Finite Group Databasebeta

← C3×#10600326 #14283303

Subgroups — C3×#10600326 #14283303

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4070C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4C3×#64672C214yesmaximal, complemented
5#10600326C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8C2×C3×C5×C22⋊C4—21no—
9C2×C3×C22⋊Dic5—21no—
10C2×C3×C4⋊Dic5C411yescharacteristic, complemented
11C3×#4070—21no—
12C3×#4070—21no—
13C3×#4070C412yescomplemented
14C3×#4070C2212yes—
15C2×C3×#683—21no—
16C2×C3×#681—21no—
17C3×C5×#95—21no—
18C3×C5×#95C2212yes—
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yes—
21C3×#1511—51nomaximal, Hall
22C2×#4070C2×C311yescharacteristic
23C5×#381C2×C311yescharacteristic
24#65496C2×C311yescharacteristic
25#64672C2×C314yescomplemented
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5—22no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×C3×Dic5—21no—
36C22×C3×Dic5—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10—42no—
39C2×C3×Dic10C2×C412yes—
40C3×C5×C22⋊C4—42no—
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—22no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5C2×C412yes—
45C3×#683—22no—
46C3×#683—22no—
47C3×#681—42no—
48C2×C3×#168—22no—
49C2×C3×C22⋊Q8—51no—
50C3×#407—51no—
51C3×#381D511yescharacteristic
52C3×#328—54no—
53C23×C4×C5C22×C311yescharacteristic
54C22×Dic10C3×C411yescharacteristic, complemented
55C2×C5×C22⋊C4—21no—
56C2×C22⋊Dic5—21no—
57C2×C4⋊Dic5C3×C411yescharacteristic, complemented
58#4070—21no—
59#4070—21no—
60#4070C3×C412yescomplemented
61#4070C22×C312yes—
62C2×#683—21no—
63C2×#681—21no—
64C5×#95—21no—
65C5×#95C22×C312yes—
66C22⋊#168—21no—
67C22⋊#168C22×C312yes—
68#1511—51noSylow
69C23×C3×C5—22no—
70C23×C3×C5—22no—
71C23×C3×C5—41no—
72C23×C3×C5C22⋊C411yescharacteristic
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5—42no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—42no—
91C2×C3×Dic5—42no—
92C3×Dic10—42no—
93C3×Dic10—42no—
94C3×#168—42no—
95C22×C3×Q8—51no—
96C23×C3×C4C2×D511yescharacteristic
97C2×C3×M16—101no—
98C3×C22⋊Q8—52no—
99C3×C22⋊Q8—52no—
100C3×C22⋊Q8—101no—
101C3×C22⋊Q8—101no—
102C2×C3×C4⋊C4—51no—
103C2×C3×C4⋊C4—101no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—101no—
106C3×C22⋊C8—52no—
107C3×C22⋊C8—101no—
108C3×#95—21no—
109C3×#95C2×D512yes—
110C24×C5C3×D411yescharacteristic
111C22×C4×C5—22no—
112C22×C4×C5—42no—
113C22×C4×C5C2×C3×C411yescharacteristic
114C22×C4×C5C2×C3×C411yescharacteristic
115C22×C4×C5C3×D411yescharacteristic
116C22×C4×C5C3×D411yescharacteristic
117C22×C4×C5C3×D411yescharacteristic
118C22×C4×C5C23×C311yescharacteristic
119C22×Dic5—21no—
120C22×Dic5—21no—
121C2×Dic10—21no—
122C2×Dic10—42no—
123C2×Dic10C2×C3×C412yes—
124C5×C22⋊C4—42no—
125C22⋊Dic5—22no—
126C22⋊Dic5—22no—
127C4⋊Dic5—21no—
128C4⋊Dic5C2×C3×C412yes—
129#683—22no—
130#683—22no—
131#681—42no—
132C2×#168—22no—
133C2×C22⋊Q8—51no—
134#407—51no—
135#381C3×D511yescharacteristic
136#328—54no—
137C22×C3×C5—21no—
138C22×C3×C5—21no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—44no—
145C22×C3×C5#9912yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C22×C3×C5#13712yes—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—82no—
153C3×Dic5—42no—
154C3×Dic5—42no—
155C24×C3C22⋊D511yescharacteristic
156C2×C3×Q8—52no—
157C2×C3×Q8—101no—
158C2×C3×Q8—202no—
159C22×C3×C4—22no—
160C22×C3×C4—42no—
161C22×C3×C4—101no—
162C22×C3×C4—101no—
163C22×C3×C4C4×D511yescharacteristic
164C22×C3×C4C4×D511yescharacteristic
165C22×C3×C4D2011yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C22×C3×C4C22×D511yescharacteristic
169C3×M16—202no—
170C2×C3×C8—102no—
171C3×C4⋊C4—52no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—102no—
175C3×C22⋊C4—42no—
176C3×C22⋊C4—102no—
177C3×C22⋊C4—102no—
178C23×C5—22no—
179C23×C5—22no—
180C23×C5—41no—
181C23×C5C3×C22⋊C411yescharacteristic
182C23×C5C3×C22⋊C411yescharacteristic
183C23×C5C2×C3×D411yescharacteristic
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5C3×C22⋊C411yescharacteristic
194C2×C4×C5C3×C22⋊C411yescharacteristic
195C2×C4×C5C22×C3×C411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—22no—
198C2×Dic5—22no—
199C2×Dic5—42no—
200C2×Dic5—42no—
201Dic10—42no—
202Dic10—42no—
203#168—42no—
204C22×Q8—51no—
205C23×C4C2×C3×D511yescharacteristic
206C2×M16—101no—
207C22⋊Q8—52no—
208C22⋊Q8—52no—
209C22⋊Q8—101no—
210C22⋊Q8—101no—
211C2×C4⋊C4—51no—
212C2×C4⋊C4—101no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—101no—
215C22⋊C8—52no—
216C22⋊C8—101no—
217#95—21no—
218#95C2×C3×D512yes—
219C2×C3×C5—22no—
220C2×C3×C5—22no—
221C2×C3×C5—41no—
222C2×C3×C5C2×#9911yescharacteristic
223C2×C3×C5#41911yescharacteristic
224C2×C3×C5#42111yescharacteristic
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—41no—
228C23×C3#68511yescharacteristic
229C23×C3#68511yescharacteristic
230C23×C3C2×C22⋊D511yescharacteristic
231C3×Q8—202no—
232C3×Q8—202no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—102no—
243C2×C3×C4—102no—
244C2×C3×C4—202no—
245C2×C3×C4—202no—
246C2×C3×C4#68511yescharacteristic
247C2×C3×C4#68511yescharacteristic
248C2×C3×C4C2×C4×D511yescharacteristic
249C2×C3×C4C2×D2011yescharacteristic
250C3×C8—202no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—44no—
259C22×C5C3×#9912yes—
260C22×C5C2×C3×C22⋊C411yescharacteristic
261C22×C5C3×#13712yes—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—82no—
267Dic5—42no—
268Dic5—42no—
269C24C3×C22⋊D511yescharacteristic
270C2×Q8—52no—
271C2×Q8—101no—
272C2×Q8—202no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—101no—
276C22×C4—101no—
277C22×C4C3×C4×D511yescharacteristic
278C22×C4C3×C4×D511yescharacteristic
279C22×C4C3×D2011yescharacteristic
280C22×C4C3×D2011yescharacteristic
281C22×C4C3×C22⋊D511yescharacteristic
282C22×C4C22×C3×D511yescharacteristic
283M16—202no—
284C2×C8—102no—
285C4⋊C4—52no—
286C4⋊C4—101no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C22⋊C4—42no—
290C22⋊C4—102no—
291C22⋊C4—102no—
292C3×C5#151111yescharacteristic, complemented, Hall
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—44no—
301C22×C3#393812yes—
302C22×C3C2×#68511yescharacteristic
303C22×C3#409712yes—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—82no—
309C3×C4—202no—
310C3×C4—202no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5—41no—
314C2×C5C2×C3×#9911yescharacteristic
315C2×C5C3×#41911yescharacteristic
316C2×C5C3×#42111yescharacteristic
317C23—22no—
318C23—22no—
319C23—41no—
320C23C3×#68511yescharacteristic
321C23C3×#68511yescharacteristic
322C23C2×C3×C22⋊D511yescharacteristic
323Q8—202no—
324Q8—202no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—102no—
335C2×C4—102no—
336C2×C4—202no—
337C2×C4—202no—
338C2×C4C3×#68511yescharacteristic
339C2×C4C3×#68511yescharacteristic
340C2×C4C2×C3×C4×D511yescharacteristic
341C2×C4C2×C3×D2011yescharacteristic
342C8—202no—
343C2×C3—22no—
344C2×C3—22no—
345C2×C3—41no—
346C2×C3C2×#393811yescharacteristic
347C2×C3#6529311yescharacteristic
348C2×C3#6529411yescharacteristic
349C5C3×#151111yescharacteristic, complemented, Sylow
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—44no—
358C22C3×#393812yes—
359C22C2×C3×#68511yescharacteristic
360C22C3×#409712yes—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—202no—
367C4—202no—
368C3#1060032611yescharacteristic, direct product factor, Sylow
369C2—22no—
370C2—22no—
371C2—41no—
372C2C2×C3×#393811yescharacteristic
373C2C3×#6529311yescharacteristic
374C2C3×#6529411yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#381C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#381D5
hypocenterC5C3×#1511
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
4. C3×#64672C2semidirect
5. #10600326C3direct (N × H)
7. C22×C3×Dic10C4semidirect
10. C2×C3×C4⋊Dic5C4semidirect
13. C3×#4070C4semidirect
25. #64672C2×C3semidirect
54. C22×Dic10C3×C4semidirect
57. C2×C4⋊Dic5C3×C4semidirect
60. #4070C3×C4semidirect
292. C3×C5#1511semidirect
349. C5C3×#1511semidirect
368. C3#10600326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40702
C3×C5×#3812
C3×#654962
C3×#646722
#106003263
C3×#15115