Subgroups — C₂×#20257760 #27123925

Order 12032.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257760	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689861	C₂	1	4	yes	maximal, complemented
3	C₂×#15689843	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689819	C₂	1	2	yes	maximal, complemented
5	C₂×#15689794	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15689791	C₂	1	2	yes	maximal, complemented
7	C₂×#15689777	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689770	C₂	1	2	yes	maximal, complemented
9	C₂×#15689769	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689747	C₂	1	2	yes	maximal, complemented
12	C₂×#15689707	C₂	1	4	yes	maximal, complemented
13	C₂×#15689701	C₂	1	2	yes	maximal, complemented
14	C₂×#15689687	C₂	1	2	yes	maximal, complemented
15	C₂×#15689686	C₂	1	2	yes	maximal, complemented
16	C₂×#15689673	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#15689657	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625350	C₂²	1	2	yes	complemented
20	C₂²×#10625350	C₂²	1	2	yes	complemented
21	C₂²×#10625352	C₂²	1	2	yes	complemented
22	C₂³×D₁₈₈	C₂²	1	2	yes	—
23	C₂²×D₄×D₄₇	C₂²	1	2	yes	—
24	#15689861	C₂²	1	64	yes	complemented
25	#15689843	C₂²	1	16	yes	complemented
26	#15689819	C₂²	1	32	yes	complemented
27	#15689794	C₂²	1	16	yes	complemented
28	#15689791	C₂²	1	32	yes	complemented
29	#15689777	C₂²	1	16	yes	complemented
30	#15689770	C₂²	1	32	yes	complemented
31	#15689769	C₂²	1	32	yes	complemented
32	D₄×D₁₈₈	C₂²	1	16	yes	complemented
33	#15689747	C₂²	1	32	yes	complemented
34	#15689707	C₂²	1	64	yes	complemented
35	#15689701	C₂²	1	32	yes	complemented
36	#15689687	C₂²	1	32	yes	complemented
37	#15689686	C₂²	1	32	yes	complemented
38	#15689673	C₂²	1	16	yes	complemented
39	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13094021	C₂²	1	1	yes	characteristic
41	C₂×#13094020	C₂²	1	2	yes	complemented
42	C₂×#13094020	C₂²	1	4	yes	complemented
43	#15689657	C₂²	1	16	yes	complemented
44	C₂×#13094019	C₂²	1	4	yes	complemented
45	C₂×#13094018	C₂²	1	2	yes	complemented
46	C₂×#13094017	C₂²	1	4	yes	complemented
47	C₂×#13094016	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13094013	C₂²	1	4	yes	complemented
49	C₂×#13094012	C₂²	1	1	yes	characteristic
50	C₂×#13094012	C₂²	1	2	yes	complemented
51	C₂×#13094011	C₂²	1	2	yes	—
52	C₂×#13094009	C₂²	1	4	yes	complemented
53	C₂×#13094008	C₂²	1	4	yes	complemented
54	C₂×#13094007	C₂²	1	2	yes	complemented
55	C₂×#13094006	C₂²	1	4	yes	complemented
56	C₂×#13094004	C₂²	1	2	yes	complemented
57	C₂×#13094003	C₂²	1	2	yes	complemented
58	C₂×#13094003	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13094000	C₂²	1	4	yes	complemented
60	C₂×#13093999	C₂²	1	2	yes	—
61	C₂×#13093998	C₂²	1	2	yes	—
62	C₂×#13093998	C₂²	1	2	yes	—
63	C₂×#13093998	C₂²	1	1	yes	characteristic
64	C₂×#13093998	C₂²	1	2	yes	complemented
65	C₂×#13093998	C₂²	1	2	yes	complemented
66	C₂×#13093998	C₂²	1	2	yes	complemented
67	C₂×#13093997	C₂²	1	4	yes	complemented
68	C₂×#13093997	C₂²	1	4	yes	complemented
69	C₂×#13093996	C₂²	1	4	yes	complemented
70	C₂×#13093996	C₂²	1	4	yes	complemented
71	C₂×#13093996	C₂²	1	4	yes	complemented
72	C₂×#13093995	C₂²	1	4	yes	complemented
73	C₂×#13093994	C₂²	1	4	yes	—
74	C₂×#13093992	C₂²	1	4	yes	complemented
75	C₂×#13093992	C₂²	1	4	yes	complemented
76	C₂×#13093992	C₂²	1	4	yes	complemented
77	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13093989	C₂²	1	2	yes	complemented
79	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
81	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
82	C₂×#13093986	C₂²	1	2	yes	complemented
83	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
84	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
85	C₂×#13093983	C₂²	1	2	yes	complemented
86	C₂×#13093981	C₂²	1	2	yes	complemented
87	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
89	C₂²×#41×C₄₇	C₂²	1	2	yes	complemented
90	C₄₇×#532	C₂²	1	16	yes	complemented
91	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
93	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
94	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
95	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#121×C₄₇	C₂²	1	2	yes	complemented
97	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
98	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
99	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
100	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₄₇	C₂³	1	4	yes	—
102	C₂×#10625350	—	4	8	no	—
103	C₂×#10625350	—	4	8	no	—
104	C₂×#10625350	C₂³	1	16	yes	complemented
105	C₂×#10625350	C₂³	1	16	yes	complemented
106	C₂×#10625352	—	4	8	no	—
107	C₂×#10625352	C₂³	1	16	yes	complemented
108	C₂²×Dic₉₄	C₂³	1	2	yes	—
109	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
110	C₂²×D₁₈₈	—	4	8	no	—
111	C₂²×D₁₈₈	C₂³	1	2	yes	—
112	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
113	C₂²×D₁₈₈	C₂³	1	2	yes	—
114	C₂²×D₁₈₈	C₂³	1	16	yes	—
115	C₂²×D₁₈₈	C₂³	1	2	yes	—
116	C₂²×D₁₈₈	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
118	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
119	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
120	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
121	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
123	C₂×D₄×D₄₇	—	4	8	no	—
124	C₂×D₄×D₄₇	C₂³	1	16	yes	—
125	C₂³×Dic₄₇	C₂³	1	4	yes	—
126	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
127	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
128	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
129	#13094024	C₂³	1	8	yes	complemented
130	#13094021	C₂³	1	8	yes	—
131	#13094020	C₂³	1	16	yes	complemented
132	#13094020	C₂³	1	32	yes	complemented
133	#13094019	C₂³	1	32	yes	complemented
134	#13094018	C₂³	1	16	yes	complemented
135	#13094017	C₂³	1	32	yes	complemented
136	#13094016	C₂³	1	8	yes	complemented
137	#13094013	C₂³	1	32	yes	complemented
138	#13094012	C₂³	1	8	yes	—
139	#13094012	C₂³	1	16	yes	complemented
140	#13094011	C₂³	1	16	yes	—
141	#13094009	C₂³	1	32	yes	complemented
142	#13094008	C₂³	1	32	yes	complemented
143	#13094007	C₂³	1	16	yes	complemented
144	#13094006	C₂³	1	32	yes	complemented
145	#13094004	C₂³	1	16	yes	complemented
146	#13094003	C₂³	1	16	yes	complemented
147	#13094003	C₂³	1	8	yes	complemented
148	#13094000	C₂³	1	32	yes	complemented
149	#13093999	C₂³	1	16	yes	—
150	#13093998	C₂³	1	16	yes	—
151	#13093998	C₂³	1	16	yes	—
152	#13093998	C₂³	1	8	yes	—
153	#13093998	C₂³	1	16	yes	complemented
154	#13093998	C₂³	1	16	yes	complemented
155	#13093998	C₂³	1	16	yes	complemented
156	#13093997	C₂³	1	32	yes	complemented
157	#13093997	C₂³	1	32	yes	complemented
158	#13093996	C₂³	1	32	yes	complemented
159	#13093996	C₂³	1	32	yes	complemented
160	#13093996	C₂³	1	32	yes	complemented
161	#13093995	C₂³	1	32	yes	complemented
162	#13093994	C₂³	1	32	yes	—
163	#13093992	C₂³	1	32	yes	complemented
164	#13093992	C₂³	1	32	yes	complemented
165	#13093992	C₂³	1	32	yes	complemented
166	C₄×Dic₉₄	C₂³	1	8	yes	complemented
167	#13093989	C₂³	1	16	yes	complemented
168	C₄×D₁₈₈	C₂³	1	8	yes	—
169	C₄×D₁₈₈	C₂³	1	16	yes	complemented
170	C₄×D₁₈₈	C₂³	1	16	yes	complemented
171	#13093986	C₂³	1	16	yes	complemented
172	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
173	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
174	#13093983	C₂³	1	16	yes	complemented
175	#13093981	C₂³	1	16	yes	complemented
176	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
179	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
182	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
186	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
188	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
189	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
190	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
199	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
200	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
201	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
202	C₂×#41×C₄₇	—	4	8	no	—
203	C₂×#41×C₄₇	C₂³	1	16	yes	complemented
204	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
205	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
206	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
207	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
208	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
209	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
210	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
211	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
214	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
215	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
216	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
217	#127×C₄₇	C₂³	1	8	yes	—
218	#124×C₄₇	C₂³	1	16	yes	complemented
219	#121×C₄₇	C₂³	1	8	yes	—
220	#121×C₄₇	C₂³	1	8	yes	complemented
221	#121×C₄₇	C₂³	1	16	yes	complemented
222	C₄×D₄×C₄₇	C₂³	1	8	yes	—
223	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
224	C₄×D₄×C₄₇	C₂³	1	8	yes	complemented
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₄₇	C₂³	1	8	yes	complemented
237	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
238	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
239	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂³×D₄₇	—	4	8	no	—
241	C₂³×D₄₇	—	4	8	no	—
242	C₂³×D₄₇	—	4	8	no	—
243	C₂³×D₄₇	C₂⁴	1	2	yes	—
244	C₂³×D₄₇	C₂⁴	1	4	yes	—
245	C₂³×D₄₇	C₂⁴	1	16	yes	—
246	#41×C₄₇	—	4	32	no	—
247	C₂×Q₈×C₄₇	—	4	4	no	—
248	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
249	C₂×D₄×C₄₇	—	2	4	no	—
250	C₂×D₄×C₄₇	—	2	4	no	—
251	C₂×D₄×C₄₇	—	4	4	no	—
252	C₂×D₄×C₄₇	—	4	4	no	—
253	C₂×D₄×C₄₇	—	4	4	no	—
254	C₂×D₄×C₄₇	—	4	4	no	—
255	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
256	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
257	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
258	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
259	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
260	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
261	C₂²×C₄×C₄₇	—	2	4	no	—
262	C₂²×C₄×C₄₇	—	2	8	no	—
263	C₂²×C₄×C₄₇	—	2	8	no	—
264	C₂²×C₄×C₄₇	—	2	4	no	—
265	C₂²×C₄×C₄₇	—	4	2	no	—
266	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₂²⋊D₄₇	—	4	8	no	—
280	C₂×C₂²⋊D₄₇	—	4	8	no	—
281	C₂×C₂²⋊D₄₇	—	4	4	no	—
282	C₂×C₂²⋊D₄₇	—	4	8	no	—
283	C₂×C₂²⋊D₄₇	—	4	8	no	—
284	C₂×C₂²⋊D₄₇	—	4	8	no	—
285	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
286	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
287	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
288	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
289	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
290	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
291	C₂²×Dic₄₇	—	4	8	no	—
292	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
293	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
294	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
295	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
296	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
297	#10625352	—	4	32	no	—
298	D₄×D₄₇	—	4	32	no	—
299	#10625350	—	4	32	no	—
300	#10625350	—	4	32	no	—
301	C₂×D₁₈₈	—	2	8	no	—
302	C₂×D₁₈₈	—	2	4	no	—
303	C₂×D₁₈₈	—	2	8	no	—
304	C₂×D₁₈₈	—	4	32	no	—
305	C₂×D₁₈₈	—	4	8	no	—
306	C₂×D₁₈₈	—	4	4	no	—
307	C₂×D₁₈₈	C₂⁴	1	8	yes	—
308	C₂×D₁₈₈	C₂⁴	1	4	yes	—
309	C₂×D₁₈₈	C₂⁴	1	8	yes	—
310	C₂×D₁₈₈	C₂⁴	1	8	yes	—
311	C₂×D₁₈₈	C₂⁴	1	16	yes	—
312	C₂×C₄×D₄₇	—	2	8	no	—
313	C₂×C₄×D₄₇	—	4	8	no	—
314	C₂×C₄×D₄₇	—	4	8	no	—
315	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
316	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
317	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
318	C₂×Dic₉₄	—	2	8	no	—
319	C₂×Dic₉₄	—	2	4	no	—
320	C₂×Dic₉₄	C₂⁴	1	8	yes	—
321	C₂×Dic₉₄	C₂⁴	1	4	yes	—
322	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
324	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
327	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
328	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
329	C₄²×C₄₇	C₂⁴	1	4	yes	—
330	C₄²×C₄₇	C₂⁴	1	4	yes	—
331	C₄²×C₄₇	C₂⁴	1	4	yes	—
332	C₄²×C₄₇	C₂⁴	1	4	yes	—
333	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
334	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
335	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
336	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
337	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
338	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
339	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
340	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
341	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
342	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
343	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
344	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
345	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
346	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
347	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
348	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
349	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
350	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
351	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
352	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
353	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
354	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
355	C₄×Dic₄₇	C₂⁴	1	8	yes	—
356	C₄×Dic₄₇	C₂⁴	1	16	yes	—
357	C₂³×C₄₇	—	2	4	no	—
358	C₂³×C₄₇	—	2	2	no	—
359	C₂³×C₄₇	—	2	4	no	—
360	C₂³×C₄₇	—	2	4	no	—
361	C₂³×C₄₇	—	2	2	no	—
362	C₂³×C₄₇	—	2	4	no	—
363	C₂³×C₄₇	—	2	2	no	—
364	C₂³×C₄₇	—	2	4	no	—
365	C₂³×C₄₇	—	2	4	no	—
366	C₂³×C₄₇	C₂⁵	1	4	yes	—
367	C₂³×C₄₇	C₂⁵	1	2	yes	—
368	C₂³×C₄₇	C₂⁵	1	4	yes	—
369	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
370	C₂²×D₄₇	—	2	4	no	—
371	C₂²×D₄₇	—	2	8	no	—
372	C₂²×D₄₇	—	2	8	no	—
373	C₂²×D₄₇	—	2	4	no	—
374	C₂²×D₄₇	—	2	8	no	—
375	C₂²×D₄₇	—	2	4	no	—
376	C₂²×D₄₇	—	4	16	no	—
377	C₂²×D₄₇	—	4	16	no	—
378	C₂²×D₄₇	—	4	16	no	—
379	C₂²×D₄₇	—	8	32	no	—
380	C₂²×D₄₇	C₂⁵	1	4	yes	—
381	C₂²×D₄₇	C₂⁵	1	8	yes	—
382	Q₈×C₄₇	—	4	8	no	—
383	D₄×C₄₇	—	2	8	no	—
384	D₄×C₄₇	—	2	8	no	—
385	D₄×C₄₇	—	4	8	no	—
386	D₄×C₄₇	—	4	8	no	—
387	D₄×C₄₇	—	4	8	no	—
388	D₄×C₄₇	—	4	8	no	—
389	C₂×C₄×C₄₇	—	2	2	no	—
390	C₂×C₄×C₄₇	—	2	4	no	—
391	C₂×C₄×C₄₇	—	2	4	no	—
392	C₂×C₄×C₄₇	—	2	2	no	—
393	C₂×C₄×C₄₇	—	2	2	no	—
394	C₂×C₄×C₄₇	—	2	2	no	—
395	C₂×C₄×C₄₇	—	2	16	no	—
396	C₂×C₄×C₄₇	—	2	8	no	—
397	C₂×C₄×C₄₇	—	2	16	no	—
398	C₂×C₄×C₄₇	—	2	8	no	—
399	C₂×C₄×C₄₇	—	4	4	no	—
400	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
401	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
402	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
403	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
404	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
405	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
406	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
407	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
408	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
409	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
410	C₂²⋊D₄₇	—	4	16	no	—
411	C₂²⋊D₄₇	—	4	16	no	—
412	C₂²⋊D₄₇	—	4	16	no	—
413	C₂²⋊D₄₇	—	4	16	no	—
414	C₂²⋊D₄₇	—	4	16	no	—
415	C₂²⋊D₄₇	—	4	8	no	—
416	C₂×Dic₄₇	—	2	4	no	—
417	C₂×Dic₄₇	—	2	8	no	—
418	C₂×Dic₄₇	—	2	4	no	—
419	C₂×Dic₄₇	—	2	4	no	—
420	C₂×Dic₄₇	—	4	16	no	—
421	C₂×Dic₄₇	C₂⁵	1	4	yes	—
422	C₂×Dic₄₇	C₂⁵	1	4	yes	—
423	C₂×Dic₄₇	C₂⁵	1	8	yes	—
424	C₂×Dic₄₇	C₂⁵	1	4	yes	—
425	D₁₈₈	—	2	8	no	—
426	D₁₈₈	—	2	16	no	—
427	D₁₈₈	—	2	16	no	—
428	D₁₈₈	—	4	16	no	—
429	D₁₈₈	—	4	8	no	—
430	C₄×D₄₇	—	2	16	no	—
431	C₄×D₄₇	—	4	16	no	—
432	C₄×D₄₇	—	4	16	no	—
433	Dic₉₄	—	2	8	no	—
434	Dic₉₄	—	2	16	no	—
435	C₂×#3546	—	47	1	no	maximal, Sylow
436	C₂²×C₄₇	—	2	4	no	—
437	C₂²×C₄₇	—	2	2	no	—
438	C₂²×C₄₇	—	2	4	no	—
439	C₂²×C₄₇	—	2	4	no	—
440	C₂²×C₄₇	—	2	2	no	—
441	C₂²×C₄₇	—	2	4	no	—
442	C₂²×C₄₇	—	2	2	no	—
443	C₂²×C₄₇	—	2	4	no	—
444	C₂²×C₄₇	—	2	4	no	—
445	C₂²×C₄₇	—	4	8	no	—
446	C₂²×C₄₇	—	4	8	no	—
447	C₂²×C₄₇	—	4	4	no	—
448	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
450	C₂²×C₄₇	#585	1	2	yes	—
451	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
452	C₂×D₄₇	—	2	4	no	—
453	C₂×D₄₇	—	2	8	no	—
454	C₂×D₄₇	—	2	8	no	—
455	C₂×D₄₇	—	2	4	no	—
456	C₂×D₄₇	—	2	8	no	—
457	C₂×D₄₇	—	2	4	no	—
458	C₂×D₄₇	—	4	16	no	—
459	C₂×D₄₇	—	4	8	no	—
460	C₂×D₄₇	—	8	32	no	—
461	C₄×C₄₇	—	2	2	no	—
462	C₄×C₄₇	—	2	4	no	—
463	C₄×C₄₇	—	2	4	no	—
464	C₄×C₄₇	—	2	2	no	—
465	C₄×C₄₇	—	2	2	no	—
466	C₄×C₄₇	—	2	2	no	—
467	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
468	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
469	Dic₄₇	—	2	4	no	—
470	Dic₄₇	—	2	8	no	—
471	Dic₄₇	—	2	4	no	—
472	Dic₄₇	—	2	4	no	—
473	#3546	—	47	32	no	—
474	C₂×#560	—	47	4	no	—
475	C₂×#556	—	47	1	no	—
476	C₂×#553	—	47	2	no	—
477	C₂×#550	—	47	2	no	—
478	C₂×#550	—	47	1	no	—
479	C₂×#547	—	47	1	no	—
480	C₂×#546	—	47	2	no	—
481	C₂×#546	—	47	2	no	—
482	C₂×D₄²	—	47	1	no	—
483	C₂×#542	—	47	2	no	—
484	C₂×#538	—	47	4	no	—
485	C₂×#537	—	47	2	no	—
486	C₂×#535	—	47	2	no	—
487	C₂×#535	—	47	2	no	—
488	C₂×#532	—	47	1	no	—
489	C₂×#532	D₄₇	1	1	yes	characteristic, complemented
490	C₂×#529	—	47	1	no	—
491	C₂×C₄₇	—	4	4	no	—
492	C₂×C₄₇	—	4	4	no	—
493	C₂×C₄₇	—	4	2	no	—
494	C₂×C₄₇	#3546	1	4	yes	complemented
495	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
498	D₄₇	—	4	8	no	—
499	D₄₇	—	4	4	no	—
500	C₂²×#41	—	47	2	no	—
501	C₂²×#41	—	47	2	no	—
502	C₂²×#41	—	47	2	no	—
503	C₂²×#41	C₂×D₄₇	1	2	yes	complemented
504	C₂³×D₄	—	47	2	no	—
505	C₂³×D₄	—	47	2	no	—
506	#560	—	47	64	no	—
507	#556	—	47	16	no	—
508	#553	—	47	32	no	—
509	#550	—	47	32	no	—
510	#550	—	47	16	no	—
511	#547	—	47	16	no	—
512	#546	—	47	32	no	—
513	#546	—	47	32	no	—
514	D₄²	—	47	16	no	—
515	#542	—	47	32	no	—
516	#538	—	47	64	no	—
517	#537	—	47	32	no	—
518	#535	—	47	32	no	—
519	#535	—	47	32	no	—
520	#532	—	47	16	no	—
521	#532	C₂×D₄₇	1	16	yes	complemented
522	C₂×C₄⋊Q₈	—	47	1	no	—
523	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
524	C₂×#127	—	47	2	no	—
525	C₂×#127	—	47	4	no	—
526	C₂×#127	—	47	1	no	—
527	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
528	#529	—	47	16	no	—
529	C₂×#126	—	47	4	no	—
530	C₂×#126	—	47	4	no	—
531	C₂×#126	—	47	2	no	—
532	C₂×#125	—	47	1	no	—
533	C₂×#124	—	47	4	no	—
534	C₂×#124	—	47	2	no	—
535	C₂×#124	—	47	1	no	—
536	C₂×#124	—	47	2	no	—
537	C₂×#124	C₂×D₄₇	1	2	yes	complemented
538	C₂×#123	—	47	2	no	—
539	C₂×#123	—	47	4	no	—
540	C₂×#123	—	47	4	no	—
541	C₂×#123	—	47	4	no	—
542	C₂×C₂²⋊Q₈	—	47	4	no	—
543	C₂×C₂²⋊Q₈	—	47	1	no	—
544	C₂×C₂²⋊Q₈	—	47	2	no	—
545	C₂×C₂²⋊Q₈	—	47	2	no	—
546	C₂×#121	—	47	4	no	—
547	C₂×#121	—	47	4	no	—
548	C₂×#121	—	47	4	no	—
549	C₂×#121	—	47	4	no	—
550	C₂×#121	—	47	1	no	—
551	C₂×#121	—	47	2	no	—
552	C₂×#121	—	47	2	no	—
553	C₂×#121	—	47	2	no	—
554	C₂×#121	—	47	2	no	—
555	C₂×#121	—	47	2	no	—
556	C₂×#121	—	47	2	no	—
557	C₂×#121	—	47	4	no	—
558	C₂×#121	—	47	4	no	—
559	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
560	C₂×#121	C₂×D₄₇	1	1	yes	characteristic, complemented
561	C₂×#121	C₂×D₄₇	1	2	yes	complemented
562	C₂×#120	—	47	4	no	—
563	C₂×#120	—	47	4	no	—
564	C₂×#120	—	47	4	no	—
565	C₂×#120	—	47	4	no	—
566	C₂×C₄×Q₈	—	47	2	no	—
567	C₂×C₄×Q₈	—	47	1	no	—
568	C₂×C₄×D₄	—	47	2	no	—
569	C₂×C₄×D₄	—	47	2	no	—
570	C₂×C₄×D₄	—	47	4	no	—
571	C₂×C₄×D₄	—	47	1	no	—
572	C₂×C₄×D₄	—	47	2	no	—
573	C₂×C₄×D₄	—	47	2	no	—
574	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
575	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	complemented
576	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
577	C₂×#117	—	47	2	no	—
578	C₂×#117	—	47	2	no	—
579	C₂²×C₄⋊C₄	—	47	2	no	—
580	C₂²×C₂²⋊C₄	—	47	4	no	—
581	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
582	C₄₇	C₂×#3546	1	1	yes	characteristic, complemented, Sylow
583	C₂⁵	—	47	4	no	—
584	C₂×#41	—	4	8	no	—
585	C₂×#41	—	47	16	no	—
586	C₂×#41	—	47	16	no	—
587	C₂×#41	—	47	16	no	—
588	C₂×#41	—	188	8	no	—
589	C₂×#41	—	188	8	no	—
590	C₂×#41	—	188	8	no	—
591	C₂×#41	C₂²×D₄₇	1	16	yes	complemented
592	C₂²×Q₈	—	47	1	no	—
593	C₂²×Q₈	—	47	2	no	—
594	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
595	C₂²×D₄	—	47	2	no	—
596	C₂²×D₄	—	47	4	no	—
597	C₂²×D₄	—	47	4	no	—
598	C₂²×D₄	—	47	4	no	—
599	C₂²×D₄	—	47	4	no	—
600	C₂²×D₄	—	47	4	no	—
601	C₂²×D₄	—	47	16	no	—
602	C₂²×D₄	—	47	1	no	—
603	C₂²×D₄	—	47	2	no	—
604	C₂²×D₄	—	47	2	no	—
605	C₂²×D₄	—	47	2	no	—
606	C₂²×D₄	—	47	4	no	—
607	C₂²×D₄	—	47	16	no	—
608	C₂²×D₄	—	188	8	no	—
609	C₂²×D₄	—	188	8	no	—
610	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
611	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
612	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
613	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
614	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
615	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
616	C₂³×C₄	—	47	4	no	—
617	C₂³×C₄	—	47	2	no	—
618	C₂³×C₄	—	47	4	no	—
619	C₂³×C₄	—	47	4	no	—
620	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
621	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
622	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
623	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
624	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
625	C₄⋊Q₈	—	47	8	no	—
626	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
627	#127	—	47	16	no	—
628	#127	—	47	32	no	—
629	#127	—	47	8	no	—
630	#127	C₂²×D₄₇	1	8	yes	—
631	#126	—	47	32	no	—
632	#126	—	47	32	no	—
633	#126	—	47	16	no	—
634	#125	—	47	8	no	—
635	#124	—	47	32	no	—
636	#124	—	47	16	no	—
637	#124	—	47	8	no	—
638	#124	—	47	16	no	—
639	#124	C₂²×D₄₇	1	16	yes	complemented
640	#123	—	47	16	no	—
641	#123	—	47	32	no	—
642	#123	—	47	32	no	—
643	#123	—	47	32	no	—
644	C₂²⋊Q₈	—	47	32	no	—
645	C₂²⋊Q₈	—	47	8	no	—
646	C₂²⋊Q₈	—	47	16	no	—
647	C₂²⋊Q₈	—	47	16	no	—
648	#121	—	47	32	no	—
649	#121	—	47	32	no	—
650	#121	—	47	32	no	—
651	#121	—	47	32	no	—
652	#121	—	47	8	no	—
653	#121	—	47	16	no	—
654	#121	—	47	16	no	—
655	#121	—	47	16	no	—
656	#121	—	47	16	no	—
657	#121	—	47	16	no	—
658	#121	—	47	16	no	—
659	#121	—	47	32	no	—
660	#121	—	47	32	no	—
661	#121	C₂²×D₄₇	1	8	yes	—
662	#121	C₂²×D₄₇	1	8	yes	complemented
663	#121	C₂²×D₄₇	1	16	yes	complemented
664	#120	—	47	32	no	—
665	#120	—	47	32	no	—
666	#120	—	47	32	no	—
667	#120	—	47	32	no	—
668	C₄×Q₈	—	47	16	no	—
669	C₄×Q₈	—	47	8	no	—
670	C₄×D₄	—	47	16	no	—
671	C₄×D₄	—	47	16	no	—
672	C₄×D₄	—	47	32	no	—
673	C₄×D₄	—	47	8	no	—
674	C₄×D₄	—	47	16	no	—
675	C₄×D₄	—	47	16	no	—
676	C₄×D₄	C₂²×D₄₇	1	8	yes	—
677	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
678	C₄×D₄	C₂²×D₄₇	1	8	yes	complemented
679	#117	—	47	16	no	—
680	#117	—	47	16	no	—
681	C₂×C₄⋊C₄	—	47	1	no	—
682	C₂×C₄⋊C₄	—	47	2	no	—
683	C₂×C₄⋊C₄	—	47	4	no	—
684	C₂×C₄⋊C₄	—	47	16	no	—
685	C₂×C₄⋊C₄	—	47	1	no	—
686	C₂×C₄⋊C₄	—	47	2	no	—
687	C₂×C₄⋊C₄	—	47	2	no	—
688	C₂×C₄⋊C₄	—	47	2	no	—
689	C₂×C₄⋊C₄	—	47	2	no	—
690	C₂×C₄⋊C₄	—	47	4	no	—
691	C₂×C₄⋊C₄	—	47	2	no	—
692	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
695	C₂×C₂²⋊C₄	—	47	4	no	—
696	C₂×C₂²⋊C₄	—	47	4	no	—
697	C₂×C₂²⋊C₄	—	47	2	no	—
698	C₂×C₂²⋊C₄	—	47	2	no	—
699	C₂×C₂²⋊C₄	—	47	4	no	—
700	C₂×C₂²⋊C₄	—	47	2	no	—
701	C₂×C₂²⋊C₄	—	47	2	no	—
702	C₂×C₂²⋊C₄	—	47	2	no	—
703	C₂×C₂²⋊C₄	—	47	4	no	—
704	C₂×C₂²⋊C₄	—	47	4	no	—
705	C₂×C₂²⋊C₄	—	47	4	no	—
706	C₂×C₂²⋊C₄	—	47	4	no	—
707	C₂×C₂²⋊C₄	—	47	32	no	—
708	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
712	C₂×C₄²	—	47	2	no	—
713	C₂×C₄²	—	47	4	no	—
714	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
715	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
716	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
717	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
718	C₂×C₄²	C₂²×D₄₇	1	8	yes	complemented
719	C₂⁴	—	47	2	no	—
720	C₂⁴	—	47	4	no	—
721	C₂⁴	—	47	16	no	—
722	C₂⁴	—	188	8	no	—
723	C₂⁴	—	188	8	no	—
724	C₂⁴	—	188	8	no	—
725	C₂⁴	C₂³×D₄₇	1	2	yes	—
726	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
727	C₂⁴	C₂³×D₄₇	1	2	yes	—
728	#41	—	4	32	no	—
729	#41	—	188	32	no	—
730	#41	—	188	32	no	—
731	#41	—	188	32	no	—
732	C₂×Q₈	—	4	4	no	—
733	C₂×Q₈	—	47	4	no	—
734	C₂×Q₈	—	47	8	no	—
735	C₂×Q₈	—	94	4	no	—
736	C₂×Q₈	—	94	8	no	—
737	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	47	8	no	—
745	C₂×D₄	—	47	16	no	—
746	C₂×D₄	—	47	16	no	—
747	C₂×D₄	—	47	16	no	—
748	C₂×D₄	—	47	16	no	—
749	C₂×D₄	—	47	16	no	—
750	C₂×D₄	—	47	4	no	—
751	C₂×D₄	—	47	8	no	—
752	C₂×D₄	—	47	8	no	—
753	C₂×D₄	—	47	8	no	—
754	C₂×D₄	—	47	16	no	—
755	C₂×D₄	—	94	4	no	—
756	C₂×D₄	—	94	8	no	—
757	C₂×D₄	—	94	8	no	—
758	C₂×D₄	—	188	32	no	—
759	C₂×D₄	—	188	4	no	—
760	C₂×D₄	—	188	8	no	—
761	C₂×D₄	—	188	32	no	—
762	C₂×D₄	—	188	4	no	—
763	C₂×D₄	—	188	8	no	—
764	C₂×D₄	—	188	8	no	—
765	C₂×D₄	—	188	8	no	—
766	C₂×D₄	—	188	8	no	—
767	C₂×D₄	—	188	8	no	—
768	C₂×D₄	C₂³×D₄₇	1	4	yes	—
769	C₂×D₄	C₂³×D₄₇	1	4	yes	—
770	C₂×D₄	C₂³×D₄₇	1	8	yes	—
771	C₂×D₄	C₂³×D₄₇	1	8	yes	—
772	C₂×D₄	C₂³×D₄₇	1	8	yes	—
773	C₂×D₄	C₂³×D₄₇	1	8	yes	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	8	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	47	2	no	—
780	C₂²×C₄	—	47	2	no	—
781	C₂²×C₄	—	47	4	no	—
782	C₂²×C₄	—	47	2	no	—
783	C₂²×C₄	—	47	16	no	—
784	C₂²×C₄	—	47	8	no	—
785	C₂²×C₄	—	47	16	no	—
786	C₂²×C₄	—	47	16	no	—
787	C₂²×C₄	—	94	8	no	—
788	C₂²×C₄	—	188	8	no	—
789	C₂²×C₄	—	188	8	no	—
790	C₂²×C₄	—	188	8	no	—
791	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
792	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
793	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
794	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
795	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
796	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
797	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
798	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
799	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
800	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
801	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
802	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
803	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
804	C₄⋊C₄	—	47	8	no	—
805	C₄⋊C₄	—	47	8	no	—
806	C₄⋊C₄	—	47	8	no	—
807	C₄⋊C₄	—	47	16	no	—
808	C₄⋊C₄	—	47	8	no	—
809	C₄⋊C₄	—	47	4	no	—
810	C₄⋊C₄	—	47	8	no	—
811	C₄⋊C₄	—	47	16	no	—
812	C₄⋊C₄	—	47	4	no	—
813	C₄⋊C₄	—	47	8	no	—
814	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
815	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
816	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
817	C₂²⋊C₄	—	47	16	no	—
818	C₂²⋊C₄	—	47	16	no	—
819	C₂²⋊C₄	—	47	8	no	—
820	C₂²⋊C₄	—	47	8	no	—
821	C₂²⋊C₄	—	47	16	no	—
822	C₂²⋊C₄	—	47	8	no	—
823	C₂²⋊C₄	—	47	8	no	—
824	C₂²⋊C₄	—	47	8	no	—
825	C₂²⋊C₄	—	47	16	no	—
826	C₂²⋊C₄	—	47	16	no	—
827	C₂²⋊C₄	—	47	16	no	—
828	C₂²⋊C₄	—	47	16	no	—
829	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
830	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
831	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
832	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
833	C₄²	—	47	8	no	—
834	C₄²	—	47	16	no	—
835	C₄²	C₂³×D₄₇	1	4	yes	—
836	C₄²	C₂³×D₄₇	1	4	yes	—
837	C₄²	C₂³×D₄₇	1	4	yes	—
838	C₄²	C₂³×D₄₇	1	4	yes	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	4	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	47	4	no	—
849	C₂³	—	47	8	no	—
850	C₂³	—	94	8	no	—
851	C₂³	—	94	4	no	—
852	C₂³	—	94	4	no	—
853	C₂³	—	94	8	no	—
854	C₂³	—	94	8	no	—
855	C₂³	—	94	4	no	—
856	C₂³	—	376	32	no	—
857	C₂³	—	188	16	no	—
858	C₂³	—	188	16	no	—
859	C₂³	—	188	16	no	—
860	C₂³	C₂⁴×D₄₇	1	4	yes	—
861	C₂³	C₂⁴×D₄₇	1	2	yes	—
862	C₂³	C₂⁴×D₄₇	1	4	yes	—
863	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
864	Q₈	—	4	8	no	—
865	Q₈	—	94	8	no	—
866	Q₈	—	94	16	no	—
867	D₄	—	2	8	no	—
868	D₄	—	2	8	no	—
869	D₄	—	4	8	no	—
870	D₄	—	4	8	no	—
871	D₄	—	4	8	no	—
872	D₄	—	4	8	no	—
873	D₄	—	94	8	no	—
874	D₄	—	94	16	no	—
875	D₄	—	94	16	no	—
876	D₄	—	188	8	no	—
877	D₄	—	188	16	no	—
878	D₄	—	188	8	no	—
879	D₄	—	188	16	no	—
880	D₄	—	188	16	no	—
881	D₄	—	188	16	no	—
882	D₄	—	188	16	no	—
883	D₄	—	188	16	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	16	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	16	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	47	4	no	—
896	C₂×C₄	—	47	4	no	—
897	C₂×C₄	—	47	8	no	—
898	C₂×C₄	—	47	4	no	—
899	C₂×C₄	—	94	4	no	—
900	C₂×C₄	—	94	4	no	—
901	C₂×C₄	—	94	8	no	—
902	C₂×C₄	—	94	4	no	—
903	C₂×C₄	—	94	16	no	—
904	C₂×C₄	—	188	16	no	—
905	C₂×C₄	—	188	16	no	—
906	C₂×C₄	—	188	16	no	—
907	C₂×C₄	#13094069	1	4	yes	—
908	C₂×C₄	#13094070	1	4	yes	—
909	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
910	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
911	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
912	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
913	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
914	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
915	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
916	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	4	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	4	8	no	—
927	C₂²	—	4	4	no	—
928	C₂²	—	4	8	no	—
929	C₂²	—	94	8	no	—
930	C₂²	—	94	4	no	—
931	C₂²	—	94	4	no	—
932	C₂²	—	94	8	no	—
933	C₂²	—	94	8	no	—
934	C₂²	—	94	4	no	—
935	C₂²	—	376	32	no	—
936	C₂²	—	188	8	no	—
937	C₂²	—	188	16	no	—
938	C₂²	C₂×#13094069	1	2	yes	—
939	C₂²	C₂×#13094070	1	2	yes	—
940	C₂²	#15689959	1	2	yes	—
941	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
942	C₄	—	2	4	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	94	4	no	—
949	C₄	—	94	4	no	—
950	C₄	—	94	8	no	—
951	C₄	—	94	4	no	—
952	C₄	C₂×#13094069	1	4	yes	—
953	C₄	C₂×#13094070	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	4	4	no	—
957	C₂	—	188	4	no	—
958	C₂	—	188	8	no	—
959	C₂	#20257760	1	4	yes	direct product factor
960	C₂	C₂²×#13094069	1	1	yes	characteristic
961	C₂	C₂²×#13094070	1	1	yes	characteristic
962	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#3546
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20257760	C₂	direct (N × H)
2. C₂×#15689861	C₂	semidirect
3. C₂×#15689843	C₂	semidirect
4. C₂×#15689819	C₂	semidirect
5. C₂×#15689794	C₂	semidirect
6. C₂×#15689791	C₂	semidirect
7. C₂×#15689777	C₂	semidirect
8. C₂×#15689770	C₂	semidirect
9. C₂×#15689769	C₂	semidirect
10. C₂×D₄×D₁₈₈	C₂	semidirect
11. C₂×#15689747	C₂	semidirect
12. C₂×#15689707	C₂	semidirect
13. C₂×#15689701	C₂	semidirect
14. C₂×#15689687	C₂	semidirect
15. C₂×#15689686	C₂	semidirect
16. C₂×#15689673	C₂	semidirect
17. C₂×#15689657	C₂	semidirect
18. C₂×C₄₇×#532	C₂	semidirect
19. C₂²×#10625350	C₂²	semidirect
20. C₂²×#10625350	C₂²	semidirect
21. C₂²×#10625352	C₂²	semidirect
24. #15689861	C₂²	semidirect
25. #15689843	C₂²	semidirect
26. #15689819	C₂²	semidirect
27. #15689794	C₂²	semidirect
28. #15689791	C₂²	semidirect
29. #15689777	C₂²	semidirect
30. #15689770	C₂²	semidirect
31. #15689769	C₂²	semidirect
32. D₄×D₁₈₈	C₂²	semidirect
33. #15689747	C₂²	semidirect
34. #15689707	C₂²	semidirect
35. #15689701	C₂²	semidirect
36. #15689687	C₂²	semidirect
37. #15689686	C₂²	semidirect
38. #15689673	C₂²	semidirect
39. C₂×#13094024	C₂²	semidirect
41. C₂×#13094020	C₂²	semidirect
42. C₂×#13094020	C₂²	semidirect
43. #15689657	C₂²	semidirect
44. C₂×#13094019	C₂²	semidirect
45. C₂×#13094018	C₂²	semidirect
46. C₂×#13094017	C₂²	semidirect
47. C₂×#13094016	C₂²	semidirect
48. C₂×#13094013	C₂²	semidirect
50. C₂×#13094012	C₂²	semidirect
52. C₂×#13094009	C₂²	semidirect
53. C₂×#13094008	C₂²	semidirect
54. C₂×#13094007	C₂²	semidirect
55. C₂×#13094006	C₂²	semidirect
56. C₂×#13094004	C₂²	semidirect
57. C₂×#13094003	C₂²	semidirect
58. C₂×#13094003	C₂²	semidirect
59. C₂×#13094000	C₂²	semidirect
64. C₂×#13093998	C₂²	semidirect
65. C₂×#13093998	C₂²	semidirect
66. C₂×#13093998	C₂²	semidirect
67. C₂×#13093997	C₂²	semidirect
68. C₂×#13093997	C₂²	semidirect
69. C₂×#13093996	C₂²	semidirect
70. C₂×#13093996	C₂²	semidirect
71. C₂×#13093996	C₂²	semidirect
72. C₂×#13093995	C₂²	semidirect
74. C₂×#13093992	C₂²	semidirect
75. C₂×#13093992	C₂²	semidirect
76. C₂×#13093992	C₂²	semidirect
77. C₂×C₄×Dic₉₄	C₂²	semidirect
78. C₂×#13093989	C₂²	semidirect
80. C₂×C₄×D₁₈₈	C₂²	semidirect
81. C₂×C₄×D₁₈₈	C₂²	semidirect
82. C₂×#13093986	C₂²	semidirect
83. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
84. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
85. C₂×#13093983	C₂²	semidirect
86. C₂×#13093981	C₂²	semidirect
87. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
89. C₂²×#41×C₄₇	C₂²	semidirect
90. C₄₇×#532	C₂²	semidirect
91. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
93. C₂×#124×C₄₇	C₂²	semidirect
95. C₂×#121×C₄₇	C₂²	semidirect
96. C₂×#121×C₄₇	C₂²	semidirect
98. C₂×C₄×D₄×C₄₇	C₂²	semidirect
99. C₂×C₄×D₄×C₄₇	C₂²	semidirect
100. C₂²×C₄²×C₄₇	C₂²	semidirect
104. C₂×#10625350	C₂³	semidirect
105. C₂×#10625350	C₂³	semidirect
107. C₂×#10625352	C₂³	semidirect
129. #13094024	C₂³	semidirect
131. #13094020	C₂³	semidirect
132. #13094020	C₂³	semidirect
133. #13094019	C₂³	semidirect
134. #13094018	C₂³	semidirect
135. #13094017	C₂³	semidirect
136. #13094016	C₂³	semidirect
137. #13094013	C₂³	semidirect
139. #13094012	C₂³	semidirect
141. #13094009	C₂³	semidirect
142. #13094008	C₂³	semidirect
143. #13094007	C₂³	semidirect
144. #13094006	C₂³	semidirect
145. #13094004	C₂³	semidirect
146. #13094003	C₂³	semidirect
147. #13094003	C₂³	semidirect
148. #13094000	C₂³	semidirect
153. #13093998	C₂³	semidirect
154. #13093998	C₂³	semidirect
155. #13093998	C₂³	semidirect
156. #13093997	C₂³	semidirect
157. #13093997	C₂³	semidirect
158. #13093996	C₂³	semidirect
159. #13093996	C₂³	semidirect
160. #13093996	C₂³	semidirect
161. #13093995	C₂³	semidirect
163. #13093992	C₂³	semidirect
164. #13093992	C₂³	semidirect
165. #13093992	C₂³	semidirect
166. C₄×Dic₉₄	C₂³	semidirect
167. #13093989	C₂³	semidirect
169. C₄×D₁₈₈	C₂³	semidirect
170. C₄×D₁₈₈	C₂³	semidirect
171. #13093986	C₂³	semidirect
172. C₄×C₂²⋊D₄₇	C₂³	semidirect
173. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
174. #13093983	C₂³	semidirect
175. #13093981	C₂³	semidirect
181. C₂×C₄⋊Dic₄₇	C₂³	semidirect
199. C₂²⋊C₄×D₄₇	C₂³	semidirect
203. C₂×#41×C₄₇	C₂³	semidirect
216. C₄⋊Q₈×C₄₇	C₂³	semidirect
218. #124×C₄₇	C₂³	semidirect
220. #121×C₄₇	C₂³	semidirect
221. #121×C₄₇	C₂³	semidirect
223. C₄×D₄×C₄₇	C₂³	semidirect
224. C₄×D₄×C₄₇	C₂³	semidirect
236. C₂×C₄²×C₄₇	C₂³	semidirect
489. C₂×#532	D₄₇	semidirect
494. C₂×C₄₇	#3546	semidirect
503. C₂²×#41	C₂×D₄₇	semidirect
521. #532	C₂×D₄₇	semidirect
523. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
537. C₂×#124	C₂×D₄₇	semidirect
560. C₂×#121	C₂×D₄₇	semidirect
561. C₂×#121	C₂×D₄₇	semidirect
575. C₂×C₄×D₄	C₂×D₄₇	semidirect
576. C₂×C₄×D₄	C₂×D₄₇	semidirect
581. C₂²×C₄²	C₂×D₄₇	semidirect
582. C₄₇	C₂×#3546	semidirect
591. C₂×#41	C₂²×D₄₇	semidirect
626. C₄⋊Q₈	C₂²×D₄₇	semidirect
639. #124	C₂²×D₄₇	semidirect
662. #121	C₂²×D₄₇	semidirect
663. #121	C₂²×D₄₇	semidirect
677. C₄×D₄	C₂²×D₄₇	semidirect
678. C₄×D₄	C₂²×D₄₇	semidirect
718. C₂×C₄²	C₂²×D₄₇	semidirect
959. C₂	#20257760	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257760	2
C₂×#15689861	2
C₂×#15689843	2
C₂×#15689819	2
C₂×#15689794	2
C₂×#15689791	2
C₂×#15689777	2
C₂×#15689770	2
C₂×#15689769	2
C₂×D₄×D₁₈₈	2
C₂×#15689747	2
C₂×#15689707	2
C₂×#15689701	2
C₂×#15689687	2
C₂×#15689686	2
C₂×#15689673	2
C₂×#15689657	2
C₂×C₄₇×#532	2
C₂×#3546	47

Subgroups — C2×#20257760 #27123925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257760 #27123925