Finite Group Databasebeta

← #14282014

Subgroups — #14282014

Order 1920.

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

normal subgroups only

This group has 524 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#11754330C211yesmaximal, characteristic
2#11752407C211yesmaximal, characteristic, complemented
3C3×C4×#704C211yesmaximal, characteristic, complemented
4#11746491C212yesmaximal, complemented
5#11746489C212yesmaximal, complemented
6#10604480—31nomaximal, Hall
7C2×#6782—21no—
8C2×C3×#704—21no—
9#91819C411yescharacteristic
10C5×#930C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91566—21no—
13#91468C411yescharacteristic
14#91451C411yescharacteristic
15#91418C2211yescharacteristic
16Dic5×D12C2211yescharacteristic
17#91405—21no—
18#91350—21no—
19#91241—21no—
20C4⋊(C3⋊#170)C2212yes—
21C4×C3⋊#170—21no—
22C3×#4002—21no—
23C3×C4×#170C2212yes—
24#69853—51nomaximal, Hall
25#65930—31no—
26C4×#704D311yescharacteristic, complemented
27#65748—31no—
28D4⋊#170—32no—
29#64871—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×#67—21no—
34C2×C5×D12C2×C411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C22×C3×Dic5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1200—21no—
41#6782—44no—
42C2×D3×Dic5—21no—
43C2×C3⋊#170—22no—
44C3×#704—24no—
45C2×C3×#170—22no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C3×C4×Dic5C2×C411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5C2311yescharacteristic
54#6668—21no—
55#6667—21no—
56(C2×D3)⋊Dic5—21no—
57#5477—51no—
58C3×C4×M16—51no—
59#4925—51no—
60#4459—52no—
61#4459—52no—
62C2×#711—61no—
63C2×#704—21no—
64C5×#121—31no—
65#4086—31no—
66#4085—61no—
67D4×Dic5—31no—
68#4076—31no—
69C2×C4×Dic5C2×D311yescharacteristic
70#4039—31no—
71#4034—31no—
72#4031—61no—
73#4027—61no—
74C22⋊#170—61no—
75#4002—21no—
76C4⋊#170—32no—
77C4×#170—61no—
78C4×#170C2×D312yes—
79#1484—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C22×C5×D3—21no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86#1220—42no—
87C2×Dic15—21no—
88D60—22no—
89C5×#67—42no—
90C2×C5×Dic3—21no—
91C5×D12—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98#1204—42no—
99#1203—42no—
100#1203—42no—
101#1200—42no—
102D3×Dic5—42no—
103C3⋊#170—42no—
104C3×#170—24no—
105C2×#235—101no—
106C2×C3×M16—101no—
107C2×C3×C42—51no—
108#930—51no—
109#930—101no—
110#930AGL(1,𝔽5)11yescharacteristic
111#875—101no—
112#874—51no—
113C4×D12—51no—
114C4×D12—51no—
115C4×D12—101no—
116#869—51no—
117C3×#97—101no—
118C3×C4×C8—52no—
119#830—101no—
120C4⋊(C3⋊C8)—52no—
121C4×C3⋊C8—101no—
122C2×C5×D4—31no—
123C2×C5×D4—61no—
124C22×C4×C5C4×D311yescharacteristic
125C2×C22⋊D5—61no—
126C2×C22⋊D5—61no—
127C2×C22⋊D5—61no—
128C22×Dic5—61no—
129C22×Dic5D1211yescharacteristic
130C22×Dic5#6711yescharacteristic
131#711—124no—
132C2×D20—31no—
133C2×C4×D5—61no—
134C2×Dic10—61no—
135#704—24no—
136C2×#170—22no—
137C2×#170—62no—
138C5×C4⋊C4—31no—
139C5×C22⋊C4—61no—
140C22⋊Dic5—61no—
141#685—61no—
142#685—61no—
143C4⋊Dic5—31no—
144#683—61no—
145C4×Dic5C4×D311yescharacteristic
146C4×Dic5D1211yescharacteristic
147C4×Dic5#6711yescharacteristic
148C4×Dic5C22×D311yescharacteristic
149#532—151no—
150#431—151no—
151C4×M16—51no—
152D4⋊C8—152no—
153D4⋊C8—152no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C2×D15—41no—
159C2×D15—41no—
160C2×D15—41no—
161C2×C5×D3—41no—
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C3×C4×C5—21no—
165C3×C4×C5#13112yes—
166Dic15—41no—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C3×Dic5#10412yes—
170C3×Dic5AGL(1,ℤ/8)12yes—
171C5×Dic3—41no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
175C2×#67—21no—
176C2×#67—101no—
177#235—204no—
178C2×D12—51no—
179C2×D12—101no—
180C2×D12—101no—
181C2×D12C2×AGL(1,𝔽5)11yescharacteristic
182C2×C4×D3—101no—
183C2×C4×D3—101no—
184C2×Dic6—101no—
185C3×M16—104no—
186C2×C3×C8—102no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42—51no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—101no—
193(C2×D3)⋊C4—101no—
194(C2×D3)⋊C4—101no—
195C4⋊Dic3—51no—
196C4⋊Dic3—101no—
197C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
198C2×C3⋊C8—102no—
199C23×C5—61no—
200C23×C5(C2×D3)⋊C411yescharacteristic
201C22×D5—61no—
202C5×D4—62no—
203C5×D4—122no—
204C2×C4×C5—22no—
205C2×C4×C5—61no—
206C2×C4×C5(C2×D3)⋊C411yescharacteristic
207C2×C4×C5C2×C4×D311yescharacteristic
208C22⋊D5—122no—
209C22⋊D5—122no—
210C22⋊D5—122no—
211C2×Dic5—22no—
212C2×Dic5—22no—
213C2×Dic5—61no—
214C2×Dic5—122no—
215C2×Dic5(C2×D3)⋊C411yescharacteristic
216C2×Dic5(C2×D3)⋊C411yescharacteristic
217C2×Dic5C2×D1211yescharacteristic
218C2×Dic5C2×#6711yescharacteristic
219D20—62no—
220C4×D5—122no—
221Dic10—122no—
222#170—24no—
223#170—122no—
224C2×#41—301no—
225C2×M16—101no—
226C4⋊Q8—151no—
227#127—151no—
228#124—301no—
229#121—31no—
230#121—151no—
231#121—301no—
232C4×D4—151no—
233C4×D4—151no—
234C4×D4—301no—
235C2×C42—51no—
236C4⋊C8—152no—
237C22⋊C8—301no—
238#97—101no—
239C4×C8—52no—
240C4×C8—301no—
241C2×C3×C5—41no—
242C2×C3×C5#40811yescharacteristic
243C2×C3×C5#41811yescharacteristic
244C2×C3×C5C2×#10411yescharacteristic
245D15—81no—
246C5×D3—81no—
247C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
248C22×D3—21no—
249C22×D3—101no—
250C2×C3×C4—22no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—102no—
256C2×C3×C4—102no—
257C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
258C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
259#67—42no—
260#67—202no—
261C2×Dic3—21no—
262C2×Dic3—101no—
263D12—22no—
264D12—102no—
265D12—202no—
266D12—202no—
267C4×D3—202no—
268C4×D3—202no—
269Dic6—202no—
270C3×C8—104no—
271C3⋊C8—202no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—121no—
276C22×C5—121no—
277C22×C5—121no—
278C22×C5C2×(C2×D3)⋊C411yescharacteristic
279C2×D5—121no—
280C2×D5—121no—
281C2×D5—121no—
282C4×C5—21no—
283C4×C5—121no—
284C4×C5#90712yes—
285Dic5—21no—
286Dic5—21no—
287Dic5—121no—
288Dic5#80512yes—
289Dic5#90812yes—
290#41—604no—
291C2×Q8—301no—
292C2×D4—31no—
293C2×D4—61no—
294C2×D4—151no—
295C2×D4—301no—
296C2×D4—301no—
297C2×D4—301no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—301no—
301C22×C4—301no—
302C22×C4D3×AGL(1,𝔽5)11yescharacteristic
303M16—104no—
304C2×C8—102no—
305C2×C8—302no—
306C4⋊C4—31no—
307C4⋊C4—151no—
308C4⋊C4—301no—
309C22⋊C4—61no—
310C22⋊C4—301no—
311C22⋊C4—301no—
312C22⋊C4—301no—
313C42—51no—
314C42—51no—
315C42—51no—
316C42—51no—
317C3×C5#148411yescharacteristic, complemented, Hall
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—201no—
326C2×D3—201no—
327C2×D3—201no—
328C3×C4—21no—
329C3×C4—52no—
330C3×C4—52no—
331C3×C4—101no—
332C3×C4—101no—
333C3×C4#413112yes—
334Dic3—41no—
335Dic3—201no—
336C2×C5—41no—
337C2×C5—241no—
338C2×C5C2×#80511yescharacteristic
339C2×C5#512911yescharacteristic
340C2×C5#513111yescharacteristic
341D5—241no—
342C23—61no—
343C23—301no—
344C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
345Q8—602no—
346D4—62no—
347D4—122no—
348D4—302no—
349D4—602no—
350D4—602no—
351D4—602no—
352C2×C4—22no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—61no—
358C2×C4—102no—
359C2×C4—102no—
360C2×C4—301no—
361C2×C4—602no—
362C2×C4—602no—
363C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
364C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
365C8—104no—
366C8—602no—
367C2×C3—41no—
368C2×C3#6576711yescharacteristic
369C2×C3#6577511yescharacteristic
370C2×C3D5⋊#10411yescharacteristic
371D3—81no—
372D3—401no—
373C5#6985311yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—21no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
384C4—21no—
385C4—52no—
386C4—52no—
387C4—101no—
388C4—101no—
389C4—121no—
390C4—601no—
391C4#9192912yes—
392C3#1060448011yescharacteristic, complemented, Sylow
393C2—41no—
394C2—241no—
395C2—1201no—
396C2#1175170711yescharacteristic
397C2D5⋊#80511yescharacteristic
398C2#1175200111yescharacteristic
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 radical#11754330C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1484
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. #11752407C2semidirect
3. C3×C4×#704C2semidirect
4. #11746491C2semidirect
5. #11746489C2semidirect
26. C4×#704D3semidirect
317. C3×C5#1484semidirect
373. C5#69853semidirect
392. C3#10604480semidirect

Maximal subgroups

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

subgroupindex
#117543302
#117524072
C3×C4×#7042
#117464912
#117464892
#106044803
#698535