Finite Group Databasebeta

← #14289033

Subgroups — #14289033

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×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic
3#11747079C211yesmaximal, characteristic
4#11747068C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602732—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×Q8×Dic3—21no—
11C5×#888—22no—
12C5×#888—21no—
13C5×#869—21no—
14C5×#869C2211yescharacteristic
15C4×C5×Dic6—21no—
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6655—22no—
20C2×#6655—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C3×#3941—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90964—21no—
26#71033—51nomaximal, Hall
27C5×Q82—31no—
28#65374—31no—
29#65316—31no—
30#65316D311yescharacteristic
31#64766—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—22no—
36C2×C5×Dic6D411yescharacteristic
37C2×C5×Dic6D412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3—22no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3D411yescharacteristic
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—44no—
58#6655—42no—
59Q8×Dic6D511yescharacteristic, complemented
60C3×#460—51no—
61#5076—51no—
62#5075—51no—
63#4535—51no—
64#4484—51no—
65#4481—51no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8—61no—
68C5×C4⋊Q8—62no—
69C5×C4⋊Q8—61no—
70C4×C5×Q8—31no—
71C4×C5×Q8—61no—
72C4×C5×Q8—61no—
73C4×C5×Q8C2×D311yescharacteristic
74C2×#688—21no—
75C2×#688—61no—
76C2×#688—62no—
77#4020C2×D311yescharacteristic
78#3941—21no—
79#3941—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1623—151noSylow
84C22×C3×D5—41no—
85C3×C5×Q8—21no—
86C3×C5×Q8SD1612yescomplemented
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C5×Dic3—21no—
93C2×C5×Dic3—22no—
94C2×C5×Dic3—21no—
95C5×Dic6—21no—
96C5×Dic6—42no—
97C5×Dic6—82no—
98C5×Dic6SD1612yescomplemented
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3⋊#168—22no—
105C3⋊#168—41no—
106C3×#168—41no—
107C2×C3×SD16—101no—
108C3×#127—51no—
109C3×C4×Q8C2×D511yescharacteristic
110Q8×Dic3—21no—
111C2×#214—101no—
112C2×#214—102no—
113#888—22no—
114#888—21no—
115#869—21no—
116#869C2×D511yescharacteristic
117C4×Dic6—21no—
118C4×Dic6C2×D511yescharacteristic
119C3×C4⋊C8—51no—
120C3×#102—101no—
121#832—101no—
122C4⋊(C3⋊C8)—51no—
123C4×C3⋊C8—51no—
124C2×C5×Q8—31no—
125C2×C5×Q8—32no—
126C2×C5×Q8—62no—
127C2×C5×Q8#6711yescharacteristic
128C2×D20—21no—
129C2×D20—21no—
130C2×D20—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—62no—
134C5×C4⋊C4—62no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4#6711yescharacteristic
139C42×C5—21no—
140C42×C5—62no—
141C42×C5—61no—
142C42×C5C22×D311yescharacteristic
143#688—42no—
144#688—124no—
145#688—122no—
146C2×#168—21no—
147C2×#168—61no—
148C2×#168—61no—
149Q82—31no—
150#492—151no—
151#460—51no—
152#460—151no—
153#333—151no—
154Q8⋊C8—151no—
155Q8⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C3×D5—81no—
158C2×C3×D5—81no—
159C2×C3×D5—81no—
160C3×C4×C5—22no—
161C3×C4×C5—21no—
162C3×C4×C5—41no—
163C3×C4×C5C2×SD1611yescharacteristic
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C3×C4×C5#13711yescharacteristic
167C5×Dic3—22no—
168C5×Dic3—42no—
169C5×Dic3—41no—
170C2×C3×Q8C22⋊D511yescharacteristic
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C2×C3×D4—101no—
174C2×Dic6—22no—
175C2×Dic6C22⋊D511yescharacteristic
176C2×Dic6C22⋊D512yes—
177C3×SD16—202no—
178C2×C3×C8—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C22⋊D511yescharacteristic
181C3×C42—21no—
182C3×C42C22×D511yescharacteristic
183#214—204no—
184#214—202no—
185C4⋊Dic3—22no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3C22⋊D511yescharacteristic
189Dic3⋊C4—22no—
190Dic3⋊C4—21no—
191C4×Dic3—22no—
192C4×Dic3—21no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C22×D5—41no—
196C5×Q8—21no—
197C5×Q8—32no—
198C5×Q8—61no—
199C5×Q8—122no—
200C5×Q8—242no—
201C5×Q8#21412yescomplemented
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—61no—
205C2×C4×C5—61no—
206C2×C4×C5—62no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210D20—42no—
211D20—41no—
212D20—41no—
213D20—41no—
214D20—41no—
215#168—41no—
216#168—62no—
217#168—121no—
218C2×SD16—101no—
219C2×SD16—301no—
220C2×SD16—302no—
221C4⋊Q8—31no—
222C4⋊Q8—61no—
223C4⋊Q8—62no—
224C4⋊Q8—61no—
225#127—51no—
226C4×Q8—31no—
227C4×Q8—61no—
228C4×Q8—61no—
229C4×Q8D3×D511yescharacteristic
230C4⋊C8—51no—
231C4⋊C8—151no—
232#102—101no—
233#102—301no—
234C4×C8—151no—
235C2×C3×C5#44811yescharacteristic
236C2×C3×C5#44811yescharacteristic
237C2×C3×C5#45311yescharacteristic
238C3×D5—161no—
239C23×C3—201no—
240C3×Q8—21no—
241C3×Q8#68812yescomplemented
242C3×D4—202no—
243C3×D4—201no—
244C3×D4—201no—
245C3×D4—201no—
246C3×D4—201no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C2×Dic3—21no—
253C2×Dic3—22no—
254C2×Dic3—21no—
255Dic6—21no—
256Dic6—42no—
257Dic6—82no—
258Dic6#68812yescomplemented
259C3×C8—201no—
260C3⋊C8—102no—
261C3⋊C8—201no—
262C22×C5#93711yescharacteristic
263C2×D5—81no—
264C2×D5—81no—
265C2×D5—81no—
266C4×C5—21no—
267C4×C5—22no—
268C4×C5—41no—
269C4×C5—62no—
270C4×C5—122no—
271C4×C5—121no—
272C4×C5D3×SD1611yescharacteristic
273C4×C5#91511yescharacteristic
274C4×C5C2×#21411yescharacteristic
275C4×C5#95111yescharacteristic
276C2×Q8—31no—
277C2×Q8—32no—
278C2×Q8—62no—
279C2×Q8#120111yescharacteristic
280C2×D4—101no—
281C2×D4—101no—
282C2×D4—101no—
283SD16—202no—
284SD16—604no—
285SD16—602no—
286C2×C8—101no—
287C2×C8—301no—
288C2×C8—301no—
289C4⋊C4—21no—
290C4⋊C4—31no—
291C4⋊C4—62no—
292C4⋊C4—62no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4#120111yescharacteristic
297C42—21no—
298C42—62no—
299C42—61no—
300C42C2×D3×D511yescharacteristic
301C3×C5#162311yescharacteristic, complemented, Hall
302C22×C3—401no—
303C22×C3—401no—
304C22×C3—401no—
305C22×C3#409911yescharacteristic
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4C2×#68811yescharacteristic
310C3×C4C2×#68811yescharacteristic
311C3×C4#408811yescharacteristic
312C3×C4#408811yescharacteristic
313Dic3—22no—
314Dic3—42no—
315Dic3—41no—
316C2×C5#504011yescharacteristic
317C2×C5#517011yescharacteristic
318C2×C5#519811yescharacteristic
319D5—161no—
320C23—201no—
321Q8—21no—
322Q8—32no—
323Q8—61no—
324Q8—122no—
325Q8—242no—
326Q8#665512yescomplemented
327D4—202no—
328D4—201no—
329D4—201no—
330D4—201no—
331D4—201no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4C2×#120111yescharacteristic
338C2×C4D3×C22⋊D511yescharacteristic
339C2×C4D3×C22⋊D511yescharacteristic
340C8—201no—
341C8—302no—
342C8—601no—
343C2×C3—801no—
344C2×C3#6551611yescharacteristic
345C2×C3#6551611yescharacteristic
346C2×C3#6553011yescharacteristic
347C5#7103311yescharacteristic, complemented, Sylow
348C22—401no—
349C22—401no—
350C22—401no—
351C22#9156811yescharacteristic
352C4—21no—
353C4—22no—
354C4—41no—
355C4—62no—
356C4—122no—
357C4—121no—
358C4C2×#665511yescharacteristic
359C4#9130711yescharacteristic
360C4D3×#68811yescharacteristic
361C4#9151811yescharacteristic
362C3#1060273211yescharacteristic, complemented, Sylow
363C2—801no—
364C2#1174853611yescharacteristic
365C2#1174927811yescharacteristic
366C2#1174941911yescharacteristic
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#1623
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×Q8×Dic6C2semidirect
5. #11746356C2semidirect
6. #11745862C2semidirect
7. #11745842C2semidirect
59. Q8×Dic6D5semidirect
86. C3×C5×Q8SD16semidirect
98. C5×Dic6SD16semidirect
201. C5×Q8#214semidirect
241. C3×Q8#688semidirect
258. Dic6#688semidirect
301. C3×C5#1623semidirect
326. Q8#6655semidirect
347. C5#71033semidirect
362. C3#10602732semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×Dic62
C3×#653162
#117470792
#117470682
#117463562
#117458622
#117458422
#106027323
#710335