Finite Group Databasebeta

← #14283294

Subgroups — #14283294

Order 1920.

652 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×#91450C211yesmaximal, characteristic
2#11752423C211yesmaximal, characteristic, complemented
3C3×#65755C211yesmaximal, characteristic, complemented
4#11746499C214yesmaximal, complemented
5#10604260—31nomaximal, Hall
6C22×D60C411yescharacteristic, complemented
7C22×C3×C4×D5C2211yescharacteristic
8C22×#1202—21no—
9C2×#6763—21no—
10C2×C3×#704—21no—
11C2×C5×C4⋊Dic3C411yescharacteristic, complemented
12C2×#6667—21no—
13#91450—21no—
14#91450—21no—
15#91450C412yescomplemented
16#91450C2212yes—
17#91235—21no—
18#91235C2212yescomplemented
19C3×#4003—21no—
20C3×#4003C2212yescomplemented
21#69978—51nomaximal, Hall
22C2×#4041—31no—
23#65764—31no—
24#65755D311yescharacteristic, complemented
25#64868—34no—
26C23×D15—21no—
27C23×C3×D5D411yescharacteristic
28C22×ΓL(1,𝔽16)—22no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C2×D60—21no—
31C2×D60—42no—
32C2×D60C2×C412yes—
33C22×C5×Dic3—21no—
34C22×C3×Dic5D411yescharacteristic
35C2×C3×C4×D5—42no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5C2311yescharacteristic
40C2×#1202—22no—
41C2×#1202—22no—
42C2×#1202—44no—
43#6763—42no—
44C3×#704—42no—
45C2×C3×#170—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3C2×C412yes—
48#6667—22no—
49#6667—22no—
50C2×#930—51no—
51C3×#407—51no—
52#5211—51no—
53#4470—54no—
54C22×D20—31no—
55C22×D20—61no—
56C22×C4×D5C2×D311yescharacteristic
57C2×C22⋊AGL(1,𝔽5)—61no—
58C2×#704—21no—
59C2×C5×C4⋊C4—31no—
60C2×#685—61no—
61#4041—32no—
62#4041—32no—
63#4041—61no—
64#4041—61no—
65(C2×AGL(1,𝔽5))⋊C4—32no—
66(C2×AGL(1,𝔽5))⋊C4—61no—
67#4003—21no—
68#4003C2×D312yescomplemented
69#1510—151noSylow
70C23×C3×C5C22⋊C411yescharacteristic
71C22×D15—22no—
72C22×D15—42no—
73C22×D15—42no—
74C22×D15—42no—
75C22×C3×D5—22no—
76C22×C3×D5—22no—
77C22×C3×D5—41no—
78C22×C3×D5C22⋊C411yescharacteristic
79C22×C3×D5C2×D411yescharacteristic
80C2×ΓL(1,𝔽16)—42no—
81C2×ΓL(1,𝔽16)—42no—
82C2×ΓL(1,𝔽16)—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86D60—42no—
87D60—42no—
88C2×C5×Dic3—22no—
89C2×C5×Dic3—42no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97#1202—44no—
98#1202—44no—
99C3×#170—42no—
100C23×C3×C4—51no—
101C22×#67—101no—
102C22×D12—51no—
103C2×C3×M16—101no—
104C2×#217—101no—
105#930—52no—
106#930—52no—
107#930—101no—
108#930—101no—
109C2×(C2×D3)⋊C4—101no—
110C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic, complemented
111C3×C22⋊C8—52no—
112C3×C22⋊C8—101no—
113C3⋊#95—52no—
114C3⋊#95—101no—
115C23×D5—61no—
116C23×D5D1211yescharacteristic
117C22×AGL(1,𝔽5)—62no—
118C22×C4×C5—61no—
119C22×C4×C5C4×D311yescharacteristic
120C22×Dic5#6711yescharacteristic
121C2×D20—32no—
122C2×D20—62no—
123C2×D20—62no—
124C2×D20—61no—
125C2×D20—122no—
126C2×D20—124no—
127C2×C4×D5—42no—
128C2×C4×D5C4×D311yescharacteristic
129C2×C4×D5D1211yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×C4×D5C22×D311yescharacteristic
132C22⋊AGL(1,𝔽5)—122no—
133#704—42no—
134C2×#170—22no—
135C5×C4⋊C4—32no—
136C5×C4⋊C4—61no—
137#685—62no—
138#685—62no—
139C2×#121—151no—
140#407—51no—
141#381—151no—
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5#9912yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×D15—42no—
148C2×D15—42no—
149C2×D15—42no—
150C2×D15—84no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—44no—
157C2×C3×D5AGL(1,ℤ/8)12yes—
158ΓL(1,𝔽16)—82no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×Dic5—21no—
162C3×Dic5—21no—
163C5×Dic3—42no—
164C24×C3—51no—
165C23×D3—101no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—202no—
172C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
173C2×#67—102no—
174C2×#67—102no—
175C2×#67—204no—
176C22×Dic3—21no—
177C22×Dic3—102no—
178C2×D12—52no—
179C2×D12—101no—
180C2×D12—202no—
181C3×M16—202no—
182C2×C3×C8—102no—
183#217—202no—
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—102no—
186C4⋊Dic3—21no—
187C4⋊Dic3C2×AGL(1,𝔽5)12yes—
188C23×C5(C2×D3)⋊C411yescharacteristic
189C22×D5—22no—
190C22×D5—22no—
191C22×D5—41no—
192C22×D5—62no—
193C22×D5—122no—
194C22×D5—122no—
195C22×D5—122no—
196C22×D5(C2×D3)⋊C411yescharacteristic
197C22×D5C2×D1211yescharacteristic
198C2×AGL(1,𝔽5)—122no—
199C2×AGL(1,𝔽5)—122no—
200C2×AGL(1,𝔽5)—122no—
201C2×C4×C5—22no—
202C2×C4×C5—62no—
203C2×C4×C5—122no—
204C2×C4×C5(C2×D3)⋊C411yescharacteristic
205C2×C4×C5C2×C4×D311yescharacteristic
206C2×Dic5—22no—
207C2×Dic5(C2×D3)⋊C411yescharacteristic
208C2×Dic5C2×#6711yescharacteristic
209D20—122no—
210D20—122no—
211D20—124no—
212D20—124no—
213C4×D5—41no—
214C4×D5—41no—
215C4×D5—41no—
216C4×D5—41no—
217#170—42no—
218C22×D4—151no—
219C22×D4—301no—
220C23×C4—51no—
221C2×M16—101no—
222#121—152no—
223#121—152no—
224#121—301no—
225#121—301no—
226C2×C4⋊C4—31no—
227C2×C22⋊C4—301no—
228C2×C22⋊C4—301no—
229C22⋊C8—52no—
230C22⋊C8—101no—
231#95—152no—
232#95—301no—
233C2×C3×C5—22no—
234C2×C3×C5C2×#9911yescharacteristic
235C2×C3×C5#41811yescharacteristic
236C2×C3×C5#42111yescharacteristic
237D15—82no—
238C3×D5—22no—
239C3×D5—41no—
240C23×C3—51no—
241C23×C3—51no—
242C23×C3—102no—
243C23×C3—102no—
244C23×C3—201no—
245C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
246C22×D3—102no—
247C22×D3—202no—
248C22×D3—202no—
249C22×D3—202no—
250C2×C3×C4—22no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—102no—
254C2×C3×C4—201no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4—201no—
258C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
259C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
260#67—204no—
261#67—204no—
262C2×Dic3—22no—
263C2×Dic3—42no—
264C2×Dic3—202no—
265C2×Dic3—202no—
266C2×Dic3—202no—
267D12—202no—
268D12—202no—
269C3×C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5#80612yes—
273C22×C5C2×(C2×D3)⋊C411yescharacteristic
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—21no—
279C2×D5—44no—
280C2×D5—122no—
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—244no—
284C2×D5#90812yes—
285AGL(1,𝔽5)—242no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—122no—
289Dic5—21no—
290Dic5—21no—
291C24—51no—
292C24—301no—
293C2×D4—152no—
294C2×D4—302no—
295C2×D4—302no—
296C2×D4—301no—
297C2×D4—602no—
298C2×D4—604no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—61no—
305C22×C4—202no—
306C22×C4—302no—
307C22×C4D3×AGL(1,𝔽5)11yescharacteristic
308M16—202no—
309C2×C8—102no—
310C4⋊C4—32no—
311C4⋊C4—61no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—602no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—52no—
319C22×C3—101no—
320C22×C3—101no—
321C22×C3—101no—
322C22×C3—101no—
323C22×C3—101no—
324C22×C3—204no—
325C22×C3#399912yes—
326C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
327C2×D3—202no—
328C2×D3—202no—
329C2×D3—202no—
330C2×D3—404no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—101no—
334C3×C4—101no—
335Dic3—42no—
336Dic3—402no—
337C2×C5—22no—
338C2×C5C2×#80611yescharacteristic
339C2×C5#513111yescharacteristic
340C2×C5#513911yescharacteristic
341D5—22no—
342D5—41no—
343D5—242no—
344C23—51no—
345C23—51no—
346C23—102no—
347C23—102no—
348C23—201no—
349C23—302no—
350C23—602no—
351C23—602no—
352C23—602no—
353C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
354D4—602no—
355D4—602no—
356D4—604no—
357D4—604no—
358C2×C4—22no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—62no—
362C2×C4—102no—
363C2×C4—122no—
364C2×C4—201no—
365C2×C4—201no—
366C2×C4—201no—
367C2×C4—201no—
368C2×C4—602no—
369C2×C4—602no—
370C2×C4—602no—
371C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—202no—
374C2×C3—22no—
375C2×C3—102no—
376C2×C3—201no—
377C2×C3C2×#399911yescharacteristic
378C2×C3#6576711yescharacteristic
379C2×C3#6578411yescharacteristic
380D3—402no—
381C5#6997811yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—52no—
385C22—101no—
386C22—101no—
387C22—101no—
388C22—101no—
389C22—101no—
390C22—204no—
391C22—602no—
392C22—602no—
393C22—602no—
394C22—1204no—
395C22#9117312yes—
396C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
397C4—21no—
398C4—21no—
399C4—101no—
400C4—101no—
401C4—122no—
402C4—1202no—
403C3#1060426011yescharacteristic, complemented, Sylow
404C2—22no—
405C2—102no—
406C2—201no—
407C2—1202no—
408C2#1175170711yescharacteristic
409C2#1175172311yescharacteristic
410C2C2×#9117311yescharacteristic
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 radicalC2×#91450C2
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752423C2semidirect
3. C3×#65755C2semidirect
4. #11746499C2semidirect
6. C22×D60C4semidirect
11. C2×C5×C4⋊Dic3C4semidirect
15. #91450C4semidirect
18. #91235C22semidirect
20. C3×#4003C22semidirect
24. #65755D3semidirect
68. #4003C2×D3semidirect
110. C2×C4⋊Dic3AGL(1,𝔽5)semidirect
315. C3×C5#1510semidirect
381. C5#69978semidirect
403. C3#10604260semidirect

Maximal subgroups

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

subgroupindex
C2×#914502
#117524232
C3×#657552
#117464992
#106042603
#699785