Finite Group Databasebeta

← #14289756

Subgroups — #14289756

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×C5×D4×Q8C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11751122C211yesmaximal, characteristic, complemented
4#11751109C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic
8#10602708—31nomaximal, Hall
9C22×C3×C5×Q8—21no—
10C3×C5×C4⋊Q8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×C22⋊Q8—21no—
13C3×C5×C22⋊Q8—22no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17#91758C2211yescharacteristic
18#91119—21no—
19#91116—21no—
20#91094—22no—
21#91092—21no—
22#91091—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71915—51nomaximal, Hall
27C5×D4×Q8D311yescharacteristic
28#65382—31no—
29#65310—31no—
30#65297—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—42no—
37C2×C3×C5×Q8—42no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C2×Dic30—21no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D412yes—
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C3×D4×Q8D511yescharacteristic
59#5093—51no—
60#5021—51no—
61#5008—51no—
62#4547—51no—
63#4535—51no—
64D4⋊(C3⋊C8)—51no—
65C22×C5×Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×C22⋊Q8—21no—
69C5×C22⋊Q8—22no—
70C4×C5×Q8C2×D311yescharacteristic
71C4×C5×D4—21no—
72C4×C5×D4C2×D311yescharacteristic
73#4015—31no—
74#3967—61no—
75#3964—61no—
76#3942—62no—
77#3940—61no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1637—151noSylow
83C23×C3×C5—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—44no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8SD1612yes—
89C3×C5×D4—21no—
90C3×C5×D4Q1612yes—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—44no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—41no—
102Dic30—42no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C22×C3×Q8—21no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8C2×D511yescharacteristic
109C3×C22⋊Q8—21no—
110C3×C22⋊Q8—22no—
111C3×C4×Q8C2×D511yescharacteristic
112C3×C4×D4—21no—
113C3×C4×D4C2×D511yescharacteristic
114#869—51no—
115#835—101no—
116#832—101no—
117#810—102no—
118#808—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—22no—
124C2×C5×Q8—21no—
125C2×C5×Q8—42no—
126C2×C5×Q8—42no—
127C2×C5×Q8#6711yescharacteristic
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C2×Dic10—61no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C5×C4⋊C4#6711yescharacteristic
137C5×C4⋊C4#6712yes—
138C5×C22⋊C4—22no—
139C5×C22⋊C4—21no—
140C42×C5—21no—
141C42×C5C22×D311yescharacteristic
142C4⋊Dic5—61no—
143C4⋊Dic5—61no—
144C2×#168—61no—
145C2×#168—61no—
146C2×#168—61no—
147D4×Q8D1511yescharacteristic
148#487—151no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5—22no—
155C22×C3×C5—41no—
156C22×C3×C5—41no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—42no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×C4×C5C2×SD1611yescharacteristic
164C3×C4×C5C2×Q1611yescharacteristic
165C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5#13711yescharacteristic
167Dic15—81no—
168C2×C3×Q8—22no—
169C2×C3×Q8—21no—
170C2×C3×Q8—42no—
171C2×C3×Q8—42no—
172C2×C3×Q8C22⋊D511yescharacteristic
173C2×C3×D4C22⋊D511yescharacteristic
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C2×Dic6—101no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C22⋊D511yescharacteristic
181C3×C4⋊C4C22⋊D511yescharacteristic
182C3×C4⋊C4C22⋊D512yes—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
185C3×C42—21no—
186C3×C42C22×D511yescharacteristic
187C4⋊Dic3—101no—
188C4⋊Dic3—101no—
189C2×C3⋊C8—101no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C5×Q8—21no—
194C5×Q8—44no—
195C5×Q8—41no—
196C5×Q8—41no—
197C5×Q8#21412yes—
198C5×D4—21no—
199C5×D4#21612yes—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—22no—
203C2×C4×C5—21no—
204C2×C4×C5—44no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5C2×#6711yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—121no—
211Dic10—122no—
212#168—121no—
213#168—121no—
214#168—121no—
215C22×Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—151no—
218C4⋊Q8C2×D1511yescharacteristic
219C22⋊Q8—21no—
220C22⋊Q8—22no—
221C4×Q8C2×D1511yescharacteristic
222C4×D4—21no—
223C4×D4C2×D1511yescharacteristic
224#107—301no—
225#106—301no—
226C4⋊C8—151no—
227C4⋊C8—151no—
228#103—301no—
229#103—302no—
230#102—301no—
231C4×C8—151no—
232C2×C3×C5—42no—
233C2×C3×C5#45011yescharacteristic
234C2×C3×C5#45111yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—21no—
237C3×Q8—21no—
238C3×Q8—44no—
239C3×Q8—41no—
240C3×Q8—41no—
241C3×Q8#68712yes—
242C3×D4—21no—
243C3×D4#68912yes—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—44no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C2×C3×C4C2×C22⋊D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×Dic3—201no—
255Dic6—202no—
256C3⋊C8—201no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—22no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#95311yescharacteristic
263C4×C5—22no—
264C4×C5—21no—
265C4×C5—42no—
266C4×C5—41no—
267C4×C5—41no—
268C4×C5#93211yescharacteristic
269C4×C5C2×#21411yescharacteristic
270C4×C5#94211yescharacteristic
271C4×C5C2×#21611yescharacteristic
272Dic5—241no—
273C2×Q8—22no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—301no—
278C2×Q8#122011yescharacteristic
279C2×D4#122011yescharacteristic
280C22×C4—22no—
281C22×C4—21no—
282C2×C8—301no—
283C2×C8—301no—
284C2×C8—301no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4#122012yes—
291C4⋊C4#122011yescharacteristic
292C4⋊C4#122011yescharacteristic
293C22⋊C4—22no—
294C22⋊C4—21no—
295C42—21no—
296C42C22×D1511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—22no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3#409911yescharacteristic
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—42no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4#407811yescharacteristic
308C3×C4C2×#68711yescharacteristic
309C3×C4#408811yescharacteristic
310C3×C4C2×#68911yescharacteristic
311Dic3—401no—
312C2×C5—42no—
313C2×C5#521811yescharacteristic
314C2×C5#522811yescharacteristic
315C2×C5#524511yescharacteristic
316C23—21no—
317Q8—21no—
318Q8—44no—
319Q8—41no—
320Q8—41no—
321Q8—602no—
322Q8#671612yes—
323D4—21no—
324D4#671812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—44no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—601no—
333C2×C4C2×#122011yescharacteristic
334C2×C4C2×#122011yescharacteristic
335C2×C4C2×#122011yescharacteristic
336C8—601no—
337C8—601no—
338C8—601no—
339C2×C3—42no—
340C2×C3#6550711yescharacteristic
341C2×C3#6551711yescharacteristic
342C2×C3#6553411yescharacteristic
343C5#7191511yescharacteristic, complemented, Sylow
344C22—22no—
345C22—41no—
346C22—41no—
347C22#9184211yescharacteristic
348C4—22no—
349C4—21no—
350C4—42no—
351C4—41no—
352C4—41no—
353C4—1201no—
354C4#9182111yescharacteristic
355C4C2×#671611yescharacteristic
356C4#9183111yescharacteristic
357C4C2×#671811yescharacteristic
358C3#1060270811yescharacteristic, complemented, Sylow
359C2—42no—
360C2#1175131911yescharacteristic
361C2#1175132911yescharacteristic
362C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4×Q8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterD4×Q8D15
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11751122C2semidirect
5. #11746368C2semidirect
6. #11746356C2semidirect
297. C3×C5#1637semidirect
343. C5#71915semidirect
358. C3#10602708semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4×Q82
#117511942
#117511222
#117511092
#117463682
#117463562
D4⋊(C3⋊#168)2
#106027083
#719155