Finite Group Databasebeta

← C3×#10599902 #14316110

Subgroups — C3×#10599902 #14316110

Order 1920.

460 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
1C2×C3×#4050C211yesmaximal, characteristic, complemented
2C3×#65404C211yesmaximal, characteristic, complemented
3C2×C3×#3932C211yesmaximal, characteristic, complemented
4C2×C3×D80C211yesmaximal, characteristic, complemented
5C3×C5×C22⋊C16C211yesmaximal, characteristic, complemented
6C3×#64729C211yesmaximal, characteristic, complemented
7C3×#64723C211yesmaximal, characteristic, complemented
8#10599902C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709—21no—
10C22×C3×C5×C8C2211yescharacteristic
11C3×#4076—21no—
12C2×C3×Dic20C2211yescharacteristic
13C3×#4050—22no—
14C3×#4050—22no—
15C2×C3×D40C2211yescharacteristic
16C2×C3×D40C2211yescharacteristic
17C2×C3×#677—21no—
18C2×C3×C5×C16C2211yescharacteristic
19C2×C3×C5×C16C2211yescharacteristic
20C3×#3953—21no—
21C3×#3950C2211yescharacteristic
22C3×#3932—22no—
23C3×D80—22no—
24C3×#2186—51nomaximal, Hall
25C2×#4050C2×C311yescharacteristic, complemented
26#65404C2×C311yescharacteristic, complemented
27C2×#3932C2×C311yescharacteristic, complemented
28C2×D80C2×C311yescharacteristic, complemented
29C5×C22⋊C16C2×C311yescharacteristic, complemented
30#64729C2×C311yescharacteristic, complemented
31#64723C2×C311yescharacteristic, complemented
32C22×C3×C4×C5D411yescharacteristic
33C2×C3×C22⋊D5—41no—
34C2×C3×C22⋊D5—41no—
35C3×#709—24no—
36C3×#709—42no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×C4×D5—41no—
40C2×C3×Dic10—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8D411yescharacteristic
44C2×C3×C5×C8C2311yescharacteristic
45C3×#685—41no—
46C3×C4⋊Dic5—21no—
47C3×Dic20—21no—
48C3×Dic20D412yescomplemented
49C3×D40—21no—
50C3×D40—21no—
51C3×D40—21no—
52C3×D40D412yescomplemented
53C3×#677—24no—
54C3×C5×C16—21no—
55C3×C5×C16—21no—
56C2×C3×#135—51no—
57C2×C3×SD32—51no—
58C2×C3×D16—51no—
59C3×#466—51no—
60C3×#358—51no—
61C3×#357—51no—
62C3×C22⋊C16D511yescharacteristic, complemented
63C2×#709—21no—
64C22×C5×C8C22×C311yescharacteristic
65#4076—21no—
66C2×Dic20C22×C311yescharacteristic
67#4050—22no—
68#4050—22no—
69C2×D40C22×C311yescharacteristic
70C2×D40C22×C311yescharacteristic
71C2×#677—21no—
72C2×C5×C16C22×C311yescharacteristic
73C2×C5×C16C22×C311yescharacteristic
74#3953—21no—
75#3950C22×C311yescharacteristic
76#3932—22no—
77D80—22no—
78#2186—51noSylow
79C23×C3×C5D811yescharacteristic
80C22×C3×D5—41no—
81C22×C3×D5—41no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5D811yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C3×C22⋊D5—44no—
87C3×C22⋊D5—82no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5—41no—
90C3×D20—22no—
91C3×D20—41no—
92C3×D20—41no—
93C3×D20—41no—
94C3×C4×D5—44no—
95C3×Dic10—22no—
96C3×Dic10—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×C3×#41—101no—
101C3×#135—102no—
102C3×#135—102no—
103C2×C3×Q16—51no—
104C2×C3×SD16—101no—
105C2×C3×D8—51no—
106C2×C3×D8—51no—
107C22×C3×C8C2×D511yescharacteristic
108C3×#121—101no—
109C3×SD32—102no—
110C3×D16—102no—
111C2×C3×C16C2×D511yescharacteristic
112C2×C3×C16C2×D511yescharacteristic
113C3×#107—51no—
114C3×#102—101no—
115C22×C4×C5C3×D411yescharacteristic
116C2×C22⋊D5—41no—
117C2×C22⋊D5—41no—
118#709—24no—
119#709—42no—
120C2×D20—21no—
121C2×D20—21no—
122C2×C4×D5—41no—
123C2×Dic10—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8C3×D411yescharacteristic
127C2×C5×C8C23×C311yescharacteristic
128#685—41no—
129C4⋊Dic5—21no—
130Dic20—21no—
131Dic20C3×D412yescomplemented
132D40—21no—
133D40—21no—
134D40—21no—
135D40C3×D412yescomplemented
136#677—24no—
137C5×C16—21no—
138C5×C16—21no—
139C2×#135—51no—
140C2×SD32—51no—
141C2×D16—51no—
142#466—51no—
143#358—51no—
144#357—51no—
145C22⋊C16C3×D511yescharacteristic, complemented
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C3×D5—42no—
151C2×C3×D5—81no—
152C2×C3×D5—81no—
153C2×C3×D5—81no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—21no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5—42no—
160C3×Dic5—81no—
161C3×#41—104no—
162C3×#41—202no—
163C2×C3×Q8—101no—
164C2×C3×D4—101no—
165C2×C3×D4—101no—
166C2×C3×D4—201no—
167C2×C3×D4—201no—
168C22×C3×C4—201no—
169C22×C3×C4D2011yescharacteristic
170C3×Q16—52no—
171C3×Q16—101no—
172C3×SD16—104no—
173C3×D8—52no—
174C3×D8—101no—
175C3×D8—101no—
176C3×D8—101no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8D2011yescharacteristic
180C2×C3×C8C22×D511yescharacteristic
181C3×C4⋊C4—101no—
182C3×C22⋊C4—201no—
183C3×C16—21no—
184C3×C16—21no—
185C23×C5C3×D811yescharacteristic
186C22×D5—41no—
187C22×D5—41no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5C3×D811yescharacteristic
191C2×C4×C5C2×C3×D411yescharacteristic
192C22⋊D5—44no—
193C22⋊D5—82no—
194C2×Dic5—41no—
195C2×Dic5—41no—
196D20—22no—
197D20—41no—
198D20—41no—
199D20—41no—
200C4×D5—44no—
201Dic10—22no—
202Dic10—41no—
203C5×C8—21no—
204C5×C8C2×C3×D411yescharacteristic
205C5×C8C2×C3×D411yescharacteristic
206C2×#41—101no—
207#135—102no—
208#135—102no—
209C2×Q16—51no—
210C2×SD16—101no—
211C2×D8—51no—
212C2×D8—51no—
213C22×C8C2×C3×D511yescharacteristic
214#121—101no—
215SD32—102no—
216D16—102no—
217C2×C16C2×C3×D511yescharacteristic
218C2×C16C2×C3×D511yescharacteristic
219#107—51no—
220#102—101no—
221C2×C3×C5—41no—
222C2×C3×C5#44711yescharacteristic
223C2×C3×C5#50811yescharacteristic
224C2×C3×C5#50911yescharacteristic
225C3×D5—82no—
226C3×D5—161no—
227C23×C3—201no—
228C23×C3—201no—
229C23×C3D4011yescharacteristic
230C3×Q8—102no—
231C3×Q8—201no—
232C3×D4—102no—
233C3×D4—204no—
234C3×D4—201no—
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—402no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—204no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4D4011yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C3×C8—21no—
246C3×C8D4×D511yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C2×C3×D811yescharacteristic
252C2×D5—42no—
253C2×D5—81no—
254C2×D5—81no—
255C2×D5—81no—
256C2×D5—81no—
257C2×D5—81no—
258C4×C5—21no—
259C4×C5C3×#12011yescharacteristic
260C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
261Dic5—42no—
262Dic5—81no—
263#41—104no—
264#41—202no—
265C2×Q8—101no—
266C2×D4—101no—
267C2×D4—101no—
268C2×D4—201no—
269C2×D4—201no—
270C22×C4—201no—
271C22×C4C3×D2011yescharacteristic
272Q16—52no—
273Q16—101no—
274SD16—104no—
275D8—52no—
276D8—101no—
277D8—101no—
278D8—101no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8C3×D2011yescharacteristic
282C2×C8C22×C3×D511yescharacteristic
283C4⋊C4—101no—
284C22⋊C4—201no—
285C16—21no—
286C16—21no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—202no—
292C22×C3—401no—
293C22×C3—401no—
294C22×C3—401no—
295C22×C3—401no—
296C22×C3—401no—
297C22×C3C2×D4011yescharacteristic
298C3×C4—21no—
299C3×C4—202no—
300C3×C4—401no—
301C3×C4#402811yescharacteristic
302C3×C4#405411yescharacteristic
303C2×C5—41no—
304C2×C5C3×#44711yescharacteristic
305C2×C5C3×#50811yescharacteristic
306C2×C5C3×#50911yescharacteristic
307D5—82no—
308D5—161no—
309C23—201no—
310C23—201no—
311C23C3×D4011yescharacteristic
312Q8—102no—
313Q8—201no—
314D4—102no—
315D4—204no—
316D4—201no—
317D4—201no—
318D4—201no—
319D4—402no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—204no—
323C2×C4—201no—
324C2×C4—201no—
325C2×C4C3×D4011yescharacteristic
326C2×C4C2×C3×D2011yescharacteristic
327C8—21no—
328C8C3×D4×D511yescharacteristic
329C8C3×D4×D511yescharacteristic
330C2×C3—41no—
331C2×C3—402no—
332C2×C3—801no—
333C2×C3#6502111yescharacteristic
334C2×C3#6519311yescharacteristic
335C2×C3#6519711yescharacteristic
336C5C3×#218611yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—202no—
341C22—401no—
342C22—401no—
343C22—401no—
344C22—401no—
345C22—401no—
346C22C2×C3×D4011yescharacteristic
347C4—21no—
348C4—202no—
349C4—401no—
350C4C3×#402811yescharacteristic
351C4C3×#405411yescharacteristic
352C3#1059990211yescharacteristic, direct product factor, Sylow
353C2—41no—
354C2—402no—
355C2—801no—
356C2C3×#6502111yescharacteristic
357C2C3×#6519311yescharacteristic
358C2C3×#6519711yescharacteristic
subgroupG/H
centerC22×C3C2×D40
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5C2×D8
hypercenterC3×C22⋊C16D5
hypocenterC5C3×#2186
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4050C2semidirect
2. C3×#65404C2semidirect
3. C2×C3×#3932C2semidirect
4. C2×C3×D80C2semidirect
5. C3×C5×C22⋊C16C2semidirect
6. C3×#64729C2semidirect
7. C3×#64723C2semidirect
8. #10599902C3direct (N × H)
25. C2×#4050C2×C3semidirect
26. #65404C2×C3semidirect
27. C2×#3932C2×C3semidirect
28. C2×D80C2×C3semidirect
29. C5×C22⋊C16C2×C3semidirect
30. #64729C2×C3semidirect
31. #64723C2×C3semidirect
48. C3×Dic20D4semidirect
52. C3×D40D4semidirect
62. C3×C22⋊C16D5semidirect
131. Dic20C3×D4semidirect
135. D40C3×D4semidirect
145. C22⋊C16C3×D5semidirect
287. C3×C5#2186semidirect
336. C5C3×#2186semidirect
352. C3#10599902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40502
C3×#654042
C2×C3×#39322
C2×C3×D802
C3×C5×C22⋊C162
C3×#647292
C3×#647232
#105999023
C3×#21865