Finite Group Databasebeta

← #14290365

Subgroups — #14290365

Order 1920.

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

normal subgroups only

This group has 424 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×#5563C211yesmaximal, characteristic
2C3×#65296C211yesmaximal, characteristic, complemented
3#11747070C211yesmaximal, characteristic, complemented
4#11746923C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602722—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#938—21no—
11C5×#930—21no—
12C5×#926—21no—
13C5×#892—21no—
14C5×#885—22no—
15C4×C5×D12C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6656—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3964—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90972—22no—
25#90970—21no—
26#71109—51nomaximal, Hall
27C5×#555—31no—
28#65370—31no—
29#65308—31no—
30#65296D311yescharacteristic, complemented
31#64766—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6D412yes—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×#217—22no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C4×C5×Dic3—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6656—42no—
57#5563D511yescharacteristic
58C3×#474—51no—
59#5093—51no—
60#5083—51no—
61D4⋊(C3⋊C8)—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8—31no—
65C5×#124—62no—
66C5×#121—61no—
67C5×#121—61no—
68C4×C5×D4—31no—
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—61no—
71C5×#117—61no—
72C2×#687—61no—
73#4015C2×D311yescharacteristic
74#3967—62no—
75#3964—21no—
76#3942—61no—
77#3939—21no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1646—151noSylow
82C23×C3×C5—21no—
83C22×C5×D3—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C5×#67—82no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—22no—
95C5×D12—21no—
96C5×D12—21no—
97C4×C5×D3—41no—
98C4×C5×D3—41no—
99C5×Dic6—42no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C3×C4⋊Q8—51no—
107C3×C4×D4C2×D511yescharacteristic
108C2×#215—101no—
109#938—21no—
110#930—21no—
111#926—21no—
112#892—21no—
113#885—22no—
114C4×D12C2×D511yescharacteristic
115#869C2×D511yescharacteristic
116C3×#107—101no—
117C3×C4⋊C8—51no—
118C3×#102—101no—
119#835—101no—
120#810—102no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—32no—
124C2×C5×D4—31no—
125C2×C5×D4—62no—
126C2×C5×D4#6711yescharacteristic
127C22×C4×C5—21no—
128C22×C4×C5—61no—
129C2×Dic10—21no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4#6711yescharacteristic
134C5×C22⋊C4—21no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C5×C22⋊C4—61no—
138C42×C5—62no—
139C42×C5C22×D311yescharacteristic
140#687—122no—
141C4⋊Dic5—21no—
142C4⋊Dic5—21no—
143C2×#168—21no—
144C2×#168—61no—
145C2×#168—61no—
146#555—31no—
147#487—151no—
148#474—51no—
149#461—151no—
150#333—151no—
151D4⋊C8—151no—
152D4⋊C8—151no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C3×Dic5—81no—
167C5×Dic3—41no—
168C5×Dic3—42no—
169C2×C3×Q8—101no—
170C2×C3×D4C22⋊D511yescharacteristic
171C22×C3×C4—21no—
172C2×#67—22no—
173C2×D12C22⋊D511yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6C22⋊D512yes—
176C2×C3×C8—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4C22⋊D511yescharacteristic
180C3×C22⋊C4—21no—
181C3×C42C22×D511yescharacteristic
182#217—22no—
183#215—202no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3C22⋊D511yescharacteristic
189C4×Dic3—22no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C23×C5—61no—
194C5×Q8—122no—
195C5×D4—21no—
196C5×D4—21no—
197C5×D4—61no—
198C5×D4—61no—
199C5×D4—242no—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—61no—
204C2×C4×C5—62no—
205C2×C4×C5—121no—
206C2×C4×C5—121no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—41no—
211Dic10—41no—
212Dic10—41no—
213#168—41no—
214#168—121no—
215#168—121no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—51no—
219#124—62no—
220#121—61no—
221#121—61no—
222C4×D4—31no—
223C4×D4D3×D511yescharacteristic
224#117—61no—
225#117—61no—
226#107—101no—
227C4⋊C8—51no—
228C4⋊C8—151no—
229#103—301no—
230#103—302no—
231#102—101no—
232C4×C8—151no—
233C2×C3×C5—81no—
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45211yescharacteristic
236C2×C3×C5#45511yescharacteristic
237C5×D3—81no—
238C23×C3—21no—
239C22×D3—21no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×D4—21no—
243C3×D4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—201no—
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251#67—82no—
252C2×Dic3—21no—
253C2×Dic3—22no—
254D12—21no—
255D12—21no—
256C4×D3—41no—
257C4×D3—41no—
258Dic6—42no—
259C3×C8—201no—
260C3⋊C8—201no—
261C3⋊C8—201no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—121no—
266C22×C5—121no—
267C22×C5—121no—
268C22×C5#93711yescharacteristic
269C4×C5—21no—
270C4×C5—41no—
271C4×C5—122no—
272C4×C5—121no—
273C4×C5#91111yescharacteristic
274C4×C5#91211yescharacteristic
275C4×C5#94211yescharacteristic
276C4×C5#95011yescharacteristic
277Dic5—81no—
278C2×Q8—32no—
279C2×Q8—101no—
280C2×D4—31no—
281C2×D4—62no—
282C2×D4#120111yescharacteristic
283C22×C4—21no—
284C22×C4—61no—
285SD16—602no—
286C2×C8—101no—
287C2×C8—301no—
288C2×C8—301no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4#120111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—61no—
299C42—62no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3#409911yescharacteristic
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—401no—
312C3×C4#409511yescharacteristic
313C3×C4#409611yescharacteristic
314C3×C4#409611yescharacteristic
315C3×C4#409711yescharacteristic
316Dic3—41no—
317Dic3—42no—
318C2×C5—81no—
319C2×C5—241no—
320C2×C5#504711yescharacteristic
321C2×C5#515811yescharacteristic
322C2×C5#520211yescharacteristic
323C23—21no—
324C23—61no—
325Q8—122no—
326Q8—201no—
327Q8—201no—
328D4—21no—
329D4—21no—
330D4—61no—
331D4—61no—
332D4—242no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—62no—
338C2×C4—121no—
339C2×C4—121no—
340C2×C4—201no—
341C2×C4C2×#120111yescharacteristic
342C2×C4D3×C22⋊D511yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C8—201no—
345C8—601no—
346C8—601no—
347C2×C3—81no—
348C2×C3#6552711yescharacteristic
349C2×C3#6552811yescharacteristic
350C2×C3#6553111yescharacteristic
351D3—81no—
352C5#7110911yescharacteristic, complemented, Sylow
353C22—41no—
354C22—41no—
355C22—41no—
356C22—121no—
357C22—121no—
358C22—121no—
359C22#9156811yescharacteristic
360C4—21no—
361C4—41no—
362C4—122no—
363C4—121no—
364C4—401no—
365C4#9129711yescharacteristic
366C4#9130911yescharacteristic
367C4#9148011yescharacteristic
368C4#9149311yescharacteristic
369C3#1060272211yescharacteristic, complemented, Sylow
370C2—81no—
371C2—241no—
372C2#1174853811yescharacteristic
373C2#1174903511yescharacteristic
374C2#1174941611yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1646
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
2. C3×#65296C2semidirect
3. #11747070C2semidirect
4. #11746923C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745862C2semidirect
7. #11745836C2semidirect
30. #65296D3semidirect
301. C3×C5#1646semidirect
352. C5#71109semidirect
369. C3#10602722semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C3×#652962
#117470702
#117469232
D4⋊(C3⋊#168)2
#117458622
#117458362
#106027223
#711095