Finite Group Databasebeta

← #14289798

Subgroups — #14289798

Order 1920.

456 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 104 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×D4×Dic6C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic
3#11746959C211yesmaximal, characteristic, complemented
4#11746924C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745857C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602708—31nomaximal, Hall
9C22×C5×Dic6—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C5×D4×Dic3—21no—
12C5×#924—21no—
13C5×#888—21no—
14C5×#878—22no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×#3964—21no—
21C3×#3940—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90989—21no—
24#90972—21no—
25#90970—22no—
26#71142—51nomaximal, Hall
27C5×D4×Q8—31no—
28#65382—31no—
29#65310—31no—
30#65297D311yescharacteristic
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×C5×Dic3—22no—
37C2×C5×Dic6—22no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—42no—
40C2×C5×Dic6—42no—
41C2×C5×Dic6D411yescharacteristic
42C2×C3×Dic10—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×#217—22no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×C4⋊Dic3D412yes—
52C5×Dic3⋊C4—22no—
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58D4×Dic6D511yescharacteristic
59C3×#476—51no—
60#5091—51no—
61#5079—51no—
62D4⋊(C3⋊C8)—51no—
63#4486—51no—
64#4484—51no—
65C22×C5×Q8—61no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8—61no—
68C5×C22⋊Q8—62no—
69C5×C22⋊Q8—61no—
70C4×C5×Q8—31no—
71C4×C5×D4—61no—
72C4×C5×D4C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74#3967—61no—
75#3964—21no—
76#3942—62no—
77#3940—21no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1637—151noSylow
83C23×C3×C5—21no—
84C3×C5×D4—21no—
85C3×C5×D4Q1612yes—
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
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—22no—
95C2×C5×Dic3—44no—
96C5×Dic6—21no—
97C5×Dic6—44no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C5×Dic6SD1612yes—
101C2×C3×Dic5—41no—
102C3×Dic10—42no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C22×Dic6—21no—
107C3×C4⋊Q8—51no—
108C3×C4×D4C2×D511yescharacteristic
109D4×Dic3—21no—
110#924—21no—
111#888—21no—
112#878—22no—
113#869C2×D511yescharacteristic
114C4×Dic6C2×D511yescharacteristic
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×#102—101no—
118#835—102no—
119#810—101no—
120#807—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—31no—
124C2×C5×Q8—62no—
125C2×C5×Q8—61no—
126C2×C5×Q8—122no—
127C2×C5×Q8—122no—
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C22×C4×C5—62no—
131C2×Dic10—21no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—62no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C22⋊C4—21no—
139C5×C22⋊C4—62no—
140C42×C5—61no—
141C42×C5C22×D311yescharacteristic
142C4⋊Dic5—21no—
143C4⋊Dic5—21no—
144C2×#168—21no—
145C2×#168—61no—
146C2×#168—61no—
147D4×Q8—31no—
148#487—151no—
149#477—151no—
150#476—51no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5—22no—
155C22×C3×C5—41no—
156C22×C3×C5—41no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—81no—
165C5×Dic3—22no—
166C5×Dic3—42no—
167C5×Dic3—41no—
168C2×C3×Q8—101no—
169C2×C3×D4C22⋊D511yescharacteristic
170C22×C3×C4—21no—
171C22×Dic3—22no—
172C2×Dic6—22no—
173C2×Dic6—21no—
174C2×Dic6—42no—
175C2×Dic6—42no—
176C2×Dic6C22⋊D511yescharacteristic
177C2×C3×C8—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4C22⋊D511yescharacteristic
181C3×C22⋊C4—21no—
182C3×C42C22×D511yescharacteristic
183#217—22no—
184C4⋊Dic3—21no—
185C4⋊Dic3C22⋊D511yescharacteristic
186C4⋊Dic3C22⋊D512yes—
187Dic3⋊C4—22no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C5×Q8—32no—
194C5×Q8—61no—
195C5×Q8—124no—
196C5×Q8—121no—
197C5×Q8—121no—
198C5×D4—21no—
199C5×D4#21612yes—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—61no—
204C2×C4×C5—61no—
205C2×C4×C5—62no—
206C2×C4×C5—124no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—41no—
211Dic10—42no—
212#168—41no—
213#168—121no—
214#168—121no—
215C22×Q8—61no—
216C4⋊Q8—31no—
217C4⋊Q8—51no—
218C4⋊Q8—61no—
219C22⋊Q8—62no—
220C22⋊Q8—61no—
221C4×Q8—31no—
222C4×D4—61no—
223C4×D4D3×D511yescharacteristic
224#107—301no—
225#106—101no—
226C4⋊C8—51no—
227C4⋊C8—151no—
228#103—302no—
229#103—301no—
230#102—101no—
231C4×C8—151no—
232C2×C3×C5—42no—
233C2×C3×C5#45011yescharacteristic
234C2×C3×C5#45111yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—21no—
237C3×Q8—202no—
238C3×D4—21no—
239C3×D4#68912yes—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—201no—
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—22no—
250C2×Dic3—44no—
251Dic6—21no—
252Dic6—44no—
253Dic6—41no—
254Dic6—41no—
255Dic6#68712yes—
256C3×C8—201no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—22no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—62no—
266C4×C5—122no—
267C4×C5—121no—
268C4×C5D3×SD1611yescharacteristic
269C4×C5#91411yescharacteristic
270C4×C5C2×#21611yescharacteristic
271C4×C5#95111yescharacteristic
272Dic5—81no—
273C2×Q8—31no—
274C2×Q8—62no—
275C2×Q8—61no—
276C2×Q8—101no—
277C2×Q8—122no—
278C2×Q8—122no—
279C2×D4#120111yescharacteristic
280C22×C4—21no—
281C22×C4—62no—
282C2×C8—101no—
283C2×C8—301no—
284C2×C8—301no—
285C4⋊C4—32no—
286C4⋊C4—31no—
287C4⋊C4—62no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4#120111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—62no—
295C42—61no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—22no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3#409911yescharacteristic
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—401no—
305C3×C4#407811yescharacteristic
306C3×C4C2×#68711yescharacteristic
307C3×C4#408811yescharacteristic
308C3×C4C2×#68911yescharacteristic
309Dic3—22no—
310Dic3—42no—
311Dic3—41no—
312C2×C5—42no—
313C2×C5#505011yescharacteristic
314C2×C5#516911yescharacteristic
315C2×C5#520111yescharacteristic
316C23—21no—
317Q8—32no—
318Q8—61no—
319Q8—124no—
320Q8—121no—
321Q8—121no—
322Q8—202no—
323D4—21no—
324D4#666112yes—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—62no—
331C2×C4—124no—
332C2×C4—201no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—201no—
337C8—601no—
338C8—601no—
339C2×C3—42no—
340C2×C3#6550711yescharacteristic
341C2×C3#6551711yescharacteristic
342C2×C3#6553411yescharacteristic
343C5#7114211yescharacteristic, complemented, Sylow
344C22—22no—
345C22—41no—
346C22—41no—
347C22#9156811yescharacteristic
348C4—21no—
349C4—41no—
350C4—62no—
351C4—121no—
352C4—122no—
353C4—401no—
354C4#9130711yescharacteristic
355C4C2×#666111yescharacteristic
356C4D3×#68711yescharacteristic
357C4#9149611yescharacteristic
358C3#1060270811yescharacteristic, complemented, Sylow
359C2—42no—
360C2#1174855911yescharacteristic
361C2#1174905811yescharacteristic
362C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1637
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
3. #11746959C2semidirect
4. #11746924C2semidirect
6. #11745857C2semidirect
7. #11745842C2semidirect
297. C3×C5#1637semidirect
343. C5#71142semidirect
358. C3#10602708semidirect

Maximal subgroups

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

subgroupindex
C5×D4×Dic62
C3×#652972
#117469592
#117469242
D4⋊(C3⋊#168)2
#117458572
#117458422
#106027083
#711425