Finite Group Databasebeta

← C3×#10600852 #14313531

Subgroups — C3×#10600852 #14313531

Order 1920.

476 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
1C3×#66159C211yesmaximal, characteristic
2C3×C5×#410C211yesmaximal, characteristic
3C3×#65529C211yesmaximal, characteristic
4C3×#64693C214yesmaximal, complemented
5#10600852C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8C3×C5×#117—21no—
9C3×#4090C412yescomplemented
10C3×#4082C2212yes—
11C3×#4081—21no—
12C3×#4081—21no—
13C3×#4072—21no—
14C3×#4072C411yescharacteristic, complemented
15C3×#4070—21no—
16C3×#4070—21no—
17C3×C5×#99—21no—
18C3×C5×#99C2212yes—
19C3×#3966—21no—
20C3×#3966C2212yes—
21C3×#2129—51nomaximal, Hall
22#66159C2×C311yescharacteristic
23C5×#410C2×C311yescharacteristic
24#65529C2×C311yescharacteristic
25#64693C2×C314yescomplemented
26C3×C5×#41—41no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C2×C3×C5×D4D411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4C2311yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×Dic5—21no—
36C2×C3×Dic10—21no—
37C2×C3×Dic10—41no—
38C2×C3×Dic10—41no—
39C2×C3×Dic10C2×C412yes—
40C3×C5×C4⋊C4—41no—
41C3×C5×C22⋊C4—22no—
42C3×C42×C5—41no—
43C3×C22⋊Dic5—21no—
44C3×C22⋊Dic5—22no—
45C3×C22⋊Dic5—22no—
46C3×C22⋊Dic5—22no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—41no—
49C3×#683—22no—
50C3×#683—22no—
51C3×C4×Dic5—41no—
52C3×C4×Dic5C2×C412yes—
53C3×#536—51no—
54C3×#410—51no—
55C3×#410D511yescharacteristic
56C3×#354—54no—
57C2×C5×#41C22×C311yescharacteristic
58C22×Dic10C3×C411yescharacteristic, complemented
59C5×#117—21no—
60#4090C3×C412yescomplemented
61#4082C22×C312yes—
62#4081—21no—
63#4081—21no—
64#4072—21no—
65#4072C3×C411yescharacteristic, complemented
66#4070—21no—
67#4070—21no—
68C5×#99—21no—
69C5×#99C22×C312yes—
70#3966—21no—
71#3966C22×C312yes—
72#2129—51noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×Q8—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×Dic5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—42no—
94C2×C3×Dic5—42no—
95C3×Dic10—41no—
96C3×Dic10—41no—
97C3×Dic10—42no—
98C2×C3×#41C2×D511yescharacteristic
99C22×C3×Q8—51no—
100C3×C4⋊Q8—52no—
101C3×#124—52no—
102C3×#123—101no—
103C3×#123—101no—
104C3×C22⋊Q8—101no—
105C3×C22⋊Q8—101no—
106C3×#117—21no—
107C3×#117—51no—
108C3×#117—101no—
109C3×#99—21no—
110C3×#99—52no—
111C3×#99—101no—
112C3×#99C2×D512yes—
113C5×#41—41no—
114C5×#41—41no—
115C2×C5×Q8C2×C3×C411yescharacteristic
116C2×C5×D4C3×D411yescharacteristic
117C2×C5×D4C3×D411yescharacteristic
118C2×C5×D4C23×C311yescharacteristic
119C22×C4×C5C2×C3×C411yescharacteristic
120C22×C4×C5C3×D411yescharacteristic
121C22×C4×C5C3×D411yescharacteristic
122C22×Dic5—21no—
123C2×Dic10—21no—
124C2×Dic10—41no—
125C2×Dic10—41no—
126C2×Dic10C2×C3×C412yes—
127C5×C4⋊C4—41no—
128C5×C22⋊C4—22no—
129C42×C5—41no—
130C22⋊Dic5—21no—
131C22⋊Dic5—22no—
132C22⋊Dic5—22no—
133C22⋊Dic5—22no—
134C4⋊Dic5—21no—
135C4⋊Dic5—41no—
136#683—22no—
137#683—22no—
138C4×Dic5—41no—
139C4×Dic5C2×C3×C412yes—
140#536—51no—
141#410—51no—
142#410C3×D511yescharacteristic
143#354—54no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—82no—
155C3×C4×C5#9911yescharacteristic
156C3×C4×C5#9911yescharacteristic
157C3×Dic5—42no—
158C3×Dic5—42no—
159C3×Dic5—82no—
160C3×#41—41no—
161C3×#41—41no—
162C2×C3×Q8—52no—
163C2×C3×Q8—101no—
164C2×C3×Q8—201no—
165C2×C3×Q8—201no—
166C2×C3×Q8C4×D511yescharacteristic
167C2×C3×D4D2011yescharacteristic
168C2×C3×D4C22⋊D511yescharacteristic
169C2×C3×D4C22×D511yescharacteristic
170C22×C3×C4—101no—
171C22×C3×C4C4×D511yescharacteristic
172C22×C3×C4D2011yescharacteristic
173C22×C3×C4C22⋊D511yescharacteristic
174C3×C4⋊C4—41no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—102no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—201no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—101no—
181C3×C22⋊C4—102no—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C42—41no—
185C3×C42—52no—
186C3×C42—201no—
187C23×C5C3×C22⋊C411yescharacteristic
188C23×C5C2×C3×D411yescharacteristic
189C23×C5C2×C3×D411yescharacteristic
190C5×Q8—41no—
191C5×D4—41no—
192C5×D4—41no—
193C5×D4—41no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—42no—
201C2×C4×C5C3×C22⋊C411yescharacteristic
202C2×C4×C5C3×C22⋊C411yescharacteristic
203C2×C4×C5C3×C22⋊C411yescharacteristic
204C2×C4×C5C22×C3×C411yescharacteristic
205C2×Dic5—22no—
206C2×Dic5—22no—
207C2×Dic5—42no—
208C2×Dic5—42no—
209Dic10—41no—
210Dic10—41no—
211Dic10—42no—
212C2×#41C2×C3×D511yescharacteristic
213C22×Q8—51no—
214C4⋊Q8—52no—
215#124—52no—
216#123—101no—
217#123—101no—
218C22⋊Q8—101no—
219C22⋊Q8—101no—
220#117—21no—
221#117—51no—
222#117—101no—
223#99—21no—
224#99—52no—
225#99—101no—
226#99C2×C3×D512yes—
227C2×C3×C5—21no—
228C2×C3×C5—41no—
229C2×C3×C5—41no—
230C2×C3×C5—41no—
231C2×C3×C5C2×#9911yescharacteristic
232C23×C3#68511yescharacteristic
233C23×C3C2×D2011yescharacteristic
234C23×C3C2×C22⋊D511yescharacteristic
235C3×Q8—41no—
236C3×Q8—202no—
237C3×Q8—201no—
238C3×Q8—201no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—42no—
249C2×C3×C4—102no—
250C2×C3×C4—102no—
251C2×C3×C4—202no—
252C2×C3×C4—202no—
253C2×C3×C4#68511yescharacteristic
254C2×C3×C4#68511yescharacteristic
255C2×C3×C4#68511yescharacteristic
256C2×C3×C4C2×C4×D511yescharacteristic
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5C2×C3×C22⋊C411yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—82no—
268C4×C5C3×#9911yescharacteristic
269C4×C5C3×#9911yescharacteristic
270Dic5—42no—
271Dic5—42no—
272Dic5—82no—
273#41—41no—
274#41—41no—
275C2×Q8—52no—
276C2×Q8—101no—
277C2×Q8—201no—
278C2×Q8—201no—
279C2×Q8C3×C4×D511yescharacteristic
280C2×D4C3×D2011yescharacteristic
281C2×D4C3×C22⋊D511yescharacteristic
282C2×D4C22×C3×D511yescharacteristic
283C22×C4—101no—
284C22×C4C3×C4×D511yescharacteristic
285C22×C4C3×D2011yescharacteristic
286C22×C4C3×C22⋊D511yescharacteristic
287C4⋊C4—41no—
288C4⋊C4—101no—
289C4⋊C4—102no—
290C4⋊C4—102no—
291C4⋊C4—201no—
292C22⋊C4—22no—
293C22⋊C4—101no—
294C22⋊C4—102no—
295C22⋊C4—102no—
296C22⋊C4—102no—
297C42—41no—
298C42—52no—
299C42—201no—
300C3×C5#212911yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C2×#68511yescharacteristic
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—82no—
312C3×C4—202no—
313C3×C4—202no—
314C3×C4—402no—
315C3×C4#393811yescharacteristic
316C3×C4#393811yescharacteristic
317C2×C5—21no—
318C2×C5—41no—
319C2×C5—41no—
320C2×C5—41no—
321C2×C5C2×C3×#9911yescharacteristic
322C23C3×#68511yescharacteristic
323C23C2×C3×D2011yescharacteristic
324C23C2×C3×C22⋊D511yescharacteristic
325Q8—41no—
326Q8—202no—
327Q8—201no—
328Q8—201no—
329D4—41no—
330D4—41no—
331D4—41no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—202no—
342C2×C4—202no—
343C2×C4C3×#68511yescharacteristic
344C2×C4C3×#68511yescharacteristic
345C2×C4C3×#68511yescharacteristic
346C2×C4C2×C3×C4×D511yescharacteristic
347C2×C3—21no—
348C2×C3—41no—
349C2×C3—41no—
350C2×C3—41no—
351C2×C3C2×#393811yescharacteristic
352C5C3×#212911yescharacteristic, complemented, Sylow
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C2×C3×#68511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—202no—
365C4—202no—
366C4—402no—
367C4C3×#393811yescharacteristic
368C4C3×#393811yescharacteristic
369C3#1060085211yescharacteristic, direct product factor, Sylow
370C2—21no—
371C2—41no—
372C2—41no—
373C2—41no—
374C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#410C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×C5×#41C22
cosocleC2×C5×D4C23×C3
hypercenterC3×#410D5
hypocenterC5C3×#2129
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
4. C3×#64693C2semidirect
5. #10600852C3direct (N × H)
7. C22×C3×Dic10C4semidirect
9. C3×#4090C4semidirect
14. C3×#4072C4semidirect
25. #64693C2×C3semidirect
58. C22×Dic10C3×C4semidirect
60. #4090C3×C4semidirect
65. #4072C3×C4semidirect
300. C3×C5#2129semidirect
352. C5C3×#2129semidirect
369. C3#10600852direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661592
C3×C5×#4102
C3×#655292
C3×#646932
#106008523
C3×#21295