Finite Group Databasebeta

← #14291252

Subgroups — #14291252

Order 1920.

368 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#66033C211yesmaximal, characteristic
2#11751165C211yesmaximal, characteristic, complemented
3#11746936C211yesmaximal, characteristic, complemented
4#11746893C211yesmaximal, characteristic
5C5×#4543C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic
8#10599171—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4044—21no—
12C3×#4044—21no—
13C3×#4043—21no—
14C3×#4042—21no—
15C3×#4040—21no—
16C3×#4034—21no—
17C3×#4021C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19#91092—21no—
20#91091—21no—
21#91087C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C5×#803C2211yescharacteristic
24#90974—21no—
25#90974—21no—
26#90971—21no—
27#90965—21no—
28#71957—51nomaximal, Hall
29#66033D311yescharacteristic
30#65354—31no—
31#65003—31no—
32#64992—31no—
33C5×#330—31no—
34#64685—31no—
35#64684—31no—
36C2×Dic30—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5D411yescharacteristic
58C3×C4⋊Dic5D411yescharacteristic
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63C3×#563—51no—
64#5069—51no—
65#5064—51no—
66#5055—51no—
67#4543—51no—
68#4543D511yescharacteristic, complemented
69#4540—51no—
70C5×#125C2×D311yescharacteristic
71#4044—21no—
72#4044—21no—
73#4043—21no—
74#4042—21no—
75#4040—21no—
76#4034—21no—
77#4021C2×D311yescharacteristic
78#4016C2×D311yescharacteristic
79#4015—31no—
80C5×#97—31no—
81C5×#97—31no—
82#3953—61no—
83#3948—61no—
84#3948—61no—
85#3948—61no—
86#3940—61no—
87#3939—61no—
88#3935—31no—
89#1664—151noSylow
90C22×C3×D5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—41no—
97Dic30—42no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×D20—41no—
102C3×C4×D5—81no—
103C3×Dic10—41no—
104C3×Dic10—81no—
105C3⋊#168—22no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8—101no—
109C3×#126—101no—
110C3×#126—101no—
111C3×#125—51no—
112C3×#125C2×D511yescharacteristic
113C3×#124—51no—
114C3×#123—101no—
115C3×C22⋊Q8—101no—
116C3×C22⋊Q8—101no—
117#869—51no—
118#835—101no—
119#832—101no—
120#810—101no—
121#810—101no—
122#808—101no—
123#807—101no—
124#803—51no—
125#803C2×D511yescharacteristic
126#803C2×D511yescharacteristic
127C2×D20#6711yescharacteristic
128C2×C4×D5—21no—
129C2×Dic10—21no—
130C2×Dic10—61no—
131C2×Dic10#6711yescharacteristic
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4#6711yescharacteristic
137C5×C4⋊C4#6711yescharacteristic
138C42×C5C22×D311yescharacteristic
139#685—21no—
140#685—21no—
141#685—21no—
142#685—21no—
143#685—21no—
144C4⋊Dic5—21no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147C4⋊Dic5#6711yescharacteristic
148C4⋊Dic5#6711yescharacteristic
149#683—21no—
150#683—21no—
151#683—21no—
152C4×Dic5—21no—
153C2×#168—61no—
154#563—51no—
155#501—151no—
156#491—151no—
157#489—151no—
158#330—31no—
159#330—151no—
160#329—151no—
161C22×C3×C5#12011yescharacteristic
162C2×C3×D5—41no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170Dic15—81no—
171C3×Dic5—41no—
172C3×Dic5—41no—
173C3×Dic5—41no—
174C2×C3×Q8—51no—
175C2×C3×Q8—101no—
176C2×C3×D4—51no—
177C22×C3×C4—101no—
178C2×Dic6—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4D2011yescharacteristic
188C3×C4⋊C4D2011yescharacteristic
189C3×C22⋊C4—101no—
190C3×C22⋊C4—101no—
191C3×C22⋊C4—101no—
192C3×C22⋊C4—101no—
193C3×C22⋊C4—101no—
194C3×C42—101no—
195C3×C42C22×D511yescharacteristic
196C4⋊Dic3—101no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C22×D5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5C2×#6711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×Dic5—21no—
208C2×Dic5—21no—
209C2×Dic5—21no—
210C2×Dic5—121no—
211D20—41no—
212C4×D5—81no—
213Dic10—41no—
214Dic10—81no—
215Dic10—122no—
216C5×C8—121no—
217C5×C8—121no—
218#168—62no—
219C4⋊Q8—101no—
220C4⋊Q8—151no—
221#126—101no—
222#126—101no—
223#125—51no—
224#125D3×D511yescharacteristic
225#124—51no—
226#123—101no—
227C22⋊Q8—101no—
228C22⋊Q8—101no—
229#107—301no—
230#106—301no—
231#103—301no—
232#103—301no—
233#103—301no—
234#102—301no—
235#97—31no—
236#97—31no—
237#97—151no—
238C2×C3×C5#45411yescharacteristic
239C2×C3×C5#45511yescharacteristic
240C2×C3×C5#45611yescharacteristic
241C3×D5—81no—
242C23×C3—101no—
243C3×Q8—201no—
244C3×Q8—401no—
245C3×D4—201no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—401no—
252C2×C3×C4C2×D2011yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×Dic3—201no—
256Dic6—202no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C3⋊C8—102no—
260C22×C5#95311yescharacteristic
261C2×D5—41no—
262C2×D5—41no—
263C2×D5—41no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—41no—
269Dic5—41no—
270Dic5—41no—
271Dic5—41no—
272Dic5—241no—
273C2×Q8—51no—
274C2×Q8—101no—
275C2×Q8—301no—
276C2×D4—51no—
277C22×C4—101no—
278C2×C8—61no—
279C2×C8—61no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—51no—
284C4⋊C4—51no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#120211yescharacteristic
292C4⋊C4#120211yescharacteristic
293C22⋊C4—101no—
294C22⋊C4—101no—
295C22⋊C4—101no—
296C22⋊C4—101no—
297C22⋊C4—101no—
298C42—101no—
299C42C2×D3×D511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3—201no—
302C22×C3—201no—
303C22×C3—201no—
304C22×C3#402811yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—201no—
311C3×C4—201no—
312C3×C4—201no—
313Dic3—401no—
314C2×C5#524211yescharacteristic
315C2×C5#524511yescharacteristic
316C2×C5#524611yescharacteristic
317D5—81no—
318C23—101no—
319Q8—201no—
320Q8—401no—
321Q8—602no—
322D4—201no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—401no—
329C2×C4—601no—
330C2×C4C2×#120211yescharacteristic
331C2×C4D5×#6711yescharacteristic
332C2×C4D5×#6711yescharacteristic
333C8—121no—
334C8—121no—
335C8—302no—
336C2×C3—401no—
337C2×C3#6504111yescharacteristic
338C2×C3#6511411yescharacteristic
339C2×C3#6511611yescharacteristic
340C5#7195711yescharacteristic, complemented, Sylow
341C22—201no—
342C22—201no—
343C22—201no—
344C22#9156411yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—201no—
351C4—201no—
352C4—201no—
353C4—1201no—
354C3#1059917111yescharacteristic, complemented, Sylow
355C2—401no—
356C2#1174939111yescharacteristic
357C2#1174945711yescharacteristic
358C2#1174946311yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenter#125D3×D5
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #11751165C2semidirect
3. #11746936C2semidirect
5. C5×#4543C2semidirect
6. #11745849C2semidirect
68. #4543D5semidirect
300. C3×C5#1664semidirect
340. C5#71957semidirect
354. C3#10599171semidirect

Maximal subgroups

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

subgroupindex
C3×#660332
#117511652
#117469362
#117468932
C5×#45432
#117458492
#117458462
#105991713
#719575