C2×C4×D5—22no—
119C2×Dic10—21no—
120C5×C4⋊C4—24no—
121C42×C5—42no—
122C42×C5C2×C3×C411yescharacteristic
123C42×C5C2×C3×C411yescharacteristic
124C42×C5C3×D411yescharacteristic
125C42×C5C3×D411yescharacteristic
126#685—22no—
127#685—22no—
128C4⋊Dic5—21no—
129C4⋊Dic5C2×C3×C412yes—
130C2×#168—22no—
131#532—51no—
132#431—51no—
133C4×C4⋊C4C3×D511yescharacteristic, complemented
134#327—54no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C22×C3×C5C2×D811yescharacteristic
139C22×C3×C5C2×SD1611yescharacteristic
140C2×C3×D5—42no—
141C2×C3×D5—42no—
142C2×C3×D5—42no—
143C3×C4×C5—21no—
144C3×C4×C5—21no—
145C3×C4×C5—21no—
146C3×C4×C5—44no—
147C3×C4×C5#10212yes—
148C3×C4×C5#10212yes—
149C3×C4×C5#10412yes—
150C3×Dic5—42no—
151C3×#41—202no—
152C3×#41—202no—
153C2×C3×Q8—101no—
154C2×C3×D4—52no—
155C2×C3×D4—102no—
156C2×C3×D4—101no—
157C2×C3×D4—101no—
158C22×C3×C4—22no—
159C22×C3×C4—102no—
160C22×C3×C4C22⋊D511yescharacteristic
161C22×C3×C4C22⋊D511yescharacteristic
162C22×C3×C4C22×D511yescharacteristic
163C2×C3×C8—102no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—52no—
166C3×C4⋊C4—101no—
167C3×C22⋊C4—102no—
168C3×C22⋊C4—102no—
169C3×C42—42no—
170C3×C42C4×D511yescharacteristic
171C3×C42C4×D511yescharacteristic
172C3×C42D2011yescharacteristic
173C3×C42D2011yescharacteristic
174C23×C5C2×C3×D411yescharacteristic
175C22×D5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—24no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5C3×C22⋊C411yescharacteristic
182C2×C4×C5C3×C22⋊C411yescharacteristic
183C2×C4×C5C3×C22⋊C411yescharacteristic
184C2×C4×C5C3×C22⋊C411yescharacteristic
185C2×C4×C5C3×D812yes—
186C2×C4×C5C3×SD1612yes—
187C2×C4×C5C22×C3×C411yescharacteristic
188C2×C4×C5C2×C3×D411yescharacteristic
189C22⋊D5—42no—
190C22⋊D5—42no—
191C2×Dic5—22no—
192D20—42no—
193D20—42no—
194D20—42no—
195C4×D5—44no—
196Dic10—42no—
197#168—42no—
198C2×#41—101no—
199C4⋊Q8—51no—
200#127—51no—
201#124—101no—
202#121—52no—
203#121—101no—
204C4×D4—52no—
205C4×D4—101no—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C2×C3×D511yescharacteristic
209C4⋊C8—101no—
210C22⋊C8—52no—
211C4×C8—101no—
212#95C2×C3×D512yes—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5#41011yescharacteristic
216C2×C3×C5C2×#10211yescharacteristic
217C2×C3×C5C2×#10411yescharacteristic
218C3×D5—82no—
219C23×C3—102no—
220C23×C3C2×C22⋊D511yescharacteristic
221C3×Q8—202no—
222C3×D4—202no—
223C3×D4—202no—
224C3×D4—202no—
225C3×D4—202no—
226C3×D4—202no—
227C2×C3×C4—22no—
228C2×C3×C4—24no—
229C2×C3×C4—41no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—102no—
233C2×C3×C4—204no—
234C2×C3×C4#68511yescharacteristic
235C2×C3×C4#68511yescharacteristic
236C2×C3×C4#68511yescharacteristic
237C2×C3×C4#68511yescharacteristic
238C2×C3×C4#68612yes—
239C2×C3×C4#68812yes—
240C2×C3×C4C2×C4×D511yescharacteristic
241C2×C3×C4C2×D2011yescharacteristic
242C3×C8—202no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5C2×C3×C22⋊C411yescharacteristic
246C22×C5C2×C3×D811yescharacteristic
247C22×C5C2×C3×SD1611yescharacteristic
248C2×D5—42no—
249C2×D5—42no—
250C2×D5—42no—
251C4×C5—21no—
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—44no—
255C4×C5C3×#10212yes—
256C4×C5C3×#10212yes—
257C4×C5C3×#10412yes—
258Dic5—42no—
259#41—202no—
260#41—202no—
261C2×Q8—101no—
262C2×D4—52no—
263C2×D4—102no—
264C2×D4—101no—
265C2×D4—101no—
266C22×C4—22no—
267C22×C4—102no—
268C22×C4C3×C22⋊D511yescharacteristic
269C22×C4C3×C22⋊D511yescharacteristic
270C22×C4C22×C3×D511yescharacteristic
271C2×C8—102no—
272C4⋊C4—24no—
273C4⋊C4—52no—
274C4⋊C4—101no—
275C22⋊C4—102no—
276C22⋊C4—102no—
277C42—42no—
278C42C3×C4×D511yescharacteristic
279C42C3×C4×D511yescharacteristic
280C42C3×D2011yescharacteristic
281C42C3×D2011yescharacteristic
282C3×C5#150211yescharacteristic, complemented, Hall
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—202no—
286C22×C3—202no—
287C22×C3—202no—
288C22×C3C2×#68511yescharacteristic
289C22×C3C2×#68611yescharacteristic
290C22×C3C2×#68811yescharacteristic
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—44no—
295C3×C4—202no—
296C3×C4#393712yes—
297C3×C4#394112yes—
298C3×C4#394112yes—
299C2×C5—21no—
300C2×C5—21no—
301C2×C5C3×#41011yescharacteristic
302C2×C5C2×C3×#10211yescharacteristic
303C2×C5C2×C3×#10411yescharacteristic
304D5—82no—
305C23—102no—
306C23C2×C3×C22⋊D511yescharacteristic
307Q8—202no—
308D4—202no—
309D4—202no—
310D4—202no—
311D4—202no—
312D4—202no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—102no—
319C2×C4—204no—
320C2×C4C3×#68511yescharacteristic
321C2×C4C3×#68511yescharacteristic
322C2×C4C3×#68511yescharacteristic
323C2×C4C3×#68511yescharacteristic
324C2×C4C3×#68612yes—
325C2×C4C3×#68812yes—
326C2×C4C2×C3×C4×D511yescharacteristic
327C2×C4C2×C3×D2011yescharacteristic
328C8—202no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—402no—
332C2×C3C2×#393711yescharacteristic
333C2×C3C2×#394111yescharacteristic
334C2×C3#6529511yescharacteristic
335C5C3×#150211yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—202no—
339C22—202no—
340C22—202no—
341C22C2×C3×#68511yescharacteristic
342C22C2×C3×#68611yescharacteristic
343C22C2×C3×#68811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—44no—
348C4—202no—
349C4C3×#393712yes—
350C4C3×#394112yes—
351C4C3×#394112yes—
352C3#1060026211yescharacteristic, direct product factor, Sylow
353C2—21no—
354C2—21no—
355C2—402no—
356C2C2×C3×#393711yescharacteristic
357C2C2×C3×#394111yescharacteristic
358C2C3×#6529511yescharacteristic
subgroupG/H
centerC2×C3×C4#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65811C2
cosocleC22×C4×C5C23×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#1502
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C4⋊C4C2semidirect
3. C3×#65214C2semidirect
4. C3×#64671C2semidirect
5. #10600262C3direct (N × H)
13. C3×#4020C4semidirect
15. C3×C4×D20C4semidirect
16. C3×#4015C4semidirect
23. C4×C5×C4⋊C4C2×C3semidirect
24. #65214C2×C3semidirect
25. #64671C2×C3semidirect
51. C3×C4×C4⋊C4D5semidirect
60. #4020C3×C4semidirect
62. C4×D20C3×C4semidirect
63. #4015C3×C4semidirect
133. C4×C4⋊C4C3×D5semidirect
282. C3×C5#1502semidirect
335. C5C3×#1502semidirect
352. C3#10600262direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658112
C3×C4×C5×C4⋊C42
C3×#652142
C3×#646712
#106002623
C3×#15025