Finite Group Databasebeta

← #14290374

Subgroups — #14290374

Order 1920.

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752718C211yesmaximal, characteristic
2C5×#4846C211yesmaximal, characteristic, complemented
3#11747059C211yesmaximal, characteristic, complemented
4#11746930C211yesmaximal, characteristic, complemented
5#11746302C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601902—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91462—22no—
14#91456—21no—
15#91449—21no—
16#91358—21no—
17#91338—21no—
18C2×#6655—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#821—21no—
22C5×#818—21no—
23C3×C4×#168C2211yescharacteristic
24#90975—22no—
25#90972—21no—
26#68207—51nomaximal, Hall
27#65897—31no—
28C5×#474—31no—
29#65382—31no—
30#65372—31no—
31D4⋊#168—31no—
32#64703D311yescharacteristic, complemented
33#64701—31no—
34C2×Dic30D412yes—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168—21no—
46C5×(C2×D3)⋊C4—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C3×#685—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C2×C3×#168—21no—
53(C2×D3)⋊Dic5—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#6655—42no—
57#5563—51no—
58#5019—51no—
59#4846D511yescharacteristic, complemented
60#4681—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4—31no—
66C2×#688—61no—
67#4084—61no—
68#4076—61no—
69#4072—61no—
70#4038—61no—
71#4031—62no—
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×#107—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#102—61no—
77#3967—61no—
78#3942—62no—
79C4⋊#168—31no—
80C4×#168C2×D311yescharacteristic
81#1646—151noSylow
82C22×C5×D3—21no—
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88Dic30—42no—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—41no—
91C5×D12—21no—
92C5×D12—21no—
93C4×C5×D3—41no—
94C4×C5×D3—41no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C2×C3×Dic5—21no—
98C3×D20—21no—
99C3×D20—21no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102#1201—82no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C3×C4×D4—51no—
107#938—101no—
108C2×#214—101no—
109#930—101no—
110#926—101no—
111#892—101no—
112#885—102no—
113C4×D12C2×D511yescharacteristic
114#869—51no—
115#869C2×D511yescharacteristic
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C4×C8—51no—
118#821—21no—
119#818—21no—
120#816—102no—
121#810—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—61no—
124C2×C5×D4—31no—
125C22×C4×C5—61no—
126C2×C22⋊D5—62no—
127C2×D20D1211yescharacteristic
128C2×C4×D5—21no—
129C2×Dic10—32no—
130C2×C5×C8—21no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C22⋊C4—61no—
135C42×C5C22×D311yescharacteristic
136C22⋊Dic5—62no—
137#688—122no—
138#685—21no—
139#685—62no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5D1211yescharacteristic
143C4×Dic5—62no—
144C2×#168—21no—
145C2×#168—61no—
146#555—151no—
147#487—151no—
148#474—31no—
149#461—151no—
150#333—151no—
151D4⋊C8—51no—
152D4⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×C5×D3—41no—
155C2×C5×D3—41no—
156C2×C5×D3—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C3×C4×C5—21no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—42no—
166C3×Dic5—41no—
167C5×Dic3—41no—
168C5×Dic3—81no—
169C2×C3×D4—51no—
170C22×C3×C4—101no—
171C2×#67—102no—
172C2×D12C22⋊D511yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6—21no—
175C2×Dic6—52no—
176C2×C3×C8—21no—
177C2×C3×C8—101no—
178C3×C4⋊C4—51no—
179C3×C22⋊C4—101no—
180C3×C42C22×D511yescharacteristic
181#217—102no—
182#214—202no—
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—101no—
188C4⋊Dic3—101no—
189C4⋊Dic3C22⋊D511yescharacteristic
190C4×Dic3—102no—
191C2×C3⋊C8—101no—
192C23×C5—61no—
193C22×D5—21no—
194C5×Q8—121no—
195C5×Q8—121no—
196C5×D4—61no—
197C5×D4—61no—
198C2×C4×C5—61no—
199C2×C4×C5—121no—
200C2×C4×C5—121no—
201C2×C4×C5—121no—
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C22⋊D5—242no—
206C2×Dic5—21no—
207C2×Dic5—62no—
208D20—21no—
209D20—21no—
210C4×D5—41no—
211C4×D5—41no—
212Dic10—122no—
213C5×C8—41no—
214#168—41no—
215#168—121no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—151no—
219#124—302no—
220#121—301no—
221#121—301no—
222C4×D4—31no—
223C4×D4—51no—
224#117—301no—
225#117—301no—
226#107—61no—
227C4⋊C8—151no—
228C4⋊C8D3×D511yescharacteristic
229#103—301no—
230#103—302no—
231#102—61no—
232C4×C8—51no—
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45211yescharacteristic
235C2×C3×C5#45511yescharacteristic
236C3×D5—81no—
237C5×D3—81no—
238C23×C3—101no—
239C22×D3—21no—
240C3×D4—101no—
241C3×D4—101no—
242C2×C3×C4—101no—
243C2×C3×C4—201no—
244C2×C3×C4—201no—
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—402no—
249C2×Dic3—21no—
250C2×Dic3—41no—
251C2×Dic3—102no—
252D12—21no—
253D12—21no—
254C4×D3—41no—
255C4×D3—41no—
256Dic6—41no—
257Dic6—41no—
258Dic6—202no—
259C3×C8—41no—
260C3×C8—201no—
261C3⋊C8—201no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#88211yescharacteristic
266C2×D5—41no—
267C2×D5—41no—
268C2×D5—41no—
269C4×C5—21no—
270C4×C5—121no—
271C4×C5—241no—
272C4×C5#90411yescharacteristic
273C4×C5#90811yescharacteristic
274C4×C5#91211yescharacteristic
275C4×C5#91511yescharacteristic
276Dic5—41no—
277Dic5—122no—
278C2×Q8—61no—
279C2×Q8—152no—
280C2×D4—31no—
281C2×D4—51no—
282C2×D4—302no—
283C22×C4—61no—
284C22×C4—101no—
285SD16—602no—
286C2×C8—21no—
287C2×C8—101no—
288C2×C8—301no—
289C4⋊C4—31no—
290C4⋊C4—51no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—61no—
296C22⋊C4—101no—
297C22⋊C4—302no—
298C22⋊C4—302no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—201no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3#408311yescharacteristic
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C3×C4—21no—
310C3×C4—201no—
311C3×C4#405711yescharacteristic
312C3×C4#405811yescharacteristic
313C3×C4#408811yescharacteristic
314C3×C4#409611yescharacteristic
315Dic3—41no—
316Dic3—81no—
317Dic3—202no—
318C2×C5—241no—
319C2×C5#473411yescharacteristic
320C2×C5#478311yescharacteristic
321C2×C5#482511yescharacteristic
322D5—81no—
323C23—61no—
324C23—101no—
325Q8—121no—
326Q8—121no—
327Q8—602no—
328D4—61no—
329D4—61no—
330D4—101no—
331D4—101no—
332D4—1202no—
333C2×C4—61no—
334C2×C4—101no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4—121no—
338C2×C4—201no—
339C2×C4—201no—
340C2×C4—302no—
341C2×C4D5×D1211yescharacteristic
342C2×C4#677711yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C8—41no—
345C8—201no—
346C8—601no—
347C2×C3—401no—
348C2×C3#6533611yescharacteristic
349C2×C3#6544711yescharacteristic
350C2×C3#6549111yescharacteristic
351D3—81no—
352C5#6820711yescharacteristic, complemented, Sylow
353C22—121no—
354C22—121no—
355C22—121no—
356C22—201no—
357C22—201no—
358C22—201no—
359C22#9147511yescharacteristic
360C4—21no—
361C4—121no—
362C4—201no—
363C4—241no—
364C4—602no—
365C4#9125011yescharacteristic
366C4#9127011yescharacteristic
367C4#9149311yescharacteristic
368C4#9151811yescharacteristic
369C3#1060190211yescharacteristic, complemented, Sylow
370C2—241no—
371C2—401no—
372C2#1174751411yescharacteristic
373C2#1174815611yescharacteristic
374C2#1174824511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752718C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1646
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4846C2semidirect
3. #11747059C2semidirect
4. #11746930C2semidirect
5. #11746302C2semidirect
6. C3×#64703C2semidirect
7. #11745837C2semidirect
32. #64703D3semidirect
59. #4846D5semidirect
301. C3×C5#1646semidirect
352. C5#68207semidirect
369. C3#10601902semidirect

Maximal subgroups

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

subgroupindex
#117527182
C5×#48462
#117470592
#117469302
#117463022
C3×#647032
#117458372
#106019023
#682075