Finite Group Databasebeta

← #14289816

Subgroups — #14289816

Order 1920.

388 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11756343C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3#11751185C211yesmaximal, characteristic
4#11751180C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic
8#10601950—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11#91835—21no—
12#91787—22no—
13#91781—21no—
14#91764—21no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×Dic30—21no—
18C3×C5×#107—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91119—22no—
22#91093—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71157—51nomaximal, Hall
27#65918—31no—
28C5×#477D311yescharacteristic, complemented
29#65373—31no—
30#65370—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×Dic30—21no—
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—22no—
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D412yes—
52#6712—22no—
53C4×Dic15—22no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56#5584—51no—
57C3×#477D511yescharacteristic, complemented
58#5084—51no—
59#5079—51no—
60#4535—51no—
61#4486—51no—
62#4483—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×Q8C2×D311yescharacteristic
65#4092—61no—
66#4044—62no—
67#4038—61no—
68#4021—61no—
69C4×D20—31no—
70#4015—31no—
71C4×Dic10—61no—
72C5×#107—21no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×#103—21no—
75#3967—62no—
76#3941—61no—
77#3940—61no—
78C4⋊#168—31no—
79C4×#168—31no—
80#1638—151noSylow
81C22×D15—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—42no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—22no—
93D60—21no—
94D60—21no—
95C4×D15—41no—
96C4×D15—41no—
97Dic30—41no—
98Dic30—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×C4×Q8C2×D511yescharacteristic
104#946—101no—
105#898—102no—
106#892—101no—
107#875—101no—
108C4×D12—51no—
109#869—51no—
110C4×Dic6—101no—
111C3×#107—21no—
112C3×C4⋊C8C2×D511yescharacteristic
113C3×#103—21no—
114#835—102no—
115#809—101no—
116#808—101no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8#6711yescharacteristic
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4#6711yescharacteristic
129C42×C5—21no—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—32no—
136C4⋊Dic5—61no—
137#683—62no—
138C4×Dic5—62no—
139C2×#168—61no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477D1511yescharacteristic, complemented
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5—81no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—42no—
161Dic15—41no—
162C2×C3×Q8—21no—
163C2×C3×Q8C22⋊D511yescharacteristic
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6—101no—
167C2×C3×C8—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C22⋊D511yescharacteristic
172C3×C42—21no—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—102no—
176(C2×D3)⋊C4—101no—
177C4⋊Dic3—51no—
178C4⋊Dic3—52no—
179C4⋊Dic3—101no—
180Dic3⋊C4—102no—
181C4×Dic3—102no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—42no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—41no—
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—61no—
195C2×Dic5—62no—
196D20—61no—
197D20—61no—
198C4×D5—121no—
199C4×D5—121no—
200Dic10—121no—
201Dic10—121no—
202C5×C8—41no—
203#168—121no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8C2×D1511yescharacteristic
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—301no—
211C4×Q8C2×D1511yescharacteristic
212C4×D4—151no—
213#117—301no—
214#107—21no—
215#106—301no—
216C4⋊C8—151no—
217C4⋊C8C2×D1511yescharacteristic
218#103—21no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—42no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—41no—
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×Dic3—101no—
237C2×Dic3—102no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—201no—
243Dic6—201no—
244C3×C8—41no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5#93711yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—81no—
255C4×C5#91811yescharacteristic
256C4×C5#91911yescharacteristic
257C4×C5#94211yescharacteristic
258C4×C5#95011yescharacteristic
259Dic5—122no—
260Dic5—121no—
261C2×Q8—21no—
262C2×Q8—301no—
263C2×Q8#122011yescharacteristic
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—21no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—152no—
273C4⋊C4—151no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4#122011yescharacteristic
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—21no—
281C42—302no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—81no—
292C3×C4#406411yescharacteristic
293C3×C4#406511yescharacteristic
294C3×C4#408811yescharacteristic
295C3×C4#409611yescharacteristic
296Dic3—201no—
297Dic3—202no—
298C2×C5#504711yescharacteristic
299C2×C5#518711yescharacteristic
300C2×C5#520111yescharacteristic
301D5—241no—
302C23—301no—
303Q8—21no—
304Q8—21no—
305Q8—42no—
306Q8—601no—
307Q8—601no—
308D4—301no—
309D4—301no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—301no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D4×D1511yescharacteristic
318C2×C4D4×D1511yescharacteristic
319C2×C4C2×#122011yescharacteristic
320C8—41no—
321C8—601no—
322C8—601no—
323C2×C3#6533611yescharacteristic
324C2×C3#6547611yescharacteristic
325C2×C3#6549011yescharacteristic
326D3—401no—
327C5#7115711yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9182611yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—602no—
337C4—601no—
338C4#9180711yescharacteristic
339C4#9180811yescharacteristic
340C4#9183111yescharacteristic
341C4#9183911yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1175114811yescharacteristic
345C2#1175128811yescharacteristic
346C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#477D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
4. #11751180C2semidirect
5. #11746356C2semidirect
6. #11746307C2semidirect
28. C5×#477D3semidirect
57. C3×#477D5semidirect
143. #477D15semidirect
283. C3×C5#1638semidirect
327. C5#71157semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
#117563432
C3×C5×#4772
#117511852
#117511802
#117463562
#117463072
#117463042
#106019503
#711575