Subgroups — C₂×C₄₇×#1904 #26060694

Order 12032.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1904	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
14	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
15	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	4	yes	complemented
16	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	4	yes	—
17	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
18	C₂²×D₈×C₄₇	C₄	1	2	yes	complemented
19	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#518	—	2	2	no	—
22	C₄₇×#518	—	2	2	no	—
23	C₄₇×#518	—	2	2	no	—
24	C₄₇×#518	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₄₇	—	2	2	no	—
26	C₂×C₄×D₄×C₄₇	—	2	2	no	—
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
31	C₄₇×#421	—	2	2	no	—
32	C₄₇×#421	C₂²	1	4	yes	complemented
33	C₂×#104×C₄₇	—	2	2	no	—
34	C₄₇×#418	—	2	2	no	—
35	C₄₇×#418	C₂²	1	4	yes	complemented
36	C₂×#102×C₄₇	—	2	2	no	—
37	C₄₇×#410	—	2	2	no	—
38	C₄₇×#410	C₂²	1	4	yes	complemented
39	C₂×#99×C₄₇	—	2	2	no	—
40	C₄₇×#344	C₂²	1	4	yes	complemented
41	C₄₇×H(3,ℤ/4)	C₂²	1	4	yes	complemented
42	C₂⁵×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂×#41×C₄₇	—	2	1	no	—
45	C₂×#41×C₄₇	—	2	1	no	—
46	C₂×#41×C₄₇	—	2	1	no	—
47	C₂×#41×C₄₇	—	2	1	no	—
48	C₂×#41×C₄₇	—	2	1	no	—
49	C₂×#41×C₄₇	—	2	1	no	—
50	C₂×#41×C₄₇	—	2	1	no	—
51	C₂×#41×C₄₇	—	2	1	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
54	C₂×#41×C₄₇	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂²×D₄×C₄₇	—	2	1	no	—
57	C₂²×D₄×C₄₇	—	2	1	no	—
58	C₂²×D₄×C₄₇	—	2	1	no	—
59	C₂²×D₄×C₄₇	—	2	1	no	—
60	C₂²×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₄₇	D₄	1	2	yes	—
68	C₂²×D₄×C₄₇	D₄	1	2	yes	—
69	C₂²×D₄×C₄₇	D₄	1	2	yes	—
70	C₂²×D₄×C₄₇	D₄	1	2	yes	—
71	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	—	2	4	no	—
73	C₂³×C₄×C₄₇	—	2	1	no	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
76	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
77	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
78	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
79	C₂×SD₁₆×C₄₇	—	2	4	no	—
80	C₂×SD₁₆×C₄₇	—	2	4	no	—
81	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₂×D₈×C₄₇	—	2	4	no	—
83	C₂×D₈×C₄₇	—	2	4	no	—
84	C₂×D₈×C₄₇	C₂×C₄	1	8	yes	complemented
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
95	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
96	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
97	C₂²×C₈×C₄₇	—	2	1	no	—
98	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
99	C₄×D₄×C₄₇	—	2	8	no	—
100	C₄×D₄×C₄₇	—	2	8	no	—
101	C₄×D₄×C₄₇	—	2	8	no	—
102	C₄×D₄×C₄₇	—	2	8	no	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	—	2	1	no	—
105	#117×C₄₇	—	2	1	no	—
106	#117×C₄₇	—	2	1	no	—
107	#117×C₄₇	—	2	1	no	—
108	#117×C₄₇	—	2	1	no	—
109	#117×C₄₇	—	2	1	no	—
110	#117×C₄₇	D₄	1	2	yes	—
111	#117×C₄₇	D₄	1	2	yes	—
112	#117×C₄₇	C₂³	1	2	yes	—
113	#117×C₄₇	C₂³	1	2	yes	—
114	#117×C₄₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
122	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
124	C₂×C₄²×C₄₇	—	2	1	no	—
125	C₂×C₄²×C₄₇	—	2	1	no	—
126	C₂×C₄²×C₄₇	D₄	1	2	yes	—
127	#104×C₄₇	—	2	8	no	—
128	#102×C₄₇	—	2	8	no	—
129	#99×C₄₇	—	2	8	no	—
130	C₂⁴×C₄₇	—	2	2	no	—
131	C₂⁴×C₄₇	—	2	2	no	—
132	C₂⁴×C₄₇	—	2	2	no	—
133	C₂⁴×C₄₇	—	2	2	no	—
134	C₂⁴×C₄₇	—	2	2	no	—
135	C₂⁴×C₄₇	—	2	2	no	—
136	C₂⁴×C₄₇	—	2	2	no	—
137	C₂⁴×C₄₇	—	2	1	no	—
138	C₂⁴×C₄₇	—	8	4	no	—
139	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
140	#41×C₄₇	—	2	2	no	—
141	#41×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	2	no	—
143	#41×C₄₇	—	2	2	no	—
144	#41×C₄₇	—	2	2	no	—
145	#41×C₄₇	—	2	2	no	—
146	#41×C₄₇	—	2	2	no	—
147	#41×C₄₇	—	2	2	no	—
148	#41×C₄₇	—	4	1	no	—
149	#41×C₄₇	—	4	1	no	—
150	#41×C₄₇	—	4	1	no	—
151	#41×C₄₇	—	4	1	no	—
152	#41×C₄₇	—	4	1	no	—
153	#41×C₄₇	—	4	1	no	—
154	#41×C₄₇	—	4	1	no	—
155	#41×C₄₇	—	4	1	no	—
156	C₂×Q₈×C₄₇	—	2	1	no	—
157	C₂×Q₈×C₄₇	—	2	1	no	—
158	C₂×Q₈×C₄₇	—	2	1	no	—
159	C₂×Q₈×C₄₇	—	2	1	no	—
160	C₂×Q₈×C₄₇	—	2	1	no	—
161	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	complemented
162	C₂×D₄×C₄₇	—	2	2	no	—
163	C₂×D₄×C₄₇	—	2	2	no	—
164	C₂×D₄×C₄₇	—	2	1	no	—
165	C₂×D₄×C₄₇	—	2	1	no	—
166	C₂×D₄×C₄₇	—	2	2	no	—
167	C₂×D₄×C₄₇	—	2	2	no	—
168	C₂×D₄×C₄₇	—	2	2	no	—
169	C₂×D₄×C₄₇	—	2	2	no	—
170	C₂×D₄×C₄₇	—	2	2	no	—
171	C₂×D₄×C₄₇	—	2	2	no	—
172	C₂×D₄×C₄₇	—	2	1	no	—
173	C₂×D₄×C₄₇	—	2	1	no	—
174	C₂×D₄×C₄₇	—	2	1	no	—
175	C₂×D₄×C₄₇	—	2	2	no	—
176	C₂×D₄×C₄₇	—	2	2	no	—
177	C₂×D₄×C₄₇	—	2	2	no	—
178	C₂×D₄×C₄₇	—	2	2	no	—
179	C₂×D₄×C₄₇	—	2	2	no	—
180	C₂×D₄×C₄₇	—	2	2	no	—
181	C₂×D₄×C₄₇	—	2	2	no	—
182	C₂×D₄×C₄₇	—	2	2	no	—
183	C₂×D₄×C₄₇	—	2	2	no	—
184	C₂×D₄×C₄₇	—	2	2	no	—
185	C₂×D₄×C₄₇	—	2	2	no	—
186	C₂×D₄×C₄₇	—	2	2	no	—
187	C₂×D₄×C₄₇	—	2	2	no	—
188	C₂×D₄×C₄₇	—	2	2	no	—
189	C₂×D₄×C₄₇	—	2	2	no	—
190	C₂×D₄×C₄₇	—	4	1	no	—
191	C₂×D₄×C₄₇	—	4	1	no	—
192	C₂×D₄×C₄₇	—	4	1	no	—
193	C₂×D₄×C₄₇	—	4	1	no	—
194	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
195	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
196	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
197	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
198	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
199	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	complemented
200	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
201	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₄₇	—	2	1	no	—
203	C₂²×C₄×C₄₇	—	2	2	no	—
204	C₂²×C₄×C₄₇	—	2	2	no	—
205	C₂²×C₄×C₄₇	—	2	16	no	—
206	C₂²×C₄×C₄₇	—	2	2	no	—
207	C₂²×C₄×C₄₇	—	2	2	no	—
208	C₂²×C₄×C₄₇	—	4	1	no	—
209	C₂²×C₄×C₄₇	—	4	1	no	—
210	C₂²×C₄×C₄₇	—	4	1	no	—
211	C₂²×C₄×C₄₇	—	4	1	no	—
212	C₂²×C₄×C₄₇	—	4	1	no	—
213	C₂²×C₄×C₄₇	—	8	8	no	—
214	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
224	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
225	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
226	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
227	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₄₇	—	2	16	no	—
229	D₈×C₄₇	—	2	16	no	—
230	M₁₆×C₄₇	—	2	2	no	—
231	M₁₆×C₄₇	—	2	2	no	—
232	M₁₆×C₄₇	—	2	2	no	—
233	M₁₆×C₄₇	—	2	2	no	—
234	M₁₆×C₄₇	—	2	2	no	—
235	M₁₆×C₄₇	—	2	2	no	—
236	M₁₆×C₄₇	—	4	1	no	—
237	M₁₆×C₄₇	—	4	1	no	—
238	C₂×C₈×C₄₇	—	2	2	no	—
239	C₂×C₈×C₄₇	—	2	2	no	—
240	C₂×C₈×C₄₇	—	2	2	no	—
241	C₂×C₈×C₄₇	—	4	1	no	—
242	C₂×C₈×C₄₇	—	4	1	no	—
243	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	complemented
244	C₄⋊C₄×C₄₇	—	2	2	no	—
245	C₄⋊C₄×C₄₇	—	2	2	no	—
246	C₄⋊C₄×C₄₇	—	2	2	no	—
247	C₄⋊C₄×C₄₇	—	2	2	no	—
248	C₄⋊C₄×C₄₇	—	2	2	no	—
249	C₄⋊C₄×C₄₇	—	4	1	no	—
250	C₂²⋊C₄×C₄₇	—	2	16	no	—
251	C₂²⋊C₄×C₄₇	—	2	2	no	—
252	C₂²⋊C₄×C₄₇	—	2	2	no	—
253	C₂²⋊C₄×C₄₇	—	2	2	no	—
254	C₂²⋊C₄×C₄₇	—	2	2	no	—
255	C₂²⋊C₄×C₄₇	—	4	1	no	—
256	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
257	C₄²×C₄₇	—	2	2	no	—
258	C₄²×C₄₇	—	2	2	no	—
259	C₄²×C₄₇	—	2	2	no	—
260	C₄²×C₄₇	—	2	2	no	—
261	C₄²×C₄₇	—	4	1	no	—
262	C₄²×C₄₇	C₂×D₄	1	4	yes	—
263	C₂³×C₄₇	—	2	4	no	—
264	C₂³×C₄₇	—	2	4	no	—
265	C₂³×C₄₇	—	2	4	no	—
266	C₂³×C₄₇	—	2	4	no	—
267	C₂³×C₄₇	—	2	4	no	—
268	C₂³×C₄₇	—	2	4	no	—
269	C₂³×C₄₇	—	2	4	no	—
270	C₂³×C₄₇	—	2	2	no	—
271	C₂³×C₄₇	—	4	2	no	—
272	C₂³×C₄₇	—	4	8	no	—
273	C₂³×C₄₇	—	4	1	no	—
274	C₂³×C₄₇	—	4	1	no	—
275	C₂³×C₄₇	—	8	4	no	—
276	C₂³×C₄₇	—	8	4	no	—
277	C₂³×C₄₇	—	8	2	no	—
278	C₂³×C₄₇	—	8	4	no	—
279	C₂³×C₄₇	—	8	4	no	—
280	C₂³×C₄₇	—	8	4	no	—
281	C₂³×C₄₇	—	8	4	no	—
282	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
283	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
284	C₂³×C₄₇	#120	1	1	yes	characteristic
285	C₂³×C₄₇	#120	1	1	yes	characteristic
286	C₂³×C₄₇	#121	1	1	yes	characteristic
287	C₂³×C₄₇	#121	1	1	yes	characteristic
288	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₄₇	—	2	2	no	—
290	Q₈×C₄₇	—	2	2	no	—
291	Q₈×C₄₇	—	4	1	no	—
292	Q₈×C₄₇	—	4	1	no	—
293	D₄×C₄₇	—	2	2	no	—
294	D₄×C₄₇	—	2	4	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	2	4	no	—
297	D₄×C₄₇	—	2	4	no	—
298	D₄×C₄₇	—	2	4	no	—
299	D₄×C₄₇	—	2	4	no	—
300	D₄×C₄₇	—	2	4	no	—
301	D₄×C₄₇	—	2	4	no	—
302	D₄×C₄₇	—	4	2	no	—
303	D₄×C₄₇	—	4	2	no	—
304	D₄×C₄₇	—	4	2	no	—
305	D₄×C₄₇	—	4	2	no	—
306	D₄×C₄₇	—	4	1	no	—
307	D₄×C₄₇	—	4	1	no	—
308	D₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
309	C₂×C₄×C₄₇	—	2	2	no	—
310	C₂×C₄×C₄₇	—	2	4	no	—
311	C₂×C₄×C₄₇	—	2	4	no	—
312	C₂×C₄×C₄₇	—	4	4	no	—
313	C₂×C₄×C₄₇	—	4	4	no	—
314	C₂×C₄×C₄₇	—	4	1	no	—
315	C₂×C₄×C₄₇	—	4	1	no	—
316	C₂×C₄×C₄₇	—	4	2	no	—
317	C₂×C₄×C₄₇	—	4	2	no	—
318	C₂×C₄×C₄₇	—	4	2	no	—
319	C₂×C₄×C₄₇	—	4	2	no	—
320	C₂×C₄×C₄₇	—	4	2	no	—
321	C₂×C₄×C₄₇	—	8	16	no	—
322	C₂×C₄×C₄₇	—	8	2	no	—
323	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
330	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
331	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
332	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
333	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
334	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
335	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
336	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
337	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
338	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
339	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
340	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
341	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
342	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
343	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
344	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
345	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
351	C₈×C₄₇	—	2	4	no	—
352	C₈×C₄₇	—	4	2	no	—
353	C₂×#1904	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂²×C₄₇	—	2	2	no	—
355	C₂²×C₄₇	—	2	2	no	—
356	C₂²×C₄₇	—	2	2	no	—
357	C₂²×C₄₇	—	2	8	no	—
358	C₂²×C₄₇	—	4	1	no	—
359	C₂²×C₄₇	—	4	1	no	—
360	C₂²×C₄₇	—	4	1	no	—
361	C₂²×C₄₇	—	4	1	no	—
362	C₂²×C₄₇	—	4	8	no	—
363	C₂²×C₄₇	—	4	8	no	—
364	C₂²×C₄₇	—	4	8	no	—
365	C₂²×C₄₇	—	4	2	no	—
366	C₂²×C₄₇	—	8	4	no	—
367	C₂²×C₄₇	—	8	4	no	—
368	C₂²×C₄₇	—	8	4	no	—
369	C₂²×C₄₇	—	8	4	no	—
370	C₂²×C₄₇	—	8	2	no	—
371	C₂²×C₄₇	—	8	2	no	—
372	C₂²×C₄₇	—	8	2	no	—
373	C₂²×C₄₇	#386	1	1	yes	characteristic
374	C₂²×C₄₇	#386	1	1	yes	characteristic
375	C₂²×C₄₇	#386	1	1	yes	characteristic
376	C₂²×C₄₇	#386	1	1	yes	characteristic
377	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
378	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
379	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
380	C₄×C₄₇	—	4	4	no	—
381	C₄×C₄₇	—	4	4	no	—
382	C₄×C₄₇	—	4	2	no	—
383	C₄×C₄₇	—	8	2	no	—
384	C₄×C₄₇	#386	1	1	yes	characteristic
385	C₄×C₄₇	#386	1	1	yes	characteristic
386	C₄×C₄₇	#386	1	1	yes	characteristic
387	C₄×C₄₇	#386	1	1	yes	characteristic
388	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
389	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
390	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
391	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
392	C₂²×AGL(1,ℤ/8)	C₂×C₄₇	1	1	yes	characteristic
393	C₂×#518	C₂×C₄₇	1	1	yes	characteristic, complemented
394	C₂×#421	C₂×C₄₇	1	1	yes	characteristic, complemented
395	C₂×#418	C₂×C₄₇	1	1	yes	characteristic, complemented
396	C₂×#410	C₂×C₄₇	1	1	yes	characteristic, complemented
397	#1904	C₂×C₄₇	1	8	yes	direct product factor
398	C₂×#344	C₂×C₄₇	1	1	yes	characteristic, complemented
399	C₂×H(3,ℤ/4)	C₂×C₄₇	1	1	yes	characteristic, complemented
400	C₂×C₄₇	—	2	1	no	—
401	C₂×C₄₇	—	2	1	no	—
402	C₂×C₄₇	—	2	1	no	—
403	C₂×C₄₇	—	2	1	no	—
404	C₂×C₄₇	—	2	1	no	—
405	C₂×C₄₇	—	2	1	no	—
406	C₂×C₄₇	—	4	8	no	—
407	C₂×C₄₇	—	8	2	no	—
408	C₂×C₄₇	#1904	1	2	yes	direct product factor
409	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
410	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
411	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
412	C₂×AGL(1,ℤ/8)	—	2	2	no	—
413	C₂×AGL(1,ℤ/8)	—	2	2	no	—
414	C₂×AGL(1,ℤ/8)	—	2	2	no	—
415	C₂×AGL(1,ℤ/8)	—	2	2	no	—
416	C₂×AGL(1,ℤ/8)	C₄×C₄₇	1	4	yes	complemented
417	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	4	yes	—
418	C₂²×SD₁₆	C₄×C₄₇	1	2	yes	complemented
419	C₂²×D₈	C₄×C₄₇	1	2	yes	complemented
420	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
421	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
422	#518	—	2	2	no	—
423	#518	—	2	2	no	—
424	#518	—	2	2	no	—
425	#518	C₂²×C₄₇	1	4	yes	complemented
426	C₂×C₄×D₄	—	2	2	no	—
427	C₂×C₄×D₄	—	2	2	no	—
428	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
429	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
430	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	—	2	2	no	—
432	#421	—	2	2	no	—
433	#421	C₂²×C₄₇	1	4	yes	complemented
434	C₂×#104	—	2	2	no	—
435	#418	—	2	2	no	—
436	#418	C₂²×C₄₇	1	4	yes	complemented
437	C₂×#102	—	2	2	no	—
438	#410	—	2	2	no	—
439	#410	C₂²×C₄₇	1	4	yes	complemented
440	C₂×#99	—	2	2	no	—
441	#344	C₂²×C₄₇	1	4	yes	complemented
442	H(3,ℤ/4)	C₂²×C₄₇	1	4	yes	complemented
443	C₄₇	C₂×#1904	1	1	yes	characteristic, direct product factor, Sylow
444	C₂⁵	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	—	2	1	no	—
451	C₂×#41	—	2	1	no	—
452	C₂×#41	—	2	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	C₂×C₄×C₄₇	1	2	yes	complemented
456	C₂×#41	C₂³×C₄₇	1	2	yes	—
457	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic, complemented
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
467	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
468	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic, complemented
469	C₂²×D₄	D₄×C₄₇	1	2	yes	—
470	C₂²×D₄	D₄×C₄₇	1	2	yes	—
471	C₂²×D₄	D₄×C₄₇	1	2	yes	—
472	C₂²×D₄	D₄×C₄₇	1	2	yes	—
473	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
474	C₂³×C₄	—	2	4	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
477	AGL(1,ℤ/8)	—	2	8	no	—
478	AGL(1,ℤ/8)	—	2	8	no	—
479	AGL(1,ℤ/8)	—	2	8	no	—
480	AGL(1,ℤ/8)	—	2	8	no	—
481	C₂×SD₁₆	—	2	4	no	—
482	C₂×SD₁₆	—	2	4	no	—
483	C₂×SD₁₆	C₂×C₄×C₄₇	1	8	yes	complemented
484	C₂×D₈	—	2	4	no	—
485	C₂×D₈	—	2	4	no	—
486	C₂×D₈	C₂×C₄×C₄₇	1	8	yes	complemented
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	—	2	1	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	1	no	—
496	C₂×M₁₆	C₂×C₄×C₄₇	1	2	yes	complemented
497	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
498	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
499	C₂²×C₈	—	2	1	no	—
500	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	complemented
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	8	no	—
505	#117	—	2	1	no	—
506	#117	—	2	1	no	—
507	#117	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	D₄×C₄₇	1	2	yes	—
513	#117	D₄×C₄₇	1	2	yes	—
514	#117	C₂³×C₄₇	1	2	yes	—
515	#117	C₂³×C₄₇	1	2	yes	—
516	#117	C₂³×C₄₇	1	2	yes	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	8	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	8	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	D₄×C₄₇	1	2	yes	—
529	#104	—	2	8	no	—
530	#102	—	2	8	no	—
531	#99	—	2	8	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	—	2	2	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	8	4	no	—
541	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
542	#41	—	2	2	no	—
543	#41	—	2	2	no	—
544	#41	—	2	2	no	—
545	#41	—	2	2	no	—
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	#41	—	2	2	no	—
549	#41	—	2	2	no	—
550	#41	—	4	1	no	—
551	#41	—	4	1	no	—
552	#41	—	4	1	no	—
553	#41	—	4	1	no	—
554	#41	—	4	1	no	—
555	#41	—	4	1	no	—
556	#41	—	4	1	no	—
557	#41	—	4	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	complemented
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	—	4	1	no	—
596	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
597	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
598	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
599	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
600	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
601	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	complemented
602	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
603	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	16	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	8	8	no	—
616	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
625	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
626	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
627	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
628	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
630	SD₁₆	—	2	16	no	—
631	D₈	—	2	16	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	2	no	—
636	M₁₆	—	2	2	no	—
637	M₁₆	—	2	2	no	—
638	M₁₆	—	4	1	no	—
639	M₁₆	—	4	1	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	4	1	no	—
644	C₂×C₈	—	4	1	no	—
645	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	complemented
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₂²⋊C₄	—	2	16	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	4	1	no	—
658	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	4	1	no	—
664	C₄²	C₂×D₄×C₄₇	1	4	yes	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	8	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	8	4	no	—
678	C₂³	—	8	4	no	—
679	C₂³	—	8	2	no	—
680	C₂³	—	8	4	no	—
681	C₂³	—	8	4	no	—
682	C₂³	—	8	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
685	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
686	C₂³	#120×C₄₇	1	1	yes	characteristic
687	C₂³	#120×C₄₇	1	1	yes	characteristic
688	C₂³	#121×C₄₇	1	1	yes	characteristic
689	C₂³	#121×C₄₇	1	1	yes	characteristic
690	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	1	no	—
694	Q₈	—	4	1	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	4	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	1	no	—
709	D₄	—	4	1	no	—
710	D₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	8	16	no	—
724	C₂×C₄	—	8	2	no	—
725	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
726	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
727	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
728	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
729	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
730	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
731	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
732	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
733	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
734	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
735	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
736	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
737	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
738	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
739	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
740	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
741	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
742	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
743	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
744	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
745	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
746	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
747	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
751	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
752	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
753	C₈	—	2	4	no	—
754	C₈	—	4	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	8	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	8	no	—
764	C₂²	—	4	8	no	—
765	C₂²	—	4	8	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	8	4	no	—
768	C₂²	—	8	4	no	—
769	C₂²	—	8	4	no	—
770	C₂²	—	8	4	no	—
771	C₂²	—	8	2	no	—
772	C₂²	—	8	2	no	—
773	C₂²	—	8	2	no	—
774	C₂²	C₄₇×#386	1	1	yes	characteristic
775	C₂²	C₄₇×#386	1	1	yes	characteristic
776	C₂²	C₄₇×#386	1	1	yes	characteristic
777	C₂²	C₄₇×#386	1	1	yes	characteristic
778	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
779	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
780	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
781	C₄	—	4	4	no	—
782	C₄	—	4	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	8	2	no	—
785	C₄	C₄₇×#386	1	1	yes	characteristic
786	C₄	C₄₇×#386	1	1	yes	characteristic
787	C₄	C₄₇×#386	1	1	yes	characteristic
788	C₄	C₄₇×#386	1	1	yes	characteristic
789	C₄	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
790	C₄	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
791	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
792	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
793	C₂	—	2	1	no	—
794	C₂	—	2	1	no	—
795	C₂	—	2	1	no	—
796	C₂	—	2	1	no	—
797	C₂	—	2	1	no	—
798	C₂	—	2	1	no	—
799	C₂	—	4	8	no	—
800	C₂	—	8	2	no	—
801	C₂	C₄₇×#1904	1	2	yes	direct product factor
802	C₂	C₂×C₄₇×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×AGL(1,ℤ/8)×C₄₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#518	C₂	semidirect
3. C₂×C₄₇×#421	C₂	semidirect
4. C₂×C₄₇×#418	C₂	semidirect
5. C₂×C₄₇×#410	C₂	semidirect
6. C₄₇×#1904	C₂	direct (N × H)
7. C₂×C₄₇×#344	C₂	semidirect
8. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
17. C₂²×SD₁₆×C₄₇	C₄	semidirect
18. C₂²×D₈×C₄₇	C₄	semidirect
24. C₄₇×#518	C₂²	semidirect
32. C₄₇×#421	C₂²	semidirect
35. C₄₇×#418	C₂²	semidirect
38. C₄₇×#410	C₂²	semidirect
40. C₄₇×#344	C₂²	semidirect
41. C₄₇×H(3,ℤ/4)	C₂²	semidirect
53. C₂×#41×C₄₇	C₂×C₄	semidirect
55. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
66. C₂²×D₄×C₄₇	C₂×C₄	semidirect
81. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
84. C₂×D₈×C₄₇	C₂×C₄	semidirect
94. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
98. C₂²×C₈×C₄₇	C₂×C₄	semidirect
161. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
199. C₂×D₄×C₄₇	C₂²×C₄	semidirect
243. C₂×C₈×C₄₇	C₂²×C₄	semidirect
353. C₂×#1904	C₄₇	direct (N × H)
393. C₂×#518	C₂×C₄₇	semidirect
394. C₂×#421	C₂×C₄₇	semidirect
395. C₂×#418	C₂×C₄₇	semidirect
396. C₂×#410	C₂×C₄₇	semidirect
397. #1904	C₂×C₄₇	direct (N × H)
398. C₂×#344	C₂×C₄₇	semidirect
399. C₂×H(3,ℤ/4)	C₂×C₄₇	semidirect
408. C₂×C₄₇	#1904	direct (N × H)
416. C₂×AGL(1,ℤ/8)	C₄×C₄₇	semidirect
418. C₂²×SD₁₆	C₄×C₄₇	semidirect
419. C₂²×D₈	C₄×C₄₇	semidirect
425. #518	C₂²×C₄₇	semidirect
433. #421	C₂²×C₄₇	semidirect
436. #418	C₂²×C₄₇	semidirect
439. #410	C₂²×C₄₇	semidirect
441. #344	C₂²×C₄₇	semidirect
442. H(3,ℤ/4)	C₂²×C₄₇	semidirect
443. C₄₇	C₂×#1904	direct (N × H)
455. C₂×#41	C₂×C₄×C₄₇	semidirect
457. C₂²×Q₈	C₂×C₄×C₄₇	semidirect
468. C₂²×D₄	C₂×C₄×C₄₇	semidirect
483. C₂×SD₁₆	C₂×C₄×C₄₇	semidirect
486. C₂×D₈	C₂×C₄×C₄₇	semidirect
496. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
500. C₂²×C₈	C₂×C₄×C₄₇	semidirect
563. C₂×Q₈	C₂²×C₄×C₄₇	semidirect
601. C₂×D₄	C₂²×C₄×C₄₇	semidirect
645. C₂×C₈	C₂²×C₄×C₄₇	semidirect
801. C₂	C₄₇×#1904	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₇	2
C₂×C₄₇×#518	2
C₂×C₄₇×#421	2
C₂×C₄₇×#418	2
C₂×C₄₇×#410	2
C₄₇×#1904	2
C₂×C₄₇×#344	2
C₂×C₄₇×H(3,ℤ/4)	2
C₂×#1904	47

Subgroups — C2×C47×#1904 #26060694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1904 #26060694