Finite Group Databasebeta

← C3×#10601807 #14289218

Subgroups — C3×#10601807 #14289218

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic10C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic
3C3×#65364C211yesmaximal, characteristic, complemented
4C3×#65359C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64704C211yesmaximal, characteristic, complemented
8#10601807C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×Dic10—21no—
10C2×C3×C5×D8—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13C3×D4×Dic5—21no—
14C2×C3×#687—21no—
15C3×#4070—21no—
16C3×#4034—21no—
17C3×#4024—22no—
18C3×#4015C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22C3×#3964—22no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1627—51nomaximal, Hall
27D4×Dic10C2×C311yescharacteristic, complemented
28C5×#459C2×C311yescharacteristic
29#65364C2×C311yescharacteristic, complemented
30#65359C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic, complemented
32#64706C2×C311yescharacteristic, complemented
33#64704C2×C311yescharacteristic, complemented
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×Dic5—22no—
40C2×C3×Dic10—22no—
41C2×C3×Dic10—21no—
42C2×C3×Dic10—42no—
43C2×C3×Dic10—42no—
44C2×C3×Dic10D411yescharacteristic
45C3×C5×D8—42no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50C3×C22⋊Dic5—22no—
51C3×#687—42no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×C4⋊Dic5D412yes—
55C3×#683—22no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C3×D4×Q8—51no—
61C3×#486—51no—
62C3×#460—51no—
63C3×#459D511yescharacteristic
64C3×#332—51no—
65C3×Q8⋊C8—51no—
66C3×D4⋊C8—51no—
67C22×Dic10—21no—
68C2×C5×D8—21no—
69C5×#127C22×C311yescharacteristic
70C4×C5×D4C22×C311yescharacteristic
71D4×Dic5—21no—
72C2×#687—21no—
73#4070—21no—
74#4034—21no—
75#4024—22no—
76#4015C22×C311yescharacteristic
77C4×Dic10C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C5×#102—21no—
80#3964—22no—
81#3964—21no—
82C4⋊#168C22×C311yescharacteristic
83C4×#168C22×C311yescharacteristic
84#1627—51noSylow
85C23×C3×C5—21no—
86C23×C3×C5—41no—
87C3×C5×D4—21no—
88C3×C5×D4—42no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4SD1612yescomplemented
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—22no—
103C2×C3×Dic5—44no—
104C3×Dic10—21no—
105C3×Dic10—44no—
106C3×Dic10—41no—
107C3×Dic10—41no—
108C3×Dic10D812yescomplemented
109C3×C5×C8—41no—
110C3×#168—41no—
111C3×#168—41no—
112C22×C3×Q8—101no—
113C2×C3×SD16—101no—
114C2×C3×D8—21no—
115C3×C4⋊Q8—51no—
116C3×C4⋊Q8—101no—
117C3×#127C2×D511yescharacteristic
118C3×C22⋊Q8—102no—
119C3×C22⋊Q8—101no—
120C3×C4×Q8—51no—
121C3×C4×D4—101no—
122C3×C4×D4C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#102—21no—
126C3×#102—101no—
127C3×#102—102no—
128C3×C4×C8—51no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4C3×D411yescharacteristic
133C22×C4×C5—21no—
134C22×Dic5—22no—
135C2×Dic10—22no—
136C2×Dic10—21no—
137C2×Dic10—42no—
138C2×Dic10—42no—
139C2×Dic10C3×D411yescharacteristic
140C5×D8—42no—
141C2×C5×C8—21no—
142C5×C4⋊C4C3×D411yescharacteristic
143C5×C22⋊C4—21no—
144C42×C5C23×C311yescharacteristic
145C22⋊Dic5—22no—
146#687—42no—
147C4⋊Dic5—21no—
148C4⋊Dic5C3×D411yescharacteristic
149C4⋊Dic5C3×D412yes—
150#683—22no—
151#683—21no—
152C4×Dic5—21no—
153C2×#168—21no—
154C2×#168—21no—
155D4×Q8—51no—
156#486—51no—
157#460—51no—
158#459C3×D511yescharacteristic
159#332—51no—
160Q8⋊C8—51no—
161D4⋊C8—51no—
162C22×C3×C5—22no—
163C22×C3×C5—41no—
164C22×C3×C5—41no—
165C22×C3×C5—81no—
166C22×C3×C5—81no—
167C22×C3×C5—81no—
168C22×C3×C5#12011yescharacteristic
169C3×C4×C5—21no—
170C3×C4×C5—41no—
171C3×C4×C5C2×D811yescharacteristic
172C3×C4×C5C2×SD1611yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175C3×Dic5—22no—
176C3×Dic5—42no—
177C3×Dic5—41no—
178C2×C3×Q8—51no—
179C2×C3×Q8—102no—
180C2×C3×Q8—101no—
181C2×C3×Q8—202no—
182C2×C3×Q8—202no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4C22⋊D511yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—102no—
189C3×SD16—202no—
190C3×D8—42no—
191C2×C3×C8—21no—
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—52no—
196C3×C4⋊C4—102no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4C22⋊D511yescharacteristic
200C3×C22⋊C4—21no—
201C3×C22⋊C4—102no—
202C3×C42—101no—
203C3×C42C22×D511yescharacteristic
204C23×C5—21no—
205C23×C5—41no—
206C5×D4—21no—
207C5×D4—42no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4C3×SD1612yescomplemented
213C2×C4×C5—21no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×C4×C5C2×C3×D411yescharacteristic
218C2×C4×C5C2×C3×D411yescharacteristic
219C2×Dic5—21no—
220C2×Dic5—21no—
221C2×Dic5—22no—
222C2×Dic5—44no—
223Dic10—21no—
224Dic10—44no—
225Dic10—41no—
226Dic10—41no—
227Dic10C3×D812yescomplemented
228C5×C8—41no—
229#168—41no—
230#168—41no—
231C22×Q8—101no—
232C2×SD16—101no—
233C2×D8—21no—
234C4⋊Q8—51no—
235C4⋊Q8—101no—
236#127C2×C3×D511yescharacteristic
237C22⋊Q8—102no—
238C22⋊Q8—101no—
239C4×Q8—51no—
240C4×D4—101no—
241C4×D4C2×C3×D511yescharacteristic
242C4⋊C8—51no—
243C4⋊C8C2×C3×D511yescharacteristic
244#102—21no—
245#102—101no—
246#102—102no—
247C4×C8—51no—
248C2×C3×C5—42no—
249C2×C3×C5—161no—
250C2×C3×C5#44711yescharacteristic
251C2×C3×C5#44811yescharacteristic
252C2×C3×C5#45411yescharacteristic
253C23×C3—21no—
254C23×C3—41no—
255C3×Q8—52no—
256C3×Q8—101no—
257C3×Q8—204no—
258C3×Q8—201no—
259C3×Q8—201no—
260C3×D4—21no—
261C3×D4—42no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—41no—
265C3×D4—41no—
266C3×D4#68712yescomplemented
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—101no—
271C2×C3×C4—101no—
272C2×C3×C4—102no—
273C2×C3×C4—204no—
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4C2×C22⋊D511yescharacteristic
277C3×C8—41no—
278C3×C8—201no—
279C3×C8—201no—
280C22×C5—22no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5C3×#12011yescharacteristic
287C4×C5—21no—
288C4×C5—41no—
289C4×C5C2×C3×D811yescharacteristic
290C4×C5C2×C3×SD1611yescharacteristic
291C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
292C4×C5C3×#13711yescharacteristic
293Dic5—22no—
294Dic5—42no—
295Dic5—41no—
296C2×Q8—51no—
297C2×Q8—102no—
298C2×Q8—101no—
299C2×Q8—202no—
300C2×Q8—202no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C3×C22⋊D511yescharacteristic
305C22×C4—21no—
306C22×C4—102no—
307SD16—202no—
308D8—42no—
309C2×C8—21no—
310C2×C8—101no—
311C2×C8—101no—
312C4⋊C4—51no—
313C4⋊C4—52no—
314C4⋊C4—102no—
315C4⋊C4—101no—
316C4⋊C4—101no—
317C4⋊C4C3×C22⋊D511yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—102no—
320C42—101no—
321C42C22×C3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—22no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3#408311yescharacteristic
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—102no—
333C3×C4—202no—
334C3×C4—201no—
335C3×C4D5×D811yescharacteristic
336C3×C4#405711yescharacteristic
337C3×C4C2×#68711yescharacteristic
338C3×C4#409711yescharacteristic
339C2×C5—42no—
340C2×C5—161no—
341C2×C5C3×#44711yescharacteristic
342C2×C5C3×#44811yescharacteristic
343C2×C5C3×#45411yescharacteristic
344C23—21no—
345C23—41no—
346Q8—52no—
347Q8—101no—
348Q8—204no—
349Q8—201no—
350Q8—201no—
351D4—21no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4C3×#68712yescomplemented
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—102no—
364C2×C4—204no—
365C2×C4C3×D4×D511yescharacteristic
366C2×C4C3×D4×D511yescharacteristic
367C2×C4C2×C3×C22⋊D511yescharacteristic
368C8—41no—
369C8—201no—
370C8—201no—
371C2×C3—42no—
372C2×C3—161no—
373C2×C3#6532911yescharacteristic
374C2×C3#6544511yescharacteristic
375C2×C3#6549011yescharacteristic
376C5C3×#162711yescharacteristic, complemented, Sylow
377C22—22no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C3×#408311yescharacteristic
384C4—21no—
385C4—41no—
386C4—102no—
387C4—202no—
388C4—201no—
389C4C3×D5×D811yescharacteristic
390C4C3×#405711yescharacteristic
391C4C2×C3×#68711yescharacteristic
392C4C3×#409711yescharacteristic
393C3#1060180711yescharacteristic, direct product factor, Sylow
394C2—42no—
395C2—161no—
396C2C3×#6532911yescharacteristic
397C2C3×#6544511yescharacteristic
398C2C3×#6549011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
Fitting, prime radicalC3×C5×#459C2
socleC22×C3×C5#120
hypercenterC3×#459D5
hypocenterC5C3×#1627
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×D4×Dic10C2semidirect
3. C3×#65364C2semidirect
4. C3×#65359C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64706C2semidirect
7. C3×#64704C2semidirect
8. #10601807C3direct (N × H)
27. D4×Dic10C2×C3semidirect
29. #65364C2×C3semidirect
30. #65359C2×C3semidirect
31. D4⋊#168C2×C3semidirect
32. #64706C2×C3semidirect
33. #64704C2×C3semidirect
93. C3×C5×D4SD16semidirect
108. C3×Dic10D8semidirect
212. C5×D4C3×SD16semidirect
227. Dic10C3×D8semidirect
266. C3×D4#687semidirect
322. C3×C5#1627semidirect
357. D4C3×#687semidirect
376. C5C3×#1627semidirect
393. C3#10601807direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D4×Dic102
C3×C5×#4592
C3×#653642
C3×#653592
C3×D4⋊#1682
C3×#647062
C3×#647042
#106018073
C3×#16275