Finite Group Databasebeta

← C3×#10604794 #14286985

Subgroups — C3×#10604794 #14286985

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65774C211yesmaximal, characteristic, complemented
2C3×D4×#170C211yesmaximal, characteristic, complemented
3C3×D8×Dic5C211yesmaximal, characteristic
4C3×D4⋊#170C211yesmaximal, characteristic, complemented
5C3×D4⋊#170C211yesmaximal, characteristic, complemented
6C3×#64883C211yesmaximal, characteristic, complemented
7C3×#170⋊C8C211yesmaximal, characteristic, complemented
8#10604794C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#704—21no—
10C22×C3×#170—21no—
11C2×C3×C5×D8C411yescharacteristic
12C3×D4×Dic5C2211yescharacteristic
13C3×D4×Dic5C2211yescharacteristic
14C3×C22⋊#170—21no—
15C3×C22⋊#170—21no—
16C3×C4⋊#170C2211yescharacteristic
17C3×C4⋊#170C2211yescharacteristic
18C3×C4×#170C2211yescharacteristic
19C3×C4×#170C2211yescharacteristic
20C3×#3964C411yescharacteristic
21C3×#3964C411yescharacteristic
22C3×#3950C411yescharacteristic
23C3×C8×Dic5C2211yescharacteristic
24C3×#1586—51nomaximal, Hall
25#65774C2×C311yescharacteristic, complemented
26D4×#170C2×C311yescharacteristic, complemented
27D8×Dic5C2×C311yescharacteristic
28D4⋊#170C2×C311yescharacteristic, complemented
29D4⋊#170C2×C311yescharacteristic, complemented
30#64883C2×C311yescharacteristic, complemented
31#170⋊C8C2×C311yescharacteristic, complemented
32C2×C3×C5×D4C2×C411yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C22×C3×Dic5—21no—
35C22×C3×Dic5—21no—
36C3×#704—42no—
37C2×C3×#170—21no—
38C2×C3×#170—21no—
39C2×C3×#170—21no—
40C2×C3×#170—42no—
41C2×C3×#170D411yescharacteristic
42C2×C3×#170D411yescharacteristic
43C3×C5×D8—22no—
44C2×C3×C5×C8C2×C411yescharacteristic
45C3×C22⋊Dic5—21no—
46C3×C22⋊Dic5—21no—
47C3×C4⋊Dic5C2×C411yescharacteristic
48C3×C4⋊Dic5C2×C411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50C2×C3×#168C2×C411yescharacteristic
51C3×C4×D8—51no—
52C3×#436—51no—
53C3×C8×D4—51no—
54C3×#334—51no—
55C3×D4⋊C8—51no—
56C3×D4⋊C8—51no—
57C3×#322—51no—
58C2×#704—21no—
59C22×#170—21no—
60C2×C5×D8C3×C411yescharacteristic
61D4×Dic5C22×C311yescharacteristic
62D4×Dic5C22×C311yescharacteristic
63C22⋊#170—21no—
64C22⋊#170—21no—
65C4⋊#170C22×C311yescharacteristic
66C4⋊#170C22×C311yescharacteristic
67C4×#170C22×C311yescharacteristic
68C4×#170C22×C311yescharacteristic
69#3964C3×C411yescharacteristic
70#3964C3×C411yescharacteristic
71#3950C3×C411yescharacteristic
72C8×Dic5C22×C311yescharacteristic
73#1586—51noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C3×C5×D4—21no—
77C3×C5×D4—21no—
78C3×C5×D4—21no—
79C3×C5×D4M1612yescomplemented
80C2×C3×C4×C5C22×C411yescharacteristic
81C2×C3×Dic5—21no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5C2×D411yescharacteristic
88C2×C3×Dic5#4111yescharacteristic
89C3×#170—22no—
90C3×#170—21no—
91C3×#170—21no—
92C3×#170—41no—
93C3×#170—41no—
94C3×C5×C8—21no—
95C3×#168—21no—
96C2×C3×D8AGL(1,𝔽5)11yescharacteristic
97C2×C3×M16—101no—
98C22×C3×C8—101no—
99C3×C4×D4—51no—
100C3×C4×D4—51no—
101C3×#107—51no—
102C3×C4⋊C8—51no—
103C3×C4⋊C8—51no—
104C3×#102—51no—
105C3×#102—51no—
106C3×C22⋊C8—101no—
107C3×C22⋊C8—101no—
108C3×C4×C8—51no—
109C3×C4×C8—51no—
110C3×C4×C8—51no—
111C2×C5×D4C2×C3×C411yescharacteristic
112C2×C5×D4C2×C3×C411yescharacteristic
113C22×Dic5—21no—
114C22×Dic5—21no—
115#704—42no—
116C2×#170—21no—
117C2×#170—21no—
118C2×#170—21no—
119C2×#170—42no—
120C2×#170C3×D411yescharacteristic
121C2×#170C3×D411yescharacteristic
122C5×D8—22no—
123C2×C5×C8C2×C3×C411yescharacteristic
124C22⋊Dic5—21no—
125C22⋊Dic5—21no—
126C4⋊Dic5C2×C3×C411yescharacteristic
127C4⋊Dic5C2×C3×C411yescharacteristic
128C4×Dic5C23×C311yescharacteristic
129C2×#168C2×C3×C411yescharacteristic
130C4×D8—51no—
131#436—51no—
132C8×D4—51no—
133#334—51no—
134D4⋊C8—51no—
135D4⋊C8—51no—
136#322—51no—
137C22×C3×C5—22no—
138C22×C3×C5—41no—
139C22×C3×C5—41no—
140C22×C3×C5—41no—
141C22×C3×C5—41no—
142C22×C3×C5—41no—
143C22×C3×C5C4×D411yescharacteristic
144C3×C4×C5C2×M1611yescharacteristic
145C3×C4×C5#13111yescharacteristic
146C3×Dic5—21no—
147C3×Dic5—41no—
148C3×Dic5—41no—
149C3×Dic5AGL(1,ℤ/8)11yescharacteristic
150C3×Dic5AGL(1,ℤ/8)11yescharacteristic
151C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
152C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
153C22×C3×C4—101no—
154C22×C3×C4—101no—
155C3×D8—22no—
156C3×M16—202no—
157C2×C3×C8—51no—
158C2×C3×C8—51no—
159C2×C3×C8—51no—
160C2×C3×C8—101no—
161C2×C3×C8—101no—
162C2×C3×C8—101no—
163C2×C3×C8—202no—
164C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
165C3×C4⋊C4—51no—
166C3×C4⋊C4—51no—
167C3×C22⋊C4—101no—
168C3×C22⋊C4—101no—
169C3×C42—51no—
170C23×C5—21no—
171C23×C5—21no—
172C5×D4—21no—
173C5×D4—21no—
174C5×D4—21no—
175C5×D4C3×M1612yescomplemented
176C2×C4×C5C22×C3×C411yescharacteristic
177C2×Dic5—21no—
178C2×Dic5—21no—
179C2×Dic5—41no—
180C2×Dic5—41no—
181C2×Dic5—41no—
182C2×Dic5—41no—
183C2×Dic5C2×C3×D411yescharacteristic
184C2×Dic5C3×#4111yescharacteristic
185#170—22no—
186#170—21no—
187#170—21no—
188#170—41no—
189#170—41no—
190C5×C8—21no—
191#168—21no—
192C2×D8C3×AGL(1,𝔽5)11yescharacteristic
193C2×M16—101no—
194C22×C8—101no—
195C4×D4—51no—
196C4×D4—51no—
197#107—51no—
198C4⋊C8—51no—
199C4⋊C8—51no—
200#102—51no—
201#102—51no—
202C22⋊C8—101no—
203C22⋊C8—101no—
204C4×C8—51no—
205C4×C8—51no—
206C4×C8—51no—
207C2×C3×C5—42no—
208C2×C3×C5—81no—
209C2×C3×C5#43511yescharacteristic
210C2×C3×C5#44211yescharacteristic
211C2×C3×C5#44311yescharacteristic
212C23×C3—21no—
213C23×C3—21no—
214C3×D4—21no—
215C3×D4—21no—
216C3×D4—21no—
217C3×D4#70412yescomplemented
218C2×C3×C4—51no—
219C2×C3×C4—51no—
220C2×C3×C4—101no—
221C2×C3×C4—101no—
222C2×C3×C4—201no—
223C2×C3×C4—201no—
224C2×C3×C4—201no—
225C2×C3×C4—201no—
226C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
227C3×C8—21no—
228C3×C8—101no—
229C3×C8—101no—
230C3×C8—102no—
231C3×C8—101no—
232C3×C8—201no—
233C3×C8—201no—
234C22×C5—22no—
235C22×C5—41no—
236C22×C5—41no—
237C22×C5—41no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5C3×C4×D411yescharacteristic
241C4×C5C2×C3×M1611yescharacteristic
242C4×C5C3×#13111yescharacteristic
243Dic5—21no—
244Dic5—41no—
245Dic5—41no—
246Dic5C3×AGL(1,ℤ/8)11yescharacteristic
247Dic5C3×AGL(1,ℤ/8)11yescharacteristic
248C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
249C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
250C22×C4—101no—
251C22×C4—101no—
252D8—22no—
253M16—202no—
254C2×C8—51no—
255C2×C8—51no—
256C2×C8—51no—
257C2×C8—101no—
258C2×C8—101no—
259C2×C8—101no—
260C2×C8—202no—
261C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
262C4⋊C4—51no—
263C4⋊C4—51no—
264C22⋊C4—101no—
265C22⋊C4—101no—
266C42—51no—
267C3×C5#158611yescharacteristic, complemented, Hall
268C22×C3—22no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3D4×AGL(1,𝔽5)11yescharacteristic
275C3×C4—51no—
276C3×C4—51no—
277C3×C4—101no—
278C3×C4—201no—
279C3×C4—201no—
280C3×C4#413111yescharacteristic
281C3×C4C2×#70411yescharacteristic
282C2×C5—42no—
283C2×C5—81no—
284C2×C5C3×#43511yescharacteristic
285C2×C5C3×#44211yescharacteristic
286C2×C5C3×#44311yescharacteristic
287C23—21no—
288C23—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4C3×#70412yescomplemented
293C2×C4—51no—
294C2×C4—51no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
302C8—21no—
303C8—101no—
304C8—101no—
305C8—102no—
306C8—101no—
307C8—201no—
308C8—201no—
309C2×C3—42no—
310C2×C3—81no—
311C2×C3#6573111yescharacteristic
312C2×C3#6573211yescharacteristic
313C2×C3#6577311yescharacteristic
314C5C3×#158611yescharacteristic, complemented, Sylow
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C3×D4×AGL(1,𝔽5)11yescharacteristic
322C4—51no—
323C4—51no—
324C4—101no—
325C4—201no—
326C4—201no—
327C4C3×#413111yescharacteristic
328C4C2×C3×#70411yescharacteristic
329C3#1060479411yescharacteristic, direct product factor, Sylow
330C2—42no—
331C2—81no—
332C2C3×#6573111yescharacteristic
333C2C3×#6573211yescharacteristic
334C2C3×#6577311yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
Fitting, prime radicalC2×C3×C5×D8C4
socleC22×C3×C5C4×D4
cosocleC4×Dic5C23×C3
hypercenterC2×C3×D8AGL(1,𝔽5)
hypocenterC5C3×#1586
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

Complements

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

NH ≅ G/Ntype
1. C3×#65774C2semidirect
2. C3×D4×#170C2semidirect
4. C3×D4⋊#170C2semidirect
5. C3×D4⋊#170C2semidirect
6. C3×#64883C2semidirect
7. C3×#170⋊C8C2semidirect
8. #10604794C3direct (N × H)
25. #65774C2×C3semidirect
26. D4×#170C2×C3semidirect
28. D4⋊#170C2×C3semidirect
29. D4⋊#170C2×C3semidirect
30. #64883C2×C3semidirect
31. #170⋊C8C2×C3semidirect
79. C3×C5×D4M16semidirect
175. C5×D4C3×M16semidirect
217. C3×D4#704semidirect
267. C3×C5#1586semidirect
292. D4C3×#704semidirect
314. C5C3×#1586semidirect
329. C3#10604794direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657742
C3×D4×#1702
C3×D8×Dic52
C3×D4⋊#1702
C3×#648832
C3×#170⋊C82
#106047943
C3×#15865