Finite Group Databasebeta

← #14285307

Subgroups — #14285307

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66050C211yesmaximal, characteristic
2#11747007C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4#11746365C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599181—31nomaximal, Hall
9C2×C3×#711—21no—
10C3×C5×#127C2211yescharacteristic
11C3×#4084—21no—
12C3×#4084C412yes—
13C3×#4082—21no—
14C3×D4×Dic5—21no—
15C3×D4×Dic5C412yes—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6649—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90982—21no—
24#90955—21no—
25#90952—21no—
26#71809—51nomaximal, Hall
27#66050D311yescharacteristic
28#65126—31no—
29#65124—31no—
30C5×#331—31no—
31#64764—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C412yes—
37C2×C3×C22⋊D5—22no—
38C22×C3×Dic5—22no—
39C3×#711—42no—
40C3×#711—42no—
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×Dic10—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—22no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C412yes—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57#6649—42no—
58C3×#532—51no—
59#4926—51no—
60#4924—51no—
61#4547—51no—
62#4547—51no—
63#4544—51no—
64#4544D511yescharacteristic, complemented
65C2×#711—21no—
66C5×#127C2×D311yescharacteristic
67#4084—21no—
68#4084Dic312yes—
69#4082—21no—
70D4×Dic5—21no—
71D4×Dic5Dic312yes—
72C2×#676—61no—
73C42×D5C2×D311yescharacteristic
74#4015C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3952—61no—
78#3947—61no—
79#3946—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82#1557—151noSylow
83C23×C3×C5—22no—
84C22×C3×D5C22⋊C411yescharacteristic
85C3×C5×D4—42no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C3×C22⋊D5—44no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5—44no—
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C22⋊C411yescharacteristic
98C2×C3×Dic5C22⋊C411yescharacteristic
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×C4×D5—41no—
104C3×Dic10—41no—
105C3×Dic10—41no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C5×C3⋊C8—41no—
109C5×C3⋊C8—41no—
110C2×C3×#41—101no—
111C3×C4⋊Q8—51no—
112C3×#127C2×D511yescharacteristic
113C3×#124—101no—
114C3×#121—52no—
115C3×#121—101no—
116C3×C4×D4—52no—
117C3×C4×D4—101no—
118C2×C3×C42—51no—
119C2×#208—101no—
120#830—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126#803—101no—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4C2×Dic312yes—
130C2×C22⋊D5—22no—
131C22×Dic5—22no—
132#711—42no—
133#711—42no—
134C2×C4×D5C2×Dic311yescharacteristic
135C2×C4×D5#6711yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×Dic10—21no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140C42×C5C22×D311yescharacteristic
141C22⋊Dic5—22no—
142C22⋊Dic5—22no—
143C4⋊Dic5—21no—
144C4⋊Dic5C2×Dic312yes—
145C4×Dic5C2×Dic311yescharacteristic
146C4×Dic5#6711yescharacteristic
147C4×Dic5#6711yescharacteristic
148C2×#168—61no—
149C2×#168—61no—
150#676—122no—
151#532—51no—
152#432—151no—
153#423—151no—
154#332—151no—
155#332—151no—
156#331—31no—
157#331—151no—
158C22×C3×C5—42no—
159C22×C3×C5—42no—
160C22×C3×C5—42no—
161C22×C3×C5C2×C22⋊C411yescharacteristic
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C3×C4×C5—21no—
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5—42no—
174C3×#41—202no—
175C3×#41—202no—
176C2×C3×Q8—101no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—102no—
180C2×C3×D4C4×D512yes—
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C22×C3×C4—102no—
185C3×C4⋊C4—52no—
186C3×C4⋊C4—101no—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—102no—
189C3×C42—51no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42C22×D511yescharacteristic
193#208—202no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—101no—
197C2×C3⋊C8—101no—
198C23×C5—22no—
199C22×D5#21711yescharacteristic
200C5×D4—42no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C2×C4×C5C22×Dic311yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C22⋊D5—44no—
209C2×Dic5—22no—
210C2×Dic5—44no—
211C2×Dic5#21711yescharacteristic
212C2×Dic5#21711yescharacteristic
213C2×Dic5#21711yescharacteristic
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—21no—
218C4×D5—41no—
219Dic10—41no—
220Dic10—41no—
221C5×C8—121no—
222C5×C8—121no—
223#168—121no—
224#168—121no—
225C2×#41—101no—
226C2×M16—301no—
227C4⋊Q8—51no—
228#127D3×D511yescharacteristic
229#124—101no—
230#121—52no—
231#121—101no—
232C4×D4—52no—
233C4×D4—101no—
234C2×C42—51no—
235C4⋊C8—31no—
236C4⋊C8—31no—
237C4⋊C8—151no—
238C4⋊C8—151no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—301no—
242C2×C3×C5—82no—
243C2×C3×C5#41311yescharacteristic
244C2×C3×C5#41711yescharacteristic
245C2×C3×C5#41811yescharacteristic
246C3×D5—41no—
247C23×C3—22no—
248C23×C3—51no—
249C3×Q8—201no—
250C3×Q8—201no—
251C3×D4—42no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—204no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—101no—
261C2×C3×C4—101no—
262C2×C3×C4—101no—
263C2×C3×C4—101no—
264C2×C3×C4—102no—
265C2×C3×C4—201no—
266C2×C3×C4—204no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C3⋊C8—41no—
271C3⋊C8—41no—
272C3⋊C8—201no—
273C3⋊C8—201no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5C2×#21711yescharacteristic
278C2×D5—21no—
279C2×D5—21no—
280C2×D5—21no—
281C4×C5—21no—
282C4×C5#93211yescharacteristic
283C4×C5#93211yescharacteristic
284C4×C5#94911yescharacteristic
285C4×C5#95111yescharacteristic
286Dic5—21no—
287Dic5—21no—
288Dic5—21no—
289Dic5—42no—
290#41—202no—
291#41—202no—
292C2×Q8—101no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—102no—
296C2×D4D5×Dic312yes—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—102no—
301M16—602no—
302C2×C8—61no—
303C2×C8—61no—
304C2×C8—301no—
305C2×C8—301no—
306C4⋊C4—52no—
307C4⋊C4—101no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42C2×D3×D511yescharacteristic
314C3×C5#155711yescharacteristic, complemented, Hall
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—101no—
319C22×C3—101no—
320C22×C3—101no—
321C22×C3D5×C22⋊C411yescharacteristic
322C3×C4—21no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—101no—
326C3×C4—202no—
327C3×C4#405711yescharacteristic
328C3×C4#405711yescharacteristic
329C3×C4#406011yescharacteristic
330C3×C4#406111yescharacteristic
331C2×C5—82no—
332C2×C5#521511yescharacteristic
333C2×C5#523211yescharacteristic
334C2×C5#523711yescharacteristic
335D5—41no—
336C23—22no—
337C23—51no—
338Q8—201no—
339Q8—201no—
340D4—42no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—41no—
345D4—204no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—102no—
354C2×C4—201no—
355C2×C4—204no—
356C2×C4C2×D5×Dic311yescharacteristic
357C2×C4D5×#6711yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C8—121no—
360C8—121no—
361C8—601no—
362C8—601no—
363C2×C3—82no—
364C2×C3—201no—
365C2×C3#6503411yescharacteristic
366C2×C3#6505911yescharacteristic
367C2×C3#6506011yescharacteristic
368C5#7180911yescharacteristic, complemented, Sylow
369C22—42no—
370C22—42no—
371C22—42no—
372C22—101no—
373C22—101no—
374C22—101no—
375C22D5×#21711yescharacteristic
376C4—21no—
377C4—101no—
378C4—101no—
379C4—101no—
380C4—202no—
381C4#9147811yescharacteristic
382C4#9148411yescharacteristic
383C4#9148911yescharacteristic
384C4#9149111yescharacteristic
385C3#1059918111yescharacteristic, complemented, Sylow
386C2—82no—
387C2—201no—
388C2#1174895111yescharacteristic
389C2#1174896211yescharacteristic
390C2#1174912311yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66050C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1557
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11747007C2semidirect
3. #11746871C2semidirect
4. #11746365C2semidirect
5. C5×#4544C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
64. #4544D5semidirect
314. C3×C5#1557semidirect
368. C5#71809semidirect
385. C3#10599181semidirect

Maximal subgroups

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

subgroupindex
C3×#660502
#117470072
#117468712
#117463652
C5×#45442
#117458562
#117458552
#105991813
#718095