Finite Group Databasebeta

← #14281972

Subgroups — #14281972

Order 1920.

468 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 102 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#11752683C211yesmaximal, characteristic
2C4×#6758C211yesmaximal, characteristic, complemented
3C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
4#11746492C212yesmaximal, complemented
5#11746488C212yesmaximal, complemented
6#10604553—31nomaximal, Hall
7C2×#6758—21no—
8C2×C3×D5⋊C8—21no—
9#91759C411yescharacteristic
10C5×#875C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91449C411yescharacteristic
13#91447—21no—
14#91440—21no—
15Dic5×D12C2211yescharacteristic
16#91398—21no—
17#91372—21no—
18#91359C411yescharacteristic
19Dic5×Dic6C2211yescharacteristic
20#91231—21no—
21C4×C3⋊#170C2212yes—
22C3×#4004—21no—
23C3×C4⋊#170C2212yes—
24#70427—51nomaximal, Hall
25#66014—31no—
26D5⋊(C4⋊C8)D311yescharacteristic, complemented
27C4×#700—31no—
28Q8⋊#170—32no—
29D4⋊#170—32no—
30C2×C5×D12C2×C411yescharacteristic
31C2×C5×Dic6C2×C411yescharacteristic
32C2×C3×C4×D5C2×C411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×#1201—21no—
36C2×D3×Dic5—21no—
37C2×C3⋊#170—22no—
38#6758—24no—
39C2×C3×#170—22no—
40C3×D5⋊C8—42no—
41C3×C42×C5C2×C411yescharacteristic
42C4⋊Dic15C2×C411yescharacteristic
43C4⋊Dic15C2×C411yescharacteristic
44#6712—21no—
45#6712—21no—
46C5×(C2×D3)⋊C4—21no—
47C5×(C2×D3)⋊C4—21no—
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5C2311yescharacteristic
51Dic3⋊Dic5—21no—
52#6669—21no—
53(C2×D3)⋊Dic5—21no—
54(C2×D3)⋊Dic5—21no—
55#6665—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C2×C3×C4⋊C8—51no—
59C4×#208—51no—
60#4484—52no—
61#4483—52no—
62C2×#700—61no—
63C2×D5⋊C8—21no—
64C5×#124—31no—
65#4092—31no—
66Q8×Dic5—31no—
67#4084—31no—
68D4×Dic5—31no—
69#4029—61no—
70#4027—61no—
71#4025—61no—
72#4023—61no—
73C42×D5C2×D311yescharacteristic
74#4016—31no—
75#4004—21no—
76#4002—61no—
77C4⋊#170C2×D312yes—
78C4×#170—32no—
79#1483—151noSylow
80C22×C5×D3—21no—
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87C2×C5×Dic3—21no—
88C5×D12—22no—
89C5×Dic6—22no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×C4×D5—22no—
94C3×C4×D5—22no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97#1201—42no—
98D3×Dic5—41no—
99D3×Dic5—41no—
100C3⋊#170—24no—
101C3×#170—42no—
102C22×C3×C8—101no—
103C2×C3×C42—51no—
104#930—51no—
105#929—101no—
106C4×#67—101no—
107#924—51no—
108C2×#208—101no—
109#876—101no—
110#875AGL(1,𝔽5)11yescharacteristic
111C4×D12—51no—
112#872—101no—
113#870—51no—
114C4×Dic6—51no—
115C3×C4⋊C8—52no—
116C3×C4⋊C8—101no—
117#803—101no—
118C4×C3⋊C8—52no—
119C2×C5×Q8—31no—
120C2×C5×D4—31no—
121C2×C22⋊D5—61no—
122C22×Dic5—61no—
123C2×C4×D5C4×D311yescharacteristic
124C2×C4×D5D1211yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×#170—22no—
127C2×#170—62no—
128#700—64no—
129D5⋊C8—42no—
130C5×C22⋊C4—61no—
131C5×C22⋊C4—61no—
132C42×C5C4×D311yescharacteristic
133C22⋊Dic5—61no—
134C22⋊Dic5—61no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138C4⋊Dic5—61no—
139#683—61no—
140#683—61no—
141#683—61no—
142C4×Dic5—61no—
143C4×Dic5D1211yescharacteristic
144C4×Dic5#6711yescharacteristic
145C4×Dic5C22×D311yescharacteristic
146#529—151no—
147C2×C4⋊C8—51no—
148C4×M16—151no—
149Q8⋊C8—152no—
150D4⋊C8—152no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C2×C3×D5—21no—
156C2×C3×D5—21no—
157C2×C3×D5#10412yes—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5#13112yes—
161Dic15—41no—
162Dic15—41no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5AGL(1,ℤ/8)11yescharacteristic
166C3×Dic5#13711yescharacteristic
167C5×Dic3—41no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C2×#67—101no—
172C2×D12C2×AGL(1,𝔽5)11yescharacteristic
173C2×C4×D3—101no—
174C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
175C2×C3×C8—102no—
176C2×C3×C8—202no—
177C3×C42—51no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42C2×AGL(1,𝔽5)11yescharacteristic
181#217—101no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—21no—
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—
193#208—104no—
194C2×C3⋊C8—102no—
195C23×C5—61no—
196C22×D5(C2×D3)⋊C411yescharacteristic
197C5×Q8—62no—
198C5×D4—62no—
199C2×C4×C5—61no—
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C2×C4×C5(C2×D3)⋊C411yescharacteristic
202C2×C4×C5C2×C4×D311yescharacteristic
203C22⋊D5—122no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—121no—
207C2×Dic5—121no—
208C2×Dic5(C2×D3)⋊C411yescharacteristic
209C2×Dic5C2×D1211yescharacteristic
210C2×Dic5C2×#6711yescharacteristic
211C4×D5—22no—
212C4×D5—22no—
213C4×D5—21no—
214C4×D5—21no—
215#170—42no—
216#170—64no—
217C2×M16—301no—
218C22×C8—101no—
219#126—301no—
220#125—151no—
221#124—31no—
222#123—301no—
223C22⋊Q8—151no—
224#121—151no—
225C4×Q8—151no—
226C4×D4—151no—
227C4×D4—301no—
228#117—301no—
229C2×C42—51no—
230C4⋊C8—52no—
231C4⋊C8—101no—
232#97—301no—
233C4×C8—152no—
234C2×C3×C5#40811yescharacteristic
235C2×C3×C5#41711yescharacteristic
236C2×C3×C5C2×#10411yescharacteristic
237C3×D5—22no—
238C5×D3—81no—
239C23×C3—51no—
240C22×D3—21no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4—102no—
247C2×C3×C4—102no—
248C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
249C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
250C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
251#67—202no—
252C2×Dic3—21no—
253C2×Dic3—101no—
254C2×Dic3—101no—
255D12—22no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—22no—
259C3×C8—202no—
260C3⋊C8—104no—
261C22×C5—121no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5C2×(C2×D3)⋊C411yescharacteristic
265C2×D5—21no—
266C2×D5—21no—
267C2×D5#82512yes—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—121no—
271C4×C5#90112yes—
272Dic5—21no—
273Dic5—21no—
274Dic5—121no—
275Dic5—121no—
276Dic5#93211yescharacteristic
277Dic5#94211yescharacteristic
278C2×Q8—31no—
279C2×D4—31no—
280C2×D4—301no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—301no—
285M16—304no—
286C2×C8—102no—
287C2×C8—202no—
288C2×C8—302no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—61no—
296C22⋊C4—61no—
297C22⋊C4—301no—
298C22⋊C4—301no—
299C22⋊C4—301no—
300C42—51no—
301C42—51no—
302C42—51no—
303C42—301no—
304C42D3×AGL(1,𝔽5)11yescharacteristic
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—52no—
307C22×C3—101no—
308C22×C3—101no—
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—51no—
316C3×C4—51no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4#413112yes—
320Dic3—41no—
321Dic3—201no—
322Dic3—201no—
323C2×C5—241no—
324C2×C5#496611yescharacteristic
325C2×C5#511011yescharacteristic
326C2×C5C2×#82511yescharacteristic
327D5—22no—
328C23—51no—
329C23—61no—
330Q8—62no—
331D4—62no—
332D4—602no—
333C2×C4—51no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—61no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—301no—
342C2×C4—301no—
343C2×C4—601no—
344C2×C4—601no—
345C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
346C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
347C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
348C8—202no—
349C8—304no—
350C2×C3—102no—
351C2×C3#6577611yescharacteristic
352C2×C3D5⋊#10411yescharacteristic
353C2×C3#6579311yescharacteristic
354D3—81no—
355C5#7042711yescharacteristic, complemented, Sylow
356C22—52no—
357C22—101no—
358C22—101no—
359C22—121no—
360C22—121no—
361C22—121no—
362C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
363C4—21no—
364C4—21no—
365C4—51no—
366C4—51no—
367C4—101no—
368C4—101no—
369C4—121no—
370C4—601no—
371C4—601no—
372C4#9191112yes—
373C3#1060455311yescharacteristic, complemented, Sylow
374C2—102no—
375C2—241no—
376C2#1175170511yescharacteristic
377C2D5⋊#82511yescharacteristic
378C2#1175180111yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#91449C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#6758C2semidirect
3. C3×D5⋊(C4⋊C8)C2semidirect
4. #11746492C2semidirect
5. #11746488C2semidirect
26. D5⋊(C4⋊C8)D3semidirect
305. C3×C5#1483semidirect
355. C5#70427semidirect
373. C3#10604553semidirect

Maximal subgroups

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

subgroupindex
#117526832
C4×#67582
C3×D5⋊(C4⋊C8)2
#117464922
#117464882
#106045533
#704275