Finite Group Databasebeta

← #14290617

Subgroups — #14290617

Order 1920.

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

normal subgroups only

This group has 400 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
1C5×#5584C211yesmaximal, characteristic
2C3×#65309C211yesmaximal, characteristic, complemented
3#11747070C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602726—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#898—22no—
12C5×#892—21no—
13C5×#875—21no—
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C4×C5×Dic6—21no—
17C3×#4015C2211yescharacteristic
18C2×#6656—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3967—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90989—22no—
25#90970—21no—
26#71126—51nomaximal, Hall
27C5×#556—31no—
28#65367—31no—
29#65309D311yescharacteristic, complemented
30#65308—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D412yes—
51C5×Dic3⋊C4—22no—
52C4×C5×Dic3—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6656—42no—
57#5584D511yescharacteristic
58C3×#475—51no—
59#5083—51no—
60#5078—51no—
61#4535—51no—
62#4486—51no—
63#4483—51no—
64C5×C4⋊Q8—31no—
65C5×#126—62no—
66C5×#124—61no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—61no—
69C4×C5×Q8C2×D311yescharacteristic
70C4×C5×D4—31no—
71C5×#117—61no—
72C2×#687—61no—
73#4015C2×D311yescharacteristic
74#3967—21no—
75#3942—61no—
76#3940—21no—
77#3939—62no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1650—151noSylow
82C22×C5×D3—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×C5×Dic3—21no—
91C2×C5×Dic3—22no—
92C5×D12—21no—
93C5×D12—21no—
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C2×C3×Dic5—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C3×#168—41no—
104C3×C4⋊Q8—51no—
105C3×C4×Q8C2×D511yescharacteristic
106#946—21no—
107C2×#215—101no—
108#898—22no—
109#892—21no—
110#875—21no—
111C4×D12C2×D511yescharacteristic
112#869C2×D511yescharacteristic
113C4×Dic6—21no—
114C3×#106—101no—
115C3×C4⋊C8—51no—
116C3×#103—101no—
117#835—101no—
118#807—102no—
119C4⋊(C3⋊C8)—51no—
120C4×C3⋊C8—51no—
121C2×C5×Q8—61no—
122C2×C5×Q8#6711yescharacteristic
123C2×C5×D4—31no—
124C22×C4×C5—61no—
125C2×Dic10—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—32no—
129C5×C4⋊C4—62no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4#6711yescharacteristic
132C5×C22⋊C4—62no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—61no—
135C42×C5—21no—
136C42×C5—62no—
137C42×C5C22×D311yescharacteristic
138#687—122no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C2×#168—21no—
142C2×#168—61no—
143C2×#168—61no—
144#556—31no—
145#500—151no—
146#475—51no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—81no—
163C5×Dic3—42no—
164C5×Dic3—41no—
165C2×C3×Q8—101no—
166C2×C3×Q8C22⋊D511yescharacteristic
167C2×D12C22⋊D511yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6—21no—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C42—21no—
176C3×C42C22×D511yescharacteristic
177#215—202no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3C22⋊D512yes—
183C4⋊Dic3C22⋊D511yescharacteristic
184Dic3⋊C4—22no—
185C4×Dic3—22no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C23×C5—61no—
189C5×Q8—21no—
190C5×Q8—21no—
191C5×Q8—121no—
192C5×Q8—121no—
193C5×D4—61no—
194C5×D4—61no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—61no—
198C2×C4×C5—62no—
199C2×C4×C5—121no—
200C2×C4×C5—121no—
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—41no—
205Dic10—41no—
206Dic10—41no—
207#168—41no—
208#168—62no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—31no—
212C4⋊Q8—51no—
213#126—62no—
214#124—61no—
215C22⋊Q8—61no—
216C4×Q8—61no—
217C4×Q8D3×D511yescharacteristic
218C4×D4—31no—
219#117—61no—
220#107—302no—
221#106—101no—
222C4⋊C8—51no—
223C4⋊C8—151no—
224#103—101no—
225#103—301no—
226C4×C8—151no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C5×D3—81no—
231C22×D3—21no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—201no—
235C3×Q8—201no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—201no—
239C2×C3×C4C2×C22⋊D511yescharacteristic
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—22no—
244D12—21no—
245D12—21no—
246C4×D3—41no—
247C4×D3—41no—
248Dic6—41no—
249Dic6—41no—
250C3×C8—201no—
251C3⋊C8—102no—
252C3⋊C8—201no—
253C22×C5—121no—
254C22×C5—121no—
255C22×C5—121no—
256C22×C5#93711yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—41no—
260C4×C5—122no—
261C4×C5—121no—
262C4×C5#91411yescharacteristic
263C4×C5#91611yescharacteristic
264C4×C5#94211yescharacteristic
265C4×C5#95011yescharacteristic
266Dic5—81no—
267C2×Q8—61no—
268C2×Q8—101no—
269C2×Q8#120111yescharacteristic
270C2×D4—31no—
271C22×C4—61no—
272SD16—602no—
273C2×C8—101no—
274C2×C8—301no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—31no—
278C4⋊C4—32no—
279C4⋊C4—62no—
280C4⋊C4—61no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4#120111yescharacteristic
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—61no—
287C42—21no—
288C42—62no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#409911yescharacteristic
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—401no—
299C3×C4#409511yescharacteristic
300C3×C4#409611yescharacteristic
301C3×C4#409611yescharacteristic
302C3×C4#409711yescharacteristic
303Dic3—42no—
304Dic3—41no—
305C2×C5—241no—
306C2×C5#504711yescharacteristic
307C2×C5#517211yescharacteristic
308C2×C5#520511yescharacteristic
309C23—61no—
310Q8—21no—
311Q8—21no—
312Q8—121no—
313Q8—121no—
314Q8—201no—
315Q8—201no—
316D4—61no—
317D4—61no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—61no—
321C2×C4—62no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—201no—
325C2×C4C2×#120111yescharacteristic
326C2×C4D3×C22⋊D511yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—201no—
329C8—302no—
330C8—601no—
331C2×C3#6552711yescharacteristic
332C2×C3#6552811yescharacteristic
333C2×C3#6553511yescharacteristic
334D3—81no—
335C5#7112611yescharacteristic, complemented, Sylow
336C22—121no—
337C22—121no—
338C22—121no—
339C22#9156811yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—122no—
344C4—121no—
345C4—401no—
346C4#9129711yescharacteristic
347C4#9130911yescharacteristic
348C4#9150411yescharacteristic
349C4#9151711yescharacteristic
350C3#1060272611yescharacteristic, complemented, Sylow
351C2—241no—
352C2#1174853811yescharacteristic
353C2#1174928111yescharacteristic
354C2#1174946511yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1650
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×#65309C2semidirect
4. #11746962C2semidirect
5. #11746356C2semidirect
6. #11745857C2semidirect
29. #65309D3semidirect
290. C3×C5#1650semidirect
335. C5#71126semidirect
350. C3#10602726semidirect

Maximal subgroups

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

subgroupindex
C5×#55842
C3×#653092
#117470702
#117469622
#117463562
#117458572
#117458362
#106027263
#711265