Finite Group Databasebeta

← C3×#10601842 #14290568

Subgroups — C3×#10601842 #14290568

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65876C211yesmaximal, characteristic
2C3×C5×#461C211yesmaximal, characteristic
3C3×#65383C211yesmaximal, characteristic, complemented
4C3×#65367C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64702C211yesmaximal, characteristic, complemented
8#10601842C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C3×#4082—21no—
13C3×#4072—21no—
14C3×#4070—21no—
15C3×#4033—21no—
16C3×#4025—22no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21C3×#3942—21no—
22C3×#3940—21no—
23C3×#3939—22no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1650—51nomaximal, Hall
27#65876C2×C311yescharacteristic
28C5×#461C2×C311yescharacteristic
29#65383C2×C311yescharacteristic, complemented
30#65367C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic
32#64704C2×C311yescharacteristic, complemented
33#64702C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C3×C5×SD16—42no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C3×C22⋊Dic5—22no—
47C3×C22⋊Dic5—22no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D412yes—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—22no—
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C3×#556—51no—
58C3×#500—51no—
59C3×#475—51no—
60C3×#461D511yescharacteristic
61C3×#332—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8—51no—
64C2×C5×SD16—21no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C4×C5×D4C22×C311yescharacteristic
67#4082—21no—
68#4072—21no—
69#4070—21no—
70#4033—21no—
71#4025—22no—
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C5×#103—21no—
76#3942—21no—
77#3940—21no—
78#3939—22no—
79C4⋊#168C22×C311yescharacteristic
80C4×#168C22×C311yescharacteristic
81#1650—51noSylow
82C23×C3×C5—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×D4—21no—
86C3×C5×D4—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—22no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—41no—
102C3×#168—22no—
103C3×#168—41no—
104C2×C3×SD16—21no—
105C3×C4⋊Q8—51no—
106C3×C4⋊Q8C2×D511yescharacteristic
107C3×#126—102no—
108C3×#124—101no—
109C3×C22⋊Q8—101no—
110C3×C4×Q8—51no—
111C3×C4×Q8—101no—
112C3×C4×D4C2×D511yescharacteristic
113C3×#117—101no—
114C3×#107—102no—
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×#103—21no—
119C3×#103—101no—
120C3×C4×C8—51no—
121C2×C5×Q8—21no—
122C2×C5×D4C3×D411yescharacteristic
123C22×C4×C5—21no—
124C2×Dic10—21no—
125C2×Dic10C3×D411yescharacteristic
126C5×SD16—42no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4C3×D411yescharacteristic
131C5×C22⋊C4—21no—
132C42×C5C23×C311yescharacteristic
133C22⋊Dic5—22no—
134C22⋊Dic5—22no—
135C4⋊Dic5—21no—
136C4⋊Dic5C3×D412yes—
137C4⋊Dic5C3×D411yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—22no—
141C4×Dic5—21no—
142C2×#168—21no—
143C2×#168—21no—
144#556—51no—
145#500—51no—
146#475—51no—
147#461C3×D511yescharacteristic
148#332—51no—
149Q8⋊C8—51no—
150D4⋊C8—51no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—42no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C2×C3×Q8—21no—
166C2×C3×Q8—51no—
167C2×C3×Q8—101no—
168C2×C3×D4C22⋊D511yescharacteristic
169C22×C3×C4—21no—
170C3×SD16—42no—
171C2×C3×C8—21no—
172C2×C3×C8—101no—
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—52no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4C22⋊D511yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—102no—
186C3×C42—101no—
187C3×C42C22×D511yescharacteristic
188C23×C5—21no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×D4—21no—
192C5×D4—21no—
193C2×C4×C5—21no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—22no—
203Dic10—21no—
204Dic10—21no—
205Dic10—41no—
206Dic10—41no—
207C5×C8—41no—
208#168—22no—
209#168—41no—
210C2×SD16—21no—
211C4⋊Q8—51no—
212C4⋊Q8C2×C3×D511yescharacteristic
213#126—102no—
214#124—101no—
215C22⋊Q8—101no—
216C4×Q8—51no—
217C4×Q8—101no—
218C4×D4C2×C3×D511yescharacteristic
219#117—101no—
220#107—102no—
221#106—101no—
222C4⋊C8—51no—
223C4⋊C8C2×C3×D511yescharacteristic
224#103—21no—
225#103—101no—
226C4×C8—51no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—101no—
235C3×Q8—101no—
236C3×Q8—201no—
237C3×Q8—201no—
238C3×D4—21no—
239C3×D4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—101no—
245C2×C3×C4—102no—
246C2×C3×C4—101no—
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C3×C8—41no—
251C3×C8—102no—
252C3×C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5C3×#12011yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—81no—
260C4×C5C3×#13511yescharacteristic
261C4×C5C3×#13511yescharacteristic
262C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
263C4×C5C3×#13711yescharacteristic
264Dic5—42no—
265Dic5—41no—
266Dic5—41no—
267C2×Q8—21no—
268C2×Q8—51no—
269C2×Q8—101no—
270C2×D4C3×C22⋊D511yescharacteristic
271C22×C4—21no—
272SD16—42no—
273C2×C8—21no—
274C2×C8—101no—
275C2×C8—101no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—51no—
279C4⋊C4—52no—
280C4⋊C4—102no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4C3×C22⋊D511yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—102no—
286C22⋊C4—102no—
287C42—102no—
288C42—101no—
289C42C22×C3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#408311yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—202no—
299C3×C4—201no—
300C3×C4—201no—
301C3×C4#406111yescharacteristic
302C3×C4#406211yescharacteristic
303C3×C4#407811yescharacteristic
304C3×C4#409611yescharacteristic
305C2×C5—81no—
306C2×C5C3×#44911yescharacteristic
307C2×C5C3×#45211yescharacteristic
308C2×C5C3×#45611yescharacteristic
309C23—21no—
310Q8—41no—
311Q8—41no—
312Q8—101no—
313Q8—101no—
314Q8—201no—
315Q8—201no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—101no—
323C2×C4—102no—
324C2×C4—101no—
325C2×C4C3×D4×D511yescharacteristic
326C2×C4C3×D4×D511yescharacteristic
327C2×C4C2×C3×C22⋊D511yescharacteristic
328C8—41no—
329C8—102no—
330C8—201no—
331C2×C3—81no—
332C2×C3#6532611yescharacteristic
333C2×C3#6546211yescharacteristic
334C2×C3#6549411yescharacteristic
335C5C3×#165011yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22C3×#408311yescharacteristic
340C4—21no—
341C4—41no—
342C4—81no—
343C4—202no—
344C4—201no—
345C4—201no—
346C4C3×#406111yescharacteristic
347C4C3×#406211yescharacteristic
348C4C3×#407811yescharacteristic
349C4C3×#409611yescharacteristic
350C3#1060184211yescharacteristic, direct product factor, Sylow
351C2—81no—
352C2C3×#6532611yescharacteristic
353C2C3×#6546211yescharacteristic
354C2C3×#6549411yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#461C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×#461D5
hypocenterC5C3×#1650
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
3. C3×#65383C2semidirect
4. C3×#65367C2semidirect
6. C3×#64704C2semidirect
7. C3×#64702C2semidirect
8. #10601842C3direct (N × H)
29. #65383C2×C3semidirect
30. #65367C2×C3semidirect
32. #64704C2×C3semidirect
33. #64702C2×C3semidirect
290. C3×C5#1650semidirect
335. C5C3×#1650semidirect
350. C3#10601842direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658762
C3×C5×#4612
C3×#653832
C3×#653672
C3×D4⋊#1682
C3×#647042
C3×#647022
#106018423
C3×#16505