Finite Group Databasebeta

← C3×#10600764 #14280987

Subgroups — C3×#10600764 #14280987

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#683C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4C3×#64689C214yesmaximal, complemented
5#10600764C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C23×C3×Dic5C411yescharacteristic
8C23×C3×Dic5C411yescharacteristic
9C2×C3×C5×M16—21no—
10C2×C3×#683—21no—
11C2×C3×#683—21no—
12C2×C3×#683—21no—
13C2×C3×#683—21no—
14C2×C3×#683C412yes—
15C2×C3×#683C2212yes—
16C2×C3×#681—21no—
17C3×C5×C22⋊C8—21no—
18C3×C5×C22⋊C8C2212yes—
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yes—
21C3×#1463—51nomaximal, Hall
22C22×#683C2×C311yescharacteristic
23C5×#407C2×C311yescharacteristic
24#65496C2×C311yescharacteristic
25#64689C2×C314yescomplemented
26C24×C3×C5C2×C411yescharacteristic
27C22×C3×C4×C5—42no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C22×C3×Dic5—21no—
35C22×C3×Dic5—21no—
36C22×C3×Dic5—24no—
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5—42no—
40C22×C3×Dic5C2×C412yes—
41C22×C3×Dic5C2×C412yes—
42C3×C5×M16—42no—
43C2×C3×C5×C8—22no—
44C3×#683—22no—
45C3×#683—22no—
46C3×#683—22no—
47C3×#683—22no—
48C3×#681—42no—
49C2×C3×#168—22no—
50C22×C3×C4⋊C4—51no—
51C3×#407—51no—
52C3×#407D511yescharacteristic
53C3×#324—54no—
54C23×C4×C5C22×C311yescharacteristic
55C23×Dic5C3×C411yescharacteristic
56C23×Dic5C3×C411yescharacteristic
57C2×C5×M16—21no—
58C2×#683—21no—
59C2×#683—21no—
60C2×#683—21no—
61C2×#683—21no—
62C2×#683C3×C412yes—
63C2×#683C22×C312yes—
64C2×#681—21no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8C22×C312yes—
67C22⋊#168—21no—
68C22⋊#168C22×C312yes—
69#1463—51noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22×C411yescharacteristic
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×Dic5—24no—
87C2×C3×Dic5—24no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—42no—
92C2×C3×Dic5—42no—
93C2×C3×Dic5—42no—
94C2×C3×Dic5M1614yescomplemented
95C3×C5×C8—42no—
96C3×#168—42no—
97C23×C3×C4—51no—
98C23×C3×C4—51no—
99C23×C3×C4C2×D511yescharacteristic
100C2×C3×M16—21no—
101C2×C3×M16—101no—
102C2×C3×C4⋊C4—52no—
103C2×C3×C4⋊C4—52no—
104C2×C3×C4⋊C4—101no—
105C2×C3×C4⋊C4—101no—
106C2×C3×C4⋊C4—101no—
107C2×C3×C4⋊C4—101no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—52no—
110C3×C22⋊C8—101no—
111C3×C22⋊C8C2×D512yes—
112C24×C5C2×C3×C411yescharacteristic
113C22×C4×C5—42no—
114C22×C4×C5C2×C3×C411yescharacteristic
115C22×C4×C5C3×D411yescharacteristic
116C22×C4×C5C3×D411yescharacteristic
117C22×C4×C5C3×D411yescharacteristic
118C22×C4×C5C3×D411yescharacteristic
119C22×C4×C5C23×C311yescharacteristic
120C22×Dic5—21no—
121C22×Dic5—21no—
122C22×Dic5—24no—
123C22×Dic5—21no—
124C22×Dic5—21no—
125C22×Dic5—42no—
126C22×Dic5C2×C3×C412yes—
127C22×Dic5C2×C3×C412yes—
128C5×M16—42no—
129C2×C5×C8—22no—
130#683—22no—
131#683—22no—
132#683—22no—
133#683—22no—
134#681—42no—
135C2×#168—22no—
136C22×C4⋊C4—51no—
137#407—51no—
138#407C3×D511yescharacteristic
139#324—54no—
140C22×C3×C5—28no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5#9912yes—
148C22×C3×C5#10112yes—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C22×C3×C5C2×M1612yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×Dic5—24no—
156C3×Dic5—42no—
157C24×C3C4×D511yescharacteristic
158C22×C3×C4—42no—
159C22×C3×C4—52no—
160C22×C3×C4—52no—
161C22×C3×C4—104no—
162C22×C3×C4—101no—
163C22×C3×C4—101no—
164C22×C3×C4—101no—
165C22×C3×C4—101no—
166C22×C3×C4—202no—
167C22×C3×C4C4×D511yescharacteristic
168C22×C3×C4D2011yescharacteristic
169C22×C3×C4D2011yescharacteristic
170C22×C3×C4C22⋊D511yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22×D511yescharacteristic
173C3×M16—42no—
174C3×M16—202no—
175C2×C3×C8—22no—
176C2×C3×C8—102no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—102no—
181C23×C5—22no—
182C23×C5—22no—
183C23×C5—22no—
184C23×C5C3×C22⋊C411yescharacteristic
185C23×C5C3×C22⋊C411yescharacteristic
186C23×C5C22×C3×C411yescharacteristic
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5C3×C22⋊C411yescharacteristic
194C2×C4×C5C3×C22⋊C411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—24no—
198C2×Dic5—24no—
199C2×Dic5—22no—
200C2×Dic5—22no—
201C2×Dic5—22no—
202C2×Dic5—42no—
203C2×Dic5—42no—
204C2×Dic5—42no—
205C2×Dic5C3×M1614yescomplemented
206C5×C8—42no—
207#168—42no—
208C23×C4—51no—
209C23×C4—51no—
210C23×C4C2×C3×D511yescharacteristic
211C2×M16—21no—
212C2×M16—101no—
213C2×C4⋊C4—52no—
214C2×C4⋊C4—52no—
215C2×C4⋊C4—101no—
216C2×C4⋊C4—101no—
217C2×C4⋊C4—101no—
218C2×C4⋊C4—101no—
219C22⋊C8—21no—
220C22⋊C8—52no—
221C22⋊C8—101no—
222C22⋊C8C2×C3×D512yes—
223C2×C3×C5—22no—
224C2×C3×C5—22no—
225C2×C3×C5—22no—
226C2×C3×C5#40711yescharacteristic
227C2×C3×C5C2×#9911yescharacteristic
228C2×C3×C5C2×#10111yescharacteristic
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3#68511yescharacteristic
233C23×C3#68511yescharacteristic
234C23×C3C2×C4×D511yescharacteristic
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—54no—
242C2×C3×C4—104no—
243C2×C3×C4—104no—
244C2×C3×C4—102no—
245C2×C3×C4—102no—
246C2×C3×C4—102no—
247C2×C3×C4—202no—
248C2×C3×C4—202no—
249C2×C3×C4—202no—
250C2×C3×C4#68511yescharacteristic
251C2×C3×C4#68511yescharacteristic
252C2×C3×C4C2×D2011yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C3×C8—42no—
255C3×C8—202no—
256C22×C5—28no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5C3×#9912yes—
264C22×C5C3×#10112yes—
265C22×C5C2×C3×C22⋊C411yescharacteristic
266C22×C5C2×C3×M1612yes—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—21no—
271Dic5—24no—
272Dic5—42no—
273C24C3×C4×D511yescharacteristic
274C22×C4—42no—
275C22×C4—52no—
276C22×C4—52no—
277C22×C4—104no—
278C22×C4—101no—
279C22×C4—101no—
280C22×C4—101no—
281C22×C4—101no—
282C22×C4—202no—
283C22×C4C3×C4×D511yescharacteristic
284C22×C4C3×D2011yescharacteristic
285C22×C4C3×D2011yescharacteristic
286C22×C4C3×C22⋊D511yescharacteristic
287C22×C4C3×C22⋊D511yescharacteristic
288C22×C4C22×C3×D511yescharacteristic
289M16—42no—
290M16—202no—
291C2×C8—22no—
292C2×C8—102no—
293C4⋊C4—102no—
294C4⋊C4—102no—
295C4⋊C4—102no—
296C4⋊C4—102no—
297C3×C5#146311yescharacteristic, complemented, Hall
298C22×C3—28no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3#393812yes—
306C22×C3#395612yes—
307C22×C3D5×M1612yes—
308C22×C3C2×#68511yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—104no—
314C3×C4—202no—
315C2×C5—22no—
316C2×C5—22no—
317C2×C5—22no—
318C2×C5C3×#40711yescharacteristic
319C2×C5C2×C3×#9911yescharacteristic
320C2×C5C2×C3×#10111yescharacteristic
321C23—22no—
322C23—22no—
323C23—22no—
324C23C3×#68511yescharacteristic
325C23C3×#68511yescharacteristic
326C23C2×C3×C4×D511yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—54no—
334C2×C4—104no—
335C2×C4—104no—
336C2×C4—102no—
337C2×C4—102no—
338C2×C4—102no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4C3×#68511yescharacteristic
343C2×C4C3×#68511yescharacteristic
344C2×C4C2×C3×D2011yescharacteristic
345C2×C4C2×C3×C22⋊D511yescharacteristic
346C8—42no—
347C8—202no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—22no—
351C2×C3C2×#393811yescharacteristic
352C2×C3#6541511yescharacteristic
353C2×C3C2×#395611yescharacteristic
354C5C3×#146311yescharacteristic, complemented, Sylow
355C22—28no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22C3×#393812yes—
363C22C3×#395612yes—
364C22C3×D5×M1612yes—
365C22C2×C3×#68511yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—104no—
371C4—202no—
372C3#1060076411yescharacteristic, direct product factor, Sylow
373C2—22no—
374C2—22no—
375C2—22no—
376C2C2×C3×#393811yescharacteristic
377C2C3×#6541511yescharacteristic
378C2C2×C3×#395611yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#407D5
hypocenterC5C3×#1463
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. C3×#64689C2semidirect
5. #10600764C3direct (N × H)
25. #64689C2×C3semidirect
94. C2×C3×Dic5M16semidirect
205. C2×Dic5C3×M16semidirect
297. C3×C5#1463semidirect
354. C5C3×#1463semidirect
372. C3#10600764direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6832
C3×C5×#4072
C3×#654962
C3×#646892
#106007643
C3×#14635