Subgroups — #20258166

Order 6016.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689960	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689932	C₂	1	3	yes	maximal, complemented
4	#15689931	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689929	C₂	1	3	yes	maximal, complemented
6	#15689928	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689927	C₂	1	3	yes	maximal, complemented
8	#15689926	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689925	C₂	1	3	yes	maximal, complemented
10	#15689922	C₂	1	3	yes	maximal, complemented
11	#15689920	C₂	1	3	yes	maximal, complemented
12	C₂×#13094051	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₄₇	C₂	1	3	yes	maximal, complemented
14	#15689888	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
16	#13094072	—	2	1	no	—
17	#13094072	C₂²	1	3	yes	complemented
18	#13094070	—	2	1	no	—
19	#13094070	—	2	3	no	—
20	#13094070	C₂²	1	3	yes	complemented
21	#13094070	C₂²	1	3	yes	complemented
22	#13094070	C₂²	1	1	yes	characteristic, complemented
23	#13094070	C₂²	1	1	yes	characteristic, complemented
24	#13094069	—	2	3	no	—
25	#13094069	C₂²	1	3	yes	complemented
26	C₂×#10625354	—	2	1	no	—
27	C₂×#10625354	C₂²	1	3	yes	complemented
28	#41×D₄₇	—	2	1	no	—
29	#41×D₄₇	—	2	3	no	—
30	#41×D₄₇	C₂²	1	1	yes	characteristic
31	#41×D₄₇	C₂²	1	3	yes	complemented
32	#41×D₄₇	C₂²	1	3	yes	complemented
33	C₂×D₄×D₄₇	—	2	3	no	—
34	C₂×D₄×D₄₇	C₂²	1	3	yes	complemented
35	#13094056	C₂²	1	3	yes	complemented
36	#13094056	C₂²	1	3	yes	complemented
37	#13094055	C₂²	1	3	yes	complemented
38	#13094053	C₂²	1	1	yes	characteristic, complemented
39	#13094053	C₂²	1	3	yes	complemented
40	#13094052	C₂²	1	3	yes	complemented
41	#13094052	C₂²	1	3	yes	complemented
42	#13094051	C₂²	1	6	yes	complemented
43	#13094051	C₂²	1	3	yes	complemented
44	#13094051	C₂²	1	6	yes	complemented
45	#13094051	C₂²	1	6	yes	complemented
46	#13094051	C₂²	1	3	yes	complemented
47	#13094050	C₂²	1	3	yes	complemented
48	#13094049	C₂²	1	3	yes	complemented
49	#13094049	C₂²	1	3	yes	complemented
50	#13094048	C₂²	1	3	yes	complemented
51	#13094048	C₂²	1	3	yes	complemented
52	#13094047	C₂²	1	6	yes	complemented
53	#13094046	C₂²	1	3	yes	complemented
54	#13094045	C₂²	1	6	yes	complemented
55	#13094044	C₂²	1	3	yes	complemented
56	#13094044	C₂²	1	3	yes	complemented
57	C₂×#10625336	C₂²	1	3	yes	complemented
58	SD₁₆×D₄₇	C₂²	1	6	yes	complemented
59	C₂×D₃₇₆	C₂²	1	3	yes	complemented
60	C₂×#10625334	C₂²	1	3	yes	complemented
61	D₈×D₄₇	C₂²	1	6	yes	complemented
62	#13094032	C₂²	1	3	yes	complemented
63	#13094031	C₂²	1	1	yes	characteristic, complemented
64	#13094030	C₂²	1	3	yes	complemented
65	C₂×#10625324	C₂²	1	3	yes	complemented
66	M₁₆×D₄₇	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic, complemented
69	#137×C₄₇	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₄₇	C₂²	1	3	yes	complemented
71	#135×C₄₇	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₄₇	C₂²	1	3	yes	complemented
73	#131×C₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₄₇	—	2	3	no	—
75	#41×C₄₇	—	2	1	no	—
76	#41×C₄₇	—	2	3	no	—
77	#41×C₄₇	C₂³	1	3	yes	—
78	#41×C₄₇	C₂³	1	1	yes	characteristic
79	#41×C₄₇	C₂³	1	3	yes	complemented
80	C₂×Q₈×C₄₇	—	2	1	no	—
81	C₂×Q₈×C₄₇	C₂³	1	3	yes	complemented
82	C₂×D₄×C₄₇	—	2	3	no	—
83	C₂×D₄×C₄₇	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₄₇	—	2	6	no	—
85	C₂×C₂²⋊D₄₇	—	2	3	no	—
86	#10625354	—	2	1	no	—
87	#10625354	—	2	1	no	—
88	#10625354	—	2	3	no	—
89	#10625354	—	2	3	no	—
90	#10625354	—	2	3	no	—
91	#10625354	D₄	1	1	yes	characteristic
92	#10625354	C₂³	1	3	yes	—
93	#10625354	C₂³	1	3	yes	—
94	#10625354	C₂³	1	6	yes	complemented
95	Q₈×D₄₇	—	2	3	no	—
96	Q₈×D₄₇	D₄	1	1	yes	characteristic
97	Q₈×D₄₇	C₂³	1	1	yes	characteristic
98	Q₈×D₄₇	C₂³	1	3	yes	complemented
99	#10625352	—	2	3	no	—
100	#10625352	—	2	3	no	—
101	#10625352	—	2	3	no	—
102	#10625352	D₄	1	3	yes	—
103	#10625352	C₂³	1	3	yes	—
104	#10625352	C₂³	1	1	yes	characteristic
105	D₄×D₄₇	—	2	3	no	—
106	D₄×D₄₇	—	2	3	no	—
107	D₄×D₄₇	—	2	3	no	—
108	D₄×D₄₇	—	2	3	no	—
109	D₄×D₄₇	—	2	6	no	—
110	D₄×D₄₇	—	2	6	no	—
111	D₄×D₄₇	—	2	3	no	—
112	D₄×D₄₇	—	2	3	no	—
113	D₄×D₄₇	—	2	3	no	—
114	D₄×D₄₇	D₄	1	3	yes	—
115	D₄×D₄₇	C₂³	1	6	yes	—
116	D₄×D₄₇	C₂³	1	3	yes	—
117	D₄×D₄₇	C₂³	1	3	yes	complemented
118	#10625350	—	2	6	no	—
119	#10625350	—	2	3	no	—
120	#10625350	—	2	3	no	—
121	#10625350	—	2	3	no	—
122	#10625350	—	2	3	no	—
123	#10625350	C₂³	1	3	yes	—
124	#10625350	C₂³	1	3	yes	—
125	#10625350	C₂³	1	3	yes	complemented
126	C₂×D₁₈₈	—	2	3	no	—
127	C₂×D₁₈₈	—	2	3	no	—
128	C₂×D₁₈₈	—	2	3	no	—
129	C₂×D₁₈₈	C₂³	1	3	yes	—
130	C₂×D₁₈₈	C₂³	1	3	yes	complemented
131	C₂×C₄×D₄₇	—	2	3	no	—
132	C₂×C₄×D₄₇	—	2	3	no	—
133	C₂×C₄×D₄₇	—	2	3	no	—
134	C₂×C₄×D₄₇	C₂³	1	3	yes	—
135	Q₁₆×C₄₇	C₂³	1	3	yes	complemented
136	SD₁₆×C₄₇	C₂³	1	3	yes	complemented
137	SD₁₆×C₄₇	C₂³	1	6	yes	complemented
138	SD₁₆×C₄₇	C₂³	1	1	yes	characteristic, complemented
139	D₈×C₄₇	C₂³	1	3	yes	complemented
140	M₁₆×C₄₇	C₂³	1	3	yes	complemented
141	C₂×C₈×C₄₇	C₂³	1	3	yes	complemented
142	#10625337	C₂³	1	1	yes	characteristic, complemented
143	#10625337	C₂³	1	3	yes	complemented
144	#10625336	C₂³	1	6	yes	complemented
145	#10625336	C₂³	1	3	yes	complemented
146	#10625336	C₂³	1	3	yes	complemented
147	#10625335	C₂³	1	3	yes	complemented
148	#10625335	C₂³	1	1	yes	characteristic, complemented
149	#10625334	C₂³	1	3	yes	complemented
150	#10625334	C₂³	1	6	yes	complemented
151	#10625334	C₂³	1	3	yes	complemented
152	#10625329	C₂³	1	3	yes	complemented
153	C₂×C₄₇⋊C₈	C₂³	1	3	yes	complemented
154	Dic₁₈₈	C₂³	1	1	yes	characteristic, complemented
155	D₃₇₆	C₂³	1	6	yes	complemented
156	D₃₇₆	C₂³	1	3	yes	complemented
157	#10625325	C₂³	1	3	yes	complemented
158	#10625325	C₂³	1	3	yes	complemented
159	#10625324	C₂³	1	3	yes	—
160	#10625324	C₂³	1	1	yes	characteristic
161	#10625324	C₂³	1	3	yes	complemented
162	#10625324	C₂³	1	3	yes	complemented
163	C₈×D₄₇	C₂³	1	6	yes	complemented
164	C₂³×C₄₇	—	2	3	no	—
165	C₂²×D₄₇	—	2	3	no	—
166	C₂²×D₄₇	—	2	3	no	—
167	C₂²×D₄₇	—	2	3	no	—
168	C₂²×D₄₇	—	2	3	no	—
169	C₂²×D₄₇	—	2	6	no	—
170	C₂²×D₄₇	—	8	6	no	—
171	C₂²×D₄₇	C₂×D₄	1	3	yes	—
172	Q₈×C₄₇	—	2	3	no	—
173	Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₄₇	C₂⁴	1	3	yes	—
175	Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
176	D₄×C₄₇	—	2	3	no	—
177	D₄×C₄₇	—	2	3	no	—
178	D₄×C₄₇	—	2	3	no	—
179	D₄×C₄₇	C₂×D₄	1	3	yes	—
180	D₄×C₄₇	C₂⁴	1	1	yes	characteristic
181	D₄×C₄₇	C₂⁴	1	3	yes	—
182	C₂×C₄×C₄₇	—	2	3	no	—
183	C₂×C₄×C₄₇	—	2	3	no	—
184	C₂×C₄×C₄₇	—	2	3	no	—
185	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
186	C₂²⋊D₄₇	—	2	3	no	—
187	C₂²⋊D₄₇	—	2	3	no	—
188	C₂²⋊D₄₇	—	2	1	no	—
189	C₂²⋊D₄₇	—	2	3	no	—
190	C₂²⋊D₄₇	—	2	3	no	—
191	C₂²⋊D₄₇	—	2	6	no	—
192	C₂²⋊D₄₇	—	2	3	no	—
193	C₂²⋊D₄₇	C₂×D₄	1	6	yes	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	3	no	—
196	C₂×Dic₄₇	C₂×D₄	1	3	yes	—
197	D₁₈₈	—	2	3	no	—
198	D₁₈₈	—	2	3	no	—
199	D₁₈₈	—	2	6	no	—
200	D₁₈₈	—	2	3	no	—
201	D₁₈₈	—	2	3	no	—
202	D₁₈₈	C₂×D₄	1	3	yes	—
203	D₁₈₈	C₂⁴	1	3	yes	—
204	D₁₈₈	C₂⁴	1	3	yes	—
205	C₄×D₄₇	—	2	1	no	—
206	C₄×D₄₇	—	2	3	no	—
207	C₄×D₄₇	—	2	3	no	—
208	C₄×D₄₇	—	2	3	no	—
209	C₄×D₄₇	—	2	3	no	—
210	C₄×D₄₇	—	2	3	no	—
211	C₄×D₄₇	—	2	6	no	—
212	C₄×D₄₇	C₂×D₄	1	3	yes	—
213	C₄×D₄₇	C₂×D₄	1	3	yes	—
214	C₄×D₄₇	C₂⁴	1	3	yes	—
215	C₄×D₄₇	C₂⁴	1	1	yes	characteristic
216	Dic₉₄	—	2	1	no	—
217	Dic₉₄	—	2	3	no	—
218	Dic₉₄	C₂×D₄	1	3	yes	—
219	Dic₉₄	C₂⁴	1	1	yes	characteristic
220	Dic₉₄	C₂⁴	1	1	yes	characteristic
221	C₈×C₄₇	C₂⁴	1	3	yes	—
222	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
223	C₄₇⋊C₈	C₂⁴	1	3	yes	—
224	C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄₇	—	2	1	no	—
226	C₂²×C₄₇	—	2	3	no	—
227	C₂²×C₄₇	—	8	3	no	—
228	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
229	C₂×D₄₇	—	2	3	no	—
230	C₂×D₄₇	—	2	3	no	—
231	C₂×D₄₇	—	4	3	no	—
232	C₂×D₄₇	—	4	6	no	—
233	C₂×D₄₇	—	8	3	no	—
234	C₂×D₄₇	—	8	6	no	—
235	C₂×D₄₇	—	8	3	no	—
236	C₂×D₄₇	—	8	3	no	—
237	C₂×D₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₄₇	C₂²×D₄	1	3	yes	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	—	2	3	no	—
241	C₄×C₄₇	C₂²×D₄	1	3	yes	—
242	C₄×C₄₇	C₂⁵	1	1	yes	characteristic
243	Dic₄₇	—	2	1	no	—
244	Dic₄₇	—	2	1	no	—
245	Dic₄₇	C₂²×D₄	1	3	yes	—
246	Dic₄₇	C₂²×D₄	1	1	yes	characteristic
247	#3585	—	47	1	no	maximal, Sylow
248	C₂×C₄₇	—	2	3	no	—
249	C₂×C₄₇	—	4	3	no	—
250	C₂×C₄₇	—	4	1	no	—
251	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
252	D₄₇	—	2	1	no	—
253	D₄₇	—	2	3	no	—
254	D₄₇	—	4	3	no	—
255	D₄₇	—	4	3	no	—
256	#585	—	47	1	no	—
257	C₂×H(5,𝔽₂)	—	47	1	no	—
258	#577	—	47	1	no	—
259	#577	—	47	3	no	—
260	#577	—	47	3	no	—
261	#577	D₄₇	1	1	yes	characteristic, complemented
262	#576	—	47	1	no	—
263	#576	—	47	3	no	—
264	#576	—	47	3	no	—
265	#576	—	47	1	no	—
266	#575	—	47	3	no	—
267	#575	—	47	3	no	—
268	C₂×AGL(1,ℤ/8)	—	47	3	no	—
269	C₂×AGL(1,ℤ/8)	—	47	3	no	—
270	#568	—	47	1	no	—
271	C₄₇	#3585	1	1	yes	characteristic, complemented, Sylow
272	2₋¹⁺⁴	—	47	3	no	—
273	2₋¹⁺⁴	—	94	1	no	—
274	2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	47	3	no	—
276	H(5,𝔽₂)	—	47	1	no	—
277	H(5,𝔽₂)	—	47	1	no	—
278	H(5,𝔽₂)	—	47	3	no	—
279	H(5,𝔽₂)	—	47	3	no	—
280	H(5,𝔽₂)	—	94	3	no	—
281	H(5,𝔽₂)	—	94	3	no	—
282	H(5,𝔽₂)	—	94	1	no	—
283	H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic, complemented
284	C₂×#41	—	47	1	no	—
285	C₂×#41	—	47	3	no	—
286	C₂×#41	—	47	3	no	—
287	C₂×#41	—	47	3	no	—
288	C₂×#41	—	94	1	no	—
289	C₂×#41	—	94	1	no	—
290	C₂×#41	—	94	3	no	—
291	C₂²×D₄	—	47	3	no	—
292	C₂²×D₄	—	94	3	no	—
293	#137	—	47	3	no	—
294	#137	—	47	3	no	—
295	#137	—	47	3	no	—
296	#137	—	47	1	no	—
297	#137	—	47	3	no	—
298	#137	C₂×D₄₇	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	47	3	no	—
300	AGL(1,ℤ/8)	—	47	3	no	—
301	AGL(1,ℤ/8)	—	47	3	no	—
302	AGL(1,ℤ/8)	—	47	6	no	—
303	AGL(1,ℤ/8)	—	47	3	no	—
304	AGL(1,ℤ/8)	—	47	6	no	—
305	AGL(1,ℤ/8)	—	47	6	no	—
306	AGL(1,ℤ/8)	—	47	3	no	—
307	AGL(1,ℤ/8)	—	47	3	no	—
308	AGL(1,ℤ/8)	—	47	3	no	—
309	AGL(1,ℤ/8)	—	47	3	no	—
310	AGL(1,ℤ/8)	—	47	3	no	—
311	AGL(1,ℤ/8)	C₂×D₄₇	1	3	yes	complemented
312	#135	—	47	3	no	—
313	#135	—	47	3	no	—
314	#135	—	47	6	no	—
315	#135	—	47	6	no	—
316	#135	—	47	3	no	—
317	#135	C₂×D₄₇	1	3	yes	complemented
318	C₂×SD₁₆	—	47	3	no	—
319	C₂×SD₁₆	—	47	6	no	—
320	C₂×SD₁₆	C₂×D₄₇	1	3	yes	complemented
321	C₂×D₈	—	47	3	no	—
322	C₂×D₈	—	47	6	no	—
323	C₂×D₈	—	47	3	no	—
324	#131	—	47	1	no	—
325	#131	—	47	3	no	—
326	#131	—	47	3	no	—
327	#131	C₂×D₄₇	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	47	3	no	—
329	C₂×M₁₆	—	47	3	no	—
330	C₂⁴	—	94	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	47	1	no	—
334	#41	—	47	3	no	—
335	#41	—	47	3	no	—
336	#41	—	47	3	no	—
337	#41	—	47	3	no	—
338	#41	—	47	6	no	—
339	#41	—	47	3	no	—
340	#41	—	47	1	no	—
341	#41	—	47	3	no	—
342	#41	—	47	3	no	—
343	#41	—	94	3	no	—
344	#41	—	94	3	no	—
345	#41	—	94	6	no	—
346	#41	—	94	3	no	—
347	#41	—	94	3	no	—
348	#41	—	94	3	no	—
349	#41	—	94	3	no	—
350	#41	—	94	3	no	—
351	#41	—	94	3	no	—
352	#41	—	94	3	no	—
353	#41	—	94	3	no	—
354	#41	—	94	1	no	—
355	#41	—	94	1	no	—
356	#41	C₂²×D₄₇	1	3	yes	—
357	#41	C₂²×D₄₇	1	1	yes	characteristic
358	#41	C₂²×D₄₇	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	47	1	no	—
361	C₂×Q₈	—	47	1	no	—
362	C₂×Q₈	—	47	3	no	—
363	C₂×Q₈	—	94	3	no	—
364	C₂×Q₈	C₂²×D₄₇	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	47	3	no	—
367	C₂×D₄	—	47	6	no	—
368	C₂×D₄	—	47	3	no	—
369	C₂×D₄	—	47	3	no	—
370	C₂×D₄	—	47	3	no	—
371	C₂×D₄	—	47	3	no	—
372	C₂×D₄	—	94	3	no	—
373	C₂×D₄	—	94	3	no	—
374	C₂×D₄	—	94	3	no	—
375	C₂×D₄	—	94	3	no	—
376	C₂×D₄	—	94	3	no	—
377	C₂×D₄	—	94	3	no	—
378	C₂×D₄	—	94	6	no	—
379	C₂×D₄	—	94	3	no	—
380	C₂×D₄	—	94	6	no	—
381	C₂×D₄	—	94	3	no	—
382	C₂×D₄	—	94	3	no	—
383	C₂×D₄	—	94	6	no	—
384	C₂×D₄	—	94	3	no	—
385	C₂×D₄	—	94	3	no	—
386	C₂×D₄	C₂²×D₄₇	1	3	yes	—
387	C₂²×C₄	—	47	3	no	—
388	C₂²×C₄	—	94	3	no	—
389	C₂²×C₄	—	94	3	no	—
390	C₂²×C₄	—	94	3	no	—
391	Q₁₆	—	47	1	no	—
392	Q₁₆	—	47	3	no	—
393	Q₁₆	—	47	1	no	—
394	Q₁₆	C₂²×D₄₇	1	3	yes	complemented
395	SD₁₆	—	47	6	no	—
396	SD₁₆	—	47	3	no	—
397	SD₁₆	—	47	3	no	—
398	SD₁₆	—	47	3	no	—
399	SD₁₆	—	47	1	no	—
400	SD₁₆	—	47	3	no	—
401	SD₁₆	—	47	3	no	—
402	SD₁₆	C₂²×D₄₇	1	6	yes	complemented
403	SD₁₆	C₂²×D₄₇	1	3	yes	complemented
404	SD₁₆	C₂²×D₄₇	1	1	yes	characteristic, complemented
405	D₈	—	47	6	no	—
406	D₈	—	47	3	no	—
407	D₈	—	47	3	no	—
408	D₈	—	47	6	no	—
409	D₈	—	47	3	no	—
410	D₈	C₂²×D₄₇	1	3	yes	complemented
411	M₁₆	—	47	3	no	—
412	M₁₆	—	47	3	no	—
413	M₁₆	—	47	1	no	—
414	M₁₆	—	47	3	no	—
415	M₁₆	—	47	3	no	—
416	M₁₆	C₂²×D₄₇	1	3	yes	complemented
417	C₂×C₈	—	47	3	no	—
418	C₂×C₈	—	47	6	no	—
419	C₂×C₈	C₂²×D₄₇	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	47	3	no	—
422	C₂³	—	94	3	no	—
423	C₂³	—	94	6	no	—
424	C₂³	—	94	3	no	—
425	C₂³	—	94	3	no	—
426	C₂³	—	94	3	no	—
427	C₂³	—	376	6	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	47	3	no	—
430	Q₈	—	47	1	no	—
431	Q₈	—	47	1	no	—
432	Q₈	—	94	3	no	—
433	Q₈	—	94	1	no	—
434	Q₈	D₄×D₄₇	1	1	yes	characteristic
435	Q₈	C₂³×D₄₇	1	3	yes	—
436	Q₈	C₂³×D₄₇	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	47	6	no	—
441	D₄	—	47	3	no	—
442	D₄	—	47	3	no	—
443	D₄	—	47	3	no	—
444	D₄	—	94	3	no	—
445	D₄	—	94	3	no	—
446	D₄	—	94	6	no	—
447	D₄	—	94	3	no	—
448	D₄	—	94	6	no	—
449	D₄	—	94	3	no	—
450	D₄	—	94	3	no	—
451	D₄	—	94	1	no	—
452	D₄	—	94	3	no	—
453	D₄	—	94	3	no	—
454	D₄	—	94	3	no	—
455	D₄	—	94	3	no	—
456	D₄	D₄×D₄₇	1	3	yes	—
457	D₄	C₂³×D₄₇	1	1	yes	characteristic
458	D₄	C₂³×D₄₇	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	47	3	no	—
463	C₂×C₄	—	47	3	no	—
464	C₂×C₄	—	47	3	no	—
465	C₂×C₄	—	47	3	no	—
466	C₂×C₄	—	47	1	no	—
467	C₂×C₄	—	94	3	no	—
468	C₂×C₄	—	94	3	no	—
469	C₂×C₄	—	94	6	no	—
470	C₂×C₄	—	94	1	no	—
471	C₂×C₄	—	94	3	no	—
472	C₂×C₄	—	94	1	no	—
473	C₂×C₄	—	94	3	no	—
474	C₂×C₄	—	94	3	no	—
475	C₂×C₄	—	94	3	no	—
476	C₂×C₄	C₂³×D₄₇	1	3	yes	—
477	C₈	—	47	3	no	—
478	C₈	—	47	1	no	—
479	C₈	C₂³×D₄₇	1	3	yes	—
480	C₈	C₂³×D₄₇	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	47	1	no	—
485	C₂²	—	47	3	no	—
486	C₂²	—	94	3	no	—
487	C₂²	—	94	3	no	—
488	C₂²	—	376	3	no	—
489	C₂²	—	376	3	no	—
490	C₂²	—	376	6	no	—
491	C₂²	—	376	3	no	—
492	C₂²	—	188	3	no	—
493	C₂²	—	188	6	no	—
494	C₂²	C₂×D₄×D₄₇	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	47	1	no	—
498	C₄	—	47	3	no	—
499	C₄	—	94	1	no	—
500	C₄	—	94	1	no	—
501	C₄	C₂×D₄×D₄₇	1	3	yes	—
502	C₄	C₂⁴×D₄₇	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	94	3	no	—
507	C₂	—	94	1	no	—
508	C₂	—	188	3	no	—
509	C₂	—	188	3	no	—
510	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁵
Frattini	C₄	C₂⁴×D₄₇
Fitting	C₄₇×#577	C₂
socle	C₂×C₄₇	C₂³×D₄
hypercenter	#577	D₄₇
hypocenter	C₄₇	#3585
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #15689960	C₂	semidirect
2. H(5,𝔽₂)×D₄₇	C₂	semidirect
3. #15689932	C₂	semidirect
4. #15689931	C₂	semidirect
5. #15689929	C₂	semidirect
6. #15689928	C₂	semidirect
7. #15689927	C₂	semidirect
8. #15689926	C₂	semidirect
9. #15689925	C₂	semidirect
10. #15689922	C₂	semidirect
11. #15689920	C₂	semidirect
12. C₂×#13094051	C₂	semidirect
13. AGL(1,ℤ/8)×D₄₇	C₂	semidirect
14. #15689888	C₂	semidirect
15. C₄₇×#577	C₂	semidirect
17. #13094072	C₂²	semidirect
20. #13094070	C₂²	semidirect
21. #13094070	C₂²	semidirect
22. #13094070	C₂²	semidirect
23. #13094070	C₂²	semidirect
25. #13094069	C₂²	semidirect
27. C₂×#10625354	C₂²	semidirect
31. #41×D₄₇	C₂²	semidirect
32. #41×D₄₇	C₂²	semidirect
34. C₂×D₄×D₄₇	C₂²	semidirect
35. #13094056	C₂²	semidirect
36. #13094056	C₂²	semidirect
37. #13094055	C₂²	semidirect
38. #13094053	C₂²	semidirect
39. #13094053	C₂²	semidirect
40. #13094052	C₂²	semidirect
41. #13094052	C₂²	semidirect
42. #13094051	C₂²	semidirect
43. #13094051	C₂²	semidirect
44. #13094051	C₂²	semidirect
45. #13094051	C₂²	semidirect
46. #13094051	C₂²	semidirect
47. #13094050	C₂²	semidirect
48. #13094049	C₂²	semidirect
49. #13094049	C₂²	semidirect
50. #13094048	C₂²	semidirect
51. #13094048	C₂²	semidirect
52. #13094047	C₂²	semidirect
53. #13094046	C₂²	semidirect
54. #13094045	C₂²	semidirect
55. #13094044	C₂²	semidirect
56. #13094044	C₂²	semidirect
57. C₂×#10625336	C₂²	semidirect
58. SD₁₆×D₄₇	C₂²	semidirect
59. C₂×D₃₇₆	C₂²	semidirect
60. C₂×#10625334	C₂²	semidirect
61. D₈×D₄₇	C₂²	semidirect
62. #13094032	C₂²	semidirect
63. #13094031	C₂²	semidirect
64. #13094030	C₂²	semidirect
65. C₂×#10625324	C₂²	semidirect
66. M₁₆×D₄₇	C₂²	semidirect
67. 2₋¹⁺⁴×C₄₇	C₂²	semidirect
68. H(5,𝔽₂)×C₄₇	C₂²	semidirect
69. #137×C₄₇	C₂²	semidirect
70. AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
71. #135×C₄₇	C₂²	semidirect
72. C₂×SD₁₆×C₄₇	C₂²	semidirect
73. #131×C₄₇	C₂²	semidirect
79. #41×C₄₇	C₂³	semidirect
81. C₂×Q₈×C₄₇	C₂³	semidirect
94. #10625354	C₂³	semidirect
98. Q₈×D₄₇	C₂³	semidirect
117. D₄×D₄₇	C₂³	semidirect
125. #10625350	C₂³	semidirect
130. C₂×D₁₈₈	C₂³	semidirect
135. Q₁₆×C₄₇	C₂³	semidirect
136. SD₁₆×C₄₇	C₂³	semidirect
137. SD₁₆×C₄₇	C₂³	semidirect
138. SD₁₆×C₄₇	C₂³	semidirect
139. D₈×C₄₇	C₂³	semidirect
140. M₁₆×C₄₇	C₂³	semidirect
141. C₂×C₈×C₄₇	C₂³	semidirect
142. #10625337	C₂³	semidirect
143. #10625337	C₂³	semidirect
144. #10625336	C₂³	semidirect
145. #10625336	C₂³	semidirect
146. #10625336	C₂³	semidirect
147. #10625335	C₂³	semidirect
148. #10625335	C₂³	semidirect
149. #10625334	C₂³	semidirect
150. #10625334	C₂³	semidirect
151. #10625334	C₂³	semidirect
152. #10625329	C₂³	semidirect
153. C₂×C₄₇⋊C₈	C₂³	semidirect
154. Dic₁₈₈	C₂³	semidirect
155. D₃₇₆	C₂³	semidirect
156. D₃₇₆	C₂³	semidirect
157. #10625325	C₂³	semidirect
158. #10625325	C₂³	semidirect
161. #10625324	C₂³	semidirect
162. #10625324	C₂³	semidirect
163. C₈×D₄₇	C₂³	semidirect
261. #577	D₄₇	semidirect
271. C₄₇	#3585	semidirect
274. 2₋¹⁺⁴	C₂×D₄₇	semidirect
283. H(5,𝔽₂)	C₂×D₄₇	semidirect
298. #137	C₂×D₄₇	semidirect
311. AGL(1,ℤ/8)	C₂×D₄₇	semidirect
317. #135	C₂×D₄₇	semidirect
320. C₂×SD₁₆	C₂×D₄₇	semidirect
327. #131	C₂×D₄₇	semidirect
358. #41	C₂²×D₄₇	semidirect
364. C₂×Q₈	C₂²×D₄₇	semidirect
394. Q₁₆	C₂²×D₄₇	semidirect
402. SD₁₆	C₂²×D₄₇	semidirect
403. SD₁₆	C₂²×D₄₇	semidirect
404. SD₁₆	C₂²×D₄₇	semidirect
410. D₈	C₂²×D₄₇	semidirect
416. M₁₆	C₂²×D₄₇	semidirect
419. C₂×C₈	C₂²×D₄₇	semidirect