Finite Group Databasebeta

← C3×#10599352 #14286496

Subgroups — C3×#10599352 #14286496

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×#65127C211yesmaximal, characteristic, complemented
2C3×#65123C211yesmaximal, characteristic, complemented
3C3×C4×D40C211yesmaximal, characteristic
4C3×C5×#335C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64674C211yesmaximal, characteristic, complemented
8#10599352C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D40C411yescharacteristic
10C2×C3×#676—21no—
11C2×C3×C8×D5—21no—
12C3×C4×D20C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17C3×#3953C411yescharacteristic
18C3×#3953C411yescharacteristic
19C3×#3952—21no—
20C3×#3952—21no—
21C3×#3950C411yescharacteristic
22C3×C4×#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1581—51nomaximal, Hall
25#65127C2×C311yescharacteristic, complemented
26#65123C2×C311yescharacteristic, complemented
27C4×D40C2×C311yescharacteristic
28C5×#335C2×C311yescharacteristic, complemented
29#64703C2×C311yescharacteristic, complemented
30#64703C2×C311yescharacteristic, complemented
31#64674C2×C311yescharacteristic, complemented
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8C2×C411yescharacteristic
39C2×C3×C5×C8C2×C411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C3×#685—21no—
42C3×#685—21no—
43C3×C4⋊Dic5C2×C411yescharacteristic
44C3×C4⋊Dic5C2×C411yescharacteristic
45C2×C3×#168—21no—
46C2×C3×#168D411yescharacteristic
47C2×C3×#168D411yescharacteristic
48C3×D40—22no—
49C3×#676—42no—
50C3×C8×D5—42no—
51C3×C4×D8—51no—
52C3×#436—51no—
53C3×C8×D4—51no—
54C3×#335D511yescharacteristic, complemented
55C3×D4⋊C8—51no—
56C3×D4⋊C8—51no—
57C3×#322—51no—
58C2×D40C3×C411yescharacteristic
59C2×#676—21no—
60C2×C8×D5—21no—
61C4×D20C22×C311yescharacteristic
62C4×D20C22×C311yescharacteristic
63C5×C4⋊C8C22×C311yescharacteristic
64C5×C4⋊C8C22×C311yescharacteristic
65C4×C5×C8C22×C311yescharacteristic
66#3953C3×C411yescharacteristic
67#3953C3×C411yescharacteristic
68#3952—21no—
69#3952—21no—
70#3950C3×C411yescharacteristic
71C4×#168C22×C311yescharacteristic
72C4×#168C22×C311yescharacteristic
73#1581—51noSylow
74C22×C3×D5—21no—
75C22×C3×D5—21no—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×C3×Dic5—21no—
80C2×C3×Dic5—21no—
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×C5×C8—21no—
90C3×C5×C8—21no—
91C3×C5×C8—41no—
92C3×C5×C8—41no—
93C3×#168—21no—
94C3×#168—41no—
95C3×#168D812yescomplemented
96C2×C3×D8—51no—
97C2×C3×M16—101no—
98C22×C3×C8—101no—
99C3×C4×D4—51no—
100C3×C4×D4—51no—
101C3×#107—51no—
102C3×C4⋊C8C2×D511yescharacteristic
103C3×C4⋊C8C2×D511yescharacteristic
104C3×#102—51no—
105C3×#102—51no—
106C3×C22⋊C8—101no—
107C3×C22⋊C8—101no—
108C3×C4×C8—51no—
109C3×C4×C8—51no—
110C3×C4×C8C2×D511yescharacteristic
111C2×D20C2×C3×C411yescharacteristic
112C2×D20C2×C3×C411yescharacteristic
113C2×C4×D5—21no—
114C2×C4×D5—21no—
115C2×C5×C8—21no—
116C2×C5×C8—21no—
117C2×C5×C8C2×C3×C411yescharacteristic
118C2×C5×C8C2×C3×C411yescharacteristic
119C42×C5C23×C311yescharacteristic
120#685—21no—
121#685—21no—
122C4⋊Dic5C2×C3×C411yescharacteristic
123C4⋊Dic5C2×C3×C411yescharacteristic
124C2×#168—21no—
125C2×#168C3×D411yescharacteristic
126C2×#168C3×D411yescharacteristic
127D40—22no—
128#676—42no—
129C8×D5—42no—
130C4×D8—51no—
131#436—51no—
132C8×D4—51no—
133#335C3×D511yescharacteristic, complemented
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—21no—
145C3×C4×C5C2×M1611yescharacteristic
146C3×C4×C5#13111yescharacteristic
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×Dic5—41no—
150C3×Dic5—41no—
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—21no—
158C2×C3×C8—21no—
159C2×C3×C8—51no—
160C2×C3×C8—51no—
161C2×C3×C8—101no—
162C2×C3×C8—202no—
163C2×C3×C8C4×D511yescharacteristic
164C2×C3×C8C4×D511yescharacteristic
165C3×C4⋊C4—51no—
166C3×C4⋊C4—51no—
167C3×C22⋊C4—101no—
168C3×C22⋊C4—101no—
169C3×C42C22×D511yescharacteristic
170C22×D5—21no—
171C22×D5—21no—
172C2×C4×C5C22×C3×C411yescharacteristic
173C2×C4×C5C2×C3×D411yescharacteristic
174C2×C4×C5C3×#4111yescharacteristic
175C2×Dic5—21no—
176C2×Dic5—21no—
177D20—21no—
178D20—21no—
179D20—21no—
180D20C3×M1612yescomplemented
181C4×D5—41no—
182C4×D5—41no—
183C4×D5—41no—
184C4×D5—41no—
185C5×C8—21no—
186C5×C8—21no—
187C5×C8—41no—
188C5×C8—41no—
189#168—21no—
190#168—41no—
191#168C3×D812yescomplemented
192C2×D8—51no—
193C2×M16—101no—
194C22×C8—101no—
195C4×D4—51no—
196C4×D4—51no—
197#107—51no—
198C4⋊C8C2×C3×D511yescharacteristic
199C4⋊C8C2×C3×D511yescharacteristic
200#102—51no—
201#102—51no—
202C22⋊C8—101no—
203C22⋊C8—101no—
204C4×C8—51no—
205C4×C8—51no—
206C4×C8C2×C3×D511yescharacteristic
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—101no—
219C2×C3×C4—101no—
220C2×C3×C4—201no—
221C2×C3×C4—201no—
222C2×C3×C4—201no—
223C2×C3×C4—201no—
224C2×C3×C4C2×C4×D511yescharacteristic
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4#71311yescharacteristic
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—52no—
232C3×C8—101no—
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—21no—
242C4×C5C2×C3×M1611yescharacteristic
243C4×C5C3×#13111yescharacteristic
244C4×C5C2×C3×D811yescharacteristic
245C4×C5C3×#13511yescharacteristic
246Dic5—41no—
247Dic5—41no—
248C2×D4—51no—
249C2×D4—51no—
250C22×C4—101no—
251C22×C4—101no—
252D8—102no—
253M16—202no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—51no—
257C2×C8—51no—
258C2×C8—101no—
259C2×C8—202no—
260C2×C8C3×C4×D511yescharacteristic
261C2×C8C3×C4×D511yescharacteristic
262C4⋊C4—51no—
263C4⋊C4—51no—
264C22⋊C4—101no—
265C22⋊C4—101no—
266C42C22×C3×D511yescharacteristic
267C3×C5#158111yescharacteristic, complemented, Hall
268C22×C3—102no—
269C22×C3—201no—
270C22×C3—201no—
271C22×C3—201no—
272C22×C3—201no—
273C22×C3—201no—
274C22×C3#403911yescharacteristic
275C3×C4—21no—
276C3×C4—201no—
277C3×C4—201no—
278C3×C4#404711yescharacteristic
279C3×C4D5×M1611yescharacteristic
280C3×C4D5×D811yescharacteristic
281C3×C4#406511yescharacteristic
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—101no—
294C2×C4—101no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4C2×C3×C4×D511yescharacteristic
300C2×C4C3×D4×D511yescharacteristic
301C2×C4C3×#71311yescharacteristic
302C8—21no—
303C8—21no—
304C8—41no—
305C8—41no—
306C8—52no—
307C8—101no—
308C8—201no—
309C2×C3—202no—
310C2×C3—401no—
311C2×C3#6512511yescharacteristic
312C2×C3#6516111yescharacteristic
313C2×C3#6518311yescharacteristic
314C5C3×#158111yescharacteristic, complemented, Sylow
315C22—102no—
316C22—201no—
317C22—201no—
318C22—201no—
319C22—201no—
320C22—201no—
321C22C3×#403911yescharacteristic
322C4—21no—
323C4—201no—
324C4—201no—
325C4C3×#404711yescharacteristic
326C4C3×D5×M1611yescharacteristic
327C4C3×D5×D811yescharacteristic
328C4C3×#406511yescharacteristic
329C3#1059935211yescharacteristic, direct product factor, Sylow
330C2—202no—
331C2—401no—
332C2C3×#6512511yescharacteristic
333C2C3×#6516111yescharacteristic
334C2C3×#6518311yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#335C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×D40C4
cosocleC42×C5C23×C3
hypercenterC3×#335D5
hypocenterC5C3×#1581
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×#335

Complements

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

NH ≅ G/Ntype
1. C3×#65127C2semidirect
2. C3×#65123C2semidirect
4. C3×C5×#335C2semidirect
5. C3×#64703C2semidirect
6. C3×#64703C2semidirect
7. C3×#64674C2semidirect
8. #10599352C3direct (N × H)
25. #65127C2×C3semidirect
26. #65123C2×C3semidirect
28. C5×#335C2×C3semidirect
29. #64703C2×C3semidirect
30. #64703C2×C3semidirect
31. #64674C2×C3semidirect
54. C3×#335D5semidirect
84. C3×D20M16semidirect
95. C3×#168D8semidirect
133. #335C3×D5semidirect
180. D20C3×M16semidirect
191. #168C3×D8semidirect
267. C3×C5#1581semidirect
314. C5C3×#1581semidirect
329. C3#10599352direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#651272
C3×#651232
C3×C4×D402
C3×C5×#3352
C3×#647032
C3×#646742
#105993523
C3×#15815