Finite Group Databasebeta

← C3×#10599026 #14281859

Subgroups — C3×#10599026 #14281859

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65914C211yesmaximal, characteristic
2C3×#65122C211yesmaximal, characteristic, complemented
3C3×#64974C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10599026C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic
11C3×#4092C411yescharacteristic
12C3×#4044—21no—
13C3×#4041C411yescharacteristic
14C3×#4040—21no—
15C3×#4036C411yescharacteristic
16C3×C4×D20—21no—
17C3×C4×D20C2211yescharacteristic
18C3×#4018—21no—
19C3×C42×D5C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22C3×#3952—21no—
23C3×#3952—21no—
24C3×#3946—21no—
25C3×C8×Dic5—21no—
26C3×C4⋊#168C2211yescharacteristic
27C3×C4×#168C2211yescharacteristic
28C3×#1482—51nomaximal, Hall
29#65914C2×C311yescharacteristic
30#65122C2×C311yescharacteristic, complemented
31#64974C2×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×#529—51no—
64C3×#431—51no—
65C3×#431—51no—
66C3×Q8⋊C8—51no—
67C3×Q8⋊C8D511yescharacteristic, complemented
68C3×D4⋊C8—51no—
69C3×D4⋊C8—51no—
70C4×C5×Q8C22×C311yescharacteristic
71#4093C3×C411yescharacteristic
72#4092C3×C411yescharacteristic
73#4044—21no—
74#4041C3×C411yescharacteristic
75#4040—21no—
76#4036C3×C411yescharacteristic
77C4×D20—21no—
78C4×D20C22×C311yescharacteristic
79#4018—21no—
80C42×D5C22×C311yescharacteristic
81C5×C4⋊C8C22×C311yescharacteristic
82C4×C5×C8C22×C311yescharacteristic
83#3952—21no—
84#3952—21no—
85#3946—21no—
86C8×Dic5—21no—
87C4⋊#168C22×C311yescharacteristic
88C4×#168C22×C311yescharacteristic
89#1482—51noSylow
90C22×C3×D5—21no—
91C22×C3×D5C22⋊C411yescharacteristic
92C3×C5×Q8—21no—
93C3×C5×Q8—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C3×D20—21no—
104C3×D20—21no—
105C3×D20—42no—
106C3×C4×D5—21no—
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113C3×C5×C8—41no—
114C3×C5×C8—41no—
115C3×#168—41no—
116C3×#168—41no—
117C3×#126—101no—
118C3×#125—51no—
119C3×#124—51no—
120C3×#123—101no—
121C3×C22⋊Q8—51no—
122C3×#121—51no—
123C3×C4×Q8C2×D511yescharacteristic
124C3×C4×D4—51no—
125C3×C4×D4—101no—
126C3×#117—101no—
127C2×C3×C42—51no—
128C3×C4⋊C8—51no—
129C3×C4⋊C8—101no—
130C3×C4⋊C8C2×D511yescharacteristic
131C3×C22⋊C8—101no—
132C3×C22⋊C8—101no—
133C3×C4×C8—51no—
134C3×C4×C8—101no—
135C3×C4×C8C2×D511yescharacteristic
136C2×C5×Q8C2×C3×C411yescharacteristic
137C2×D20—21no—
138C2×D20C2×C3×C411yescharacteristic
139C2×C4×D5—21no—
140C2×C4×D5C2×C3×C411yescharacteristic
141C2×C4×D5C3×D411yescharacteristic
142C2×C4×D5C3×D411yescharacteristic
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4C2×C3×C411yescharacteristic
147C42×C5—21no—
148C42×C5C23×C311yescharacteristic
149#685—21no—
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5C2×C3×C411yescharacteristic
156#683—21no—
157#683—21no—
158C4×Dic5C2×C3×C411yescharacteristic
159C4×Dic5C3×D411yescharacteristic
160C4×Dic5C3×D411yescharacteristic
161C2×#168—21no—
162C2×#168—21no—
163#529—51no—
164#431—51no—
165#431—51no—
166Q8⋊C8—51no—
167Q8⋊C8C3×D511yescharacteristic, complemented
168D4⋊C8—51no—
169D4⋊C8—51no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5#13511yescharacteristic
184C3×Dic5—21no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—41no—
188C2×C3×Q8C4×D511yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—101no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—51no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4C4×D511yescharacteristic
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C42—21no—
211C3×C42—51no—
212C3×C42—51no—
213C3×C42—51no—
214C3×C42C22×D511yescharacteristic
215C22×D5—21no—
216C22×D5C3×C22⋊C411yescharacteristic
217C5×Q8—21no—
218C5×Q8—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5C22×C3×C411yescharacteristic
222C2×C4×C5C2×C3×D411yescharacteristic
223C2×C4×C5C2×C3×D411yescharacteristic
224C2×Dic5—21no—
225C2×Dic5C3×C22⋊C411yescharacteristic
226C2×Dic5C3×C22⋊C411yescharacteristic
227C2×Dic5C3×C22⋊C411yescharacteristic
228D20—21no—
229D20—21no—
230D20—42no—
231C4×D5—21no—
232C4×D5—21no—
233C4×D5—21no—
234C4×D5—21no—
235C4×D5—41no—
236C4×D5—41no—
237C4×D5—41no—
238C5×C8—41no—
239C5×C8—41no—
240#168—41no—
241#168—41no—
242#126—101no—
243#125—51no—
244#124—51no—
245#123—101no—
246C22⋊Q8—51no—
247#121—51no—
248C4×Q8C2×C3×D511yescharacteristic
249C4×D4—51no—
250C4×D4—101no—
251#117—101no—
252C2×C42—51no—
253C4⋊C8—51no—
254C4⋊C8—101no—
255C4⋊C8C2×C3×D511yescharacteristic
256C22⋊C8—101no—
257C22⋊C8—101no—
258C4×C8—51no—
259C4×C8—101no—
260C4×C8C2×C3×D511yescharacteristic
261C2×C3×C5#40811yescharacteristic
262C2×C3×C5#41611yescharacteristic
263C2×C3×C5#42111yescharacteristic
264C3×D5—41no—
265C3×D5—81no—
266C23×C3—51no—
267C23×C3—101no—
268C3×Q8—21no—
269C3×Q8—21no—
270C3×D4—101no—
271C3×D4—101no—
272C3×D4—202no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—101no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4—201no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C3×C8—41no—
290C3×C8—41no—
291C3×C8—201no—
292C3×C8—201no—
293C22×C5C2×C3×C22⋊C411yescharacteristic
294C2×D5—21no—
295C2×D5—21no—
296C2×D5—21no—
297C2×D5—41no—
298C2×D5—41no—
299C2×D5—41no—
300C4×C5—21no—
301C4×C5—41no—
302C4×C5—41no—
303C4×C5C3×#13111yescharacteristic
304C4×C5C3×#13111yescharacteristic
305C4×C5C3×#13511yescharacteristic
306C4×C5C3×#13511yescharacteristic
307Dic5—21no—
308Dic5—21no—
309Dic5—21no—
310Dic5—41no—
311C2×Q8C3×C4×D511yescharacteristic
312C2×D4—51no—
313C2×D4—101no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—101no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—101no—
321C2×C8—101no—
322C4⋊C4—21no—
323C4⋊C4—51no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4C3×C4×D511yescharacteristic
328C22⋊C4—101no—
329C22⋊C4—101no—
330C22⋊C4—101no—
331C22⋊C4—101no—
332C22⋊C4—101no—
333C42—21no—
334C42—51no—
335C42—51no—
336C42—51no—
337C42C22×C3×D511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—101no—
340C22×C3—101no—
341C22×C3—101no—
342C22×C3—201no—
343C22×C3—201no—
344C22×C3—201no—
345C22×C3D5×C22⋊C411yescharacteristic
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—101no—
350C3×C4—101no—
351C3×C4—101no—
352C3×C4—201no—
353C3×C4#404711yescharacteristic
354C3×C4#405311yescharacteristic
355C3×C4#406211yescharacteristic
356C3×C4#406511yescharacteristic
357C2×C5C3×#40811yescharacteristic
358C2×C5C3×#41611yescharacteristic
359C2×C5C3×#42111yescharacteristic
360D5—41no—
361D5—81no—
362C23—51no—
363C23—101no—
364Q8—21no—
365Q8—21no—
366D4—101no—
367D4—101no—
368D4—202no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—51no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4—201no—
382C2×C4C2×C3×C4×D511yescharacteristic
383C2×C4C3×D4×D511yescharacteristic
384C2×C4C3×D4×D511yescharacteristic
385C8—41no—
386C8—41no—
387C8—201no—
388C8—201no—
389C2×C3—201no—
390C2×C3—401no—
391C2×C3#6501611yescharacteristic
392C2×C3#6509311yescharacteristic
393C2×C3#6511011yescharacteristic
394C5C3×#148211yescharacteristic, complemented, Sylow
395C22—101no—
396C22—101no—
397C22—101no—
398C22—201no—
399C22—201no—
400C22—201no—
401C22C3×D5×C22⋊C411yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—101no—
406C4—101no—
407C4—101no—
408C4—201no—
409C4C3×#404711yescharacteristic
410C4C3×#405311yescharacteristic
411C4C3×#406211yescharacteristic
412C4C3×#406511yescharacteristic
413C3#1059902611yescharacteristic, direct product factor, Sylow
414C2—201no—
415C2—401no—
416C2C3×#6501611yescharacteristic
417C2C3×#6509311yescharacteristic
418C2C3×#6511011yescharacteristic
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×#1482
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×#65122C2semidirect
3. C3×#64974C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. C3×Q8⋊#168C2semidirect
6. C3×#64703C2semidirect
7. C3×#64679C2semidirect
8. #10599026C3direct (N × H)
30. #65122C2×C3semidirect
31. #64974C2×C3semidirect
32. C5×Q8⋊C8C2×C3semidirect
33. Q8⋊#168C2×C3semidirect
34. #64703C2×C3semidirect
35. #64679C2×C3semidirect
67. C3×Q8⋊C8D5semidirect
167. Q8⋊C8C3×D5semidirect
338. C3×C5#1482semidirect
394. C5C3×#1482semidirect
413. C3#10599026direct (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×#651222
C3×#649742
C3×C5×Q8⋊C82
C3×Q8⋊#1682
C3×#647032
C3×#646792
#105990263
C3×#14825