Finite Group Databasebeta

← C3×#10601956 #14289749

Subgroups — C3×#10601956 #14289749

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D20C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3C3×#65373C211yesmaximal, characteristic
4C3×#65370C211yesmaximal, characteristic, complemented
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic
7C3×#64702C211yesmaximal, characteristic, complemented
8#10601956C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C3×#4043—21no—
13C3×#4043—22no—
14C3×C4×D20—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4015—21no—
17C3×#4015C2211yescharacteristic
18C3×C5×#107—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21C3×#3967—22no—
22C3×#3941—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1637—51nomaximal, Hall
27Q8×D20C2×C311yescharacteristic
28C5×#477C2×C311yescharacteristic, complemented
29#65373C2×C311yescharacteristic
30#65370C2×C311yescharacteristic, complemented
31Q8⋊#168C2×C311yescharacteristic, complemented
32#64703C2×C311yescharacteristic
33#64702C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C3×Q8×D5—42no—
37C3×Q8×D5—42no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5—21no—
41C2×C3×Dic10—22no—
42C2×C3×Dic10—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5—21no—
49C3×C42×C5C2311yescharacteristic
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4⋊Dic5D412yes—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C3×D4×Q8—51no—
59C3×#487—51no—
60C3×#477D511yescharacteristic, complemented
61C3×#476—51no—
62C3×#332—51no—
63C3×Q8⋊C8—51no—
64C3×D4⋊C8—51no—
65C2×Q8×D5—21no—
66C5×C4⋊Q8C22×C311yescharacteristic
67C4×C5×Q8C22×C311yescharacteristic
68#4043—21no—
69#4043—22no—
70C4×D20—21no—
71C4×D20C22×C311yescharacteristic
72#4015—21no—
73#4015C22×C311yescharacteristic
74C5×#107—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#103—21no—
77#3967—22no—
78#3941—21no—
79#3940—21no—
80C4⋊#168C22×C311yescharacteristic
81C4×#168C22×C311yescharacteristic
82#1637—51noSylow
83C22×C3×D5—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C3×C5×Q8SD1612yes—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—22no—
95C3×D20—21no—
96C3×D20Q1612yes—
97C3×C4×D5—44no—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×Dic10—44no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C3×#168—41no—
106C22×C3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C22⋊Q8—102no—
111C3×C22⋊Q8—101no—
112C3×C4×Q8C2×D511yescharacteristic
113C3×C4×D4—51no—
114C3×C4×D4—101no—
115C3×#107—21no—
116C3×#106—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#103—21no—
120C3×#103—102no—
121C3×#102—101no—
122C3×C4×C8—51no—
123C2×C5×Q8—21no—
124C2×C5×Q8C3×D411yescharacteristic
125Q8×D5—42no—
126Q8×D5—42no—
127C2×D20C3×D411yescharacteristic
128C2×C4×D5—22no—
129C2×C4×D5—21no—
130C2×Dic10—22no—
131C2×Dic10—21no—
132C2×C5×C8—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4C3×D411yescharacteristic
137C42×C5—21no—
138C42×C5C23×C311yescharacteristic
139#685—22no—
140#685—21no—
141C4⋊Dic5—22no—
142C4⋊Dic5—21no—
143C4⋊Dic5C3×D411yescharacteristic
144C4⋊Dic5C3×D412yes—
145C2×#168—21no—
146C2×#168—21no—
147D4×Q8—51no—
148#487—51no—
149#477C3×D511yescharacteristic, complemented
150#476—51no—
151#332—51no—
152Q8⋊C8—51no—
153D4⋊C8—51no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—22no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—81no—
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5C2×Q1611yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C3×Dic5—41no—
167C3×Dic5—42no—
168C2×C3×Q8—21no—
169C2×C3×Q8—102no—
170C2×C3×Q8—101no—
171C2×C3×Q8—202no—
172C2×C3×Q8—202no—
173C2×C3×Q8C22⋊D511yescharacteristic
174C2×C3×D4—51no—
175C22×C3×C4—102no—
176C22×C3×C4—101no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—52no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—102no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4C22⋊D511yescharacteristic
188C3×C22⋊C4—102no—
189C3×C22⋊C4—101no—
190C3×C42—21no—
191C3×C42C22×D511yescharacteristic
192C22×D5—21no—
193C5×Q8—21no—
194C5×Q8—42no—
195C5×Q8C3×SD1612yes—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C2×C4×C5C2×C3×D411yescharacteristic
202C2×Dic5—21no—
203C2×Dic5—22no—
204D20—21no—
205D20C3×Q1612yes—
206C4×D5—44no—
207C4×D5—41no—
208C4×D5—41no—
209Dic10—44no—
210Dic10—41no—
211Dic10—41no—
212C5×C8—41no—
213#168—41no—
214#168—41no—
215C22×Q8—101no—
216C4⋊Q8—51no—
217C4⋊Q8—101no—
218C4⋊Q8C2×C3×D511yescharacteristic
219C22⋊Q8—102no—
220C22⋊Q8—101no—
221C4×Q8C2×C3×D511yescharacteristic
222C4×D4—51no—
223C4×D4—101no—
224#107—21no—
225#106—101no—
226C4⋊C8—51no—
227C4⋊C8C2×C3×D511yescharacteristic
228#103—21no—
229#103—102no—
230#102—101no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×Q8—21no—
238C3×Q8—42no—
239C3×Q8—204no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×Q8#68812yes—
243C3×D4—52no—
244C3×D4—101no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—102no—
249C2×C3×C4—101no—
250C2×C3×C4—204no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C3×C8—41no—
257C3×C8—201no—
258C3×C8—201no—
259C22×C5C3×#12011yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—22no—
264C4×C5—21no—
265C4×C5—41no—
266C4×C5—81no—
267C4×C5C2×C3×SD1611yescharacteristic
268C4×C5C2×C3×Q1611yescharacteristic
269C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
270C4×C5C3×#13711yescharacteristic
271Dic5—41no—
272Dic5—42no—
273C2×Q8—21no—
274C2×Q8—102no—
275C2×Q8—101no—
276C2×Q8—202no—
277C2×Q8—202no—
278C2×Q8C3×C22⋊D511yescharacteristic
279C2×D4—51no—
280C22×C4—102no—
281C22×C4—101no—
282C2×C8—21no—
283C2×C8—101no—
284C2×C8—101no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—52no—
289C4⋊C4—51no—
290C4⋊C4—102no—
291C4⋊C4—101no—
292C4⋊C4C3×C22⋊D511yescharacteristic
293C22⋊C4—102no—
294C22⋊C4—101no—
295C42—21no—
296C42C22×C3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—102no—
299C22×C3—201no—
300C22×C3—201no—
301C22×C3#408311yescharacteristic
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—81no—
306C3×C4—202no—
307C3×C4—201no—
308C3×C4D5×Q1611yescharacteristic
309C3×C4#406411yescharacteristic
310C3×C4C2×#68811yescharacteristic
311C3×C4#409511yescharacteristic
312C2×C5C3×#45011yescharacteristic
313C2×C5C3×#45111yescharacteristic
314C2×C5C3×#45411yescharacteristic
315D5—42no—
316C23—101no—
317Q8—21no—
318Q8—42no—
319Q8—204no—
320Q8—201no—
321Q8—201no—
322Q8C3×#68812yes—
323D4—52no—
324D4—101no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—102no—
329C2×C4—101no—
330C2×C4—204no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4C3×D4×D511yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C2×C3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—201no—
339C2×C3—202no—
340C2×C3#6533511yescharacteristic
341C2×C3#6547511yescharacteristic
342C2×C3#6549011yescharacteristic
343C5C3×#163711yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22C3×#408311yescharacteristic
348C4—22no—
349C4—21no—
350C4—41no—
351C4—81no—
352C4—202no—
353C4—201no—
354C4C3×D5×Q1611yescharacteristic
355C4C3×#406411yescharacteristic
356C4C2×C3×#68811yescharacteristic
357C4C3×#409511yescharacteristic
358C3#1060195611yescharacteristic, direct product factor, Sylow
359C2—202no—
360C2C3×#6533511yescharacteristic
361C2C3×#6547511yescharacteristic
362C2C3×#6549011yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#477D5
hypocenterC5C3×#1637
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
4. C3×#65370C2semidirect
5. C3×Q8⋊#168C2semidirect
7. C3×#64702C2semidirect
8. #10601956C3direct (N × H)
28. C5×#477C2×C3semidirect
30. #65370C2×C3semidirect
31. Q8⋊#168C2×C3semidirect
33. #64702C2×C3semidirect
60. C3×#477D5semidirect
149. #477C3×D5semidirect
297. C3×C5#1637semidirect
343. C5C3×#1637semidirect
358. C3#10601956direct (N × H)

Maximal subgroups

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

subgroupindex
C3×Q8×D202
C3×C5×#4772
C3×#653732
C3×#653702
C3×Q8⋊#1682
C3×#647032
C3×#647022
#106019563
C3×#16375