Finite Group Databasebeta

← #14289533

Subgroups — #14289533

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11756338C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11747100C211yesmaximal, characteristic, complemented
4#11746942C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic
8#10599039—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91785—22no—
12C4⋊C4×D15—21no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91759—21no—
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6662—22no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90987—21no—
25#90968—21no—
26#71156—51nomaximal, Hall
27#65913—31no—
28#65310D311yescharacteristic, complemented
29#65131—31no—
30#64988—31no—
31C5×Q8⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30D412yes—
39C2×C3×Dic10—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45#6714—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D411yescharacteristic
49#6712—22no—
50#6712—22no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6662—44no—
57#5579—51no—
58C3×#477—51no—
59#5092—51no—
60#5084—51no—
61#4535D511yescharacteristic, complemented
62#4483—51no—
63#4481—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—61no—
66C2×Dic20—62no—
67#4042—62no—
68D5×C4⋊C4—61no—
69C4×D20—31no—
70C4×D20—61no—
71#4016—61no—
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3967—21no—
77#3953—61no—
78#3949—61no—
79#3939—21no—
80C4⋊#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—22no—
92D60—21no—
93D60Q1612yescomplemented
94C4×D15—41no—
95C4×D15—41no—
96C4×D15—82no—
97Dic30—42no—
98C2×C3×Dic5—41no—
99C3×Dic10—42no—
100C3×#168—41no—
101C5×C3⋊C8—22no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104C3×C4×Q8C2×D511yescharacteristic
105#946—101no—
106C2×#216—102no—
107#896—102no—
108D3×C4⋊C4—101no—
109C4×D12—51no—
110C4×D12—101no—
111#870—101no—
112#869—51no—
113C3×#107—101no—
114C3×C4⋊C8—51no—
115C3×#103—101no—
116#809—101no—
117#808—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4×C3⋊C8C2×D511yescharacteristic
120C2×C5×Q8#6711yescharacteristic
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×C4×D5—62no—
124C2×Dic10—21no—
125C2×Dic10—32no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4#6711yescharacteristic
130C42×C5—21no—
131C42×C5C22×D311yescharacteristic
132#685—62no—
133#685—61no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C2×#168—21no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—51no—
146#476—151no—
147#333—151no—
148Q8⋊C8—31no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—42no—
163C3×Dic5—81no—
164C2×C3×Q8—101no—
165C2×C3×Q8D2011yescharacteristic
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×C4×D3—102no—
169C2×Dic6—52no—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4D2011yescharacteristic
175C3×C42—21no—
176C3×C42C22×D511yescharacteristic
177#216—204no—
178(C2×D3)⋊C4—102no—
179(C2×D3)⋊C4—101no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C22×D5—61no—
188C5×Q8—21no—
189C5×Q8—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—41no—
196C2×Dic5—61no—
197C2×Dic5—62no—
198D20—32no—
199D20—61no—
200C4×D5—121no—
201C4×D5—121no—
202C4×D5—242no—
203Dic10—42no—
204Dic10—122no—
205C5×C8—62no—
206C5×C8—121no—
207#168—41no—
208C2×Q16—302no—
209C4⋊Q8—51no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8D3×D511yescharacteristic
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—101no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222#103—101no—
223#102—301no—
224C4×C8—31no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—202no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—201no—
236C2×C3×C4C2×D2011yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×Dic3—101no—
240C2×Dic3—102no—
241D12—52no—
242D12—101no—
243C4×D3—201no—
244C4×D3—201no—
245C4×D3—402no—
246Dic6—202no—
247C3×C8—201no—
248C3⋊C8—22no—
249C3⋊C8—41no—
250C22×C5#93711yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5D3×Q1611yescharacteristic
258C4×C5#91811yescharacteristic
259C4×C5#94211yescharacteristic
260C4×C5#95011yescharacteristic
261Dic5—81no—
262Dic5—122no—
263Dic5—121no—
264C2×Q8—101no—
265C2×Q8—152no—
266C2×Q8#120211yescharacteristic
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—151no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4#120211yescharacteristic
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—21no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—401no—
296C3×C4#405011yescharacteristic
297C3×C4#405511yescharacteristic
298C3×C4#406111yescharacteristic
299C3×C4D5×Q1611yescharacteristic
300Dic3—202no—
301Dic3—201no—
302C2×C5#504711yescharacteristic
303C2×C5#518611yescharacteristic
304C2×C5#519811yescharacteristic
305D5—122no—
306C23—301no—
307Q8—21no—
308Q8—21no—
309Q8—202no—
310Q8—602no—
311D4—152no—
312D4—301no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—201no—
316C2×C4—301no—
317C2×C4—302no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×#120211yescharacteristic
322C2×C4#679011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—62no—
325C8—121no—
326C8—201no—
327C2×C3#6502211yescharacteristic
328C2×C3#6509711yescharacteristic
329C2×C3#6511111yescharacteristic
330D3—202no—
331C5#7115611yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9157211yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—401no—
340C4—602no—
341C4—601no—
342C4#9131111yescharacteristic
343C4#9131511yescharacteristic
344C4#9151111yescharacteristic
345C4#9152411yescharacteristic
346C3#1059903911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1174855211yescharacteristic
349C2#1174931011yescharacteristic
350C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1632
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. C3×#65310C2semidirect
3. #11747100C2semidirect
5. C5×#4535C2semidirect
6. #11745863C2semidirect
28. #65310D3semidirect
61. #4535D5semidirect
93. D60Q16semidirect
287. C3×C5#1632semidirect
331. C5#71156semidirect
346. C3#10599039semidirect

Maximal subgroups

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

subgroupindex
#117563382
C3×#653102
#117471002
#117469422
C5×#45352
#117458632
#117458382
#105990393
#711565