Finite Group Databasebeta

← C3×#10599034 #14282455

Subgroups — C3×#10599034 #14282455

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65914C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3C3×C4×C8×D5C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10599034C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic
11C3×#4092C411yescharacteristic
12C2×C3×C8×D5—21no—
13C3×#4044—21no—
14C3×#4041C411yescharacteristic
15C3×#4040—21no—
16C3×#4036C411yescharacteristic
17C3×C4×D20—21no—
18C3×C4×D20C2211yescharacteristic
19C3×#4018—21no—
20C3×C42×D5C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3952—21no—
24C3×#3947—21no—
25C3×C8×Dic5—21no—
26C3×C4⋊#168C2211yescharacteristic
27C3×C4×#168C2211yescharacteristic
28C3×#1494—51nomaximal, Hall
29#65914C2×C311yescharacteristic
30#65124C2×C311yescharacteristic, complemented
31C4×C8×D5C2×C311yescharacteristic, complemented
32C5×Q8⋊C8C2×C311yescharacteristic, complemented
33Q8⋊#168C2×C311yescharacteristic, complemented
34#64703C2×C311yescharacteristic, complemented
35#64679C2×C311yescharacteristic, complemented
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×C8×D5—24no—
64C3×#529—51no—
65C3×#432—51no—
66C2×C3×C4×C8—51no—
67C3×Q8⋊C8—51no—
68C3×Q8⋊C8D511yescharacteristic, complemented
69C3×D4⋊C8—51no—
70C3×D4⋊C8—51no—
71C4×C5×Q8C22×C311yescharacteristic
72#4093C3×C411yescharacteristic
73#4092C3×C411yescharacteristic
74C2×C8×D5—21no—
75#4044—21no—
76#4041C3×C411yescharacteristic
77#4040—21no—
78#4036C3×C411yescharacteristic
79C4×D20—21no—
80C4×D20C22×C311yescharacteristic
81#4018—21no—
82C42×D5C22×C311yescharacteristic
83C5×C4⋊C8C22×C311yescharacteristic
84C4×C5×C8C22×C311yescharacteristic
85#3952—21no—
86#3947—21no—
87C8×Dic5—21no—
88C4⋊#168C22×C311yescharacteristic
89C4×#168C22×C311yescharacteristic
90#1494—51noSylow
91C22×C3×D5—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C3×C5×Q8—21no—
94C3×C5×Q8—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C3×D20—21no—
105C3×D20—21no—
106C3×D20—42no—
107C3×C4×D5—22no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×C5×C8—22no—
115C3×C5×C8—41no—
116C3×#168—22no—
117C3×#168—41no—
118C22×C3×C8—101no—
119C3×#126—101no—
120C3×#125—51no—
121C3×#124—51no—
122C3×#123—101no—
123C3×C22⋊Q8—51no—
124C3×#121—51no—
125C3×C4×Q8C2×D511yescharacteristic
126C3×C4×D4—51no—
127C3×C4×D4—101no—
128C3×#117—101no—
129C2×C3×C42—51no—
130C3×C4⋊C8—51no—
131C3×C4⋊C8C2×D511yescharacteristic
132C3×C22⋊C8—101no—
133C3×#97—101no—
134C3×C4×C8—51no—
135C3×C4×C8—101no—
136C3×C4×C8C2×D511yescharacteristic
137C2×C5×Q8C2×C3×C411yescharacteristic
138C2×D20—21no—
139C2×D20C2×C3×C411yescharacteristic
140C2×C4×D5—21no—
141C2×C4×D5C2×C3×C411yescharacteristic
142C2×C4×D5C3×D411yescharacteristic
143C2×C4×D5C3×D411yescharacteristic
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4C2×C3×C411yescharacteristic
148C42×C5—21no—
149C42×C5C23×C311yescharacteristic
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5C2×C3×C411yescharacteristic
157#683—21no—
158#683—21no—
159C4×Dic5C2×C3×C411yescharacteristic
160C4×Dic5C3×D411yescharacteristic
161C4×Dic5C3×D411yescharacteristic
162C2×#168—21no—
163C2×#168—21no—
164C8×D5—24no—
165#529—51no—
166#432—51no—
167C2×C4×C8—51no—
168Q8⋊C8—51no—
169Q8⋊C8C3×D511yescharacteristic, complemented
170D4⋊C8—51no—
171D4⋊C8—51no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5#10412yes—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5#13111yescharacteristic
183C3×C4×C5#13111yescharacteristic
184C3×C4×C5#13511yescharacteristic
185C3×C4×C5#13511yescharacteristic
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—41no—
190C2×C3×Q8C4×D511yescharacteristic
191C2×C3×D4—51no—
192C2×C3×D4—101no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—101no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—104no—
200C2×C3×C8—101no—
201C2×C3×C8—101no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—51no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4C4×D511yescharacteristic
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C42—21no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—51no—
217C3×C42C22×D511yescharacteristic
218C22×D5—21no—
219C22×D5C3×C22⋊C411yescharacteristic
220C5×Q8—21no—
221C5×Q8—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5C22×C3×C411yescharacteristic
225C2×C4×C5C2×C3×D411yescharacteristic
226C2×C4×C5C2×C3×D411yescharacteristic
227C2×Dic5—21no—
228C2×Dic5C3×C22⋊C411yescharacteristic
229C2×Dic5C3×C22⋊C411yescharacteristic
230C2×Dic5C3×C22⋊C411yescharacteristic
231D20—21no—
232D20—21no—
233D20—42no—
234C4×D5—22no—
235C4×D5—21no—
236C4×D5—21no—
237C4×D5—21no—
238C4×D5—21no—
239C4×D5—41no—
240C4×D5—41no—
241C5×C8—22no—
242C5×C8—41no—
243#168—22no—
244#168—41no—
245C22×C8—101no—
246#126—101no—
247#125—51no—
248#124—51no—
249#123—101no—
250C22⋊Q8—51no—
251#121—51no—
252C4×Q8C2×C3×D511yescharacteristic
253C4×D4—51no—
254C4×D4—101no—
255#117—101no—
256C2×C42—51no—
257C4⋊C8—51no—
258C4⋊C8C2×C3×D511yescharacteristic
259C22⋊C8—101no—
260#97—101no—
261C4×C8—51no—
262C4×C8—101no—
263C4×C8C2×C3×D511yescharacteristic
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267C3×D5—22no—
268C3×D5—81no—
269C23×C3—51no—
270C23×C3—101no—
271C3×Q8—21no—
272C3×Q8—21no—
273C3×D4—101no—
274C3×D4—101no—
275C3×D4—202no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—102no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4C2×C4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C3×C8—22no—
293C3×C8—41no—
294C3×C8—102no—
295C3×C8—201no—
296C22×C5C2×C3×C22⋊C411yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—41no—
300C2×D5—41no—
301C2×D5—41no—
302C2×D5C3×#10412yes—
303C4×C5—21no—
304C4×C5—41no—
305C4×C5—41no—
306C4×C5C3×#13111yescharacteristic
307C4×C5C3×#13111yescharacteristic
308C4×C5C3×#13511yescharacteristic
309C4×C5C3×#13511yescharacteristic
310Dic5—21no—
311Dic5—21no—
312Dic5—21no—
313Dic5—41no—
314C2×Q8C3×C4×D511yescharacteristic
315C2×D4—51no—
316C2×D4—101no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—101no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—104no—
324C2×C8—101no—
325C2×C8—101no—
326C4⋊C4—21no—
327C4⋊C4—51no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—101no—
331C4⋊C4C3×C4×D511yescharacteristic
332C22⋊C4—101no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—101no—
337C42—21no—
338C42—51no—
339C42—51no—
340C42—51no—
341C42C22×C3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3—201no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3D5×C22⋊C411yescharacteristic
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—101no—
354C3×C4—101no—
355C3×C4—101no—
356C3×C4—201no—
357C3×C4#404711yescharacteristic
358C3×C4#405311yescharacteristic
359C3×C4#406211yescharacteristic
360C3×C4#406511yescharacteristic
361C2×C5C3×#40811yescharacteristic
362C2×C5C3×#41611yescharacteristic
363C2×C5C2×C3×#10411yescharacteristic
364D5—22no—
365D5—81no—
366C23—51no—
367C23—101no—
368Q8—21no—
369Q8—21no—
370D4—101no—
371D4—101no—
372D4—202no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—102no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—201no—
385C2×C4—201no—
386C2×C4C2×C3×C4×D511yescharacteristic
387C2×C4C3×D4×D511yescharacteristic
388C2×C4C3×D4×D511yescharacteristic
389C8—22no—
390C8—41no—
391C8—102no—
392C8—201no—
393C2×C3—102no—
394C2×C3—401no—
395C2×C3#6501611yescharacteristic
396C2×C3#6509311yescharacteristic
397C2×C3D5×#10411yescharacteristic
398C5C3×#149411yescharacteristic, complemented, Sylow
399C22—52no—
400C22—101no—
401C22—101no—
402C22—201no—
403C22—201no—
404C22—201no—
405C22C3×D5×C22⋊C411yescharacteristic
406C4—21no—
407C4—41no—
408C4—41no—
409C4—101no—
410C4—101no—
411C4—101no—
412C4—201no—
413C4C3×#404711yescharacteristic
414C4C3×#405311yescharacteristic
415C4C3×#406211yescharacteristic
416C4C3×#406511yescharacteristic
417C3#1059903411yescharacteristic, direct product factor, Sylow
418C2—102no—
419C2—401no—
420C2C3×#6501611yescharacteristic
421C2C3×#6509311yescharacteristic
422C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4041C4
cosocleC42×C5C23×C3
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1494
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65124C2semidirect
3. C3×C4×C8×D5C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. C3×Q8⋊#168C2semidirect
6. C3×#64703C2semidirect
7. C3×#64679C2semidirect
8. #10599034C3direct (N × H)
30. #65124C2×C3semidirect
31. C4×C8×D5C2×C3semidirect
32. C5×Q8⋊C8C2×C3semidirect
33. Q8⋊#168C2×C3semidirect
34. #64703C2×C3semidirect
35. #64679C2×C3semidirect
68. C3×Q8⋊C8D5semidirect
169. Q8⋊C8C3×D5semidirect
342. C3×C5#1494semidirect
398. C5C3×#1494semidirect
417. C3#10599034direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659142
C3×#651242
C3×C4×C8×D52
C3×C5×Q8⋊C82
C3×Q8⋊#1682
C3×#647032
C3×#646792
#105990343
C3×#14945