Finite Group Databasebeta

← #14289413

Subgroups — #14289413

Order 1920.

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

normal subgroups only

This group has 436 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#11752636C211yesmaximal, characteristic
2#11750951C211yesmaximal, characteristic, complemented
3#11747071C211yesmaximal, characteristic
4#11746961C211yesmaximal, characteristic, complemented
5C5×#4484C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7#11745844C211yesmaximal, characteristic, complemented
8#10599053—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13#91434—21no—
14Dic3×D20—21no—
15#91407—22no—
16#91368—21no—
17#91364—21no—
18C2×#6657—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91102—21no—
21#91100—21no—
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90988—21no—
25#90973—21no—
26#68404—51nomaximal, Hall
27#65919—31no—
28#65310—31no—
29#65139—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64705D311yescharacteristic
33#64676—31no—
34C2×Dic30—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D412yes—
40C2×D5×Dic3—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C2×C3×#168—21no—
53#6665—22no—
54#6665—22no—
55#6665—22no—
56#6657—44no—
57#5713—51no—
58#5076—51no—
59#4850—51no—
60#4850—51no—
61C3×#331—51no—
62#4484—51no—
63#4484D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4093—61no—
66C2×#677—62no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020C2×D311yescharacteristic
71C4×D20—61no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3967—61no—
77#3950—61no—
78#3948—61no—
79#3939—61no—
80C4⋊#168C2×D311yescharacteristic
81#1630—151noSylow
82C22×C3×D5—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88C2×Dic15—41no—
89Dic30—21no—
90Dic30—21no—
91Dic30—42no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101D5×Dic3—82no—
102C3×C5×C8—41no—
103C3×#168—41no—
104C5×C3⋊C8—22no—
105C3×#127—51no—
106#936—101no—
107#936—101no—
108#935—102no—
109D4×Dic3—101no—
110D4×Dic3—101no—
111C2×#214—102no—
112#869—51no—
113C4×Dic6—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117#818—101no—
118#818—101no—
119#816—101no—
120#816—101no—
121C4×C3⋊C8C2×D511yescharacteristic
122C2×C5×Q8—31no—
123C2×D20—21no—
124C2×D20—21no—
125C2×D20D1212yes—
126C2×C4×D5—62no—
127C2×Dic10—31no—
128C2×Dic10—61no—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#685—62no—
136#685—62no—
137#685—62no—
138C4⋊Dic5—31no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141#683—61no—
142C4×Dic5—61no—
143C2×#168—21no—
144#677—124no—
145#559—151no—
146#492—151no—
147#477—151no—
148#477—151no—
149#331—51no—
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#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—41no—
163Dic15—81no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C2×C3×D4—52no—
167C2×C3×D4—101no—
168C2×C3×D4—101no—
169C22×Dic3—102no—
170C2×Dic6—51no—
171C2×Dic6—101no—
172C2×Dic6D2011yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—101no—
175C3×C42C22×D511yescharacteristic
176#217—102no—
177#217—102no—
178#217—102no—
179#214—204no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183C4⋊Dic3D2011yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—101no—
186C4×Dic3—21no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189C22×D5—22no—
190C5×Q8—61no—
191C5×Q8—61no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—61no—
198C2×Dic5—61no—
199C2×Dic5—121no—
200D20—42no—
201D20—41no—
202D20—41no—
203D20—41no—
204D20—41no—
205C4×D5—242no—
206Dic10—61no—
207Dic10—61no—
208Dic10—122no—
209C5×C8—41no—
210C5×C8—62no—
211#168—41no—
212C2×SD16—302no—
213C4⋊Q8—151no—
214#127—51no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—31no—
219C4×Q8—151no—
220C4×D4—301no—
221C4×D4—301no—
222#107—301no—
223#107—301no—
224C4⋊C8—51no—
225C4⋊C8D3×D511yescharacteristic
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×D4—202no—
235C3×D4—201no—
236C3×D4—201no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4C2×D2011yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—101no—
245C2×Dic3—101no—
246C2×Dic3—201no—
247C2×Dic3—402no—
248Dic6—21no—
249Dic6—21no—
250Dic6—101no—
251Dic6—101no—
252Dic6—202no—
253C3×C8—41no—
254C3×C8—201no—
255C3⋊C8—22no—
256C22×C5#88211yescharacteristic
257C2×D5—42no—
258C2×D5—42no—
259C2×D5—42no—
260C4×C5—21no—
261C4×C5—121no—
262C4×C5—121no—
263C4×C5#91211yescharacteristic
264C4×C5#91211yescharacteristic
265C4×C5#91511yescharacteristic
266C4×C5#91511yescharacteristic
267Dic5—121no—
268Dic5—121no—
269Dic5—241no—
270C2×Q8—31no—
271C2×Q8—151no—
272C2×Q8—301no—
273C2×D4—52no—
274C2×D4—101no—
275C2×D4—101no—
276C22×C4—302no—
277SD16—604no—
278C2×C8—21no—
279C2×C8—61no—
280C2×C8—101no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—151no—
284C4⋊C4—301no—
285C4⋊C4—301no—
286C4⋊C4—301no—
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—61no—
291C42—301no—
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#405011yescharacteristic
300C3×C4#405511yescharacteristic
301C3×C4#406211yescharacteristic
302C3×C4#406411yescharacteristic
303Dic3—41no—
304Dic3—41no—
305Dic3—201no—
306Dic3—201no—
307Dic3—401no—
308C2×C5#474711yescharacteristic
309C2×C5#478311yescharacteristic
310C2×C5#478311yescharacteristic
311D5—82no—
312C23—102no—
313Q8—61no—
314Q8—61no—
315Q8—301no—
316Q8—301no—
317Q8—602no—
318D4—202no—
319D4—201no—
320D4—201no—
321D4—201no—
322D4—201no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—301no—
326C2×C4—301no—
327C2×C4—601no—
328C2×C4—1202no—
329C2×C4D5×D1211yescharacteristic
330C2×C4D3×D2011yescharacteristic
331C2×C4#679011yescharacteristic
332C8—41no—
333C8—62no—
334C8—201no—
335C2×C3—402no—
336C2×C3#6502211yescharacteristic
337C2×C3#6509911yescharacteristic
338C2×C3#6511111yescharacteristic
339C5#6840411yescharacteristic, complemented, Sylow
340C22—202no—
341C22—202no—
342C22—202no—
343C22#9147611yescharacteristic
344C4—21no—
345C4—121no—
346C4—121no—
347C4—601no—
348C4—601no—
349C4—1201no—
350C4#9127311yescharacteristic
351C4#9127411yescharacteristic
352C4#9149711yescharacteristic
353C4#9152211yescharacteristic
354C3#1059905311yescharacteristic, complemented, Sylow
355C2—402no—
356C2#1174751911yescharacteristic
357C2#1174816211yescharacteristic
358C2#1174824811yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1630
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. #11750951C2semidirect
4. #11746961C2semidirect
5. C5×#4484C2semidirect
7. #11745844C2semidirect
63. #4484D5semidirect
293. C3×C5#1630semidirect
339. C5#68404semidirect
354. C3#10599053semidirect

Maximal subgroups

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

subgroupindex
#117526362
#117509512
#117470712
#117469612
C5×#44842
C3×#647052
#117458442
#105990533
#684045