Finite Group Databasebeta

← #14281929

Subgroups — #14281929

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C3×C4×C5×M16C211yesmaximal, characteristic, complemented
3C2×C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
4#11746280C212yesmaximal, complemented
5#11746277C212yesmaximal, complemented
6#10600645—31nomaximal, Hall
7C2×C3×C5×M16—21no—
8C2×C3×C42×C5C2211yescharacteristic
9#91819C411yescharacteristic
10#91818—21no—
11C4×#1220—21no—
12#91813C411yescharacteristic
13C22×C3⋊#168—21no—
14#91765—21no—
15#91764C411yescharacteristic
16C4×D60C2211yescharacteristic
17#91761—21no—
18#91759C411yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×#97—21no—
21C3×C4×C5×C8C2212yes—
22C4⋊(C3⋊#168)—21no—
23C4⋊(C3⋊#168)C2212yes—
24#69852—51nomaximal, Hall
25#65813—31no—
26C4×C5×M16D311yescharacteristic, complemented
27C2×C4⋊#168—31no—
28#64679—32no—
29#64676—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C3×C5×M16—24no—
38C2×C3×C5×C8—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5C2311yescharacteristic
43#6719—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47#6714—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C4⋊Dic15C2×C411yescharacteristic
50#6712—21no—
51#6712—21no—
52#6712—21no—
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—22no—
56C2×C3⋊#168—42no—
57#5479—51no—
58C3×C4×M16D511yescharacteristic, complemented
59C2×C4⋊(C3⋊C8)—51no—
60#4459—52no—
61#4456—52no—
62C2×C5×M16—21no—
63C2×C42×C5C2×D311yescharacteristic
64#4076—31no—
65#4075—61no—
66C4×C22⋊D5—61no—
67#4070—31no—
68C22×#168—61no—
69#4022—61no—
70#4021—31no—
71C4×D20—31no—
72#4018—61no—
73#4016—31no—
74C4×Dic10—31no—
75C5×#97—21no—
76C4×C5×C8C2×D312yes—
77C4⋊#168—32no—
78C4⋊#168—61no—
79#1483—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92#1220—42no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—21no—
96D60—22no—
97C4×D15—41no—
98C4×D15—41no—
99Dic30—22no—
100C3×C5×C8—24no—
101C3⋊#168—42no—
102C2×C3×M16—21no—
103C2×C3×C42C2×D511yescharacteristic
104#930—51no—
105#929—101no—
106C4×#67—101no—
107#924—51no—
108C22×C3⋊C8—101no—
109#876—101no—
110#875—51no—
111C4×D12—51no—
112#872—101no—
113#870—51no—
114C4×Dic6—51no—
115C3×#97—21no—
116C3×C4×C8C2×D512yes—
117C4⋊(C3⋊C8)—52no—
118C4⋊(C3⋊C8)—101no—
119C22×C4×C5C4×D311yescharacteristic
120C22×C4×C5D1211yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C2×C22⋊D5—61no—
123C2×D20—31no—
124C2×C4×D5—61no—
125C2×Dic10—31no—
126C5×M16—24no—
127C2×C5×C8—22no—
128C42×C5C4×D311yescharacteristic
129C42×C5D1211yescharacteristic
130C42×C5#6711yescharacteristic
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—61no—
133#685—61no—
134#685—61no—
135#685—61no—
136#685—61no—
137C4⋊Dic5—31no—
138C4⋊Dic5—31no—
139#683—61no—
140#683—61no—
141#683—61no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—62no—
145C2×#168—122no—
146#529—151no—
147C2×C4⋊C8—151no—
148C4×M16D1511yescharacteristic, complemented
149Q8⋊C8—152no—
150D4⋊C8—152no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×D15—41no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5#13112yes—
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—41no—
167Dic15—41no—
168C22×C3×C4C4×D511yescharacteristic
169C22×C3×C4D2011yescharacteristic
170C22×C3×C4C22⋊D511yescharacteristic
171C2×#67—101no—
172C2×D12—51no—
173C2×C4×D3—101no—
174C2×Dic6—51no—
175C3×M16—24no—
176C2×C3×C8—22no—
177C3×C42C4×D511yescharacteristic
178C3×C42D2011yescharacteristic
179C3×C42C22⋊D511yescharacteristic
180C3×C42C22×D511yescharacteristic
181#217—101no—
182(C2×D3)⋊C4—101no—
183(C2×D3)⋊C4—101no—
184(C2×D3)⋊C4—101no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3—51no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191Dic3⋊C4—101no—
192C4×Dic3—101no—
193C2×C3⋊C8—102no—
194C2×C3⋊C8—202no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C22×D5—61no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5(C2×D3)⋊C411yescharacteristic
202C2×C4×C5(C2×D3)⋊C411yescharacteristic
203C2×C4×C5(C2×D3)⋊C411yescharacteristic
204C2×C4×C5C2×C4×D311yescharacteristic
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C22⋊D5—122no—
208C2×Dic5—61no—
209C2×Dic5—61no—
210C2×Dic5—61no—
211D20—62no—
212C4×D5—121no—
213C4×D5—121no—
214Dic10—62no—
215C5×C8—24no—
216#168—122no—
217C2×M16—21no—
218C22×C8—301no—
219#126—301no—
220#125—151no—
221#124—151no—
222#123—301no—
223C22⋊Q8—151no—
224#121—151no—
225C4×Q8—151no—
226C4×D4—151no—
227C4×D4—301no—
228#117—301no—
229C2×C42C2×D1511yescharacteristic
230C4⋊C8—152no—
231C4⋊C8—301no—
232#97—21no—
233C4×C8C2×D1512yes—
234C2×C3×C5—22no—
235C2×C3×C5#40811yescharacteristic
236C2×C3×C5#41711yescharacteristic
237C2×C3×C5C2×#10411yescharacteristic
238D15—81no—
239C23×C3#68511yescharacteristic
240C22×D3—101no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4#68511yescharacteristic
246C2×C3×C4#68511yescharacteristic
247C2×C3×C4#68511yescharacteristic
248C2×C3×C4C2×C4×D511yescharacteristic
249C2×C3×C4C2×D2011yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251#67—202no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254C2×Dic3—101no—
255D12—102no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—102no—
259C3×C8—24no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5#80512yes—
264C22×C5C2×(C2×D3)⋊C411yescharacteristic
265C2×D5—121no—
266C2×D5—121no—
267C2×D5—121no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5#90712yes—
273C4×C5#90811yescharacteristic
274C4×C5#90911yescharacteristic
275Dic5—121no—
276Dic5—121no—
277Dic5—121no—
278C2×Q8—151no—
279C2×D4—151no—
280C2×D4—301no—
281C22×C4—301no—
282C22×C4C4×D1511yescharacteristic
283C22×C4D6011yescharacteristic
284C22×C4#122011yescharacteristic
285M16—24no—
286C2×C8—22no—
287C2×C8—302no—
288C2×C8—602no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—301no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C22⋊C4—301no—
299C22⋊C4—301no—
300C42—301no—
301C42C4×D1511yescharacteristic
302C42D6011yescharacteristic
303C42#122011yescharacteristic
304C42C22×D1511yescharacteristic
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—21no—
307C22×C3—21no—
308C22×C3#393712yes—
309C22×C3C2×#68511yescharacteristic
310C2×D3—201no—
311C2×D3—201no—
312C2×D3—201no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4#405312yes—
318C3×C4#405411yescharacteristic
319C3×C4#405511yescharacteristic
320Dic3—201no—
321Dic3—201no—
322Dic3—201no—
323C2×C5—22no—
324C2×C5C2×#80511yescharacteristic
325C2×C5#512911yescharacteristic
326C2×C5#513311yescharacteristic
327D5—241no—
328C23—301no—
329C23#671411yescharacteristic
330Q8—302no—
331D4—302no—
332D4—602no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—301no—
338C2×C4—301no—
339C2×C4—301no—
340C2×C4—601no—
341C2×C4—601no—
342C2×C4#671411yescharacteristic
343C2×C4#671411yescharacteristic
344C2×C4#671411yescharacteristic
345C2×C4C2×C4×D1511yescharacteristic
346C2×C4C2×D6011yescharacteristic
347C2×C4C2×#122011yescharacteristic
348C8—24no—
349C8—602no—
350C2×C3—22no—
351C2×C3C2×#393711yescharacteristic
352C2×C3#6541811yescharacteristic
353C2×C3#6542211yescharacteristic
354D3—401no—
355C5#6985211yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—601no—
359C22—601no—
360C22—601no—
361C22#9108912yes—
362C22C2×#671411yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—601no—
368C4—601no—
369C4—601no—
370C4#9179612yes—
371C4#9179711yescharacteristic
372C4#9179811yescharacteristic
373C3#1060064511yescharacteristic, complemented, Sylow
374C2—22no—
375C2—1201no—
376C2C2×#9108911yescharacteristic
377C2#1175123011yescharacteristic
378C2#1175123411yescharacteristic
subgroupG/H
centerC2×C4C2×D60
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C4×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenterC4×M16D15
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×M16C2semidirect
3. C2×C4⋊(C3⋊#168)C2semidirect
4. #11746280C2semidirect
5. #11746277C2semidirect
26. C4×C5×M16D3semidirect
58. C3×C4×M16D5semidirect
148. C4×M16D15semidirect
305. C3×C5#1483semidirect
355. C5#69852semidirect
373. C3#10600645semidirect

Maximal subgroups

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

subgroupindex
#117562382
C3×C4×C5×M162
C2×C4⋊(C3⋊#168)2
#117462802
#117462772
#106006453
#698525