Subgroups — C₄₇×#20623 #26060321

Order 12032.

3644 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#421	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1796	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1795	C₂	1	4	yes	maximal, complemented
8	C₄₇×#585	—	2	4	no	—
9	C₄₇×#585	—	2	4	no	—
10	C₄₇×#585	—	2	4	no	—
11	C₄₇×#585	—	2	4	no	—
12	C₂×2₋¹⁺⁴×C₄₇	—	2	1	no	—
13	C₂×2₋¹⁺⁴×C₄₇	C₄	1	2	yes	complemented
14	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	2	yes	—
15	C₂×H(5,𝔽₂)×C₄₇	—	2	1	no	—
16	C₂×H(5,𝔽₂)×C₄₇	—	2	2	no	—
17	C₂×H(5,𝔽₂)×C₄₇	C₄	1	2	yes	complemented
18	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	2	yes	—
19	C₂²×#41×C₄₇	—	2	2	no	—
20	C₂²×#41×C₄₇	—	2	2	no	—
21	C₂²×#41×C₄₇	C₄	1	4	yes	complemented
22	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	complemented
26	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
27	C₄₇×#421	—	2	4	no	—
28	C₄₇×#421	C₂²	1	8	yes	complemented
29	C₂×#104×C₄₇	—	2	4	no	—
30	C₄₇×#419	C₂²	1	4	yes	complemented
31	C₄₇×#418	C₂²	1	4	yes	complemented
32	C₄₇×#417	—	2	4	no	—
33	C₄₇×#416	—	2	4	no	—
34	C₄₇×#413	—	2	2	no	—
35	C₄₇×#413	C₂²	1	4	yes	complemented
36	C₂×#101×C₄₇	—	2	1	no	—
37	C₂×#100×C₄₇	—	2	1	no	—
38	C₄₇×#410	—	2	2	no	—
39	C₄₇×#410	C₂²	1	4	yes	complemented
40	C₂×#99×C₄₇	—	2	2	no	—
41	2₋¹⁺⁴×C₄₇	—	2	8	no	—
42	2₋¹⁺⁴×C₄₇	—	2	8	no	—
43	2₋¹⁺⁴×C₄₇	—	2	8	no	—
44	2₋¹⁺⁴×C₄₇	—	2	8	no	—
45	2₋¹⁺⁴×C₄₇	—	2	8	no	—
46	2₋¹⁺⁴×C₄₇	—	2	8	no	—
47	H(5,𝔽₂)×C₄₇	—	2	8	no	—
48	H(5,𝔽₂)×C₄₇	—	2	8	no	—
49	H(5,𝔽₂)×C₄₇	—	2	16	no	—
50	H(5,𝔽₂)×C₄₇	—	2	16	no	—
51	H(5,𝔽₂)×C₄₇	—	2	8	no	—
52	H(5,𝔽₂)×C₄₇	—	2	8	no	—
53	H(5,𝔽₂)×C₄₇	—	2	8	no	—
54	H(5,𝔽₂)×C₄₇	—	2	8	no	—
55	C₂×#41×C₄₇	—	2	16	no	—
56	C₂×#41×C₄₇	—	2	16	no	—
57	C₂×#41×C₄₇	—	2	16	no	—
58	C₂×#41×C₄₇	—	2	16	no	—
59	C₂×#41×C₄₇	—	2	8	no	—
60	C₂×#41×C₄₇	—	2	8	no	—
61	C₂×#41×C₄₇	—	2	8	no	—
62	C₂×#41×C₄₇	—	2	8	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	—	2	4	no	—
66	C₂×#41×C₄₇	—	2	2	no	—
67	C₂×#41×C₄₇	—	2	2	no	—
68	C₂×#41×C₄₇	—	2	4	no	—
69	C₂×#41×C₄₇	—	2	4	no	—
70	C₂×#41×C₄₇	—	2	4	no	—
71	C₂×#41×C₄₇	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	1	no	—
73	C₂×#41×C₄₇	—	2	1	no	—
74	C₂×#41×C₄₇	—	2	1	no	—
75	C₂×#41×C₄₇	—	2	2	no	—
76	C₂×#41×C₄₇	—	2	2	no	—
77	C₂×#41×C₄₇	—	2	2	no	—
78	C₂×#41×C₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	—	2	2	no	—
80	C₂×#41×C₄₇	—	2	2	no	—
81	C₂×#41×C₄₇	—	2	2	no	—
82	C₂×#41×C₄₇	—	2	2	no	—
83	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
86	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
88	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₂×#41×C₄₇	D₄	1	4	yes	—
90	C₂×#41×C₄₇	D₄	1	4	yes	—
91	C₂×#41×C₄₇	D₄	1	4	yes	—
92	C₂×#41×C₄₇	D₄	1	4	yes	—
93	C₂×#41×C₄₇	D₄	1	2	yes	—
94	C₂×#41×C₄₇	D₄	1	2	yes	—
95	C₂×#41×C₄₇	C₂³	1	2	yes	—
96	C₂×#41×C₄₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₄₇	—	2	2	no	—
98	C₂²×Q₈×C₄₇	—	2	2	no	—
99	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
101	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
102	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₄₇	—	2	4	no	—
104	C₂²×D₄×C₄₇	—	2	1	no	—
105	C₂²×D₄×C₄₇	—	2	1	no	—
106	C₂²×D₄×C₄₇	—	2	2	no	—
107	C₂²×D₄×C₄₇	—	2	4	no	—
108	C₂²×D₄×C₄₇	—	2	4	no	—
109	C₂²×D₄×C₄₇	—	2	2	no	—
110	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
112	C₂²×D₄×C₄₇	D₄	1	2	yes	—
113	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
114	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₄₇	—	2	4	no	—
116	C₂³×C₄×C₄₇	—	2	1	no	—
117	C₂³×C₄×C₄₇	—	2	1	no	—
118	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
119	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₄₇	—	2	2	no	—
121	C₂×M₁₆×C₄₇	—	2	2	no	—
122	C₂×M₁₆×C₄₇	—	2	2	no	—
123	C₂×M₁₆×C₄₇	—	2	2	no	—
124	C₂×M₁₆×C₄₇	—	2	2	no	—
125	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
126	C₂²×C₈×C₄₇	—	2	2	no	—
127	#117×C₄₇	—	2	2	no	—
128	#117×C₄₇	—	2	2	no	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
133	C₂×C₄²×C₄₇	—	2	2	no	—
134	#104×C₄₇	—	2	16	no	—
135	#103×C₄₇	—	2	8	no	—
136	#102×C₄₇	—	2	8	no	—
137	#101×C₄₇	—	2	4	no	—
138	#100×C₄₇	—	2	4	no	—
139	#99×C₄₇	—	2	8	no	—
140	C₂⁴×C₄₇	—	2	1	no	—
141	C₂⁴×C₄₇	—	2	4	no	—
142	C₂⁴×C₄₇	—	2	1	no	—
143	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
144	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
145	#41×C₄₇	—	2	16	no	—
146	#41×C₄₇	—	2	16	no	—
147	#41×C₄₇	—	2	32	no	—
148	#41×C₄₇	—	2	32	no	—
149	#41×C₄₇	—	2	16	no	—
150	#41×C₄₇	—	2	16	no	—
151	#41×C₄₇	—	2	16	no	—
152	#41×C₄₇	—	2	16	no	—
153	#41×C₄₇	—	2	16	no	—
154	#41×C₄₇	—	2	16	no	—
155	#41×C₄₇	—	2	8	no	—
156	#41×C₄₇	—	2	8	no	—
157	#41×C₄₇	—	2	8	no	—
158	#41×C₄₇	—	2	8	no	—
159	#41×C₄₇	—	2	2	no	—
160	#41×C₄₇	—	2	2	no	—
161	#41×C₄₇	—	2	2	no	—
162	#41×C₄₇	—	2	2	no	—
163	#41×C₄₇	—	2	4	no	—
164	#41×C₄₇	—	2	4	no	—
165	#41×C₄₇	—	2	4	no	—
166	#41×C₄₇	—	2	4	no	—
167	#41×C₄₇	—	2	4	no	—
168	#41×C₄₇	—	2	4	no	—
169	#41×C₄₇	—	2	4	no	—
170	#41×C₄₇	—	2	4	no	—
171	#41×C₄₇	—	2	4	no	—
172	#41×C₄₇	—	2	4	no	—
173	#41×C₄₇	—	2	4	no	—
174	#41×C₄₇	—	2	4	no	—
175	#41×C₄₇	—	2	4	no	—
176	#41×C₄₇	—	2	4	no	—
177	#41×C₄₇	—	2	4	no	—
178	#41×C₄₇	—	2	4	no	—
179	#41×C₄₇	—	2	4	no	—
180	#41×C₄₇	—	2	4	no	—
181	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
182	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
183	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
184	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
185	#41×C₄₇	C₂²⋊C₄	1	8	yes	—
186	#41×C₄₇	C₂×D₄	1	8	yes	—
187	C₂×Q₈×C₄₇	—	2	16	no	—
188	C₂×Q₈×C₄₇	—	2	16	no	—
189	C₂×Q₈×C₄₇	—	2	8	no	—
190	C₂×Q₈×C₄₇	—	2	8	no	—
191	C₂×Q₈×C₄₇	—	2	1	no	—
192	C₂×Q₈×C₄₇	—	2	4	no	—
193	C₂×Q₈×C₄₇	—	2	2	no	—
194	C₂×Q₈×C₄₇	—	2	2	no	—
195	C₂×Q₈×C₄₇	—	2	2	no	—
196	C₂×Q₈×C₄₇	—	2	1	no	—
197	C₂×Q₈×C₄₇	—	2	2	no	—
198	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
199	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
200	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
201	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
202	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
203	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₄₇	—	2	32	no	—
205	C₂×D₄×C₄₇	—	2	16	no	—
206	C₂×D₄×C₄₇	—	2	16	no	—
207	C₂×D₄×C₄₇	—	2	32	no	—
208	C₂×D₄×C₄₇	—	2	16	no	—
209	C₂×D₄×C₄₇	—	2	16	no	—
210	C₂×D₄×C₄₇	—	2	2	no	—
211	C₂×D₄×C₄₇	—	2	2	no	—
212	C₂×D₄×C₄₇	—	2	2	no	—
213	C₂×D₄×C₄₇	—	2	4	no	—
214	C₂×D₄×C₄₇	—	2	4	no	—
215	C₂×D₄×C₄₇	—	2	4	no	—
216	C₂×D₄×C₄₇	—	2	4	no	—
217	C₂×D₄×C₄₇	—	2	4	no	—
218	C₂×D₄×C₄₇	—	2	4	no	—
219	C₂×D₄×C₄₇	—	2	4	no	—
220	C₂×D₄×C₄₇	—	2	4	no	—
221	C₂×D₄×C₄₇	—	2	2	no	—
222	C₂×D₄×C₄₇	—	2	8	no	—
223	C₂×D₄×C₄₇	—	2	8	no	—
224	C₂×D₄×C₄₇	—	2	1	no	—
225	C₂×D₄×C₄₇	—	2	4	no	—
226	C₂×D₄×C₄₇	—	2	2	no	—
227	C₂×D₄×C₄₇	—	2	2	no	—
228	C₂×D₄×C₄₇	—	2	2	no	—
229	C₂×D₄×C₄₇	—	2	1	no	—
230	C₂×D₄×C₄₇	—	2	2	no	—
231	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
232	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
233	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
234	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
235	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
236	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₄₇	—	2	16	no	—
240	C₂²×C₄×C₄₇	—	2	16	no	—
241	C₂²×C₄×C₄₇	—	2	1	no	—
242	C₂²×C₄×C₄₇	—	2	4	no	—
243	C₂²×C₄×C₄₇	—	2	1	no	—
244	C₂²×C₄×C₄₇	—	2	2	no	—
245	C₂²×C₄×C₄₇	—	2	2	no	—
246	C₂²×C₄×C₄₇	—	2	2	no	—
247	C₂²×C₄×C₄₇	—	2	4	no	—
248	C₂²×C₄×C₄₇	—	2	4	no	—
249	C₂²×C₄×C₄₇	—	2	2	no	—
250	C₂²×C₄×C₄₇	—	2	2	no	—
251	C₂²×C₄×C₄₇	—	2	2	no	—
252	C₂²×C₄×C₄₇	—	2	2	no	—
253	C₂²×C₄×C₄₇	—	2	4	no	—
254	C₂²×C₄×C₄₇	—	2	4	no	—
255	C₂²×C₄×C₄₇	—	2	4	no	—
256	C₂²×C₄×C₄₇	—	2	4	no	—
257	C₂²×C₄×C₄₇	—	2	2	no	—
258	C₂²×C₄×C₄₇	—	4	2	no	—
259	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
260	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
261	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
262	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
263	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
264	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
272	M₁₆×C₄₇	—	2	4	no	—
273	M₁₆×C₄₇	—	2	4	no	—
274	M₁₆×C₄₇	—	4	2	no	—
275	M₁₆×C₄₇	—	4	2	no	—
276	C₂×C₈×C₄₇	—	2	4	no	—
277	C₂×C₈×C₄₇	—	4	2	no	—
278	C₂×C₈×C₄₇	—	4	2	no	—
279	C₄⋊C₄×C₄₇	—	2	4	no	—
280	C₄⋊C₄×C₄₇	—	4	2	no	—
281	C₂²⋊C₄×C₄₇	—	2	4	no	—
282	C₂²⋊C₄×C₄₇	—	4	2	no	—
283	C₄²×C₄₇	—	2	4	no	—
284	C₄²×C₄₇	—	4	2	no	—
285	C₂³×C₄₇	—	2	16	no	—
286	C₂³×C₄₇	—	2	2	no	—
287	C₂³×C₄₇	—	2	2	no	—
288	C₂³×C₄₇	—	2	4	no	—
289	C₂³×C₄₇	—	2	2	no	—
290	C₂³×C₄₇	—	2	2	no	—
291	C₂³×C₄₇	—	2	4	no	—
292	C₂³×C₄₇	—	8	1	no	—
293	C₂³×C₄₇	—	8	2	no	—
294	C₂³×C₄₇	—	8	2	no	—
295	C₂³×C₄₇	—	8	2	no	—
296	C₂³×C₄₇	—	8	8	no	—
297	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
298	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂³×C₄₇	#120	1	2	yes	—
301	C₂³×C₄₇	#120	1	2	yes	—
302	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₄₇	—	2	16	no	—
304	Q₈×C₄₇	—	2	2	no	—
305	Q₈×C₄₇	—	2	2	no	—
306	Q₈×C₄₇	—	2	4	no	—
307	Q₈×C₄₇	—	2	4	no	—
308	Q₈×C₄₇	—	2	4	no	—
309	Q₈×C₄₇	—	2	4	no	—
310	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
311	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
312	D₄×C₄₇	—	2	16	no	—
313	D₄×C₄₇	—	2	16	no	—
314	D₄×C₄₇	—	2	16	no	—
315	D₄×C₄₇	—	2	8	no	—
316	D₄×C₄₇	—	2	8	no	—
317	D₄×C₄₇	—	2	4	no	—
318	D₄×C₄₇	—	2	4	no	—
319	D₄×C₄₇	—	2	4	no	—
320	D₄×C₄₇	—	2	4	no	—
321	D₄×C₄₇	—	2	8	no	—
322	D₄×C₄₇	—	2	8	no	—
323	D₄×C₄₇	—	2	2	no	—
324	D₄×C₄₇	—	2	2	no	—
325	D₄×C₄₇	—	2	4	no	—
326	D₄×C₄₇	—	2	4	no	—
327	D₄×C₄₇	—	2	4	no	—
328	D₄×C₄₇	—	2	4	no	—
329	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
330	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
331	C₂×C₄×C₄₇	—	2	16	no	—
332	C₂×C₄×C₄₇	—	2	16	no	—
333	C₂×C₄×C₄₇	—	2	16	no	—
334	C₂×C₄×C₄₇	—	2	2	no	—
335	C₂×C₄×C₄₇	—	2	2	no	—
336	C₂×C₄×C₄₇	—	2	4	no	—
337	C₂×C₄×C₄₇	—	2	4	no	—
338	C₂×C₄×C₄₇	—	2	2	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	4	no	—
341	C₂×C₄×C₄₇	—	2	4	no	—
342	C₂×C₄×C₄₇	—	2	8	no	—
343	C₂×C₄×C₄₇	—	2	4	no	—
344	C₂×C₄×C₄₇	—	2	4	no	—
345	C₂×C₄×C₄₇	—	2	4	no	—
346	C₂×C₄×C₄₇	—	2	8	no	—
347	C₂×C₄×C₄₇	—	2	4	no	—
348	C₂×C₄×C₄₇	—	2	4	no	—
349	C₂×C₄×C₄₇	—	2	4	no	—
350	C₂×C₄×C₄₇	—	4	4	no	—
351	C₂×C₄×C₄₇	—	8	4	no	—
352	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
353	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×C₄₇	#120	1	2	yes	—
362	C₂×C₄×C₄₇	#120	1	2	yes	—
363	C₂×C₄×C₄₇	#120	1	2	yes	—
364	C₂×C₄×C₄₇	#120	1	2	yes	—
365	C₂×C₄×C₄₇	#120	1	2	yes	—
366	C₂×C₄×C₄₇	#120	1	2	yes	—
367	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
371	C₈×C₄₇	—	4	4	no	—
372	#20623	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
373	C₂²×C₄₇	—	2	4	no	—
374	C₂²×C₄₇	—	2	4	no	—
375	C₂²×C₄₇	—	2	4	no	—
376	C₂²×C₄₇	—	4	2	no	—
377	C₂²×C₄₇	—	4	1	no	—
378	C₂²×C₄₇	—	4	1	no	—
379	C₂²×C₄₇	—	4	1	no	—
380	C₂²×C₄₇	—	4	2	no	—
381	C₂²×C₄₇	—	4	4	no	—
382	C₂²×C₄₇	—	4	4	no	—
383	C₂²×C₄₇	—	4	4	no	—
384	C₂²×C₄₇	—	8	2	no	—
385	C₂²×C₄₇	—	8	2	no	—
386	C₂²×C₄₇	—	8	4	no	—
387	C₂²×C₄₇	—	8	4	no	—
388	C₂²×C₄₇	—	8	16	no	—
389	C₂²×C₄₇	#379	1	2	yes	—
390	C₂²×C₄₇	#379	1	1	yes	characteristic
391	C₂²×C₄₇	#379	1	1	yes	characteristic
392	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²×C₄₇	C₂×#120	1	2	yes	—
394	C₄×C₄₇	—	2	4	no	—
395	C₄×C₄₇	—	2	4	no	—
396	C₄×C₄₇	—	2	4	no	—
397	C₄×C₄₇	—	8	4	no	—
398	C₄×C₄₇	#379	1	1	yes	characteristic
399	C₄×C₄₇	#379	1	2	yes	—
400	C₄×C₄₇	#379	1	1	yes	characteristic
401	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
402	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
403	C₄×C₄₇	C₂×#120	1	2	yes	—
404	C₂×#585	C₂×C₄₇	1	1	yes	characteristic
405	C₂×#421	C₂×C₄₇	1	2	yes	complemented
406	#2896	C₂×C₄₇	1	2	yes	complemented
407	C₂×#413	C₂×C₄₇	1	1	yes	characteristic, complemented
408	C₂×#410	C₂×C₄₇	1	1	yes	characteristic, complemented
409	#1796	C₂×C₄₇	1	4	yes	complemented
410	#1795	C₂×C₄₇	1	4	yes	complemented
411	C₂×C₄₇	—	2	2	no	—
412	C₂×C₄₇	—	2	1	no	—
413	C₂×C₄₇	—	2	1	no	—
414	C₂×C₄₇	—	2	2	no	—
415	C₂×C₄₇	—	2	1	no	—
416	C₂×C₄₇	—	4	4	no	—
417	C₂×C₄₇	—	4	4	no	—
418	C₂×C₄₇	—	4	4	no	—
419	C₂×C₄₇	C₂×#379	1	1	yes	characteristic
420	#585	—	2	4	no	—
421	#585	—	2	4	no	—
422	#585	—	2	4	no	—
423	#585	—	2	4	no	—
424	C₂×2₋¹⁺⁴	—	2	1	no	—
425	C₂×2₋¹⁺⁴	C₄×C₄₇	1	2	yes	complemented
426	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	2	yes	—
427	C₂×H(5,𝔽₂)	—	2	1	no	—
428	C₂×H(5,𝔽₂)	—	2	2	no	—
429	C₂×H(5,𝔽₂)	C₄×C₄₇	1	2	yes	complemented
430	C₂×H(5,𝔽₂)	C₂²×C₄₇	1	2	yes	—
431	C₂²×#41	—	2	2	no	—
432	C₂²×#41	—	2	2	no	—
433	C₂²×#41	C₄×C₄₇	1	4	yes	complemented
434	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
435	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
436	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
437	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	complemented
438	C₂×#117	C₂²×C₄₇	1	2	yes	complemented
439	#421	—	2	4	no	—
440	#421	C₂²×C₄₇	1	8	yes	complemented
441	C₂×#104	—	2	4	no	—
442	#419	C₂²×C₄₇	1	4	yes	complemented
443	#418	C₂²×C₄₇	1	4	yes	complemented
444	#417	—	2	4	no	—
445	#416	—	2	4	no	—
446	#413	—	2	2	no	—
447	#413	C₂²×C₄₇	1	4	yes	complemented
448	C₂×#101	—	2	1	no	—
449	C₂×#100	—	2	1	no	—
450	#410	—	2	2	no	—
451	#410	C₂²×C₄₇	1	4	yes	complemented
452	C₂×#99	—	2	2	no	—
453	C₄₇	#20623	1	1	yes	characteristic, direct product factor, Sylow
454	2₋¹⁺⁴	—	2	8	no	—
455	2₋¹⁺⁴	—	2	8	no	—
456	2₋¹⁺⁴	—	2	8	no	—
457	2₋¹⁺⁴	—	2	8	no	—
458	2₋¹⁺⁴	—	2	8	no	—
459	2₋¹⁺⁴	—	2	8	no	—
460	H(5,𝔽₂)	—	2	8	no	—
461	H(5,𝔽₂)	—	2	8	no	—
462	H(5,𝔽₂)	—	2	16	no	—
463	H(5,𝔽₂)	—	2	16	no	—
464	H(5,𝔽₂)	—	2	8	no	—
465	H(5,𝔽₂)	—	2	8	no	—
466	H(5,𝔽₂)	—	2	8	no	—
467	H(5,𝔽₂)	—	2	8	no	—
468	C₂×#41	—	2	16	no	—
469	C₂×#41	—	2	16	no	—
470	C₂×#41	—	2	16	no	—
471	C₂×#41	—	2	16	no	—
472	C₂×#41	—	2	8	no	—
473	C₂×#41	—	2	8	no	—
474	C₂×#41	—	2	8	no	—
475	C₂×#41	—	2	8	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	4	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	—	2	1	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
497	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
498	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
499	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
500	C₂×#41	C₂×C₄×C₄₇	1	4	yes	complemented
501	C₂×#41	C₂×C₄×C₄₇	1	4	yes	complemented
502	C₂×#41	D₄×C₄₇	1	4	yes	—
503	C₂×#41	D₄×C₄₇	1	4	yes	—
504	C₂×#41	D₄×C₄₇	1	4	yes	—
505	C₂×#41	D₄×C₄₇	1	4	yes	—
506	C₂×#41	D₄×C₄₇	1	2	yes	—
507	C₂×#41	D₄×C₄₇	1	2	yes	—
508	C₂×#41	C₂³×C₄₇	1	2	yes	—
509	C₂×#41	C₂³×C₄₇	1	2	yes	—
510	C₂²×Q₈	—	2	2	no	—
511	C₂²×Q₈	—	2	2	no	—
512	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
513	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	complemented
514	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
516	C₂²×D₄	—	2	4	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	2	no	—
523	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
524	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	complemented
525	C₂²×D₄	D₄×C₄₇	1	2	yes	—
526	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
528	C₂³×C₄	—	2	4	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
532	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
533	C₂×M₁₆	—	2	2	no	—
534	C₂×M₁₆	—	2	2	no	—
535	C₂×M₁₆	—	2	2	no	—
536	C₂×M₁₆	—	2	2	no	—
537	C₂×M₁₆	—	2	2	no	—
538	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
539	C₂²×C₈	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	C₂³×C₄₇	1	4	yes	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₂²⋊C₄	—	2	2	no	—
546	C₂×C₄²	—	2	2	no	—
547	#104	—	2	16	no	—
548	#103	—	2	8	no	—
549	#102	—	2	8	no	—
550	#101	—	2	4	no	—
551	#100	—	2	4	no	—
552	#99	—	2	8	no	—
553	C₂⁴	—	2	1	no	—
554	C₂⁴	—	2	4	no	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
557	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
558	#41	—	2	16	no	—
559	#41	—	2	16	no	—
560	#41	—	2	32	no	—
561	#41	—	2	32	no	—
562	#41	—	2	16	no	—
563	#41	—	2	16	no	—
564	#41	—	2	16	no	—
565	#41	—	2	16	no	—
566	#41	—	2	16	no	—
567	#41	—	2	16	no	—
568	#41	—	2	8	no	—
569	#41	—	2	8	no	—
570	#41	—	2	8	no	—
571	#41	—	2	8	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	2	4	no	—
579	#41	—	2	4	no	—
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	#41	—	2	4	no	—
583	#41	—	2	4	no	—
584	#41	—	2	4	no	—
585	#41	—	2	4	no	—
586	#41	—	2	4	no	—
587	#41	—	2	4	no	—
588	#41	—	2	4	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	C₂²⋊C₄×C₄₇	1	4	yes	—
595	#41	C₂²⋊C₄×C₄₇	1	4	yes	—
596	#41	C₂²⋊C₄×C₄₇	1	4	yes	—
597	#41	C₂²⋊C₄×C₄₇	1	4	yes	—
598	#41	C₂²⋊C₄×C₄₇	1	8	yes	—
599	#41	C₂×D₄×C₄₇	1	8	yes	—
600	C₂×Q₈	—	2	16	no	—
601	C₂×Q₈	—	2	16	no	—
602	C₂×Q₈	—	2	8	no	—
603	C₂×Q₈	—	2	8	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	—
612	C₂×Q₈	C₂²⋊C₄×C₄₇	1	2	yes	—
613	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
614	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
615	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
616	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
617	C₂×D₄	—	2	32	no	—
618	C₂×D₄	—	2	16	no	—
619	C₂×D₄	—	2	16	no	—
620	C₂×D₄	—	2	32	no	—
621	C₂×D₄	—	2	16	no	—
622	C₂×D₄	—	2	16	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	8	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
645	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
646	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
647	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
648	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
649	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
650	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
651	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
652	C₂²×C₄	—	2	16	no	—
653	C₂²×C₄	—	2	16	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
673	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
674	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
675	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
676	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
685	M₁₆	—	2	4	no	—
686	M₁₆	—	2	4	no	—
687	M₁₆	—	4	2	no	—
688	M₁₆	—	4	2	no	—
689	C₂×C₈	—	2	4	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	—	4	2	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	—	4	2	no	—
698	C₂³	—	2	16	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	4	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	8	1	no	—
706	C₂³	—	8	2	no	—
707	C₂³	—	8	2	no	—
708	C₂³	—	8	2	no	—
709	C₂³	—	8	8	no	—
710	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
711	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
712	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
713	C₂³	#120×C₄₇	1	2	yes	—
714	C₂³	#120×C₄₇	1	2	yes	—
715	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
716	Q₈	—	2	16	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	4	no	—
720	Q₈	—	2	4	no	—
721	Q₈	—	2	4	no	—
722	Q₈	—	2	4	no	—
723	Q₈	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
724	Q₈	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
725	D₄	—	2	16	no	—
726	D₄	—	2	16	no	—
727	D₄	—	2	16	no	—
728	D₄	—	2	8	no	—
729	D₄	—	2	8	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	2	4	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	8	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	4	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	4	no	—
742	D₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
743	D₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
744	C₂×C₄	—	2	16	no	—
745	C₂×C₄	—	2	16	no	—
746	C₂×C₄	—	2	16	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	8	4	no	—
765	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
766	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
767	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
768	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
769	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
770	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
771	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
772	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
773	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
774	C₂×C₄	#120×C₄₇	1	2	yes	—
775	C₂×C₄	#120×C₄₇	1	2	yes	—
776	C₂×C₄	#120×C₄₇	1	2	yes	—
777	C₂×C₄	#120×C₄₇	1	2	yes	—
778	C₂×C₄	#120×C₄₇	1	2	yes	—
779	C₂×C₄	#120×C₄₇	1	2	yes	—
780	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
783	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
784	C₈	—	4	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	8	4	no	—
797	C₂²	—	8	4	no	—
798	C₂²	—	8	2	no	—
799	C₂²	—	8	2	no	—
800	C₂²	—	8	16	no	—
801	C₂²	C₄₇×#379	1	2	yes	—
802	C₂²	C₄₇×#379	1	1	yes	characteristic
803	C₂²	C₄₇×#379	1	1	yes	characteristic
804	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
805	C₂²	C₂×#120×C₄₇	1	2	yes	—
806	C₄	—	2	4	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	4	no	—
809	C₄	—	8	4	no	—
810	C₄	C₄₇×#379	1	1	yes	characteristic
811	C₄	C₄₇×#379	1	1	yes	characteristic
812	C₄	C₄₇×#379	1	2	yes	—
813	C₄	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
814	C₄	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
815	C₄	C₂×#120×C₄₇	1	2	yes	—
816	C₂	—	2	2	no	—
817	C₂	—	2	1	no	—
818	C₂	—	2	1	no	—
819	C₂	—	2	2	no	—
820	C₂	—	2	1	no	—
821	C₂	—	4	4	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	4	no	—
824	C₂	C₂×C₄₇×#379	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₇	#379
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂×C₄₇	C₂×#379
prime radical	C₂×C₄₇×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#421	C₂	semidirect
3. C₄₇×#2896	C₂	semidirect
4. C₂×C₄₇×#413	C₂	semidirect
5. C₂×C₄₇×#410	C₂	semidirect
6. C₄₇×#1796	C₂	semidirect
7. C₄₇×#1795	C₂	semidirect
13. C₂×2₋¹⁺⁴×C₄₇	C₄	semidirect
17. C₂×H(5,𝔽₂)×C₄₇	C₄	semidirect
21. C₂²×#41×C₄₇	C₄	semidirect
25. C₂²×M₁₆×C₄₇	C₂²	semidirect
26. C₂×#117×C₄₇	C₂²	semidirect
28. C₄₇×#421	C₂²	semidirect
30. C₄₇×#419	C₂²	semidirect
31. C₄₇×#418	C₂²	semidirect
35. C₄₇×#413	C₂²	semidirect
39. C₄₇×#410	C₂²	semidirect
87. C₂×#41×C₄₇	C₂×C₄	semidirect
88. C₂×#41×C₄₇	C₂×C₄	semidirect
100. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
111. C₂²×D₄×C₄₇	C₂×C₄	semidirect
372. #20623	C₄₇	direct (N × H)
405. C₂×#421	C₂×C₄₇	semidirect
406. #2896	C₂×C₄₇	semidirect
407. C₂×#413	C₂×C₄₇	semidirect
408. C₂×#410	C₂×C₄₇	semidirect
409. #1796	C₂×C₄₇	semidirect
410. #1795	C₂×C₄₇	semidirect
425. C₂×2₋¹⁺⁴	C₄×C₄₇	semidirect
429. C₂×H(5,𝔽₂)	C₄×C₄₇	semidirect
433. C₂²×#41	C₄×C₄₇	semidirect
437. C₂²×M₁₆	C₂²×C₄₇	semidirect
438. C₂×#117	C₂²×C₄₇	semidirect
440. #421	C₂²×C₄₇	semidirect
442. #419	C₂²×C₄₇	semidirect
443. #418	C₂²×C₄₇	semidirect
447. #413	C₂²×C₄₇	semidirect
451. #410	C₂²×C₄₇	semidirect
453. C₄₇	#20623	direct (N × H)
500. C₂×#41	C₂×C₄×C₄₇	semidirect
501. C₂×#41	C₂×C₄×C₄₇	semidirect
513. C₂²×Q₈	C₂×C₄×C₄₇	semidirect
524. C₂²×D₄	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#585	2
C₂×C₄₇×#421	2
C₄₇×#2896	2
C₂×C₄₇×#413	2
C₂×C₄₇×#410	2
C₄₇×#1796	2
C₄₇×#1795	2
#20623	47

Subgroups — C47×#20623 #26060321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20623 #26060321