Finite Group Databasebeta

← #14290368

Subgroups — #14290368

Order 1920.

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

normal subgroups only

This group has 424 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×#65897C211yesmaximal, characteristic
2#11751108C211yesmaximal, characteristic, complemented
3#11747062C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10598976—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4084—21no—
12C3×#4076—21no—
13C3×#4072—21no—
14C3×#4038—21no—
15C3×#4031—22no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6657—21no—
19#91116—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90974—21no—
25#90971—22no—
26#71929—51nomaximal, Hall
27#65897D311yescharacteristic
28#65296—31no—
29#65130—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C3×C22⋊D5—22no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10D412yes—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8—21no—
49C3×C22⋊Dic5—22no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4×Dic5—22no—
56#6657—42no—
57C3×#555—51no—
58#5079—51no—
59#5019—51no—
60#5007—51no—
61#4546—51no—
62D4⋊(C3⋊C8)—51no—
63D4⋊(C3⋊C8)D511yescharacteristic, complemented
64C4×C5×D4C2×D311yescharacteristic
65#4084—21no—
66#4076—21no—
67#4072—21no—
68C2×#677—61no—
69#4038—21no—
70#4031—22no—
71C4×D20C2×D311yescharacteristic
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3964—61no—
77#3948—62no—
78#3948—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1646—151noSylow
82C23×C3×C5—21no—
83C22×C3×D5—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—41no—
93Dic30—41no—
94Dic30—41no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—22no—
98C3×D20—21no—
99C3×D20—21no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102C3×Dic10—42no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×#124—102no—
108C3×#121—101no—
109C3×#121—101no—
110C3×C4×D4—51no—
111C3×C4×D4C2×D511yescharacteristic
112C3×#117—101no—
113C3×#117—101no—
114C2×#214—101no—
115#869—51no—
116#835—102no—
117#832—101no—
118#810—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C2×C22⋊D5—22no—
126C2×D20#6711yescharacteristic
127C2×C4×D5—21no—
128C2×Dic10—61no—
129C2×Dic10#6712yes—
130C2×C5×C8—61no—
131C2×C5×C8—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—22no—
136#685—22no—
137#685—21no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5#6711yescharacteristic
143C4×Dic5—22no—
144C2×#168—61no—
145#677—122no—
146#555—51no—
147#487—151no—
148#474—151no—
149#461—151no—
150#333—151no—
151D4⋊C8—31no—
152D4⋊C8—151no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5#12011yescharacteristic
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166Dic15—81no—
167C3×Dic5—41no—
168C3×Dic5—42no—
169C2×C3×Q8—52no—
170C2×C3×D4—51no—
171C2×C3×D4—102no—
172C2×C3×D4D2011yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—101no—
175C2×Dic6—101no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4D2011yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—102no—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—101no—
184C3×C42—102no—
185C3×C42C22×D511yescharacteristic
186#214—202no—
187C4⋊Dic3—101no—
188C4⋊Dic3—101no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C22×D5—21no—
194C5×D4—21no—
195C5×D4—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5C2×#6711yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C22⋊D5—82no—
203C2×Dic5—21no—
204C2×Dic5—22no—
205C2×Dic5—121no—
206D20—21no—
207D20—21no—
208C4×D5—41no—
209C4×D5—41no—
210Dic10—42no—
211Dic10—121no—
212Dic10—121no—
213C5×C8—121no—
214C5×C8—121no—
215#168—121no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—151no—
219#124—102no—
220#121—101no—
221#121—101no—
222C4×D4—51no—
223C4×D4D3×D511yescharacteristic
224#117—101no—
225#117—101no—
226#107—301no—
227C4⋊C8—31no—
228C4⋊C8—151no—
229#103—301no—
230#103—302no—
231#102—301no—
232C4×C8—31no—
233C2×C3×C5—81no—
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45211yescharacteristic
236C2×C3×C5#45511yescharacteristic
237C3×D5—81no—
238C23×C3—21no—
239C23×C3—101no—
240C3×Q8—202no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—101no—
244C3×D4—101no—
245C3×D4—402no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—101no—
250C2×C3×C4—102no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×Dic3—201no—
257Dic6—201no—
258Dic6—201no—
259C3⋊C8—41no—
260C3⋊C8—41no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5#95311yescharacteristic
266C2×D5—41no—
267C2×D5—41no—
268C2×D5—41no—
269C4×C5—21no—
270C4×C5—41no—
271C4×C5#94911yescharacteristic
272C4×C5#95011yescharacteristic
273C4×C5#95011yescharacteristic
274C4×C5#95111yescharacteristic
275Dic5—41no—
276Dic5—42no—
277Dic5—241no—
278C2×Q8—52no—
279C2×Q8—301no—
280C2×D4—51no—
281C2×D4—102no—
282C2×D4#120211yescharacteristic
283C22×C4—21no—
284C22×C4—101no—
285SD16—602no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—301no—
289C4⋊C4—51no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4#120211yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—102no—
297C22⋊C4—102no—
298C22⋊C4—101no—
299C42—102no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—201no—
306C22×C3—201no—
307C22×C3—201no—
308C22×C3#402811yescharacteristic
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—202no—
312C3×C4—201no—
313C3×C4#405011yescharacteristic
314C3×C4#405511yescharacteristic
315C3×C4#405711yescharacteristic
316C3×C4#406211yescharacteristic
317Dic3—401no—
318C2×C5—81no—
319C2×C5#523811yescharacteristic
320C2×C5#523911yescharacteristic
321C2×C5#524211yescharacteristic
322D5—81no—
323C23—21no—
324C23—101no—
325Q8—202no—
326Q8—601no—
327Q8—601no—
328D4—21no—
329D4—21no—
330D4—101no—
331D4—101no—
332D4—402no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—101no—
337C2×C4—102no—
338C2×C4—201no—
339C2×C4—201no—
340C2×C4—601no—
341C2×C4C2×#120211yescharacteristic
342C2×C4D5×#6711yescharacteristic
343C2×C4D5×#6711yescharacteristic
344C8—121no—
345C8—121no—
346C8—601no—
347C2×C3—81no—
348C2×C3—401no—
349C2×C3#6502211yescharacteristic
350C2×C3#6507011yescharacteristic
351C2×C3#6511411yescharacteristic
352C5#7192911yescharacteristic, complemented, Sylow
353C22—41no—
354C22—41no—
355C22—41no—
356C22—201no—
357C22—201no—
358C22—201no—
359C22#9156411yescharacteristic
360C4—21no—
361C4—41no—
362C4—202no—
363C4—201no—
364C4—1201no—
365C4#9131111yescharacteristic
366C4#9131311yescharacteristic
367C4#9147811yescharacteristic
368C4#9149211yescharacteristic
369C3#1059897611yescharacteristic, complemented, Sylow
370C2—81no—
371C2—401no—
372C2#1174853111yescharacteristic
373C2#1174902611yescharacteristic
374C2#1174946311yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65897C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1646
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11751108C2semidirect
3. #11747062C2semidirect
4. #11746920C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745861C2semidirect
7. #11745835C2semidirect
63. D4⋊(C3⋊C8)D5semidirect
301. C3×C5#1646semidirect
352. C5#71929semidirect
369. C3#10598976semidirect

Maximal subgroups

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

subgroupindex
C3×#658972
#117511082
#117470622
#117469202
C5×D4⋊(C3⋊C8)2
#117458612
#117458352
#105989763
#719295