Finite Group Databasebeta

← #14281964

Subgroups — #14281964

Order 1920.

468 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 106 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#11754410C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊#170C211yesmaximal, characteristic, complemented
4#11746494C212yesmaximal, complemented
5#11746488C212yesmaximal, complemented
6#10604479—31nomaximal, Hall
7C2×#6762—21no—
8C22×C3×#170—21no—
9#91813C411yescharacteristic
10C5×#930C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12Dic5×#67—21no—
13#91539—21no—
14Dic5×D12C2211yescharacteristic
15#91398—21no—
16#91388C411yescharacteristic
17#91373C411yescharacteristic
18#91372—21no—
19#91333C2211yescharacteristic
20#91231—21no—
21C4×C3⋊#170C2212yes—
22C3×C4⋊#170—21no—
23C3×C4⋊#170C2212yes—
24#70427—51nomaximal, Hall
25#65934—31no—
26C4×#704—31no—
27C2×C4⋊#170D311yescharacteristic, complemented
28D4⋊#170—32no—
29#64872—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×#67—21no—
33C2×C5×D12C2×C411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×D3×Dic5—21no—
37#6762—24no—
38C2×C3⋊#170—22no—
39C2×C3×#170—22no—
40C2×C3×#170—42no—
41#6719—21no—
42C4⋊Dic15C2×C411yescharacteristic
43#6712—21no—
44C5×(C2×D3)⋊C4—21no—
45C5×C4⋊Dic3C2×C411yescharacteristic
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51#6669—21no—
52#6669—21no—
53(C2×D3)⋊Dic5—21no—
54(C2×D3)⋊Dic5—21no—
55(C2×D3)⋊Dic5—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C2×C3×C4⋊C8—51no—
59C4×#208—51no—
60#4484—52no—
61#4483—52no—
62C2×#704—61no—
63C22×#170—21no—
64C5×#121—31no—
65#4082—31no—
66#4081—61no—
67D4×Dic5—31no—
68D4×Dic5—61no—
69#4070—31no—
70C2×C4×Dic5C2×D311yescharacteristic
71#4036—31no—
72#4033—31no—
73#4025—61no—
74#4023—61no—
75#4002—61no—
76C4⋊#170—21no—
77C4⋊#170C2×D312yes—
78C4×#170—32no—
79#1483—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×C5×D3—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87Dic30—22no—
88C5×#67—42no—
89C2×C5×Dic3—21no—
90C5×D12—22no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98D3×Dic5—41no—
99D3×Dic5—41no—
100C3⋊#170—24no—
101C3×#170—42no—
102C22×C3×C8—101no—
103C2×C3×C42—51no—
104#930AGL(1,𝔽5)11yescharacteristic
105#929—101no—
106C4×#67—101no—
107#924—51no—
108C2×#208—101no—
109#876—101no—
110#875—51no—
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×D4—31no—
120C2×C5×D4—61no—
121C22×C4×C5C4×D311yescharacteristic
122C22×Dic5—61no—
123C22×Dic5D1211yescharacteristic
124C22×Dic5#6711yescharacteristic
125C2×Dic10—31no—
126#704—64no—
127C2×#170—22no—
128C2×#170—42no—
129C2×#170—62no—
130C5×C4⋊C4—31no—
131C5×C22⋊C4—61no—
132C22⋊Dic5—61no—
133C22⋊Dic5—61no—
134C22⋊Dic5—61no—
135C22⋊Dic5—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138#683—61no—
139#683—61no—
140#683—61no—
141C4×Dic5—61no—
142C4×Dic5C4×D311yescharacteristic
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×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×C5×D3—41no—
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C3×C4×C5—21no—
159C3×C4×C5#13112yes—
160Dic15—41no—
161Dic15—41no—
162C3×Dic5—21no—
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×C4C2×AGL(1,𝔽5)11yescharacteristic
171C2×#67—21no—
172C2×D12C2×AGL(1,𝔽5)11yescharacteristic
173C2×C4×D3—101no—
174C2×Dic6—51no—
175C2×C3×C8—102no—
176C2×C3×C8—202no—
177C3×C42—51no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181#217—101no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—101no—
184(C2×D3)⋊C4—101no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
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—
196C23×C5(C2×D3)⋊C411yescharacteristic
197C5×D4—62no—
198C5×D4—122no—
199C2×C4×C5—22no—
200C2×C4×C5—61no—
201C2×C4×C5(C2×D3)⋊C411yescharacteristic
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×Dic5—22no—
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—61no—
207C2×Dic5—61no—
208C2×Dic5—121no—
209C2×Dic5—121no—
210C2×Dic5(C2×D3)⋊C411yescharacteristic
211C2×Dic5(C2×D3)⋊C411yescharacteristic
212C2×Dic5C2×D1211yescharacteristic
213C2×Dic5C2×#6711yescharacteristic
214Dic10—62no—
215#170—42no—
216#170—64no—
217C2×M16—301no—
218C22×C8—101no—
219#126—301no—
220#125—151no—
221#124—151no—
222#123—301no—
223C22⋊Q8—151no—
224#121—31no—
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—22no—
235C2×C3×C5#40811yescharacteristic
236C2×C3×C5#41711yescharacteristic
237C2×C3×C5C2×#10411yescharacteristic
238C5×D3—81no—
239C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
240C22×D3—21no—
241C2×C3×C4—22no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—102no—
249C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
250C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
251#67—42no—
252C2×Dic3—21no—
253C2×Dic3—101no—
254C2×Dic3—101no—
255D12—22no—
256C4×D3—201no—
257C4×D3—201no—
258Dic6—102no—
259C3×C8—202no—
260C3⋊C8—104no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5—121no—
266C22×C5#82512yes—
267C22×C5C2×(C2×D3)⋊C411yescharacteristic
268C4×C5—21no—
269C4×C5—121no—
270C4×C5#90112yes—
271Dic5—21no—
272Dic5—21no—
273Dic5—21no—
274Dic5—121no—
275Dic5—121no—
276Dic5#93211yescharacteristic
277Dic5#94211yescharacteristic
278C2×Q8—151no—
279C2×D4—31no—
280C2×D4—61no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—301no—
284C22×C4D3×AGL(1,𝔽5)11yescharacteristic
285M16—304no—
286C2×C8—102no—
287C2×C8—202no—
288C2×C8—302no—
289C4⋊C4—31no—
290C4⋊C4—151no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—61no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C22⋊C4—301no—
299C22⋊C4—301no—
300C42—51no—
301C42—51no—
302C42—51no—
303C42—51no—
304C42—301no—
305C3×C5#148311yescharacteristic, complemented, Hall
306C22×C3—21no—
307C22×C3—21no—
308C22×C3#400812yes—
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C3×C4—21no—
314C3×C4—51no—
315C3×C4—51no—
316C3×C4—101no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4#413112yes—
320Dic3—41no—
321Dic3—201no—
322Dic3—201no—
323C2×C5—22no—
324C2×C5—241no—
325C2×C5#496611yescharacteristic
326C2×C5#511011yescharacteristic
327C2×C5C2×#82511yescharacteristic
328C23—61no—
329C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
330Q8—302no—
331D4—62no—
332D4—122no—
333C2×C4—22no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—61no—
339C2×C4—101no—
340C2×C4—101no—
341C2×C4—102no—
342C2×C4—301no—
343C2×C4—301no—
344C2×C4—601no—
345C2×C4—601no—
346C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
347C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
348C8—202no—
349C8—304no—
350C2×C3—22no—
351C2×C3C2×#400811yescharacteristic
352C2×C3#6577511yescharacteristic
353C2×C3#6579311yescharacteristic
354D3—81no—
355C5#7042711yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—121no—
359C22—121no—
360C22—121no—
361C22#9115512yes—
362C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
363C4—21no—
364C4—51no—
365C4—51no—
366C4—101no—
367C4—101no—
368C4—101no—
369C4—121no—
370C4—601no—
371C4—601no—
372C4#9192712yes—
373C3#1060447911yescharacteristic, complemented, Sylow
374C2—22no—
375C2—241no—
376C2#1175170511yescharacteristic
377C2C2×#9115511yescharacteristic
378C2#1175199911yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6762C2semidirect
3. C2×C3×C4⋊#170C2semidirect
4. #11746494C2semidirect
5. #11746488C2semidirect
27. C2×C4⋊#170D3semidirect
305. C3×C5#1483semidirect
355. C5#70427semidirect
373. C3#10604479semidirect

Maximal subgroups

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

subgroupindex
#117544102
C4×#67622
C2×C3×C4⋊#1702
#117464942
#117464882
#106044793
#704275