Finite Group Databasebeta

← #14291225

Subgroups — #14291225

Order 1920.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×C5×#563C211yesmaximal, characteristic
2#11751170C211yesmaximal, characteristic, complemented
3#11751165C211yesmaximal, characteristic, complemented
4#11751156C211yesmaximal, characteristic
5#11746364C211yesmaximal, characteristic, complemented
6#11746364C211yesmaximal, characteristic, complemented
7#11746361C211yesmaximal, characteristic
8#10602750—31nomaximal, Hall
9C3×C5×C4⋊Q8—21no—
10C3×C5×#126—21no—
11C3×C5×#126—21no—
12C3×C5×#125C2211yescharacteristic
13C3×C5×#125C2211yescharacteristic
14C3×C5×#124C2211yescharacteristic
15C3×C5×#123—21no—
16C3×C5×C22⋊Q8—21no—
17C3×C5×C22⋊Q8—21no—
18#91758C2211yescharacteristic
19#91119—21no—
20#91116—21no—
21#91094—21no—
22#91094—21no—
23#91092—21no—
24#91091—21no—
25#91087C2211yescharacteristic
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71957—51nomaximal, Hall
29C5×#563D311yescharacteristic
30#65358—31no—
31#65354—31no—
32#65344—31no—
33#64763—31no—
34#64763—31no—
35#64760—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C2×Dic30—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57C3×C42×C5C2311yescharacteristic
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C3×#563D511yescharacteristic
64#5069—51no—
65#5064—51no—
66#5055—51no—
67#4543—51no—
68#4543—51no—
69#4540—51no—
70C5×C4⋊Q8—21no—
71C5×#126—21no—
72C5×#126—21no—
73C5×#125C2×D311yescharacteristic
74C5×#125C2×D311yescharacteristic
75C5×#124C2×D311yescharacteristic
76C5×#123—21no—
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—21no—
79#4015—31no—
80#3967—61no—
81#3964—61no—
82#3942—61no—
83#3942—61no—
84#3940—61no—
85#3939—61no—
86#3935—31no—
87#3935—31no—
88#3935—31no—
89#1664—151noSylow
90C23×C3×C5—21no—
91C3×C5×Q8—41no—
92C3×C5×Q8—81no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—81no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—41no—
104Dic30—42no—
105C3⋊#168—22no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C3×C4⋊Q8—21no—
109C3×#126—21no—
110C3×#126—21no—
111C3×#125C2×D511yescharacteristic
112C3×#125C2×D511yescharacteristic
113C3×#124C2×D511yescharacteristic
114C3×#123—21no—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—21no—
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#803—51no—
126#803—51no—
127C2×C5×Q8—21no—
128C2×C5×Q8#6711yescharacteristic
129C2×C5×D4#6711yescharacteristic
130C22×C4×C5—21no—
131C2×Dic10—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4#6711yescharacteristic
139C5×C4⋊C4#6711yescharacteristic
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—21no—
146C5×C22⋊C4—21no—
147C42×C5—21no—
148C42×C5C22×D311yescharacteristic
149C4⋊Dic5—61no—
150C4⋊Dic5—61no—
151C2×#168—61no—
152C2×#168—61no—
153C2×#168—61no—
154#563D1511yescharacteristic
155#501—151no—
156#491—151no—
157#489—151no—
158#330—151no—
159#330—151no—
160#329—151no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×C4×C5—41no—
171C3×C4×C5—41no—
172C3×C4×C5—41no—
173Dic15—81no—
174C2×C3×Q8—21no—
175C2×C3×Q8C22⋊D511yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4—21no—
178C2×Dic6—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C4⋊C4C22⋊D511yescharacteristic
187C3×C4⋊C4C22⋊D511yescharacteristic
188C3×C4⋊C4C22⋊D511yescharacteristic
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C42—21no—
195C3×C42C22×D511yescharacteristic
196C4⋊Dic3—101no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—101no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C5×Q8—41no—
203C5×Q8—81no—
204C5×D4—41no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—81no—
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—121no—
215Dic10—122no—
216#168—62no—
217#168—121no—
218#168—121no—
219C4⋊Q8—21no—
220C4⋊Q8—151no—
221#126—21no—
222#126—21no—
223#125C2×D1511yescharacteristic
224#125C2×D1511yescharacteristic
225#124C2×D1511yescharacteristic
226#123—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229#107—301no—
230#106—301no—
231#103—301no—
232#103—301no—
233#103—301no—
234#102—301no—
235#97—151no—
236#97—151no—
237#97—151no—
238C2×C3×C5—81no—
239C2×C3×C5#45411yescharacteristic
240C2×C3×C5#45511yescharacteristic
241C2×C3×C5#45611yescharacteristic
242C23×C3—21no—
243C3×Q8—41no—
244C3×Q8—81no—
245C3×D4—41no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—81no—
252C2×C3×C4C2×C22⋊D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×Dic3—201no—
256Dic6—202no—
257C3⋊C8—102no—
258C3⋊C8—201no—
259C3⋊C8—201no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5#95311yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—41no—
272Dic5—241no—
273C2×Q8—21no—
274C2×Q8—301no—
275C2×Q8#122011yescharacteristic
276C2×D4#122011yescharacteristic
277C22×C4—21no—
278C2×C8—301no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4#122011yescharacteristic
290C4⋊C4#122011yescharacteristic
291C4⋊C4#122011yescharacteristic
292C4⋊C4#122011yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C42—21no—
299C42C22×D1511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3#409911yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—41no—
313Dic3—401no—
314C2×C5—81no—
315C2×C5#524211yescharacteristic
316C2×C5#524511yescharacteristic
317C2×C5#524611yescharacteristic
318C23—21no—
319Q8—41no—
320Q8—81no—
321Q8—602no—
322D4—41no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—601no—
330C2×C4C2×#122011yescharacteristic
331C2×C4C2×#122011yescharacteristic
332C2×C4C2×#122011yescharacteristic
333C8—302no—
334C8—601no—
335C8—601no—
336C2×C3—81no—
337C2×C3#6553111yescharacteristic
338C2×C3#6553411yescharacteristic
339C2×C3#6553511yescharacteristic
340C5#7195711yescharacteristic, complemented, Sylow
341C22—41no—
342C22—41no—
343C22—41no—
344C22#9184211yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1201no—
354C3#1060275011yescharacteristic, complemented, Sylow
355C2—81no—
356C2#1175134311yescharacteristic
357C2#1175134611yescharacteristic
358C2#1175134711yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#563C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#563D15
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #11751170C2semidirect
3. #11751165C2semidirect
5. #11746364C2semidirect
6. #11746364C2semidirect
300. C3×C5#1664semidirect
340. C5#71957semidirect
354. C3#10602750semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5632
#117511702
#117511652
#117511562
#117463642
#117463612
#106027503
#719575