Finite Group Databasebeta

← #14289630

Subgroups — #14289630

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11751109C211yesmaximal, characteristic, complemented
4#11751109C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602704—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#123—22no—
12C3×C5×C22⋊Q8—21no—
13C3×C5×#121—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C2×C3×C5×C4⋊C4—21no—
17#91758C2211yescharacteristic
18#91116—21no—
19#91116—21no—
20#91094—22no—
21#91092—21no—
22#91092—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71911—51nomaximal, Hall
27C5×#547D311yescharacteristic
28#65382—31no—
29#65297—31no—
30#65297—31no—
31#64767—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C2×Dic30—21no—
44C3×C5×C4⋊C4—22no—
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×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C3×#547D511yescharacteristic
59#5093—51no—
60#5008—51no—
61#5008—51no—
62#4547—51no—
63D4⋊(C3⋊C8)—51no—
64D4⋊(C3⋊C8)—51no—
65C2×C5×#41—21no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#123—22no—
68C5×C22⋊Q8—21no—
69C5×#121—21no—
70C4×C5×D4C2×D311yescharacteristic
71C4×C5×D4C2×D311yescharacteristic
72C2×C5×C4⋊C4—21no—
73#4015—31no—
74#3964—61no—
75#3964—61no—
76#3942—62no—
77#3940—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1635—151noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—44no—
91C3×C5×D4SD1612yes—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—44no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—41no—
104Dic30—42no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C2×C3×#41—21no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#123—22no—
111C3×C22⋊Q8—21no—
112C3×#121—21no—
113C3×C4×D4C2×D511yescharacteristic
114C3×C4×D4C2×D511yescharacteristic
115C2×C3×C4⋊C4—21no—
116#869—51no—
117#832—101no—
118#832—101no—
119#810—102no—
120#808—101no—
121#808—101no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C5×#41—42no—
126C5×#41—42no—
127C2×C5×Q8—21no—
128C2×C5×D4—22no—
129C2×C5×D4#6711yescharacteristic
130C2×C5×D4#6711yescharacteristic
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C2×Dic10—61no—
135C5×C4⋊C4—22no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C4⋊C4#6711yescharacteristic
139C5×C4⋊C4#6712yes—
140C5×C22⋊C4—22no—
141C5×C22⋊C4—21no—
142C5×C22⋊C4—21no—
143C42×C5C22×D311yescharacteristic
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146C2×#168—61no—
147C2×#168—61no—
148C2×#168—61no—
149#547D1511yescharacteristic
150#487—151no—
151#476—151no—
152#476—151no—
153#332—151no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—42no—
166C3×C4×C5—41no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171Dic15—81no—
172C3×#41—42no—
173C3×#41—42no—
174C2×C3×Q8—21no—
175C2×C3×D4—22no—
176C2×C3×D4C22⋊D511yescharacteristic
177C2×C3×D4C22⋊D511yescharacteristic
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C2×Dic6—101no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C4⋊C4C22⋊D512yes—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C42C22×D511yescharacteristic
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C23×C5—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×D4—21no—
201C5×D4—21no—
202C5×D4—21no—
203C5×D4—44no—
204C5×D4#21412yes—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—22no—
208C2×C4×C5—44no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5C2×#6711yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×Dic5—121no—
217Dic10—122no—
218#168—121no—
219#168—121no—
220#168—121no—
221C2×#41—21no—
222C4⋊Q8—151no—
223C4⋊Q8C2×D1511yescharacteristic
224#123—22no—
225C22⋊Q8—21no—
226#121—21no—
227C4×D4C2×D1511yescharacteristic
228C4×D4C2×D1511yescharacteristic
229C2×C4⋊C4—21no—
230#106—301no—
231#106—301no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234#103—302no—
235#102—301no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5—42no—
239C2×C3×C5—81no—
240C2×C3×C5#45011yescharacteristic
241C2×C3×C5#45211yescharacteristic
242C2×C3×C5#45411yescharacteristic
243C23×C3—21no—
244C23×C3—21no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—44no—
251C3×D4#68712yes—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—44no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263C2×Dic3—201no—
264Dic6—202no—
265C3⋊C8—201no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5#95311yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—42no—
278C4×C5—41no—
279C4×C5#93211yescharacteristic
280C4×C5C2×#21411yescharacteristic
281C4×C5#95011yescharacteristic
282C4×C5#95111yescharacteristic
283Dic5—241no—
284#41—42no—
285#41—42no—
286C2×Q8—21no—
287C2×Q8—301no—
288C2×D4—22no—
289C2×D4#122011yescharacteristic
290C2×D4#122011yescharacteristic
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C2×C8—301no—
295C2×C8—301no—
296C2×C8—301no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4#122012yes—
302C4⋊C4#122011yescharacteristic
303C4⋊C4#122011yescharacteristic
304C22⋊C4—22no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C42C22×D1511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3#409911yescharacteristic
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4#407811yescharacteristic
321C3×C4C2×#68711yescharacteristic
322C3×C4#409611yescharacteristic
323C3×C4#409711yescharacteristic
324Dic3—401no—
325C2×C5—42no—
326C2×C5—81no—
327C2×C5#521811yescharacteristic
328C2×C5#523911yescharacteristic
329C2×C5#524511yescharacteristic
330C23—21no—
331C23—21no—
332Q8—41no—
333Q8—41no—
334Q8—602no—
335D4—21no—
336D4—21no—
337D4—21no—
338D4—44no—
339D4#671612yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—601no—
349C2×C4C2×#122011yescharacteristic
350C2×C4C2×#122011yescharacteristic
351C2×C4C2×#122011yescharacteristic
352C8—601no—
353C8—601no—
354C8—601no—
355C2×C3—42no—
356C2×C3—81no—
357C2×C3#6550711yescharacteristic
358C2×C3#6552811yescharacteristic
359C2×C3#6553411yescharacteristic
360C5#7191111yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22#9184211yescharacteristic
368C4—21no—
369C4—41no—
370C4—42no—
371C4—41no—
372C4—1201no—
373C4#9182111yescharacteristic
374C4C2×#671611yescharacteristic
375C4#9183911yescharacteristic
376C4#9184011yescharacteristic
377C3#1060270411yescharacteristic, complemented, Sylow
378C2—42no—
379C2—81no—
380C2#1175131911yescharacteristic
381C2#1175134011yescharacteristic
382C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#547C2
socleC22×C3×C5#120
hypercenter#547D15
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11751109C2semidirect
4. #11751109C2semidirect
5. #11746368C2semidirect
6. D4⋊(C3⋊#168)C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
308. C3×C5#1635semidirect
360. C5#71911semidirect
377. C3#10602704semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5472
#117511942
#117511092
#117463682
D4⋊(C3⋊#168)2
#106027043
#719115