Finite Group Databasebeta

← #14290870

Subgroups — #14290870

Order 1920.

480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5555C211yesmaximal, characteristic
2#11751108C211yesmaximal, characteristic, complemented
3#11747077C211yesmaximal, characteristic, complemented
4#11746941C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10602706—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91758C2211yescharacteristic
12C5×#930—21no—
13C2×C5×C4⋊Dic3—21no—
14C5×#897—21no—
15C5×#886—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#90985—22no—
25#90975—21no—
26#68185—51nomaximal, Hall
27C5×#547—31no—
28#65368—31no—
29#65308—31no—
30#65296—31no—
31#64767—31no—
32D4⋊#168—31no—
33D4⋊#168D311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C5×#67—22no—
38C22×C5×Dic3—22no—
39C5×#237—42no—
40C5×#237—42no—
41C2×C5×D12D411yescharacteristic
42C2×C4×C5×D3—21no—
43C2×C5×Dic6—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—22no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3—22no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D412yes—
55C5×C4⋊Dic3D411yescharacteristic
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58#6659—42no—
59#5555D511yescharacteristic
60#5007—51no—
61#4841—51no—
62#4680—51no—
63C3×D4⋊C8—51no—
64#4486—51no—
65#4459—51no—
66C2×C5×#41—61no—
67C5×C4⋊Q8—31no—
68C5×#123—62no—
69C5×C22⋊Q8—61no—
70C5×#121—61no—
71C4×C5×D4—31no—
72C4×C5×D4C2×D311yescharacteristic
73C2×C5×C4⋊C4—61no—
74C2×#687—61no—
75#4015—31no—
76#3964—61no—
77#3942—61no—
78#3940—62no—
79#3939—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168C2×D311yescharacteristic
83#1654—151noSylow
84C23×C3×C5—21no—
85C22×C5×D3—21no—
86C3×C5×D4—21no—
87C3×C5×D4SD1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—41no—
95Dic30—41no—
96Dic30—41no—
97C5×#67—44no—
98C2×C5×Dic3—22no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—44no—
101C5×D12—21no—
102C5×D12—21no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C5×Dic6—41no—
106C5×Dic6—41no—
107C3⋊#168—41no—
108C3×#168—22no—
109C3×#168—41no—
110C2×#237—21no—
111C3×C4×D4C2×D511yescharacteristic
112#930—21no—
113C2×C4⋊Dic3—21no—
114C2×#204—101no—
115#897—21no—
116#886—22no—
117C4×D12C2×D511yescharacteristic
118#869—51no—
119#869C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4×C8—51no—
122#832—101no—
123#817—102no—
124#816—101no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C5×#41—122no—
128C5×#41—122no—
129C2×C5×Q8—61no—
130C2×C5×D4—31no—
131C2×C5×D4—62no—
132C2×C5×D4D1211yescharacteristic
133C22×C4×C5—21no—
134C22×C4×C5—62no—
135C22×C4×C5—61no—
136C2×Dic10—61no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—32no—
139C5×C4⋊C4—62no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4D1211yescharacteristic
142C5×C22⋊C4—21no—
143C5×C22⋊C4—62no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#687—122no—
147C4⋊Dic5—61no—
148C4⋊Dic5—61no—
149C2×#168—21no—
150C2×#168—21no—
151C2×#168—61no—
152#547—31no—
153#498—151no—
154#474—151no—
155#461—151no—
156#332—151no—
157D4⋊C8—51no—
158D4⋊C8—151no—
159C22×C3×C5—22no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C3×C4×C5—21no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172Dic15—81no—
173C5×Dic3—42no—
174C5×Dic3—41no—
175C2×C3×D4C22⋊D511yescharacteristic
176C22×C3×C4—21no—
177C2×#67—22no—
178C22×Dic3—22no—
179#237—42no—
180#237—42no—
181C2×D12C22⋊D511yescharacteristic
182C2×C4×D3—21no—
183C2×Dic6—21no—
184C2×Dic6—101no—
185C2×C3×C8—101no—
186C2×C3×C8—101no—
187C3×C4⋊C4C22⋊D511yescharacteristic
188C3×C22⋊C4—21no—
189C3×C42C22×D511yescharacteristic
190(C2×D3)⋊C4—22no—
191(C2×D3)⋊C4—21no—
192C4⋊Dic3—22no—
193C4⋊Dic3—21no—
194C4⋊Dic3—101no—
195C4⋊Dic3—101no—
196C4⋊Dic3C22⋊D511yescharacteristic
197C4⋊Dic3C22⋊D512yes—
198C2×C3⋊C8—101no—
199#204—202no—
200C23×C5—21no—
201C23×C5—61no—
202C5×Q8—121no—
203C5×Q8—121no—
204C5×D4—21no—
205C5×D4—61no—
206C5×D4—61no—
207C5×D4—124no—
208C5×D4#20412yescomplemented
209C2×C4×C5—21no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—61no—
213C2×C4×C5—62no—
214C2×C4×C5—124no—
215C2×C4×C5—121no—
216C2×C4×C5—121no—
217C2×C4×C5C2×D1211yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×Dic5—121no—
221Dic10—121no—
222Dic10—121no—
223#168—22no—
224#168—41no—
225#168—121no—
226C2×#41—61no—
227C2×SD16—301no—
228C4⋊Q8—31no—
229C4⋊Q8—151no—
230#123—62no—
231C22⋊Q8—61no—
232#121—61no—
233C4×D4—31no—
234C4×D4D3×D511yescharacteristic
235C2×C4⋊C4—61no—
236#107—301no—
237#106—302no—
238C4⋊C8—51no—
239C4⋊C8—151no—
240#103—301no—
241#102—301no—
242C4×C8—51no—
243C2×C3×C5—42no—
244C2×C3×C5#44911yescharacteristic
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45611yescharacteristic
247C5×D3—81no—
248C23×C3—21no—
249C22×D3—21no—
250C3×D4—21no—
251C3×D4#68712yescomplemented
252C2×C3×C4—21no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C2×C3×C4C2×C22⋊D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258#67—44no—
259C2×Dic3—22no—
260C2×Dic3—21no—
261C2×Dic3—44no—
262C2×Dic3—201no—
263D12—21no—
264D12—21no—
265C4×D3—41no—
266C4×D3—41no—
267Dic6—41no—
268Dic6—41no—
269Dic6—201no—
270Dic6—201no—
271C3×C8—102no—
272C3×C8—201no—
273C3⋊C8—201no—
274C22×C5—22no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5—121no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5#88211yescharacteristic
281C4×C5—21no—
282C4×C5—41no—
283C4×C5—121no—
284C4×C5—122no—
285C4×C5C2×#20411yescharacteristic
286C4×C5#90811yescharacteristic
287C4×C5#91111yescharacteristic
288C4×C5#91611yescharacteristic
289Dic5—241no—
290#41—122no—
291#41—122no—
292C2×Q8—61no—
293C2×Q8—301no—
294C2×D4—31no—
295C2×D4—62no—
296C2×D4#120311yescharacteristic
297C22×C4—21no—
298C22×C4—62no—
299C22×C4—61no—
300SD16—602no—
301C2×C8—101no—
302C2×C8—101no—
303C2×C8—301no—
304C4⋊C4—31no—
305C4⋊C4—32no—
306C4⋊C4—62no—
307C4⋊C4—61no—
308C4⋊C4—301no—
309C4⋊C4—301no—
310C4⋊C4#120311yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—62no—
313C22⋊C4—61no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3#409911yescharacteristic
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4#407811yescharacteristic
326C3×C4C2×#68711yescharacteristic
327C3×C4#409511yescharacteristic
328C3×C4#409611yescharacteristic
329Dic3—42no—
330Dic3—41no—
331Dic3—401no—
332C2×C5—42no—
333C2×C5—241no—
334C2×C5#473111yescharacteristic
335C2×C5#478111yescharacteristic
336C2×C5#482611yescharacteristic
337C23—21no—
338C23—61no—
339Q8—121no—
340Q8—121no—
341Q8—601no—
342Q8—601no—
343D4—21no—
344D4—61no—
345D4—61no—
346D4—124no—
347D4#665912yescomplemented
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—61no—
352C2×C4—62no—
353C2×C4—124no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4—601no—
357C2×C4C2×#120311yescharacteristic
358C2×C4D3×C22⋊D511yescharacteristic
359C2×C4D3×C22⋊D511yescharacteristic
360C8—102no—
361C8—201no—
362C8—601no—
363C2×C3—42no—
364C2×C3#6550711yescharacteristic
365C2×C3#6552711yescharacteristic
366C2×C3#6553511yescharacteristic
367D3—81no—
368C5#6818511yescharacteristic, complemented, Sylow
369C22—22no—
370C22—41no—
371C22—41no—
372C22—121no—
373C22—121no—
374C22—121no—
375C22#9157011yescharacteristic
376C4—21no—
377C4—41no—
378C4—121no—
379C4—122no—
380C4—1201no—
381C4#9130411yescharacteristic
382C4C2×#665911yescharacteristic
383C4#9148011yescharacteristic
384C4#9149511yescharacteristic
385C3#1060270611yescharacteristic, complemented, Sylow
386C2—42no—
387C2—241no—
388C2#1174854311yescharacteristic
389C2#1174903611yescharacteristic
390C2#1174942311yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5555C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1654
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. #11746941C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745857C2semidirect
7. #11745837C2semidirect
33. D4⋊#168D3semidirect
87. C3×C5×D4SD16semidirect
208. C5×D4#204semidirect
251. C3×D4#687semidirect
315. C3×C5#1654semidirect
347. D4#6659semidirect
368. C5#68185semidirect
385. C3#10602706semidirect

Maximal subgroups

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

subgroupindex
C5×#55552
#117511082
#117470772
#117469412
C3×D4⋊#1682
#117458572
#117458372
#106027063
#681855