Finite Group Databasebeta

← #14290604

Subgroups — #14290604

Order 1920.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752486C211yesmaximal, characteristic
2C5×#4682C211yesmaximal, characteristic, complemented
3#11747087C211yesmaximal, characteristic
4#11746918C211yesmaximal, characteristic, complemented
5#11746280C211yesmaximal, characteristic
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745858C211yesmaximal, characteristic, complemented
8#10602163—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91390—21no—
14#91375—21no—
15#91347—21no—
16#91337—22no—
17Dic5×Dic6—21no—
18C2×#6660—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#818—22no—
22C3×C4⋊#168C2211yescharacteristic
23#90986—21no—
24#90973—21no—
25#90970—21no—
26#68250—51nomaximal, Hall
27#66066—31no—
28C5×#500—31no—
29#65383—31no—
30#65372—31no—
31#64767—31no—
32#64679—31no—
33#64676D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D412yes—
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—21no—
50C3×C4×Dic5—21no—
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#6660—42no—
57#5584—51no—
58#5020—51no—
59#4841—51no—
60#4682D511yescharacteristic, complemented
61C3×Q8⋊C8—51no—
62#4482—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C5×C4⋊Q8—31no—
66#4093—61no—
67Q8×Dic5—61no—
68C2×#688—61no—
69#4044—62no—
70#4043—61no—
71#4038—61no—
72C4×D20—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×#107—62no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3942—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1650—151noSylow
82C22×D15—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87D60—21no—
88D60—21no—
89C4×D15—41no—
90C4×D15—41no—
91C2×C5×Dic3—22no—
92C2×C5×Dic3—41no—
93C5×Dic6—41no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×C5×C8—22no—
102C3⋊#168—41no—
103C3×#168—41no—
104C3×C4×Q8—51no—
105#946—101no—
106C2×#204—101no—
107#898—102no—
108#892—101no—
109#875—101no—
110C4×D12—51no—
111#869C2×D511yescharacteristic
112#869C2×D511yescharacteristic
113C4×Dic6—101no—
114C3×C4⋊C8—51no—
115C3×C4×C8C2×D511yescharacteristic
116#835—101no—
117#818—22no—
118#816—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×Q8—61no—
122C2×C5×Q8—61no—
123C2×D20—31no—
124C2×C4×D5—61no—
125C2×Dic10D1211yescharacteristic
126C2×C5×C8—21no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5C22×D311yescharacteristic
132#688—122no—
133#685—62no—
134#685—62no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—62no—
138C4⋊Dic5D1211yescharacteristic
139#683—21no—
140C4×Dic5—21no—
141C4×Dic5—62no—
142C2×#168—21no—
143C2×#168—61no—
144#556—151no—
145#500—31no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—51no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C3×C4×C5—21no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C5×Dic3—42no—
164C5×Dic3—81no—
165C2×C3×Q8—51no—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×Dic6—21no—
169C2×Dic6—21no—
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—101no—
174C3×C42—101no—
175C3×C42C22×D511yescharacteristic
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—101no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—51no—
183C4⋊Dic3C22⋊D512yes—
184Dic3⋊C4—102no—
185C4×Dic3—102no—
186C2×C3⋊C8—101no—
187#204—202no—
188C22×D5—61no—
189C5×Q8—121no—
190C5×Q8—121no—
191C5×Q8—121no—
192C5×Q8—121no—
193C2×C4×C5—62no—
194C2×C4×C5—121no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—61no—
201D20—61no—
202D20—61no—
203C4×D5—121no—
204C4×D5—121no—
205Dic10—21no—
206Dic10—21no—
207C5×C8—22no—
208#168—41no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—31no—
212C4⋊Q8—31no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—51no—
217C4×Q8—301no—
218C4×D4—151no—
219#117—301no—
220#107—62no—
221#106—301no—
222C4⋊C8—51no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8D3×D511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230D15—81no—
231C22×D3—101no—
232C3×Q8—101no—
233C3×Q8—101no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239C2×Dic3—22no—
240C2×Dic3—41no—
241C2×Dic3—101no—
242D12—101no—
243D12—101no—
244C4×D3—201no—
245C4×D3—201no—
246Dic6—41no—
247Dic6—41no—
248Dic6—41no—
249Dic6—41no—
250C3×C8—22no—
251C3×C8—201no—
252C3⋊C8—201no—
253C22×C5#88211yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—122no—
259C4×C5—241no—
260C4×C5#90411yescharacteristic
261C4×C5#90911yescharacteristic
262C4×C5#91411yescharacteristic
263C4×C5#91911yescharacteristic
264Dic5—41no—
265Dic5—41no—
266Dic5—121no—
267C2×Q8—51no—
268C2×Q8—61no—
269C2×Q8—61no—
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—32no—
277C4⋊C4—51no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—101no—
282C4⋊C4—151no—
283C4⋊C4—302no—
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—101no—
288C42—302no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#408311yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—201no—
297C3×C4—201no—
298C3×C4#405711yescharacteristic
299C3×C4#405811yescharacteristic
300C3×C4#406411yescharacteristic
301C3×C4#406511yescharacteristic
302Dic3—42no—
303Dic3—81no—
304Dic3—201no—
305C2×C5#473311yescharacteristic
306C2×C5#481011yescharacteristic
307C2×C5#482611yescharacteristic
308D5—241no—
309C23—301no—
310Q8—101no—
311Q8—101no—
312Q8—121no—
313Q8—121no—
314Q8—121no—
315Q8—121no—
316D4—301no—
317D4—301no—
318C2×C4—62no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—121no—
322C2×C4—301no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4D5×D1211yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—22no—
329C8—201no—
330C8—601no—
331C2×C3#6538411yescharacteristic
332C2×C3#6544711yescharacteristic
333C2×C3#6547611yescharacteristic
334D3—401no—
335C5#6825011yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9147511yescharacteristic
340C4—21no—
341C4—122no—
342C4—201no—
343C4—201no—
344C4—241no—
345C4—601no—
346C4#9125711yescharacteristic
347C4#9126111yescharacteristic
348C4#9127111yescharacteristic
349C4#9127911yescharacteristic
350C3#1060216311yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1174712211yescharacteristic
353C2#1174815711yescharacteristic
354C2#1174815911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C5×#4682C2semidirect
4. #11746918C2semidirect
6. C3×#64676C2semidirect
7. #11745858C2semidirect
33. #64676D3semidirect
60. #4682D5semidirect
290. C3×C5#1650semidirect
335. C5#68250semidirect
350. C3#10602163semidirect

Maximal subgroups

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

subgroupindex
#117524862
C5×#46822
#117470872
#117469182
#117462802
C3×#646762
#117458582
#106021633
#682505