Finite Group Databasebeta

← C3×#10599002 #14290580

Subgroups — C3×#10599002 #14290580

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×#65308C211yesmaximal, characteristic
3C3×#65140C211yesmaximal, characteristic, complemented
4C3×#64971C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10599002C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4082—21no—
11C2×C3×#687—21no—
12C3×#4072—21no—
13C3×#4070—21no—
14C3×#4033—21no—
15C3×#4025—22no—
16C3×#4015C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3950—22no—
22C3×#3949—21no—
23C3×#3948—21no—
24C3×#3942—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1650—51nomaximal, Hall
27#65876C2×C311yescharacteristic
28#65308C2×C311yescharacteristic
29#65140C2×C311yescharacteristic, complemented
30#64971C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic
32#64706C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C3×Dic10—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C3×C22⋊Dic5—22no—
45C3×C22⋊Dic5—22no—
46C3×#687—42no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×C4⋊Dic5D412yes—
52C3×#683—22no—
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57C3×#556—51no—
58C3×#500—51no—
59C3×#475—51no—
60C3×#461—51no—
61C3×#332—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8D511yescharacteristic
64C4×C5×D4C22×C311yescharacteristic
65#4082—21no—
66C2×#687—21no—
67#4072—21no—
68#4070—21no—
69#4033—21no—
70#4025—22no—
71#4015C22×C311yescharacteristic
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C4×C5×C8C22×C311yescharacteristic
76#3950—22no—
77#3949—21no—
78#3948—21no—
79#3942—21no—
80C4⋊#168C22×C311yescharacteristic
81#1650—51noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—41no—
95C3×Dic10—21no—
96C3×Dic10—21no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—22no—
102C3×C5×C8—41no—
103C3×#168—41no—
104C2×C3×SD16—101no—
105C3×C4⋊Q8—51no—
106C3×C4⋊Q8—51no—
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—101no—
119C3×#103—101no—
120C3×C4×C8C2×D511yescharacteristic
121C2×C5×D4C3×D411yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—21no—
124C2×Dic10—21no—
125C2×Dic10C3×D411yescharacteristic
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4C3×D411yescharacteristic
129C5×C22⋊C4—21no—
130C42×C5C23×C311yescharacteristic
131C22⋊Dic5—22no—
132C22⋊Dic5—22no—
133#687—42no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5C3×D411yescharacteristic
138C4⋊Dic5C3×D412yes—
139#683—22no—
140#683—21no—
141C4×Dic5—22no—
142C4×Dic5—21no—
143C2×#168—21no—
144#556—51no—
145#500—51no—
146#475—51no—
147#461—51no—
148#332—51no—
149Q8⋊C8—51no—
150D4⋊C8C3×D511yescharacteristic
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#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—42no—
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5—81no—
165C2×C3×Q8—51no—
166C2×C3×Q8—101no—
167C2×C3×Q8—101no—
168C2×C3×D4D2011yescharacteristic
169C22×C3×C4—21no—
170C3×SD16—202no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—101no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—52no—
176C3×C4⋊C4—102no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4D2011yescharacteristic
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×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—22no—
200C2×Dic5—41no—
201Dic10—21no—
202Dic10—21no—
203Dic10—41no—
204Dic10—41no—
205Dic10—41no—
206Dic10—41no—
207C5×C8—22no—
208C5×C8—41no—
209#168—41no—
210C2×SD16—101no—
211C4⋊Q8—51no—
212C4⋊Q8—51no—
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—101no—
225#103—101no—
226C4×C8C2×C3×D511yescharacteristic
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—101no—
233C3×Q8—101no—
234C3×Q8—201no—
235C3×Q8—201no—
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—101no—
244C2×C3×C4—102no—
245C2×C3×C4—101no—
246C2×C3×C4—201no—
247C2×C3×C4C2×D2011yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C3×C8—22no—
251C3×C8—41no—
252C3×C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5C3×#12011yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5C3×#13511yescharacteristic
260C4×C5C3×#13511yescharacteristic
261C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
262C4×C5C3×#13711yescharacteristic
263Dic5—42no—
264Dic5—41no—
265Dic5—41no—
266Dic5—81no—
267C2×Q8—51no—
268C2×Q8—101no—
269C2×Q8—101no—
270C2×D4C3×D2011yescharacteristic
271C22×C4—21no—
272SD16—202no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—101no—
276C4⋊C4—51no—
277C4⋊C4—52no—
278C4⋊C4—102no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4C3×D2011yescharacteristic
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#402811yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—201no—
298C3×C4—201no—
299C3×C4—202no—
300C3×C4—401no—
301C3×C4#405011yescharacteristic
302C3×C4#405411yescharacteristic
303C3×C4#405811yescharacteristic
304C3×C4#406111yescharacteristic
305C2×C5—81no—
306C2×C5C3×#44911yescharacteristic
307C2×C5C3×#45211yescharacteristic
308C2×C5C3×#45611yescharacteristic
309C23—21no—
310Q8—101no—
311Q8—101no—
312Q8—201no—
313Q8—201no—
314Q8—201no—
315Q8—201no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—101no—
324C2×C4—201no—
325C2×C4C2×C3×D2011yescharacteristic
326C2×C4C3×D4×D511yescharacteristic
327C2×C4C3×D4×D511yescharacteristic
328C8—22no—
329C8—41no—
330C8—201no—
331C2×C3—81no—
332C2×C3#6502311yescharacteristic
333C2×C3#6507211yescharacteristic
334C2×C3#6511511yescharacteristic
335C5C3×#165011yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22C3×#402811yescharacteristic
340C4—21no—
341C4—41no—
342C4—201no—
343C4—201no—
344C4—202no—
345C4—401no—
346C4C3×#405011yescharacteristic
347C4C3×#405411yescharacteristic
348C4C3×#405811yescharacteristic
349C4C3×#406111yescharacteristic
350C3#1059900211yescharacteristic, direct product factor, Sylow
351C2—81no—
352C2C3×#6502311yescharacteristic
353C2C3×#6507211yescharacteristic
354C2C3×#6511511yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1650
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#65140C2semidirect
4. C3×#64971C2semidirect
6. C3×#64706C2semidirect
7. C3×#64676C2semidirect
8. #10599002C3direct (N × H)
29. #65140C2×C3semidirect
30. #64971C2×C3semidirect
32. #64706C2×C3semidirect
33. #64676C2×C3semidirect
290. C3×C5#1650semidirect
335. C5C3×#1650semidirect
350. C3#10599002direct (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×#653082
C3×#651402
C3×#649712
C3×C5×D4⋊C82
C3×#647062
C3×#646762
#105990023
C3×#16505