Finite Group Databasebeta

← C3×#10602029 #14289683

Subgroups — C3×#10602029 #14289683

Order 1920.

376 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66055C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic
3C3×#65380C211yesmaximal, characteristic
4C3×#65380C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic
6C3×#64676C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic
8#10602029C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×Q8×Dic5—21no—
12C3×#4090—21no—
13C3×#4036—21no—
14C3×#4035—22no—
15C3×#4033—21no—
16C3×C4×Dic10C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C3×C5×#103—22no—
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3942—21no—
21C3×#3942—21no—
22C3×#3939—21no—
23C3×#3939—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1636—51nomaximal, Hall
27#66055C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic
29#65380C2×C311yescharacteristic
30#65380C2×C311yescharacteristic
31#64767C2×C311yescharacteristic
32#64676C2×C311yescharacteristic
33#64676C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×Dic10D411yescharacteristic
37C2×C3×Dic10D411yescharacteristic
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44C3×C4⋊Dic5—22no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×C4⋊Dic5D411yescharacteristic
47C3×#683—22no—
48C3×#683—22no—
49C3×#683—21no—
50C3×#683—21no—
51C3×C4×Dic5—22no—
52C3×C4×Dic5—21no—
53C3×C4×Dic5—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C3×#557—51no—
57C3×#487D511yescharacteristic
58C3×#477—51no—
59C3×#477—51no—
60C3×#332—51no—
61C3×Q8⋊C8—51no—
62C3×Q8⋊C8—51no—
63C5×C4⋊Q8C22×C311yescharacteristic
64C5×C4⋊Q8C22×C311yescharacteristic
65Q8×Dic5—21no—
66#4090—21no—
67#4036—21no—
68#4035—22no—
69#4033—21no—
70C4×Dic10C22×C311yescharacteristic
71C4×Dic10C22×C311yescharacteristic
72C5×#103—22no—
73C4×C5×C8C22×C311yescharacteristic
74#3942—21no—
75#3942—21no—
76#3939—21no—
77#3939—21no—
78C4⋊#168C22×C311yescharacteristic
79C4⋊#168C22×C311yescharacteristic
80#1636—51noSylow
81C3×C5×Q8—42no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×Dic10—21no—
94C3×Dic10—21no—
95C3×Dic10—21no—
96C3×Dic10Q1612yes—
97C3×C5×C8—41no—
98C3×#168—41no—
99C3×#168—41no—
100C3×C4⋊Q8—101no—
101C3×C4⋊Q8C2×D511yescharacteristic
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#125—101no—
104C3×#125—102no—
105C3×C4×Q8—51no—
106C3×C4×Q8—51no—
107C3×C4×Q8—101no—
108C3×C4×Q8—101no—
109C3×#107—101no—
110C3×#107—101no—
111C3×C4⋊C8—51no—
112C3×C4⋊C8—51no—
113C3×#103—22no—
114C3×#103—101no—
115C3×#103—101no—
116C3×C4×C8C2×D511yescharacteristic
117C2×C5×Q8—21no—
118C2×C5×Q8—21no—
119C2×Dic10C3×D411yescharacteristic
120C2×Dic10C3×D411yescharacteristic
121C2×C5×C8—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4C3×D412yes—
126C42×C5C23×C311yescharacteristic
127C4⋊Dic5—22no—
128C4⋊Dic5C3×D411yescharacteristic
129C4⋊Dic5C3×D411yescharacteristic
130#683—22no—
131#683—22no—
132#683—21no—
133#683—21no—
134C4×Dic5—22no—
135C4×Dic5—21no—
136C4×Dic5—21no—
137C2×#168—21no—
138C2×#168—21no—
139#557—51no—
140#487C3×D511yescharacteristic
141#477—51no—
142#477—51no—
143#332—51no—
144Q8⋊C8—51no—
145Q8⋊C8—51no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5—81no—
150C3×C4×C5C2×Q1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×C4×C5#13711yescharacteristic
154C3×Dic5—22no—
155C3×Dic5—41no—
156C3×Dic5—41no—
157C3×Dic5—41no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—51no—
161C2×C3×Q8—51no—
162C2×C3×C8—21no—
163C2×C3×C8—101no—
164C2×C3×C8—101no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—102no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4C22⋊D512yes—
176C3×C42—102no—
177C3×C42—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180C5×Q8—42no—
181C5×Q8—41no—
182C5×Q8—41no—
183C2×C4×C5—22no—
184C2×C4×C5—41no—
185C2×C4×C5C2×C3×D411yescharacteristic
186C2×C4×C5C2×C3×D411yescharacteristic
187C2×C4×C5C2×C3×D411yescharacteristic
188C2×Dic5—21no—
189C2×Dic5—21no—
190C2×Dic5—21no—
191C2×Dic5—21no—
192Dic10—21no—
193Dic10—21no—
194Dic10—21no—
195Dic10C3×Q1612yes—
196C5×C8—41no—
197#168—41no—
198#168—41no—
199C4⋊Q8—101no—
200C4⋊Q8C2×C3×D511yescharacteristic
201C4⋊Q8C2×C3×D511yescharacteristic
202#125—101no—
203#125—102no—
204C4×Q8—51no—
205C4×Q8—51no—
206C4×Q8—101no—
207C4×Q8—101no—
208#107—101no—
209#107—101no—
210C4⋊C8—51no—
211C4⋊C8—51no—
212#103—22no—
213#103—101no—
214#103—101no—
215C4×C8C2×C3×D511yescharacteristic
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—42no—
220C3×Q8—41no—
221C3×Q8—41no—
222C3×Q8—52no—
223C3×Q8—101no—
224C3×Q8—101no—
225C3×Q8—101no—
226C2×C3×C4—22no—
227C2×C3×C4—41no—
228C2×C3×C4—101no—
229C2×C3×C4—101no—
230C2×C3×C4—101no—
231C2×C3×C4—101no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C3×C8—41no—
236C3×C8—201no—
237C3×C8—201no—
238C22×C5C3×#12011yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5—81no—
242C4×C5C2×C3×Q1611yescharacteristic
243C4×C5C3×#13511yescharacteristic
244C4×C5C3×#13711yescharacteristic
245C4×C5C3×#13711yescharacteristic
246Dic5—22no—
247Dic5—41no—
248Dic5—41no—
249Dic5—41no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—51no—
253C2×Q8—51no—
254C2×C8—21no—
255C2×C8—101no—
256C2×C8—101no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—51no—
261C4⋊C4—51no—
262C4⋊C4—102no—
263C4⋊C4—102no—
264C4⋊C4—102no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4C3×C22⋊D512yes—
268C42—102no—
269C42—101no—
270C42—101no—
271C42C22×C3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4—81no—
277C3×C4—102no—
278C3×C4—201no—
279C3×C4—201no—
280C3×C4—201no—
281C3×C4#406111yescharacteristic
282C3×C4#406211yescharacteristic
283C3×C4D5×Q1611yescharacteristic
284C3×C4#406411yescharacteristic
285C2×C5C3×#45111yescharacteristic
286C2×C5C3×#45211yescharacteristic
287C2×C5C3×#45411yescharacteristic
288Q8—42no—
289Q8—41no—
290Q8—41no—
291Q8—52no—
292Q8—101no—
293Q8—101no—
294Q8—101no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—101no—
301C2×C4C3×D4×D511yescharacteristic
302C2×C4C3×D4×D511yescharacteristic
303C2×C4C2×C3×C22⋊D511yescharacteristic
304C8—41no—
305C8—201no—
306C8—201no—
307C2×C3#6535111yescharacteristic
308C2×C3#6546211yescharacteristic
309C2×C3#6547511yescharacteristic
310C5C3×#163611yescharacteristic, complemented, Sylow
311C22C3×#408311yescharacteristic
312C4—21no—
313C4—42no—
314C4—81no—
315C4—102no—
316C4—201no—
317C4—201no—
318C4—201no—
319C4C3×#406111yescharacteristic
320C4C3×#406211yescharacteristic
321C4C3×D5×Q1611yescharacteristic
322C4C3×#406411yescharacteristic
323C3#1060202911yescharacteristic, direct product factor, Sylow
324C2C3×#6535111yescharacteristic
325C2C3×#6546211yescharacteristic
326C2C3×#6547511yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#487C2
socle, prime radicalC22×C3×C5#120
hypercenterC3×#487D5
hypocenterC5C3×#1636
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
8. #10602029C3direct (N × H)
272. C3×C5#1636semidirect
310. C5C3×#1636semidirect
323. C3#10602029direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660552
C3×C5×#4872
C3×#653802
C3×#647672
C3×#646762
#106020293
C3×#16365