Finite Group Databasebeta

← #14281841

Subgroups — #14281841

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752500C211yesmaximal, characteristic
2C5×#4685C211yesmaximal, characteristic
3D3×C4⋊#168C211yesmaximal, characteristic
4#11746277C211yesmaximal, characteristic, complemented
5C3×#64676C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10601561—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C42×C5×D3C2211yescharacteristic
11C3×C4×Dic10C2211yescharacteristic
12#91469C411yescharacteristic
13C4×#1204—21no—
14#91389C411yescharacteristic
15#91379—21no—
16#91371—21no—
17#91369C411yescharacteristic
18#91365C411yescharacteristic
19#91352—21no—
20C2×D3×#168—21no—
21C3×C4×C5×C8C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×(C2×D3)⋊C8—21no—
24C5×Dic3⋊C8—21no—
25C4×C5×C3⋊C8C2211yescharacteristic
26C3×C4⋊#168C2211yescharacteristic
27Dic3⋊#168—21no—
28#68232—51nomaximal, Hall
29#65804—31no—
30C5×#431—31no—
31C2×C4⋊#168—31no—
32#64676—31no—
33#64676—31no—
34#64676—31no—
35#64676D311yescharacteristic, complemented
36C2×Dic30C2×C411yescharacteristic
37C2×C4×C5×D3C2×C411yescharacteristic
38C2×C4×C5×D3D411yescharacteristic
39C2×C4×C5×D3D411yescharacteristic
40C2×C3×Dic10C2×C411yescharacteristic
41C2×#1204—21no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15C2×C411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C4×C5×Dic3C2×C411yescharacteristic
49C4×C5×Dic3D411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5C2×C411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6668—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63D3×#168—42no—
64#5578—51no—
65D3×C4⋊C8—51no—
66#4685D511yescharacteristic
67C3×Q8⋊C8—51no—
68#4535—51no—
69#4484—51no—
70#4456—51no—
71C2×C42×C5—31no—
72#4072—61no—
73#4070—31no—
74#4070—31no—
75#4070—61no—
76C22×#168—61no—
77#4016—61no—
78#4015—31no—
79#4015—31no—
80C4×Dic10—31no—
81C4×Dic10—61no—
82C4×Dic10C2×D311yescharacteristic
83C5×C4⋊C8—61no—
84C5×C22⋊C8—61no—
85C4×C5×C8—31no—
86C4×C5×C8C2×D311yescharacteristic
87C4⋊#168—31no—
88C4⋊#168—61no—
89C4⋊#168C2×D311yescharacteristic
90#1481—151noSylow
91C22×C5×D3C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97Dic30—21no—
98Dic30—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C4×C5×D3—21no—
103C4×C5×D3—21no—
104C4×C5×D3—41no—
105C4×C5×D3SD1612yes—
106C4×C5×D3Q1612yes—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C3×Dic10—21no—
110C3×Dic10—21no—
111#1204—42no—
112C3×C5×C8—41no—
113C3⋊#168—41no—
114C3×#168—41no—
115C5×C3⋊C8—41no—
116C3×C4×Q8—51no—
117#946—51no—
118#944—51no—
119C2×D3×C8—101no—
120#897—51no—
121#896—101no—
122#889—101no—
123#888—51no—
124#872—101no—
125C42×D3C2×D511yescharacteristic
126C4×Dic6—51no—
127C4×Dic6—101no—
128C3×C4⋊C8—51no—
129C3×C4×C8C2×D511yescharacteristic
130(C2×D3)⋊C8—21no—
131Dic3⋊C8—21no—
132Dic3⋊C8—101no—
133C4⋊(C3⋊C8)—51no—
134C4×C3⋊C8C2×D511yescharacteristic
135C22×C4×C5—31no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C2×Dic10—31no—
139C2×Dic10—61no—
140C2×Dic10C4×D311yescharacteristic
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C42×C5—31no—
144C42×C5—31no—
145C42×C5—31no—
146C42×C5C22×D311yescharacteristic
147C22⋊Dic5—61no—
148C22⋊Dic5—61no—
149C4⋊Dic5—31no—
150C4⋊Dic5—61no—
151C4⋊Dic5—61no—
152C4⋊Dic5—61no—
153C4⋊Dic5C4×D311yescharacteristic
154#683—21no—
155#683—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—21no—
159C4×Dic5—61no—
160C2×#168—21no—
161C2×#168—61no—
162C2×#168—122no—
163#533—151no—
164#431—31no—
165C2×C4⋊C8—151no—
166Q8⋊C8—51no—
167Q8⋊C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C5×D3#10312yes—
174C3×C4×C5—21no—
175C3×C4×C5#13111yescharacteristic
176C3×C4×C5#13111yescharacteristic
177C3×C4×C5C2×SD1611yescharacteristic
178C3×C4×C5C2×Q1611yescharacteristic
179Dic15—41no—
180Dic15—41no—
181C3×Dic5—41no—
182C3×Dic5—41no—
183C5×Dic3—21no—
184C5×Dic3—21no—
185C5×Dic3#10312yes—
186C2×C3×Q8—51no—
187C2×C4×D3C4×D511yescharacteristic
188C2×C4×D3D2011yescharacteristic
189C2×C4×D3C22⋊D511yescharacteristic
190C2×Dic6—51no—
191C2×Dic6—101no—
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—101no—
196C3×C42—101no—
197C3×C42C22×D511yescharacteristic
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—101no—
208C4×Dic3C4×D511yescharacteristic
209C4×Dic3D2011yescharacteristic
210C4×Dic3C22⋊D511yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213D3×C8—202no—
214C23×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—32no—
217C2×C4×C5—32no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—61no—
221C2×C4×C5—61no—
222C2×C4×C5—121no—
223C2×C4×C5C2×C4×D311yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—61no—
229C2×Dic5—61no—
230Dic10—21no—
231Dic10—21no—
232Dic10—61no—
233Dic10—61no—
234Dic10—122no—
235C5×C8—41no—
236C5×C8—121no—
237#168—41no—
238#168—121no—
239C22×C8—301no—
240C4⋊Q8—151no—
241C4⋊Q8—151no—
242#125—301no—
243C22⋊Q8—151no—
244C22⋊Q8—151no—
245C22⋊Q8—301no—
246C4×Q8—51no—
247C4×Q8—151no—
248C4×Q8—301no—
249#117—301no—
250C2×C42—31no—
251C4⋊C8—51no—
252C4⋊C8—61no—
253C4⋊C8—151no—
254C4⋊C8—301no—
255C22⋊C8—61no—
256C4×C8—31no—
257C4×C8D3×D511yescharacteristic
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5C2×#10311yescharacteristic
260C2×C3×C5#42111yescharacteristic
261C5×D3—22no—
262C22×D3#68511yescharacteristic
263C3×Q8—101no—
264C3×Q8—101no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4C2×D2011yescharacteristic
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×Dic3—101no—
271C2×Dic3—101no—
272C2×Dic3#68511yescharacteristic
273C2×Dic3#68511yescharacteristic
274C2×Dic3#68511yescharacteristic
275C4×D3—21no—
276C4×D3—21no—
277C4×D3—41no—
278C4×D3#67712yes—
279C4×D3Dic2012yes—
280Dic6—101no—
281Dic6—101no—
282Dic6—202no—
283C3×C8—41no—
284C3×C8—201no—
285C3⋊C8—41no—
286C3⋊C8—201no—
287C22×C5—32no—
288C22×C5—61no—
289C22×C5—61no—
290C22×C5D3×C22⋊C411yescharacteristic
291C4×C5—21no—
292C4×C5—32no—
293C4×C5—61no—
294C4×C5—61no—
295C4×C5#90111yescharacteristic
296C4×C5#90711yescharacteristic
297C4×C5D3×SD1611yescharacteristic
298C4×C5D3×Q1611yescharacteristic
299Dic5—41no—
300Dic5—41no—
301Dic5—121no—
302Dic5—121no—
303C2×Q8—51no—
304C2×Q8—151no—
305C2×Q8—301no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—31no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—101no—
312C2×C8—301no—
313C2×C8—602no—
314C4⋊C4—51no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C22⋊C4—301no—
324C22⋊C4—301no—
325C42—31no—
326C42—31no—
327C42—31no—
328C42—101no—
329C42—301no—
330C42C2×D3×D511yescharacteristic
331C3×C5#148111yescharacteristic, complemented, Hall
332C22×C3C2×#68511yescharacteristic
333C2×D3—21no—
334C2×D3—21no—
335C2×D3#394812yes—
336C3×C4—21no—
337C3×C4—201no—
338C3×C4—201no—
339C3×C4C2×#67711yescharacteristic
340C3×C4C2×Dic2011yescharacteristic
341C3×C4#405311yescharacteristic
342C3×C4#405311yescharacteristic
343Dic3—21no—
344Dic3—21no—
345Dic3—201no—
346Dic3—201no—
347Dic3#394812yes—
348C2×C5—62no—
349C2×C5#472711yescharacteristic
350C2×C5D3×#10311yescharacteristic
351C2×C5#482111yescharacteristic
352C23—31no—
353Q8—101no—
354Q8—101no—
355Q8—301no—
356Q8—301no—
357Q8—602no—
358C2×C4—31no—
359C2×C4—32no—
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—101no—
366C2×C4—101no—
367C2×C4—121no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4C4×D3×D511yescharacteristic
371C2×C4D3×D2011yescharacteristic
372C2×C4D3×C22⋊D511yescharacteristic
373C8—41no—
374C8—121no—
375C8—201no—
376C8—601no—
377C2×C3#6529411yescharacteristic
378C2×C3C2×#394811yescharacteristic
379C2×C3#6541811yescharacteristic
380D3—22no—
381C5#6823211yescharacteristic, complemented, Sylow
382C22—32no—
383C22—61no—
384C22—61no—
385C22D3×#68511yescharacteristic
386C4—21no—
387C4—32no—
388C4—61no—
389C4—61no—
390C4—201no—
391C4—201no—
392C4—601no—
393C4—601no—
394C4D3×#67711yescharacteristic
395C4D3×Dic2011yescharacteristic
396C4#9126611yescharacteristic
397C4#9126811yescharacteristic
398C3#1060156111yescharacteristic, complemented, Sylow
399C2—62no—
400C2#1174711111yescharacteristic
401C2D3×#394811yescharacteristic
402C2#1174814011yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#1481
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. #11746277C2semidirect
5. C3×#64676C2semidirect
6. #11745844C2semidirect
7. #11745841C2semidirect
35. #64676D3semidirect
331. C3×C5#1481semidirect
381. C5#68232semidirect
398. C3#10601561semidirect

Maximal subgroups

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

subgroupindex
#117525002
C5×#46852
D3×C4⋊#1682
#117462772
C3×#646762
#117458442
#117458412
#106015613
#682325