Finite Group Databasebeta

← #14285157

Subgroups — #14285157

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66059C211yesmaximal, characteristic
2#11746871C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746368C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599219—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093—21no—
12C3×#4041—21no—
13C3×#4041C412yes—
14C3×#4039—21no—
15C3×#4039C412yes—
16C3×#4020C2211yescharacteristic
17C3×C42×D5C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90955—21no—
23#90955—21no—
24#90952—21no—
25Dic5×C3⋊C8—21no—
26#71808—51nomaximal, Hall
27#66059D311yescharacteristic
28#65124—31no—
29#65122—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705—31no—
34C2×C3×C5×Q8—21no—
35C3×#713—42no—
36C3×#713—42no—
37C2×C3×D20—22no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×C3×C4×D5—22no—
42C2×C3×C4×D5C2×C411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C412yes—
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—22no—
53C3×#685—22no—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57C3×#532—51no—
58#4926—51no—
59#4925—51no—
60#4547—51no—
61#4547D511yescharacteristic, complemented
62#4544—51no—
63#4544—51no—
64C2×#713—21no—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4093—21no—
67#4041—21no—
68#4041Dic312yes—
69#4039—21no—
70#4039Dic312yes—
71#4020C2×D311yescharacteristic
72C42×D5C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3952—61no—
77#3947—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1553—151noSylow
82C22×C3×D5—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C3×D20—42no—
94C3×D20—44no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×C4×D5—41no—
104C3×C4×D5—44no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C5×C3⋊C8—41no—
108C5×C3⋊C8—41no—
109C2×C3×#41—101no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#127—51no—
112C3×#124—101no—
113C3×#121—52no—
114C3×#121—101no—
115C3×C4×D4—52no—
116C3×C4×D4—101no—
117C2×C3×C42—51no—
118#830—101no—
119#830—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124#803—101no—
125C4×C3⋊C8—101no—
126C2×C5×Q8—21no—
127#713—42no—
128#713—42no—
129C2×D20—22no—
130C2×D20—21no—
131C2×D20—21no—
132C2×D20C2×Dic312yes—
133C2×C4×D5—22no—
134C2×C4×D5C2×Dic311yescharacteristic
135C2×C4×D5#6711yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4C2×Dic312yes—
141C42×C5C22×D311yescharacteristic
142#685—22no—
143#685—22no—
144C4×Dic5C2×Dic311yescharacteristic
145C4×Dic5#6711yescharacteristic
146C4×Dic5#6711yescharacteristic
147C2×#168—61no—
148C2×#168—61no—
149#532—51no—
150#432—151no—
151#431—151no—
152#332—31no—
153#332—151no—
154#331—151no—
155#331—151no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C2×C3×D5—42no—
161C2×C3×D5—42no—
162C2×C3×D5—42no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×#41—202no—
173C3×#41—202no—
174C2×C3×Q8—21no—
175C2×C3×D4—52no—
176C2×C3×D4—102no—
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4—102no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C4×D512yes—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42—51no—
190C3×C42C22×D511yescharacteristic
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C22×D5—22no—
196C22×D5#21711yescharacteristic
197C5×Q8—41no—
198C5×Q8—41no—
199C2×C4×C5—22no—
200C2×C4×C5C22×Dic311yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5#21711yescharacteristic
204C2×Dic5#21711yescharacteristic
205C2×Dic5#21711yescharacteristic
206D20—42no—
207D20—44no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—41no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—41no—
217C4×D5—44no—
218C5×C8—121no—
219C5×C8—121no—
220#168—121no—
221#168—121no—
222C2×#41—101no—
223C4⋊Q8D3×D511yescharacteristic
224#127—51no—
225#124—101no—
226#121—52no—
227#121—101no—
228C4×D4—52no—
229C4×D4—101no—
230C2×C42—51no—
231C4⋊C8—31no—
232C4⋊C8—31no—
233C4⋊C8—151no—
234C4⋊C8—151no—
235C22⋊C8—301no—
236C22⋊C8—301no—
237#97—301no—
238C4×C8—301no—
239C2×C3×C5#41311yescharacteristic
240C2×C3×C5#41611yescharacteristic
241C2×C3×C5#41811yescharacteristic
242C3×D5—41no—
243C3×D5—82no—
244C23×C3—51no—
245C23×C3—102no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—202no—
249C3×D4—204no—
250C3×D4—201no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C2×C3×C4—22no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—201no—
263C2×C3×C4—204no—
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C3⋊C8—41no—
268C3⋊C8—41no—
269C3⋊C8—201no—
270C3⋊C8—201no—
271C22×C5C2×#21711yescharacteristic
272C2×D5—21no—
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—42no—
276C2×D5—42no—
277C2×D5—42no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5#93211yescharacteristic
281C4×C5#93211yescharacteristic
282C4×C5#95011yescharacteristic
283C4×C5#95011yescharacteristic
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287#41—202no—
288#41—202no—
289C2×Q8—21no—
290C2×D4—52no—
291C2×D4—102no—
292C2×D4—101no—
293C2×D4—101no—
294C22×C4—51no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—102no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—301no—
301C2×C8—301no—
302C4⋊C4—21no—
303C4⋊C4D5×Dic312yes—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42C2×D3×D511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3—101no—
312C22×C3—101no—
313C22×C3—101no—
314C22×C3—202no—
315C22×C3—202no—
316C22×C3—202no—
317C22×C3D5×C22⋊C411yescharacteristic
318C3×C4—21no—
319C3×C4—42no—
320C3×C4—101no—
321C3×C4—101no—
322C3×C4—101no—
323C3×C4#405711yescharacteristic
324C3×C4#406011yescharacteristic
325C3×C4#406211yescharacteristic
326C3×C4#406511yescharacteristic
327C2×C5#521511yescharacteristic
328C2×C5#523311yescharacteristic
329C2×C5#523711yescharacteristic
330D5—41no—
331D5—82no—
332C23—51no—
333C23—102no—
334Q8—41no—
335Q8—41no—
336D4—202no—
337D4—204no—
338D4—201no—
339D4—201no—
340D4—201no—
341D4—201no—
342C2×C4—22no—
343C2×C4—51no—
344C2×C4—51no—
345C2×C4—51no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—201no—
351C2×C4—204no—
352C2×C4C2×D5×Dic311yescharacteristic
353C2×C4D5×#6711yescharacteristic
354C2×C4D5×#6711yescharacteristic
355C8—121no—
356C8—121no—
357C8—601no—
358C8—601no—
359C2×C3—201no—
360C2×C3—402no—
361C2×C3#6504011yescharacteristic
362C2×C3#6505911yescharacteristic
363C2×C3#6509311yescharacteristic
364C5#7180811yescharacteristic, complemented, Sylow
365C22—101no—
366C22—101no—
367C22—101no—
368C22—202no—
369C22—202no—
370C22—202no—
371C22D5×#21711yescharacteristic
372C4—21no—
373C4—42no—
374C4—101no—
375C4—101no—
376C4—101no—
377C4#9148911yescharacteristic
378C4#9149111yescharacteristic
379C4#9151411yescharacteristic
380C4#9151611yescharacteristic
381C3#1059921911yescharacteristic, complemented, Sylow
382C2—201no—
383C2—402no—
384C2#1174896211yescharacteristic
385C2#1174920711yescharacteristic
386C2#1174936911yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11746871C2semidirect
3. #11746869C2semidirect
4. #11746368C2semidirect
5. C5×#4547C2semidirect
6. #11745852C2semidirect
7. #11745852C2semidirect
61. #4547D5semidirect
310. C3×C5#1553semidirect
364. C5#71808semidirect
381. C3#10599219semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
#117468712
#117468692
#117463682
C5×#45472
#117458522
#105992193
#718085