Finite Group Databasebeta

← #14290367

Subgroups — #14290367

Order 1920.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756322C211yesmaximal, characteristic
2C3×#65296C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic, complemented
4#11746921C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598976—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91827—21no—
11#91819—21no—
12#91815—21no—
13#91781—21no—
14#91774—22no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6658—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90974—22no—
25#90971—21no—
26#71109—51nomaximal, Hall
27#65897—31no—
28#65296D311yescharacteristic, complemented
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×#1220—22no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30D412yes—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6719—22no—
45#6714—22no—
46#6714—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50C4×Dic15—22no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6658—42no—
57#5563—51no—
58C3×#474—51no—
59#5093—51no—
60#5083—51no—
61D4⋊(C3⋊C8)D511yescharacteristic, complemented
62#4483—51no—
63#4481—51no—
64C4×C5×D4C2×D311yescharacteristic
65#4084—61no—
66#4076—61no—
67#4072—61no—
68C2×#677—61no—
69#4038—61no—
70#4031—62no—
71C4×D20—31no—
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3964—21no—
77#3948—62no—
78#3948—61no—
79#3939—21no—
80C4⋊#168C2×D311yescharacteristic
81#1646—151noSylow
82C23×C3×C5—21no—
83C22×D15—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
92#1220—82no—
93C2×Dic15—21no—
94C2×Dic15—22no—
95D60—21no—
96D60—21no—
97C4×D15—41no—
98C4×D15—41no—
99Dic30—42no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×C4×D4C2×D511yescharacteristic
108C2×#215—101no—
109#938—101no—
110#930—101no—
111#926—101no—
112#892—101no—
113#885—102no—
114C4×D12—51no—
115#869—51no—
116C3×#107—101no—
117C3×C4⋊C8—51no—
118C3×#102—101no—
119#835—101no—
120#810—102no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C2×C22⋊D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×Dic10—21no—
129C2×Dic10—32no—
130C2×C5×C8—61no—
131C2×C5×C8—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—62no—
136#685—62no—
137#685—61no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—31no—
141C4⋊Dic5—61no—
142C4⋊Dic5—61no—
143C4×Dic5—62no—
144C2×#168—21no—
145#677—122no—
146#555—151no—
147#487—151no—
148#474—51no—
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×D15—41no—
158C2×D15—41no—
159C2×D15—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—41no—
167Dic15—42no—
168C3×Dic5—81no—
169C2×C3×Q8—101no—
170C2×C3×D4D2011yescharacteristic
171C22×C3×C4—21no—
172C2×#67—102no—
173C2×D12—51no—
174C2×C4×D3—101no—
175C2×Dic6—52no—
176C2×C3×C8—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4D2011yescharacteristic
180C3×C22⋊C4—21no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183#215—202no—
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3—101no—
188C4⋊Dic3—101no—
189C4×Dic3—102no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C23×C5—21no—
193C22×D5—61no—
194C5×D4—21no—
195C5×D4—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C22⋊D5—242no—
203C2×Dic5—41no—
204C2×Dic5—61no—
205C2×Dic5—62no—
206D20—61no—
207D20—61no—
208C4×D5—121no—
209C4×D5—121no—
210Dic10—41no—
211Dic10—41no—
212Dic10—122no—
213C5×C8—121no—
214C5×C8—121no—
215#168—41no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—151no—
219#124—302no—
220#121—301no—
221#121—301no—
222C4×D4—151no—
223C4×D4D3×D511yescharacteristic
224#117—301no—
225#117—301no—
226#107—101no—
227C4⋊C8—31no—
228C4⋊C8—51no—
229#103—302no—
230#103—301no—
231#102—101no—
232C4×C8—31no—
233C2×C3×C5—81no—
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45211yescharacteristic
236C2×C3×C5#45511yescharacteristic
237D15—81no—
238C23×C3—21no—
239C22×D3—101no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×D4—21no—
243C3×D4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—201no—
248C2×C3×C4C2×D2011yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251#67—402no—
252C2×Dic3—101no—
253C2×Dic3—102no—
254D12—101no—
255D12—101no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—202no—
259C3×C8—201no—
260C3⋊C8—41no—
261C3⋊C8—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5#93711yescharacteristic
266C2×D5—121no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—41no—
271C4×C5#91111yescharacteristic
272C4×C5#91211yescharacteristic
273C4×C5#94211yescharacteristic
274C4×C5#95011yescharacteristic
275Dic5—81no—
276Dic5—122no—
277Dic5—121no—
278C2×Q8—101no—
279C2×Q8—152no—
280C2×D4—151no—
281C2×D4—302no—
282C2×D4#120211yescharacteristic
283C22×C4—21no—
284C22×C4—301no—
285SD16—602no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—101no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4—151no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4#120211yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—302no—
297C22⋊C4—302no—
298C22⋊C4—301no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3#402811yescharacteristic
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—401no—
312C3×C4#405011yescharacteristic
313C3×C4#405511yescharacteristic
314C3×C4#405711yescharacteristic
315C3×C4#406211yescharacteristic
316Dic3—202no—
317Dic3—201no—
318C2×C5—81no—
319C2×C5#504711yescharacteristic
320C2×C5#515811yescharacteristic
321C2×C5#520211yescharacteristic
322D5—241no—
323C23—21no—
324C23—301no—
325Q8—201no—
326Q8—201no—
327Q8—602no—
328D4—21no—
329D4—21no—
330D4—301no—
331D4—301no—
332D4—1202no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—201no—
337C2×C4—301no—
338C2×C4—302no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4C2×#120211yescharacteristic
342C2×C4#679011yescharacteristic
343C2×C4#679011yescharacteristic
344C8—121no—
345C8—121no—
346C8—201no—
347C2×C3—81no—
348C2×C3#6502211yescharacteristic
349C2×C3#6507011yescharacteristic
350C2×C3#6511411yescharacteristic
351D3—401no—
352C5#7110911yescharacteristic, complemented, Sylow
353C22—41no—
354C22—41no—
355C22—41no—
356C22—601no—
357C22—601no—
358C22—601no—
359C22#9157211yescharacteristic
360C4—21no—
361C4—41no—
362C4—401no—
363C4—602no—
364C4—601no—
365C4#9131111yescharacteristic
366C4#9131511yescharacteristic
367C4#9148211yescharacteristic
368C4#9149711yescharacteristic
369C3#1059897611yescharacteristic, complemented, Sylow
370C2—81no—
371C2—1201no—
372C2#1174855211yescharacteristic
373C2#1174904211yescharacteristic
374C2#1174946711yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756322C2
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. C3×#65296C2semidirect
3. #11747085C2semidirect
4. #11746921C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745863C2semidirect
7. #11745838C2semidirect
28. #65296D3semidirect
61. D4⋊(C3⋊C8)D5semidirect
301. C3×C5#1646semidirect
352. C5#71109semidirect
369. C3#10598976semidirect

Maximal subgroups

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

subgroupindex
#117563222
C3×#652962
#117470852
#117469212
C5×D4⋊(C3⋊C8)2
#117458632
#117458382
#105989763
#711095