Finite Group Databasebeta

← #14289513

Subgroups — #14289513

Order 1920.

428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5543C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic, complemented
4#11746959C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745862C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602717—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×D4×Dic3—21no—
11C2×C5×C4⋊Dic3—21no—
12C5×#924—21no—
13C5×#890—21no—
14C5×#878—22no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3964—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90989—21no—
25#90972—21no—
26#71144—51nomaximal, Hall
27C5×#554—31no—
28#65381—31no—
29#65310—31no—
30#65297D311yescharacteristic
31#64766—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×C5×Dic3—22no—
37C2×C5×Dic6D411yescharacteristic
38C2×C5×Dic6D412yes—
39C2×C3×Dic10—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×#217—22no—
46C5×C4⋊Dic3—22no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—22no—
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6661—44no—
57#5543D511yescharacteristic
58C3×#476—51no—
59#5092—51no—
60#5091—51no—
61D4⋊(C3⋊C8)—51no—
62#4484—51no—
63#4481—51no—
64C5×C4⋊Q8—31no—
65C5×#125—61no—
66C5×C22⋊Q8—62no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—31no—
69C4×C5×D4—61no—
70C4×C5×D4C2×D311yescharacteristic
71C2×C5×C4⋊C4—61no—
72C2×#689—62no—
73#4015C2×D311yescharacteristic
74#3967—61no—
75#3964—21no—
76#3940—21no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1632—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4Q1612yescomplemented
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—22no—
94C2×C5×Dic3—82no—
95C5×Dic6—21no—
96C5×Dic6—21no—
97C5×Dic6—42no—
98C2×C3×Dic5—41no—
99C3×Dic10—42no—
100C3⋊#168—22no—
101C3⋊#168—41no—
102C3×#168—41no—
103C3×C4⋊Q8—51no—
104C3×C4×D4C2×D511yescharacteristic
105C2×#216—102no—
106D4×Dic3—21no—
107C2×C4⋊Dic3—21no—
108#924—21no—
109#890—21no—
110#878—22no—
111#869C2×D511yescharacteristic
112C4×Dic6C2×D511yescharacteristic
113C3×#106—101no—
114C3×C4⋊C8—51no—
115C3×#102—101no—
116#810—101no—
117#807—101no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—31no—
121C2×C5×Q8—32no—
122C2×C5×D4#6711yescharacteristic
123C22×C4×C5—21no—
124C22×C4×C5—62no—
125C2×Dic10—21no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—62no—
128C5×C4⋊C4—62no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C5×C22⋊C4—62no—
135C42×C5—61no—
136C42×C5C22×D311yescharacteristic
137#689—124no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C2×#168—21no—
141C2×#168—61no—
142C2×#168—61no—
143#554—31no—
144#494—151no—
145#477—151no—
146#476—51no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×Dic5—81no—
161C5×Dic3—41no—
162C5×Dic3—42no—
163C5×Dic3—41no—
164C2×C3×Q8—101no—
165C2×C3×D4C22⋊D511yescharacteristic
166C22×C3×C4—21no—
167C22×Dic3—22no—
168C2×Dic6C22⋊D511yescharacteristic
169C2×Dic6C22⋊D512yes—
170C2×C3×C8—101no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4C22⋊D511yescharacteristic
174C3×C22⋊C4—21no—
175C3×C42C22×D511yescharacteristic
176#217—22no—
177#216—204no—
178C4⋊Dic3—22no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3C22⋊D511yescharacteristic
182Dic3⋊C4—22no—
183Dic3⋊C4—21no—
184C4×Dic3—21no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C23×C5—21no—
188C5×Q8—61no—
189C5×Q8—61no—
190C5×Q8—122no—
191C5×D4—21no—
192C5×D4#21612yescomplemented
193C2×C4×C5—21no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5—62no—
199C2×C4×C5—242no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5—41no—
204Dic10—42no—
205#168—41no—
206#168—62no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
211#125—61no—
212C22⋊Q8—62no—
213C22⋊Q8—61no—
214C4×Q8—31no—
215C4×D4—61no—
216C4×D4D3×D511yescharacteristic
217C2×C4⋊C4—61no—
218#107—301no—
219#106—101no—
220C4⋊C8—51no—
221C4⋊C8—151no—
222#103—301no—
223#102—101no—
224C4×C8—151no—
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×Q8—202no—
231C3×D4—21no—
232C3×D4#68912yescomplemented
233C2×C3×C4—21no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—201no—
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239C2×C3×C4C2×C22⋊D511yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—22no—
243C2×Dic3—82no—
244Dic6—21no—
245Dic6—21no—
246Dic6—42no—
247C3×C8—201no—
248C3⋊C8—102no—
249C3⋊C8—201no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#93711yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—121no—
257C4×C5—121no—
258C4×C5—122no—
259C4×C5#91511yescharacteristic
260C4×C5#91611yescharacteristic
261C4×C5C2×#21611yescharacteristic
262C4×C5#95111yescharacteristic
263Dic5—81no—
264C2×Q8—31no—
265C2×Q8—32no—
266C2×Q8—101no—
267C2×D4#120111yescharacteristic
268C22×C4—21no—
269C22×C4—62no—
270Q16—604no—
271C2×C8—101no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4#120111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—62no—
285C42—61no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3#409911yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—401no—
295C3×C4#408811yescharacteristic
296C3×C4C2×#68911yescharacteristic
297C3×C4#409611yescharacteristic
298C3×C4#409711yescharacteristic
299Dic3—41no—
300Dic3—42no—
301Dic3—41no—
302C2×C5—42no—
303C2×C5#505011yescharacteristic
304C2×C5#517311yescharacteristic
305C2×C5#519811yescharacteristic
306C23—21no—
307Q8—61no—
308Q8—61no—
309Q8—122no—
310Q8—202no—
311D4—21no—
312D4#666112yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—62no—
319C2×C4—201no—
320C2×C4—242no—
321C2×C4C2×#120111yescharacteristic
322C2×C4D3×C22⋊D511yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—201no—
325C8—302no—
326C8—601no—
327C2×C3—42no—
328C2×C3#6551711yescharacteristic
329C2×C3#6552811yescharacteristic
330C2×C3#6553011yescharacteristic
331C5#7114411yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22#9156811yescharacteristic
336C4—21no—
337C4—41no—
338C4—121no—
339C4—122no—
340C4—121no—
341C4—401no—
342C4#9130711yescharacteristic
343C4C2×#666111yescharacteristic
344C4#9148611yescharacteristic
345C4#9149511yescharacteristic
346C3#1060271711yescharacteristic, complemented, Sylow
347C2—42no—
348C2#1174855911yescharacteristic
349C2#1174905911yescharacteristic
350C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11747103C2semidirect
4. #11746959C2semidirect
6. #11745862C2semidirect
7. #11745842C2semidirect
84. C3×C5×D4Q16semidirect
192. C5×D4#216semidirect
232. C3×D4#689semidirect
287. C3×C5#1632semidirect
312. D4#6661semidirect
331. C5#71144semidirect
346. C3#10602717semidirect

Maximal subgroups

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

subgroupindex
C5×#55432
C3×#652972
#117471032
#117469592
D4⋊(C3⋊#168)2
#117458622
#117458422
#106027173
#711445