Finite Group Databasebeta

← #14285162

Subgroups — #14285162

Order 1920.

484 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752671C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic, complemented
3C3×#65678C211yesmaximal, characteristic, complemented
4#11746509C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10604410—31nomaximal, Hall
7C2×#6771—21no—
8C4×D60C411yescharacteristic
9C4×C5×D12C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91468C2211yescharacteristic
12#91451C2211yescharacteristic
13#91450C411yescharacteristic
14#91449C411yescharacteristic
15#91448—21no—
16C4×#1203—21no—
17#91350—21no—
18#91233C2212yes—
19#91232—21no—
20#91231—21no—
21C3×#4004C2212yes—
22C3×#4003—21no—
23C3×C4×#170—21no—
24#70775—51nomaximal, Hall
25#65882—31no—
26#65684—31no—
27#65678D311yescharacteristic, complemented
28#64925—32no—
29#64873—32no—
30C2×D60C2×C411yescharacteristic
31C2×C4×D15—21no—
32C2×C5×D12C2×C411yescharacteristic
33C2×C4×C5×D3—21no—
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1202—21no—
41C2×#1201—21no—
42#6771—44no—
43C2×C3⋊#170—22no—
44C2×C3×#170—22no—
45C3×C42×C5C2×C411yescharacteristic
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5C2311yescharacteristic
53#6668—21no—
54#6667—21no—
55(C2×D3)⋊Dic5—21no—
56#5477—51no—
57C3×#431—51no—
58#4926—51no—
59#4485—52no—
60#4482—52no—
61C2×#709—61no—
62C4×C5×D4—31no—
63#4086—31no—
64#4084—31no—
65C4×C22⋊D5—61no—
66#4041—31no—
67#4034—31no—
68#4031—61no—
69#4030—61no—
70C4×D20—31no—
71C42×D5C2×D311yescharacteristic
72#4004—32no—
73#4004C2×D312yes—
74#4003—21no—
75#4003—61no—
76#4002—61no—
77C4×#170—21no—
78#1553—151noSylow
79C22×D15—21no—
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—
86D60—41no—
87C4×D15—42no—
88C2×C5×Dic3—21no—
89C5×D12—41no—
90C4×C5×D3—42no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5—22no—
95C3×C4×D5—22no—
96C3×C4×D5—41no—
97#1204—42no—
98#1203—42no—
99#1203—42no—
100#1202—42no—
101#1201—42no—
102C3⋊#170—42no—
103C3×#170—42no—
104C2×#235—101no—
105C2×C3×C42—51no—
106#930—51no—
107#930—51no—
108#930—101no—
109#875—101no—
110#874—51no—
111C4×D12—51no—
112C4×D12—101no—
113C4×D12AGL(1,𝔽5)11yescharacteristic
114#869—51no—
115C3×C4⋊C8—52no—
116C3×C22⋊C8—101no—
117C3×C4×C8—101no—
118#830—101no—
119C4⋊(C3⋊C8)—52no—
120#803—101no—
121C2×C5×D4—31no—
122C22×C4×C5—61no—
123C2×C22⋊D5—61no—
124C2×C22⋊D5—61no—
125C2×C22⋊D5—61no—
126#709—124no—
127C2×D20—31no—
128C2×D20—61no—
129C2×C4×D5—61no—
130C2×C4×D5C4×D311yescharacteristic
131C2×C4×D5D1211yescharacteristic
132C2×C4×D5#6711yescharacteristic
133C2×Dic10—61no—
134C2×#170—22no—
135C2×#170—62no—
136C5×C4⋊C4—31no—
137C5×C22⋊C4—61no—
138C42×C5C4×D311yescharacteristic
139C22⋊Dic5—61no—
140#685—61no—
141#685—61no—
142C4⋊Dic5—31no—
143#683—61no—
144C4×Dic5D1211yescharacteristic
145C4×Dic5#6711yescharacteristic
146C4×Dic5C22×D311yescharacteristic
147#532—151no—
148#432—151no—
149#431—51no—
150#332—152no—
151#331—152no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165Dic15—41no—
166C3×Dic5—21no—
167C3×Dic5#13512yes—
168C3×Dic5AGL(1,ℤ/8)12yes—
169C5×Dic3—41no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C2×#67—101no—
174C2×#67—101no—
175#235—204no—
176C2×D12—51no—
177C2×D12—101no—
178C2×D12—101no—
179C2×D12C2×AGL(1,𝔽5)11yescharacteristic
180C2×C4×D3—21no—
181C2×C4×D3—101no—
182C2×Dic6—101no—
183C2×C3×C8—102no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42C2×AGL(1,𝔽5)11yescharacteristic
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—101no—
190(C2×D3)⋊C4—101no—
191(C2×D3)⋊C4—101no—
192C4⋊Dic3—51no—
193C4⋊Dic3—101no—
194C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
195C2×C3⋊C8—102no—
196C23×C5—61no—
197C22×D5—61no—
198C22×D5(C2×D3)⋊C411yescharacteristic
199C5×D4—121no—
200C2×C4×C5—61no—
201C2×C4×C5—122no—
202C2×C4×C5(C2×D3)⋊C411yescharacteristic
203C2×C4×C5(C2×D3)⋊C411yescharacteristic
204C2×C4×C5C2×C4×D311yescharacteristic
205C22⋊D5—122no—
206C22⋊D5—122no—
207C22⋊D5—122no—
208C2×Dic5—61no—
209C2×Dic5(C2×D3)⋊C411yescharacteristic
210C2×Dic5C2×D1211yescharacteristic
211C2×Dic5C2×#6711yescharacteristic
212D20—121no—
213D20—122no—
214C4×D5—22no—
215C4×D5—22no—
216C4×D5—41no—
217C4×D5—122no—
218Dic10—122no—
219#170—42no—
220#170—122no—
221C2×#41—301no—
222C4⋊Q8—151no—
223#127—151no—
224#124—301no—
225#121—151no—
226#121—151no—
227#121—301no—
228C4×D4—31no—
229C4×D4—151no—
230C4×D4—301no—
231C2×C42—51no—
232C4⋊C8—52no—
233C4⋊C8—152no—
234C22⋊C8—101no—
235C22⋊C8—301no—
236#97—301no—
237C4×C8—101no—
238C2×C3×C5#41311yescharacteristic
239C2×C3×C5#41611yescharacteristic
240C2×C3×C5#41811yescharacteristic
241D15—81no—
242C3×D5—41no—
243C5×D3—81no—
244C23×C3—51no—
245C22×D3—21no—
246C22×D3—101no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—102no—
251C2×C3×C4—102no—
252C2×C3×C4—201no—
253C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
254C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
255C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
256#67—202no—
257#67—202no—
258C2×Dic3—21no—
259C2×Dic3—101no—
260D12—41no—
261D12—201no—
262D12—202no—
263D12—202no—
264C4×D3—42no—
265C4×D3—202no—
266Dic6—202no—
267C3×C8—202no—
268C3⋊C8—202no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5—121no—
272C22×C5C2×(C2×D3)⋊C411yescharacteristic
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—121no—
277C2×D5—121no—
278C2×D5—121no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—121no—
283Dic5—21no—
284Dic5—121no—
285Dic5#90412yes—
286Dic5#94912yes—
287#41—604no—
288C2×Q8—301no—
289C2×D4—31no—
290C2×D4—151no—
291C2×D4—301no—
292C2×D4—301no—
293C2×D4—301no—
294C2×D4—301no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—61no—
299C22×C4—301no—
300C2×C8—102no—
301C2×C8—302no—
302C4⋊C4—31no—
303C4⋊C4—151no—
304C4⋊C4—301no—
305C22⋊C4—61no—
306C22⋊C4—301no—
307C22⋊C4—301no—
308C22⋊C4—301no—
309C42—51no—
310C42—51no—
311C42—51no—
312C42D3×AGL(1,𝔽5)11yescharacteristic
313C3×C5#155311yescharacteristic, complemented, Hall
314C22×C3—101no—
315C22×C3—101no—
316C22×C3—101no—
317C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—201no—
322C2×D3—201no—
323C2×D3—201no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—52no—
328C3×C4—52no—
329C3×C4—101no—
330Dic3—41no—
331Dic3—201no—
332C2×C5—241no—
333C2×C5#500111yescharacteristic
334C2×C5#511311yescharacteristic
335C2×C5#513211yescharacteristic
336D5—41no—
337D5—241no—
338C23—51no—
339C23—61no—
340C23—301no—
341Q8—602no—
342D4—121no—
343D4—601no—
344D4—602no—
345D4—602no—
346D4—602no—
347D4—602no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—51no—
351C2×C4—61no—
352C2×C4—102no—
353C2×C4—102no—
354C2×C4—122no—
355C2×C4—201no—
356C2×C4—301no—
357C2×C4—602no—
358C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
359C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
360C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
361C8—202no—
362C8—602no—
363C2×C3—201no—
364C2×C3#6576111yescharacteristic
365C2×C3#6576711yescharacteristic
366C2×C3#6579411yescharacteristic
367D3—81no—
368D3—401no—
369C5#7077511yescharacteristic, complemented, Sylow
370C22—101no—
371C22—101no—
372C22—101no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—52no—
384C4—52no—
385C4—101no—
386C4—121no—
387C4—601no—
388C3#1060441011yescharacteristic, complemented, Sylow
389C2—201no—
390C2—241no—
391C2—1201no—
392C2#1175170411yescharacteristic
393C2#1175170611yescharacteristic
394C2#1175181811yescharacteristic
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#11752671C2
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752343C2semidirect
3. C3×#65678C2semidirect
4. #11746509C2semidirect
5. #11746508C2semidirect
27. #65678D3semidirect
313. C3×C5#1553semidirect
369. C5#70775semidirect
388. C3#10604410semidirect

Maximal subgroups

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

subgroupindex
#117526712
#117523432
C3×#656782
#117465092
#117465082
#106044103
#707755