Finite Group Databasebeta

← #14289838

Subgroups — #14289838

Order 1920.

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

normal subgroups only

This group has 388 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×#5732C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602725—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#947—21no—
12C5×Q8×Dic3—21no—
13C5×#898—22no—
14C5×#897—21no—
15C5×#892—21no—
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90985—21no—
24#90973—21no—
25#90967—21no—
26#68435—51nomaximal, Hall
27C5×#556—31no—
28#65382—31no—
29#65310—31no—
30#65297—31no—
31#64767D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C5×Dic6D411yescharacteristic
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D412yes—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—22no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—22no—
53C4×C5×Dic3—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#5732D511yescharacteristic
57#5093—51no—
58#4850—51no—
59#4842—51no—
60C3×#332—51no—
61#4484—51no—
62#4483—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C5×#126—62no—
65C5×#124—61no—
66C5×C22⋊Q8—61no—
67C4×C5×Q8—31no—
68C4×C5×Q8—61no—
69C4×C5×D4—31no—
70C5×#117—61no—
71#4015—31no—
72#3967—61no—
73#3964—61no—
74#3942—62no—
75#3940—61no—
76#3939—61no—
77C4⋊#168C2×D311yescharacteristic
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1638—151noSylow
81C22×C5×D3—21no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
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×D12—21no—
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C5×Dic6—21no—
98C5×Dic6—21no—
99C3⋊#168—41no—
100C3×#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103#947—21no—
104Q8×Dic3—21no—
105#898—22no—
106#897—21no—
107#892—21no—
108C4×D12C2×D511yescharacteristic
109#869—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×C4⋊C8—51no—
112C3×C4⋊C8—51no—
113#821—101no—
114#818—101no—
115#817—101no—
116#816—101no—
117#810—102no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×C5×Q8—31no—
121C2×C5×D4—31no—
122C22×C4×C5—61no—
123C2×Dic10—61no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—62no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4D1212yes—
130C5×C22⋊C4—62no—
131C5×C22⋊C4—62no—
132C5×C22⋊C4—61no—
133C42×C5—62no—
134C42×C5—61no—
135C42×C5C22×D311yescharacteristic
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C2×#168—21no—
139C2×#168—21no—
140C2×#168—61no—
141#556—31no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332—51no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—81no—
159C5×Dic3—41no—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C2×C3×Q8—21no—
163C2×D12C22⋊D511yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6—101no—
166C2×Dic6C22⋊D511yescharacteristic
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C22⋊D512yes—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—22no—
174(C2×D3)⋊C4—21no—
175C4⋊Dic3—22no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178C4⋊Dic3C22⋊D511yescharacteristic
179C4⋊Dic3C22⋊D511yescharacteristic
180Dic3⋊C4—21no—
181C4×Dic3—22no—
182C4×Dic3—21no—
183C2×C3⋊C8—101no—
184C23×C5—61no—
185C5×Q8—41no—
186C5×Q8—41no—
187C5×Q8—61no—
188C5×Q8—61no—
189C5×D4—61no—
190C5×D4—61no—
191C2×C4×C5—22no—
192C2×C4×C5—61no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5—121no—
196C2×C4×C5—121no—
197C2×C4×C5C2×D1211yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×Dic5—121no—
201Dic10—122no—
202#168—41no—
203#168—41no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8D3×D511yescharacteristic
207#126—62no—
208#124—61no—
209C22⋊Q8—61no—
210C4×Q8—31no—
211C4×Q8—61no—
212C4×D4—31no—
213#117—61no—
214#107—301no—
215#106—301no—
216C4⋊C8—51no—
217C4⋊C8—51no—
218#103—301no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C5×D3—81no—
226C22×D3—21no—
227C3×Q8—41no—
228C3×Q8—41no—
229C2×C3×C4—22no—
230C2×C3×C4C2×C22⋊D511yescharacteristic
231C2×C3×C4C2×C22⋊D511yescharacteristic
232C2×C3×C4C2×C22⋊D511yescharacteristic
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—201no—
237D12—21no—
238D12—21no—
239C4×D3—41no—
240C4×D3—41no—
241Dic6—21no—
242Dic6—21no—
243Dic6—202no—
244C3×C8—201no—
245C3×C8—201no—
246C3⋊C8—201no—
247C22×C5—121no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5#88211yescharacteristic
251C4×C5—21no—
252C4×C5—42no—
253C4×C5—121no—
254C4×C5—121no—
255C4×C5—121no—
256C4×C5#91211yescharacteristic
257C4×C5#91511yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5#91811yescharacteristic
260Dic5—241no—
261C2×Q8—21no—
262C2×Q8—31no—
263C2×Q8—301no—
264C2×D4—31no—
265C22×C4—61no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—31no—
271C4⋊C4—31no—
272C4⋊C4—62no—
273C4⋊C4—61no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4#120312yes—
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—61no—
280C42—62no—
281C42—61no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#409911yescharacteristic
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C3×C4—21no—
289C3×C4—42no—
290C3×C4#409611yescharacteristic
291C3×C4#409611yescharacteristic
292C3×C4#409711yescharacteristic
293C3×C4#409711yescharacteristic
294Dic3—41no—
295Dic3—41no—
296Dic3—41no—
297Dic3—401no—
298C2×C5—241no—
299C2×C5#475311yescharacteristic
300C2×C5#478311yescharacteristic
301C2×C5#480811yescharacteristic
302C23—61no—
303Q8—41no—
304Q8—41no—
305Q8—61no—
306Q8—61no—
307Q8—602no—
308D4—61no—
309D4—61no—
310C2×C4—22no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—601no—
317C2×C4C2×#120311yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C2×C4D3×C22⋊D511yescharacteristic
320C8—201no—
321C8—201no—
322C8—601no—
323C2×C3#6552811yescharacteristic
324C2×C3#6552811yescharacteristic
325C2×C3#6553411yescharacteristic
326D3—81no—
327C5#6843511yescharacteristic, complemented, Sylow
328C22—121no—
329C22—121no—
330C22—121no—
331C22#9157011yescharacteristic
332C4—21no—
333C4—42no—
334C4—121no—
335C4—121no—
336C4—121no—
337C4—1201no—
338C4#9148611yescharacteristic
339C4#9149311yescharacteristic
340C4#9151011yescharacteristic
341C4#9151711yescharacteristic
342C3#1060272511yescharacteristic, complemented, Sylow
343C2—241no—
344C2#1174905411yescharacteristic
345C2#1174930011yescharacteristic
346C2#1174938711yescharacteristic
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#1638
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. #11751194C2semidirect
3. #11746961C2semidirect
5. C3×#64767C2semidirect
6. #11745842C2semidirect
31. #64767D3semidirect
283. C3×C5#1638semidirect
327. C5#68435semidirect
342. C3#10602725semidirect

Maximal subgroups

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

subgroupindex
C5×#57322
#117511942
#117469612
#117468832
C3×#647672
#117458422
#117458362
#106027253
#684355