Subgroups — C₄₇×#36569 #26076267

Order 12032.

1826 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2855	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2590	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2589	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2586	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2564	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#2556	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2522	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2520	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2473	C₂	1	2	yes	maximal, complemented
12	C₄₇×#2449	C₂	1	2	yes	maximal
13	C₄₇×#2370	C₂	1	2	yes	maximal, complemented
14	C₄₇×#2368	C₂	1	2	yes	maximal, complemented
15	C₄₇×#2368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₇×#2349	C₂	1	1	yes	maximal, characteristic
17	C₄×#123×C₄₇	C₂	1	1	yes	maximal, characteristic
18	C₄×#123×C₄₇	C₂	1	2	yes	maximal
19	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#125×C₄₇	C₂²	1	2	yes	—
21	C₂×#123×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
30	C₄₇×#400	C₂²	1	2	yes	—
31	C₄₇×#400	C₂²	1	1	yes	characteristic
32	C₄₇×#399	C₂²	1	2	yes	—
33	C₄₇×#399	C₂²	1	1	yes	characteristic
34	C₄₇×#398	C₂²	1	2	yes	—
35	C₄₇×#398	C₂²	1	2	yes	—
36	C₄₇×#398	C₂²	1	2	yes	—
37	C₄₇×#398	C₂²	1	2	yes	—
38	C₄₇×#398	C₂²	1	2	yes	—
39	C₄₇×#396	C₂²	1	2	yes	—
40	C₄₇×#395	C₂²	1	2	yes	—
41	C₄₇×#395	C₂²	1	2	yes	—
42	C₄₇×#395	C₂²	1	1	yes	characteristic
43	C₄₇×#393	C₂²	1	1	yes	characteristic
44	C₄₇×#391	C₂²	1	2	yes	—
45	C₄₇×#391	C₂²	1	2	yes	—
46	C₄₇×#391	C₂²	1	2	yes	—
47	C₄₇×#391	C₂²	1	2	yes	—
48	C₄₇×#391	C₂²	1	2	yes	—
49	C₄₇×#389	C₂²	1	2	yes	—
50	C₄₇×#389	C₂²	1	2	yes	—
51	C₄₇×#389	C₂²	1	2	yes	—
52	C₄₇×#389	C₂²	1	2	yes	—
53	C₄₇×#389	C₂²	1	2	yes	—
54	C₄₇×#389	C₂²	1	2	yes	—
55	C₄₇×#389	C₂²	1	2	yes	—
56	C₄₇×#388	C₂²	1	2	yes	—
57	C₄₇×#388	C₂²	1	2	yes	—
58	C₄₇×#388	C₂²	1	2	yes	—
59	C₄₇×#387	C₂²	1	2	yes	—
60	C₄₇×#387	C₂²	1	2	yes	—
61	C₄₇×#387	C₂²	1	2	yes	—
62	C₄₇×#387	C₂²	1	2	yes	—
63	C₄₇×#387	C₂²	1	2	yes	—
64	C₄₇×#387	C₂²	1	2	yes	—
65	C₄₇×#387	C₂²	1	2	yes	—
66	C₄₇×#387	C₂²	1	2	yes	—
67	C₄₇×#387	C₂²	1	2	yes	—
68	C₄₇×#387	C₂²	1	2	yes	—
69	C₄₇×#387	C₂²	1	2	yes	—
70	C₄₇×#387	C₂²	1	2	yes	—
71	C₄₇×#387	C₂²	1	2	yes	—
72	C₄₇×#387	C₂²	1	2	yes	—
73	C₄₇×#387	C₂²	1	2	yes	—
74	C₄₇×#386	C₂²	1	2	yes	—
75	C₄₇×#386	C₂²	1	1	yes	characteristic
76	C₄₇×#385	C₂²	1	2	yes	—
77	C₄₇×#385	C₂²	1	2	yes	—
78	C₄₇×#385	C₂²	1	2	yes	—
79	C₄₇×#385	C₂²	1	1	yes	characteristic
80	C₄₇×#385	C₂²	1	2	yes	—
81	C₄₇×#385	C₂²	1	2	yes	—
82	C₄₇×#385	C₂²	1	2	yes	—
83	C₄₇×#385	C₂²	1	2	yes	—
84	C₄₇×#382	C₂²	1	1	yes	characteristic
85	C₄₇×#381	C₂²	1	2	yes	—
86	C₄₇×#381	C₂²	1	1	yes	characteristic
87	C₄₇×#380	C₂²	1	1	yes	characteristic
88	C₄₇×#380	C₂²	1	1	yes	characteristic
89	C₄₇×#380	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
104	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
106	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
117	#125×C₄₇	—	2	8	no	—
118	#123×C₄₇	Q₈	1	8	yes	complemented
119	C₂²⋊Q₈×C₄₇	—	2	4	no	—
120	C₂²⋊Q₈×C₄₇	—	2	8	no	—
121	C₂²⋊Q₈×C₄₇	—	4	4	no	—
122	C₄×D₄×C₄₇	—	2	4	no	—
123	C₄×D₄×C₄₇	—	4	4	no	—
124	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
125	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₄₇	—	2	4	no	—
161	C₂×C₄²×C₄₇	—	4	4	no	—
162	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
167	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
173	#95×C₄₇	C₂³	1	1	yes	characteristic
174	#95×C₄₇	C₂³	1	1	yes	characteristic
175	#95×C₄₇	C₂³	1	2	yes	—
176	#95×C₄₇	C₂³	1	2	yes	—
177	#95×C₄₇	C₂³	1	1	yes	characteristic
178	#95×C₄₇	C₂³	1	1	yes	characteristic
179	#95×C₄₇	C₂³	1	1	yes	characteristic
180	#95×C₄₇	C₂³	1	2	yes	—
181	#95×C₄₇	C₂³	1	2	yes	—
182	#95×C₄₇	C₂³	1	2	yes	—
183	#95×C₄₇	C₂³	1	2	yes	—
184	#95×C₄₇	C₂³	1	2	yes	—
185	#95×C₄₇	C₂³	1	2	yes	—
186	#95×C₄₇	C₂³	1	2	yes	—
187	#95×C₄₇	C₂³	1	2	yes	—
188	#95×C₄₇	C₂³	1	2	yes	—
189	#95×C₄₇	C₂³	1	2	yes	—
190	#95×C₄₇	C₂³	1	1	yes	characteristic
191	#95×C₄₇	C₂³	1	2	yes	—
192	#95×C₄₇	C₂³	1	2	yes	—
193	#95×C₄₇	C₂³	1	2	yes	—
194	#95×C₄₇	C₂³	1	2	yes	—
195	#95×C₄₇	C₂³	1	2	yes	—
196	#95×C₄₇	C₂³	1	2	yes	—
197	#95×C₄₇	C₂³	1	2	yes	—
198	#95×C₄₇	C₂³	1	2	yes	—
199	#95×C₄₇	C₂³	1	2	yes	—
200	#95×C₄₇	C₂³	1	2	yes	—
201	#95×C₄₇	C₂³	1	2	yes	—
202	#95×C₄₇	C₂³	1	2	yes	—
203	#95×C₄₇	C₂³	1	2	yes	—
204	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
205	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₄₇	—	2	2	no	—
207	C₂×Q₈×C₄₇	—	2	4	no	—
208	C₂×Q₈×C₄₇	—	4	2	no	—
209	C₂×Q₈×C₄₇	—	4	2	no	—
210	C₂×Q₈×C₄₇	—	4	2	no	—
211	C₂×D₄×C₄₇	—	2	2	no	—
212	C₂×D₄×C₄₇	—	2	2	no	—
213	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
214	C₂²×C₄×C₄₇	—	2	2	no	—
215	C₂²×C₄×C₄₇	—	2	2	no	—
216	C₂²×C₄×C₄₇	—	2	2	no	—
217	C₂²×C₄×C₄₇	—	2	4	no	—
218	C₂²×C₄×C₄₇	—	2	4	no	—
219	C₂²×C₄×C₄₇	—	2	4	no	—
220	C₂²×C₄×C₄₇	—	2	4	no	—
221	C₂²×C₄×C₄₇	—	2	4	no	—
222	C₂²×C₄×C₄₇	—	2	2	no	—
223	C₂²×C₄×C₄₇	—	2	4	no	—
224	C₂²×C₄×C₄₇	—	4	2	no	—
225	C₂²×C₄×C₄₇	—	4	2	no	—
226	C₂²×C₄×C₄₇	—	4	2	no	—
227	C₂²×C₄×C₄₇	—	4	2	no	—
228	C₂²×C₄×C₄₇	—	4	2	no	—
229	C₂²×C₄×C₄₇	—	4	2	no	—
230	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
231	C₂²×C₄×C₄₇	#41	1	4	yes	—
232	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₄₇	—	2	4	no	—
250	C₄⋊C₄×C₄₇	—	2	4	no	—
251	C₄⋊C₄×C₄₇	—	2	4	no	—
252	C₄⋊C₄×C₄₇	—	2	2	no	—
253	C₄⋊C₄×C₄₇	—	2	2	no	—
254	C₄⋊C₄×C₄₇	—	2	4	no	—
255	C₄⋊C₄×C₄₇	—	2	4	no	—
256	C₄⋊C₄×C₄₇	—	2	4	no	—
257	C₄⋊C₄×C₄₇	—	2	4	no	—
258	C₄⋊C₄×C₄₇	—	2	4	no	—
259	C₄⋊C₄×C₄₇	—	2	4	no	—
260	C₄⋊C₄×C₄₇	—	2	4	no	—
261	C₄⋊C₄×C₄₇	—	2	4	no	—
262	C₄⋊C₄×C₄₇	—	4	2	no	—
263	C₄⋊C₄×C₄₇	—	4	2	no	—
264	C₄⋊C₄×C₄₇	—	4	2	no	—
265	C₄⋊C₄×C₄₇	—	4	2	no	—
266	C₄⋊C₄×C₄₇	—	4	2	no	—
267	C₄⋊C₄×C₄₇	—	4	2	no	—
268	C₄⋊C₄×C₄₇	—	4	2	no	—
269	C₄⋊C₄×C₄₇	—	4	2	no	—
270	C₄⋊C₄×C₄₇	—	4	2	no	—
271	C₄⋊C₄×C₄₇	C₂×Q₈	1	8	yes	—
272	C₄⋊C₄×C₄₇	#41	1	8	yes	—
273	C₂²⋊C₄×C₄₇	—	2	2	no	—
274	C₂²⋊C₄×C₄₇	—	2	4	no	—
275	C₂²⋊C₄×C₄₇	—	2	4	no	—
276	C₂²⋊C₄×C₄₇	—	2	2	no	—
277	C₂²⋊C₄×C₄₇	—	2	2	no	—
278	C₂²⋊C₄×C₄₇	—	2	4	no	—
279	C₂²⋊C₄×C₄₇	—	2	4	no	—
280	C₂²⋊C₄×C₄₇	—	4	2	no	—
281	C₂²⋊C₄×C₄₇	—	4	2	no	—
282	C₂²⋊C₄×C₄₇	C₂×Q₈	1	4	yes	—
283	C₂²⋊C₄×C₄₇	C₂×Q₈	1	8	yes	—
284	C₄²×C₄₇	—	2	4	no	—
285	C₄²×C₄₇	—	2	4	no	—
286	C₄²×C₄₇	—	2	2	no	—
287	C₄²×C₄₇	—	2	4	no	—
288	C₄²×C₄₇	—	4	2	no	—
289	C₄²×C₄₇	—	4	2	no	—
290	C₄²×C₄₇	—	4	2	no	—
291	C₄²×C₄₇	—	4	2	no	—
292	C₄²×C₄₇	—	4	2	no	—
293	C₄²×C₄₇	—	4	2	no	—
294	C₄²×C₄₇	—	4	2	no	—
295	C₂³×C₄₇	—	2	2	no	—
296	C₂³×C₄₇	—	2	2	no	—
297	C₂³×C₄₇	—	2	2	no	—
298	C₂³×C₄₇	—	2	1	no	—
299	C₂³×C₄₇	—	2	1	no	—
300	C₂³×C₄₇	—	2	2	no	—
301	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
302	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
303	C₂³×C₄₇	C₂×#41	1	2	yes	—
304	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
305	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
306	Q₈×C₄₇	—	8	2	no	—
307	Q₈×C₄₇	—	8	4	no	—
308	D₄×C₄₇	—	2	8	no	—
309	C₂×C₄×C₄₇	—	2	8	no	—
310	C₂×C₄×C₄₇	—	2	8	no	—
311	C₂×C₄×C₄₇	—	2	2	no	—
312	C₂×C₄×C₄₇	—	2	2	no	—
313	C₂×C₄×C₄₇	—	2	2	no	—
314	C₂×C₄×C₄₇	—	2	1	no	—
315	C₂×C₄×C₄₇	—	2	2	no	—
316	C₂×C₄×C₄₇	—	2	2	no	—
317	C₂×C₄×C₄₇	—	2	2	no	—
318	C₂×C₄×C₄₇	—	2	1	no	—
319	C₂×C₄×C₄₇	—	2	2	no	—
320	C₂×C₄×C₄₇	—	2	2	no	—
321	C₂×C₄×C₄₇	—	2	2	no	—
322	C₂×C₄×C₄₇	—	2	2	no	—
323	C₂×C₄×C₄₇	—	2	2	no	—
324	C₂×C₄×C₄₇	—	2	2	no	—
325	C₂×C₄×C₄₇	—	2	1	no	—
326	C₂×C₄×C₄₇	—	2	2	no	—
327	C₂×C₄×C₄₇	—	2	2	no	—
328	C₂×C₄×C₄₇	—	2	2	no	—
329	C₂×C₄×C₄₇	—	2	1	no	—
330	C₂×C₄×C₄₇	—	2	2	no	—
331	C₂×C₄×C₄₇	—	2	2	no	—
332	C₂×C₄×C₄₇	—	2	2	no	—
333	C₂×C₄×C₄₇	—	2	2	no	—
334	C₂×C₄×C₄₇	—	2	2	no	—
335	C₂×C₄×C₄₇	—	2	2	no	—
336	C₂×C₄×C₄₇	—	2	2	no	—
337	C₂×C₄×C₄₇	—	2	2	no	—
338	C₂×C₄×C₄₇	—	2	2	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	2	no	—
341	C₂×C₄×C₄₇	—	2	2	no	—
342	C₂×C₄×C₄₇	—	2	2	no	—
343	C₂×C₄×C₄₇	—	2	2	no	—
344	C₂×C₄×C₄₇	—	2	2	no	—
345	C₂×C₄×C₄₇	—	2	2	no	—
346	C₂×C₄×C₄₇	—	2	2	no	—
347	C₂×C₄×C₄₇	—	2	2	no	—
348	C₂×C₄×C₄₇	—	2	2	no	—
349	C₂×C₄×C₄₇	—	2	2	no	—
350	C₂×C₄×C₄₇	—	4	4	no	—
351	C₂×C₄×C₄₇	—	4	8	no	—
352	C₂×C₄×C₄₇	—	4	8	no	—
353	C₂×C₄×C₄₇	—	8	2	no	—
354	C₂×C₄×C₄₇	—	8	4	no	—
355	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
356	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
357	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
358	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
359	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
360	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
361	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
362	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
363	#36569	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂²×C₄₇	—	2	2	no	—
365	C₂²×C₄₇	—	2	4	no	—
366	C₂²×C₄₇	—	2	2	no	—
367	C₂²×C₄₇	—	2	4	no	—
368	C₂²×C₄₇	—	2	2	no	—
369	C₂²×C₄₇	—	2	4	no	—
370	C₂²×C₄₇	—	4	1	no	—
371	C₂²×C₄₇	—	4	1	no	—
372	C₂²×C₄₇	—	4	2	no	—
373	C₂²×C₄₇	#554	1	4	yes	—
374	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
375	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₄₇	C₂²×#41	1	2	yes	—
377	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₄₇	#585	1	2	yes	—
379	C₄×C₄₇	—	2	4	no	—
380	C₄×C₄₇	—	2	4	no	—
381	C₄×C₄₇	—	2	2	no	—
382	C₄×C₄₇	—	2	4	no	—
383	C₄×C₄₇	—	2	2	no	—
384	C₄×C₄₇	—	2	2	no	—
385	C₄×C₄₇	—	2	4	no	—
386	C₄×C₄₇	—	2	4	no	—
387	C₄×C₄₇	—	4	1	no	—
388	C₄×C₄₇	—	4	2	no	—
389	C₄×C₄₇	—	4	1	no	—
390	C₄×C₄₇	—	4	2	no	—
391	C₄×C₄₇	—	4	2	no	—
392	C₄×C₄₇	—	4	2	no	—
393	C₄×C₄₇	—	4	2	no	—
394	C₄×C₄₇	—	4	2	no	—
395	C₄×C₄₇	—	4	2	no	—
396	#2855	C₂×C₄₇	1	1	yes	characteristic, complemented
397	#2855	C₂×C₄₇	1	2	yes	complemented
398	#2590	C₂×C₄₇	1	2	yes	complemented
399	#2589	C₂×C₄₇	1	2	yes	complemented
400	#2586	C₂×C₄₇	1	2	yes	complemented
401	#2564	C₂×C₄₇	1	1	yes	characteristic
402	#2556	C₂×C₄₇	1	2	yes	complemented
403	#2549	C₂×C₄₇	1	1	yes	characteristic, complemented
404	#2522	C₂×C₄₇	1	2	yes	complemented
405	#2520	C₂×C₄₇	1	2	yes	complemented
406	#2473	C₂×C₄₇	1	2	yes	complemented
407	#2449	C₂×C₄₇	1	2	yes	—
408	#2370	C₂×C₄₇	1	2	yes	complemented
409	#2368	C₂×C₄₇	1	1	yes	characteristic, complemented
410	#2368	C₂×C₄₇	1	2	yes	complemented
411	#2349	C₂×C₄₇	1	1	yes	characteristic
412	C₄×#123	C₂×C₄₇	1	1	yes	characteristic
413	C₄×#123	C₂×C₄₇	1	2	yes	—
414	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
415	C₂×C₄₇	—	2	4	no	—
416	C₂×C₄₇	—	4	2	no	—
417	C₂×C₄₇	#3444	1	1	yes	characteristic
418	C₂×C₄₇	C₂×#554	1	1	yes	characteristic
419	C₂×C₄₇	Q₈×#41	1	2	yes	—
420	C₂×C₄₇	#3491	1	1	yes	characteristic
421	C₂×C₄₇	#3513	1	2	yes	—
422	C₂×#125	C₂²×C₄₇	1	2	yes	—
423	C₂×#123	C₂²×C₄₇	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
425	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
430	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
431	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
432	#400	C₂²×C₄₇	1	1	yes	characteristic
433	#400	C₂²×C₄₇	1	2	yes	—
434	#399	C₂²×C₄₇	1	1	yes	characteristic
435	#399	C₂²×C₄₇	1	2	yes	—
436	#398	C₂²×C₄₇	1	2	yes	—
437	#398	C₂²×C₄₇	1	2	yes	—
438	#398	C₂²×C₄₇	1	2	yes	—
439	#398	C₂²×C₄₇	1	2	yes	—
440	#398	C₂²×C₄₇	1	2	yes	—
441	#396	C₂²×C₄₇	1	2	yes	—
442	#395	C₂²×C₄₇	1	1	yes	characteristic
443	#395	C₂²×C₄₇	1	2	yes	—
444	#395	C₂²×C₄₇	1	2	yes	—
445	#393	C₂²×C₄₇	1	1	yes	characteristic
446	#391	C₂²×C₄₇	1	2	yes	—
447	#391	C₂²×C₄₇	1	2	yes	—
448	#391	C₂²×C₄₇	1	2	yes	—
449	#391	C₂²×C₄₇	1	2	yes	—
450	#391	C₂²×C₄₇	1	2	yes	—
451	#389	C₂²×C₄₇	1	2	yes	—
452	#389	C₂²×C₄₇	1	2	yes	—
453	#389	C₂²×C₄₇	1	2	yes	—
454	#389	C₂²×C₄₇	1	2	yes	—
455	#389	C₂²×C₄₇	1	2	yes	—
456	#389	C₂²×C₄₇	1	2	yes	—
457	#389	C₂²×C₄₇	1	2	yes	—
458	#388	C₂²×C₄₇	1	2	yes	—
459	#388	C₂²×C₄₇	1	2	yes	—
460	#388	C₂²×C₄₇	1	2	yes	—
461	#387	C₂²×C₄₇	1	2	yes	—
462	#387	C₂²×C₄₇	1	2	yes	—
463	#387	C₂²×C₄₇	1	2	yes	—
464	#387	C₂²×C₄₇	1	2	yes	—
465	#387	C₂²×C₄₇	1	2	yes	—
466	#387	C₂²×C₄₇	1	2	yes	—
467	#387	C₂²×C₄₇	1	2	yes	—
468	#387	C₂²×C₄₇	1	2	yes	—
469	#387	C₂²×C₄₇	1	2	yes	—
470	#387	C₂²×C₄₇	1	2	yes	—
471	#387	C₂²×C₄₇	1	2	yes	—
472	#387	C₂²×C₄₇	1	2	yes	—
473	#387	C₂²×C₄₇	1	2	yes	—
474	#387	C₂²×C₄₇	1	2	yes	—
475	#387	C₂²×C₄₇	1	2	yes	—
476	#386	C₂²×C₄₇	1	2	yes	—
477	#386	C₂²×C₄₇	1	1	yes	characteristic
478	#385	C₂²×C₄₇	1	2	yes	—
479	#385	C₂²×C₄₇	1	2	yes	—
480	#385	C₂²×C₄₇	1	2	yes	—
481	#385	C₂²×C₄₇	1	2	yes	—
482	#385	C₂²×C₄₇	1	2	yes	—
483	#385	C₂²×C₄₇	1	2	yes	—
484	#385	C₂²×C₄₇	1	1	yes	characteristic
485	#385	C₂²×C₄₇	1	2	yes	—
486	#382	C₂²×C₄₇	1	1	yes	characteristic
487	#381	C₂²×C₄₇	1	1	yes	characteristic
488	#381	C₂²×C₄₇	1	2	yes	—
489	#380	C₂²×C₄₇	1	2	yes	—
490	#380	C₂²×C₄₇	1	1	yes	characteristic
491	#380	C₂²×C₄₇	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
497	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
506	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
507	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
508	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
509	C₄₇	#36569	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
511	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
515	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
516	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
518	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
520	#125	—	2	8	no	—
521	#123	Q₈×C₄₇	1	8	yes	complemented
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₂²⋊Q₈	—	4	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	4	4	no	—
527	C₂×C₄⋊C₄	—	2	8	no	—
528	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
563	C₂×C₄²	—	2	4	no	—
564	C₂×C₄²	—	4	4	no	—
565	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
567	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
568	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
569	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
570	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
571	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
572	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
573	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
574	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
575	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
576	#95	C₂³×C₄₇	1	1	yes	characteristic
577	#95	C₂³×C₄₇	1	1	yes	characteristic
578	#95	C₂³×C₄₇	1	2	yes	—
579	#95	C₂³×C₄₇	1	2	yes	—
580	#95	C₂³×C₄₇	1	1	yes	characteristic
581	#95	C₂³×C₄₇	1	1	yes	characteristic
582	#95	C₂³×C₄₇	1	1	yes	characteristic
583	#95	C₂³×C₄₇	1	2	yes	—
584	#95	C₂³×C₄₇	1	2	yes	—
585	#95	C₂³×C₄₇	1	2	yes	—
586	#95	C₂³×C₄₇	1	2	yes	—
587	#95	C₂³×C₄₇	1	2	yes	—
588	#95	C₂³×C₄₇	1	2	yes	—
589	#95	C₂³×C₄₇	1	2	yes	—
590	#95	C₂³×C₄₇	1	2	yes	—
591	#95	C₂³×C₄₇	1	2	yes	—
592	#95	C₂³×C₄₇	1	2	yes	—
593	#95	C₂³×C₄₇	1	1	yes	characteristic
594	#95	C₂³×C₄₇	1	2	yes	—
595	#95	C₂³×C₄₇	1	2	yes	—
596	#95	C₂³×C₄₇	1	2	yes	—
597	#95	C₂³×C₄₇	1	2	yes	—
598	#95	C₂³×C₄₇	1	2	yes	—
599	#95	C₂³×C₄₇	1	2	yes	—
600	#95	C₂³×C₄₇	1	2	yes	—
601	#95	C₂³×C₄₇	1	2	yes	—
602	#95	C₂³×C₄₇	1	2	yes	—
603	#95	C₂³×C₄₇	1	2	yes	—
604	#95	C₂³×C₄₇	1	2	yes	—
605	#95	C₂³×C₄₇	1	2	yes	—
606	#95	C₂³×C₄₇	1	2	yes	—
607	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
608	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	C₂×Q₈×C₄₇	1	4	yes	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
634	C₂²×C₄	#41×C₄₇	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	C₂×Q₈×C₄₇	1	8	yes	—
675	C₄⋊C₄	#41×C₄₇	1	8	yes	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	C₂×Q₈×C₄₇	1	4	yes	—
686	C₂²⋊C₄	C₂×Q₈×C₄₇	1	8	yes	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
705	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
706	C₂³	C₂×#41×C₄₇	1	2	yes	—
707	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
708	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
709	Q₈	—	8	2	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	C₂²×Q₈×C₄₇	1	4	yes	—
759	C₂×C₄	C₂²×Q₈×C₄₇	1	4	yes	—
760	C₂×C₄	C₂²×Q₈×C₄₇	1	2	yes	—
761	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
762	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
763	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
764	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
765	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	2	no	—
775	C₂²	C₄₇×#554	1	4	yes	—
776	C₂²	C₂³×Q₈×C₄₇	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
778	C₂²	C₂²×#41×C₄₇	1	2	yes	—
779	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
780	C₂²	C₄₇×#585	1	2	yes	—
781	C₄	—	2	4	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	4	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	4	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₂	—	2	4	no	—
799	C₂	—	4	2	no	—
800	C₂	C₄₇×#3444	1	1	yes	characteristic
801	C₂	C₂×C₄₇×#554	1	1	yes	characteristic
802	C₂	Q₈×#41×C₄₇	1	2	yes	—
803	C₂	C₄₇×#3491	1	1	yes	characteristic
804	C₂	C₄₇×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂²×D₄×C₄₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2855	C₂	semidirect
2. C₄₇×#2855	C₂	semidirect
3. C₄₇×#2590	C₂	semidirect
4. C₄₇×#2589	C₂	semidirect
5. C₄₇×#2586	C₂	semidirect
7. C₄₇×#2556	C₂	semidirect
8. C₄₇×#2549	C₂	semidirect
9. C₄₇×#2522	C₂	semidirect
10. C₄₇×#2520	C₂	semidirect
11. C₄₇×#2473	C₂	semidirect
13. C₄₇×#2370	C₂	semidirect
14. C₄₇×#2368	C₂	semidirect
15. C₄₇×#2368	C₂	semidirect
19. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
118. #123×C₄₇	Q₈	semidirect
363. #36569	C₄₇	direct (N × H)
396. #2855	C₂×C₄₇	semidirect
397. #2855	C₂×C₄₇	semidirect
398. #2590	C₂×C₄₇	semidirect
399. #2589	C₂×C₄₇	semidirect
400. #2586	C₂×C₄₇	semidirect
402. #2556	C₂×C₄₇	semidirect
403. #2549	C₂×C₄₇	semidirect
404. #2522	C₂×C₄₇	semidirect
405. #2520	C₂×C₄₇	semidirect
406. #2473	C₂×C₄₇	semidirect
408. #2370	C₂×C₄₇	semidirect
409. #2368	C₂×C₄₇	semidirect
410. #2368	C₂×C₄₇	semidirect
414. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
509. C₄₇	#36569	direct (N × H)
521. #123	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2855	2
C₄₇×#2590	2
C₄₇×#2589	2
C₄₇×#2586	2
C₄₇×#2564	2
C₄₇×#2556	2
C₄₇×#2549	2
C₄₇×#2522	2
C₄₇×#2520	2
C₄₇×#2473	2
C₄₇×#2449	2
C₄₇×#2370	2
C₄₇×#2368	2
C₄₇×#2349	2
C₄×#123×C₄₇	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#36569	47

Subgroups — C47×#36569 #26076267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#36569 #26076267