Finite Group Databasebeta

← C3×#10604080 #14303617

Subgroups — C3×#10604080 #14303617

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65708C211yesmaximal, characteristic
2C3×#65701C211yesmaximal, characteristic
3C3×#65169C211yesmaximal, characteristic
4C3×#64896C211yesmaximal, characteristic
5C3×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic
6C3×#64875C211yesmaximal, characteristic
7C3×#64875C211yesmaximal, characteristic
8#10604080C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
10C2×C3×#700C2211yescharacteristic
11C2×C3×#700C2211yescharacteristic
12C2×C3×D5⋊C8C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C3×#4038C2211yescharacteristic
15C3×#4038C2211yescharacteristic
16C3×#4004—21no—
17C3×#4002—21no—
18C3×C4⋊#170—21no—
19C3×C4×#170—21no—
20C3×C5×#107C411yescharacteristic, complemented
21C3×#3950C411yescharacteristic, complemented
22C3×#3940C411yescharacteristic, complemented
23C3×#3940C411yescharacteristic, complemented
24C3×#1922—51nomaximal, Hall
25#65708C2×C311yescharacteristic
26#65701C2×C311yescharacteristic
27#65169C2×C311yescharacteristic
28#64896C2×C311yescharacteristic
29(C2×AGL(1,𝔽5))⋊C8C2×C311yescharacteristic
30#64875C2×C311yescharacteristic
31#64875C2×C311yescharacteristic
32C22×C3×AGL(1,𝔽5)—21no—
33C2×C3×C4×D5C2311yescharacteristic
34C2×C3×#170—21no—
35C2×C3×#170—21no—
36C2×C3×#170D411yescharacteristic
37C2×C3×#170D411yescharacteristic
38C3×C4×AGL(1,𝔽5)—21no—
39C3×C4×AGL(1,𝔽5)—21no—
40C3×#700—21no—
41C3×#700—21no—
42C3×#700—21no—
43C3×#700Q812yes—
44C3×D5⋊C8—21no—
45C3×D5⋊C8—21no—
46C2×C3×C5×C8C2×C411yescharacteristic
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×#685—21no—
50C3×#685—21no—
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168C2×C411yescharacteristic
56C3×C8×D5—21no—
57C3×C8×D5—21no—
58C3×#427—51no—
59C3×#424—51no—
60C3×#405—51no—
61C3×#341—51no—
62C3×#339—51no—
63C3×#339—51no—
64C3×#336—51no—
65C2×C4×AGL(1,𝔽5)C22×C311yescharacteristic
66C2×#700C22×C311yescharacteristic
67C2×#700C22×C311yescharacteristic
68C2×D5⋊C8C22×C311yescharacteristic
69C2×C8×D5C22×C311yescharacteristic
70#4038C22×C311yescharacteristic
71#4038C22×C311yescharacteristic
72#4004—21no—
73#4002—21no—
74C4⋊#170—21no—
75C4×#170—21no—
76C5×#107C3×C411yescharacteristic, complemented
77#3950C3×C411yescharacteristic, complemented
78#3940C3×C411yescharacteristic, complemented
79#3940C3×C411yescharacteristic, complemented
80#1922—51noSylow
81C22×C3×D5#4111yescharacteristic
82C2×C3×AGL(1,𝔽5)—22no—
83C2×C3×AGL(1,𝔽5)—41no—
84C2×C3×AGL(1,𝔽5)—41no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5C2×Q811yescharacteristic
92C3×C4×D5#4111yescharacteristic
93C3×C4×D5#4111yescharacteristic
94C3×C4×D5#4111yescharacteristic
95C3×#170—22no—
96C3×#170—21no—
97C3×#170—21no—
98C3×#170—41no—
99C3×C5×C8—21no—
100C3×#168—21no—
101C2×C3×M16—51no—
102C2×C3×M16—51no—
103C22×C3×C8—51no—
104C22×C3×C8—51no—
105C3×#117—51no—
106C3×#117—51no—
107C2×C3×C42—51no—
108C3×#107—51no—
109C3×#107AGL(1,𝔽5)11yescharacteristic, complemented
110C3×#106—51no—
111C3×#106—51no—
112C3×C4⋊C8—101no—
113C3×C4⋊C8—101no—
114C3×#97—101no—
115C3×C4×C8—101no—
116C22×AGL(1,𝔽5)—21no—
117C2×C4×D5C23×C311yescharacteristic
118C2×#170—21no—
119C2×#170—21no—
120C2×#170C3×D411yescharacteristic
121C2×#170C3×D411yescharacteristic
122C4×AGL(1,𝔽5)—21no—
123C4×AGL(1,𝔽5)—21no—
124#700—21no—
125#700—21no—
126#700—21no—
127#700C3×Q812yes—
128D5⋊C8—21no—
129D5⋊C8—21no—
130C2×C5×C8C2×C3×C411yescharacteristic
131C5×C4⋊C4C2×C3×C411yescharacteristic
132C5×C4⋊C4C2×C3×C411yescharacteristic
133#685—21no—
134#685—21no—
135C4⋊Dic5C2×C3×C411yescharacteristic
136C4⋊Dic5C2×C3×C411yescharacteristic
137C4×Dic5—21no—
138C4×Dic5—21no—
139C2×#168C2×C3×C411yescharacteristic
140C8×D5—21no—
141C8×D5—21no—
142#427—51no—
143#424—51no—
144#405—51no—
145#341—51no—
146#339—51no—
147#339—51no—
148#336—51no—
149C22×C3×C5C4×D411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#12511yescharacteristic
153C2×C3×D5#12611yescharacteristic
154C3×AGL(1,𝔽5)—42no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5#11711yescharacteristic
158C3×C4×C5C4×Q811yescharacteristic
159C3×Dic5—41no—
160C3×Dic5—41no—
161C3×Dic5C22⋊Q811yescharacteristic
162C3×Dic5#12311yescharacteristic
163C22×C3×C4—51no—
164C22×C3×C4—101no—
165C3×M16—52no—
166C3×M16—101no—
167C3×M16—101no—
168C3×M16—101no—
169C2×C3×C8—51no—
170C2×C3×C8—51no—
171C2×C3×C8—51no—
172C2×C3×C8—101no—
173C2×C3×C8—101no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
179C3×C4⋊C4—51no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
182C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
183C3×C22⋊C4—101no—
184C3×C22⋊C4—101no—
185C3×C42—101no—
186C3×C42—101no—
187C3×C42—101no—
188C3×C42—101no—
189C22×D5C3×#4111yescharacteristic
190C2×AGL(1,𝔽5)—22no—
191C2×AGL(1,𝔽5)—41no—
192C2×AGL(1,𝔽5)—41no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5C22×C3×C411yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5C2×C3×D411yescharacteristic
199C4×D5C2×C3×Q811yescharacteristic
200C4×D5C3×#4111yescharacteristic
201C4×D5C3×#4111yescharacteristic
202C4×D5C3×#4111yescharacteristic
203#170—22no—
204#170—21no—
205#170—21no—
206#170—41no—
207C5×C8—21no—
208#168—21no—
209C2×M16—51no—
210C2×M16—51no—
211C22×C8—51no—
212C22×C8—51no—
213#117—51no—
214#117—51no—
215C2×C42—51no—
216#107—51no—
217#107C3×AGL(1,𝔽5)11yescharacteristic, complemented
218#106—51no—
219#106—51no—
220C4⋊C8—101no—
221C4⋊C8—101no—
222#97—101no—
223C4×C8—101no—
224C2×C3×C5#38711yescharacteristic
225C2×C3×C5#44311yescharacteristic
226C2×C3×C5#44411yescharacteristic
227C3×D5—21no—
228C3×D5—21no—
229C23×C3—51no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
243C3×C8—21no—
244C3×C8—101no—
245C3×C8—101no—
246C3×C8—102no—
247C3×C8—101no—
248C3×C8—201no—
249C22×C5C3×C4×D411yescharacteristic
250C2×D5—21no—
251C2×D5—21no—
252C2×D5C3×#12511yescharacteristic
253C2×D5C3×#12611yescharacteristic
254AGL(1,𝔽5)—42no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5C3×#11711yescharacteristic
258C4×C5C3×C4×Q811yescharacteristic
259Dic5—41no—
260Dic5—41no—
261Dic5C3×C22⋊Q811yescharacteristic
262Dic5C3×#12311yescharacteristic
263C22×C4—51no—
264C22×C4—101no—
265M16—52no—
266M16—101no—
267M16—101no—
268M16—101no—
269C2×C8—51no—
270C2×C8—51no—
271C2×C8—51no—
272C2×C8—101no—
273C2×C8—101no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8—101no—
278C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
282C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
283C22⋊C4—101no—
284C22⋊C4—101no—
285C42—101no—
286C42—101no—
287C42—101no—
288C42—101no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—51no—
291C22×C3—51no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3D4×AGL(1,𝔽5)11yescharacteristic
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—51no—
298C3×C4—51no—
299C3×C4—202no—
300C3×C4—201no—
301C3×C4—201no—
302C3×C4#413011yescharacteristic
303C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
304C2×C5C3×#38711yescharacteristic
305C2×C5C3×#44311yescharacteristic
306C2×C5C3×#44411yescharacteristic
307D5—21no—
308D5—21no—
309C23—51no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—51no—
313C2×C4—51no—
314C2×C4—51no—
315C2×C4—51no—
316C2×C4—51no—
317C2×C4—102no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—201no—
321C2×C4—201no—
322C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
323C8—21no—
324C8—101no—
325C8—101no—
326C8—102no—
327C8—101no—
328C8—201no—
329C2×C3—101no—
330C2×C3—101no—
331C2×C3#6571111yescharacteristic
332C2×C3#6573311yescharacteristic
333C2×C3#6574011yescharacteristic
334C5C3×#192211yescharacteristic, complemented, Sylow
335C22—51no—
336C22—51no—
337C22—101no—
338C22—101no—
339C22C3×D4×AGL(1,𝔽5)11yescharacteristic
340C4—41no—
341C4—41no—
342C4—51no—
343C4—51no—
344C4—202no—
345C4—201no—
346C4—201no—
347C4C3×#413011yescharacteristic
348C4C3×Q8×AGL(1,𝔽5)11yescharacteristic
349C3#1060408011yescharacteristic, direct product factor, Sylow
350C2—101no—
351C2—101no—
352C2C3×#6571111yescharacteristic
353C2C3×#6573311yescharacteristic
354C2C3×#6574011yescharacteristic
subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#107C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5#41
cosocleC2×C4×D5C23×C3
hypercenterC3×#107AGL(1,𝔽5)
hypocenterC5C3×#1922
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#107

Complements

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

NH ≅ G/Ntype
8. #10604080C3direct (N × H)
20. C3×C5×#107C4semidirect
21. C3×#3950C4semidirect
22. C3×#3940C4semidirect
23. C3×#3940C4semidirect
76. C5×#107C3×C4semidirect
77. #3950C3×C4semidirect
78. #3940C3×C4semidirect
79. #3940C3×C4semidirect
109. C3×#107AGL(1,𝔽5)semidirect
217. #107C3×AGL(1,𝔽5)semidirect
289. C3×C5#1922semidirect
334. C5C3×#1922semidirect
349. C3#10604080direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657082
C3×#657012
C3×#651692
C3×#648962
C3×(C2×AGL(1,𝔽5))⋊C82
C3×#648752
#106040803
C3×#19225