Finite Group Databasebeta

← #14284719

Subgroups — #14284719

Order 1920.

492 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 100 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#11752556C211yesmaximal, characteristic
2#11750934C211yesmaximal, characteristic, complemented
3#11746859C211yesmaximal, characteristic, complemented
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599275—31nomaximal, Hall
9C2×#6766C412yes—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13#91465—21no—
14#91465—21no—
15#91434—21no—
16#91434—21no—
17#91368C412yes—
18C3×C5×C4⋊C8C2211yescharacteristic
19#91104—21no—
20C8×Dic15—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90957—21no—
25#90951—21no—
26#68382—51nomaximal, Hall
27#66059—31no—
28#65122—31no—
29#65122—31no—
30C5×#333—31no—
31#64766—31no—
32#64705—31no—
33#64705D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6C2×C412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×#1202—22no—
42C2×D5×Dic3—22no—
43#6766—44no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46C4×Dic15C2×C411yescharacteristic
47C4×Dic15D411yescharacteristic
48C4×Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C2×C3×#168—21no—
54#6665—22no—
55#6665—22no—
56#5716—51no—
57#4833—51no—
58#4833—51no—
59C3×#331—51no—
60#4544—51no—
61#4481—51no—
62#4481D511yescharacteristic, complemented
63C2×#713—32no—
64C5×C4⋊Q8—31no—
65#4093—32no—
66#4041—61no—
67#4041—61no—
68#4039—61no—
69#4039—61no—
70#4020C2×D311yescharacteristic
71C42×D5—31no—
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3952—61no—
75#3952—61no—
76C8×Dic5—61no—
77C8×Dic5—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1543—151noSylow
81C22×D15C22⋊C411yescharacteristic
82C22×C3×D5—22no—
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15C22⋊C411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C4×D15—21no—
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—22no—
94C2×C5×Dic3—22no—
95C5×Dic6—42no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101#1202—44no—
102D5×Dic3—44no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C2×#237—52no—
108C3×#127—51no—
109#938—101no—
110#938—101no—
111#936—52no—
112D4×Dic3—101no—
113D4×Dic3—101no—
114C42×D3—51no—
115#869C2×D511yescharacteristic
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118(C2×D3)⋊C8—101no—
119(C2×D3)⋊C8—101no—
120C8×Dic3—101no—
121C8×Dic3—101no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C2×C5×Q8—32no—
125#713—124no—
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—62no—
129C2×D20C4×D312yes—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—62no—
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139#685—62no—
140#685—62no—
141C4×Dic5—31no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C2×#168—21no—
145C2×#168—61no—
146#532—151no—
147#431—151no—
148#431—151no—
149#333—31no—
150#333—151no—
151#331—51no—
152#331—151no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×C3×D5—42no—
158C2×C3×D5—42no—
159C2×C3×D5—42no—
160C3×C4×C5—21no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13511yescharacteristic
165Dic15—21no—
166Dic15—21no—
167Dic15#10012yes—
168C5×Dic3—42no—
169C2×C3×D4—52no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C2×#67—102no—
173C22×Dic3—102no—
174#237—204no—
175C2×C4×D3—51no—
176C2×C4×D3—51no—
177C2×C4×D3—51no—
178C2×Dic6C4×D512yes—
179C2×C3×C8—21no—
180C2×C3×C8—101no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183#217—102no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4×Dic3—51no—
187C4×Dic3—51no—
188C4×Dic3—51no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C22×D5—22no—
192C22×D5—31no—
193C5×Q8—122no—
194C2×C4×C5—62no—
195C2×C4×C5C2×C4×D311yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—31no—
199C2×Dic5—31no—
200C2×Dic5—31no—
201D20—42no—
202D20—41no—
203D20—41no—
204D20—41no—
205D20—41no—
206D20—124no—
207C4×D5—62no—
208C4×D5—61no—
209C4×D5—61no—
210C4×D5—61no—
211C4×D5—61no—
212C4×D5—124no—
213C5×C8—41no—
214C5×C8—121no—
215#168—41no—
216#168—121no—
217C2×#41—152no—
218C4⋊Q8—31no—
219#127—51no—
220#124—152no—
221#121—301no—
222#121—301no—
223C4×D4—301no—
224C4×D4—301no—
225C2×C42—151no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228C4⋊C8—151no—
229C4⋊C8D3×D511yescharacteristic
230C22⋊C8—301no—
231C22⋊C8—301no—
232C4×C8—301no—
233C4×C8—301no—
234C2×C3×C5C2×#10011yescharacteristic
235C2×C3×C5#41611yescharacteristic
236C2×C3×C5#41611yescharacteristic
237D15—41no—
238C3×D5—82no—
239C23×C3—102no—
240C22×D3—51no—
241C3×D4—202no—
242C3×D4—201no—
243C3×D4—201no—
244C3×D4—201no—
245C3×D4—201no—
246C2×C3×C4C2×C4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249#67—204no—
250C2×Dic3—22no—
251C2×Dic3—51no—
252C2×Dic3—51no—
253C2×Dic3—51no—
254C2×Dic3—204no—
255C4×D3—102no—
256C4×D3—101no—
257C4×D3—101no—
258C4×D3—101no—
259C4×D3—101no—
260Dic6—42no—
261C3×C8—41no—
262C3×C8—201no—
263C3⋊C8—41no—
264C3⋊C8—201no—
265C22×C5D3×C22⋊C411yescharacteristic
266C2×D5—42no—
267C2×D5—42no—
268C2×D5—42no—
269C2×D5—61no—
270C2×D5—61no—
271C2×D5—61no—
272C4×C5—21no—
273C4×C5—122no—
274C4×C5#91211yescharacteristic
275C4×C5#91211yescharacteristic
276C4×C5#91611yescharacteristic
277C4×C5#91611yescharacteristic
278Dic5—32no—
279Dic5—61no—
280Dic5—61no—
281#41—604no—
282C2×Q8—32no—
283C2×D4—52no—
284C2×D4—101no—
285C2×D4—101no—
286C2×D4—302no—
287C22×C4—151no—
288C22×C4—151no—
289C22×C4—151no—
290C22×C4—302no—
291C2×C8—21no—
292C2×C8—61no—
293C2×C8—101no—
294C2×C8—301no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C22⋊C4—302no—
298C22⋊C4—302no—
299C42—151no—
300C42—151no—
301C42—151no—
302C42C2×D3×D511yescharacteristic
303C3×C5#154311yescharacteristic, complemented, Hall
304C22×C3—202no—
305C22×C3—202no—
306C22×C3—202no—
307C22×C3D5×C22⋊C411yescharacteristic
308C2×D3—101no—
309C2×D3—101no—
310C2×D3—101no—
311C3×C4—21no—
312C3×C4#406211yescharacteristic
313C3×C4#406211yescharacteristic
314C3×C4#406511yescharacteristic
315C3×C4#406511yescharacteristic
316Dic3—42no—
317Dic3—52no—
318Dic3—101no—
319Dic3—101no—
320C2×C5D3×#10011yescharacteristic
321C2×C5#477211yescharacteristic
322C2×C5#477211yescharacteristic
323D5—82no—
324D5—121no—
325C23—102no—
326C23—151no—
327Q8—122no—
328D4—202no—
329D4—201no—
330D4—201no—
331D4—201no—
332D4—201no—
333D4—604no—
334C2×C4—62no—
335C2×C4—151no—
336C2×C4—151no—
337C2×C4—151no—
338C2×C4—302no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4—301no—
342C2×C4—301no—
343C2×C4—604no—
344C2×C4C4×D3×D511yescharacteristic
345C2×C4#677711yescharacteristic
346C2×C4#679011yescharacteristic
347C8—41no—
348C8—121no—
349C8—201no—
350C8—601no—
351C2×C3—402no—
352C2×C3D5×#10011yescharacteristic
353C2×C3#6509311yescharacteristic
354C2×C3#6509311yescharacteristic
355D3—201no—
356C5#6838211yescharacteristic, complemented, Sylow
357C22—202no—
358C22—202no—
359C22—202no—
360C22—301no—
361C22—301no—
362C22—301no—
363C22#9147311yescharacteristic
364C4—21no—
365C4—122no—
366C4—152no—
367C4—301no—
368C4—301no—
369C4#9127611yescharacteristic
370C4#9127711yescharacteristic
371C4#9149711yescharacteristic
372C4#9152111yescharacteristic
373C3#1059927511yescharacteristic, complemented, Sylow
374C2—402no—
375C2—601no—
376C2#1174750611yescharacteristic
377C2#1174814111yescharacteristic
378C2#1174822411yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752556C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×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. #11750934C2semidirect
3. #11746859C2semidirect
4. C5×#4481C2semidirect
5. C3×#64705C2semidirect
6. #11745862C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
62. #4481D5semidirect
303. C3×C5#1543semidirect
356. C5#68382semidirect
373. C3#10599275semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509342
#117468592
C5×#44812
C3×#647052
#117458622
#117458522
#105992753
#683825