Finite Group Databasebeta

← #14289612

Subgroups — #14289612

Order 1920.

436 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11752718C211yesmaximal, characteristic
2#11750800C211yesmaximal, characteristic, complemented
3#11746883C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic, complemented
5C5×#4459C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7#11745863C211yesmaximal, characteristic, complemented
8#10598996—31nomaximal, Hall
9C2×Dic60—22no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91462—22no—
15#91456—21no—
16#91449—21no—
17#91358—21no—
18#91338—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90987—21no—
23#90985—21no—
24#90967—21no—
25#90965—21no—
26#68203—51nomaximal, Hall
27#65897—31no—
28#65297—31no—
29#65131—31no—
30#64988—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64679D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×Dic30D412yes—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47Dic60—44no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54(C2×D3)⋊Dic5—22no—
55#6665—22no—
56Dic3×Dic5—22no—
57#5563—51no—
58#5008—51no—
59#4842—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4459D511yescharacteristic, complemented
64C4×C5×D4—31no—
65#4084—61no—
66#4076—61no—
67#4072—61no—
68C2×Dic20—62no—
69#4038—61no—
70#4031—62no—
71C4×D20C2×D311yescharacteristic
72#4015—31no—
73#4015—31no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3953—61no—
78#3949—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81#1634—151noSylow
82C22×C5×D3—21no—
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15—41no—
89Dic30—42no—
90Dic30—42no—
91C2×C5×Dic3—21no—
92C5×D12—21no—
93C5×D12—21no—
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1201—82no—
102C3×C5×C8—22no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C3×C4×D4—51no—
106#938—101no—
107#930—101no—
108#926—101no—
109C2×Dic12—102no—
110#892—101no—
111#885—102no—
112C4×D12C2×D511yescharacteristic
113#869—51no—
114#869—51no—
115C3×C4⋊C8—51no—
116C3×C4×C8C2×D511yescharacteristic
117#832—101no—
118#821—101no—
119#817—101no—
120#808—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×D4—31no—
123C22×C4×C5—61no—
124C2×C22⋊D5—62no—
125C2×D20D1211yescharacteristic
126C2×C4×D5—21no—
127C2×Dic10—32no—
128C2×Dic10—61no—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C22⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135#685—21no—
136#685—62no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141C4⋊Dic5D1211yescharacteristic
142C4×Dic5—62no—
143C2×#168—21no—
144Dic20—124no—
145#555—151no—
146#494—151no—
147#476—151no—
148#476—151no—
149#333—151no—
150D4⋊C8—31no—
151D4⋊C8—51no—
152C22×C3×C5#12011yescharacteristic
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C2×C5×D3—41no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C3×C4×C5—21no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—42no—
165Dic15—81no—
166C3×Dic5—41no—
167C5×Dic3—41no—
168C2×C3×D4—51no—
169C22×C3×C4—101no—
170C2×#67—102no—
171C2×D12D2011yescharacteristic
172C2×C4×D3—21no—
173C2×Dic6—52no—
174C2×Dic6—101no—
175C2×C3×C8—21no—
176C2×C3×C8—101no—
177C3×C4⋊C4—51no—
178C3×C22⋊C4—101no—
179C3×C42C22×D511yescharacteristic
180#217—102no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—102no—
183C4⋊Dic3—101no—
184C4⋊Dic3—101no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3D2011yescharacteristic
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190Dic12—204no—
191C23×C5—61no—
192C22×D5—21no—
193C5×D4—61no—
194C5×D4—61no—
195C2×C4×C5—61no—
196C2×C4×C5—121no—
197C2×C4×C5—121no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C22⋊D5—242no—
202C2×Dic5—21no—
203C2×Dic5—62no—
204C2×Dic5—121no—
205D20—21no—
206D20—21no—
207C4×D5—41no—
208C4×D5—41no—
209Dic10—122no—
210Dic10—122no—
211C5×C8—22no—
212C5×C8—121no—
213#168—41no—
214C2×Q16—302no—
215C4⋊Q8—151no—
216C4⋊Q8—151no—
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—31no—
221C4×D4—51no—
222#117—301no—
223#117—301no—
224#106—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—301no—
229#102—301no—
230C4×C8D3×D511yescharacteristic
231C2×C3×C5#45211yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45311yescharacteristic
234C3×D5—81no—
235C5×D3—81no—
236C23×C3—101no—
237C22×D3—21no—
238C3×D4—101no—
239C3×D4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246#67—402no—
247C2×Dic3—21no—
248C2×Dic3—102no—
249C2×Dic3—201no—
250D12—21no—
251D12—21no—
252C4×D3—41no—
253C4×D3—41no—
254Dic6—202no—
255Dic6—202no—
256C3×C8—22no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5—121no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#88211yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C4×C5—21no—
267C4×C5—121no—
268C4×C5#90411yescharacteristic
269C4×C5#90911yescharacteristic
270C4×C5#91211yescharacteristic
271C4×C5#91511yescharacteristic
272Dic5—41no—
273Dic5—122no—
274Dic5—241no—
275C2×Q8—152no—
276C2×Q8—301no—
277C2×D4—31no—
278C2×D4—51no—
279C2×D4—302no—
280C22×C4—61no—
281C22×C4—101no—
282Q16—604no—
283C2×C8—21no—
284C2×C8—61no—
285C2×C8—101no—
286C4⋊C4—31no—
287C4⋊C4—51no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C22⋊C4—61no—
293C22⋊C4—101no—
294C22⋊C4—302no—
295C22⋊C4—302no—
296C42—302no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—201no—
300C22×C3—201no—
301C22×C3—201no—
302C22×C3#402811yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—201no—
308C3×C4#405011yescharacteristic
309C3×C4#405511yescharacteristic
310C3×C4#405811yescharacteristic
311C3×C4#406111yescharacteristic
312Dic3—41no—
313Dic3—202no—
314Dic3—401no—
315C2×C5—241no—
316C2×C5#473311yescharacteristic
317C2×C5#478311yescharacteristic
318C2×C5#482211yescharacteristic
319D5—81no—
320C23—61no—
321C23—101no—
322Q8—602no—
323Q8—602no—
324D4—61no—
325D4—61no—
326D4—101no—
327D4—101no—
328D4—1202no—
329C2×C4—61no—
330C2×C4—101no—
331C2×C4—121no—
332C2×C4—121no—
333C2×C4—201no—
334C2×C4—201no—
335C2×C4—302no—
336C2×C4—601no—
337C2×C4D5×D1211yescharacteristic
338C2×C4D3×D2011yescharacteristic
339C2×C4#679011yescharacteristic
340C8—22no—
341C8—121no—
342C8—201no—
343C2×C3—401no—
344C2×C3#6502211yescharacteristic
345C2×C3#6507211yescharacteristic
346C2×C3#6511111yescharacteristic
347D3—81no—
348C5#6820311yescharacteristic, complemented, Sylow
349C22—121no—
350C22—121no—
351C22—121no—
352C22—201no—
353C22—201no—
354C22—201no—
355C22#9147611yescharacteristic
356C4—21no—
357C4—121no—
358C4—201no—
359C4—602no—
360C4—1201no—
361C4#9126011yescharacteristic
362C4#9127011yescharacteristic
363C4#9127311yescharacteristic
364C4#9127411yescharacteristic
365C3#1059899611yescharacteristic, complemented, Sylow
366C2—241no—
367C2—401no—
368C2#1174711811yescharacteristic
369C2#1174816211yescharacteristic
370C2#1174816411yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752718C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11750800C2semidirect
3. #11746883C2semidirect
4. #11746881C2semidirect
5. C5×#4459C2semidirect
6. C3×#64679C2semidirect
7. #11745863C2semidirect
33. #64679D3semidirect
63. #4459D5semidirect
298. C3×C5#1634semidirect
348. C5#68203semidirect
365. C3#10598996semidirect

Maximal subgroups

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

subgroupindex
#117527182
#117508002
#117468832
#117468812
C5×#44592
C3×#646792
#117458632
#105989963
#682035