Finite Group Databasebeta

← C3×#10599103 #14283065

Subgroups — C3×#10599103 #14283065

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65956C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic
3C3×#64937C211yesmaximal, characteristic
4C3×C5×#328C211yesmaximal, characteristic
5C3×#64758C211yesmaximal, characteristic
6C3×#64687C211yesmaximal, characteristic
7C3×#64672C211yesmaximal, characteristic
8#10599103C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×Q8×Dic5C411yescharacteristic, complemented
11C3×#4090C411yescharacteristic, complemented
12C3×#4070C2211yescharacteristic
13C2×C3×C4×Dic5—21no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×#4035—21no—
16C3×#4034C411yescharacteristic, complemented
17C3×#4033—21no—
18C3×#4033C411yescharacteristic, complemented
19C3×#4024—21no—
20C3×#4023—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22C3×C5×#95C2211yescharacteristic
23C3×#3963—21no—
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3947—21no—
27C3×#3946—21no—
28C3×#1506—51nomaximal, Hall
29#65956C2×C311yescharacteristic
30#65008C2×C311yescharacteristic
31#64937C2×C311yescharacteristic
32C5×#328C2×C311yescharacteristic
33#64758C2×C311yescharacteristic
34#64687C2×C311yescharacteristic
35#64672C2×C311yescharacteristic
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×Dic5—21no—
40C22×C3×Dic5D411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C22⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5C2×C411yescharacteristic
51C3×#683—21no—
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×C4×Dic5—24no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C2×C3×#168—21no—
64C3×#533—51no—
65C3×#432—51no—
66C3×#376—51no—
67C3×#328—51no—
68C3×#328—51no—
69C3×#328—51no—
70C3×#328D511yescharacteristic
71C5×C22⋊Q8C22×C311yescharacteristic
72Q8×Dic5C3×C411yescharacteristic, complemented
73#4090C3×C411yescharacteristic, complemented
74#4070C22×C311yescharacteristic
75C2×C4×Dic5—21no—
76C2×C4×Dic5C22×C311yescharacteristic
77#4035—21no—
78#4034C3×C411yescharacteristic, complemented
79#4033—21no—
80#4033C3×C411yescharacteristic, complemented
81#4024—21no—
82#4023—21no—
83C5×C22⋊C8C22×C311yescharacteristic
84C5×#95C22×C311yescharacteristic
85#3963—21no—
86#3963C22×C311yescharacteristic
87C22⋊#168C22×C311yescharacteristic
88#3947—21no—
89#3946—21no—
90#1506—51noSylow
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—22no—
104C2×C3×Dic5—22no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C22⋊C411yescharacteristic
113C3×Dic10—42no—
114C3×Dic10—41no—
115C3×C5×C8—41no—
116C3×#168—41no—
117C3×C4⋊Q8—51no—
118C3×C4⋊Q8—51no—
119C3×#125—101no—
120C3×C22⋊Q8—51no—
121C3×C22⋊Q8—101no—
122C3×C22⋊Q8C2×D511yescharacteristic
123C3×C4×Q8—51no—
124C3×C4×Q8—51no—
125C3×C4×Q8—101no—
126C3×#117—101no—
127C2×C3×C42—51no—
128C2×C3×C42—101no—
129C3×C4⋊C8—101no—
130C3×C22⋊C8—51no—
131C3×C22⋊C8C2×D511yescharacteristic
132C3×#97—101no—
133C3×#95—51no—
134C3×#95—101no—
135C3×#95C2×D511yescharacteristic
136C2×C5×Q8C2×C3×C411yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5C23×C311yescharacteristic
139C22×Dic5—21no—
140C22×Dic5C3×D411yescharacteristic
141C22×Dic5C3×D411yescharacteristic
142C2×Dic10—21no—
143C2×Dic10C2×C3×C411yescharacteristic
144C2×C5×C8—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4C2×C3×C411yescharacteristic
147C5×C22⋊C4—21no—
148C22⋊Dic5—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5C2×C3×C411yescharacteristic
151#683—21no—
152#683—21no—
153#683—21no—
154#683—21no—
155#683—21no—
156C4×Dic5—24no—
157C4×Dic5—21no—
158C4×Dic5—21no—
159C4×Dic5C2×C3×C411yescharacteristic
160C4×Dic5C2×C3×C411yescharacteristic
161C4×Dic5C3×D411yescharacteristic
162C4×Dic5C3×D411yescharacteristic
163C2×#168—21no—
164#533—51no—
165#432—51no—
166#376—51no—
167#328—51no—
168#328—51no—
169#328—51no—
170#328C3×D511yescharacteristic
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C22×C3×C5#13711yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—42no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×Dic5—21no—
182C3×Dic5—21no—
183C3×Dic5—21no—
184C3×Dic5—42no—
185C3×Dic5—41no—
186C3×Dic5—41no—
187C3×Dic5#10412yes—
188C2×C3×Q8—51no—
189C2×C3×Q8—101no—
190C2×C3×Q8C4×D511yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C22×C3×C4C22×D511yescharacteristic
196C2×C3×C8—21no—
197C2×C3×C8—101no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4C4×D511yescharacteristic
207C3×C22⋊C4—21no—
208C3×C22⋊C4—101no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42—51no—
212C3×C42—51no—
213C3×C42—101no—
214C3×C42—101no—
215C3×C42—104no—
216C23×C5C2×C3×D411yescharacteristic
217C5×Q8—41no—
218C2×C4×C5—22no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5C22×C3×C411yescharacteristic
225C2×C4×C5C2×C3×D411yescharacteristic
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—22no—
229C2×Dic5—22no—
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—41no—
233C2×Dic5—41no—
234C2×Dic5C3×C22⋊C411yescharacteristic
235C2×Dic5C3×C22⋊C411yescharacteristic
236C2×Dic5C3×C22⋊C411yescharacteristic
237C2×Dic5C3×C22⋊C411yescharacteristic
238Dic10—42no—
239Dic10—41no—
240C5×C8—41no—
241#168—41no—
242C4⋊Q8—51no—
243C4⋊Q8—51no—
244#125—101no—
245C22⋊Q8—51no—
246C22⋊Q8—101no—
247C22⋊Q8C2×C3×D511yescharacteristic
248C4×Q8—51no—
249C4×Q8—51no—
250C4×Q8—101no—
251#117—101no—
252C2×C42—51no—
253C2×C42—101no—
254C4⋊C8—101no—
255C22⋊C8—51no—
256C22⋊C8C2×C3×D511yescharacteristic
257#97—101no—
258#95—51no—
259#95—101no—
260#95C2×C3×D511yescharacteristic
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#41011yescharacteristic
264C2×C3×C5#41911yescharacteristic
265C2×C3×C5C2×#10411yescharacteristic
266C23×C3D4×D511yescharacteristic
267C3×Q8—41no—
268C3×Q8—201no—
269C3×Q8—202no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—102no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—102no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—201no—
287C2×C3×C4—201no—
288C2×C3×C4C2×C4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C3×C8—41no—
291C3×C8—201no—
292C22×C5—21no—
293C22×C5—21no—
294C22×C5C2×C3×C22⋊C411yescharacteristic
295C22×C5C3×#13711yescharacteristic
296C22×C5C3×#13711yescharacteristic
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—42no—
300C4×C5—41no—
301C4×C5—41no—
302Dic5—21no—
303Dic5—21no—
304Dic5—21no—
305Dic5—42no—
306Dic5—41no—
307Dic5—41no—
308Dic5C3×#10412yes—
309C2×Q8—51no—
310C2×Q8—101no—
311C2×Q8C3×C4×D511yescharacteristic
312C22×C4—21no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—101no—
316C22×C4C22×C3×D511yescharacteristic
317C2×C8—21no—
318C2×C8—101no—
319C4⋊C4—21no—
320C4⋊C4—51no—
321C4⋊C4—101no—
322C4⋊C4—101no—
323C4⋊C4—101no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4C3×C4×D511yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—101no—
330C42—51no—
331C42—51no—
332C42—51no—
333C42—51no—
334C42—101no—
335C42—101no—
336C42—104no—
337C3×C5#150611yescharacteristic, complemented, Hall
338C22×C3—21no—
339C22×C3—21no—
340C22×C3D5×C22⋊C411yescharacteristic
341C22×C3#406111yescharacteristic
342C22×C3#406411yescharacteristic
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—42no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—52no—
349C3×C4—101no—
350C3×C4—101no—
351C3×C4—101no—
352C3×C4—202no—
353C3×C4—201no—
354C3×C4—201no—
355C2×C5—21no—
356C2×C5—21no—
357C2×C5C3×#41011yescharacteristic
358C2×C5C3×#41911yescharacteristic
359C2×C5C2×C3×#10411yescharacteristic
360C23C3×D4×D511yescharacteristic
361Q8—41no—
362Q8—201no—
363Q8—202no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—51no—
371C2×C4—51no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—102no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—102no—
378C2×C4—101no—
379C2×C4—101no—
380C2×C4—201no—
381C2×C4—201no—
382C2×C4C2×C3×C4×D511yescharacteristic
383C2×C4C3×D4×D511yescharacteristic
384C8—41no—
385C8—201no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3#6502911yescharacteristic
389C2×C3#6509111yescharacteristic
390C2×C3D5×#10411yescharacteristic
391C5C3×#150611yescharacteristic, complemented, Sylow
392C22—21no—
393C22—21no—
394C22C3×D5×C22⋊C411yescharacteristic
395C22C3×#406111yescharacteristic
396C22C3×#406411yescharacteristic
397C4—21no—
398C4—21no—
399C4—42no—
400C4—41no—
401C4—41no—
402C4—52no—
403C4—101no—
404C4—101no—
405C4—101no—
406C4—202no—
407C4—201no—
408C4—201no—
409C3#1059910311yescharacteristic, direct product factor, Sylow
410C2—21no—
411C2—21no—
412C2C3×#6502911yescharacteristic
413C2C3×#6509111yescharacteristic
414C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#328D5
hypocenterC5C3×#1506
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
8. #10599103C3direct (N × H)
10. C3×Q8×Dic5C4semidirect
11. C3×#4090C4semidirect
16. C3×#4034C4semidirect
18. C3×#4033C4semidirect
72. Q8×Dic5C3×C4semidirect
73. #4090C3×C4semidirect
78. #4034C3×C4semidirect
80. #4033C3×C4semidirect
337. C3×C5#1506semidirect
391. C5C3×#1506semidirect
409. C3#10599103direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659562
C3×#650082
C3×#649372
C3×C5×#3282
C3×#647582
C3×#646872
C3×#646722
#105991033
C3×#15065