Subgroups — C₂×#19148320 #26004937

Order 11008.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148320	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583614	C₂	1	2	yes	maximal, complemented
3	C₂×#14583599	C₂	1	2	yes	maximal, complemented
4	C₂×#14583599	C₂	1	2	yes	maximal, complemented
5	C₂×#14583575	C₂	1	4	yes	maximal, complemented
6	C₂×#14583554	C₂	1	2	yes	maximal, complemented
7	C₂×#14583539	C₂	1	4	yes	maximal, complemented
8	C₂×#14583527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14583514	C₂	1	2	yes	maximal, complemented
10	C₂×#14583500	C₂	1	2	yes	maximal, complemented
11	C₂×#14583466	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14583446	C₂	1	2	yes	maximal, complemented
13	C₂×#14583431	C₂	1	2	yes	maximal, complemented
14	C₂×#14583411	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13063296	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14583379	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10621898	C₂²	1	1	yes	characteristic
20	C₂²×#10621898	C₂²	1	4	yes	complemented
21	C₂³×C₂²⋊D₄₃	C₂²	1	2	yes	—
22	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic
23	#14583614	C₂²	1	32	yes	complemented
24	#14583599	C₂²	1	32	yes	complemented
25	#14583599	C₂²	1	32	yes	complemented
26	#14583575	C₂²	1	64	yes	complemented
27	#14583554	C₂²	1	32	yes	complemented
28	#14583539	C₂²	1	64	yes	complemented
29	#14583527	C₂²	1	16	yes	complemented
30	#14583514	C₂²	1	32	yes	complemented
31	#14583500	C₂²	1	32	yes	complemented
32	#14583466	C₂²	1	16	yes	complemented
33	#14583446	C₂²	1	32	yes	complemented
34	C₂×#13063325	C₂²	1	2	yes	complemented
35	C₂×#13063324	C₂²	1	2	yes	complemented
36	C₂×#13063321	C₂²	1	2	yes	complemented
37	#14583431	C₂²	1	32	yes	complemented
38	C₂×#13063318	C₂²	1	4	yes	complemented
39	C₂×#13063318	C₂²	1	4	yes	complemented
40	C₂×#13063317	C₂²	1	2	yes	complemented
41	C₂×#13063316	C₂²	1	2	yes	complemented
42	C₂×#13063312	C₂²	1	2	yes	complemented
43	C₂×#13063311	C₂²	1	4	yes	complemented
44	C₂×#13063311	C₂²	1	4	yes	complemented
45	#14583411	C₂²	1	16	yes	complemented
46	C₂×#13063309	C₂²	1	2	yes	—
47	C₂×#13063308	C₂²	1	4	yes	complemented
48	C₂×#13063308	C₂²	1	4	yes	complemented
49	C₂×#13063307	C₂²	1	4	yes	complemented
50	C₂×#13063307	C₂²	1	4	yes	complemented
51	C₂×#13063305	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13063305	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13063304	C₂²	1	4	yes	complemented
54	C₂×#13063302	C₂²	1	4	yes	—
55	C₂×#13063300	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13063300	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13063299	C₂²	1	4	yes	complemented
58	C₂×#13063298	C₂²	1	4	yes	complemented
59	C₂×#13063298	C₂²	1	4	yes	complemented
60	C₂×#13063296	C₂²	1	2	yes	—
61	C₂×#13063296	C₂²	1	2	yes	—
62	C₂×#13063296	C₂²	1	2	yes	—
63	C₂×#13063296	C₂²	1	2	yes	—
64	C₂×#13063296	C₂²	1	16	yes	complemented
65	C₂×#13063296	C₂²	1	2	yes	complemented
66	C₂×#13063296	C₂²	1	2	yes	complemented
67	C₂×#13063295	C₂²	1	2	yes	—
68	C₂×#13063294	C₂²	1	4	yes	—
69	#14583379	C₂²	1	16	yes	complemented
70	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
71	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
72	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
73	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
75	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
76	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
77	C₂×#13063284	C₂²	1	1	yes	characteristic
78	C₂×#13063284	C₂²	1	4	yes	complemented
79	C₂×#13063283	C₂²	1	2	yes	complemented
80	C₂×#13063283	C₂²	1	1	yes	characteristic, complemented
81	C₂×#13063283	C₂²	1	1	yes	characteristic, complemented
82	C₂×#13063282	C₂²	1	2	yes	complemented
83	C₂×#13063281	C₂²	1	2	yes	—
84	#117×D₄₃	C₂²	1	16	yes	complemented
85	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
86	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
87	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
89	C₂²×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
90	C₂×C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
91	C₂×C₄²×D₄₃	C₂²	1	2	yes	complemented
92	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
93	C₄₃×#518	C₂²	1	16	yes	complemented
94	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
95	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
96	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
97	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
98	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
99	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
100	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
101	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
102	C₂×#10621898	—	2	8	no	—
103	C₂×#10621898	—	4	16	no	—
104	C₂×#10621898	C₂³	1	8	yes	—
105	C₂×#10621898	C₂³	1	32	yes	complemented
106	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
107	C₂²×Dic₈₆	C₂³	1	4	yes	—
108	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
109	C₂²×D₁₇₂	C₂³	1	2	yes	—
110	C₂²×D₁₇₂	C₂³	1	2	yes	—
111	C₂²×C₂²⋊D₄₃	—	4	8	no	—
112	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
113	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₄₃	C₂³	1	16	yes	—
118	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
119	C₂³×Dic₄₃	C₂³	1	2	yes	—
120	C₂²×C₄×D₄₃	—	2	8	no	—
121	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
125	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
126	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
129	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
130	#13063325	C₂³	1	16	yes	complemented
131	#13063324	C₂³	1	16	yes	complemented
132	#13063321	C₂³	1	16	yes	complemented
133	#13063318	C₂³	1	32	yes	complemented
134	#13063318	C₂³	1	32	yes	complemented
135	#13063317	C₂³	1	16	yes	complemented
136	#13063316	C₂³	1	16	yes	complemented
137	#13063312	C₂³	1	16	yes	complemented
138	#13063311	C₂³	1	32	yes	complemented
139	#13063311	C₂³	1	32	yes	complemented
140	#13063309	C₂³	1	16	yes	—
141	#13063308	C₂³	1	32	yes	complemented
142	#13063308	C₂³	1	32	yes	complemented
143	#13063307	C₂³	1	32	yes	complemented
144	#13063307	C₂³	1	32	yes	complemented
145	#13063305	C₂³	1	8	yes	complemented
146	#13063305	C₂³	1	8	yes	complemented
147	#13063304	C₂³	1	32	yes	complemented
148	#13063302	C₂³	1	32	yes	—
149	#13063300	C₂³	1	8	yes	complemented
150	#13063300	C₂³	1	8	yes	complemented
151	#13063299	C₂³	1	32	yes	complemented
152	#13063298	C₂³	1	32	yes	complemented
153	#13063298	C₂³	1	32	yes	complemented
154	#13063296	C₂³	1	16	yes	—
155	#13063296	C₂³	1	16	yes	—
156	#13063296	C₂³	1	16	yes	—
157	#13063296	C₂³	1	16	yes	—
158	#13063296	C₂³	1	16	yes	complemented
159	#13063296	C₂³	1	16	yes	complemented
160	#13063295	C₂³	1	16	yes	—
161	#13063294	C₂³	1	32	yes	—
162	C₄×Dic₈₆	C₂³	1	16	yes	complemented
163	C₄×D₁₇₂	C₂³	1	16	yes	complemented
164	C₄×D₁₇₂	C₂³	1	16	yes	complemented
165	C₄×D₁₇₂	C₂³	1	16	yes	complemented
166	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
167	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
168	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	—
169	#13063284	C₂³	1	8	yes	—
170	#13063284	C₂³	1	32	yes	complemented
171	#13063283	C₂³	1	8	yes	complemented
172	#13063283	C₂³	1	16	yes	complemented
173	#13063283	C₂³	1	8	yes	complemented
174	#13063282	C₂³	1	16	yes	complemented
175	#13063281	C₂³	1	16	yes	—
176	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
177	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
181	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
183	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
184	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
185	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
186	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
187	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
188	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
189	C₄⋊C₄×D₄₃	C₂³	1	8	yes	complemented
190	C₄⋊C₄×D₄₃	C₂³	1	16	yes	complemented
191	C₄⋊C₄×D₄₃	C₂³	1	8	yes	complemented
192	C₂×C₂²⋊Dic₄₃	C₂³	1	16	yes	—
193	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
195	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
196	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
197	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
200	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
201	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
202	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
203	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
204	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
205	C₂²⋊C₄×D₄₃	C₂³	1	16	yes	—
206	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
207	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
208	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
209	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
210	C₄²×D₄₃	C₂³	1	16	yes	complemented
211	C₂⁵×C₄₃	C₂³	1	2	yes	—
212	C₂²×D₄×C₄₃	—	2	8	no	—
213	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
214	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
215	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
216	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
217	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
218	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₄₃	C₂³	1	16	yes	complemented
220	C₄×D₄×C₄₃	C₂³	1	16	yes	complemented
221	C₄×D₄×C₄₃	C₂³	1	16	yes	complemented
222	C₄×D₄×C₄₃	C₂³	1	16	yes	complemented
223	#117×C₄₃	C₂³	1	8	yes	—
224	#117×C₄₃	C₂³	1	8	yes	—
225	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
233	C₂×C₂²⋊C₄×C₄₃	C₂³	1	32	yes	—
234	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
235	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
236	C₂⁴×C₄₃	—	2	8	no	—
237	C₂⁴×C₄₃	—	4	4	no	—
238	C₂⁴×C₄₃	—	4	4	no	—
239	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
240	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₄₃	C₂⁴	1	8	yes	—
242	C₂³×D₄₃	—	2	4	no	—
243	C₂³×D₄₃	—	2	4	no	—
244	C₂³×D₄₃	—	4	2	no	—
245	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
246	C₂³×D₄₃	C₂⁴	1	2	yes	—
247	C₂³×D₄₃	C₂⁴	1	4	yes	—
248	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₄₃	—	2	8	no	—
250	C₂×D₄×C₄₃	—	2	8	no	—
251	C₂×D₄×C₄₃	—	2	32	no	—
252	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
253	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
254	C₂²×C₄×C₄₃	—	4	8	no	—
255	C₂²×C₄×C₄₃	—	4	8	no	—
256	C₂²×C₄×C₄₃	#41	1	8	yes	complemented
257	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
262	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
263	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
266	C₂×C₂²⋊D₄₃	—	2	8	no	—
267	C₂×C₂²⋊D₄₃	—	2	16	no	—
268	C₂×C₂²⋊D₄₃	—	4	8	no	—
269	C₂×C₂²⋊D₄₃	—	4	8	no	—
270	C₂×C₂²⋊D₄₃	—	4	8	no	—
271	C₂×C₂²⋊D₄₃	—	4	32	no	—
272	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
273	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
274	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
276	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
277	C₂²×Dic₄₃	—	2	4	no	—
278	C₂²×Dic₄₃	—	4	4	no	—
279	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
280	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
281	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
282	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
283	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
284	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
285	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
286	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
287	#10621898	—	2	32	no	—
288	#10621898	—	4	64	no	—
289	C₂×D₁₇₂	—	2	4	no	—
290	C₂×D₁₇₂	—	2	8	no	—
291	C₂×D₁₇₂	—	4	4	no	—
292	C₂×D₁₇₂	C₂⁴	1	4	yes	—
293	C₂×D₁₇₂	C₂⁴	1	8	yes	—
294	C₂×D₁₇₂	C₂⁴	1	8	yes	—
295	C₂×C₄×D₄₃	—	2	4	no	—
296	C₂×C₄×D₄₃	—	2	4	no	—
297	C₂×C₄×D₄₃	—	2	4	no	—
298	C₂×C₄×D₄₃	—	2	4	no	—
299	C₂×C₄×D₄₃	—	2	8	no	—
300	C₂×C₄×D₄₃	—	2	32	no	—
301	C₂×C₄×D₄₃	—	2	8	no	—
302	C₂×C₄×D₄₃	—	4	4	no	—
303	C₂×C₄×D₄₃	—	4	8	no	—
304	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
305	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
306	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
307	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
308	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
309	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
310	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
311	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
312	C₂×Dic₈₆	—	2	4	no	—
313	C₂×Dic₈₆	—	4	8	no	—
314	C₂×Dic₈₆	C₂⁴	1	4	yes	—
315	C₂×Dic₈₆	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
317	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
320	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
323	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
324	C₄²×C₄₃	C₂⁴	1	8	yes	—
325	C₄²×C₄₃	C₂⁴	1	8	yes	—
326	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
327	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
328	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
329	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
330	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
331	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
332	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
333	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
334	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
335	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
336	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
337	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
338	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
339	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
340	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
341	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
342	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
343	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
344	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
345	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
346	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
347	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
348	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
349	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
350	C₄×Dic₄₃	C₂⁴	1	8	yes	—
351	C₄×Dic₄₃	C₂⁴	1	8	yes	—
352	C₄×Dic₄₃	C₂⁴	1	8	yes	—
353	C₄×Dic₄₃	C₂⁴	1	16	yes	—
354	C₂³×C₄₃	—	2	2	no	—
355	C₂³×C₄₃	—	2	2	no	—
356	C₂³×C₄₃	—	2	8	no	—
357	C₂³×C₄₃	—	2	8	no	—
358	C₂³×C₄₃	—	2	8	no	—
359	C₂³×C₄₃	—	2	16	no	—
360	C₂³×C₄₃	—	4	8	no	—
361	C₂³×C₄₃	—	4	8	no	—
362	C₂³×C₄₃	—	8	16	no	—
363	C₂³×C₄₃	C₂×#41	1	4	yes	—
364	C₂³×C₄₃	C₂⁵	1	8	yes	—
365	C₂³×C₄₃	C₂⁵	1	2	yes	—
366	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
367	C₂²×D₄₃	—	2	2	no	—
368	C₂²×D₄₃	—	2	2	no	—
369	C₂²×D₄₃	—	2	8	no	—
370	C₂²×D₄₃	—	2	2	no	—
371	C₂²×D₄₃	—	2	4	no	—
372	C₂²×D₄₃	—	2	4	no	—
373	C₂²×D₄₃	—	2	2	no	—
374	C₂²×D₄₃	—	2	2	no	—
375	C₂²×D₄₃	—	2	4	no	—
376	C₂²×D₄₃	—	2	8	no	—
377	C₂²×D₄₃	—	4	4	no	—
378	C₂²×D₄₃	—	4	16	no	—
379	C₂²×D₄₃	H(5,𝔽₂)	1	4	yes	—
380	C₂²×D₄₃	C₂⁵	1	2	yes	—
381	C₂²×D₄₃	C₂⁵	1	4	yes	—
382	C₂²×D₄₃	C₂⁵	1	2	yes	—
383	D₄×C₄₃	—	2	16	no	—
384	D₄×C₄₃	—	2	16	no	—
385	C₂×C₄×C₄₃	—	2	4	no	—
386	C₂×C₄×C₄₃	—	2	4	no	—
387	C₂×C₄×C₄₃	—	2	4	no	—
388	C₂×C₄×C₄₃	—	2	4	no	—
389	C₂×C₄×C₄₃	—	4	16	no	—
390	C₂×C₄×C₄₃	—	4	16	no	—
391	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
392	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
393	C₂×C₄×C₄₃	C₂×#41	1	16	yes	complemented
394	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
395	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
396	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
397	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
398	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
399	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
400	C₂²⋊D₄₃	—	2	16	no	—
401	C₂²⋊D₄₃	—	2	32	no	—
402	C₂²⋊D₄₃	—	4	16	no	—
403	C₂²⋊D₄₃	—	4	16	no	—
404	C₂²⋊D₄₃	—	4	16	no	—
405	C₂×Dic₄₃	—	2	4	no	—
406	C₂×Dic₄₃	—	2	8	no	—
407	C₂×Dic₄₃	—	2	2	no	—
408	C₂×Dic₄₃	—	2	2	no	—
409	C₂×Dic₄₃	—	2	4	no	—
410	C₂×Dic₄₃	—	2	8	no	—
411	C₂×Dic₄₃	—	2	4	no	—
412	C₂×Dic₄₃	—	4	8	no	—
413	C₂×Dic₄₃	C₂⁵	1	2	yes	—
414	C₂×Dic₄₃	C₂⁵	1	4	yes	—
415	C₂×Dic₄₃	C₂⁵	1	4	yes	—
416	C₂×Dic₄₃	C₂⁵	1	4	yes	—
417	C₂×Dic₄₃	C₂⁵	1	8	yes	—
418	C₂×Dic₄₃	C₂⁵	1	2	yes	—
419	D₁₇₂	—	2	16	no	—
420	D₁₇₂	—	2	8	no	—
421	D₁₇₂	—	4	8	no	—
422	C₄×D₄₃	—	2	16	no	—
423	C₄×D₄₃	—	2	8	no	—
424	C₄×D₄₃	—	2	8	no	—
425	C₄×D₄₃	—	2	8	no	—
426	C₄×D₄₃	—	2	8	no	—
427	C₄×D₄₃	—	2	16	no	—
428	C₄×D₄₃	—	4	8	no	—
429	C₄×D₄₃	—	4	16	no	—
430	Dic₈₆	—	2	8	no	—
431	Dic₈₆	—	4	16	no	—
432	C₂×#3494	—	43	1	no	maximal, Sylow
433	C₂²×C₄₃	—	2	2	no	—
434	C₂²×C₄₃	—	2	2	no	—
435	C₂²×C₄₃	—	2	8	no	—
436	C₂²×C₄₃	—	2	8	no	—
437	C₂²×C₄₃	—	2	8	no	—
438	C₂²×C₄₃	—	2	8	no	—
439	C₂²×C₄₃	—	4	16	no	—
440	C₂²×C₄₃	—	8	16	no	—
441	C₂²×C₄₃	C₂²×#41	1	4	yes	—
442	C₂²×C₄₃	C₂²×#41	1	2	yes	—
443	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₂²×C₄₃	#585	1	2	yes	—
445	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
446	C₂×D₄₃	—	2	2	no	—
447	C₂×D₄₃	—	2	2	no	—
448	C₂×D₄₃	—	2	8	no	—
449	C₂×D₄₃	—	2	2	no	—
450	C₂×D₄₃	—	2	4	no	—
451	C₂×D₄₃	—	2	2	no	—
452	C₂×D₄₃	—	2	4	no	—
453	C₂×D₄₃	—	2	2	no	—
454	C₂×D₄₃	—	2	4	no	—
455	C₂×D₄₃	—	4	16	no	—
456	C₂×D₄₃	—	4	8	no	—
457	C₂×D₄₃	—	4	4	no	—
458	C₂×D₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
459	C₄×C₄₃	—	2	4	no	—
460	C₄×C₄₃	—	2	4	no	—
461	C₄×C₄₃	—	2	4	no	—
462	C₄×C₄₃	—	2	4	no	—
463	C₄×C₄₃	C₂²×#41	1	4	yes	—
464	C₄×C₄₃	C₂²×#41	1	4	yes	—
465	Dic₄₃	—	2	4	no	—
466	Dic₄₃	—	2	2	no	—
467	Dic₄₃	—	2	2	no	—
468	Dic₄₃	—	2	4	no	—
469	Dic₄₃	—	2	8	no	—
470	Dic₄₃	—	2	4	no	—
471	#3494	—	43	32	no	—
472	C₂×#555	—	43	2	no	—
473	C₂×#553	—	43	2	no	—
474	C₂×#553	—	43	2	no	—
475	C₂×#551	—	43	4	no	—
476	C₂×#547	—	43	2	no	—
477	C₂×#546	—	43	4	no	—
478	C₂×#544	—	43	1	no	—
479	C₂×#542	—	43	2	no	—
480	C₂×#540	—	43	2	no	—
481	C₂×#535	—	43	1	no	—
482	C₂×#532	—	43	2	no	—
483	C₂×#529	—	43	2	no	—
484	C₂×#525	—	43	1	no	—
485	C₂²×#121	—	43	1	no	—
486	C₂×#520	—	43	1	no	—
487	C₂×#518	D₄₃	1	1	yes	characteristic, complemented
488	C₂²×#117	—	43	1	no	—
489	C₂×C₄₃	—	2	4	no	—
490	C₂×C₄₃	—	4	8	no	—
491	C₂×C₄₃	#3494	1	4	yes	complemented
492	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
493	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄₃	C₂×#585	1	1	yes	characteristic
495	D₄₃	—	2	4	no	—
496	D₄₃	—	4	4	no	—
497	D₄₃	—	4	2	no	—
498	C₂²×#41	—	43	1	no	—
499	C₂²×#41	—	43	4	no	—
500	C₂³×D₄	—	43	2	no	—
501	C₂³×D₄	C₂×D₄₃	1	1	yes	characteristic
502	C₂⁴×C₄	—	43	1	no	—
503	#555	—	43	32	no	—
504	#553	—	43	32	no	—
505	#553	—	43	32	no	—
506	#551	—	43	64	no	—
507	#547	—	43	32	no	—
508	#546	—	43	64	no	—
509	#544	—	43	16	no	—
510	#542	—	43	32	no	—
511	#540	—	43	32	no	—
512	#535	—	43	16	no	—
513	#532	—	43	32	no	—
514	C₂×C₄⋊Q₈	—	43	2	no	—
515	C₂×C₄⋊Q₈	—	43	2	no	—
516	C₂×#127	—	43	2	no	—
517	#529	—	43	32	no	—
518	C₂×#126	—	43	4	no	—
519	C₂×#126	—	43	4	no	—
520	C₂×#125	—	43	2	no	—
521	C₂×#125	—	43	2	no	—
522	C₂×#124	—	43	2	no	—
523	C₂×#124	—	43	4	no	—
524	C₂×#124	—	43	4	no	—
525	#525	—	43	16	no	—
526	C₂×#123	—	43	4	no	—
527	C₂×#123	—	43	4	no	—
528	C₂×#123	—	43	4	no	—
529	C₂×#123	—	43	4	no	—
530	C₂×#123	—	43	2	no	—
531	C₂×C₂²⋊Q₈	—	43	4	no	—
532	C₂×C₂²⋊Q₈	—	43	1	no	—
533	C₂×C₂²⋊Q₈	—	43	1	no	—
534	C₂×C₂²⋊Q₈	—	43	4	no	—
535	C₂×#121	—	43	2	no	—
536	C₂×#121	—	43	2	no	—
537	C₂×#121	—	43	2	no	—
538	C₂×#121	—	43	2	no	—
539	C₂×#121	—	43	16	no	—
540	C₂×#121	—	43	2	no	—
541	C₂×#121	—	43	2	no	—
542	C₂×#121	—	43	4	no	—
543	C₂×#121	—	43	1	no	—
544	C₂×#121	—	43	1	no	—
545	C₂×#121	—	43	4	no	—
546	C₂×#121	—	43	4	no	—
547	C₂×#120	—	43	4	no	—
548	C₂×#120	—	43	2	no	—
549	#520	—	43	16	no	—
550	#518	C₂×D₄₃	1	16	yes	complemented
551	C₂×C₄×Q₈	—	43	2	no	—
552	C₂×C₄×D₄	—	43	4	no	—
553	C₂×C₄×D₄	—	43	4	no	—
554	C₂×C₄×D₄	—	43	4	no	—
555	C₂×C₄×D₄	—	43	2	no	—
556	C₂×C₄×D₄	—	43	2	no	—
557	C₂×C₄×D₄	—	43	2	no	—
558	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
559	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
560	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
561	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
562	C₂×#117	—	43	1	no	—
563	C₂×#117	—	43	4	no	—
564	C₂×#117	—	43	16	no	—
565	C₂×#117	—	43	1	no	—
566	C₂×#117	—	43	1	no	—
567	C₂×#117	—	43	2	no	—
568	C₂×#117	—	43	2	no	—
569	C₂×#117	—	43	2	no	—
570	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
571	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
572	C₂²×C₄⋊C₄	—	43	1	no	—
573	C₂²×C₄⋊C₄	—	43	1	no	—
574	C₂²×C₄⋊C₄	—	43	1	no	—
575	C₂²×C₄⋊C₄	—	43	2	no	—
576	C₂²×C₂²⋊C₄	—	43	2	no	—
577	C₂²×C₂²⋊C₄	—	43	2	no	—
578	C₂²×C₂²⋊C₄	C₂×D₄₃	1	4	yes	—
579	C₂²×C₄²	—	43	2	no	—
580	C₄₃	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
581	C₂⁵	—	43	1	no	—
582	C₂⁵	C₂²×D₄₃	1	2	yes	—
583	C₂×#41	—	43	8	no	—
584	C₂×#41	—	43	32	no	—
585	C₂×#41	—	86	8	no	—
586	C₂×#41	—	172	16	no	—
587	C₂²×Q₈	—	43	1	no	—
588	C₂²×Q₈	—	43	4	no	—
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	43	2	no	—
591	C₂²×D₄	—	43	4	no	—
592	C₂²×D₄	—	43	4	no	—
593	C₂²×D₄	—	43	4	no	—
594	C₂²×D₄	—	43	4	no	—
595	C₂²×D₄	—	43	16	no	—
596	C₂²×D₄	—	43	1	no	—
597	C₂²×D₄	—	43	2	no	—
598	C₂²×D₄	—	43	2	no	—
599	C₂²×D₄	—	172	8	no	—
600	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
601	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
602	C₂²×D₄	C₂²×D₄₃	1	8	yes	—
603	C₂³×C₄	—	43	1	no	—
604	C₂³×C₄	—	43	2	no	—
605	C₂³×C₄	—	43	2	no	—
606	C₂³×C₄	—	43	1	no	—
607	C₂³×C₄	—	43	2	no	—
608	C₂³×C₄	—	43	1	no	—
609	C₂³×C₄	—	43	1	no	—
610	C₂³×C₄	—	43	8	no	—
611	C₂³×C₄	—	43	1	no	—
612	C₂³×C₄	—	43	2	no	—
613	C₂³×C₄	—	43	4	no	—
614	C₂³×C₄	—	86	8	no	—
615	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
616	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
617	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
618	C₄⋊Q₈	—	43	16	no	—
619	C₄⋊Q₈	—	43	16	no	—
620	#127	—	43	16	no	—
621	#126	—	43	32	no	—
622	#126	—	43	32	no	—
623	#125	—	43	16	no	—
624	#125	—	43	16	no	—
625	#124	—	43	16	no	—
626	#124	—	43	32	no	—
627	#124	—	43	32	no	—
628	#123	—	43	32	no	—
629	#123	—	43	32	no	—
630	#123	—	43	16	no	—
631	#123	—	43	32	no	—
632	#123	—	43	32	no	—
633	C₂²⋊Q₈	—	43	32	no	—
634	C₂²⋊Q₈	—	43	8	no	—
635	C₂²⋊Q₈	—	43	8	no	—
636	C₂²⋊Q₈	—	43	32	no	—
637	#121	—	43	16	no	—
638	#121	—	43	16	no	—
639	#121	—	43	16	no	—
640	#121	—	43	16	no	—
641	#121	—	43	16	no	—
642	#121	—	43	16	no	—
643	#121	—	43	32	no	—
644	#121	—	43	8	no	—
645	#121	—	43	8	no	—
646	#121	—	43	32	no	—
647	#121	—	43	32	no	—
648	#120	—	43	32	no	—
649	#120	—	43	16	no	—
650	C₄×Q₈	—	43	16	no	—
651	C₄×D₄	—	43	32	no	—
652	C₄×D₄	—	43	32	no	—
653	C₄×D₄	—	43	32	no	—
654	C₄×D₄	—	43	16	no	—
655	C₄×D₄	—	43	16	no	—
656	C₄×D₄	—	43	16	no	—
657	C₄×D₄	C₂²×D₄₃	1	16	yes	complemented
658	C₄×D₄	C₂²×D₄₃	1	16	yes	complemented
659	C₄×D₄	C₂²×D₄₃	1	16	yes	complemented
660	C₄×D₄	C₂²×D₄₃	1	16	yes	complemented
661	#117	—	43	8	no	—
662	#117	—	43	32	no	—
663	#117	—	43	8	no	—
664	#117	—	43	8	no	—
665	#117	—	43	16	no	—
666	#117	—	43	16	no	—
667	#117	—	43	16	no	—
668	#117	C₂²×D₄₃	1	8	yes	—
669	#117	C₂²×D₄₃	1	8	yes	—
670	C₂×C₄⋊C₄	—	43	2	no	—
671	C₂×C₄⋊C₄	—	43	1	no	—
672	C₂×C₄⋊C₄	—	43	1	no	—
673	C₂×C₄⋊C₄	—	43	2	no	—
674	C₂×C₄⋊C₄	—	43	2	no	—
675	C₂×C₄⋊C₄	—	43	2	no	—
676	C₂×C₄⋊C₄	—	43	4	no	—
677	C₂×C₄⋊C₄	—	43	8	no	—
678	C₂×C₄⋊C₄	—	43	2	no	—
679	C₂×C₄⋊C₄	—	43	4	no	—
680	C₂×C₄⋊C₄	—	43	4	no	—
681	C₂×C₄⋊C₄	—	43	4	no	—
682	C₂×C₄⋊C₄	—	43	2	no	—
683	C₂×C₄⋊C₄	—	43	8	no	—
684	C₂×C₄⋊C₄	—	43	8	no	—
685	C₂×C₄⋊C₄	—	43	16	no	—
686	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	—	43	2	no	—
691	C₂×C₂²⋊C₄	—	43	4	no	—
692	C₂×C₂²⋊C₄	—	43	4	no	—
693	C₂×C₂²⋊C₄	—	43	16	no	—
694	C₂×C₂²⋊C₄	—	43	4	no	—
695	C₂×C₂²⋊C₄	—	43	4	no	—
696	C₂×C₂²⋊C₄	—	43	2	no	—
697	C₂×C₂²⋊C₄	—	43	2	no	—
698	C₂×C₂²⋊C₄	—	43	4	no	—
699	C₂×C₂²⋊C₄	—	43	2	no	—
700	C₂×C₂²⋊C₄	—	43	2	no	—
701	C₂×C₂²⋊C₄	—	43	2	no	—
702	C₂×C₂²⋊C₄	—	43	2	no	—
703	C₂×C₂²⋊C₄	—	43	16	no	—
704	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₄₃	1	32	yes	—
709	C₂×C₄²	—	43	2	no	—
710	C₂×C₄²	—	43	4	no	—
711	C₂×C₄²	—	43	2	no	—
712	C₂×C₄²	—	43	2	no	—
713	C₂×C₄²	—	43	16	no	—
714	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
715	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
716	C₂⁴	—	2	8	no	—
717	C₂⁴	—	4	4	no	—
718	C₂⁴	—	4	4	no	—
719	C₂⁴	—	43	1	no	—
720	C₂⁴	—	43	1	no	—
721	C₂⁴	—	43	2	no	—
722	C₂⁴	—	43	4	no	—
723	C₂⁴	—	86	4	no	—
724	C₂⁴	—	86	4	no	—
725	C₂⁴	—	172	2	no	—
726	C₂⁴	C₂³×D₄₃	1	4	yes	—
727	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
728	C₂⁴	C₂³×D₄₃	1	8	yes	—
729	#41	—	86	32	no	—
730	#41	—	172	64	no	—
731	C₂×Q₈	—	43	4	no	—
732	C₂×Q₈	—	43	16	no	—
733	C₂×Q₈	—	86	4	no	—
734	C₂×Q₈	—	172	8	no	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	32	no	—
738	C₂×D₄	—	43	8	no	—
739	C₂×D₄	—	43	16	no	—
740	C₂×D₄	—	43	16	no	—
741	C₂×D₄	—	43	16	no	—
742	C₂×D₄	—	43	16	no	—
743	C₂×D₄	—	43	4	no	—
744	C₂×D₄	—	43	8	no	—
745	C₂×D₄	—	43	8	no	—
746	C₂×D₄	—	86	8	no	—
747	C₂×D₄	—	86	16	no	—
748	C₂×D₄	—	86	8	no	—
749	C₂×D₄	—	86	4	no	—
750	C₂×D₄	—	172	4	no	—
751	C₂×D₄	—	172	8	no	—
752	C₂×D₄	—	172	8	no	—
753	C₂×D₄	—	172	8	no	—
754	C₂×D₄	—	172	32	no	—
755	C₂×D₄	C₂³×D₄₃	1	8	yes	—
756	C₂×D₄	C₂³×D₄₃	1	8	yes	—
757	C₂²×C₄	—	4	8	no	—
758	C₂²×C₄	—	4	8	no	—
759	C₂²×C₄	—	43	4	no	—
760	C₂²×C₄	—	43	1	no	—
761	C₂²×C₄	—	43	2	no	—
762	C₂²×C₄	—	43	2	no	—
763	C₂²×C₄	—	43	2	no	—
764	C₂²×C₄	—	43	4	no	—
765	C₂²×C₄	—	43	1	no	—
766	C₂²×C₄	—	43	8	no	—
767	C₂²×C₄	—	43	4	no	—
768	C₂²×C₄	—	43	8	no	—
769	C₂²×C₄	—	43	4	no	—
770	C₂²×C₄	—	43	8	no	—
771	C₂²×C₄	—	43	4	no	—
772	C₂²×C₄	—	43	4	no	—
773	C₂²×C₄	—	43	8	no	—
774	C₂²×C₄	—	43	16	no	—
775	C₂²×C₄	—	86	8	no	—
776	C₂²×C₄	—	86	4	no	—
777	C₂²×C₄	—	86	4	no	—
778	C₂²×C₄	—	86	4	no	—
779	C₂²×C₄	—	86	4	no	—
780	C₂²×C₄	—	86	4	no	—
781	C₂²×C₄	—	86	8	no	—
782	C₂²×C₄	—	86	32	no	—
783	C₂²×C₄	—	172	8	no	—
784	C₂²×C₄	—	172	4	no	—
785	C₂²×C₄	—	172	4	no	—
786	C₂²×C₄	#10621898	1	8	yes	complemented
787	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
788	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
789	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
790	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
791	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
792	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
793	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
794	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
796	C₄⋊C₄	—	43	8	no	—
797	C₄⋊C₄	—	43	4	no	—
798	C₄⋊C₄	—	43	4	no	—
799	C₄⋊C₄	—	43	8	no	—
800	C₄⋊C₄	—	43	8	no	—
801	C₄⋊C₄	—	43	8	no	—
802	C₄⋊C₄	—	43	16	no	—
803	C₄⋊C₄	—	43	8	no	—
804	C₄⋊C₄	—	43	16	no	—
805	C₄⋊C₄	—	43	16	no	—
806	C₄⋊C₄	—	43	16	no	—
807	C₄⋊C₄	—	43	8	no	—
808	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
809	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
810	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
811	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
812	C₂²⋊C₄	—	43	8	no	—
813	C₂²⋊C₄	—	43	16	no	—
814	C₂²⋊C₄	—	43	16	no	—
815	C₂²⋊C₄	—	43	16	no	—
816	C₂²⋊C₄	—	43	16	no	—
817	C₂²⋊C₄	—	43	8	no	—
818	C₂²⋊C₄	—	43	8	no	—
819	C₂²⋊C₄	—	43	16	no	—
820	C₂²⋊C₄	—	43	8	no	—
821	C₂²⋊C₄	—	43	8	no	—
822	C₂²⋊C₄	—	43	8	no	—
823	C₂²⋊C₄	—	43	8	no	—
824	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
825	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
826	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
827	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
828	C₄²	—	43	8	no	—
829	C₄²	—	43	8	no	—
830	C₄²	—	43	8	no	—
831	C₄²	—	43	16	no	—
832	C₄²	C₂³×D₄₃	1	8	yes	—
833	C₄²	C₂³×D₄₃	1	8	yes	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	8	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	16	no	—
840	C₂³	—	4	8	no	—
841	C₂³	—	4	8	no	—
842	C₂³	—	8	16	no	—
843	C₂³	—	43	4	no	—
844	C₂³	—	43	2	no	—
845	C₂³	—	43	2	no	—
846	C₂³	—	43	4	no	—
847	C₂³	—	86	8	no	—
848	C₂³	—	86	2	no	—
849	C₂³	—	86	2	no	—
850	C₂³	—	86	8	no	—
851	C₂³	—	86	2	no	—
852	C₂³	—	86	4	no	—
853	C₂³	—	86	4	no	—
854	C₂³	—	86	2	no	—
855	C₂³	—	86	4	no	—
856	C₂³	—	86	2	no	—
857	C₂³	—	172	4	no	—
858	C₂³	—	172	16	no	—
859	C₂³	C₂×#10621898	1	4	yes	—
860	C₂³	C₂⁴×D₄₃	1	8	yes	—
861	C₂³	C₂⁴×D₄₃	1	2	yes	—
862	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
863	Q₈	—	86	8	no	—
864	Q₈	—	172	16	no	—
865	D₄	—	2	16	no	—
866	D₄	—	2	16	no	—
867	D₄	—	86	16	no	—
868	D₄	—	86	32	no	—
869	D₄	—	86	16	no	—
870	D₄	—	86	8	no	—
871	D₄	—	172	8	no	—
872	D₄	—	172	16	no	—
873	D₄	—	172	16	no	—
874	D₄	—	172	16	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	4	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	4	16	no	—
880	C₂×C₄	—	4	16	no	—
881	C₂×C₄	—	43	2	no	—
882	C₂×C₄	—	43	4	no	—
883	C₂×C₄	—	43	4	no	—
884	C₂×C₄	—	43	4	no	—
885	C₂×C₄	—	43	8	no	—
886	C₂×C₄	—	43	2	no	—
887	C₂×C₄	—	86	16	no	—
888	C₂×C₄	—	86	8	no	—
889	C₂×C₄	—	86	2	no	—
890	C₂×C₄	—	86	2	no	—
891	C₂×C₄	—	86	4	no	—
892	C₂×C₄	—	86	4	no	—
893	C₂×C₄	—	86	8	no	—
894	C₂×C₄	—	86	4	no	—
895	C₂×C₄	—	86	8	no	—
896	C₂×C₄	—	86	8	no	—
897	C₂×C₄	—	86	8	no	—
898	C₂×C₄	—	86	8	no	—
899	C₂×C₄	—	86	16	no	—
900	C₂×C₄	—	172	16	no	—
901	C₂×C₄	—	172	8	no	—
902	C₂×C₄	—	172	8	no	—
903	C₂×C₄	C₂×#10621898	1	4	yes	—
904	C₂×C₄	C₂×#10621898	1	4	yes	—
905	C₂×C₄	C₂×#10621898	1	16	yes	complemented
906	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
907	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
908	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
909	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
910	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
911	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	8	no	—
916	C₂²	—	2	8	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	4	16	no	—
919	C₂²	—	8	16	no	—
920	C₂²	—	43	4	no	—
921	C₂²	—	86	8	no	—
922	C₂²	—	86	2	no	—
923	C₂²	—	86	2	no	—
924	C₂²	—	86	2	no	—
925	C₂²	—	86	4	no	—
926	C₂²	—	86	4	no	—
927	C₂²	—	86	2	no	—
928	C₂²	—	86	4	no	—
929	C₂²	—	86	2	no	—
930	C₂²	—	172	16	no	—
931	C₂²	—	172	4	no	—
932	C₂²	—	172	8	no	—
933	C₂²	C₂²×#10621898	1	4	yes	—
934	C₂²	C₂²×#10621898	1	2	yes	—
935	C₂²	H(5,𝔽₂)×D₄₃	1	2	yes	—
936	C₂²	#14583734	1	2	yes	—
937	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
938	C₄	—	2	4	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	86	2	no	—
943	C₄	—	86	2	no	—
944	C₄	—	86	4	no	—
945	C₄	—	86	4	no	—
946	C₄	—	86	8	no	—
947	C₄	—	86	4	no	—
948	C₄	C₂²×#10621898	1	4	yes	—
949	C₄	C₂²×#10621898	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	4	8	no	—
952	C₂	—	86	4	no	—
953	C₂	—	172	2	no	—
954	C₂	—	172	4	no	—
955	C₂	#19148320	1	4	yes	direct product factor
956	C₂	C₂³×#10621898	1	1	yes	characteristic
957	C₂	C₂×H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
958	C₂	C₂×#14583734	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#518	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#518	D₄₃
hypocenter	C₄₃	C₂×#3494
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. #19148320	C₂	direct (N × H)
2. C₂×#14583614	C₂	semidirect
3. C₂×#14583599	C₂	semidirect
4. C₂×#14583599	C₂	semidirect
5. C₂×#14583575	C₂	semidirect
6. C₂×#14583554	C₂	semidirect
7. C₂×#14583539	C₂	semidirect
8. C₂×#14583527	C₂	semidirect
9. C₂×#14583514	C₂	semidirect
10. C₂×#14583500	C₂	semidirect
11. C₂×#14583466	C₂	semidirect
12. C₂×#14583446	C₂	semidirect
13. C₂×#14583431	C₂	semidirect
14. C₂×#14583411	C₂	semidirect
15. C₂²×#13063296	C₂	semidirect
16. C₂×#14583379	C₂	semidirect
17. C₂×#117×D₄₃	C₂	semidirect
18. C₂×C₄₃×#518	C₂	semidirect
20. C₂²×#10621898	C₂²	semidirect
23. #14583614	C₂²	semidirect
24. #14583599	C₂²	semidirect
25. #14583599	C₂²	semidirect
26. #14583575	C₂²	semidirect
27. #14583554	C₂²	semidirect
28. #14583539	C₂²	semidirect
29. #14583527	C₂²	semidirect
30. #14583514	C₂²	semidirect
31. #14583500	C₂²	semidirect
32. #14583466	C₂²	semidirect
33. #14583446	C₂²	semidirect
34. C₂×#13063325	C₂²	semidirect
35. C₂×#13063324	C₂²	semidirect
36. C₂×#13063321	C₂²	semidirect
37. #14583431	C₂²	semidirect
38. C₂×#13063318	C₂²	semidirect
39. C₂×#13063318	C₂²	semidirect
40. C₂×#13063317	C₂²	semidirect
41. C₂×#13063316	C₂²	semidirect
42. C₂×#13063312	C₂²	semidirect
43. C₂×#13063311	C₂²	semidirect
44. C₂×#13063311	C₂²	semidirect
45. #14583411	C₂²	semidirect
47. C₂×#13063308	C₂²	semidirect
48. C₂×#13063308	C₂²	semidirect
49. C₂×#13063307	C₂²	semidirect
50. C₂×#13063307	C₂²	semidirect
51. C₂×#13063305	C₂²	semidirect
52. C₂×#13063305	C₂²	semidirect
53. C₂×#13063304	C₂²	semidirect
55. C₂×#13063300	C₂²	semidirect
56. C₂×#13063300	C₂²	semidirect
57. C₂×#13063299	C₂²	semidirect
58. C₂×#13063298	C₂²	semidirect
59. C₂×#13063298	C₂²	semidirect
64. C₂×#13063296	C₂²	semidirect
65. C₂×#13063296	C₂²	semidirect
66. C₂×#13063296	C₂²	semidirect
69. #14583379	C₂²	semidirect
70. C₂×C₄×Dic₈₆	C₂²	semidirect
71. C₂×C₄×D₁₇₂	C₂²	semidirect
72. C₂×C₄×D₁₇₂	C₂²	semidirect
73. C₂×C₄×D₁₇₂	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
78. C₂×#13063284	C₂²	semidirect
79. C₂×#13063283	C₂²	semidirect
80. C₂×#13063283	C₂²	semidirect
81. C₂×#13063283	C₂²	semidirect
82. C₂×#13063282	C₂²	semidirect
84. #117×D₄₃	C₂²	semidirect
86. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
87. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
88. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
91. C₂×C₄²×D₄₃	C₂²	semidirect
93. C₄₃×#518	C₂²	semidirect
94. C₂×C₄×D₄×C₄₃	C₂²	semidirect
95. C₂×C₄×D₄×C₄₃	C₂²	semidirect
96. C₂×C₄×D₄×C₄₃	C₂²	semidirect
97. C₂×C₄×D₄×C₄₃	C₂²	semidirect
105. C₂×#10621898	C₂³	semidirect
130. #13063325	C₂³	semidirect
131. #13063324	C₂³	semidirect
132. #13063321	C₂³	semidirect
133. #13063318	C₂³	semidirect
134. #13063318	C₂³	semidirect
135. #13063317	C₂³	semidirect
136. #13063316	C₂³	semidirect
137. #13063312	C₂³	semidirect
138. #13063311	C₂³	semidirect
139. #13063311	C₂³	semidirect
141. #13063308	C₂³	semidirect
142. #13063308	C₂³	semidirect
143. #13063307	C₂³	semidirect
144. #13063307	C₂³	semidirect
145. #13063305	C₂³	semidirect
146. #13063305	C₂³	semidirect
147. #13063304	C₂³	semidirect
149. #13063300	C₂³	semidirect
150. #13063300	C₂³	semidirect
151. #13063299	C₂³	semidirect
152. #13063298	C₂³	semidirect
153. #13063298	C₂³	semidirect
158. #13063296	C₂³	semidirect
159. #13063296	C₂³	semidirect
162. C₄×Dic₈₆	C₂³	semidirect
163. C₄×D₁₇₂	C₂³	semidirect
164. C₄×D₁₇₂	C₂³	semidirect
165. C₄×D₁₇₂	C₂³	semidirect
166. C₄×C₂²⋊D₄₃	C₂³	semidirect
167. C₄×C₂²⋊D₄₃	C₂³	semidirect
170. #13063284	C₂³	semidirect
171. #13063283	C₂³	semidirect
172. #13063283	C₂³	semidirect
173. #13063283	C₂³	semidirect
174. #13063282	C₂³	semidirect
189. C₄⋊C₄×D₄₃	C₂³	semidirect
190. C₄⋊C₄×D₄₃	C₂³	semidirect
191. C₄⋊C₄×D₄₃	C₂³	semidirect
210. C₄²×D₄₃	C₂³	semidirect
219. C₄×D₄×C₄₃	C₂³	semidirect
220. C₄×D₄×C₄₃	C₂³	semidirect
221. C₄×D₄×C₄₃	C₂³	semidirect
222. C₄×D₄×C₄₃	C₂³	semidirect
256. C₂²×C₄×C₄₃	#41	semidirect
393. C₂×C₄×C₄₃	C₂×#41	semidirect
487. C₂×#518	D₄₃	semidirect
491. C₂×C₄₃	#3494	semidirect
550. #518	C₂×D₄₃	semidirect
558. C₂×C₄×D₄	C₂×D₄₃	semidirect
559. C₂×C₄×D₄	C₂×D₄₃	semidirect
560. C₂×C₄×D₄	C₂×D₄₃	semidirect
561. C₂×C₄×D₄	C₂×D₄₃	semidirect
580. C₄₃	C₂×#3494	semidirect
657. C₄×D₄	C₂²×D₄₃	semidirect
658. C₄×D₄	C₂²×D₄₃	semidirect
659. C₄×D₄	C₂²×D₄₃	semidirect
660. C₄×D₄	C₂²×D₄₃	semidirect
786. C₂²×C₄	#10621898	semidirect
905. C₂×C₄	C₂×#10621898	semidirect
955. C₂	#19148320	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148320	2
C₂×#14583614	2
C₂×#14583599	2
C₂×#14583575	2
C₂×#14583554	2
C₂×#14583539	2
C₂×#14583527	2
C₂×#14583514	2
C₂×#14583500	2
C₂×#14583466	2
C₂×#14583446	2
C₂×#14583431	2
C₂×#14583411	2
C₂²×#13063296	2
C₂×#14583379	2
C₂×#117×D₄₃	2
C₂×C₄₃×#518	2
C₂×#3494	43

Subgroups — C2×#19148320 #26004937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148320 #26004937