Finite Group Databasebeta

← #14281756

Subgroups — #14281756

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic5C211yesmaximal, characteristic
2#11751793C211yesmaximal, characteristic
3#11751754C211yesmaximal, characteristic
4#11746801C211yesmaximal, characteristic, complemented
5C3×Q8⋊#170C211yesmaximal, characteristic, complemented
6#11746493C211yesmaximal, characteristic, complemented
7#11746492C211yesmaximal, characteristic, complemented
8#10604967—31nomaximal, Hall
9C2×C5×D3×Q8C411yescharacteristic
10Q8×Dic15C411yescharacteristic
11C3×Q8×Dic5C2211yescharacteristic
12D3×C4⋊Dic5—21no—
13D3×C4⋊Dic5C411yescharacteristic
14C4×D3×Dic5—21no—
15C4×D3×Dic5C2211yescharacteristic
16#91344—21no—
17#91344C411yescharacteristic
18Dic5×Dic6—21no—
19Dic5×Dic6C2211yescharacteristic
20C4⋊(C3⋊#170)C2211yescharacteristic
21C4×C3⋊#170C2211yescharacteristic
22C3×C4⋊#170C2211yescharacteristic
23C3×C4×#170C2211yescharacteristic
24Dic3⋊#170—21no—
25(C2×D3)⋊#170—21no—
26(C2×D3)⋊#170—21no—
27Dic3×#170—21no—
28#68231—51nomaximal, Hall
29C2×Q8×Dic5—31no—
30#65748—31no—
31#65748—31no—
32Q8⋊#170—31no—
33Q8⋊#170—31no—
34Q8⋊#170—31no—
35Q8⋊#170D311yescharacteristic, complemented
36C2×C3×C5×Q8C2×C411yescharacteristic
37C5×D3×Q8—22no—
38C5×D3×Q8C814yescomplemented
39C2×C4×C5×D3—21no—
40C2×C4×C5×D3C2×C411yescharacteristic
41C2×C5×Dic6—21no—
42C2×C5×Dic6C2×C411yescharacteristic
43C2×D3×Dic5—21no—
44C2×D3×Dic5D411yescharacteristic
45C2×D3×Dic5D411yescharacteristic
46C2×C3⋊#170—21no—
47C2×C3⋊#170—21no—
48C2×C3×#170—21no—
49C2×C3×#170—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15C2×C411yescharacteristic
52C4×Dic15—21no—
53C4×Dic15C2×C411yescharacteristic
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×C4×Dic5—21no—
57C3×C4×Dic5C2311yescharacteristic
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—21no—
60Dic3⋊Dic5—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65C4×D3×Q8—51no—
66#4833—51no—
67#4685—51no—
68C3×Q8⋊C8—51no—
69#4535—51no—
70#4484—51no—
71#4456—51no—
72C22×C5×Q8—31no—
73Q8×Dic5—31no—
74Q8×Dic5—31no—
75Q8×Dic5—31no—
76Q8×Dic5—61no—
77Q8×Dic5—61no—
78Q8×Dic5C2×D311yescharacteristic
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5—61no—
81C2×C4×Dic5—31no—
82C2×C4×Dic5—61no—
83C22⋊#170—61no—
84C22⋊#170—61no—
85C4⋊#170—31no—
86C4⋊#170—61no—
87C4⋊#170C2×D311yescharacteristic
88C4×#170—31no—
89C4×#170—61no—
90C4×#170C2×D311yescharacteristic
91#1479—151noSylow
92C22×C5×D3C22⋊C411yescharacteristic
93C3×C5×Q8—21no—
94C3×C5×Q8C2×C812yes—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100C2×C5×Dic3—21no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C4×C5×D3—24no—
103C4×C5×D3C2×C812yes—
104C4×C5×D3M1612yes—
105C5×Dic6—21no—
106C5×Dic6—24no—
107C5×Dic6C2×C812yes—
108C2×C3×Dic5—21no—
109C2×C3×Dic5C2×D411yescharacteristic
110C2×C3×Dic5C2×D411yescharacteristic
111D3×Dic5—21no—
112D3×Dic5—21no—
113D3×Dic5—41no—
114D3×Dic5—42no—
115C3⋊#170—41no—
116C3⋊#170—41no—
117C3×#170—41no—
118C3×#170—41no—
119C2×D3×Q8AGL(1,𝔽5)11yescharacteristic
120C3×C4×Q8—51no—
121Q8×Dic3—51no—
122D3×C4⋊C4—51no—
123D3×C4⋊C4—101no—
124#887—51no—
125#887—101no—
126C42×D3—51no—
127C42×D3—101no—
128C4×Dic6—51no—
129C4×Dic6—101no—
130C3×C4⋊C8—51no—
131C3×C4×C8—51no—
132(C2×D3)⋊C8—101no—
133(C2×D3)⋊C8—101no—
134Dic3⋊C8—101no—
135C8×Dic3—101no—
136C4⋊(C3⋊C8)—51no—
137C4×C3⋊C8—51no—
138C2×C5×Q8—34no—
139C2×C5×Q8—31no—
140C2×C5×Q8—61no—
141C2×C5×Q8—62no—
142C2×C5×Q8C4×D311yescharacteristic
143C22×C4×C5—31no—
144C22×C4×C5—61no—
145C22×Dic5—31no—
146C22×Dic5—31no—
147C22×Dic5—61no—
148C2×#170—21no—
149C2×#170—21no—
150C2×#170—61no—
151C2×#170—61no—
152C4⋊Dic5—21no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158C4⋊Dic5C4×D311yescharacteristic
159C4×Dic5—21no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C4×Dic5—61no—
164C4×Dic5—61no—
165C4×Dic5—61no—
166C4×Dic5C22×D311yescharacteristic
167C2×C4×Q8—151no—
168#431—151no—
169#431—151no—
170Q8⋊C8—51no—
171Q8⋊C8—151no—
172Q8⋊C8—151no—
173Q8⋊C8—151no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C5×D3—21no—
176C2×C5×D3—21no—
177C2×C5×D3C22⋊C812yes—
178C3×C4×C5—22no—
179C3×C4×C5C22×C811yescharacteristic
180C3×C4×C5C2×M1611yescharacteristic
181Dic15—21no—
182Dic15—21no—
183Dic15—41no—
184C3×Dic5—21no—
185C3×Dic5—41no—
186C3×Dic5#13711yescharacteristic
187C3×Dic5#13711yescharacteristic
188C5×Dic3—22no—
189C5×Dic3C22⋊C812yes—
190C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
191D3×Q8—22no—
192D3×Q8#17014yescomplemented
193C2×C4×D3—21no—
194C2×C4×D3—51no—
195C2×C4×D3—51no—
196C2×C4×D3—101no—
197C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
198C2×Dic6—21no—
199C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
200C2×C3×C8—101no—
201C2×C3×C8—101no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4—101no—
204C3×C42—51no—
205C3×C42—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—51no—
212C4×Dic3—51no—
213C4×Dic3—51no—
214C4×Dic3—101no—
215C4×Dic3—101no—
216C4×Dic3—101no—
217C2×C3⋊C8—101no—
218C2×C3⋊C8—101no—
219C23×C5—31no—
220C5×Q8—21no—
221C5×Q8—32no—
222C5×Q8—64no—
223C5×Q8—61no—
224C5×Q8D3×C812yes—
225C2×C4×C5—21no—
226C2×C4×C5—31no—
227C2×C4×C5—32no—
228C2×C4×C5—32no—
229C2×C4×C5—64no—
230C2×C4×C5—61no—
231C2×C4×C5C2×C4×D311yescharacteristic
232C2×Dic5—21no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—61no—
236C2×Dic5—61no—
237C2×Dic5—61no—
238C2×Dic5—121no—
239C2×Dic5—122no—
240C2×Dic5D3×D411yescharacteristic
241C2×Dic5D3×D411yescharacteristic
242#170—41no—
243#170—41no—
244#170—121no—
245#170—121no—
246C22×Q8—31no—
247C4×Q8—51no—
248C4×Q8—151no—
249C4×Q8—151no—
250C4×Q8—151no—
251C4×Q8—301no—
252C4×Q8—301no—
253C2×C4⋊C4—151no—
254C2×C4⋊C4—301no—
255C2×C42—151no—
256C2×C42—301no—
257C4⋊C8—51no—
258C4⋊C8—151no—
259C4⋊C8—301no—
260C22⋊C8—301no—
261C22⋊C8—301no—
262C4×C8—51no—
263C4×C8—151no—
264C4×C8—301no—
265C2×C3×C5C2×C22⋊C811yescharacteristic
266C2×C3×C5#41911yescharacteristic
267C2×C3×C5#42111yescharacteristic
268C5×D3—22no—
269C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
270C3×Q8—21no—
271C3×Q8C2×#17012yes—
272C2×C3×C4—21no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—101no—
276C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
277C2×Dic3—21no—
278C2×Dic3—51no—
279C2×Dic3—51no—
280C2×Dic3—101no—
281C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
282C4×D3—24no—
283C4×D3—101no—
284C4×D3—101no—
285C4×D3—201no—
286C4×D3—202no—
287C4×D3C2×#17012yes—
288C4×D3#70412yes—
289Dic6—21no—
290Dic6—24no—
291Dic6C2×#17012yes—
292C3×C8—201no—
293C3×C8—201no—
294C3⋊C8—201no—
295C3⋊C8—201no—
296C22×C5—32no—
297C22×C5—61no—
298C22×C5—61no—
299C22×C5D3×C22⋊C411yescharacteristic
300C4×C5—22no—
301C4×C5—32no—
302C4×C5—62no—
303C4×C5C2×D3×C811yescharacteristic
304C4×C5D3×M1611yescharacteristic
305Dic5—21no—
306Dic5—41no—
307Dic5—61no—
308Dic5—61no—
309Dic5—121no—
310Dic5#91511yescharacteristic
311Dic5#91811yescharacteristic
312C2×Q8—34no—
313C2×Q8—31no—
314C2×Q8—61no—
315C2×Q8—62no—
316C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
317C22×C4—31no—
318C22×C4—61no—
319C22×C4—151no—
320C22×C4—151no—
321C22×C4—301no—
322C2×C8—101no—
323C2×C8—101no—
324C2×C8—301no—
325C2×C8—301no—
326C4⋊C4—51no—
327C4⋊C4—101no—
328C4⋊C4—151no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C4⋊C4—301no—
333C42—51no—
334C42—101no—
335C42—151no—
336C42—151no—
337C42—151no—
338C42—301no—
339C42—301no—
340C42—301no—
341C3×C5#147911yescharacteristic, complemented, Hall
342C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
343C2×D3—21no—
344C2×D3—21no—
345C2×D3C22⋊#17012yes—
346C3×C4—22no—
347C3×C4—51no—
348C3×C4—51no—
349C3×C4—101no—
350C3×C4—201no—
351C3×C4C22×#17011yescharacteristic
352C3×C4C2×#70411yescharacteristic
353Dic3—22no—
354Dic3—101no—
355Dic3—101no—
356Dic3—201no—
357Dic3C22⋊#17012yes—
358C2×C5—62no—
359C2×C5D3×C22⋊C811yescharacteristic
360C2×C5#480211yescharacteristic
361C2×C5#482111yescharacteristic
362C23—31no—
363Q8—21no—
364Q8—32no—
365Q8—64no—
366Q8—61no—
367Q8D3×#17012yes—
368C2×C4—21no—
369C2×C4—31no—
370C2×C4—32no—
371C2×C4—32no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—64no—
375C2×C4—61no—
376C2×C4—101no—
377C2×C4—151no—
378C2×C4—151no—
379C2×C4—301no—
380C2×C4—301no—
381C2×C4—301no—
382C2×C4—601no—
383C2×C4—602no—
384C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
385C8—201no—
386C8—201no—
387C8—601no—
388C8—601no—
389C2×C3#6578211yescharacteristic
390C2×C3#6578411yescharacteristic
391C2×C3C2×C22⋊#17011yescharacteristic
392D3—22no—
393C5#6823111yescharacteristic, complemented, Sylow
394C22—32no—
395C22—61no—
396C22—61no—
397C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
398C4—22no—
399C4—32no—
400C4—51no—
401C4—51no—
402C4—62no—
403C4—101no—
404C4—201no—
405C4—301no—
406C4—301no—
407C4—601no—
408C4C2×D3×#17011yescharacteristic
409C4D3×#70411yescharacteristic
410C3#1060496711yescharacteristic, complemented, Sylow
411C2—62no—
412C2#1175196211yescharacteristic
413C2#1175197411yescharacteristic
414C2D3×C22⋊#17011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C8
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1479
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. #11746801C2semidirect
5. C3×Q8⋊#170C2semidirect
6. #11746493C2semidirect
7. #11746492C2semidirect
35. Q8⋊#170D3semidirect
38. C5×D3×Q8C8semidirect
192. D3×Q8#170semidirect
341. C3×C5#1479semidirect
393. C5#68231semidirect
410. C3#10604967semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic52
#117517932
#117517542
#117468012
C3×Q8⋊#1702
#117464932
#117464922
#106049673
#682315