Finite Group Databasebeta

← #14289402

Subgroups — #14289402

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5585C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11747081C211yesmaximal, characteristic
4#11746959C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11745853C211yesmaximal, characteristic
7#11745842C211yesmaximal, characteristic, complemented
8#10602737—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#947—21no—
11C5×#894—22no—
12C5×#893—21no—
13C5×#875—21no—
14C5×#874C2211yescharacteristic
15C4×C5×D12—21no—
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6656—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3967—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90989—21no—
25#90972—21no—
26#71159—51nomaximal, Hall
27C5×#559—31no—
28#65365—31no—
29#65310—31no—
30#65310D311yescharacteristic, complemented
31#64764—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C4×C5×D3—22no—
39C2×C5×Dic6D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—22no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6656—44no—
57#5585D511yescharacteristic
58C3×#477—51no—
59#5091—51no—
60#5085—51no—
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C5×#127—31no—
65C5×#124—61no—
66C5×#124—61no—
67C5×#123—62no—
68C4×C5×Q8—31no—
69C4×C5×Q8C2×D311yescharacteristic
70C4×C5×D4—61no—
71C4×C5×D4—61no—
72C2×#687—62no—
73#4015C2×D311yescharacteristic
74#3967—21no—
75#3967—61no—
76#3939—21no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1630—151noSylow
82C22×C5×D3—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×D12—42no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C4×C5×D3—82no—
98C5×Dic6—21no—
99C5×Dic6—21no—
100C2×C3×Dic5—41no—
101C3×Dic10—42no—
102C3⋊#168—22no—
103C3⋊#168—41no—
104C3×#168—41no—
105C3×C4⋊Q8—51no—
106C3×C4×Q8C2×D511yescharacteristic
107#947—21no—
108C2×#215—102no—
109#894—22no—
110#893—21no—
111#875—21no—
112#874C2×D511yescharacteristic
113C4×D12—21no—
114C4×Dic6C2×D511yescharacteristic
115C3×#107—101no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#810—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4×C3⋊C8—51no—
122C2×C5×Q8—31no—
123C2×C5×Q8#6711yescharacteristic
124C2×C5×D4—32no—
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C22×C4×C5—62no—
128C2×Dic10—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—62no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C42×C5—21no—
137C42×C5—61no—
138C42×C5C22×D311yescharacteristic
139#687—124no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C2×#168—21no—
143C2×#168—61no—
144C2×#168—61no—
145#559—31no—
146#492—151no—
147#477—51no—
148#477—151no—
149#331—151no—
150Q8⋊C8—151no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×C5×D3—42no—
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×Dic5—81no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C2×C3×Q8—101no—
167C2×C3×Q8C22⋊D511yescharacteristic
168C2×D12—21no—
169C2×D12—21no—
170C2×D12C22⋊D512yes—
171C2×C4×D3—22no—
172C2×Dic6C22⋊D511yescharacteristic
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180#215—204no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184C4⋊Dic3C22⋊D511yescharacteristic
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5—62no—
190C5×Q8—21no—
191C5×Q8—21no—
192C5×Q8—61no—
193C5×Q8—61no—
194C5×D4—122no—
195C5×D4—121no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—61no—
202C2×C4×C5—61no—
203C2×C4×C5—242no—
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×Dic5—41no—
208Dic10—42no—
209#168—41no—
210#168—62no—
211#168—121no—
212C2×SD16—302no—
213C4⋊Q8—51no—
214#127—31no—
215#124—61no—
216#124—61no—
217#123—62no—
218C4×Q8—31no—
219C4×Q8D3×D511yescharacteristic
220C4×D4—61no—
221C4×D4—61no—
222#107—101no—
223#107—301no—
224C4⋊C8—51no—
225C4⋊C8—151no—
226#103—101no—
227#103—301no—
228C4×C8—151no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C5×D3—82no—
233C22×D3—22no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—202no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—201no—
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245D12—42no—
246D12—41no—
247D12—41no—
248D12—41no—
249D12—41no—
250C4×D3—82no—
251Dic6—21no—
252Dic6—21no—
253C3×C8—201no—
254C3⋊C8—102no—
255C3⋊C8—201no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—122no—
259C22×C5#93711yescharacteristic
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5—121no—
264C4×C5—121no—
265C4×C5#91811yescharacteristic
266C4×C5#91911yescharacteristic
267C4×C5#94211yescharacteristic
268C4×C5#95011yescharacteristic
269Dic5—81no—
270C2×Q8—31no—
271C2×Q8—101no—
272C2×Q8#120111yescharacteristic
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—61no—
276C22×C4—62no—
277SD16—604no—
278C2×C8—101no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—101no—
285C4⋊C4—101no—
286C4⋊C4#120111yescharacteristic
287C22⋊C4—62no—
288C22⋊C4—62no—
289C22⋊C4—62no—
290C42—21no—
291C42—61no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3#409911yescharacteristic
295C2×D3—42no—
296C2×D3—42no—
297C2×D3—42no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—401no—
302C3×C4#409611yescharacteristic
303C3×C4#409611yescharacteristic
304C3×C4#409711yescharacteristic
305C3×C4#409711yescharacteristic
306Dic3—41no—
307Dic3—41no—
308C2×C5—242no—
309C2×C5#504711yescharacteristic
310C2×C5#518711yescharacteristic
311C2×C5#519811yescharacteristic
312C23—62no—
313Q8—21no—
314Q8—21no—
315Q8—61no—
316Q8—61no—
317Q8—202no—
318D4—122no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—201no—
328C2×C4—242no—
329C2×C4C2×#120111yescharacteristic
330C2×C4D3×C22⋊D511yescharacteristic
331C2×C4D3×C22⋊D511yescharacteristic
332C8—201no—
333C8—302no—
334C8—601no—
335C2×C3#6552811yescharacteristic
336C2×C3#6552811yescharacteristic
337C2×C3#6553011yescharacteristic
338D3—82no—
339C5#7115911yescharacteristic, complemented, Sylow
340C22—122no—
341C22—122no—
342C22—122no—
343C22#9156811yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—121no—
348C4—121no—
349C4—401no—
350C4#9129711yescharacteristic
351C4#9130911yescharacteristic
352C4#9151011yescharacteristic
353C4#9151911yescharacteristic
354C3#1060273711yescharacteristic, complemented, Sylow
355C2—242no—
356C2#1174853811yescharacteristic
357C2#1174930511yescharacteristic
358C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65310C2semidirect
4. #11746959C2semidirect
5. #11746356C2semidirect
7. #11745842C2semidirect
30. #65310D3semidirect
293. C3×C5#1630semidirect
339. C5#71159semidirect
354. C3#10602737semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C3×#653102
#117470812
#117469592
#117463562
#117458532
#117458422
#106027373
#711595