Finite Group Databasebeta

← #14289174

Subgroups — #14289174

Order 1920.

420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752490C211yesmaximal, characteristic, complemented
2#11751171C211yesmaximal, characteristic
3C5×#5075C211yesmaximal, characteristic
4C3×#65364C211yesmaximal, characteristic
5#11745860C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601823—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10#91758C2211yescharacteristic
11C2×C5×#214—21no—
12C4×C5×Dic6C2211yescharacteristic
13C2×C3×#687—21no—
14C3×C4×Dic10C2211yescharacteristic
15#91389—21no—
16#91388—21no—
17#91343—22no—
18#91340—21no—
19Dic5×Dic6—21no—
20#91116—22no—
21C4×C3⋊#168C2211yescharacteristic
22C5×#832—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71034—51nomaximal, Hall
27#65904—31no—
28C5×#460—31no—
29#65364D311yescharacteristic
30#65359—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15D412yes—
43C2×C3⋊#168—21no—
44C5×#214—42no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#687—42no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55Dic3⋊Dic5—22no—
56#6669—22no—
57Dic3×Dic5—22no—
58#5567—51no—
59C3×#460—51no—
60#5075D511yescharacteristic
61#5070—51no—
62#4535—51no—
63#4484—51no—
64#4482—51no—
65C2×C5×SD16—61no—
66C5×#127C2×D311yescharacteristic
67C4×C5×Q8—31no—
68Q8×Dic5—61no—
69C2×#687—21no—
70#4036—61no—
71#4036—62no—
72#4015—31no—
73#4015—61no—
74C4×Dic10—61no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×#102—61no—
78#3964—21no—
79#3964—62no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1626—151noSylow
83C23×C3×C5—41no—
84C3×C5×D4—42no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—22no—
93Dic30—41no—
94Dic30—41no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C5×Dic6—21no—
98C5×Dic6SD1612yescomplemented
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×Dic10—21no—
102C3×Dic10—21no—
103C3⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×C3×SD16—101no—
107C3×#127C2×D511yescharacteristic
108C3×C4×Q8—51no—
109#944—101no—
110C2×#214—21no—
111#889—102no—
112#887—101no—
113#870—101no—
114#869—51no—
115C4×Dic6—101no—
116C4×Dic6C2×D511yescharacteristic
117C3×C4⋊C8—51no—
118C3×#102—101no—
119#832—21no—
120#832—102no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—31no—
124C2×C5×D4—21no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×Dic10—61no—
128C2×Dic10#6711yescharacteristic
129C5×SD16—122no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#687—42no—
136C4⋊Dic5—32no—
137C4⋊Dic5—62no—
138C4⋊Dic5—62no—
139C4⋊Dic5—61no—
140C4⋊Dic5#6711yescharacteristic
141#683—21no—
142#683—62no—
143C4×Dic5—21no—
144C4×Dic5—62no—
145C2×#168—21no—
146C2×#168—61no—
147#557—151no—
148#486—151no—
149#460—31no—
150#460—51no—
151#332—151no—
152Q8⋊C8—151no—
153Q8⋊C8—151no—
154C22×C3×C5—81no—
155C22×C3×C5—81no—
156C22×C3×C5—81no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5C2×SD1611yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—42no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×Q8—51no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×Dic6—101no—
173C2×Dic6C22⋊D511yescharacteristic
174C3×SD16—202no—
175C2×C3×C8—101no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180#214—42no—
181C4⋊Dic3—52no—
182C4⋊Dic3—101no—
183C4⋊Dic3C22⋊D511yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—102no—
186Dic3⋊C4—102no—
187Dic3⋊C4—102no—
188C4×Dic3—21no—
189C4×Dic3—102no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C23×C5—41no—
193C5×Q8—32no—
194C5×Q8—61no—
195C5×D4—42no—
196C5×D4—41no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—62no—
208Dic10—21no—
209Dic10—21no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213#168—41no—
214#168—121no—
215C2×SD16—61no—
216C2×SD16—101no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219#127D3×D511yescharacteristic
220#125—301no—
221#125—302no—
222C4×Q8—31no—
223C4×Q8—51no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—61no—
229#102—101no—
230#102—302no—
231C4×C8—151no—
232C2×C3×C5—161no—
233C2×C3×C5#44811yescharacteristic
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—41no—
237C3×Q8—101no—
238C3×Q8—101no—
239C3×D4—42no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—102no—
252Dic6—21no—
253Dic6—201no—
254Dic6—201no—
255Dic6#68712yescomplemented
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—81no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—121no—
266C4×C5D3×SD1611yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5#93211yescharacteristic
269C4×C5#95011yescharacteristic
270Dic5—41no—
271Dic5—41no—
272Dic5—122no—
273C2×Q8—31no—
274C2×Q8—51no—
275C2×Q8—301no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279SD16—122no—
280SD16—202no—
281C2×C8—61no—
282C2×C8—101no—
283C2×C8—301no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—61no—
287C4⋊C4—101no—
288C4⋊C4—152no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C42—61no—
294C42—101no—
295C42—302no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—81no—
299C22×C3—81no—
300C22×C3—81no—
301C22×C3#408311yescharacteristic
302C3×C4—21no—
303C3×C4—201no—
304C3×C4—201no—
305C3×C4#406011yescharacteristic
306C3×C4#406211yescharacteristic
307C3×C4C2×#68711yescharacteristic
308C3×C4#409711yescharacteristic
309Dic3—22no—
310Dic3—41no—
311Dic3—202no—
312C2×C5—161no—
313C2×C5#503711yescharacteristic
314C2×C5#517011yescharacteristic
315C2×C5#520111yescharacteristic
316C23—41no—
317Q8—32no—
318Q8—61no—
319Q8—101no—
320Q8—101no—
321Q8—601no—
322Q8—601no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—41no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—302no—
333C2×C4D5×#6711yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3—161no—
340C2×C3#6532911yescharacteristic
341C2×C3#6546111yescharacteristic
342C2×C3#6549011yescharacteristic
343C5#7103411yescharacteristic, complemented, Sylow
344C22—81no—
345C22—81no—
346C22—81no—
347C22#9157711yescharacteristic
348C4—21no—
349C4—62no—
350C4—121no—
351C4—201no—
352C4—201no—
353C4—602no—
354C4D3×#68711yescharacteristic
355C4#9148611yescharacteristic
356C4#9149111yescharacteristic
357C4#9149211yescharacteristic
358C3#1060182311yescharacteristic, complemented, Sylow
359C2—161no—
360C2#1174915511yescharacteristic
361C2#1174916011yescharacteristic
362C2#1174916611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752490C2semidirect
5. #11745860C2semidirect
6. #11745842C2semidirect
7. #11745840C2semidirect
98. C5×Dic6SD16semidirect
255. Dic6#687semidirect
297. C3×C5#1626semidirect
343. C5#71034semidirect
358. C3#10601823semidirect

Maximal subgroups

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

subgroupindex
#117524902
#117511712
C5×#50752
C3×#653642
#117458602
#117458422
#117458402
#106018233
#710345