Finite Group Databasebeta

← C3×#10598979 #14288900

Subgroups — C3×#10598979 #14288900

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×#65887C211yesmaximal, characteristic, complemented
2C3×#65304C211yesmaximal, characteristic, complemented
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#64984C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598979C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C3×#4086—21no—
12C2×C3×#686—21no—
13C3×#4076—21no—
14C2×C3×D40—22no—
15C2×C3×#677—21no—
16C3×#4039—21no—
17C3×#4030—22no—
18C3×#4020C2211yescharacteristic
19C3×#4020C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3953—21no—
24C3×#3941—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1621—51nomaximal, Hall
27#65887C2×C311yescharacteristic, complemented
28#65304C2×C311yescharacteristic, complemented
29#65137C2×C311yescharacteristic, complemented
30#64984C2×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×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20D412yes—
46C2×C3×C4×D5—22no—
47C2×C3×Dic10D411yescharacteristic
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C3×#686—42no—
54C3×#685—22no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C2×C3×#168—21no—
59C3×D40—44no—
60C3×#677—42no—
61C3×#550—51no—
62C3×#493—51no—
63C3×#460—51no—
64C3×#459—51no—
65C3×#331—51no—
66C3×Q8⋊C8—51no—
67C3×D4⋊C8D511yescharacteristic, complemented
68C2×#709—21no—
69C4×C5×D4C22×C311yescharacteristic
70#4086—21no—
71C2×#686—21no—
72#4076—21no—
73C2×D40—22no—
74C2×#677—21no—
75#4039—21no—
76#4030—22no—
77#4020C22×C311yescharacteristic
78#4020C22×C311yescharacteristic
79C4×Dic10C22×C311yescharacteristic
80C5×C4⋊C8C22×C311yescharacteristic
81C4×C5×C8C22×C311yescharacteristic
82#3953—21no—
83#3941—21no—
84C4⋊#168C22×C311yescharacteristic
85#1621—51noSylow
86C23×C3×C5—21no—
87C22×C3×D5—22no—
88C22×C3×D5—41no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—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—
101C3×D20—42no—
102C3×D20—42no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—41no—
111C3×C4×D5—44no—
112C3×Dic10—21no—
113C3×Dic10D812yescomplemented
114C3×C5×C8—22no—
115C3×C5×C8—41no—
116C3×#168—41no—
117C2×C3×#41—101no—
118C2×C3×SD16—101no—
119C2×C3×D8—102no—
120C2×C3×D8—101no—
121C3×#127—51no—
122C3×#127—51no—
123C3×#127—101no—
124C3×#121—102no—
125C3×#121—101no—
126C3×C4×Q8—51no—
127C3×C4×D4—101no—
128C3×C4×D4C2×D511yescharacteristic
129C3×C4⋊C8—51no—
130C3×C4⋊C8C2×D511yescharacteristic
131C3×#102—101no—
132C3×#102—101no—
133C3×C4×C8C2×D511yescharacteristic
134C2×C5×D4C3×D411yescharacteristic
135C22×C4×C5—21no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—22no—
138#709—42no—
139#709—42no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20C3×D412yes—
146C2×C4×D5—22no—
147C2×Dic10C3×D411yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C5×C4⋊C4C3×D411yescharacteristic
151C5×C22⋊C4—21no—
152C42×C5C23×C311yescharacteristic
153#686—42no—
154#685—22no—
155C4⋊Dic5C3×D411yescharacteristic
156#683—21no—
157C4×Dic5—21no—
158C2×#168—21no—
159D40—44no—
160#677—42no—
161#550—51no—
162#493—51no—
163#460—51no—
164#459—51no—
165#331—51no—
166Q8⋊C8—51no—
167D4⋊C8C3×D511yescharacteristic, complemented
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12011yescharacteristic
172C2×C3×D5—42no—
173C2×C3×D5—42no—
174C2×C3×D5—42no—
175C2×C3×D5—81no—
176C2×C3×D5—81no—
177C2×C3×D5—81no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5C2×D811yescharacteristic
181C3×C4×C5#13511yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×Dic5—22no—
185C3×Dic5—41no—
186C3×#41—202no—
187C3×#41—202no—
188C2×C3×Q8—51no—
189C2×C3×D4—52no—
190C2×C3×D4—102no—
191C2×C3×D4—102no—
192C2×C3×D4—101no—
193C2×C3×D4—101no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4D2011yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—102no—
200C3×SD16—202no—
201C3×D8—204no—
202C3×D8—202no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—101no—
206C3×C4⋊C4—51no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4D2011yescharacteristic
209C3×C22⋊C4—21no—
210C3×C22⋊C4—102no—
211C3×C42—101no—
212C3×C42C22×D511yescharacteristic
213C23×C5—21no—
214C22×D5—22no—
215C22×D5—41no—
216C5×D4—21no—
217C5×D4—21no—
218C2×C4×C5—21no—
219C2×C4×C5—41no—
220C2×C4×C5—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—
228D20—42no—
229D20—42no—
230D20—41no—
231D20—41no—
232D20—41no—
233D20—41no—
234D20—41no—
235D20—41no—
236D20—41no—
237D20—41no—
238C4×D5—44no—
239Dic10—21no—
240Dic10C3×D812yescomplemented
241C5×C8—22no—
242C5×C8—41no—
243#168—41no—
244C2×#41—101no—
245C2×SD16—101no—
246C2×D8—102no—
247C2×D8—101no—
248#127—51no—
249#127—51no—
250#127—101no—
251#121—102no—
252#121—101no—
253C4×Q8—51no—
254C4×D4—101no—
255C4×D4C2×C3×D511yescharacteristic
256C4⋊C8—51no—
257C4⋊C8C2×C3×D511yescharacteristic
258#102—101no—
259#102—101no—
260C4×C8C2×C3×D511yescharacteristic
261C2×C3×C5—81no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265C3×D5—82no—
266C3×D5—161no—
267C23×C3—21no—
268C23×C3—102no—
269C23×C3—201no—
270C3×Q8—52no—
271C3×Q8—101no—
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—202no—
275C3×D4—202no—
276C3×D4—204no—
277C3×D4—201no—
278C3×D4—201no—
279C3×D4—201no—
280C3×D4—201no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—201no—
284C3×D4—201no—
285C3×D4—402no—
286C2×C3×C4—21no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—204no—
292C2×C3×C4C2×D2011yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C3×C8—22no—
296C3×C8—41no—
297C3×C8—201no—
298C22×C5—41no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5C3×#12011yescharacteristic
302C2×D5—42no—
303C2×D5—42no—
304C2×D5—42no—
305C2×D5—81no—
306C2×D5—81no—
307C2×D5—81no—
308C4×C5—21no—
309C4×C5—41no—
310C4×C5C2×C3×D811yescharacteristic
311C4×C5C3×#13511yescharacteristic
312C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
313C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
314Dic5—22no—
315Dic5—41no—
316#41—202no—
317#41—202no—
318C2×Q8—51no—
319C2×D4—52no—
320C2×D4—102no—
321C2×D4—102no—
322C2×D4—101no—
323C2×D4—101no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4C3×D2011yescharacteristic
328C22×C4—21no—
329C22×C4—102no—
330SD16—202no—
331D8—204no—
332D8—202no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—101no—
336C4⋊C4—51no—
337C4⋊C4—101no—
338C4⋊C4C3×D2011yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—102no—
341C42—101no—
342C42C22×C3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—202no—
348C22×C3—202no—
349C22×C3—202no—
350C22×C3—401no—
351C22×C3—401no—
352C22×C3—401no—
353C22×C3#402811yescharacteristic
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—102no—
357C3×C4—201no—
358C3×C4#405011yescharacteristic
359C3×C4#405411yescharacteristic
360C3×C4D5×D811yescharacteristic
361C3×C4#406011yescharacteristic
362C2×C5—81no—
363C2×C5C3×#44711yescharacteristic
364C2×C5C3×#44911yescharacteristic
365C2×C5C3×#45311yescharacteristic
366D5—82no—
367D5—161no—
368C23—21no—
369C23—102no—
370C23—201no—
371Q8—52no—
372Q8—101no—
373D4—21no—
374D4—21no—
375D4—202no—
376D4—202no—
377D4—204no—
378D4—201no—
379D4—201no—
380D4—201no—
381D4—201no—
382D4—201no—
383D4—201no—
384D4—201no—
385D4—201no—
386D4—402no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—204no—
393C2×C4C2×C3×D2011yescharacteristic
394C2×C4C3×D4×D511yescharacteristic
395C2×C4C3×D4×D511yescharacteristic
396C8—22no—
397C8—41no—
398C8—201no—
399C2×C3—81no—
400C2×C3—402no—
401C2×C3—801no—
402C2×C3#6502311yescharacteristic
403C2×C3#6506211yescharacteristic
404C2×C3#6511111yescharacteristic
405C5C3×#162111yescharacteristic, complemented, Sylow
406C22—41no—
407C22—41no—
408C22—41no—
409C22—202no—
410C22—202no—
411C22—202no—
412C22—401no—
413C22—401no—
414C22—401no—
415C22C3×#402811yescharacteristic
416C4—21no—
417C4—41no—
418C4—102no—
419C4—201no—
420C4C3×#405011yescharacteristic
421C4C3×#405411yescharacteristic
422C4C3×D5×D811yescharacteristic
423C4C3×#406011yescharacteristic
424C3#1059897911yescharacteristic, direct product factor, Sylow
425C2—81no—
426C2—402no—
427C2—801no—
428C2C3×#6502311yescharacteristic
429C2C3×#6506211yescharacteristic
430C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1621
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
1. C3×#65887C2semidirect
2. C3×#65304C2semidirect
3. C3×#65137C2semidirect
4. C3×#64984C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C3×#64705C2semidirect
7. C3×#64676C2semidirect
8. #10598979C3direct (N × H)
27. #65887C2×C3semidirect
28. #65304C2×C3semidirect
29. #65137C2×C3semidirect
30. #64984C2×C3semidirect
31. C5×D4⋊C8C2×C3semidirect
32. #64705C2×C3semidirect
33. #64676C2×C3semidirect
67. C3×D4⋊C8D5semidirect
113. C3×Dic10D8semidirect
167. D4⋊C8C3×D5semidirect
240. Dic10C3×D8semidirect
343. C3×C5#1621semidirect
405. C5C3×#1621semidirect
424. C3#10598979direct (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×#653042
C3×#651372
C3×#649842
C3×C5×D4⋊C82
C3×#647052
C3×#646762
#105989793
C3×#16215