Finite Group Databasebeta

← #14290594

Subgroups — #14290594

Order 1920.

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

normal subgroups only

This group has 400 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×#5732C211yesmaximal, characteristic
2#11751179C211yesmaximal, characteristic, complemented
3#11747077C211yesmaximal, characteristic
4#11746945C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602726—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#947—21no—
12C5×Q8×Dic3—21no—
13C5×#898—22no—
14C5×#897—21no—
15C5×#892—21no—
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C2×#6659—21no—
19#91091—22no—
20C4×C3⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90985—21no—
24#90975—21no—
25#90973—21no—
26#68437—51nomaximal, Hall
27C5×#556—31no—
28#65367—31no—
29#65309—31no—
30#65308—31no—
31#64767D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C5×Dic6D411yescharacteristic
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D412yes—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—22no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—22no—
53C4×C5×Dic3—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6659—42no—
57#5732D511yescharacteristic
58#5078—51no—
59#4851—51no—
60#4841—51no—
61C3×#332—51no—
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C5×#126—62no—
66C5×#124—61no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—31no—
69C4×C5×Q8—61no—
70C4×C5×D4—31no—
71C5×#117—61no—
72C2×#687—61no—
73#4015—31no—
74#3967—61no—
75#3942—61no—
76#3940—61no—
77#3939—62no—
78C4⋊#168C2×D311yescharacteristic
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1650—151noSylow
82C22×C5×D3—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—41no—
90Dic30—41no—
91Dic30—41no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12—21no—
97C4×C5×D3—41no—
98C4×C5×D3—41no—
99C5×Dic6—21no—
100C5×Dic6—21no—
101C3⋊#168—22no—
102C3×#168—41no—
103C3×#168—41no—
104C3×C4⋊Q8C2×D511yescharacteristic
105#947—21no—
106Q8×Dic3—21no—
107C2×#204—101no—
108#898—22no—
109#897—21no—
110#892—21no—
111C4×D12C2×D511yescharacteristic
112#869—51no—
113C4×Dic6C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×C4⋊C8—51no—
116#817—101no—
117#816—101no—
118#816—101no—
119#807—102no—
120C4×C3⋊C8—51no—
121C2×C5×Q8—21no—
122C2×C5×Q8—31no—
123C2×C5×D4—31no—
124C22×C4×C5—61no—
125C2×Dic10—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—62no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4D1212yes—
132C5×C22⋊C4—62no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—61no—
135C42×C5—62no—
136C42×C5—61no—
137C42×C5C22×D311yescharacteristic
138#687—122no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141C2×#168—21no—
142C2×#168—21no—
143C2×#168—61no—
144#556—31no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332—51no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—81no—
162C5×Dic3—41no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—21no—
166C2×D12C22⋊D511yescharacteristic
167C2×C4×D3—21no—
168C2×Dic6—101no—
169C2×Dic6C22⋊D511yescharacteristic
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C22⋊D512yes—
174C3×C42C22×D511yescharacteristic
175(C2×D3)⋊C4—22no—
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—21no—
178C4⋊Dic3—22no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3C22⋊D511yescharacteristic
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—21no—
184C4×Dic3—22no—
185C4×Dic3—21no—
186C2×C3⋊C8—101no—
187#204—202no—
188C23×C5—61no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×Q8—61no—
192C5×Q8—61no—
193C5×D4—61no—
194C5×D4—61no—
195C2×C4×C5—22no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5—121no—
200C2×C4×C5—121no—
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×Dic5—121no—
205Dic10—121no—
206Dic10—121no—
207#168—41no—
208#168—41no—
209#168—62no—
210C2×SD16—301no—
211C4⋊Q8—151no—
212C4⋊Q8D3×D511yescharacteristic
213#126—62no—
214#124—61no—
215C22⋊Q8—61no—
216C4×Q8—31no—
217C4×Q8—61no—
218C4×D4—31no—
219#117—61no—
220#107—302no—
221#106—301no—
222C4⋊C8—51no—
223C4⋊C8—51no—
224#103—301no—
225#103—301no—
226C4×C8—151no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C5×D3—81no—
231C22×D3—21no—
232C3×Q8—41no—
233C3×Q8—41no—
234C2×C3×C4—22no—
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—201no—
242D12—21no—
243D12—21no—
244C4×D3—41no—
245C4×D3—41no—
246Dic6—21no—
247Dic6—21no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—201no—
251C3×C8—201no—
252C3⋊C8—102no—
253C22×C5—121no—
254C22×C5—121no—
255C22×C5—121no—
256C22×C5#88211yescharacteristic
257C4×C5—21no—
258C4×C5—42no—
259C4×C5—121no—
260C4×C5—121no—
261C4×C5—121no—
262C4×C5#91111yescharacteristic
263C4×C5#91611yescharacteristic
264C4×C5#91611yescharacteristic
265C4×C5#91811yescharacteristic
266Dic5—241no—
267C2×Q8—21no—
268C2×Q8—31no—
269C2×Q8—301no—
270C2×D4—31no—
271C22×C4—61no—
272SD16—602no—
273C2×C8—101no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—31no—
278C4⋊C4—31no—
279C4⋊C4—62no—
280C4⋊C4—61no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4#120312yes—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—61no—
287C42—62no—
288C42—61no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#409911yescharacteristic
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C3×C4—21no—
296C3×C4—42no—
297C3×C4#409511yescharacteristic
298C3×C4#409611yescharacteristic
299C3×C4#409611yescharacteristic
300C3×C4#409711yescharacteristic
301Dic3—41no—
302Dic3—41no—
303Dic3—41no—
304Dic3—401no—
305C2×C5—241no—
306C2×C5#475211yescharacteristic
307C2×C5#478111yescharacteristic
308C2×C5#480811yescharacteristic
309C23—61no—
310Q8—41no—
311Q8—41no—
312Q8—61no—
313Q8—61no—
314Q8—601no—
315Q8—601no—
316D4—61no—
317D4—61no—
318C2×C4—22no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—601no—
325C2×C4C2×#120311yescharacteristic
326C2×C4D3×C22⋊D511yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—201no—
329C8—201no—
330C8—302no—
331C2×C3#6552711yescharacteristic
332C2×C3#6552811yescharacteristic
333C2×C3#6553511yescharacteristic
334D3—81no—
335C5#6843711yescharacteristic, complemented, Sylow
336C22—121no—
337C22—121no—
338C22—121no—
339C22#9157011yescharacteristic
340C4—21no—
341C4—42no—
342C4—121no—
343C4—121no—
344C4—121no—
345C4—1201no—
346C4#9148011yescharacteristic
347C4#9149511yescharacteristic
348C4#9151011yescharacteristic
349C4#9151711yescharacteristic
350C3#1060272611yescharacteristic, complemented, Sylow
351C2—241no—
352C2#1174903611yescharacteristic
353C2#1174930011yescharacteristic
354C2#1174939411yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1650
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. #11751179C2semidirect
4. #11746945C2semidirect
5. C3×#64767C2semidirect
6. #11745842C2semidirect
31. #64767D3semidirect
290. C3×C5#1650semidirect
335. C5#68437semidirect
350. C3#10602726semidirect

Maximal subgroups

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

subgroupindex
C5×#57322
#117511792
#117470772
#117469452
C3×#647672
#117458422
#117458362
#106027263
#684375