Subgroups — #20241632

Order 6016.

780 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₇⋊C₄	—	2	2	no	—
13	C₂×Dic₄₇⋊C₄	—	2	2	no	—
14	C₂×Dic₄₇⋊C₄	—	2	2	no	—
15	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
16	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
17	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
18	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
19	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
20	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
21	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
22	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
23	C₂×(C₂×D₄₇)⋊C₄	C₄	1	4	yes	complemented
24	C₄₇⋊#95	—	2	2	no	—
25	C₄₇⋊#95	—	2	2	no	—
26	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
29	#95×C₄₇	—	2	2	no	—
30	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
31	C₂³×D₄₇	—	2	1	no	—
32	C₂³×D₄₇	—	2	1	no	—
33	C₂³×D₄₇	—	2	1	no	—
34	C₂³×D₄₇	—	2	1	no	—
35	C₂³×D₄₇	—	2	1	no	—
36	C₂³×D₄₇	—	2	1	no	—
37	C₂³×D₄₇	—	2	1	no	—
38	C₂³×D₄₇	—	2	1	no	—
39	C₂³×D₄₇	—	2	1	no	—
40	C₂³×D₄₇	—	2	1	no	—
41	C₂³×D₄₇	—	2	1	no	—
42	C₂³×D₄₇	—	2	1	no	—
43	C₂³×D₄₇	C₂×C₄	1	2	yes	—
44	C₂³×D₄₇	D₄	1	2	yes	—
45	C₂³×D₄₇	Q₈	1	2	yes	—
46	C₂²×C₄×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	—	2	1	no	—
48	C₂²×C₄×C₄₇	—	2	1	no	—
49	C₂²×C₄×C₄₇	—	2	1	no	—
50	C₂²×C₄×C₄₇	—	2	1	no	—
51	C₂²×C₄×C₄₇	—	2	1	no	—
52	C₂²×C₄×C₄₇	—	2	1	no	—
53	C₂²×C₄×C₄₇	—	2	1	no	—
54	C₂²×C₄×C₄₇	—	2	1	no	—
55	C₂²×C₄×C₄₇	—	2	1	no	—
56	C₂²×C₄×C₄₇	—	2	1	no	—
57	C₂²×C₄×C₄₇	—	2	1	no	—
58	C₂²×C₄×C₄₇	—	2	1	no	—
59	C₂²×C₄×C₄₇	—	2	1	no	—
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂²×C₄×C₄₇	D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	D₄	1	2	yes	—
67	C₂²×Dic₄₇	—	2	1	no	—
68	C₂²×Dic₄₇	—	2	1	no	—
69	C₂²×Dic₄₇	—	2	1	no	—
70	C₂²×Dic₄₇	—	2	1	no	—
71	C₂²×Dic₄₇	—	2	1	no	—
72	C₂²×Dic₄₇	—	2	1	no	—
73	C₂²×Dic₄₇	—	2	1	no	—
74	C₂²×Dic₄₇	—	2	1	no	—
75	C₂²×Dic₄₇	—	2	1	no	—
76	C₂²×Dic₄₇	—	2	1	no	—
77	C₂²×Dic₄₇	—	2	1	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂²×Dic₄₇	—	2	1	no	—
81	C₂²×Dic₄₇	—	2	1	no	—
82	C₂²×Dic₄₇	—	2	1	no	—
83	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
84	C₂²×Dic₄₇	D₄	1	2	yes	—
85	C₂²×Dic₄₇	D₄	1	2	yes	—
86	C₂²×Dic₄₇	D₄	1	2	yes	—
87	C₂²×Dic₄₇	D₄	1	2	yes	—
88	(C₂×D₄₇)⋊C₄	—	2	8	no	—
89	(C₂×D₄₇)⋊C₄	—	2	8	no	—
90	(C₂×D₄₇)⋊C₄	—	2	8	no	—
91	Dic₄₇⋊C₄	—	2	8	no	—
92	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₂³×C₄₇	#41	1	1	yes	characteristic
102	C₂³×C₄₇	#41	1	1	yes	characteristic
103	C₂³×C₄₇	#41	1	1	yes	characteristic
104	C₂³×C₄₇	#41	1	1	yes	characteristic
105	C₂³×C₄₇	#41	1	1	yes	characteristic
106	C₂³×C₄₇	#41	1	1	yes	characteristic
107	C₂²×D₄₇	—	2	2	no	—
108	C₂²×D₄₇	—	2	2	no	—
109	C₂²×D₄₇	—	2	2	no	—
110	C₂²×D₄₇	—	2	2	no	—
111	C₂²×D₄₇	—	2	2	no	—
112	C₂²×D₄₇	—	2	2	no	—
113	C₂²×D₄₇	—	2	2	no	—
114	C₂²×D₄₇	—	2	2	no	—
115	C₂²×D₄₇	—	2	2	no	—
116	C₂²×D₄₇	—	2	2	no	—
117	C₂²×D₄₇	—	2	2	no	—
118	C₂²×D₄₇	—	2	2	no	—
119	C₂²×D₄₇	—	2	2	no	—
120	C₂²×D₄₇	—	2	2	no	—
121	C₂²×D₄₇	—	2	2	no	—
122	C₂²×D₄₇	—	2	2	no	—
123	C₂²×D₄₇	—	2	2	no	—
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	4	1	no	—
126	C₂²×D₄₇	—	4	1	no	—
127	C₂²×D₄₇	—	4	1	no	—
128	C₂²×D₄₇	—	4	1	no	—
129	C₂²×D₄₇	—	4	1	no	—
130	C₂²×D₄₇	—	4	1	no	—
131	C₂²×D₄₇	—	4	1	no	—
132	C₂²×D₄₇	—	4	1	no	—
133	C₂²×D₄₇	—	4	1	no	—
134	C₂²×D₄₇	—	4	1	no	—
135	C₂²×D₄₇	—	4	1	no	—
136	C₂²×D₄₇	—	4	1	no	—
137	C₂²×D₄₇	—	4	1	no	—
138	C₂²×D₄₇	—	4	1	no	—
139	C₂²×D₄₇	—	4	1	no	—
140	C₂²×D₄₇	—	4	1	no	—
141	C₂²×D₄₇	C₄⋊C₄	1	4	yes	complemented
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	1	no	—
153	C₂×C₄×C₄₇	—	4	1	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	4	1	no	—
176	C₂×Dic₄₇	—	4	1	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	—	4	1	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	C₂²⋊C₄	1	4	yes	complemented
184	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₇	#117	1	1	yes	characteristic
187	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂²×C₄₇	#120	1	1	yes	characteristic
192	C₂²×C₄₇	#120	1	1	yes	characteristic
193	C₂²×C₄₇	#120	1	1	yes	characteristic
194	C₂²×C₄₇	#121	1	1	yes	characteristic
195	C₂²×C₄₇	#121	1	1	yes	characteristic
196	C₂²×C₄₇	#121	1	1	yes	characteristic
197	C₂²×C₄₇	#121	1	1	yes	characteristic
198	C₂²×C₄₇	#121	1	1	yes	characteristic
199	C₂²×C₄₇	#121	1	1	yes	characteristic
200	C₂²×C₄₇	#121	1	1	yes	characteristic
201	C₂²×C₄₇	#121	1	1	yes	characteristic
202	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂²×C₄₇	#123	1	1	yes	characteristic
209	C₂²×C₄₇	#123	1	1	yes	characteristic
210	C₂²×C₄₇	#123	1	1	yes	characteristic
211	C₂²×C₄₇	#123	1	1	yes	characteristic
212	C₂²×C₄₇	#123	1	1	yes	characteristic
213	C₂²×C₄₇	#124	1	1	yes	characteristic
214	C₂²×C₄₇	#124	1	1	yes	characteristic
215	C₂²×C₄₇	#124	1	1	yes	characteristic
216	C₂²×C₄₇	#126	1	1	yes	characteristic
217	C₂²×C₄₇	#126	1	1	yes	characteristic
218	C₂²×C₄₇	#127	1	1	yes	characteristic
219	C₂×D₄₇	—	2	4	no	—
220	C₂×D₄₇	—	2	4	no	—
221	C₂×D₄₇	—	2	4	no	—
222	C₂×D₄₇	—	4	2	no	—
223	C₂×D₄₇	—	4	2	no	—
224	C₂×D₄₇	—	4	2	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₂×D₄₇	—	4	2	no	—
227	C₂×D₄₇	—	4	2	no	—
228	C₂×D₄₇	—	4	2	no	—
229	C₂×D₄₇	—	4	2	no	—
230	C₂×D₄₇	—	4	2	no	—
231	C₂×D₄₇	—	4	2	no	—
232	C₂×D₄₇	—	4	2	no	—
233	C₂×D₄₇	—	4	2	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	2	no	—
237	Dic₄₇	—	2	4	no	—
238	Dic₄₇	—	4	2	no	—
239	Dic₄₇	—	4	2	no	—
240	#1439	—	47	1	no	maximal, Sylow
241	C₂×C₄₇	#380	1	1	yes	characteristic
242	C₂×C₄₇	#385	1	1	yes	characteristic
243	C₂×C₄₇	#385	1	1	yes	characteristic
244	C₂×C₄₇	#386	1	1	yes	characteristic
245	C₂×C₄₇	#388	1	1	yes	characteristic
246	C₂×C₄₇	#388	1	1	yes	characteristic
247	C₂×C₄₇	#390	1	1	yes	characteristic
248	C₂×C₄₇	#392	1	1	yes	characteristic
249	C₂×C₄₇	#393	1	1	yes	characteristic
250	C₂×C₄₇	#394	1	1	yes	characteristic
251	C₂×C₄₇	#394	1	1	yes	characteristic
252	C₂×C₄₇	#396	1	1	yes	characteristic
253	C₂×C₄₇	#396	1	1	yes	characteristic
254	C₂×C₄₇	#397	1	1	yes	characteristic
255	C₂×C₄₇	#399	1	1	yes	characteristic
256	D₄₇	—	4	4	no	—
257	C₂²×C₄⋊C₄	—	47	1	no	—
258	C₂²×C₂²⋊C₄	—	47	1	no	—
259	C₂²×C₂²⋊C₄	—	47	1	no	—
260	C₂²×C₂²⋊C₄	—	47	1	no	—
261	C₂×#95	—	47	1	no	—
262	C₂×#95	—	47	1	no	—
263	C₂×#95	D₄₇	1	1	yes	characteristic, complemented
264	C₄₇	#1439	1	1	yes	characteristic, complemented, Sylow
265	C₂⁵	—	47	1	no	—
266	C₂³×C₄	—	47	1	no	—
267	C₂³×C₄	—	47	1	no	—
268	C₂³×C₄	—	47	1	no	—
269	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
270	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
271	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	—	94	2	no	—
274	C₂×C₄⋊C₄	—	94	2	no	—
275	C₂×C₂²⋊C₄	—	47	4	no	—
276	C₂×C₂²⋊C₄	—	94	2	no	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₂²⋊C₄	—	94	2	no	—
279	C₂×C₂²⋊C₄	—	94	2	no	—
280	C₂×C₂²⋊C₄	—	94	2	no	—
281	C₂×C₂²⋊C₄	—	94	2	no	—
282	C₂×C₂²⋊C₄	—	94	2	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	#95	—	2	2	no	—
285	#95	—	94	2	no	—
286	#95	—	94	2	no	—
287	C₂⁴	—	47	2	no	—
288	C₂⁴	—	47	2	no	—
289	C₂⁴	—	47	2	no	—
290	C₂⁴	—	94	1	no	—
291	C₂⁴	—	94	1	no	—
292	C₂⁴	—	94	1	no	—
293	C₂⁴	—	94	1	no	—
294	C₂⁴	—	94	1	no	—
295	C₂⁴	—	94	1	no	—
296	C₂⁴	—	94	1	no	—
297	C₂⁴	—	94	1	no	—
298	C₂⁴	—	94	1	no	—
299	C₂⁴	—	94	1	no	—
300	C₂⁴	—	94	1	no	—
301	C₂⁴	—	94	1	no	—
302	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	—	94	1	no	—
329	C₂²×C₄	—	94	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	—	94	1	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	C₄×D₄₇	1	2	yes	—
343	C₂²×C₄	D₁₈₈	1	2	yes	—
344	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
345	C₄⋊C₄	—	94	8	no	—
346	C₂²⋊C₄	—	94	8	no	—
347	C₂²⋊C₄	—	94	8	no	—
348	C₂²⋊C₄	—	94	8	no	—
349	C₂³	—	47	4	no	—
350	C₂³	—	94	2	no	—
351	C₂³	—	94	2	no	—
352	C₂³	—	94	2	no	—
353	C₂³	—	94	2	no	—
354	C₂³	—	94	2	no	—
355	C₂³	—	94	2	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	94	2	no	—
358	C₂³	—	94	2	no	—
359	C₂³	—	94	2	no	—
360	C₂³	—	94	2	no	—
361	C₂³	—	94	2	no	—
362	C₂³	—	94	2	no	—
363	C₂³	—	94	2	no	—
364	C₂³	—	94	2	no	—
365	C₂³	—	94	2	no	—
366	C₂³	—	94	2	no	—
367	C₂³	—	94	2	no	—
368	C₂³	—	188	1	no	—
369	C₂³	—	188	1	no	—
370	C₂³	—	188	1	no	—
371	C₂³	—	188	1	no	—
372	C₂³	—	188	1	no	—
373	C₂³	—	188	1	no	—
374	C₂³	—	188	1	no	—
375	C₂³	—	188	1	no	—
376	C₂³	—	188	1	no	—
377	C₂³	—	188	1	no	—
378	C₂³	—	188	1	no	—
379	C₂³	—	188	1	no	—
380	C₂³	—	188	1	no	—
381	C₂³	—	188	1	no	—
382	C₂³	—	188	1	no	—
383	C₂³	—	188	1	no	—
384	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
386	C₂³	#10625350	1	1	yes	characteristic
387	C₂³	#10625350	1	1	yes	characteristic
388	C₂³	#10625350	1	1	yes	characteristic
389	C₂³	#10625350	1	1	yes	characteristic
390	C₂³	D₄×D₄₇	1	1	yes	characteristic
391	C₂³	D₄×D₄₇	1	1	yes	characteristic
392	C₂³	D₄×D₄₇	1	1	yes	characteristic
393	C₂³	D₄×D₄₇	1	1	yes	characteristic
394	C₂³	D₄×D₄₇	1	1	yes	characteristic
395	C₂³	#10625352	1	1	yes	characteristic
396	C₂³	Q₈×D₄₇	1	1	yes	characteristic
397	C₂³	#10625354	1	1	yes	characteristic
398	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	47	4	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	94	2	no	—
428	C₂×C₄	—	94	2	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	94	2	no	—
431	C₂×C₄	—	94	2	no	—
432	C₂×C₄	—	94	2	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	1	no	—
435	C₂×C₄	—	188	1	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	—	188	1	no	—
438	C₂×C₄	—	188	1	no	—
439	C₂×C₄	—	188	1	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂²	—	94	4	no	—
442	C₂²	—	94	4	no	—
443	C₂²	—	94	4	no	—
444	C₂²	—	188	2	no	—
445	C₂²	—	188	2	no	—
446	C₂²	—	188	2	no	—
447	C₂²	—	188	2	no	—
448	C₂²	—	188	2	no	—
449	C₂²	—	188	2	no	—
450	C₂²	—	188	2	no	—
451	C₂²	—	188	2	no	—
452	C₂²	—	188	2	no	—
453	C₂²	—	188	2	no	—
454	C₂²	—	188	2	no	—
455	C₂²	—	188	2	no	—
456	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
457	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
458	C₂²	#13093981	1	1	yes	characteristic
459	C₂²	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
460	C₂²	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
461	C₂²	#13093986	1	1	yes	characteristic
462	C₂²	C₄×D₁₈₈	1	1	yes	characteristic
463	C₂²	#13093992	1	1	yes	characteristic
464	C₂²	#13093994	1	1	yes	characteristic
465	C₂²	#13093994	1	1	yes	characteristic
466	C₂²	#13093996	1	1	yes	characteristic
467	C₂²	#13093997	1	1	yes	characteristic
468	C₂²	#13093997	1	1	yes	characteristic
469	C₂²	#13093997	1	1	yes	characteristic
470	C₂²	#13093997	1	1	yes	characteristic
471	C₂²	#13093997	1	1	yes	characteristic
472	C₂²	#13093998	1	1	yes	characteristic
473	C₂²	#13093999	1	1	yes	characteristic
474	C₂²	#13094000	1	1	yes	characteristic
475	C₂²	#13094002	1	1	yes	characteristic
476	C₂²	#13094002	1	1	yes	characteristic
477	C₂²	#13094002	1	1	yes	characteristic
478	C₂²	#13094002	1	1	yes	characteristic
479	C₂²	#13094004	1	1	yes	characteristic
480	C₂²	#13094006	1	1	yes	characteristic
481	C₂²	#13094007	1	1	yes	characteristic
482	C₂²	#13094009	1	1	yes	characteristic
483	C₂²	#13094009	1	1	yes	characteristic
484	C₂²	#13094009	1	1	yes	characteristic
485	C₂²	#13094010	1	1	yes	characteristic
486	C₂²	#13094010	1	1	yes	characteristic
487	C₂²	#13094012	1	1	yes	characteristic
488	C₂²	#13094018	1	1	yes	characteristic
489	C₂²	#13094019	1	1	yes	characteristic
490	C₂²	#13094020	1	1	yes	characteristic
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	94	4	no	—
495	C₄	—	188	2	no	—
496	C₄	—	188	2	no	—
497	C₂	—	188	4	no	—
498	C₂	#15688982	1	1	yes	characteristic
499	C₂	#15688994	1	1	yes	characteristic
500	C₂	#15688997	1	1	yes	characteristic
501	C₂	#15689001	1	1	yes	characteristic
502	C₂	#15689012	1	1	yes	characteristic
503	C₂	#15689014	1	1	yes	characteristic
504	C₂	#15689023	1	1	yes	characteristic
505	C₂	#15689032	1	1	yes	characteristic
506	C₂	#15689036	1	1	yes	characteristic
507	C₂	#15689038	1	1	yes	characteristic
508	C₂	#15689041	1	1	yes	characteristic
509	C₂	#15689045	1	1	yes	characteristic
510	C₂	#15689047	1	1	yes	characteristic
511	C₂	#15689052	1	1	yes	characteristic
512	C₂	#15689058	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#1439
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₄₇⋊C₄	C₂	semidirect
5. C₂×C₄₇⋊#95	C₂	semidirect
6. C₂×C₄₇⋊#95	C₂	semidirect
7. C₂×#95×C₄₇	C₂	semidirect
23. C₂×(C₂×D₄₇)⋊C₄	C₄	semidirect
141. C₂²×D₄₇	C₄⋊C₄	semidirect
183. C₂×Dic₄₇	C₂²⋊C₄	semidirect
263. C₂×#95	D₄₇	semidirect
264. C₄₇	#1439	semidirect