Finite Group Databasebeta

← #14289405

Subgroups — #14289405

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#65919C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic, complemented
3#11747071C211yesmaximal, characteristic
4#11746916C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic, complemented
8#10599053—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4093—21no—
12C3×#4040—22no—
13C3×#4039—21no—
14C3×#4021—21no—
15C3×#4020C2211yescharacteristic
16C3×C4×D20—21no—
17C3×C4×Dic10C2211yescharacteristic
18C2×#6657—22no—
19#91119—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90990—21no—
25#90971—21no—
26#71944—51nomaximal, Hall
27#65919D311yescharacteristic
28#65310—31no—
29#65139—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D412yes—
39C2×C3×C4×D5—22no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—22no—
51C3×#685—22no—
52C3×#685—22no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5—21no—
56#6657—44no—
57C3×#559—51no—
58#5076—51no—
59#5021—51no—
60#5021—51no—
61#4544—51no—
62#4535—51no—
63#4535D511yescharacteristic, complemented
64C4×C5×Q8C2×D311yescharacteristic
65#4093—21no—
66C2×#677—62no—
67#4040—22no—
68#4039—21no—
69#4021—21no—
70#4020C2×D311yescharacteristic
71C4×D20—21no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3967—61no—
77#3950—61no—
78#3948—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1630—151noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—41no—
91Dic30—42no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C3×D20—42no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×C4×D5—82no—
100C3×Dic10—21no—
101C3×Dic10—21no—
102C3⋊#168—41no—
103C5×C3⋊C8—22no—
104C5×C3⋊C8—41no—
105C3×#127—51no—
106C3×#124—101no—
107C3×#124—101no—
108C3×#123—102no—
109C3×C4×Q8—51no—
110C3×C4×Q8C2×D511yescharacteristic
111C3×C4×D4—101no—
112C3×C4×D4—101no—
113C2×#214—102no—
114#869—51no—
115#835—101no—
116#835—101no—
117#807—101no—
118#807—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8C2×D511yescharacteristic
122C2×C5×Q8#6711yescharacteristic
123C2×D20—21no—
124C2×D20—21no—
125C2×D20#6712yes—
126C2×C4×D5—22no—
127C2×Dic10—61no—
128C2×Dic10#6711yescharacteristic
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4#6711yescharacteristic
133C42×C5—21no—
134C42×C5C22×D311yescharacteristic
135#685—22no—
136#685—22no—
137#685—22no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140C4⋊Dic5#6711yescharacteristic
141#683—21no—
142C4×Dic5—21no—
143C2×#168—61no—
144#677—124no—
145#559—51no—
146#492—151no—
147#477—151no—
148#477—151no—
149#331—151no—
150Q8⋊C8—31no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—81no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C2×C3×Q8—51no—
167C2×C3×Q8D2011yescharacteristic
168C2×C3×D4—52no—
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C22×C3×C4—102no—
172C2×Dic6—101no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4D2011yescharacteristic
177C3×C22⋊C4—102no—
178C3×C22⋊C4—102no—
179C3×C22⋊C4—102no—
180C3×C42—21no—
181C3×C42—101no—
182C3×C42C22×D511yescharacteristic
183#214—204no—
184C4⋊Dic3—101no—
185C4⋊Dic3—101no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—101no—
189C22×D5—22no—
190C5×Q8—21no—
191C5×Q8—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—121no—
200D20—42no—
201D20—41no—
202D20—41no—
203D20—41no—
204D20—41no—
205C4×D5—82no—
206Dic10—21no—
207Dic10—21no—
208Dic10—122no—
209C5×C8—62no—
210C5×C8—121no—
211#168—121no—
212C2×SD16—302no—
213C4⋊Q8—151no—
214#127—51no—
215#124—101no—
216#124—101no—
217#123—102no—
218C4×Q8—51no—
219C4×Q8D3×D511yescharacteristic
220C4×D4—101no—
221C4×D4—101no—
222#107—301no—
223#107—301no—
224C4⋊C8—31no—
225C4⋊C8—151no—
226#103—301no—
227#103—301no—
228C4×C8—31no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C3×D5—82no—
233C23×C3—102no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—101no—
237C3×Q8—101no—
238C3×D4—202no—
239C3×D4—201no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—402no—
248C2×C3×C4C2×D2011yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×Dic3—201no—
252Dic6—202no—
253C3⋊C8—22no—
254C3⋊C8—41no—
255C3⋊C8—201no—
256C22×C5#95311yescharacteristic
257C2×D5—42no—
258C2×D5—42no—
259C2×D5—42no—
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5#95011yescharacteristic
264C4×C5#95011yescharacteristic
265C4×C5#95111yescharacteristic
266C4×C5#95111yescharacteristic
267Dic5—41no—
268Dic5—41no—
269Dic5—241no—
270C2×Q8—51no—
271C2×Q8—301no—
272C2×Q8#120211yescharacteristic
273C2×D4—52no—
274C2×D4—101no—
275C2×D4—101no—
276C22×C4—102no—
277SD16—604no—
278C2×C8—61no—
279C2×C8—61no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—51no—
283C4⋊C4—101no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4#120211yescharacteristic
287C22⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—102no—
290C42—21no—
291C42—101no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3—202no—
295C22×C3—202no—
296C22×C3—202no—
297C22×C3#402811yescharacteristic
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—201no—
302C3×C4—201no—
303C3×C4#405011yescharacteristic
304C3×C4#405511yescharacteristic
305C3×C4#406211yescharacteristic
306C3×C4#406411yescharacteristic
307Dic3—401no—
308C2×C5#523911yescharacteristic
309C2×C5#523911yescharacteristic
310C2×C5#524111yescharacteristic
311D5—82no—
312C23—102no—
313Q8—21no—
314Q8—21no—
315Q8—101no—
316Q8—101no—
317Q8—602no—
318D4—202no—
319D4—201no—
320D4—201no—
321D4—201no—
322D4—201no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—402no—
328C2×C4—601no—
329C2×C4C2×#120211yescharacteristic
330C2×C4D5×#6711yescharacteristic
331C2×C4D5×#6711yescharacteristic
332C8—62no—
333C8—121no—
334C8—601no—
335C2×C3—402no—
336C2×C3#6502211yescharacteristic
337C2×C3#6509911yescharacteristic
338C2×C3#6511111yescharacteristic
339C5#7194411yescharacteristic, complemented, Sylow
340C22—202no—
341C22—202no—
342C22—202no—
343C22#9156411yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—201no—
348C4—201no—
349C4—1201no—
350C4#9131111yescharacteristic
351C4#9131311yescharacteristic
352C4#9150811yescharacteristic
353C4#9151411yescharacteristic
354C3#1059905311yescharacteristic, complemented, Sylow
355C2—402no—
356C2#1174853111yescharacteristic
357C2#1174929511yescharacteristic
358C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11751122C2semidirect
4. #11746916C2semidirect
5. C5×#4535C2semidirect
7. #11745841C2semidirect
63. #4535D5semidirect
293. C3×C5#1630semidirect
339. C5#71944semidirect
354. C3#10599053semidirect

Maximal subgroups

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

subgroupindex
C3×#659192
#117511222
#117470712
#117469162
C5×#45352
#117458522
#117458412
#105990533
#719445