Finite Group Databasebeta

← C3×#10598983 #14290016

Subgroups — C3×#10598983 #14290016

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×#65887C211yesmaximal, characteristic
2C3×#65296C211yesmaximal, characteristic, complemented
3C3×#65138C211yesmaximal, characteristic, complemented
4C3×#64983C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598983C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C3×#4086—21no—
12C3×#4076—21no—
13C2×C3×Dic20—21no—
14C3×#4039—21no—
15C3×#4030—22no—
16C3×#4020C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3953—22no—
23C3×#3948—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1641—51nomaximal, Hall
27#65887C2×C311yescharacteristic
28#65296C2×C311yescharacteristic, complemented
29#65138C2×C311yescharacteristic, complemented
30#64983C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C3×#709—42no—
39C3×#709—42no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20D412yes—
43C2×C3×C4×D5—22no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10D411yescharacteristic
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51C3×#685—22no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C3×Dic20—42no—
59C3×#550—51no—
60C3×#486—51no—
61C3×#474—51no—
62C3×#462—51no—
63C3×#331—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8D511yescharacteristic, complemented
66C2×#709—21no—
67C4×C5×D4C22×C311yescharacteristic
68#4086—21no—
69#4076—21no—
70C2×Dic20—21no—
71#4039—21no—
72#4030—22no—
73#4020C22×C311yescharacteristic
74#4015C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×C4⋊C8C22×C311yescharacteristic
77C4×C5×C8C22×C311yescharacteristic
78#3964—21no—
79#3953—22no—
80#3948—21no—
81#3939—21no—
82C4⋊#168C22×C311yescharacteristic
83#1641—51noSylow
84C23×C3×C5—21no—
85C22×C3×D5—22no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
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
94C3×C22⋊D5—44no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—41no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×C4×D5—44no—
105C3×Dic10—21no—
106C3×Dic10—41no—
107C3×Dic10—41no—
108C3×Dic10D812yes—
109C3×C5×C8—41no—
110C3×C5×C8—41no—
111C3×#168—41no—
112C2×C3×#41—101no—
113C2×C3×Q16—101no—
114C3×C4⋊Q8—51no—
115C3×#127—51no—
116C3×#127—101no—
117C3×#121—102no—
118C3×#121—101no—
119C3×C4×Q8—51no—
120C3×C4×D4—101no—
121C3×C4×D4C2×D511yescharacteristic
122C3×#107—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#103—101no—
126C3×#102—102no—
127C3×#102—101no—
128C3×C4×C8C2×D511yescharacteristic
129C2×C5×D4C3×D411yescharacteristic
130C22×C4×C5—21no—
131C2×C22⋊D5—22no—
132C2×C22⋊D5—22no—
133#709—42no—
134#709—42no—
135C2×D20—21no—
136C2×D20—21no—
137C2×D20C3×D412yes—
138C2×C4×D5—22no—
139C2×Dic10—21no—
140C2×Dic10C3×D411yescharacteristic
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C5×C4⋊C4C3×D411yescharacteristic
144C5×C22⋊C4—21no—
145C42×C5C23×C311yescharacteristic
146#685—22no—
147C4⋊Dic5—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5C3×D411yescharacteristic
150#683—21no—
151C4×Dic5—21no—
152C2×#168—21no—
153Dic20—42no—
154#550—51no—
155#486—51no—
156#474—51no—
157#462—51no—
158#331—51no—
159Q8⋊C8—51no—
160D4⋊C8C3×D511yescharacteristic, complemented
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C2×C3×D5—42no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174C3×Dic5—22no—
175C3×Dic5—41no—
176C3×Dic5—81no—
177C3×#41—202no—
178C3×#41—202no—
179C2×C3×Q8—51no—
180C2×C3×Q8—101no—
181C2×C3×D4—52no—
182C2×C3×D4—102no—
183C2×C3×D4—102no—
184C2×C3×D4—101no—
185C2×C3×D4—101no—
186C2×C3×D4D2011yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—102no—
189C3×Q16—202no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—101no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4D2011yescharacteristic
198C3×C22⋊C4—21no—
199C3×C22⋊C4—102no—
200C3×C42—101no—
201C3×C42C22×D511yescharacteristic
202C23×C5—21no—
203C22×D5—22no—
204C5×D4—21no—
205C5×D4—21no—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C22⋊D5—44no—
213C22⋊D5—82no—
214C2×Dic5—21no—
215C2×Dic5—21no—
216C2×Dic5—41no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—44no—
223Dic10—21no—
224Dic10—41no—
225Dic10—41no—
226Dic10C3×D812yes—
227C5×C8—41no—
228C5×C8—41no—
229#168—41no—
230C2×#41—101no—
231C2×Q16—101no—
232C4⋊Q8—51no—
233#127—51no—
234#127—101no—
235#121—102no—
236#121—101no—
237C4×Q8—51no—
238C4×D4—101no—
239C4×D4C2×C3×D511yescharacteristic
240#107—101no—
241C4⋊C8—51no—
242C4⋊C8C2×C3×D511yescharacteristic
243#103—101no—
244#102—102no—
245#102—101no—
246C4×C8C2×C3×D511yescharacteristic
247C2×C3×C5—81no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#45211yescharacteristic
250C2×C3×C5#45511yescharacteristic
251C3×D5—82no—
252C23×C3—21no—
253C23×C3—102no—
254C3×Q8—52no—
255C3×Q8—101no—
256C3×Q8—201no—
257C3×Q8—201no—
258C3×D4—21no—
259C3×D4—21no—
260C3×D4—202no—
261C3×D4—204no—
262C3×D4—201no—
263C3×D4—201no—
264C3×D4—201no—
265C3×D4—201no—
266C3×D4—402no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—101no—
271C2×C3×C4—101no—
272C2×C3×C4—204no—
273C2×C3×C4—201no—
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C3×C8—41no—
278C3×C8—41no—
279C3×C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5C3×#12011yescharacteristic
284C2×D5—42no—
285C2×D5—42no—
286C2×D5—42no—
287C4×C5—21no—
288C4×C5—41no—
289C4×C5C2×C3×D811yescharacteristic
290C4×C5C3×#13511yescharacteristic
291C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
292C4×C5C3×#13711yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—81no—
296#41—202no—
297#41—202no—
298C2×Q8—51no—
299C2×Q8—101no—
300C2×D4—52no—
301C2×D4—102no—
302C2×D4—102no—
303C2×D4—101no—
304C2×D4—101no—
305C2×D4C3×D2011yescharacteristic
306C22×C4—21no—
307C22×C4—102no—
308Q16—202no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—101no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4C3×D2011yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—102no—
319C42—101no—
320C42C22×C3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—202no—
328C22×C3#402811yescharacteristic
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—102no—
332C3×C4—201no—
333C3×C4—401no—
334C3×C4#405011yescharacteristic
335C3×C4#405511yescharacteristic
336C3×C4D5×D811yescharacteristic
337C3×C4#406011yescharacteristic
338C2×C5—81no—
339C2×C5C3×#44711yescharacteristic
340C2×C5C3×#45211yescharacteristic
341C2×C5C3×#45511yescharacteristic
342D5—82no—
343C23—21no—
344C23—102no—
345Q8—52no—
346Q8—101no—
347Q8—201no—
348Q8—201no—
349D4—21no—
350D4—21no—
351D4—202no—
352D4—204no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—201no—
357D4—402no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—204no—
364C2×C4—201no—
365C2×C4C2×C3×D2011yescharacteristic
366C2×C4C3×D4×D511yescharacteristic
367C2×C4C3×D4×D511yescharacteristic
368C8—41no—
369C8—41no—
370C8—201no—
371C2×C3—81no—
372C2×C3—402no—
373C2×C3#6502211yescharacteristic
374C2×C3#6506211yescharacteristic
375C2×C3#6511411yescharacteristic
376C5C3×#164111yescharacteristic, complemented, Sylow
377C22—41no—
378C22—41no—
379C22—41no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22C3×#402811yescharacteristic
384C4—21no—
385C4—41no—
386C4—102no—
387C4—201no—
388C4—401no—
389C4C3×#405011yescharacteristic
390C4C3×#405511yescharacteristic
391C4C3×D5×D811yescharacteristic
392C4C3×#406011yescharacteristic
393C3#1059898311yescharacteristic, direct product factor, Sylow
394C2—81no—
395C2—402no—
396C2C3×#6502211yescharacteristic
397C2C3×#6506211yescharacteristic
398C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC3×#65887C2
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1641
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
2. C3×#65296C2semidirect
3. C3×#65138C2semidirect
4. C3×#64983C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C3×#64705C2semidirect
7. C3×#64676C2semidirect
8. #10598983C3direct (N × H)
28. #65296C2×C3semidirect
29. #65138C2×C3semidirect
30. #64983C2×C3semidirect
31. C5×D4⋊C8C2×C3semidirect
32. #64705C2×C3semidirect
33. #64676C2×C3semidirect
65. C3×D4⋊C8D5semidirect
160. D4⋊C8C3×D5semidirect
321. C3×C5#1641semidirect
376. C5C3×#1641semidirect
393. C3#10598983direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658872
C3×#652962
C3×#651382
C3×#649832
C3×C5×D4⋊C82
C3×#647052
C3×#646762
#105989833
C3×#16415