Finite Group Databasebeta

← #14290369

Subgroups — #14290369

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#11752715C211yesmaximal, characteristic
2#11750947C211yesmaximal, characteristic, complemented
3#11747062C211yesmaximal, characteristic, complemented
4#11746929C211yesmaximal, characteristic, complemented
5C5×#4481C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10599288—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91465—21no—
14#91455—22no—
15#91450—21no—
16#91358—21no—
17#91347—21no—
18C2×#6657—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91105—21no—
21#91102—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90974—21no—
25#90973—22no—
26#68207—51nomaximal, Hall
27#66068—31no—
28#65370—31no—
29#65135—31no—
30#65130—31no—
31C5×#333—31no—
32#64703—31no—
33#64703D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30—21no—
37C2×C5×Dic6D412yes—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1202—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C2×C3×#168—21no—
53#6667—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#6657—42no—
57#5563—51no—
58#5019—51no—
59#4846—51no—
60#4681—51no—
61C3×D4⋊C8—51no—
62#4481D511yescharacteristic, complemented
63#4459—51no—
64C5×C4⋊Q8—31no—
65#4093—62no—
66C2×#677—61no—
67#4041—61no—
68#4041—61no—
69#4038—61no—
70#4038—61no—
71C4×D20—31no—
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3967—62no—
77#3953—61no—
78#3950—61no—
79#3948—61no—
80C4×#168C2×D311yescharacteristic
81#1646—151noSylow
82C22×D15—21no—
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—41no—
89D60—21no—
90D60—21no—
91C4×D15—41no—
92C4×D15—41no—
93Dic30—41no—
94Dic30—41no—
95C2×C5×Dic3—22no—
96C5×Dic6—42no—
97C2×C3×Dic5—21no—
98C3×D20—21no—
99C3×D20—21no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102#1202—82no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4×D4—51no—
107#938—101no—
108C2×#214—101no—
109#930—101no—
110#926—101no—
111#892—101no—
112#885—102no—
113C4×D12—51no—
114#869—51no—
115#869C2×D511yescharacteristic
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C4×C8—51no—
118#821—101no—
119#818—101no—
120#816—102no—
121#810—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—32no—
124C2×D20—31no—
125C2×D20—62no—
126C2×D20D1211yescharacteristic
127C2×C4×D5—21no—
128C2×C4×D5—61no—
129C2×Dic10—61no—
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C42×C5C22×D311yescharacteristic
135#685—21no—
136#685—62no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5D1211yescharacteristic
143C4×Dic5—62no—
144C2×#168—21no—
145#677—122no—
146#555—151no—
147#487—151no—
148#474—151no—
149#461—151no—
150#333—31no—
151D4⋊C8—51no—
152D4⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—41no—
155C2×D15—41no—
156C2×D15—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—41no—
166Dic15—81no—
167C3×Dic5—41no—
168C5×Dic3—42no—
169C2×C3×D4—51no—
170C22×C3×C4—101no—
171C2×#67—102no—
172C2×D12—51no—
173C2×C4×D3—101no—
174C2×Dic6—101no—
175C2×Dic6D2012yes—
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—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—51no—
188C4⋊Dic3—101no—
189C4⋊Dic3—101no—
190C4×Dic3—102no—
191C2×C3⋊C8—21no—
192C22×D5—21no—
193C22×D5—61no—
194C5×Q8—122no—
195C2×C4×C5—62no—
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—61no—
201C2×Dic5—121no—
202D20—21no—
203D20—21no—
204D20—61no—
205D20—61no—
206D20—242no—
207C4×D5—41no—
208C4×D5—41no—
209C4×D5—121no—
210C4×D5—121no—
211Dic10—121no—
212Dic10—121no—
213C5×C8—41no—
214C5×C8—121no—
215#168—41no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—151no—
219#124—302no—
220#121—301no—
221#121—301no—
222C4×D4—51no—
223C4×D4—151no—
224#117—301no—
225#117—301no—
226#107—301no—
227C4⋊C8—31no—
228C4⋊C8D3×D511yescharacteristic
229#103—301no—
230#103—302no—
231#102—301no—
232C4×C8—51no—
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45211yescharacteristic
235C2×C3×C5#45511yescharacteristic
236D15—81no—
237C3×D5—81no—
238C23×C3—101no—
239C22×D3—101no—
240C3×D4—101no—
241C3×D4—101no—
242C2×C3×C4—101no—
243C2×C3×C4—201no—
244C2×C3×C4—201no—
245C2×C3×C4C2×D2011yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248#67—402no—
249C2×Dic3—22no—
250C2×Dic3—101no—
251C2×Dic3—201no—
252D12—101no—
253D12—101no—
254C4×D3—201no—
255C4×D3—201no—
256Dic6—42no—
257Dic6—201no—
258Dic6—201no—
259C3×C8—41no—
260C3×C8—201no—
261C3⋊C8—41no—
262C22×C5#88211yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C2×D5—121no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—122no—
271C4×C5#90411yescharacteristic
272C4×C5#90811yescharacteristic
273C4×C5#91211yescharacteristic
274C4×C5#91511yescharacteristic
275Dic5—41no—
276Dic5—121no—
277Dic5—241no—
278C2×Q8—32no—
279C2×Q8—301no—
280C2×D4—51no—
281C2×D4—151no—
282C2×D4—302no—
283C22×C4—101no—
284C22×C4—301no—
285SD16—602no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—101no—
289C4⋊C4—51no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—151no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—101no—
296C22⋊C4—302no—
297C22⋊C4—302no—
298C22⋊C4—301no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3—201no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3#402811yescharacteristic
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—201no—
311C3×C4#406011yescharacteristic
312C3×C4#406211yescharacteristic
313C3×C4#406411yescharacteristic
314C3×C4#406511yescharacteristic
315Dic3—42no—
316Dic3—201no—
317Dic3—401no—
318C2×C5#473411yescharacteristic
319C2×C5#478311yescharacteristic
320C2×C5#482511yescharacteristic
321D5—81no—
322D5—241no—
323C23—101no—
324C23—301no—
325Q8—122no—
326Q8—601no—
327Q8—601no—
328D4—101no—
329D4—101no—
330D4—301no—
331D4—301no—
332D4—1202no—
333C2×C4—62no—
334C2×C4—101no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4—301no—
338C2×C4—601no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4D5×D1211yescharacteristic
342C2×C4D3×D2011yescharacteristic
343C2×C4#679011yescharacteristic
344C8—41no—
345C8—121no—
346C8—201no—
347C2×C3—401no—
348C2×C3#6503511yescharacteristic
349C2×C3#6509911yescharacteristic
350C2×C3#6510011yescharacteristic
351D3—401no—
352C5#6820711yescharacteristic, complemented, Sylow
353C22—201no—
354C22—201no—
355C22—201no—
356C22—601no—
357C22—601no—
358C22—601no—
359C22#9147611yescharacteristic
360C4—21no—
361C4—122no—
362C4—201no—
363C4—601no—
364C4—1201no—
365C4#9124911yescharacteristic
366C4#9127111yescharacteristic
367C4#9149711yescharacteristic
368C4#9152211yescharacteristic
369C3#1059928811yescharacteristic, complemented, Sylow
370C2—401no—
371C2—1201no—
372C2#1174751911yescharacteristic
373C2#1174816011yescharacteristic
374C2#1174825111yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752715C2
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. #11750947C2semidirect
3. #11747062C2semidirect
4. #11746929C2semidirect
5. C5×#4481C2semidirect
6. C3×#64703C2semidirect
7. #11745839C2semidirect
33. #64703D3semidirect
62. #4481D5semidirect
301. C3×C5#1646semidirect
352. C5#68207semidirect
369. C3#10599288semidirect

Maximal subgroups

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

subgroupindex
#117527152
#117509472
#117470622
#117469292
C5×#44812
C3×#647032
#117458392
#105992883
#682075