Finite Group Databasebeta

← #14289607

Subgroups — #14289607

Order 1920.

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

normal subgroups only

This group has 436 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×#5563C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic, complemented
3#11747096C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10602721—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#938—21no—
12C5×#930—21no—
13C5×#926—21no—
14C5×#892—21no—
15C5×#885—22no—
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6663—22no—
19#91116—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90985—21no—
25#90967—21no—
26#68203—51nomaximal, Hall
27C5×#555—31no—
28#65381—31no—
29#65297—31no—
30#65297—31no—
31#64766—31no—
32D4⋊#168—31no—
33D4⋊#168D311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C5×#67—22no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6D412yes—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C5×#217—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C4×C5×Dic3—22no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—44no—
57#5563D511yescharacteristic
58#5008—51no—
59#4842—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C5×#124—62no—
66C5×#121—61no—
67C5×#121—61no—
68C4×C5×D4—31no—
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—61no—
71C5×#117—61no—
72C2×#689—62no—
73#4015—31no—
74#3964—61no—
75#3964—61no—
76#3940—61no—
77#3940—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1634—151noSylow
82C23×C3×C5—21no—
83C22×C5×D3—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—41no—
93Dic30—42no—
94C5×#67—82no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—22no—
97C5×D12—21no—
98C5×D12—21no—
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C5×Dic6—42no—
102C3⋊#168—41no—
103C3×#168—22no—
104C3×#168—41no—
105C3×C4×D4C2×D511yescharacteristic
106#938—21no—
107#930—21no—
108#926—21no—
109C2×Dic12—102no—
110#892—21no—
111#885—22no—
112C4×D12C2×D511yescharacteristic
113#869—51no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4×C8—51no—
117#832—101no—
118#821—101no—
119#817—101no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C2×C5×Q8—32no—
123C2×C5×D4—31no—
124C2×C5×D4—62no—
125C2×C5×D4D1211yescharacteristic
126C22×C4×C5—21no—
127C22×C4×C5—61no—
128C2×Dic10—61no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4D1211yescharacteristic
133C5×C22⋊C4—21no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—61no—
137C42×C5—62no—
138C42×C5C22×D311yescharacteristic
139#689—124no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C2×#168—21no—
143C2×#168—21no—
144C2×#168—61no—
145#555—31no—
146#494—151no—
147#476—151no—
148#476—151no—
149#333—151no—
150D4⋊C8—51no—
151D4⋊C8—151no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—81no—
166C5×Dic3—41no—
167C5×Dic3—42no—
168C2×C3×D4C22⋊D511yescharacteristic
169C22×C3×C4—21no—
170C2×#67—22no—
171C2×D12C22⋊D511yescharacteristic
172C2×C4×D3—21no—
173C2×Dic6—101no—
174C2×Dic6C22⋊D512yes—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C22⋊C4—21no—
179C3×C42C22×D511yescharacteristic
180#217—22no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3C22⋊D511yescharacteristic
188C4×Dic3—22no—
189C2×C3⋊C8—101no—
190Dic12—204no—
191C23×C5—21no—
192C23×C5—61no—
193C5×Q8—122no—
194C5×D4—21no—
195C5×D4—21no—
196C5×D4—61no—
197C5×D4—61no—
198C5×D4—242no—
199C2×C4×C5—21no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—61no—
203C2×C4×C5—62no—
204C2×C4×C5—121no—
205C2×C4×C5—121no—
206C2×C4×C5C2×D1211yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×Dic5—121no—
210Dic10—122no—
211#168—22no—
212#168—41no—
213#168—121no—
214C2×Q16—302no—
215C4⋊Q8—31no—
216C4⋊Q8—151no—
217#124—62no—
218#121—61no—
219#121—61no—
220C4×D4—31no—
221C4×D4D3×D511yescharacteristic
222#117—61no—
223#117—61no—
224#106—301no—
225#106—301no—
226C4⋊C8—51no—
227C4⋊C8—151no—
228#102—301no—
229#102—301no—
230C4×C8—51no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C5×D3—81no—
236C23×C3—21no—
237C22×D3—21no—
238C3×D4—21no—
239C3×D4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246#67—82no—
247C2×Dic3—21no—
248C2×Dic3—22no—
249C2×Dic3—201no—
250D12—21no—
251D12—21no—
252C4×D3—41no—
253C4×D3—41no—
254Dic6—42no—
255Dic6—202no—
256C3×C8—102no—
257C3×C8—201no—
258C3⋊C8—201no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#88211yescharacteristic
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—121no—
269C4×C5—122no—
270C4×C5#90411yescharacteristic
271C4×C5#90911yescharacteristic
272C4×C5#91211yescharacteristic
273C4×C5#91511yescharacteristic
274Dic5—241no—
275C2×Q8—32no—
276C2×Q8—301no—
277C2×D4—31no—
278C2×D4—62no—
279C2×D4#120311yescharacteristic
280C22×C4—21no—
281C22×C4—61no—
282Q16—604no—
283C2×C8—101no—
284C2×C8—101no—
285C2×C8—301no—
286C4⋊C4—31no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#120311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—62no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3#409911yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4#409611yescharacteristic
309C3×C4#409611yescharacteristic
310C3×C4#409711yescharacteristic
311C3×C4#409711yescharacteristic
312Dic3—41no—
313Dic3—42no—
314Dic3—401no—
315C2×C5—81no—
316C2×C5—241no—
317C2×C5#473311yescharacteristic
318C2×C5#478311yescharacteristic
319C2×C5#482211yescharacteristic
320C23—21no—
321C23—61no—
322Q8—122no—
323Q8—602no—
324D4—21no—
325D4—21no—
326D4—61no—
327D4—61no—
328D4—242no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—61no—
333C2×C4—62no—
334C2×C4—121no—
335C2×C4—121no—
336C2×C4—601no—
337C2×C4C2×#120311yescharacteristic
338C2×C4D3×C22⋊D511yescharacteristic
339C2×C4D3×C22⋊D511yescharacteristic
340C8—102no—
341C8—201no—
342C8—601no—
343C2×C3—81no—
344C2×C3#6552811yescharacteristic
345C2×C3#6552811yescharacteristic
346C2×C3#6553011yescharacteristic
347D3—81no—
348C5#6820311yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22#9157011yescharacteristic
356C4—21no—
357C4—41no—
358C4—121no—
359C4—122no—
360C4—1201no—
361C4#9130311yescharacteristic
362C4#9132211yescharacteristic
363C4#9148611yescharacteristic
364C4#9149311yescharacteristic
365C3#1060272111yescharacteristic, complemented, Sylow
366C2—81no—
367C2—241no—
368C2#1174836111yescharacteristic
369C2#1174905411yescharacteristic
370C2#1174942011yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11751109C2semidirect
3. #11747096C2semidirect
4. #11746883C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745862C2semidirect
7. #11745837C2semidirect
33. D4⋊#168D3semidirect
298. C3×C5#1634semidirect
348. C5#68203semidirect
365. C3#10602721semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
#117511092
#117470962
#117468832
C3×D4⋊#1682
#117458622
#117458372
#106027213
#682035