Finite Group Databasebeta

← C3×#10599196 #14288894

Subgroups — C3×#10599196 #14288894

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66052C211yesmaximal, characteristic, complemented
2C3×#65362C211yesmaximal, characteristic, complemented
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#65132C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10599196C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711—21no—
10C3×C5×#127C2211yescharacteristic
11C3×#4086—21no—
12C3×#4085—22no—
13C3×#4084—21no—
14C3×D4×Dic5—21no—
15C2×C3×#686—22no—
16C2×C3×D40—21no—
17C2×C3×#677—21no—
18C3×#4020C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×C4⋊C8C2211yescharacteristic
23C3×#3953—21no—
24C3×#3953—21no—
25C3×C4×#168C2211yescharacteristic
26C3×#1621—51nomaximal, Hall
27#66052C2×C311yescharacteristic, complemented
28#65362C2×C311yescharacteristic, complemented
29#65137C2×C311yescharacteristic, complemented
30#65132C2×C311yescharacteristic, complemented
31C5×#331C2×C311yescharacteristic, complemented
32#64704C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C22×C3×Dic5—22no—
40C3×#711—42no—
41C3×#711—42no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10D411yescharacteristic
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51C3×C22⋊Dic5—22no—
52C3×#686—44no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C2×C3×#168—21no—
59C3×D40—42no—
60C3×#677—42no—
61C3×#550—51no—
62C3×#493—51no—
63C3×#460—51no—
64C3×#459—51no—
65C3×#331D511yescharacteristic, complemented
66C3×Q8⋊C8—51no—
67C3×D4⋊C8—51no—
68C2×#711—21no—
69C5×#127C22×C311yescharacteristic
70#4086—21no—
71#4085—22no—
72#4084—21no—
73D4×Dic5—21no—
74C2×#686—22no—
75C2×D40—21no—
76C2×#677—21no—
77#4020C22×C311yescharacteristic
78C4×D20C22×C311yescharacteristic
79C4×Dic10C22×C311yescharacteristic
80C5×C4⋊C8C22×C311yescharacteristic
81C5×C4⋊C8C22×C311yescharacteristic
82#3953—21no—
83#3953—21no—
84C4×#168C22×C311yescharacteristic
85#1621—51noSylow
86C23×C3×C5—22no—
87C22×C3×D5—21no—
88C22×C3×D5—41no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C3×C22⋊D5—44no—
98C3×C22⋊D5—82no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—44no—
103C3×D20—21no—
104C3×D20—21no—
105C3×D20—42no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112C3×Dic10—21no—
113C3×Dic10D812yescomplemented
114C3×C5×C8—41no—
115C3×C5×C8—41no—
116C3×#168—22no—
117C2×C3×#41—101no—
118C2×C3×SD16—101no—
119C2×C3×D8—101no—
120C2×C3×D8—102no—
121C3×#127—51no—
122C3×#127—101no—
123C3×#127C2×D511yescharacteristic
124C3×#121—101no—
125C3×#121—102no—
126C3×C4×Q8—51no—
127C3×C4×D4—51no—
128C3×C4×D4—101no—
129C3×C4⋊C8C2×D511yescharacteristic
130C3×C4⋊C8C2×D511yescharacteristic
131C3×#102—101no—
132C3×#102—101no—
133C3×C4×C8—51no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4C3×D412yes—
137C2×C22⋊D5—22no—
138C2×C22⋊D5—22no—
139C22×Dic5—22no—
140#711—42no—
141#711—42no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20C3×D411yescharacteristic
146C2×C4×D5—21no—
147C2×Dic10C3×D411yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C42×C5C23×C311yescharacteristic
151C22⋊Dic5—22no—
152#686—44no—
153#685—21no—
154C4⋊Dic5C3×D411yescharacteristic
155C4⋊Dic5C3×D411yescharacteristic
156#683—21no—
157C4×Dic5—21no—
158C2×#168—21no—
159D40—42no—
160#677—42no—
161#550—51no—
162#493—51no—
163#460—51no—
164#459—51no—
165#331C3×D511yescharacteristic, complemented
166Q8⋊C8—51no—
167D4⋊C8—51no—
168C22×C3×C5—42no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5#12011yescharacteristic
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—81no—
176C2×C3×D5—81no—
177C2×C3×D5—81no—
178C3×C4×C5—21no—
179C3×C4×C5C2×D811yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×Dic5—22no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×#41—202no—
187C3×#41—202no—
188C2×C3×Q8—51no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—51no—
192C2×C3×D4—102no—
193C2×C3×D4—102no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4D2012yes—
198C22×C3×C4—102no—
199C22×C3×C4—101no—
200C3×SD16—202no—
201C3×D8—202no—
202C3×D8—204no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—101no—
206C3×C4⋊C4—51no—
207C3×C4⋊C4—51no—
208C3×C4⋊C4—101no—
209C3×C22⋊C4—102no—
210C3×C22⋊C4—101no—
211C3×C42—101no—
212C3×C42C22×D511yescharacteristic
213C23×C5—22no—
214C22×D5—21no—
215C22×D5—41no—
216C5×D4—42no—
217C5×D4—41no—
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×C4×C5C2×C3×D411yescharacteristic
223C2×C4×C5C2×C3×D411yescharacteristic
224C22⋊D5—44no—
225C22⋊D5—82no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—44no—
230D20—21no—
231D20—21no—
232D20—42no—
233D20—41no—
234D20—41no—
235D20—41no—
236D20—41no—
237C4×D5—41no—
238C4×D5—41no—
239Dic10—21no—
240Dic10C3×D812yescomplemented
241C5×C8—41no—
242C5×C8—41no—
243#168—22no—
244C2×#41—101no—
245C2×SD16—101no—
246C2×D8—101no—
247C2×D8—102no—
248#127—51no—
249#127—101no—
250#127C2×C3×D511yescharacteristic
251#121—101no—
252#121—102no—
253C4×Q8—51no—
254C4×D4—51no—
255C4×D4—101no—
256C4⋊C8C2×C3×D511yescharacteristic
257C4⋊C8C2×C3×D511yescharacteristic
258#102—101no—
259#102—101no—
260C4×C8—51no—
261C2×C3×C5—82no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265C3×D5—81no—
266C3×D5—161no—
267C23×C3—22no—
268C23×C3—101no—
269C23×C3—201no—
270C3×Q8—52no—
271C3×Q8—101no—
272C3×D4—42no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—101no—
278C3×D4—101no—
279C3×D4—202no—
280C3×D4—204no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—201no—
284C3×D4—201no—
285C3×D4—402no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4—204no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C3×C8—41no—
296C3×C8—41no—
297C3×C8—102no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5C3×#12011yescharacteristic
302C2×D5—41no—
303C2×D5—41no—
304C2×D5—41no—
305C2×D5—81no—
306C2×D5—81no—
307C2×D5—81no—
308C4×C5—21no—
309C4×C5C2×C3×D811yescharacteristic
310C4×C5C3×#13511yescharacteristic
311C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
312C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
313Dic5—22no—
314Dic5—41no—
315Dic5—41no—
316#41—202no—
317#41—202no—
318C2×Q8—51no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—51no—
322C2×D4—102no—
323C2×D4—102no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4C3×D2012yes—
328C22×C4—102no—
329C22×C4—101no—
330SD16—202no—
331D8—202no—
332D8—204no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—101no—
336C4⋊C4—51no—
337C4⋊C4—51no—
338C4⋊C4—101no—
339C22⋊C4—102no—
340C22⋊C4—101no—
341C42—101no—
342C42C22×C3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3—201no—
350C22×C3—401no—
351C22×C3—401no—
352C22×C3—401no—
353C22×C3#402811yescharacteristic
354C3×C4—21no—
355C3×C4—102no—
356C3×C4—201no—
357C3×C4—201no—
358C3×C4D5×D811yescharacteristic
359C3×C4#405711yescharacteristic
360C3×C4#406011yescharacteristic
361C3×C4#406211yescharacteristic
362C2×C5—82no—
363C2×C5C3×#44711yescharacteristic
364C2×C5C3×#44911yescharacteristic
365C2×C5C3×#45311yescharacteristic
366D5—81no—
367D5—161no—
368C23—22no—
369C23—101no—
370C23—201no—
371Q8—52no—
372Q8—101no—
373D4—42no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—101no—
379D4—101no—
380D4—202no—
381D4—204no—
382D4—201no—
383D4—201no—
384D4—201no—
385D4—201no—
386D4—402no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—204no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4C2×C3×D2011yescharacteristic
394C2×C4C3×D4×D511yescharacteristic
395C2×C4C3×D4×D511yescharacteristic
396C8—41no—
397C8—41no—
398C8—102no—
399C2×C3—82no—
400C2×C3—401no—
401C2×C3—801no—
402C2×C3#6503611yescharacteristic
403C2×C3#6506211yescharacteristic
404C2×C3#6507011yescharacteristic
405C5C3×#162111yescharacteristic, complemented, Sylow
406C22—42no—
407C22—42no—
408C22—42no—
409C22—201no—
410C22—201no—
411C22—201no—
412C22—401no—
413C22—401no—
414C22—401no—
415C22C3×#402811yescharacteristic
416C4—21no—
417C4—102no—
418C4—201no—
419C4—201no—
420C4C3×D5×D811yescharacteristic
421C4C3×#405711yescharacteristic
422C4C3×#406011yescharacteristic
423C4C3×#406211yescharacteristic
424C3#1059919611yescharacteristic, direct product factor, Sylow
425C2—82no—
426C2—401no—
427C2—801no—
428C2C3×#6503611yescharacteristic
429C2C3×#6506211yescharacteristic
430C2C3×#6507011yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5#120
hypercenterC3×#331D5
hypocenterC5C3×#1621
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#66052C2semidirect
2. C3×#65362C2semidirect
3. C3×#65137C2semidirect
4. C3×#65132C2semidirect
5. C3×C5×#331C2semidirect
6. C3×#64704C2semidirect
7. C3×#64703C2semidirect
8. #10599196C3direct (N × H)
27. #66052C2×C3semidirect
28. #65362C2×C3semidirect
29. #65137C2×C3semidirect
30. #65132C2×C3semidirect
31. C5×#331C2×C3semidirect
32. #64704C2×C3semidirect
33. #64703C2×C3semidirect
65. C3×#331D5semidirect
113. C3×Dic10D8semidirect
165. #331C3×D5semidirect
240. Dic10C3×D8semidirect
343. C3×C5#1621semidirect
405. C5C3×#1621semidirect
424. C3#10599196direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660522
C3×#653622
C3×#651372
C3×#651322
C3×C5×#3312
C3×#647042
C3×#647032
#105991963
C3×#16215