Finite Group Databasebeta

← #14289523

Subgroups — #14289523

Order 1920.

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

normal subgroups only

This group has 428 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#11752648C211yesmaximal, characteristic
2C3×#65131C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic, complemented
4#11746917C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10599285—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91434—21no—
14#91421—22no—
15D5×C4⋊Dic3—21no—
16#91384—21no—
17#91360—21no—
18C2×#6661—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3953—21no—
23C3×#3949—21no—
24#90990—21no—
25#90974—21no—
26#71144—51nomaximal, Hall
27#66064—31no—
28#65381—31no—
29#65139—31no—
30#65131D311yescharacteristic
31C5×#333—31no—
32#64704—31no—
33#64703—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6D412yes—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—21no—
39C2×D5×Dic3—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#685—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53Dic3⋊Dic5—22no—
54#6668—22no—
55#6665—22no—
56#6661—44no—
57#5543—51no—
58C3×#476—51no—
59#5092—51no—
60#5091—51no—
61D4⋊(C3⋊C8)—51no—
62#4484—51no—
63#4481D511yescharacteristic, complemented
64C5×C4⋊Q8—31no—
65#4092—62no—
66C2×#689—62no—
67#4043—61no—
68#4039—61no—
69D5×C4⋊C4—61no—
70#4036—61no—
71C4×D20C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3953—21no—
77#3950—61no—
78#3949—21no—
79#3948—61no—
80C4×#168—31no—
81#1632—151noSylow
82C22×C3×D5—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C2×C5×Dic3—22no—
91C5×Dic6—42no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—41no—
94C3×D20—21no—
95C3×D20Q1612yescomplemented
96C3×C4×D5—41no—
97C3×C4×D5—41no—
98C3×Dic10—42no—
99D5×Dic3—82no—
100C3×C5×C8—41no—
101C3⋊#168—22no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104C3×C4×D4—51no—
105C2×#216—102no—
106D4×Dic3—101no—
107C2×C4⋊Dic3—101no—
108#924—101no—
109#890—101no—
110#878—102no—
111#869C2×D511yescharacteristic
112C4×Dic6—51no—
113C3×#106—101no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×#102—101no—
116#810—101no—
117#807—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4×C3⋊C8—51no—
120C2×C5×Q8—32no—
121C2×D20#6711yescharacteristic
122C2×C4×D5—21no—
123C2×C4×D5—62no—
124C2×Dic10—21no—
125C2×Dic10—31no—
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131#689—124no—
132#685—21no—
133#685—62no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—31no—
137C4⋊Dic5—62no—
138C4⋊Dic5#6711yescharacteristic
139#683—62no—
140#683—61no—
141C4×Dic5—61no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—51no—
147#333—31no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160Dic15—41no—
161C3×Dic5—41no—
162C3×Dic5—81no—
163C5×Dic3—42no—
164C2×C3×Q8—101no—
165C2×C3×D4—51no—
166C22×C3×C4—101no—
167C22×Dic3—102no—
168C2×Dic6—51no—
169C2×Dic6D2012yes—
170C2×C3×C8—21no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C22⋊C4—101no—
175C3×C42C22×D511yescharacteristic
176#217—102no—
177#216—204no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182Dic3⋊C4—102no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C22×D5—21no—
188C5×Q8—122no—
189C2×C4×C5—62no—
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—41no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197D20—21no—
198D20#21612yescomplemented
199C4×D5—41no—
200C4×D5—41no—
201C4×D5—242no—
202Dic10—42no—
203Dic10—61no—
204Dic10—61no—
205C5×C8—41no—
206C5×C8—121no—
207#168—62no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—151no—
215C4×D4—51no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—101no—
220C4⋊C8—31no—
221C4⋊C8D3×D511yescharacteristic
222#103—301no—
223#102—101no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—202no—
231C3×D4—52no—
232C3×D4—101no—
233C2×C3×C4—101no—
234C2×C3×C4—201no—
235C2×C3×C4—201no—
236C2×C3×C4—201no—
237C2×C3×C4C2×D2011yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243C2×Dic3—402no—
244Dic6—42no—
245Dic6—101no—
246Dic6—101no—
247C3×C8—41no—
248C3⋊C8—41no—
249C3⋊C8—102no—
250C22×C5#93711yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#91511yescharacteristic
257C4×C5#91611yescharacteristic
258C4×C5C2×#21611yescharacteristic
259C4×C5#95111yescharacteristic
260Dic5—41no—
261Dic5—81no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—32no—
265C2×Q8—101no—
266C2×Q8—151no—
267C2×D4—51no—
268C22×C4—101no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—301no—
274C4⋊C4—51no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—151no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C22⋊C4—101no—
284C22⋊C4—302no—
285C42—301no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—102no—
289C22×C3—201no—
290C22×C3—201no—
291C22×C3#402811yescharacteristic
292C3×C4—21no—
293C3×C4—201no—
294C3×C4—401no—
295C3×C4#406111yescharacteristic
296C3×C4#406211yescharacteristic
297C3×C4D5×Q1611yescharacteristic
298C3×C4#406411yescharacteristic
299Dic3—42no—
300Dic3—201no—
301Dic3—201no—
302C2×C5#505011yescharacteristic
303C2×C5#517311yescharacteristic
304C2×C5#519811yescharacteristic
305D5—42no—
306C23—101no—
307Q8—122no—
308Q8—202no—
309Q8—301no—
310Q8—301no—
311D4—52no—
312D4—101no—
313C2×C4—62no—
314C2×C4—101no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4—1202no—
321C2×C4D3×D2011yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—41no—
325C8—121no—
326C8—302no—
327C2×C3—202no—
328C2×C3#6503611yescharacteristic
329C2×C3#6509711yescharacteristic
330C2×C3#6509911yescharacteristic
331C5#7114411yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9147411yescharacteristic
336C4—21no—
337C4—122no—
338C4—201no—
339C4—401no—
340C4—601no—
341C4—601no—
342C4#9127611yescharacteristic
343C4#9127811yescharacteristic
344C4#9148411yescharacteristic
345C4D5×#21611yescharacteristic
346C3#1059928511yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174749211yescharacteristic
349C2#1174814811yescharacteristic
350C2#1174824311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1632
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
3. #11747103C2semidirect
4. #11746917C2semidirect
5. #11746305C2semidirect
6. C5×#4481C2semidirect
63. #4481D5semidirect
95. C3×D20Q16semidirect
198. D20#216semidirect
287. C3×C5#1632semidirect
331. C5#71144semidirect
346. C3#10599285semidirect

Maximal subgroups

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

subgroupindex
#117526482
C3×#651312
#117471032
#117469172
#117463052
C5×#44812
#117458342
#105992853
#711445