Subgroups — C₂×#20257075 #27124187

Order 12032.

9502 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257075	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689804	C₂	1	4	yes	maximal, complemented
3	C₂×#15689799	C₂	1	4	yes	maximal, complemented
4	C₂×#15689767	C₂	1	4	yes	maximal, complemented
5	C₂×#15689760	C₂	1	4	yes	maximal, complemented
6	C₂×#15689749	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689708	C₂	1	4	yes	maximal, complemented
8	C₂×#15689682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689629	C₂	1	4	yes	maximal, complemented
10	C₂²×#13093993	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689598	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689596	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#10625352	C₂²	1	4	yes	complemented
16	C₂³×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
18	C₂⁴×Dic₄₇	C₂²	1	2	yes	complemented
19	#15689804	C₂²	1	64	yes	complemented
20	#15689799	C₂²	1	64	yes	complemented
21	#15689767	C₂²	1	64	yes	complemented
22	#15689760	C₂²	1	64	yes	complemented
23	#15689749	C₂²	1	16	yes	complemented
24	#15689708	C₂²	1	64	yes	complemented
25	#15689682	C₂²	1	16	yes	complemented
26	C₂×#13094017	C₂²	1	4	yes	complemented
27	C₂×#13094017	C₂²	1	4	yes	complemented
28	C₂×#13094011	C₂²	1	4	yes	complemented
29	C₂×#13094010	C₂²	1	4	yes	complemented
30	#15689629	C₂²	1	64	yes	complemented
31	C₂×#13094008	C₂²	1	4	yes	complemented
32	C₂×#13094007	C₂²	1	2	yes	complemented
33	C₂×#13094006	C₂²	1	4	yes	complemented
34	C₂×#13094005	C₂²	1	4	yes	complemented
35	C₂×#13094005	C₂²	1	4	yes	complemented
36	C₂×#13094005	C₂²	1	2	yes	complemented
37	C₂×#13094003	C₂²	1	4	yes	complemented
38	C₂×#13094001	C₂²	1	4	yes	complemented
39	C₂×#13094001	C₂²	1	4	yes	complemented
40	C₂×#13094001	C₂²	1	4	yes	complemented
41	C₂×#13093996	C₂²	1	4	yes	complemented
42	C₂×#13093996	C₂²	1	4	yes	complemented
43	C₂×#13093996	C₂²	1	4	yes	complemented
44	C₂×#13093995	C₂²	1	4	yes	complemented
45	C₂×#13093993	C₂²	1	4	yes	—
46	C₂×#13093993	C₂²	1	2	yes	complemented
47	C₂×#13093993	C₂²	1	2	yes	complemented
48	C₂×#13093993	C₂²	1	16	yes	complemented
49	C₂×#13093993	C₂²	1	2	yes	complemented
50	C₂×#13093992	C₂²	1	2	yes	complemented
51	#15689598	C₂²	1	16	yes	complemented
52	#15689596	C₂²	1	16	yes	complemented
53	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
54	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
55	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
56	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
57	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
58	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
59	C₂×#13093983	C₂²	1	2	yes	complemented
60	C₂×#13093980	C₂²	1	2	yes	complemented
61	C₂×#13093980	C₂²	1	4	yes	complemented
62	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
64	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
66	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
67	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
68	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
69	C₂²×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
70	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
71	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
72	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
73	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
74	C₂³×D₄×C₄₇	C₂²	1	2	yes	complemented
75	C₂×#120×C₄₇	C₂²	1	4	yes	—
76	C₂×#120×C₄₇	C₂²	1	2	yes	complemented
77	C₂×#120×C₄₇	C₂²	1	2	yes	complemented
78	C₂×#120×C₄₇	C₂²	1	16	yes	complemented
79	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
80	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
81	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
82	C₂×#10625352	—	4	16	no	—
83	C₂×#10625352	C₂³	1	32	yes	complemented
84	C₂²×Dic₉₄	C₂³	1	4	yes	complemented
85	C₂²×C₂²⋊D₄₇	—	2	8	no	—
86	C₂²×C₂²⋊D₄₇	—	4	8	no	—
87	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
88	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
89	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
90	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
91	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
92	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
93	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	complemented
94	C₂³×Dic₄₇	—	4	8	no	—
95	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
96	C₂³×Dic₄₇	C₂³	1	4	yes	—
97	C₂³×Dic₄₇	C₂³	1	2	yes	—
98	C₂³×Dic₄₇	C₂³	1	2	yes	—
99	C₂³×Dic₄₇	C₂³	1	2	yes	—
100	C₂³×Dic₄₇	C₂³	1	4	yes	—
101	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
102	C₂³×Dic₄₇	C₂³	1	4	yes	complemented
103	C₂²×C₄×D₄₇	C₂³	1	4	yes	complemented
104	#13094017	C₂³	1	32	yes	complemented
105	#13094017	C₂³	1	32	yes	complemented
106	#13094011	C₂³	1	32	yes	complemented
107	#13094010	C₂³	1	32	yes	complemented
108	#13094008	C₂³	1	32	yes	complemented
109	#13094007	C₂³	1	16	yes	complemented
110	#13094006	C₂³	1	32	yes	complemented
111	#13094005	C₂³	1	32	yes	complemented
112	#13094005	C₂³	1	32	yes	complemented
113	#13094005	C₂³	1	16	yes	complemented
114	#13094003	C₂³	1	32	yes	complemented
115	#13094001	C₂³	1	32	yes	complemented
116	#13094001	C₂³	1	32	yes	complemented
117	#13094001	C₂³	1	32	yes	complemented
118	#13093996	C₂³	1	32	yes	complemented
119	#13093996	C₂³	1	32	yes	complemented
120	#13093996	C₂³	1	32	yes	complemented
121	#13093995	C₂³	1	32	yes	complemented
122	#13093993	C₂³	1	32	yes	—
123	#13093993	C₂³	1	16	yes	complemented
124	#13093993	C₂³	1	16	yes	complemented
125	#13093993	C₂³	1	16	yes	complemented
126	#13093992	C₂³	1	16	yes	complemented
127	D₄×Dic₄₇	C₂³	1	32	yes	complemented
128	D₄×Dic₄₇	C₂³	1	32	yes	complemented
129	D₄×Dic₄₇	C₂³	1	32	yes	complemented
130	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
131	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
132	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
133	#13093983	C₂³	1	16	yes	complemented
134	#13093980	C₂³	1	32	yes	complemented
135	#13093980	C₂³	1	16	yes	complemented
136	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	complemented
137	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	complemented
138	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
139	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
140	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
141	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
142	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
143	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
144	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
147	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
154	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
155	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
156	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
157	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
158	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
159	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
160	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	complemented
161	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	complemented
162	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	complemented
163	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	complemented
164	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	complemented
165	C₂×C₄×Dic₄₇	C₂³	1	4	yes	complemented
166	C₂×C₄×Dic₄₇	C₂³	1	4	yes	complemented
167	C₂⁵×C₄₇	—	2	8	no	—
168	C₂⁵×C₄₇	—	4	8	no	—
169	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
170	C₂⁵×C₄₇	C₂³	1	2	yes	—
171	C₂⁵×C₄₇	C₂³	1	2	yes	—
172	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
173	C₂⁵×C₄₇	C₂³	1	8	yes	—
174	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
175	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
176	C₂²×D₄×C₄₇	—	2	8	no	—
177	C₂²×D₄×C₄₇	—	4	8	no	—
178	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
179	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
180	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
181	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
182	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
183	C₂²×D₄×C₄₇	C₂³	1	16	yes	complemented
184	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
185	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
186	#120×C₄₇	C₂³	1	32	yes	—
187	#120×C₄₇	C₂³	1	16	yes	complemented
188	#120×C₄₇	C₂³	1	16	yes	complemented
189	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
190	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	complemented
195	C₂⁴×C₄₇	—	2	4	no	—
196	C₂⁴×C₄₇	—	2	8	no	—
197	C₂⁴×C₄₇	—	2	8	no	—
198	C₂⁴×C₄₇	—	2	8	no	—
199	C₂⁴×C₄₇	—	2	4	no	—
200	C₂⁴×C₄₇	—	2	32	no	—
201	C₂⁴×C₄₇	—	2	8	no	—
202	C₂⁴×C₄₇	—	2	8	no	—
203	C₂⁴×C₄₇	—	2	4	no	—
204	C₂⁴×C₄₇	—	4	4	no	—
205	C₂⁴×C₄₇	—	4	4	no	—
206	C₂⁴×C₄₇	—	4	4	no	—
207	C₂⁴×C₄₇	—	4	32	no	—
208	C₂⁴×C₄₇	—	4	4	no	—
209	C₂⁴×C₄₇	—	4	4	no	—
210	C₂⁴×C₄₇	—	4	64	no	—
211	C₂⁴×C₄₇	#41	1	8	yes	complemented
212	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
213	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
214	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
215	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
216	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
217	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
221	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
222	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
223	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
224	C₂³×D₄₇	—	2	4	no	—
225	C₂³×D₄₇	—	4	4	no	—
226	C₂³×D₄₇	C₂⁴	1	2	yes	—
227	C₂³×D₄₇	C₂⁴	1	4	yes	—
228	C₂×D₄×C₄₇	—	2	8	no	—
229	C₂×D₄×C₄₇	—	2	8	no	—
230	C₂×D₄×C₄₇	—	2	32	no	—
231	C₂×D₄×C₄₇	—	2	16	no	—
232	C₂×D₄×C₄₇	—	4	8	no	—
233	C₂×D₄×C₄₇	—	4	32	no	—
234	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
235	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
236	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
237	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
238	C₂²×C₄×C₄₇	—	2	4	no	—
239	C₂²×C₄×C₄₇	—	4	4	no	—
240	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
244	C₂×C₂²⋊D₄₇	—	2	8	no	—
245	C₂×C₂²⋊D₄₇	—	2	8	no	—
246	C₂×C₂²⋊D₄₇	—	2	32	no	—
247	C₂×C₂²⋊D₄₇	—	2	16	no	—
248	C₂×C₂²⋊D₄₇	—	4	8	no	—
249	C₂×C₂²⋊D₄₇	—	4	8	no	—
250	C₂×C₂²⋊D₄₇	—	4	32	no	—
251	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
252	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
253	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
254	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
255	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	complemented
256	C₂²×Dic₄₇	—	2	4	no	—
257	C₂²×Dic₄₇	—	2	16	no	—
258	C₂²×Dic₄₇	—	4	4	no	—
259	C₂²×Dic₄₇	—	4	8	no	—
260	C₂²×Dic₄₇	—	4	4	no	—
261	C₂²×Dic₄₇	—	4	32	no	—
262	C₂²×Dic₄₇	—	4	4	no	—
263	C₂²×Dic₄₇	—	4	8	no	—
264	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
265	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
266	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
267	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
268	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
269	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
270	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
271	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
272	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
273	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
274	C₂²×Dic₄₇	C₂⁴	1	16	yes	complemented
275	#10625352	—	4	64	no	—
276	C₂×C₄×D₄₇	—	4	8	no	—
277	C₂×C₄×D₄₇	C₂⁴	1	16	yes	complemented
278	C₂×Dic₉₄	—	4	8	no	—
279	C₂×Dic₉₄	C₂⁴	1	16	yes	complemented
280	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
281	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
283	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
284	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
285	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
286	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
287	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
288	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
289	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
290	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
291	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
292	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
293	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
294	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	complemented
295	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	complemented
296	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	complemented
297	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	complemented
298	C₄⋊Dic₄₇	C₂⁴	1	16	yes	complemented
299	C₄⋊Dic₄₇	C₂⁴	1	16	yes	complemented
300	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
301	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
302	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
303	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
304	C₄×Dic₄₇	C₂⁴	1	16	yes	complemented
305	C₄×Dic₄₇	C₂⁴	1	16	yes	complemented
306	C₂³×C₄₇	—	2	32	no	—
307	C₂³×C₄₇	—	2	8	no	—
308	C₂³×C₄₇	—	2	4	no	—
309	C₂³×C₄₇	—	2	16	no	—
310	C₂³×C₄₇	—	2	4	no	—
311	C₂³×C₄₇	—	2	4	no	—
312	C₂³×C₄₇	—	2	4	no	—
313	C₂³×C₄₇	—	2	4	no	—
314	C₂³×C₄₇	—	2	4	no	—
315	C₂³×C₄₇	—	2	16	no	—
316	C₂³×C₄₇	—	2	16	no	—
317	C₂³×C₄₇	—	2	8	no	—
318	C₂³×C₄₇	—	2	4	no	—
319	C₂³×C₄₇	—	2	8	no	—
320	C₂³×C₄₇	—	2	16	no	—
321	C₂³×C₄₇	—	2	4	no	—
322	C₂³×C₄₇	—	2	16	no	—
323	C₂³×C₄₇	—	2	4	no	—
324	C₂³×C₄₇	—	2	8	no	—
325	C₂³×C₄₇	—	4	16	no	—
326	C₂³×C₄₇	—	4	8	no	—
327	C₂³×C₄₇	—	4	8	no	—
328	C₂³×C₄₇	—	4	8	no	—
329	C₂³×C₄₇	—	4	8	no	—
330	C₂³×C₄₇	—	4	8	no	—
331	C₂³×C₄₇	—	4	32	no	—
332	C₂³×C₄₇	—	4	32	no	—
333	C₂³×C₄₇	—	4	128	no	—
334	C₂³×C₄₇	—	4	16	no	—
335	C₂³×C₄₇	—	8	8	no	—
336	C₂³×C₄₇	C₂×#41	1	4	yes	—
337	C₂³×C₄₇	C₂×#41	1	4	yes	—
338	C₂³×C₄₇	C₂×#41	1	4	yes	—
339	C₂³×C₄₇	C₂×#41	1	16	yes	complemented
340	C₂³×C₄₇	H(5,𝔽₂)	1	8	yes	—
341	C₂³×C₄₇	C₂⁵	1	4	yes	—
342	C₂³×C₄₇	C₂⁵	1	4	yes	—
343	C₂³×C₄₇	C₂⁵	1	2	yes	—
344	C₂³×C₄₇	C₂⁵	1	2	yes	—
345	C₂³×C₄₇	C₂⁵	1	2	yes	—
346	C₂³×C₄₇	C₂⁵	1	4	yes	—
347	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
348	C₂²×D₄₇	—	2	4	no	—
349	C₂²×D₄₇	—	2	8	no	—
350	C₂²×D₄₇	—	2	8	no	—
351	C₂²×D₄₇	—	4	8	no	—
352	C₂²×D₄₇	—	8	8	no	—
353	C₂²×D₄₇	C₂⁵	1	4	yes	—
354	D₄×C₄₇	—	2	16	no	—
355	D₄×C₄₇	—	2	16	no	—
356	D₄×C₄₇	—	2	32	no	—
357	D₄×C₄₇	—	4	16	no	—
358	C₂×C₄×C₄₇	—	2	8	no	—
359	C₂×C₄×C₄₇	—	2	4	no	—
360	C₂×C₄×C₄₇	—	2	8	no	—
361	C₂×C₄×C₄₇	—	4	8	no	—
362	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
363	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
364	C₂²⋊D₄₇	—	2	16	no	—
365	C₂²⋊D₄₇	—	2	16	no	—
366	C₂²⋊D₄₇	—	2	32	no	—
367	C₂²⋊D₄₇	—	4	16	no	—
368	C₂²⋊D₄₇	—	4	16	no	—
369	C₂×Dic₄₇	—	2	8	no	—
370	C₂×Dic₄₇	—	2	4	no	—
371	C₂×Dic₄₇	—	2	8	no	—
372	C₂×Dic₄₇	—	2	8	no	—
373	C₂×Dic₄₇	—	2	8	no	—
374	C₂×Dic₄₇	—	2	32	no	—
375	C₂×Dic₄₇	—	4	16	no	—
376	C₂×Dic₄₇	—	4	8	no	—
377	C₂×Dic₄₇	—	4	16	no	—
378	C₂×Dic₄₇	—	4	8	no	—
379	C₂×Dic₄₇	—	4	8	no	—
380	C₂×Dic₄₇	C₂⁵	1	4	yes	—
381	C₂×Dic₄₇	C₂⁵	1	8	yes	—
382	C₂×Dic₄₇	C₂⁵	1	8	yes	—
383	C₂×Dic₄₇	C₂⁵	1	8	yes	—
384	C₄×D₄₇	—	4	16	no	—
385	Dic₉₄	—	4	16	no	—
386	C₂×#3490	—	47	1	no	maximal, Sylow
387	C₂²×C₄₇	—	2	32	no	—
388	C₂²×C₄₇	—	2	4	no	—
389	C₂²×C₄₇	—	2	4	no	—
390	C₂²×C₄₇	—	2	4	no	—
391	C₂²×C₄₇	—	2	4	no	—
392	C₂²×C₄₇	—	2	4	no	—
393	C₂²×C₄₇	—	2	8	no	—
394	C₂²×C₄₇	—	2	8	no	—
395	C₂²×C₄₇	—	2	16	no	—
396	C₂²×C₄₇	—	2	8	no	—
397	C₂²×C₄₇	—	2	4	no	—
398	C₂²×C₄₇	—	2	4	no	—
399	C₂²×C₄₇	—	2	8	no	—
400	C₂²×C₄₇	—	2	4	no	—
401	C₂²×C₄₇	—	2	4	no	—
402	C₂²×C₄₇	—	4	16	no	—
403	C₂²×C₄₇	—	4	32	no	—
404	C₂²×C₄₇	—	4	32	no	—
405	C₂²×C₄₇	—	4	16	no	—
406	C₂²×C₄₇	—	4	8	no	—
407	C₂²×C₄₇	—	4	8	no	—
408	C₂²×C₄₇	—	8	8	no	—
409	C₂²×C₄₇	C₂²×#41	1	4	yes	—
410	C₂²×C₄₇	C₂²×#41	1	4	yes	—
411	C₂²×C₄₇	C₂²×#41	1	4	yes	—
412	C₂²×C₄₇	C₂²×#41	1	2	yes	—
413	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	8	yes	—
414	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
415	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
416	C₂×D₄₇	—	2	4	no	—
417	C₂×D₄₇	—	2	8	no	—
418	C₂×D₄₇	—	4	8	no	—
419	C₂×D₄₇	—	8	8	no	—
420	C₄×C₄₇	—	2	4	no	—
421	C₄×C₄₇	—	2	8	no	—
422	Dic₄₇	—	2	4	no	—
423	Dic₄₇	—	2	8	no	—
424	Dic₄₇	—	2	8	no	—
425	Dic₄₇	—	2	8	no	—
426	#3490	—	47	32	no	—
427	C₂×#551	—	47	4	no	—
428	C₂×#551	—	47	4	no	—
429	C₂×#546	—	47	4	no	—
430	C₂×#546	—	47	4	no	—
431	C₂×#543	—	47	1	no	—
432	C₂×#538	—	47	4	no	—
433	C₂×#534	—	47	1	no	—
434	C₂×#525	—	47	4	no	—
435	C₂²×#120	—	47	1	no	—
436	C₂²×#120	D₄₇	1	1	yes	characteristic, complemented
437	C₂×#518	—	47	1	no	—
438	C₂×#518	—	47	1	no	—
439	C₂³×C₂²⋊C₄	—	47	1	no	—
440	C₂×C₄₇	—	2	4	no	—
441	C₂×C₄₇	—	2	4	no	—
442	C₂×C₄₇	—	2	8	no	—
443	C₂×C₄₇	—	2	4	no	—
444	C₂×C₄₇	—	4	4	no	—
445	C₂×C₄₇	—	4	4	no	—
446	C₂×C₄₇	#3490	1	4	yes	complemented
447	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
448	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	2	yes	—
449	D₄₇	—	4	4	no	—
450	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
451	C₂²×#41	—	47	4	no	—
452	C₂³×D₄	—	47	1	no	—
453	C₂³×D₄	—	47	2	no	—
454	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
455	C₂³×D₄	C₂×D₄₇	1	2	yes	complemented
456	C₂⁴×C₄	—	47	2	no	—
457	#551	—	47	64	no	—
458	#551	—	47	64	no	—
459	#546	—	47	64	no	—
460	#546	—	47	64	no	—
461	#543	—	47	16	no	—
462	#538	—	47	64	no	—
463	#534	—	47	16	no	—
464	C₂×#126	—	47	4	no	—
465	C₂×#126	—	47	4	no	—
466	C₂×#124	—	47	4	no	—
467	C₂×#124	—	47	4	no	—
468	#525	—	47	64	no	—
469	C₂×#123	—	47	4	no	—
470	C₂×#123	—	47	2	no	—
471	C₂×#123	—	47	4	no	—
472	C₂×#123	—	47	2	no	—
473	C₂×#123	—	47	4	no	—
474	C₂×#123	—	47	4	no	—
475	C₂×C₂²⋊Q₈	—	47	4	no	—
476	C₂×C₂²⋊Q₈	—	47	4	no	—
477	C₂×C₂²⋊Q₈	—	47	4	no	—
478	C₂×C₂²⋊Q₈	—	47	4	no	—
479	C₂×#121	—	47	4	no	—
480	C₂×#121	—	47	4	no	—
481	C₂×#121	—	47	4	no	—
482	C₂×#121	—	47	4	no	—
483	C₂×#120	—	47	2	no	—
484	C₂×#120	—	47	2	no	—
485	C₂×#120	—	47	4	no	—
486	C₂×#120	—	47	16	no	—
487	C₂×#120	—	47	2	no	—
488	C₂×#120	—	47	2	no	—
489	C₂×#120	C₂×D₄₇	1	4	yes	—
490	C₂×#120	C₂×D₄₇	1	2	yes	complemented
491	C₂×#120	C₂×D₄₇	1	2	yes	complemented
492	C₂×#120	C₂×D₄₇	1	16	yes	complemented
493	#518	—	47	16	no	—
494	#518	—	47	16	no	—
495	C₂×C₄×D₄	—	47	4	no	—
496	C₂×C₄×D₄	—	47	4	no	—
497	C₂×C₄×D₄	—	47	4	no	—
498	C₂×C₄×D₄	—	47	4	no	—
499	C₂×C₄×D₄	—	47	4	no	—
500	C₂×C₄×D₄	—	47	4	no	—
501	C₂×#117	—	47	2	no	—
502	C₂×#117	—	47	2	no	—
503	C₂×#117	—	47	4	no	—
504	C₂²×C₂²⋊C₄	—	47	1	no	—
505	C₂²×C₂²⋊C₄	—	47	1	no	—
506	C₂²×C₂²⋊C₄	—	47	2	no	—
507	C₂²×C₂²⋊C₄	—	47	4	no	—
508	C₂²×C₂²⋊C₄	—	47	4	no	—
509	C₂²×C₂²⋊C₄	—	47	16	no	—
510	C₂²×C₂²⋊C₄	—	47	1	no	—
511	C₂²×C₂²⋊C₄	—	47	2	no	—
512	C₂²×C₂²⋊C₄	—	47	2	no	—
513	C₂²×C₂²⋊C₄	—	47	2	no	—
514	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
515	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	complemented
516	C₄₇	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
517	C₂⁵	—	2	8	no	—
518	C₂⁵	—	4	8	no	—
519	C₂⁵	—	47	1	no	—
520	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
521	C₂⁵	C₂²×D₄₇	1	2	yes	—
522	C₂⁵	C₂²×D₄₇	1	2	yes	—
523	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
524	C₂⁵	C₂²×D₄₇	1	8	yes	—
525	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
526	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
527	C₂×#41	—	47	32	no	—
528	C₂×#41	—	188	16	no	—
529	C₂²×Q₈	—	47	4	no	—
530	C₂²×D₄	—	2	8	no	—
531	C₂²×D₄	—	4	8	no	—
532	C₂²×D₄	—	47	2	no	—
533	C₂²×D₄	—	47	2	no	—
534	C₂²×D₄	—	47	4	no	—
535	C₂²×D₄	—	47	8	no	—
536	C₂²×D₄	—	47	4	no	—
537	C₂²×D₄	—	47	4	no	—
538	C₂²×D₄	—	47	16	no	—
539	C₂²×D₄	—	94	8	no	—
540	C₂²×D₄	—	188	8	no	—
541	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
542	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
543	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
544	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
545	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
546	C₂²×D₄	C₂²×D₄₇	1	16	yes	complemented
547	C₂³×C₄	—	47	1	no	—
548	C₂³×C₄	—	47	4	no	—
549	C₂³×C₄	—	47	2	no	—
550	C₂³×C₄	—	47	4	no	—
551	C₂³×C₄	—	47	2	no	—
552	C₂³×C₄	—	47	2	no	—
553	C₂³×C₄	—	47	16	no	—
554	C₂³×C₄	—	47	4	no	—
555	C₂³×C₄	—	47	4	no	—
556	C₂³×C₄	—	188	8	no	—
557	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
558	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
559	#126	—	47	32	no	—
560	#126	—	47	32	no	—
561	#124	—	47	32	no	—
562	#124	—	47	32	no	—
563	#123	—	47	32	no	—
564	#123	—	47	16	no	—
565	#123	—	47	32	no	—
566	#123	—	47	16	no	—
567	#123	—	47	32	no	—
568	#123	—	47	32	no	—
569	C₂²⋊Q₈	—	47	32	no	—
570	C₂²⋊Q₈	—	47	32	no	—
571	C₂²⋊Q₈	—	47	32	no	—
572	C₂²⋊Q₈	—	47	32	no	—
573	#121	—	47	32	no	—
574	#121	—	47	32	no	—
575	#121	—	47	32	no	—
576	#121	—	47	32	no	—
577	#120	—	47	16	no	—
578	#120	—	47	16	no	—
579	#120	—	47	32	no	—
580	#120	—	47	16	no	—
581	#120	—	47	16	no	—
582	#120	C₂²×D₄₇	1	32	yes	—
583	#120	C₂²×D₄₇	1	16	yes	complemented
584	#120	C₂²×D₄₇	1	16	yes	complemented
585	C₄×D₄	—	47	32	no	—
586	C₄×D₄	—	47	32	no	—
587	C₄×D₄	—	47	32	no	—
588	C₄×D₄	—	47	32	no	—
589	C₄×D₄	—	47	32	no	—
590	C₄×D₄	—	47	32	no	—
591	#117	—	47	16	no	—
592	#117	—	47	16	no	—
593	#117	—	47	32	no	—
594	C₂×C₄⋊C₄	—	47	4	no	—
595	C₂×C₄⋊C₄	—	47	4	no	—
596	C₂×C₄⋊C₄	—	47	4	no	—
597	C₂×C₄⋊C₄	—	47	4	no	—
598	C₂×C₄⋊C₄	—	47	4	no	—
599	C₂×C₄⋊C₄	—	47	4	no	—
600	C₂×C₂²⋊C₄	—	47	2	no	—
601	C₂×C₂²⋊C₄	—	47	2	no	—
602	C₂×C₂²⋊C₄	—	47	8	no	—
603	C₂×C₂²⋊C₄	—	47	2	no	—
604	C₂×C₂²⋊C₄	—	47	2	no	—
605	C₂×C₂²⋊C₄	—	47	4	no	—
606	C₂×C₂²⋊C₄	—	47	4	no	—
607	C₂×C₂²⋊C₄	—	47	8	no	—
608	C₂×C₂²⋊C₄	—	47	16	no	—
609	C₂×C₂²⋊C₄	—	47	32	no	—
610	C₂×C₂²⋊C₄	—	47	32	no	—
611	C₂×C₂²⋊C₄	—	47	2	no	—
612	C₂×C₂²⋊C₄	—	47	4	no	—
613	C₂×C₂²⋊C₄	—	47	2	no	—
614	C₂×C₂²⋊C₄	—	47	4	no	—
615	C₂×C₂²⋊C₄	—	47	8	no	—
616	C₂×C₂²⋊C₄	—	47	16	no	—
617	C₂×C₂²⋊C₄	—	47	4	no	—
618	C₂×C₂²⋊C₄	—	47	16	no	—
619	C₂×C₂²⋊C₄	—	47	4	no	—
620	C₂×C₂²⋊C₄	—	47	4	no	—
621	C₂×C₂²⋊C₄	—	47	4	no	—
622	C₂×C₂²⋊C₄	—	47	16	no	—
623	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
626	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
628	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	complemented
629	C₂×C₄²	—	47	4	no	—
630	C₂×C₄²	—	47	4	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	2	8	no	—
633	C₂⁴	—	2	8	no	—
634	C₂⁴	—	2	8	no	—
635	C₂⁴	—	2	4	no	—
636	C₂⁴	—	2	32	no	—
637	C₂⁴	—	2	8	no	—
638	C₂⁴	—	2	8	no	—
639	C₂⁴	—	2	4	no	—
640	C₂⁴	—	4	4	no	—
641	C₂⁴	—	4	4	no	—
642	C₂⁴	—	4	4	no	—
643	C₂⁴	—	4	32	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	4	64	no	—
647	C₂⁴	—	47	2	no	—
648	C₂⁴	—	47	4	no	—
649	C₂⁴	—	94	4	no	—
650	C₂⁴	—	188	4	no	—
651	C₂⁴	#10625352	1	8	yes	complemented
652	C₂⁴	C₂³×D₄₇	1	4	yes	—
653	C₂⁴	C₂³×D₄₇	1	2	yes	—
654	C₂⁴	C₂³×D₄₇	1	2	yes	—
655	C₂⁴	C₂³×D₄₇	1	8	yes	—
656	C₂⁴	C₂³×D₄₇	1	8	yes	—
657	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
658	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
659	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
660	C₂⁴	C₂³×D₄₇	1	2	yes	—
661	C₂⁴	C₂³×D₄₇	1	4	yes	—
662	C₂⁴	C₂³×D₄₇	1	4	yes	—
663	C₂⁴	C₂³×D₄₇	1	4	yes	—
664	#41	—	188	64	no	—
665	C₂×Q₈	—	47	16	no	—
666	C₂×Q₈	—	188	8	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	32	no	—
670	C₂×D₄	—	2	16	no	—
671	C₂×D₄	—	4	8	no	—
672	C₂×D₄	—	4	32	no	—
673	C₂×D₄	—	47	8	no	—
674	C₂×D₄	—	47	8	no	—
675	C₂×D₄	—	47	16	no	—
676	C₂×D₄	—	47	16	no	—
677	C₂×D₄	—	47	16	no	—
678	C₂×D₄	—	94	8	no	—
679	C₂×D₄	—	94	8	no	—
680	C₂×D₄	—	94	32	no	—
681	C₂×D₄	—	94	16	no	—
682	C₂×D₄	—	188	8	no	—
683	C₂×D₄	—	188	8	no	—
684	C₂×D₄	—	188	32	no	—
685	C₂×D₄	C₂³×D₄₇	1	8	yes	—
686	C₂×D₄	C₂³×D₄₇	1	8	yes	—
687	C₂×D₄	C₂³×D₄₇	1	16	yes	—
688	C₂×D₄	C₂³×D₄₇	1	16	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	47	4	no	—
692	C₂²×C₄	—	47	16	no	—
693	C₂²×C₄	—	47	2	no	—
694	C₂²×C₄	—	47	4	no	—
695	C₂²×C₄	—	47	4	no	—
696	C₂²×C₄	—	47	4	no	—
697	C₂²×C₄	—	47	8	no	—
698	C₂²×C₄	—	47	16	no	—
699	C₂²×C₄	—	47	8	no	—
700	C₂²×C₄	—	47	8	no	—
701	C₂²×C₄	—	47	16	no	—
702	C₂²×C₄	—	47	16	no	—
703	C₂²×C₄	—	94	4	no	—
704	C₂²×C₄	—	94	16	no	—
705	C₂²×C₄	—	188	8	no	—
706	C₂²×C₄	—	188	4	no	—
707	C₂²×C₄	—	188	8	no	—
708	C₂²×C₄	—	188	4	no	—
709	C₂²×C₄	—	188	32	no	—
710	C₂²×C₄	—	188	4	no	—
711	C₂²×C₄	—	188	8	no	—
712	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
713	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
714	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
715	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
716	C₄⋊C₄	—	47	16	no	—
717	C₄⋊C₄	—	47	16	no	—
718	C₄⋊C₄	—	47	16	no	—
719	C₄⋊C₄	—	47	16	no	—
720	C₄⋊C₄	—	47	16	no	—
721	C₄⋊C₄	—	47	16	no	—
722	C₂²⋊C₄	—	47	8	no	—
723	C₂²⋊C₄	—	47	8	no	—
724	C₂²⋊C₄	—	47	8	no	—
725	C₂²⋊C₄	—	47	8	no	—
726	C₂²⋊C₄	—	47	16	no	—
727	C₂²⋊C₄	—	47	16	no	—
728	C₂²⋊C₄	—	47	8	no	—
729	C₂²⋊C₄	—	47	16	no	—
730	C₂²⋊C₄	—	47	8	no	—
731	C₂²⋊C₄	—	47	16	no	—
732	C₂²⋊C₄	—	47	16	no	—
733	C₂²⋊C₄	—	47	16	no	—
734	C₂²⋊C₄	—	47	16	no	—
735	C₂²⋊C₄	—	47	16	no	—
736	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
737	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
738	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
739	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
740	C₄²	—	47	16	no	—
741	C₄²	—	47	16	no	—
742	C₂³	—	2	32	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	16	no	—
747	C₂³	—	2	4	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	2	4	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	2	16	no	—
752	C₂³	—	2	16	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	16	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	16	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	8	no	—
761	C₂³	—	4	16	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	8	no	—
767	C₂³	—	4	32	no	—
768	C₂³	—	4	32	no	—
769	C₂³	—	4	128	no	—
770	C₂³	—	4	16	no	—
771	C₂³	—	8	8	no	—
772	C₂³	—	47	4	no	—
773	C₂³	—	94	8	no	—
774	C₂³	—	94	4	no	—
775	C₂³	—	94	8	no	—
776	C₂³	—	376	8	no	—
777	C₂³	—	188	8	no	—
778	C₂³	C₂×#10625352	1	4	yes	—
779	C₂³	C₂×#10625352	1	4	yes	—
780	C₂³	C₂×#10625352	1	4	yes	—
781	C₂³	C₂×#10625352	1	16	yes	complemented
782	C₂³	#13094069	1	8	yes	—
783	C₂³	C₂⁴×D₄₇	1	4	yes	—
784	C₂³	C₂⁴×D₄₇	1	4	yes	—
785	C₂³	C₂⁴×D₄₇	1	2	yes	—
786	C₂³	C₂⁴×D₄₇	1	2	yes	—
787	C₂³	C₂⁴×D₄₇	1	2	yes	—
788	C₂³	C₂⁴×D₄₇	1	4	yes	—
789	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
790	Q₈	—	188	16	no	—
791	D₄	—	2	16	no	—
792	D₄	—	2	16	no	—
793	D₄	—	2	32	no	—
794	D₄	—	4	16	no	—
795	D₄	—	94	16	no	—
796	D₄	—	94	16	no	—
797	D₄	—	94	32	no	—
798	D₄	—	188	16	no	—
799	D₄	—	188	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	47	4	no	—
805	C₂×C₄	—	47	8	no	—
806	C₂×C₄	—	47	8	no	—
807	C₂×C₄	—	47	8	no	—
808	C₂×C₄	—	94	8	no	—
809	C₂×C₄	—	94	4	no	—
810	C₂×C₄	—	94	8	no	—
811	C₂×C₄	—	94	8	no	—
812	C₂×C₄	—	94	32	no	—
813	C₂×C₄	—	94	8	no	—
814	C₂×C₄	—	188	16	no	—
815	C₂×C₄	—	188	8	no	—
816	C₂×C₄	—	188	16	no	—
817	C₂×C₄	—	188	8	no	—
818	C₂×C₄	—	188	8	no	—
819	C₂×C₄	—	188	16	no	—
820	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
821	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
822	C₂²	—	2	32	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	16	no	—
825	C₂²	—	2	8	no	—
826	C₂²	—	2	8	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	8	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	4	16	no	—
838	C₂²	—	4	32	no	—
839	C₂²	—	4	32	no	—
840	C₂²	—	4	16	no	—
841	C₂²	—	4	8	no	—
842	C₂²	—	4	8	no	—
843	C₂²	—	8	8	no	—
844	C₂²	—	94	4	no	—
845	C₂²	—	94	8	no	—
846	C₂²	—	376	8	no	—
847	C₂²	—	188	8	no	—
848	C₂²	C₂²×#10625352	1	4	yes	—
849	C₂²	C₂²×#10625352	1	4	yes	—
850	C₂²	C₂²×#10625352	1	4	yes	—
851	C₂²	C₂²×#10625352	1	2	yes	—
852	C₂²	C₂×#13094069	1	8	yes	—
853	C₂²	C₂×#13094069	1	4	yes	—
854	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	94	4	no	—
858	C₄	—	94	8	no	—
859	C₄	—	94	8	no	—
860	C₄	—	94	8	no	—
861	C₂	—	2	4	no	—
862	C₂	—	2	8	no	—
863	C₂	—	2	4	no	—
864	C₂	—	2	4	no	—
865	C₂	—	4	4	no	—
866	C₂	—	4	4	no	—
867	C₂	—	188	4	no	—
868	C₂	#20257075	1	4	yes	direct product factor
869	C₂	C₂³×#10625352	1	1	yes	characteristic
870	C₂	C₂²×#13094069	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×#120×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#120	D₄₇
hypocenter	C₄₇	C₂×#3490
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. #20257075	C₂	direct (N × H)
2. C₂×#15689804	C₂	semidirect
3. C₂×#15689799	C₂	semidirect
4. C₂×#15689767	C₂	semidirect
5. C₂×#15689760	C₂	semidirect
6. C₂×#15689749	C₂	semidirect
7. C₂×#15689708	C₂	semidirect
8. C₂×#15689682	C₂	semidirect
9. C₂×#15689629	C₂	semidirect
10. C₂²×#13093993	C₂	semidirect
11. C₂×#15689598	C₂	semidirect
12. C₂×#15689596	C₂	semidirect
13. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
14. C₂²×#120×C₄₇	C₂	semidirect
15. C₂²×#10625352	C₂²	semidirect
17. C₂³×C₂²⋊D₄₇	C₂²	semidirect
18. C₂⁴×Dic₄₇	C₂²	semidirect
19. #15689804	C₂²	semidirect
20. #15689799	C₂²	semidirect
21. #15689767	C₂²	semidirect
22. #15689760	C₂²	semidirect
23. #15689749	C₂²	semidirect
24. #15689708	C₂²	semidirect
25. #15689682	C₂²	semidirect
26. C₂×#13094017	C₂²	semidirect
27. C₂×#13094017	C₂²	semidirect
28. C₂×#13094011	C₂²	semidirect
29. C₂×#13094010	C₂²	semidirect
30. #15689629	C₂²	semidirect
31. C₂×#13094008	C₂²	semidirect
32. C₂×#13094007	C₂²	semidirect
33. C₂×#13094006	C₂²	semidirect
34. C₂×#13094005	C₂²	semidirect
35. C₂×#13094005	C₂²	semidirect
36. C₂×#13094005	C₂²	semidirect
37. C₂×#13094003	C₂²	semidirect
38. C₂×#13094001	C₂²	semidirect
39. C₂×#13094001	C₂²	semidirect
40. C₂×#13094001	C₂²	semidirect
41. C₂×#13093996	C₂²	semidirect
42. C₂×#13093996	C₂²	semidirect
43. C₂×#13093996	C₂²	semidirect
44. C₂×#13093995	C₂²	semidirect
46. C₂×#13093993	C₂²	semidirect
47. C₂×#13093993	C₂²	semidirect
48. C₂×#13093993	C₂²	semidirect
49. C₂×#13093993	C₂²	semidirect
50. C₂×#13093992	C₂²	semidirect
51. #15689598	C₂²	semidirect
52. #15689596	C₂²	semidirect
53. C₂×D₄×Dic₄₇	C₂²	semidirect
54. C₂×D₄×Dic₄₇	C₂²	semidirect
55. C₂×D₄×Dic₄₇	C₂²	semidirect
56. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
57. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
58. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
59. C₂×#13093983	C₂²	semidirect
60. C₂×#13093980	C₂²	semidirect
61. C₂×#13093980	C₂²	semidirect
65. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
66. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
67. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
68. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
69. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
70. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
74. C₂³×D₄×C₄₇	C₂²	semidirect
76. C₂×#120×C₄₇	C₂²	semidirect
77. C₂×#120×C₄₇	C₂²	semidirect
78. C₂×#120×C₄₇	C₂²	semidirect
80. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
83. C₂×#10625352	C₂³	semidirect
84. C₂²×Dic₉₄	C₂³	semidirect
92. C₂²×C₂²⋊D₄₇	C₂³	semidirect
93. C₂²×C₂²⋊D₄₇	C₂³	semidirect
101. C₂³×Dic₄₇	C₂³	semidirect
102. C₂³×Dic₄₇	C₂³	semidirect
103. C₂²×C₄×D₄₇	C₂³	semidirect
104. #13094017	C₂³	semidirect
105. #13094017	C₂³	semidirect
106. #13094011	C₂³	semidirect
107. #13094010	C₂³	semidirect
108. #13094008	C₂³	semidirect
109. #13094007	C₂³	semidirect
110. #13094006	C₂³	semidirect
111. #13094005	C₂³	semidirect
112. #13094005	C₂³	semidirect
113. #13094005	C₂³	semidirect
114. #13094003	C₂³	semidirect
115. #13094001	C₂³	semidirect
116. #13094001	C₂³	semidirect
117. #13094001	C₂³	semidirect
118. #13093996	C₂³	semidirect
119. #13093996	C₂³	semidirect
120. #13093996	C₂³	semidirect
121. #13093995	C₂³	semidirect
123. #13093993	C₂³	semidirect
124. #13093993	C₂³	semidirect
125. #13093993	C₂³	semidirect
126. #13093992	C₂³	semidirect
127. D₄×Dic₄₇	C₂³	semidirect
128. D₄×Dic₄₇	C₂³	semidirect
129. D₄×Dic₄₇	C₂³	semidirect
130. C₄×C₂²⋊D₄₇	C₂³	semidirect
131. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
132. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
133. #13093983	C₂³	semidirect
134. #13093980	C₂³	semidirect
135. #13093980	C₂³	semidirect
136. C₂×C₄⋊Dic₄₇	C₂³	semidirect
137. C₂×C₄⋊Dic₄₇	C₂³	semidirect
138. C₂×Dic₄₇⋊C₄	C₂³	semidirect
139. C₂×Dic₄₇⋊C₄	C₂³	semidirect
140. C₂×Dic₄₇⋊C₄	C₂³	semidirect
141. C₂×Dic₄₇⋊C₄	C₂³	semidirect
155. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
156. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
157. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
158. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
159. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
160. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
161. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
162. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
163. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
164. C₂²⋊C₄×D₄₇	C₂³	semidirect
165. C₂×C₄×Dic₄₇	C₂³	semidirect
166. C₂×C₄×Dic₄₇	C₂³	semidirect
183. C₂²×D₄×C₄₇	C₂³	semidirect
187. #120×C₄₇	C₂³	semidirect
188. #120×C₄₇	C₂³	semidirect
194. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
211. C₂⁴×C₄₇	#41	semidirect
255. C₂×C₂²⋊D₄₇	C₂⁴	semidirect
274. C₂²×Dic₄₇	C₂⁴	semidirect
277. C₂×C₄×D₄₇	C₂⁴	semidirect
279. C₂×Dic₉₄	C₂⁴	semidirect
294. C₂²⋊Dic₄₇	C₂⁴	semidirect
295. C₂²⋊Dic₄₇	C₂⁴	semidirect
296. (C₂×D₄₇)⋊C₄	C₂⁴	semidirect
297. (C₂×D₄₇)⋊C₄	C₂⁴	semidirect
298. C₄⋊Dic₄₇	C₂⁴	semidirect
299. C₄⋊Dic₄₇	C₂⁴	semidirect
300. Dic₄₇⋊C₄	C₂⁴	semidirect
301. Dic₄₇⋊C₄	C₂⁴	semidirect
302. Dic₄₇⋊C₄	C₂⁴	semidirect
303. Dic₄₇⋊C₄	C₂⁴	semidirect
304. C₄×Dic₄₇	C₂⁴	semidirect
305. C₄×Dic₄₇	C₂⁴	semidirect
339. C₂³×C₄₇	C₂×#41	semidirect
436. C₂²×#120	D₄₇	semidirect
446. C₂×C₄₇	#3490	semidirect
455. C₂³×D₄	C₂×D₄₇	semidirect
490. C₂×#120	C₂×D₄₇	semidirect
491. C₂×#120	C₂×D₄₇	semidirect
492. C₂×#120	C₂×D₄₇	semidirect
515. C₂²×C₂²⋊C₄	C₂×D₄₇	semidirect
516. C₄₇	C₂×#3490	semidirect
546. C₂²×D₄	C₂²×D₄₇	semidirect
583. #120	C₂²×D₄₇	semidirect
584. #120	C₂²×D₄₇	semidirect
628. C₂×C₂²⋊C₄	C₂²×D₄₇	semidirect
651. C₂⁴	#10625352	semidirect
781. C₂³	C₂×#10625352	semidirect
868. C₂	#20257075	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257075	2
C₂×#15689804	2
C₂×#15689799	2
C₂×#15689767	2
C₂×#15689760	2
C₂×#15689749	2
C₂×#15689708	2
C₂×#15689682	2
C₂×#15689629	2
C₂²×#13093993	2
C₂×#15689598	2
C₂×#15689596	2
C₂³×C₂²⋊Dic₄₇	2
C₂²×#120×C₄₇	2
C₂×#3490	47

Subgroups — C2×#20257075 #27124187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257075 #27124187