Finite Group Databasebeta

← #14289222

Subgroups — #14289222

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D4×Q8C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11751128C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602707—31nomaximal, Hall
9C22×C3×C5×Q8—21no—
10C3×C5×C4⋊Q8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×C22⋊Q8—21no—
13C3×C5×C22⋊Q8—22no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6717—21no—
18C2×#6715—21no—
19#91763C2211yescharacteristic
20#91093—22no—
21#91093—21no—
22#91093—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71914—51nomaximal, Hall
27C5×D4×Q8D311yescharacteristic, complemented
28#65377—31no—
29#65316—31no—
30#65304—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—42no—
37C2×C3×C5×Q8—42no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C3×C5×C4⋊C4—22no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D412yes—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5—21no—
54C3×C42×C5C2311yescharacteristic
55#6717—42no—
56#6715—42no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C3×D4×Q8D511yescharacteristic, complemented
61#5088—51no—
62#5027—51no—
63#5015—51no—
64#4547—51no—
65#4535—51no—
66D4⋊(C3⋊C8)—51no—
67C22×C5×Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8C2×D311yescharacteristic
70C5×C22⋊Q8—21no—
71C5×C22⋊Q8—22no—
72C4×C5×Q8C2×D311yescharacteristic
73C4×C5×D4—21no—
74C4×C5×D4C2×D311yescharacteristic
75C2×#688—61no—
76C2×#686—61no—
77#4020—31no—
78#3941—61no—
79#3941—61no—
80#3941—62no—
81C4⋊#168—31no—
82C4⋊#168—31no—
83C4×#168—31no—
84#1627—151noSylow
85C23×C3×C5—21no—
86C22×D15—41no—
87C3×C5×Q8—21no—
88C3×C5×Q8—44no—
89C3×C5×Q8—41no—
90C3×C5×Q8—41no—
91C3×C5×Q8D812yescomplemented
92C3×C5×D4—21no—
93C3×C5×D4SD1612yescomplemented
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—44no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104D60—42no—
105D60—41no—
106D60—41no—
107D60—41no—
108D60—41no—
109C3⋊#168—41no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C22×C3×Q8—21no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8C2×D511yescharacteristic
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—22no—
117C3×C4×Q8C2×D511yescharacteristic
118C3×C4×D4—21no—
119C3×C4×D4C2×D511yescharacteristic
120C2×#215—101no—
121C2×#213—101no—
122#874—51no—
123#809—101no—
124#809—101no—
125#809—102no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)—51no—
128C4×C3⋊C8—51no—
129C2×C5×Q8—22no—
130C2×C5×Q8—21no—
131C2×C5×Q8—42no—
132C2×C5×Q8—42no—
133C2×C5×Q8#6711yescharacteristic
134C2×C5×D4#6711yescharacteristic
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C2×D20—61no—
138C2×D20—61no—
139C2×D20—61no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4#6711yescharacteristic
144C5×C4⋊C4#6711yescharacteristic
145C5×C4⋊C4#6712yes—
146C5×C22⋊C4—22no—
147C5×C22⋊C4—21no—
148C42×C5—21no—
149C42×C5C22×D311yescharacteristic
150#688—122no—
151#686—122no—
152C2×#168—61no—
153C2×#168—61no—
154C2×#168—61no—
155D4×Q8D1511yescharacteristic, complemented
156#486—151no—
157#460—151no—
158#459—151no—
159#332—151no—
160Q8⋊C8—151no—
161D4⋊C8—151no—
162C22×C3×C5—22no—
163C22×C3×C5—41no—
164C22×C3×C5—41no—
165C22×C3×C5#12011yescharacteristic
166C2×D15—81no—
167C2×D15—81no—
168C2×D15—81no—
169C3×C4×C5—22no—
170C3×C4×C5—21no—
171C3×C4×C5—42no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C3×C4×C5C2×D811yescharacteristic
175C3×C4×C5C2×SD1611yescharacteristic
176C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
177C3×C4×C5#13711yescharacteristic
178C2×C3×Q8—22no—
179C2×C3×Q8—21no—
180C2×C3×Q8—42no—
181C2×C3×Q8—42no—
182C2×C3×Q8C22⋊D511yescharacteristic
183C2×C3×D4C22⋊D511yescharacteristic
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C2×D12—101no—
187C2×D12—101no—
188C2×D12—101no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4C22⋊D511yescharacteristic
193C3×C4⋊C4C22⋊D511yescharacteristic
194C3×C4⋊C4C22⋊D512yes—
195C3×C22⋊C4—22no—
196C3×C22⋊C4—21no—
197C3×C42—21no—
198C3×C42C22×D511yescharacteristic
199#215—202no—
200#213—202no—
201C2×C3⋊C8—101no—
202C2×C3⋊C8—101no—
203C2×C3⋊C8—101no—
204C23×C5—21no—
205C22×D5—121no—
206C5×Q8—21no—
207C5×Q8—44no—
208C5×Q8—41no—
209C5×Q8—41no—
210C5×Q8#21312yescomplemented
211C5×D4—21no—
212C5×D4#21512yescomplemented
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—22no—
216C2×C4×C5—21no—
217C2×C4×C5—44no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223D20—122no—
224D20—121no—
225D20—121no—
226D20—121no—
227D20—121no—
228#168—121no—
229#168—121no—
230#168—121no—
231C22×Q8—21no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—21no—
235C4⋊Q8C2×D1511yescharacteristic
236#127—151no—
237C22⋊Q8—21no—
238C22⋊Q8—22no—
239C4×Q8C2×D1511yescharacteristic
240C4×D4—21no—
241C4×D4C2×D1511yescharacteristic
242C4⋊C8—151no—
243C4⋊C8—151no—
244#102—301no—
245#102—301no—
246#102—302no—
247C4×C8—151no—
248C2×C3×C5—42no—
249C2×C3×C5#44711yescharacteristic
250C2×C3×C5#44811yescharacteristic
251C2×C3×C5#45411yescharacteristic
252D15—161no—
253C23×C3—21no—
254C22×D3—201no—
255C3×Q8—21no—
256C3×Q8—44no—
257C3×Q8—41no—
258C3×Q8—41no—
259C3×Q8#68612yescomplemented
260C3×D4—21no—
261C3×D4#68812yescomplemented
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—44no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272D12—202no—
273D12—201no—
274D12—201no—
275D12—201no—
276D12—201no—
277C3⋊C8—201no—
278C3⋊C8—201no—
279C3⋊C8—201no—
280C22×C5—22no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5#95311yescharacteristic
284C2×D5—241no—
285C2×D5—241no—
286C2×D5—241no—
287C4×C5—22no—
288C4×C5—21no—
289C4×C5—42no—
290C4×C5—41no—
291C4×C5—41no—
292C4×C5C2×#21311yescharacteristic
293C4×C5#93211yescharacteristic
294C4×C5C2×#21511yescharacteristic
295C4×C5#94211yescharacteristic
296C2×Q8—22no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C2×Q8#122011yescharacteristic
301C2×D4—301no—
302C2×D4—301no—
303C2×D4—301no—
304C2×D4#122011yescharacteristic
305C22×C4—22no—
306C22×C4—21no—
307SD16—602no—
308D8—602no—
309C2×C8—301no—
310C2×C8—301no—
311C2×C8—301no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4#122011yescharacteristic
316C4⋊C4#122011yescharacteristic
317C4⋊C4#122012yes—
318C22⋊C4—22no—
319C22⋊C4—21no—
320C42—21no—
321C42C22×D1511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—22no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3#409911yescharacteristic
327C2×D3—401no—
328C2×D3—401no—
329C2×D3—401no—
330C3×C4—22no—
331C3×C4—21no—
332C3×C4—42no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4C2×#68611yescharacteristic
336C3×C4#407811yescharacteristic
337C3×C4C2×#68811yescharacteristic
338C3×C4#408811yescharacteristic
339C2×C5—42no—
340C2×C5#521711yescharacteristic
341C2×C5#522711yescharacteristic
342C2×C5#524511yescharacteristic
343D5—481no—
344C23—21no—
345C23—601no—
346Q8—21no—
347Q8—44no—
348Q8—41no—
349Q8—41no—
350Q8#671512yescomplemented
351D4—21no—
352D4—602no—
353D4—601no—
354D4—601no—
355D4—601no—
356D4—601no—
357D4#671712yescomplemented
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4C2×#122011yescharacteristic
366C2×C4C2×#122011yescharacteristic
367C2×C4C2×#122011yescharacteristic
368C8—601no—
369C8—601no—
370C8—601no—
371C2×C3—42no—
372C2×C3#6550611yescharacteristic
373C2×C3#6551611yescharacteristic
374C2×C3#6553411yescharacteristic
375D3—801no—
376C5#7191411yescharacteristic, complemented, Sylow
377C22—22no—
378C22—41no—
379C22—41no—
380C22—1201no—
381C22—1201no—
382C22—1201no—
383C22#9184211yescharacteristic
384C4—22no—
385C4—21no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4C2×#671511yescharacteristic
390C4#9182111yescharacteristic
391C4C2×#671711yescharacteristic
392C4#9183111yescharacteristic
393C3#1060270711yescharacteristic, complemented, Sylow
394C2—42no—
395C2—2401no—
396C2#1175131811yescharacteristic
397C2#1175132811yescharacteristic
398C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4×Q8C2
socleC22×C3×C5#120
prime radical#11751116C2
hypercenterD4×Q8D15
hypocenterC3×C5#1627
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C5×D4×Q8C2semidirect
2. #11751189C2semidirect
3. #11751128C2semidirect
5. #11746368C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
27. C5×D4×Q8D3semidirect
60. C3×D4×Q8D5semidirect
91. C3×C5×Q8D8semidirect
93. C3×C5×D4SD16semidirect
155. D4×Q8D15semidirect
210. C5×Q8#213semidirect
212. C5×D4#215semidirect
259. C3×Q8#686semidirect
261. C3×D4#688semidirect
322. C3×C5#1627semidirect
350. Q8#6715semidirect
357. D4#6717semidirect
376. C5#71914semidirect
393. C3#10602707semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4×Q82
#117511892
#117511282
#117511162
#117463682
#117463562
D4⋊(C3⋊#168)2
#106027073
#719145