Finite Group Databasebeta

← #14291249

Subgroups — #14291249

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
1C5×#5699C211yesmaximal, characteristic
2C3×#65354C211yesmaximal, characteristic, complemented
3#11746925C211yesmaximal, characteristic, complemented
4#11746904C211yesmaximal, characteristic
5#11746364C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic
8#10602750—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#898—21no—
11C5×#898—21no—
12C5×#897—21no—
13C5×#896—21no—
14C5×#894—21no—
15C5×#888—21no—
16C5×#875C2211yescharacteristic
17C5×#870C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91087C2211yescharacteristic
20#91087C2211yescharacteristic
21C3×#3940—21no—
22C3×#3939—21no—
23C3×#3935C2211yescharacteristic
24#90972—21no—
25#90970—21no—
26#90970—21no—
27#90966—21no—
28#71394—51nomaximal, Hall
29C5×#563—31no—
30#65358—31no—
31#65354D311yescharacteristic, complemented
32#65344—31no—
33#64763—31no—
34#64763—31no—
35#64760—31no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C5×C4⋊Dic3D411yescharacteristic
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C4×C5×Dic3—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63#5699D511yescharacteristic
64C3×#501—51no—
65#5089—51no—
66#5082—51no—
67#4543—51no—
68#4465—51no—
69#4464—51no—
70C5×C4⋊Q8—61no—
71C5×#126—61no—
72C5×#126—61no—
73C5×#125—31no—
74C5×#125C2×D311yescharacteristic
75C5×#124—31no—
76C5×#123—61no—
77C5×C22⋊Q8—61no—
78C5×C22⋊Q8—61no—
79#4015C2×D311yescharacteristic
80#3967—61no—
81#3964—61no—
82#3942—61no—
83#3942—61no—
84#3940—21no—
85#3939—21no—
86#3935—31no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1664—151noSylow
90C22×C5×D3—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×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C5×D12—41no—
100C4×C5×D3—81no—
101C5×Dic6—41no—
102C5×Dic6—81no—
103C2×C3×Dic5—41no—
104C3×Dic10—42no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C3×#168—22no—
108C3×C4⋊Q8—51no—
109C3×#125C2×D511yescharacteristic
110#898—21no—
111#898—21no—
112#897—21no—
113#896—21no—
114#894—21no—
115#888—21no—
116#875C2×D511yescharacteristic
117#870C2×D511yescharacteristic
118C3×#107—101no—
119C3×#106—101no—
120C3×#97—51no—
121#835—101no—
122#835—101no—
123#810—101no—
124#809—101no—
125#803—51no—
126#803—51no—
127C2×C5×Q8—31no—
128C2×C5×Q8—61no—
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×Dic10—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C5×C22⋊C4—61no—
143C5×C22⋊C4—61no—
144C5×C22⋊C4—61no—
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C42×C5—61no—
148C42×C5C22×D311yescharacteristic
149C4⋊Dic5—21no—
150C4⋊Dic5—21no—
151C2×#168—21no—
152C2×#168—61no—
153C2×#168—61no—
154#563—31no—
155#501—51no—
156#491—151no—
157#489—151no—
158#330—151no—
159#330—151no—
160#329—151no—
161C22×C3×C5#12011yescharacteristic
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×Dic5—81no—
171C5×Dic3—41no—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×Q8—101no—
175C2×D12C22⋊D511yescharacteristic
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×Dic6C22⋊D511yescharacteristic
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3C22⋊D511yescharacteristic
194C4⋊Dic3C22⋊D511yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—61no—
202C5×Q8—121no—
203C5×Q8—241no—
204C5×D4—121no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—61no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5—241no—
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—41no—
215Dic10—42no—
216#168—22no—
217#168—121no—
218#168—121no—
219C4⋊Q8—51no—
220C4⋊Q8—61no—
221#126—61no—
222#126—61no—
223#125—31no—
224#125D3×D511yescharacteristic
225#124—31no—
226#123—61no—
227C22⋊Q8—61no—
228C22⋊Q8—61no—
229#107—101no—
230#106—101no—
231#103—301no—
232#103—301no—
233#103—301no—
234#102—301no—
235#97—51no—
236#97—151no—
237#97—151no—
238C2×C3×C5#45411yescharacteristic
239C2×C3×C5#45511yescharacteristic
240C2×C3×C5#45611yescharacteristic
241C5×D3—81no—
242C22×D3—21no—
243C3×Q8—202no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—201no—
247C2×C3×C4C2×C22⋊D511yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253D12—41no—
254C4×D3—81no—
255Dic6—41no—
256Dic6—81no—
257C3×C8—102no—
258C3⋊C8—201no—
259C3⋊C8—201no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5—121no—
263C22×C5#93711yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5—121no—
270C4×C5—121no—
271C4×C5—121no—
272Dic5—81no—
273C2×Q8—31no—
274C2×Q8—61no—
275C2×Q8—101no—
276C2×D4—31no—
277C22×C4—61no—
278C2×C8—101no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4#120111yescharacteristic
292C4⋊C4#120111yescharacteristic
293C22⋊C4—61no—
294C22⋊C4—61no—
295C22⋊C4—61no—
296C22⋊C4—61no—
297C22⋊C4—61no—
298C42—61no—
299C42C2×D3×D511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3#409911yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—401no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314C2×C5—241no—
315C2×C5#509511yescharacteristic
316C2×C5#520111yescharacteristic
317C2×C5#520211yescharacteristic
318C23—61no—
319Q8—121no—
320Q8—202no—
321Q8—241no—
322D4—121no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—201no—
329C2×C4—241no—
330C2×C4C2×#120111yescharacteristic
331C2×C4D3×C22⋊D511yescharacteristic
332C2×C4D3×C22⋊D511yescharacteristic
333C8—102no—
334C8—601no—
335C8—601no—
336C2×C3#6553111yescharacteristic
337C2×C3#6553411yescharacteristic
338C2×C3#6553511yescharacteristic
339D3—81no—
340C5#7139411yescharacteristic, complemented, Sylow
341C22—121no—
342C22—121no—
343C22—121no—
344C22#9156811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4—401no—
354C3#1060275011yescharacteristic, complemented, Sylow
355C2—241no—
356C2#1174939311yescharacteristic
357C2#1174941611yescharacteristic
358C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
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. C3×#65354C2semidirect
3. #11746925C2semidirect
5. #11746364C2semidirect
6. #11745850C2semidirect
31. #65354D3semidirect
300. C3×C5#1664semidirect
340. C5#71394semidirect
354. C3#10602750semidirect

Maximal subgroups

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

subgroupindex
C5×#56992
C3×#653542
#117469252
#117469042
#117463642
#117458502
#117458472
#106027503
#713945