Finite Group Databasebeta

← #14289810

Subgroups — #14289810

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#11756491C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic, complemented
8#10602022—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91836—21no—
12Q8×Dic15—21no—
13#91787—22no—
14#91786—21no—
15#91781—21no—
16C4×D60C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×#103—22no—
19C3×C4×C5×C8C2211yescharacteristic
20#91094—21no—
21#91093—21no—
22#91092—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71229—51nomaximal, Hall
27#66066—31no—
28C5×#487D311yescharacteristic, complemented
29#65380—31no—
30#65373—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45#6714—22no—
46#6714—22no—
47#6714—21no—
48C4⋊Dic15—22no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—22no—
53C4×Dic15—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56#5732—51no—
57C3×#487D511yescharacteristic, complemented
58#5091—51no—
59#5084—51no—
60#4547—51no—
61#4459—51no—
62#4456—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×C4⋊Q8C2×D311yescharacteristic
65#4093—61no—
66Q8×Dic5—61no—
67#4044—62no—
68#4043—61no—
69#4038—61no—
70C4×D20—31no—
71C4×Dic10—31no—
72C5×#103—22no—
73C4×C5×C8C2×D311yescharacteristic
74#3942—61no—
75#3941—61no—
76#3940—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
80#1638—151noSylow
81C22×D15—21no—
82C3×C5×Q8—42no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93D60—21no—
94D60—21no—
95C4×D15—41no—
96C4×D15—41no—
97Dic30—21no—
98Dic30—21no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×C4⋊Q8C2×D511yescharacteristic
104#947—101no—
105Q8×Dic3—101no—
106#898—102no—
107#897—101no—
108#892—101no—
109C4×D12—51no—
110C4×Dic6—51no—
111C3×#103—22no—
112C3×C4×C8C2×D511yescharacteristic
113#810—101no—
114#809—101no—
115#808—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8—21no—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—31no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4#6712yes—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131#685—62no—
132#685—61no—
133C4⋊Dic5—31no—
134C4⋊Dic5—31no—
135C4⋊Dic5—62no—
136#683—61no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—61no—
140C2×#168—61no—
141#556—151no—
142#487D1511yescharacteristic, complemented
143#477—151no—
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—42no—
154C3×C4×C5—81no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160Dic15—41no—
161Dic15—41no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6—51no—
167C2×C3×C8—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C22⋊D512yes—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—101no—
176C4⋊Dic3—51no—
177C4⋊Dic3—51no—
178C4⋊Dic3—102no—
179Dic3⋊C4—101no—
180C4×Dic3—102no—
181C4×Dic3—101no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—42no—
186C5×Q8—41no—
187C5×Q8—41no—
188C2×C4×C5—22no—
189C2×C4×C5—41no—
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5—61no—
196D20—61no—
197D20—61no—
198C4×D5—121no—
199C4×D5—121no—
200Dic10—61no—
201Dic10—61no—
202C5×C8—41no—
203#168—121no—
204#168—121no—
205C4⋊Q8C2×D1511yescharacteristic
206C4⋊Q8C2×D1511yescharacteristic
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—151no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8—151no—
217C4⋊C8—151no—
218#103—22no—
219#103—301no—
220#102—301no—
221C4×C8C2×D1511yescharacteristic
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—42no—
228C3×Q8—41no—
229C3×Q8—41no—
230C2×C3×C4—22no—
231C2×C3×C4—41no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—101no—
236C2×Dic3—101no—
237C2×Dic3—101no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—101no—
243Dic6—101no—
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—42no—
253C4×C5—81no—
254C4×C5#91511yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#91811yescharacteristic
257C4×C5#91911yescharacteristic
258Dic5—121no—
259Dic5—121no—
260Dic5—121no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—151no—
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—151no—
273C4⋊C4—151no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4#122012yes—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—302no—
281C42—301no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—42no—
290C3×C4—81no—
291C3×C4#406111yescharacteristic
292C3×C4#406211yescharacteristic
293C3×C4#406411yescharacteristic
294C3×C4#406511yescharacteristic
295Dic3—201no—
296Dic3—201no—
297Dic3—201no—
298C2×C5#506211yescharacteristic
299C2×C5#517311yescharacteristic
300C2×C5#518711yescharacteristic
301D5—241no—
302C23—301no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—301no—
307Q8—301no—
308D4—301no—
309D4—301no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D4×D1511yescharacteristic
318C2×C4D4×D1511yescharacteristic
319C2×C4C2×#122011yescharacteristic
320C8—41no—
321C8—601no—
322C8—601no—
323C2×C3#6535111yescharacteristic
324C2×C3#6546211yescharacteristic
325C2×C3#6547611yescharacteristic
326D3—401no—
327C5#7122911yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9182611yescharacteristic
332C4—21no—
333C4—42no—
334C4—81no—
335C4—601no—
336C4—601no—
337C4—601no—
338C4#9180411yescharacteristic
339C4#9180511yescharacteristic
340C4#9180711yescharacteristic
341C4#9180811yescharacteristic
342C3#1060202211yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1175116311yescharacteristic
345C2#1175127411yescharacteristic
346C2#1175128811yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#487C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#487D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C3×C5×#487C2semidirect
3. #11751192C2semidirect
5. #11746368C2semidirect
7. #11746277C2semidirect
28. C5×#487D3semidirect
57. C3×#487D5semidirect
142. #487D15semidirect
283. C3×C5#1638semidirect
327. C5#71229semidirect
342. C3#10602022semidirect

Maximal subgroups

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

subgroupindex
#117564912
C3×C5×#4872
#117511922
#117511852
#117463682
#117462802
#117462772
#106020223
#712295