Finite Group Databasebeta

← C3×#10604063 #14286516

Subgroups — C3×#10604063 #14286516

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×#65705C211yesmaximal, characteristic, complemented
2C3×#65702C211yesmaximal, characteristic, complemented
3C3×#65161C211yesmaximal, characteristic
4C3×#64884C211yesmaximal, characteristic, complemented
5C3×#170⋊C8C211yesmaximal, characteristic, complemented
6C3×#64871C211yesmaximal, characteristic, complemented
7C3×#64871C211yesmaximal, characteristic, complemented
8#10604063C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#700—21no—
10C2×C3×D5⋊C8—21no—
11C2×C3×D40C411yescharacteristic
12C3×#4039C2211yescharacteristic
13C3×#4039C2211yescharacteristic
14C3×#4003—21no—
15C3×#4003—21no—
16C3×C4⋊#170C2211yescharacteristic
17C3×C4⋊#170C2211yescharacteristic
18C3×C4×#170C2211yescharacteristic
19C3×C4×#170C2211yescharacteristic
20C3×C5×#107C411yescharacteristic
21C3×C8×Dic5C2211yescharacteristic
22C3×#3941C411yescharacteristic
23C3×#3941C411yescharacteristic
24C3×#1581—51nomaximal, Hall
25#65705C2×C311yescharacteristic, complemented
26#65702C2×C311yescharacteristic, complemented
27#65161C2×C311yescharacteristic
28#64884C2×C311yescharacteristic, complemented
29#170⋊C8C2×C311yescharacteristic, complemented
30#64871C2×C311yescharacteristic, complemented
31#64871C2×C311yescharacteristic, complemented
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—21no—
36C2×C3×#170—21no—
37C2×C3×#170—21no—
38C2×C3×#170—21no—
39C2×C3×#170D411yescharacteristic
40C2×C3×#170D411yescharacteristic
41C3×#700—42no—
42C3×D5⋊C8—42no—
43C2×C3×C5×C8C2×C411yescharacteristic
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×#685—21no—
47C3×#685—21no—
48C3×C4×Dic5C2311yescharacteristic
49C2×C3×#168C2×C411yescharacteristic
50C3×D40—22no—
51C3×C4×D8—51no—
52C3×#436—51no—
53C3×C8×D4—51no—
54C3×#335—51no—
55C3×D4⋊C8—51no—
56C3×D4⋊C8—51no—
57C3×#322—51no—
58C2×#700—21no—
59C2×D5⋊C8—21no—
60C2×D40C3×C411yescharacteristic
61#4039C22×C311yescharacteristic
62#4039C22×C311yescharacteristic
63#4003—21no—
64#4003—21no—
65C4⋊#170C22×C311yescharacteristic
66C4⋊#170C22×C311yescharacteristic
67C4×#170C22×C311yescharacteristic
68C4×#170C22×C311yescharacteristic
69C5×#107C3×C411yescharacteristic
70C8×Dic5C22×C311yescharacteristic
71#3941C3×C411yescharacteristic
72#3941C3×C411yescharacteristic
73#1581—51noSylow
74C22×C3×D5—21no—
75C22×C3×D5—21no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C2×C3×Dic5#4111yescharacteristic
81C3×D20—21no—
82C3×D20—21no—
83C3×D20—21no—
84C3×D20M1612yescomplemented
85C3×C4×D5—41no—
86C3×C4×D5—41no—
87C3×C4×D5—41no—
88C3×C4×D5—41no—
89C3×#170—21no—
90C3×#170—41no—
91C3×#170—41no—
92C3×#170—41no—
93C3×#170D812yescomplemented
94C3×C5×C8—21no—
95C3×#168—21no—
96C2×C3×D8—51no—
97C2×C3×M16—101no—
98C22×C3×C8—101no—
99C3×C4×D4—51no—
100C3×C4×D4—51no—
101C3×#107AGL(1,𝔽5)11yescharacteristic
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×D20C2×C3×C411yescharacteristic
112C2×D20C2×C3×C411yescharacteristic
113C2×C4×D5—21no—
114C2×C4×D5—21no—
115C2×#170—21no—
116C2×#170—21no—
117C2×#170—21no—
118C2×#170C3×D411yescharacteristic
119C2×#170C3×D411yescharacteristic
120#700—42no—
121D5⋊C8—42no—
122C2×C5×C8C2×C3×C411yescharacteristic
123C5×C4⋊C4C2×C3×C411yescharacteristic
124C5×C4⋊C4C2×C3×C411yescharacteristic
125#685—21no—
126#685—21no—
127C4×Dic5C23×C311yescharacteristic
128C2×#168C2×C3×C411yescharacteristic
129D40—22no—
130C4×D8—51no—
131#436—51no—
132C8×D4—51no—
133#335—51no—
134D4⋊C8—51no—
135D4⋊C8—51no—
136#322—51no—
137C22×C3×C5C4×D411yescharacteristic
138C2×C3×D5—22no—
139C2×C3×D5—41no—
140C2×C3×D5—41no—
141C2×C3×D5—41no—
142C2×C3×D5—41no—
143C2×C3×D5—41no—
144C3×C4×C5—41no—
145C3×C4×C5—41no—
146C3×C4×C5C2×M1611yescharacteristic
147C3×C4×C5#13111yescharacteristic
148C3×Dic5—21no—
149C3×Dic5C2×D811yescharacteristic
150C3×Dic5#13511yescharacteristic
151C2×C3×D4—51no—
152C2×C3×D4—51no—
153C22×C3×C4—101no—
154C22×C3×C4—101no—
155C3×D8—102no—
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⋊C4C2×AGL(1,𝔽5)11yescharacteristic
166C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
167C3×C22⋊C4—101no—
168C3×C22⋊C4—101no—
169C3×C42—51no—
170C22×D5—21no—
171C22×D5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5C22×C3×C411yescharacteristic
175C2×Dic5C2×C3×D411yescharacteristic
176C2×Dic5C3×#4111yescharacteristic
177D20—21no—
178D20—21no—
179D20—21no—
180D20C3×M1612yescomplemented
181C4×D5—41no—
182C4×D5—41no—
183C4×D5—41no—
184C4×D5—41no—
185#170—21no—
186#170—41no—
187#170—41no—
188#170—41no—
189#170C3×D812yescomplemented
190C5×C8—21no—
191#168—21no—
192C2×D8—51no—
193C2×M16—101no—
194C22×C8—101no—
195C4×D4—51no—
196C4×D4—51no—
197#107C3×AGL(1,𝔽5)11yescharacteristic
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#43511yescharacteristic
208C2×C3×C5C4×D811yescharacteristic
209C2×C3×C5#44411yescharacteristic
210C3×D5—42no—
211C3×D5—81no—
212C23×C3—101no—
213C23×C3—101no—
214C3×D4—52no—
215C3×D4—101no—
216C3×D4—101no—
217C3×D4—101no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—51no—
221C2×C3×C4—51no—
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—52no—
229C3×C8—101no—
230C3×C8—101no—
231C3×C8—201no—
232C3×C8—201no—
233C3×C8—201no—
234C22×C5C3×C4×D411yescharacteristic
235C2×D5—22no—
236C2×D5—41no—
237C2×D5—41no—
238C2×D5—41no—
239C2×D5—41no—
240C2×D5—41no—
241C4×C5—41no—
242C4×C5—41no—
243C4×C5C2×C3×M1611yescharacteristic
244C4×C5C3×#13111yescharacteristic
245Dic5—21no—
246Dic5C2×C3×D811yescharacteristic
247Dic5C3×#13511yescharacteristic
248C2×D4—51no—
249C2×D4—51no—
250C22×C4—101no—
251C22×C4—101no—
252D8—102no—
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⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
263C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
264C22⋊C4—101no—
265C22⋊C4—101no—
266C42—51no—
267C3×C5#158111yescharacteristic, complemented, Hall
268C22×C3—102no—
269C22×C3—201no—
270C22×C3—201no—
271C22×C3—201no—
272C22×C3—201no—
273C22×C3—201no—
274C22×C3D4×AGL(1,𝔽5)11yescharacteristic
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—51no—
278C3×C4—51no—
279C3×C4—101no—
280C3×C4D5⋊M1611yescharacteristic
281C3×C4#413311yescharacteristic
282C2×C5C3×#43511yescharacteristic
283C2×C5C3×C4×D811yescharacteristic
284C2×C5C3×#44411yescharacteristic
285D5—42no—
286D5—81no—
287C23—101no—
288C23—101no—
289D4—52no—
290D4—101no—
291D4—101no—
292D4—101no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
302C8—21no—
303C8—52no—
304C8—101no—
305C8—101no—
306C8—201no—
307C8—201no—
308C8—201no—
309C2×C3—202no—
310C2×C3—401no—
311C2×C3#6570411yescharacteristic
312C2×C3D8×AGL(1,𝔽5)11yescharacteristic
313C2×C3#6574111yescharacteristic
314C5C3×#158111yescharacteristic, complemented, Sylow
315C22—102no—
316C22—201no—
317C22—201no—
318C22—201no—
319C22—201no—
320C22—201no—
321C22C3×D4×AGL(1,𝔽5)11yescharacteristic
322C4—41no—
323C4—41no—
324C4—51no—
325C4—51no—
326C4—101no—
327C4C3×D5⋊M1611yescharacteristic
328C4C3×#413311yescharacteristic
329C3#1060406311yescharacteristic, direct product factor, Sylow
330C2—202no—
331C2—401no—
332C2C3×#6570411yescharacteristic
333C2C3×D8×AGL(1,𝔽5)11yescharacteristic
334C2C3×#6574111yescharacteristic
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 radicalC2×C3×D40C4
cosocleC4×Dic5C23×C3
hypercenterC3×#107AGL(1,𝔽5)
hypocenterC5C3×#1581
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
1. C3×#65705C2semidirect
2. C3×#65702C2semidirect
4. C3×#64884C2semidirect
5. C3×#170⋊C8C2semidirect
6. C3×#64871C2semidirect
7. C3×#64871C2semidirect
8. #10604063C3direct (N × H)
25. #65705C2×C3semidirect
26. #65702C2×C3semidirect
28. #64884C2×C3semidirect
29. #170⋊C8C2×C3semidirect
30. #64871C2×C3semidirect
31. #64871C2×C3semidirect
84. C3×D20M16semidirect
93. C3×#170D8semidirect
180. D20C3×M16semidirect
189. #170C3×D8semidirect
267. C3×C5#1581semidirect
314. C5C3×#1581semidirect
329. C3#10604063direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#657052
C3×#657022
C3×#651612
C3×#648842
C3×#170⋊C82
C3×#648712
#106040633
C3×#15815