Finite Group Databasebeta

← #14290366

Subgroups — #14290366

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
1C5×#5563C211yesmaximal, characteristic
2#11751108C211yesmaximal, characteristic, complemented
3#11747077C211yesmaximal, characteristic, complemented
4#11746929C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10602722—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#938—21no—
12C5×#930—21no—
13C5×#926—21no—
14C5×#892—21no—
15C5×#885—22no—
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6659—21no—
19#91116—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90975—21no—
25#90973—22no—
26#68183—51nomaximal, Hall
27C5×#555—31no—
28#65370—31no—
29#65308—31no—
30#65296—31no—
31#64766—31no—
32D4⋊#168—31no—
33D4⋊#168D311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C5×#67—22no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6D412yes—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C5×#217—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C4×C5×Dic3—22no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6659—42no—
57#5563D511yescharacteristic
58#5007—51no—
59#4841—51no—
60#4681—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C5×#124—62no—
66C5×#121—61no—
67C5×#121—61no—
68C4×C5×D4—31no—
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—61no—
71C5×#117—61no—
72C2×#687—61no—
73#4015—31no—
74#3967—62no—
75#3964—61no—
76#3942—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1646—151noSylow
82C23×C3×C5—21no—
83C22×C5×D3—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—
95C5×#67—82no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—22no—
98C5×D12—21no—
99C5×D12—21no—
100C4×C5×D3—41no—
101C4×C5×D3—41no—
102C5×Dic6—42no—
103C3⋊#168—41no—
104C3×#168—41no—
105C3×#168—41no—
106C3×C4×D4C2×D511yescharacteristic
107#938—21no—
108#930—21no—
109#926—21no—
110C2×#204—101no—
111#892—21no—
112#885—22no—
113C4×D12C2×D511yescharacteristic
114#869—51no—
115#869C2×D511yescharacteristic
116C3×C4⋊C8—51no—
117C3×C4×C8—51no—
118#832—101no—
119#816—102no—
120#816—101no—
121#807—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—32no—
124C2×C5×D4—31no—
125C2×C5×D4—62no—
126C2×C5×D4D1211yescharacteristic
127C22×C4×C5—21no—
128C22×C4×C5—61no—
129C2×Dic10—61no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4D1211yescharacteristic
134C5×C22⋊C4—21no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C5×C22⋊C4—61no—
138C42×C5—62no—
139C42×C5C22×D311yescharacteristic
140#687—122no—
141C4⋊Dic5—61no—
142C4⋊Dic5—61no—
143C2×#168—21no—
144C2×#168—21no—
145C2×#168—61no—
146#555—31no—
147#487—151no—
148#474—151no—
149#461—151no—
150#333—151no—
151D4⋊C8—51no—
152D4⋊C8—151no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—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—
167C5×Dic3—41no—
168C5×Dic3—42no—
169C2×C3×D4C22⋊D511yescharacteristic
170C22×C3×C4—21no—
171C2×#67—22no—
172C2×D12C22⋊D511yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6—101no—
175C2×Dic6C22⋊D512yes—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4C22⋊D511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C42C22×D511yescharacteristic
181#217—22no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4⋊Dic3C22⋊D511yescharacteristic
189C4×Dic3—22no—
190C2×C3⋊C8—101no—
191#204—202no—
192C23×C5—21no—
193C23×C5—61no—
194C5×Q8—122no—
195C5×D4—21no—
196C5×D4—21no—
197C5×D4—61no—
198C5×D4—61no—
199C5×D4—242no—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—61no—
204C2×C4×C5—62no—
205C2×C4×C5—121no—
206C2×C4×C5—121no—
207C2×C4×C5C2×D1211yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×Dic5—121no—
211Dic10—121no—
212Dic10—121no—
213#168—41no—
214#168—41no—
215#168—121no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—151no—
219#124—62no—
220#121—61no—
221#121—61no—
222C4×D4—31no—
223C4×D4D3×D511yescharacteristic
224#117—61no—
225#117—61no—
226#107—301no—
227C4⋊C8—51no—
228C4⋊C8—151no—
229#103—301no—
230#103—302no—
231#102—301no—
232C4×C8—51no—
233C2×C3×C5—81no—
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45211yescharacteristic
236C2×C3×C5#45511yescharacteristic
237C5×D3—81no—
238C23×C3—21no—
239C22×D3—21no—
240C3×D4—21no—
241C3×D4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—82no—
249C2×Dic3—21no—
250C2×Dic3—22no—
251C2×Dic3—201no—
252D12—21no—
253D12—21no—
254C4×D3—41no—
255C4×D3—41no—
256Dic6—42no—
257Dic6—201no—
258Dic6—201no—
259C3×C8—201no—
260C3×C8—201no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—121no—
266C22×C5—121no—
267C22×C5—121no—
268C22×C5#88211yescharacteristic
269C4×C5—21no—
270C4×C5—41no—
271C4×C5—121no—
272C4×C5—122no—
273C4×C5#90411yescharacteristic
274C4×C5#90911yescharacteristic
275C4×C5#91111yescharacteristic
276C4×C5#91611yescharacteristic
277Dic5—241no—
278C2×Q8—32no—
279C2×Q8—301no—
280C2×D4—31no—
281C2×D4—62no—
282C2×D4#120311yescharacteristic
283C22×C4—21no—
284C22×C4—61no—
285SD16—602no—
286C2×C8—101no—
287C2×C8—101no—
288C2×C8—301no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4#120311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—61no—
299C42—62no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3#409911yescharacteristic
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C3×C4—21no—
310C3×C4—41no—
311C3×C4#409511yescharacteristic
312C3×C4#409611yescharacteristic
313C3×C4#409611yescharacteristic
314C3×C4#409711yescharacteristic
315Dic3—41no—
316Dic3—42no—
317Dic3—401no—
318C2×C5—81no—
319C2×C5—241no—
320C2×C5#473311yescharacteristic
321C2×C5#478111yescharacteristic
322C2×C5#482511yescharacteristic
323C23—21no—
324C23—61no—
325Q8—122no—
326Q8—601no—
327Q8—601no—
328D4—21no—
329D4—21no—
330D4—61no—
331D4—61no—
332D4—242no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—62no—
338C2×C4—121no—
339C2×C4—121no—
340C2×C4—601no—
341C2×C4C2×#120311yescharacteristic
342C2×C4D3×C22⋊D511yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C8—201no—
345C8—201no—
346C8—601no—
347C2×C3—81no—
348C2×C3#6552711yescharacteristic
349C2×C3#6552811yescharacteristic
350C2×C3#6553111yescharacteristic
351D3—81no—
352C5#6818311yescharacteristic, complemented, Sylow
353C22—41no—
354C22—41no—
355C22—41no—
356C22—121no—
357C22—121no—
358C22—121no—
359C22#9157011yescharacteristic
360C4—21no—
361C4—41no—
362C4—121no—
363C4—122no—
364C4—1201no—
365C4#9130311yescharacteristic
366C4#9132211yescharacteristic
367C4#9148011yescharacteristic
368C4#9149511yescharacteristic
369C3#1060272211yescharacteristic, complemented, Sylow
370C2—81no—
371C2—241no—
372C2#1174836111yescharacteristic
373C2#1174903611yescharacteristic
374C2#1174946611yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5563C2
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. #11747077C2semidirect
4. #11746929C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745862C2semidirect
7. #11745837C2semidirect
33. D4⋊#168D3semidirect
301. C3×C5#1646semidirect
352. C5#68183semidirect
369. C3#10602722semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
#117511082
#117470772
#117469292
C3×D4⋊#1682
#117458622
#117458372
#106027223
#681835