Finite Group Databasebeta

← C3×#10599053 #14289389

Subgroups — C3×#10599053 #14289389

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65919C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3C3×#65139C211yesmaximal, characteristic, complemented
4C3×#64982C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10599053C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093—21no—
11C2×C3×#677—22no—
12C3×#4040—22no—
13C3×#4039—21no—
14C3×#4021—21no—
15C3×#4020C2211yescharacteristic
16C3×C4×D20—21no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3950—21no—
23C3×#3948—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1630—51nomaximal, Hall
27#65919C2×C311yescharacteristic
28#65310C2×C311yescharacteristic, complemented
29#65139C2×C311yescharacteristic, complemented
30#64982C2×C311yescharacteristic
31C5×Q8⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20D412yes—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—22no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C3×#677—44no—
57C3×#559—51no—
58C3×#492—51no—
59C3×#477—51no—
60C3×#477—51no—
61C3×#331—51no—
62C3×Q8⋊C8—51no—
63C3×Q8⋊C8D511yescharacteristic, complemented
64C4×C5×Q8C22×C311yescharacteristic
65#4093—21no—
66C2×#677—22no—
67#4040—22no—
68#4039—21no—
69#4021—21no—
70#4020C22×C311yescharacteristic
71C4×D20—21no—
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C4×C5×C8C22×C311yescharacteristic
76#3967—21no—
77#3950—21no—
78#3948—21no—
79#3939—21no—
80C4⋊#168C22×C311yescharacteristic
81#1630—51noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—41no—
93C3×D20—42no—
94C3×D20—41no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×C4×D5—82no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×Dic10—42no—
102C3×C5×C8—22no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C2×C3×SD16—102no—
106C3×C4⋊Q8—51no—
107C3×#127—51no—
108C3×#124—101no—
109C3×#124—101no—
110C3×#123—102no—
111C3×C4×Q8—51no—
112C3×C4×Q8C2×D511yescharacteristic
113C3×C4×D4—101no—
114C3×C4×D4—101no—
115C3×#107—101no—
116C3×#107—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#103—101no—
120C3×#103—101no—
121C3×C4×C8C2×D511yescharacteristic
122C2×C5×Q8C3×D411yescharacteristic
123C2×D20—21no—
124C2×D20—21no—
125C2×D20C3×D412yes—
126C2×C4×D5—22no—
127C2×Dic10—21no—
128C2×Dic10C3×D411yescharacteristic
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C3×D411yescharacteristic
133C42×C5—21no—
134C42×C5C23×C311yescharacteristic
135#685—22no—
136#685—22no—
137#685—22no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5C3×D411yescharacteristic
141#683—21no—
142C4×Dic5—21no—
143C2×#168—21no—
144#677—44no—
145#559—51no—
146#492—51no—
147#477—51no—
148#477—51no—
149#331—51no—
150Q8⋊C8—51no—
151Q8⋊C8C3×D511yescharacteristic, complemented
152C22×C3×C5#12011yescharacteristic
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×Dic5—41no—
164C3×Dic5—41no—
165C3×Dic5—81no—
166C2×C3×Q8—51no—
167C2×C3×Q8—101no—
168C2×C3×Q8D2011yescharacteristic
169C2×C3×D4—52no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C22×C3×C4—102no—
173C3×SD16—204no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—101no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4D2011yescharacteristic
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C22⋊C4—102no—
186C3×C42—21no—
187C3×C42—101no—
188C3×C42C22×D511yescharacteristic
189C22×D5—22no—
190C5×Q8—21no—
191C5×Q8—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—41no—
200D20—42no—
201D20—41no—
202D20—41no—
203D20—41no—
204D20—41no—
205C4×D5—82no—
206Dic10—21no—
207Dic10—21no—
208Dic10—42no—
209C5×C8—22no—
210C5×C8—41no—
211#168—41no—
212C2×SD16—102no—
213C4⋊Q8—51no—
214#127—51no—
215#124—101no—
216#124—101no—
217#123—102no—
218C4×Q8—51no—
219C4×Q8C2×C3×D511yescharacteristic
220C4×D4—101no—
221C4×D4—101no—
222#107—101no—
223#107—101no—
224C4⋊C8—51no—
225C4⋊C8C2×C3×D511yescharacteristic
226#103—101no—
227#103—101no—
228C4×C8C2×C3×D511yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C3×D5—82no—
233C23×C3—102no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—101no—
237C3×Q8—101no—
238C3×Q8—202no—
239C3×D4—202no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—201no—
249C2×C3×C4—402no—
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C3×C8—22no—
254C3×C8—41no—
255C3×C8—201no—
256C22×C5C3×#12011yescharacteristic
257C2×D5—42no—
258C2×D5—42no—
259C2×D5—42no—
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5C3×#13511yescharacteristic
264C4×C5C3×#13511yescharacteristic
265C4×C5C3×#13711yescharacteristic
266C4×C5C3×#13711yescharacteristic
267Dic5—41no—
268Dic5—41no—
269Dic5—81no—
270C2×Q8—51no—
271C2×Q8—101no—
272C2×Q8C3×D2011yescharacteristic
273C2×D4—52no—
274C2×D4—101no—
275C2×D4—101no—
276C22×C4—102no—
277SD16—204no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—101no—
281C4⋊C4—21no—
282C4⋊C4—51no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4C3×D2011yescharacteristic
287C22⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C42—21no—
291C42—101no—
292C42C22×C3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3—202no—
295C22×C3—202no—
296C22×C3—202no—
297C22×C3#402811yescharacteristic
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—201no—
302C3×C4—201no—
303C3×C4—401no—
304C3×C4#405011yescharacteristic
305C3×C4#405511yescharacteristic
306C3×C4#406211yescharacteristic
307C3×C4#406411yescharacteristic
308C2×C5C3×#45211yescharacteristic
309C2×C5C3×#45211yescharacteristic
310C2×C5C3×#45311yescharacteristic
311D5—82no—
312C23—102no—
313Q8—21no—
314Q8—21no—
315Q8—101no—
316Q8—101no—
317Q8—202no—
318D4—202no—
319D4—201no—
320D4—201no—
321D4—201no—
322D4—201no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—201no—
328C2×C4—402no—
329C2×C4C2×C3×D2011yescharacteristic
330C2×C4C3×D4×D511yescharacteristic
331C2×C4C3×D4×D511yescharacteristic
332C8—22no—
333C8—41no—
334C8—201no—
335C2×C3—402no—
336C2×C3#6502211yescharacteristic
337C2×C3#6509911yescharacteristic
338C2×C3#6511111yescharacteristic
339C5C3×#163011yescharacteristic, complemented, Sylow
340C22—202no—
341C22—202no—
342C22—202no—
343C22C3×#402811yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—201no—
348C4—201no—
349C4—401no—
350C4C3×#405011yescharacteristic
351C4C3×#405511yescharacteristic
352C4C3×#406211yescharacteristic
353C4C3×#406411yescharacteristic
354C3#1059905311yescharacteristic, direct product factor, Sylow
355C2—402no—
356C2C3×#6502211yescharacteristic
357C2C3×#6509911yescharacteristic
358C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1630
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65310C2semidirect
3. C3×#65139C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
7. C3×#64676C2semidirect
8. #10599053C3direct (N × H)
28. #65310C2×C3semidirect
29. #65139C2×C3semidirect
31. C5×Q8⋊C8C2×C3semidirect
33. #64676C2×C3semidirect
63. C3×Q8⋊C8D5semidirect
151. Q8⋊C8C3×D5semidirect
293. C3×C5#1630semidirect
339. C5C3×#1630semidirect
354. C3#10599053direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659192
C3×#653102
C3×#651392
C3×#649822
C3×C5×Q8⋊C82
C3×#647052
C3×#646762
#105990533
C3×#16305