Finite Group Databasebeta

← #14289508

Subgroups — #14289508

Order 1920.

428 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5730C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C3×#64766C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602717—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—22no—
11#91758C2211yescharacteristic
12C5×#946—22no—
13C5×#897—21no—
14C5×#893—21no—
15C5×D3×C4⋊C4—21no—
16C5×#890—21no—
17C4×C5×D12C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90985—21no—
24#90973—21no—
25#90967—21no—
26#68492—51nomaximal, Hall
27C5×#554—31no—
28#65381—31no—
29#65310—31no—
30#65297—31no—
31#64766D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D412yes—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C4×C5×D3—22no—
39C2×C5×Dic6D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6718—44no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—22no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—22no—
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#5730D511yescharacteristic
58#5092—51no—
59#4850—51no—
60#4842—51no—
61C3×#333—51no—
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C5×#125—61no—
66C5×C22⋊Q8—61no—
67C5×C22⋊Q8—62no—
68C4×C5×Q8—31no—
69C4×C5×D4—31no—
70C4×C5×D4—61no—
71C2×C5×C4⋊C4—61no—
72C2×#689—62no—
73#4015—31no—
74#3967—61no—
75#3964—61no—
76#3940—61no—
77#3939—61no—
78C4⋊#168C2×D311yescharacteristic
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1632—151noSylow
82C22×C5×D3—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—41no—
89Dic30—42no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×D12—21no—
94C5×D12Q1612yescomplemented
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C4×C5×D3—82no—
98C5×Dic6—21no—
99C5×Dic6—21no—
100C3⋊#168—22no—
101C3×#168—41no—
102C3×#168—41no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#946—22no—
105C2×#216—102no—
106#897—21no—
107#893—21no—
108D3×C4⋊C4—21no—
109#890—21no—
110C4×D12C2×D511yescharacteristic
111#869—51no—
112C4×Dic6C2×D511yescharacteristic
113C3×C4⋊C8—51no—
114C3×C4⋊C8—51no—
115#821—101no—
116#818—101no—
117#817—101no—
118#816—101no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—31no—
121C2×C5×Q8D1212yes—
122C2×C5×D4—31no—
123C22×C4×C5—62no—
124C22×C4×C5—61no—
125C2×Dic10—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—62no—
131C5×C4⋊C4—62no—
132C5×C4⋊C4—61no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—61no—
135C42×C5—61no—
136C42×C5C22×D311yescharacteristic
137#689—124no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140C2×#168—21no—
141C2×#168—21no—
142C2×#168—61no—
143#554—31no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—51no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×C5×D3—22no—
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C3×C4×C5—21no—
155C3×C4×C5—42no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—81no—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C5×Dic3—41no—
164C2×C3×Q8C22⋊D512yes—
165C2×D12C22⋊D511yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—22no—
168C2×Dic6—101no—
169C2×Dic6C22⋊D511yescharacteristic
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C42C22×D511yescharacteristic
175#216—204no—
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—21no—
178C4⋊Dic3—22no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3C22⋊D511yescharacteristic
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—22no—
184Dic3⋊C4—21no—
185C4×Dic3—21no—
186C2×C3⋊C8—101no—
187C23×C5—61no—
188C5×Q8—42no—
189C5×Q8—61no—
190C5×Q8—61no—
191C5×D4—32no—
192C5×D4—61no—
193C2×C4×C5—22no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5—121no—
198C2×C4×C5—121no—
199C2×C4×C5—242no—
200C2×C4×C5C2×D1211yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×Dic5—121no—
204Dic10—122no—
205#168—41no—
206#168—41no—
207#168—62no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8D3×D511yescharacteristic
211#125—61no—
212C22⋊Q8—61no—
213C22⋊Q8—62no—
214C4×Q8—31no—
215C4×D4—31no—
216C4×D4—61no—
217C2×C4⋊C4—61no—
218#107—301no—
219#106—301no—
220C4⋊C8—51no—
221C4⋊C8—51no—
222#103—301no—
223#102—301no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C5×D3—42no—
229C22×D3—21no—
230C3×Q8—42no—
231C2×C3×C4—22no—
232C2×C3×C4C2×C22⋊D511yescharacteristic
233C2×C3×C4C2×C22⋊D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—201no—
239D12—21no—
240D12#68912yescomplemented
241C4×D3—41no—
242C4×D3—41no—
243C4×D3—82no—
244Dic6—21no—
245Dic6—21no—
246Dic6—202no—
247C3×C8—201no—
248C3×C8—201no—
249C3⋊C8—102no—
250C22×C5—62no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5#88211yescharacteristic
254C4×C5—21no—
255C4×C5—42no—
256C4×C5—121no—
257C4×C5—121no—
258C4×C5—121no—
259C4×C5#91511yescharacteristic
260C4×C5#91611yescharacteristic
261C4×C5D3×Q1611yescharacteristic
262C4×C5#91811yescharacteristic
263Dic5—241no—
264C2×Q8—31no—
265C2×Q8—301no—
266C2×Q8#120312yes—
267C2×D4—31no—
268C22×C4—62no—
269C22×C4—61no—
270Q16—604no—
271C2×C8—101no—
272C2×C8—101no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—62no—
279C4⋊C4—62no—
280C4⋊C4—61no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—62no—
284C22⋊C4—61no—
285C42—61no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#409911yescharacteristic
289C2×D3—22no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—42no—
294C3×C4#408811yescharacteristic
295C3×C4C2×#68911yescharacteristic
296C3×C4#409611yescharacteristic
297C3×C4#409711yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—41no—
301Dic3—401no—
302C2×C5—122no—
303C2×C5#474711yescharacteristic
304C2×C5#480811yescharacteristic
305C2×C5#480911yescharacteristic
306C23—61no—
307Q8—42no—
308Q8—61no—
309Q8—61no—
310Q8—602no—
311D4—32no—
312D4—61no—
313C2×C4—22no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—121no—
318C2×C4—121no—
319C2×C4—242no—
320C2×C4—601no—
321C2×C4C2×#120311yescharacteristic
322C2×C4D3×C22⋊D511yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—201no—
325C8—201no—
326C8—302no—
327C2×C3#6551711yescharacteristic
328C2×C3#6552811yescharacteristic
329C2×C3#6553011yescharacteristic
330D3—42no—
331C5#6849211yescharacteristic, complemented, Sylow
332C22—62no—
333C22—121no—
334C22—121no—
335C22#9157011yescharacteristic
336C4—21no—
337C4—42no—
338C4—121no—
339C4—121no—
340C4—121no—
341C4—1201no—
342C4D3×#68911yescharacteristic
343C4#9151011yescharacteristic
344C4#9151711yescharacteristic
345C4#9151811yescharacteristic
346C3#1060271711yescharacteristic, complemented, Sylow
347C2—122no—
348C2#1174914111yescharacteristic
349C2#1174930011yescharacteristic
350C2#1174930211yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1632
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. #11751193C2semidirect
3. #11746961C2semidirect
5. C3×#64766C2semidirect
6. #11745842C2semidirect
31. #64766D3semidirect
94. C5×D12Q16semidirect
240. D12#689semidirect
287. C3×C5#1632semidirect
331. C5#68492semidirect
346. C3#10602717semidirect

Maximal subgroups

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

subgroupindex
C5×#57302
#117511932
#117469612
#117468832
C3×#647662
#117458422
#117458362
#106027173
#684925