Finite Group Databasebeta

← #14289201

Subgroups — #14289201

Order 1920.

420 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5570C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic
3#11747068C211yesmaximal, characteristic
4#11746895C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602728—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×Q8×Dic3—21no—
11C5×#890—21no—
12C5×#890—22no—
13C5×#869—21no—
14C5×#869C2211yescharacteristic
15C4×C5×Dic6—21no—
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6655—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C3×#3941—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90964—22no—
25#90964—21no—
26#71030—51nomaximal, Hall
27C5×#557—31no—
28#65377—31no—
29#65316—31no—
30#65316D311yescharacteristic
31#64767—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—22no—
47C5×C4⋊Dic3—22no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D412yes—
51C5×Dic3⋊C4—22no—
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—22no—
54C4×C5×Dic3—21no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6655—42no—
58#5570D511yescharacteristic, complemented
59C3×#460—51no—
60#5075—51no—
61#5070—51no—
62#4535—51no—
63#4486—51no—
64#4484—51no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8—61no—
67C5×#125—62no—
68C5×#125—61no—
69C4×C5×Q8—31no—
70C4×C5×Q8—61no—
71C4×C5×Q8—61no—
72C4×C5×Q8C2×D311yescharacteristic
73C2×#688—21no—
74C2×#688—61no—
75#4020C2×D311yescharacteristic
76#3941—21no—
77#3941—61no—
78#3941—62no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1626—151noSylow
83C22×C3×D5—41no—
84C3×C5×Q8—21no—
85C3×C5×Q8SD1612yescomplemented
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—22no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C2×C3×SD16—101no—
107C3×#127—51no—
108C3×C4×Q8C2×D511yescharacteristic
109Q8×Dic3—21no—
110C2×#214—101no—
111#890—21no—
112#890—22no—
113#869—21no—
114#869C2×D511yescharacteristic
115C4×Dic6—21no—
116C4×Dic6C2×D511yescharacteristic
117C3×C4⋊C8—51no—
118C3×#102—101no—
119#832—102no—
120#832—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—31no—
124C2×C5×Q8—61no—
125C2×C5×Q8#6711yescharacteristic
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—32no—
132C5×C4⋊C4—62no—
133C5×C4⋊C4—62no—
134C5×C4⋊C4—62no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4#6711yescharacteristic
138C42×C5—21no—
139C42×C5—62no—
140C42×C5—61no—
141C42×C5C22×D311yescharacteristic
142#688—42no—
143#688—122no—
144C2×#168—21no—
145C2×#168—61no—
146C2×#168—61no—
147#557—31no—
148#486—151no—
149#460—51no—
150#460—151no—
151#332—151no—
152Q8⋊C8—151no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C5×Dic3—41no—
166C5×Dic3—42no—
167C5×Dic3—41no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C2×Dic6—21no—
173C2×Dic6C22⋊D511yescharacteristic
174C3×SD16—202no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180#214—202no—
181C4⋊Dic3—22no—
182C4⋊Dic3—22no—
183C4⋊Dic3—21no—
184C4⋊Dic3C22⋊D511yescharacteristic
185C4⋊Dic3C22⋊D512yes—
186Dic3⋊C4—22no—
187Dic3⋊C4—21no—
188C4×Dic3—22no—
189C4×Dic3—21no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C22×D5—41no—
193C5×Q8—21no—
194C5×Q8—61no—
195C5×Q8—61no—
196C5×Q8—121no—
197C5×Q8—121no—
198C5×Q8#21412yescomplemented
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—61no—
202C2×C4×C5—62no—
203C2×C4×C5—61no—
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207D20—42no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—41no—
212#168—41no—
213#168—121no—
214#168—121no—
215C2×SD16—101no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—61no—
219#127—51no—
220#125—62no—
221#125—61no—
222C4×Q8—31no—
223C4×Q8—61no—
224C4×Q8—61no—
225C4×Q8D3×D511yescharacteristic
226C4⋊C8—51no—
227C4⋊C8—151no—
228#102—101no—
229#102—301no—
230#102—302no—
231C4×C8—151no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—161no—
236C23×C3—201no—
237C3×Q8—21no—
238C3×Q8#68812yescomplemented
239C3×D4—202no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—22no—
252Dic6—21no—
253Dic6—21no—
254Dic6—41no—
255Dic6—41no—
256C3×C8—201no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—81no—
263C4×C5—21no—
264C4×C5—22no—
265C4×C5—41no—
266C4×C5—121no—
267C4×C5—122no—
268C4×C5—121no—
269C4×C5#91411yescharacteristic
270C4×C5#91611yescharacteristic
271C4×C5C2×#21411yescharacteristic
272C4×C5#95111yescharacteristic
273C2×Q8—31no—
274C2×Q8—61no—
275C2×Q8#120111yescharacteristic
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279SD16—202no—
280SD16—602no—
281C2×C8—101no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—31no—
286C4⋊C4—32no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4#120111yescharacteristic
293C42—21no—
294C42—62no—
295C42—61no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—401no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3#409911yescharacteristic
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4C2×#68811yescharacteristic
306C3×C4#408811yescharacteristic
307C3×C4#409511yescharacteristic
308C3×C4#409611yescharacteristic
309Dic3—41no—
310Dic3—42no—
311Dic3—41no—
312C2×C5#504011yescharacteristic
313C2×C5#517211yescharacteristic
314C2×C5#520111yescharacteristic
315D5—161no—
316C23—201no—
317Q8—21no—
318Q8—61no—
319Q8—61no—
320Q8—121no—
321Q8—121no—
322Q8#665512yescomplemented
323D4—202no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—61no—
331C2×C4—62no—
332C2×C4—61no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—201no—
337C8—601no—
338C8—601no—
339C2×C3—801no—
340C2×C3#6551611yescharacteristic
341C2×C3#6552711yescharacteristic
342C2×C3#6553411yescharacteristic
343C5#7103011yescharacteristic, complemented, Sylow
344C22—401no—
345C22—401no—
346C22—401no—
347C22#9156811yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—121no—
352C4—121no—
353C4—122no—
354C4C2×#665511yescharacteristic
355C4#9130711yescharacteristic
356C4#9150411yescharacteristic
357C4#9151711yescharacteristic
358C3#1060272811yescharacteristic, complemented, Sylow
359C2—801no—
360C2#1174853611yescharacteristic
361C2#1174928111yescharacteristic
362C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1626
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
1. C5×#5570C2semidirect
5. #11746356C2semidirect
6. #11745857C2semidirect
7. #11745842C2semidirect
58. #5570D5semidirect
85. C3×C5×Q8SD16semidirect
198. C5×Q8#214semidirect
238. C3×Q8#688semidirect
297. C3×C5#1626semidirect
322. Q8#6655semidirect
343. C5#71030semidirect
358. C3#10602728semidirect

Maximal subgroups

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

subgroupindex
C5×#55702
C3×#653162
#117470682
#117468952
#117463562
#117458572
#117458422
#106027283
#710305