Finite Group Databasebeta

← #14289776

Subgroups — #14289776

Order 1920.

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

normal subgroups only

This group has 456 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
1#11756486C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic
4#11746917C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10599252—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91835—21no—
12#91785—22no—
13#91782—21no—
14#91777—21no—
15C4×D60C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×#3942—22no—
21C3×C4×#168C2211yescharacteristic
22#90990—21no—
23#90987—21no—
24#90974—21no—
25#90968—21no—
26#71237—51nomaximal, Hall
27#66061—31no—
28#65382D311yescharacteristic, complemented
29#65139—31no—
30#65131—31no—
31C5×#332—31no—
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60D411yescharacteristic
38C2×C4×D15—22no—
39C2×C4×D15—21no—
40C2×Dic30—22no—
41C2×Dic30D411yescharacteristic
42C2×C3×Dic10—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D412yes—
45C3×C42×C5C2311yescharacteristic
46#6714—22no—
47#6714—21no—
48C4⋊Dic15D411yescharacteristic
49C4⋊Dic15D411yescharacteristic
50#6712—22no—
51#6712—21no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#5727—51no—
59C3×#487—51no—
60#5091—51no—
61#5084—51no—
62#4547D511yescharacteristic, complemented
63#4459—51no—
64#4456—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4092—61no—
68#4042—62no—
69#4039—61no—
70#4034—61no—
71C4×D20—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3953—61no—
77#3950—61no—
78#3949—61no—
79#3948—61no—
80#3942—22no—
81C4×#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×D15—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93D60—21no—
94D60Q1612yes—
95C4×D15—44no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—21no—
99Dic30—44no—
100Dic30SD1612yes—
101C2×C3×Dic5—41no—
102C3×Dic10—42no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8C2×D511yescharacteristic
109#946—101no—
110#896—102no—
111#893—101no—
112#888—101no—
113C4×D12—51no—
114C4×Dic6—51no—
115C3×#103—102no—
116C3×C4×C8—51no—
117#810—101no—
118#809—101no—
119#808—101no—
120#807—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—21no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20—31no—
127C2×C4×D5—62no—
128C2×C4×D5—61no—
129C2×Dic10—21no—
130C2×Dic10—31no—
131C2×Dic10—62no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6712yes—
136C42×C5C22×D311yescharacteristic
137#685—62no—
138#685—61no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5—31no—
143#683—62no—
144#683—61no—
145C4×Dic5—61no—
146C2×#168—21no—
147D4×Q8—151no—
148#487—51no—
149#477—151no—
150#476—151no—
151#332—31no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—22no—
165Dic15—41no—
166Dic15—41no—
167C3×Dic5—81no—
168C2×C3×Q8—21no—
169C2×C3×Q8—101no—
170D3×Q8—202no—
171D3×Q8—202no—
172C2×D12—51no—
173C2×C4×D3—102no—
174C2×C4×D3—101no—
175C2×Dic6—51no—
176C2×Dic6—102no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4D2012yes—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—51no—
186C4⋊Dic3—51no—
187Dic3⋊C4—102no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C22×D5—61no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—22no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—41no—
200C2×Dic5—61no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—32no—
204D20—61no—
205C4×D5—124no—
206C4×D5—121no—
207C4×D5—121no—
208Dic10—32no—
209Dic10—42no—
210Dic10—61no—
211Dic10—124no—
212C5×C8—121no—
213C5×C8—121no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—51no—
217C4⋊Q8—301no—
218C4⋊Q8D3×D511yescharacteristic
219C22⋊Q8—301no—
220C22⋊Q8—302no—
221C4×Q8—151no—
222C4×D4—151no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—31no—
228#103—102no—
229#103—301no—
230#102—301no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—42no—
236C22×D3—101no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—202no—
240C2×C3×C4—22no—
241C2×C3×C4—201no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—101no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248D12—52no—
249D12—101no—
250C4×D3—204no—
251C4×D3—201no—
252C4×D3—201no—
253Dic6—52no—
254Dic6—101no—
255Dic6—204no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5#93711yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5D3×SD1611yescharacteristic
266C4×C5#91411yescharacteristic
267C4×C5D3×Q1611yescharacteristic
268C4×C5#91811yescharacteristic
269Dic5—62no—
270Dic5—81no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—101no—
275C2×Q8—151no—
276C2×Q8—302no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—101no—
285C4⋊C4—21no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—151no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C4⋊C4#120212yes—
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—102no—
300C2×D3—201no—
301C2×D3—201no—
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—401no—
305C3×C4#405711yescharacteristic
306C3×C4D5×SD1611yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4D5×Q1611yescharacteristic
309Dic3—102no—
310Dic3—201no—
311Dic3—201no—
312C2×C5#506211yescharacteristic
313C2×C5#516911yescharacteristic
314C2×C5#518611yescharacteristic
315D5—122no—
316C23—301no—
317Q8—41no—
318Q8—41no—
319Q8—152no—
320Q8—202no—
321Q8—301no—
322Q8—604no—
323D4—152no—
324D4—301no—
325C2×C4—22no—
326C2×C4—201no—
327C2×C4—301no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—604no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4C2×#120211yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—121no—
338C8—201no—
339C2×C3#6504211yescharacteristic
340C2×C3#6506511yescharacteristic
341C2×C3#6509711yescharacteristic
342D3—202no—
343C5#7123711yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9157211yescharacteristic
348C4—21no—
349C4—42no—
350C4—302no—
351C4—401no—
352C4—601no—
353C4—601no—
354C4#9148711yescharacteristic
355C4#9150011yescharacteristic
356C4#9151111yescharacteristic
357C4#9152411yescharacteristic
358C3#1059925211yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1174906411yescharacteristic
361C2#1174931011yescharacteristic
362C2#1174938811yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1637
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×#65382C2semidirect
4. #11746917C2semidirect
5. C5×#4547C2semidirect
6. #11745845C2semidirect
28. #65382D3semidirect
62. #4547D5semidirect
297. C3×C5#1637semidirect
343. C5#71237semidirect
358. C3#10599252semidirect

Maximal subgroups

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

subgroupindex
#117564862
C3×#653822
#117469422
#117469172
C5×#45472
#117458452
#117458392
#105992523
#712375