Subgroups — C₂×#19148641 #26004599

Order 11008.

7910 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148641	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583617	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583605	C₂	1	2	yes	maximal, complemented
4	C₂×#14583587	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14583574	C₂	1	2	yes	maximal, complemented
6	C₂×#14583573	C₂	1	2	yes	maximal, complemented
7	C₂×#14583562	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14583561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14583558	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14583551	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14583550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14583541	C₂	1	2	yes	maximal, complemented
13	C₂×#14583515	C₂	1	2	yes	maximal, complemented
14	C₂×#14583497	C₂	1	2	yes	maximal, complemented
15	C₂×#14583493	C₂	1	2	yes	maximal, complemented
16	C₂×#14583453	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#14583434	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583412	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#14583411	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#13063305	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₂²⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14583379	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#10621902	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#10621898	C₂²	1	2	yes	—
27	C₂²×#10621898	C₂²	1	1	yes	characteristic, complemented
28	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₄×D₄₃	C₂²	1	1	yes	characteristic
31	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic
32	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic
33	#14583617	C₂²	1	16	yes	complemented
34	#14583605	C₂²	1	32	yes	complemented
35	#14583587	C₂²	1	16	yes	complemented
36	#14583574	C₂²	1	32	yes	complemented
37	#14583573	C₂²	1	32	yes	complemented
38	#14583562	C₂²	1	16	yes	complemented
39	#14583561	C₂²	1	16	yes	complemented
40	#14583558	C₂²	1	16	yes	complemented
41	#14583551	C₂²	1	16	yes	complemented
42	#14583550	C₂²	1	16	yes	complemented
43	#14583541	C₂²	1	32	yes	complemented
44	#14583515	C₂²	1	32	yes	complemented
45	#14583497	C₂²	1	32	yes	complemented
46	#14583493	C₂²	1	32	yes	complemented
47	#14583453	C₂²	1	16	yes	complemented
48	C₂×#13063324	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13063324	C₂²	1	2	yes	complemented
50	C₂×#13063323	C₂²	1	1	yes	characteristic, complemented
51	#14583434	C₂²	1	16	yes	complemented
52	C₂×#13063320	C₂²	1	2	yes	complemented
53	C₂×#13063320	C₂²	1	2	yes	complemented
54	C₂×#13063319	C₂²	1	2	yes	complemented
55	C₂×#13063318	C₂²	1	2	yes	complemented
56	C₂×#13063316	C₂²	1	2	yes	complemented
57	C₂×#13063315	C₂²	1	2	yes	complemented
58	C₂×#13063313	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13063313	C₂²	1	2	yes	complemented
60	C₂×#13063311	C₂²	1	2	yes	—
61	C₂×#13063311	C₂²	1	2	yes	complemented
62	#14583412	C₂²	1	16	yes	complemented
63	#14583411	C₂²	1	16	yes	complemented
64	C₂×#13063310	C₂²	1	2	yes	—
65	C₂×#13063310	C₂²	1	2	yes	—
66	C₂×#13063310	C₂²	1	2	yes	complemented
67	C₂×#13063310	C₂²	1	2	yes	complemented
68	C₂×#13063310	C₂²	1	2	yes	complemented
69	C₂×#13063309	C₂²	1	2	yes	complemented
70	C₂×#13063308	C₂²	1	2	yes	complemented
71	C₂×#13063307	C₂²	1	2	yes	complemented
72	C₂×#13063305	C₂²	1	1	yes	characteristic
73	C₂×#13063305	C₂²	1	2	yes	—
74	C₂×#13063305	C₂²	1	1	yes	characteristic
75	C₂×#13063305	C₂²	1	1	yes	characteristic, complemented
76	C₂×#13063305	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13063305	C₂²	1	2	yes	complemented
78	C₂×#13063305	C₂²	1	1	yes	characteristic, complemented
79	C₂×#13063305	C₂²	1	2	yes	complemented
80	C₂×#13063305	C₂²	1	16	yes	complemented
81	C₂×#13063304	C₂²	1	1	yes	characteristic, complemented
82	C₂×#13063303	C₂²	1	2	yes	—
83	C₂×#13063303	C₂²	1	2	yes	—
84	C₂×#13063303	C₂²	1	2	yes	complemented
85	C₂×#13063303	C₂²	1	2	yes	complemented
86	C₂×#13063303	C₂²	1	2	yes	complemented
87	C₂×#13063302	C₂²	1	2	yes	complemented
88	C₂×#13063302	C₂²	1	2	yes	complemented
89	C₂×#13063301	C₂²	1	1	yes	characteristic
90	C₂²⋊Q₈×D₄₃	C₂²	1	16	yes	complemented
91	C₂×#13063300	C₂²	1	2	yes	—
92	C₂×#13063300	C₂²	1	1	yes	characteristic
93	C₂×#13063300	C₂²	1	1	yes	characteristic, complemented
94	C₂×#13063299	C₂²	1	1	yes	characteristic, complemented
95	C₂×#13063298	C₂²	1	2	yes	—
96	C₂×#13063297	C₂²	1	2	yes	—
97	C₂×#13063295	C₂²	1	2	yes	—
98	C₂×#13063295	C₂²	1	2	yes	—
99	#14583379	C₂²	1	32	yes	complemented
100	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
101	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
102	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13063290	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
106	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
107	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
108	C₂×D₄×Dic₄₃	C₂²	1	1	yes	characteristic
109	C₂×#13063287	C₂²	1	2	yes	—
110	C₂×#13063287	C₂²	1	2	yes	—
111	C₂×#13063287	C₂²	1	1	yes	characteristic
112	C₂×#13063287	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
115	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
116	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
117	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
118	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
119	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
120	C₄×D₄×D₄₃	C₂²	1	16	yes	complemented
121	C₂×#13063283	C₂²	1	2	yes	complemented
122	C₂×#13063283	C₂²	1	2	yes	complemented
123	C₂×#13063283	C₂²	1	1	yes	characteristic, complemented
124	C₂×#13063282	C₂²	1	2	yes	—
125	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
126	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
127	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
129	C₂×C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
131	C₂×C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
132	C₂×C₂²⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
134	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
135	C₄₃×#552	C₂²	1	16	yes	complemented
136	C₂×#126×C₄₃	C₂²	1	2	yes	complemented
137	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×#125×C₄₃	C₂²	1	2	yes	complemented
139	C₂×#123×C₄₃	C₂²	1	2	yes	—
140	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
141	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
144	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
145	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
146	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
148	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
149	C₂×#10621902	—	4	4	no	—
150	C₂×#10621902	C₂³	1	8	yes	complemented
151	C₂×#10621898	—	2	16	no	—
152	C₂×#10621898	—	4	4	no	—
153	C₂×#10621898	C₂³	1	16	yes	—
154	C₂×#10621898	C₂³	1	8	yes	complemented
155	C₂²×Dic₈₆	—	4	4	no	—
156	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
157	C₂²×Dic₈₆	C₂³	1	2	yes	—
158	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
159	C₂²×Dic₈₆	C₂³	1	2	yes	—
160	C₂²×Dic₈₆	C₂³	1	2	yes	—
161	C₂²×Dic₈₆	C₂³	1	8	yes	complemented
162	C₂×Q₈×D₄₃	—	4	4	no	—
163	C₂×Q₈×D₄₃	C₂³	1	8	yes	complemented
164	C₂²×D₁₇₂	C₂³	1	2	yes	—
165	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
166	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
167	C₂²×D₁₇₂	C₂³	1	2	yes	—
168	C₂²×D₁₇₂	C₂³	1	2	yes	—
169	C₂²×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
170	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
171	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
172	C₂²×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
173	C₂×D₄×D₄₃	—	2	8	no	—
174	C₂×D₄×D₄₃	C₂³	1	8	yes	—
175	C₂³×Dic₄₃	C₂³	1	2	yes	—
176	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
177	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₄₃	—	4	4	no	—
179	C₂²×C₄×D₄₃	—	4	4	no	—
180	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
184	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
186	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
187	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
190	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
192	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
193	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
194	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
195	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
196	#13063324	C₂³	1	16	yes	complemented
197	#13063324	C₂³	1	8	yes	complemented
198	#13063323	C₂³	1	8	yes	complemented
199	#13063320	C₂³	1	16	yes	complemented
200	#13063320	C₂³	1	16	yes	complemented
201	#13063319	C₂³	1	16	yes	complemented
202	#13063318	C₂³	1	16	yes	complemented
203	#13063316	C₂³	1	16	yes	complemented
204	#13063315	C₂³	1	16	yes	complemented
205	#13063313	C₂³	1	8	yes	complemented
206	#13063313	C₂³	1	16	yes	complemented
207	#13063311	C₂³	1	16	yes	—
208	#13063311	C₂³	1	16	yes	complemented
209	#13063310	C₂³	1	16	yes	—
210	#13063310	C₂³	1	16	yes	—
211	#13063310	C₂³	1	16	yes	complemented
212	#13063310	C₂³	1	16	yes	complemented
213	#13063310	C₂³	1	16	yes	complemented
214	#13063309	C₂³	1	16	yes	complemented
215	#13063308	C₂³	1	16	yes	complemented
216	#13063307	C₂³	1	16	yes	complemented
217	#13063305	C₂³	1	16	yes	—
218	#13063305	C₂³	1	8	yes	—
219	#13063305	C₂³	1	8	yes	—
220	#13063305	C₂³	1	16	yes	complemented
221	#13063305	C₂³	1	8	yes	complemented
222	#13063305	C₂³	1	8	yes	complemented
223	#13063305	C₂³	1	8	yes	complemented
224	#13063305	C₂³	1	16	yes	complemented
225	#13063304	C₂³	1	8	yes	complemented
226	#13063303	C₂³	1	16	yes	—
227	#13063303	C₂³	1	16	yes	—
228	#13063303	C₂³	1	16	yes	complemented
229	#13063303	C₂³	1	16	yes	complemented
230	#13063303	C₂³	1	16	yes	complemented
231	#13063302	C₂³	1	16	yes	complemented
232	#13063302	C₂³	1	16	yes	complemented
233	#13063301	C₂³	1	8	yes	—
234	#13063300	C₂³	1	16	yes	—
235	#13063300	C₂³	1	8	yes	—
236	#13063300	C₂³	1	8	yes	complemented
237	#13063299	C₂³	1	8	yes	complemented
238	#13063298	C₂³	1	16	yes	—
239	#13063297	C₂³	1	16	yes	—
240	#13063295	C₂³	1	16	yes	—
241	#13063295	C₂³	1	16	yes	—
242	C₄×Dic₈₆	C₂³	1	8	yes	complemented
243	C₄×Dic₈₆	C₂³	1	16	yes	complemented
244	C₄×Dic₈₆	C₂³	1	16	yes	complemented
245	#13063290	C₂³	1	8	yes	complemented
246	C₄×D₁₇₂	C₂³	1	8	yes	—
247	C₄×D₁₇₂	C₂³	1	16	yes	—
248	C₄×D₁₇₂	C₂³	1	16	yes	complemented
249	C₄×D₁₇₂	C₂³	1	16	yes	complemented
250	D₄×Dic₄₃	C₂³	1	8	yes	—
251	#13063287	C₂³	1	16	yes	—
252	#13063287	C₂³	1	16	yes	—
253	#13063287	C₂³	1	8	yes	—
254	#13063287	C₂³	1	8	yes	complemented
255	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
256	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
257	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	—
258	(C₂²⋊D₄₃)⋊C₄	C₂³	1	8	yes	—
259	(C₂²⋊D₄₃)⋊C₄	C₂³	1	8	yes	—
260	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	complemented
261	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	complemented
262	#13063283	C₂³	1	16	yes	complemented
263	#13063283	C₂³	1	8	yes	complemented
264	#13063283	C₂³	1	16	yes	complemented
265	#13063282	C₂³	1	16	yes	—
266	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
268	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
269	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
271	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
272	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
273	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	complemented
274	C₂×Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
277	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
278	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
279	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
280	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
281	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
282	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
283	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
284	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
285	C₄⋊C₄×D₄₃	C₂³	1	8	yes	complemented
286	C₄⋊C₄×D₄₃	C₂³	1	16	yes	complemented
287	C₄⋊C₄×D₄₃	C₂³	1	16	yes	complemented
288	C₂×C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
291	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	—
292	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
294	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
299	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
300	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
302	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
303	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
304	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
305	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
306	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
307	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
308	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
309	C₂²⋊C₄×D₄₃	C₂³	1	8	yes	—
310	C₂²⋊C₄×D₄₃	C₂³	1	8	yes	—
311	C₂²⋊C₄×D₄₃	C₂³	1	16	yes	—
312	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
314	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
315	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
316	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
317	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
318	C₄²×D₄₃	C₂³	1	8	yes	—
319	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
320	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
322	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
323	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
324	#126×C₄₃	C₂³	1	16	yes	complemented
325	#125×C₄₃	C₂³	1	8	yes	complemented
326	#125×C₄₃	C₂³	1	16	yes	complemented
327	#123×C₄₃	C₂³	1	16	yes	—
328	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	complemented
329	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	complemented
330	C₄×Q₈×C₄₃	C₂³	1	8	yes	complemented
331	C₄×D₄×C₄₃	C₂³	1	8	yes	—
332	#117×C₄₃	C₂³	1	16	yes	complemented
333	#117×C₄₃	C₂³	1	8	yes	complemented
334	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
337	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
338	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
340	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
342	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
343	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
344	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	complemented
345	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
348	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
350	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
351	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
352	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
353	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₂³×D₄₃	—	2	4	no	—
356	C₂³×D₄₃	—	2	4	no	—
357	C₂³×D₄₃	—	2	4	no	—
358	C₂³×D₄₃	—	2	4	no	—
359	C₂³×D₄₃	—	4	2	no	—
360	C₂³×D₄₃	—	4	2	no	—
361	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
362	C₂³×D₄₃	C₂⁴	1	2	yes	—
363	C₂³×D₄₃	C₂⁴	1	4	yes	—
364	C₂³×D₄₃	C₂⁴	1	4	yes	—
365	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
366	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
367	C₂×Q₈×C₄₃	—	2	4	no	—
368	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
369	C₂×D₄×C₄₃	—	2	4	no	—
370	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
371	C₂²×C₄×C₄₃	—	2	4	no	—
372	C₂²×C₄×C₄₃	—	2	4	no	—
373	C₂²×C₄×C₄₃	—	2	8	no	—
374	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
384	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
385	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₂²⋊D₄₃	—	2	4	no	—
387	C₂×C₂²⋊D₄₃	—	2	8	no	—
388	C₂×C₂²⋊D₄₃	—	4	4	no	—
389	C₂×C₂²⋊D₄₃	#41	1	8	yes	complemented
390	C₂×C₂²⋊D₄₃	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
392	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
393	C₂×C₂²⋊D₄₃	C₂⁴	1	4	yes	—
394	C₂²×Dic₄₃	—	4	2	no	—
395	C₂²×Dic₄₃	—	4	2	no	—
396	C₂²×Dic₄₃	—	4	4	no	—
397	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
399	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
402	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
403	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
405	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
406	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
407	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
408	#10621902	—	4	16	no	—
409	Q₈×D₄₃	—	4	16	no	—
410	D₄×D₄₃	—	2	32	no	—
411	#10621898	—	2	64	no	—
412	#10621898	—	4	16	no	—
413	C₂×D₁₇₂	—	2	4	no	—
414	C₂×D₁₇₂	—	2	4	no	—
415	C₂×D₁₇₂	—	2	8	no	—
416	C₂×D₁₇₂	—	2	8	no	—
417	C₂×D₁₇₂	—	4	4	no	—
418	C₂×D₁₇₂	C₂⁴	1	8	yes	—
419	C₂×D₁₇₂	C₂⁴	1	4	yes	—
420	C₂×D₁₇₂	C₂⁴	1	4	yes	—
421	C₂×D₁₇₂	C₂⁴	1	8	yes	—
422	C₂×D₁₇₂	C₂⁴	1	8	yes	—
423	C₂×C₄×D₄₃	—	2	4	no	—
424	C₂×C₄×D₄₃	—	2	4	no	—
425	C₂×C₄×D₄₃	—	2	4	no	—
426	C₂×C₄×D₄₃	—	2	4	no	—
427	C₂×C₄×D₄₃	—	2	8	no	—
428	C₂×C₄×D₄₃	—	2	8	no	—
429	C₂×C₄×D₄₃	—	2	4	no	—
430	C₂×C₄×D₄₃	—	4	2	no	—
431	C₂×C₄×D₄₃	—	4	2	no	—
432	C₂×C₄×D₄₃	—	4	2	no	—
433	C₂×C₄×D₄₃	—	4	2	no	—
434	C₂×C₄×D₄₃	—	4	4	no	—
435	C₂×C₄×D₄₃	—	4	4	no	—
436	C₂×C₄×D₄₃	—	4	4	no	—
437	C₂×C₄×D₄₃	—	4	16	no	—
438	C₂×C₄×D₄₃	—	4	16	no	—
439	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
440	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
441	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
442	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
443	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
444	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
445	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
446	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
447	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
448	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
449	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
450	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
451	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
452	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
453	C₂×Dic₈₆	—	2	4	no	—
454	C₂×Dic₈₆	—	2	4	no	—
455	C₂×Dic₈₆	—	2	8	no	—
456	C₂×Dic₈₆	—	4	16	no	—
457	C₂×Dic₈₆	—	4	4	no	—
458	C₂×Dic₈₆	—	4	4	no	—
459	C₂×Dic₈₆	C₂⁴	1	4	yes	—
460	C₂×Dic₈₆	C₂⁴	1	8	yes	—
461	C₂×Dic₈₆	C₂⁴	1	4	yes	—
462	C₂×Dic₈₆	C₂⁴	1	8	yes	—
463	C₂×Dic₈₆	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
465	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
466	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
467	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
468	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
469	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
470	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
471	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
472	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
473	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
474	C₂²⋊C₄×C₄₃	C₂⁴	1	4	yes	—
475	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
476	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
477	C₂²⋊C₄×C₄₃	C₂⁴	1	4	yes	—
478	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
479	C₄²×C₄₃	C₂⁴	1	8	yes	—
480	C₄²×C₄₃	C₂⁴	1	8	yes	—
481	C₄²×C₄₃	C₂⁴	1	4	yes	—
482	C₂²⋊Dic₄₃	C₂⁴	1	4	yes	—
483	C₂²⋊Dic₄₃	C₂⁴	1	4	yes	—
484	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
485	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
486	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
487	(C₂×D₄₃)⋊C₄	C₂⁴	1	4	yes	—
488	(C₂×D₄₃)⋊C₄	C₂⁴	1	4	yes	—
489	(C₂×D₄₃)⋊C₄	C₂⁴	1	4	yes	—
490	(C₂×D₄₃)⋊C₄	C₂⁴	1	4	yes	—
491	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
492	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
493	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
494	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
495	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
496	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
497	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
498	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
499	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
500	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
501	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
502	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
503	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
504	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
505	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
506	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
507	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
508	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
509	Dic₄₃⋊C₄	C₂⁴	1	4	yes	—
510	Dic₄₃⋊C₄	C₂⁴	1	4	yes	—
511	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
512	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
513	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
514	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
515	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
516	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
517	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
518	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
519	C₄×Dic₄₃	C₂⁴	1	4	yes	—
520	C₄×Dic₄₃	C₂⁴	1	4	yes	—
521	C₄×Dic₄₃	C₂⁴	1	4	yes	—
522	C₄×Dic₄₃	C₂⁴	1	8	yes	—
523	C₄×Dic₄₃	C₂⁴	1	8	yes	—
524	C₄×Dic₄₃	C₂⁴	1	8	yes	—
525	C₂³×C₄₃	—	2	2	no	—
526	C₂³×C₄₃	—	2	2	no	—
527	C₂³×C₄₃	—	2	2	no	—
528	C₂³×C₄₃	—	2	2	no	—
529	C₂³×C₄₃	—	2	2	no	—
530	C₂³×C₄₃	C₂×#41	1	4	yes	—
531	C₂³×C₄₃	C₂⁵	1	2	yes	—
532	C₂³×C₄₃	C₂⁵	1	2	yes	—
533	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
534	C₂²×D₄₃	—	2	2	no	—
535	C₂²×D₄₃	—	2	2	no	—
536	C₂²×D₄₃	—	2	2	no	—
537	C₂²×D₄₃	—	2	2	no	—
538	C₂²×D₄₃	—	2	4	no	—
539	C₂²×D₄₃	—	2	2	no	—
540	C₂²×D₄₃	—	2	8	no	—
541	C₂²×D₄₃	—	2	2	no	—
542	C₂²×D₄₃	—	2	4	no	—
543	C₂²×D₄₃	—	2	4	no	—
544	C₂²×D₄₃	—	2	2	no	—
545	C₂²×D₄₃	—	2	8	no	—
546	C₂²×D₄₃	—	2	8	no	—
547	C₂²×D₄₃	—	2	8	no	—
548	C₂²×D₄₃	—	4	4	no	—
549	C₂²×D₄₃	—	4	4	no	—
550	C₂²×D₄₃	—	4	16	no	—
551	C₂²×D₄₃	—	4	16	no	—
552	C₂²×D₄₃	C₂×#41	1	4	yes	—
553	C₂²×D₄₃	2₋¹⁺⁴	1	4	yes	—
554	C₂²×D₄₃	C₂⁵	1	2	yes	—
555	C₂²×D₄₃	C₂⁵	1	4	yes	—
556	C₂²×D₄₃	C₂⁵	1	2	yes	—
557	C₂²×D₄₃	C₂⁵	1	2	yes	—
558	Q₈×C₄₃	—	2	8	no	—
559	D₄×C₄₃	—	2	8	no	—
560	C₂×C₄×C₄₃	—	2	4	no	—
561	C₂×C₄×C₄₃	—	2	4	no	—
562	C₂×C₄×C₄₃	—	2	2	no	—
563	C₂×C₄×C₄₃	—	2	16	no	—
564	C₂×C₄×C₄₃	—	2	2	no	—
565	C₂×C₄×C₄₃	—	2	4	no	—
566	C₂×C₄×C₄₃	—	2	2	no	—
567	C₂×C₄×C₄₃	—	2	2	no	—
568	C₂×C₄×C₄₃	—	2	4	no	—
569	C₂×C₄×C₄₃	—	2	8	no	—
570	C₂×C₄×C₄₃	—	2	8	no	—
571	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
572	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
573	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
574	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
575	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
576	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
577	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
578	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
579	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
580	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
581	C₂²⋊D₄₃	—	2	16	no	—
582	C₂²⋊D₄₃	—	2	8	no	—
583	C₂²⋊D₄₃	—	4	8	no	—
584	C₂²⋊D₄₃	C₂×#41	1	16	yes	complemented
585	C₂×Dic₄₃	—	2	4	no	—
586	C₂×Dic₄₃	—	2	4	no	—
587	C₂×Dic₄₃	—	2	4	no	—
588	C₂×Dic₄₃	—	2	2	no	—
589	C₂×Dic₄₃	—	2	2	no	—
590	C₂×Dic₄₃	—	2	2	no	—
591	C₂×Dic₄₃	—	2	2	no	—
592	C₂×Dic₄₃	—	4	8	no	—
593	C₂×Dic₄₃	—	4	4	no	—
594	C₂×Dic₄₃	—	4	4	no	—
595	C₂×Dic₄₃	C₂×#41	1	4	yes	—
596	C₂×Dic₄₃	C₂⁵	1	2	yes	—
597	C₂×Dic₄₃	C₂⁵	1	4	yes	—
598	C₂×Dic₄₃	C₂⁵	1	2	yes	—
599	C₂×Dic₄₃	C₂⁵	1	2	yes	—
600	C₂×Dic₄₃	C₂⁵	1	4	yes	—
601	C₂×Dic₄₃	C₂⁵	1	4	yes	—
602	C₂×Dic₄₃	C₂⁵	1	2	yes	—
603	C₂×Dic₄₃	C₂⁵	1	2	yes	—
604	D₁₇₂	—	2	16	no	—
605	D₁₇₂	—	2	8	no	—
606	D₁₇₂	—	2	16	no	—
607	D₁₇₂	—	2	8	no	—
608	D₁₇₂	—	4	8	no	—
609	C₄×D₄₃	—	2	16	no	—
610	C₄×D₄₃	—	2	8	no	—
611	C₄×D₄₃	—	2	8	no	—
612	C₄×D₄₃	—	2	8	no	—
613	C₄×D₄₃	—	2	8	no	—
614	C₄×D₄₃	—	2	16	no	—
615	C₄×D₄₃	—	2	8	no	—
616	C₄×D₄₃	—	4	4	no	—
617	C₄×D₄₃	—	4	4	no	—
618	C₄×D₄₃	—	4	4	no	—
619	C₄×D₄₃	—	4	4	no	—
620	C₄×D₄₃	—	4	8	no	—
621	C₄×D₄₃	—	4	8	no	—
622	C₄×D₄₃	—	4	8	no	—
623	Dic₈₆	—	2	8	no	—
624	Dic₈₆	—	2	8	no	—
625	Dic₈₆	—	2	16	no	—
626	Dic₈₆	—	4	8	no	—
627	Dic₈₆	—	4	8	no	—
628	C₂×#3520	—	43	1	no	maximal, Sylow
629	C₂²×C₄₃	—	2	2	no	—
630	C₂²×C₄₃	—	2	2	no	—
631	C₂²×C₄₃	—	2	8	no	—
632	C₂²×C₄₃	—	2	2	no	—
633	C₂²×C₄₃	—	2	2	no	—
634	C₂²×C₄₃	—	2	2	no	—
635	C₂²×C₄₃	—	4	4	no	—
636	C₂²×C₄₃	C₂²×#41	1	4	yes	—
637	C₂²×C₄₃	C₂²×#41	1	2	yes	—
638	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
639	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
640	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
641	C₂×D₄₃	—	2	2	no	—
642	C₂×D₄₃	—	2	2	no	—
643	C₂×D₄₃	—	2	2	no	—
644	C₂×D₄₃	—	2	2	no	—
645	C₂×D₄₃	—	2	8	no	—
646	C₂×D₄₃	—	2	8	no	—
647	C₂×D₄₃	—	2	2	no	—
648	C₂×D₄₃	—	2	4	no	—
649	C₂×D₄₃	—	2	2	no	—
650	C₂×D₄₃	—	2	4	no	—
651	C₂×D₄₃	—	2	2	no	—
652	C₂×D₄₃	—	2	4	no	—
653	C₂×D₄₃	—	4	16	no	—
654	C₂×D₄₃	—	4	16	no	—
655	C₂×D₄₃	—	4	8	no	—
656	C₂×D₄₃	—	4	4	no	—
657	C₂×D₄₃	C₂²×#41	1	4	yes	—
658	C₂×D₄₃	C₂×2₋¹⁺⁴	1	4	yes	—
659	C₄×C₄₃	—	2	4	no	—
660	C₄×C₄₃	—	2	4	no	—
661	C₄×C₄₃	—	2	2	no	—
662	C₄×C₄₃	—	2	2	no	—
663	C₄×C₄₃	—	2	4	no	—
664	C₄×C₄₃	—	2	2	no	—
665	C₄×C₄₃	—	2	2	no	—
666	C₄×C₄₃	—	2	4	no	—
667	C₄×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
668	Dic₄₃	—	2	4	no	—
669	Dic₄₃	—	2	4	no	—
670	Dic₄₃	—	2	4	no	—
671	Dic₄₃	—	2	2	no	—
672	Dic₄₃	—	2	2	no	—
673	Dic₄₃	—	2	2	no	—
674	Dic₄₃	—	2	2	no	—
675	Dic₄₃	C₂²×#41	1	4	yes	—
676	#3520	—	43	32	no	—
677	C₂×#556	—	43	1	no	—
678	C₂×#554	—	43	2	no	—
679	C₂×#552	—	43	1	no	—
680	C₂×#552	D₄₃	1	1	yes	characteristic, complemented
681	C₂×#551	—	43	2	no	—
682	C₂×#551	—	43	2	no	—
683	C₂×D₄×Q₈	—	43	1	no	—
684	C₂×#548	—	43	1	no	—
685	C₂×#548	—	43	1	no	—
686	C₂×#547	—	43	1	no	—
687	C₂×#547	—	43	1	no	—
688	C₂×#546	—	43	2	no	—
689	C₂×#542	—	43	2	no	—
690	C₂×#539	—	43	2	no	—
691	C₂×#539	—	43	2	no	—
692	C₂×#533	—	43	1	no	—
693	C₂×#529	—	43	1	no	—
694	C₂×#525	—	43	1	no	—
695	C₂×#525	—	43	1	no	—
696	C₂²×C₂²⋊Q₈	—	43	1	no	—
697	C₂²×C₂²⋊Q₈	—	43	1	no	—
698	C₂×#520	—	43	2	no	—
699	C₂²×C₄×D₄	—	43	1	no	—
700	C₂×C₄₃	—	2	4	no	—
701	C₂×C₄₃	—	4	2	no	—
702	C₂×C₄₃	#3520	1	4	yes	complemented
703	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
704	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
706	D₄₃	—	2	4	no	—
707	D₄₃	—	2	4	no	—
708	D₄₃	—	4	4	no	—
709	D₄₃	—	4	2	no	—
710	C₂²×#41	—	43	1	no	—
711	C₂²×#41	—	43	2	no	—
712	C₂²×#41	—	43	1	no	—
713	C₂³×Q₈	—	43	1	no	—
714	C₂³×Q₈	—	43	1	no	—
715	C₂³×D₄	—	43	1	no	—
716	C₂⁴×C₄	—	43	1	no	—
717	C₂⁴×C₄	—	43	1	no	—
718	#556	—	43	16	no	—
719	#554	—	43	32	no	—
720	#552	—	43	16	no	—
721	#552	C₂×D₄₃	1	16	yes	complemented
722	#551	—	43	32	no	—
723	#551	—	43	32	no	—
724	D₄×Q₈	—	43	16	no	—
725	#548	—	43	16	no	—
726	#548	—	43	16	no	—
727	#547	—	43	16	no	—
728	#547	—	43	16	no	—
729	#546	—	43	32	no	—
730	#542	—	43	32	no	—
731	#539	—	43	32	no	—
732	#539	—	43	32	no	—
733	#533	—	43	16	no	—
734	C₂×C₄⋊Q₈	—	43	1	no	—
735	C₂×C₄⋊Q₈	—	43	1	no	—
736	C₂×C₄⋊Q₈	—	43	2	no	—
737	#529	—	43	16	no	—
738	C₂×#126	—	43	2	no	—
739	C₂×#126	—	43	2	no	—
740	C₂×#126	—	43	2	no	—
741	C₂×#126	—	43	2	no	—
742	C₂×#126	C₂×D₄₃	1	2	yes	complemented
743	C₂×#125	—	43	2	no	—
744	C₂×#125	—	43	2	no	—
745	C₂×#125	C₂×D₄₃	1	1	yes	characteristic, complemented
746	C₂×#125	C₂×D₄₃	1	2	yes	complemented
747	C₂×#124	—	43	2	no	—
748	C₂×#124	—	43	2	no	—
749	C₂×#124	—	43	1	no	—
750	C₂×#124	—	43	2	no	—
751	#525	—	43	16	no	—
752	#525	—	43	16	no	—
753	C₂×#123	—	43	2	no	—
754	C₂×#123	—	43	2	no	—
755	C₂×#123	—	43	2	no	—
756	C₂×#123	—	43	2	no	—
757	C₂×#123	—	43	2	no	—
758	C₂×#123	—	43	2	no	—
759	C₂×#123	—	43	2	no	—
760	C₂×#123	—	43	2	no	—
761	C₂×#123	C₂×D₄₃	1	2	yes	—
762	C₂×C₂²⋊Q₈	—	43	1	no	—
763	C₂×C₂²⋊Q₈	—	43	1	no	—
764	C₂×C₂²⋊Q₈	—	43	16	no	—
765	C₂×C₂²⋊Q₈	—	43	2	no	—
766	C₂×C₂²⋊Q₈	—	43	2	no	—
767	C₂×C₂²⋊Q₈	—	43	2	no	—
768	C₂×C₂²⋊Q₈	—	43	2	no	—
769	C₂×C₂²⋊Q₈	—	43	2	no	—
770	C₂×C₂²⋊Q₈	—	43	1	no	—
771	C₂×C₂²⋊Q₈	—	43	1	no	—
772	C₂×C₂²⋊Q₈	—	43	2	no	—
773	C₂×C₂²⋊Q₈	—	43	2	no	—
774	C₂×C₂²⋊Q₈	—	43	1	no	—
775	C₂×C₂²⋊Q₈	—	43	1	no	—
776	C₂×C₂²⋊Q₈	—	43	1	no	—
777	C₂×C₂²⋊Q₈	—	43	2	no	—
778	C₂×C₂²⋊Q₈	—	43	16	no	—
779	C₂×C₂²⋊Q₈	—	43	2	no	—
780	C₂×C₂²⋊Q₈	—	43	2	no	—
781	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
782	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
783	C₂×#121	—	43	2	no	—
784	C₂×#121	—	43	1	no	—
785	C₂×#121	—	43	1	no	—
786	C₂×#121	—	43	2	no	—
787	C₂×#121	—	43	1	no	—
788	C₂×#121	—	43	2	no	—
789	C₂×#120	—	43	2	no	—
790	C₂×#120	—	43	2	no	—
791	#520	—	43	32	no	—
792	C₂×C₄×Q₈	—	43	1	no	—
793	C₂×C₄×Q₈	—	43	2	no	—
794	C₂×C₄×Q₈	—	43	2	no	—
795	C₂×C₄×Q₈	—	43	1	no	—
796	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
797	C₂×C₄×D₄	—	43	1	no	—
798	C₂×C₄×D₄	—	43	1	no	—
799	C₂×C₄×D₄	—	43	1	no	—
800	C₂×C₄×D₄	—	43	16	no	—
801	C₂×C₄×D₄	—	43	1	no	—
802	C₂×C₄×D₄	—	43	2	no	—
803	C₂×C₄×D₄	—	43	2	no	—
804	C₂×C₄×D₄	—	43	1	no	—
805	C₂×C₄×D₄	—	43	1	no	—
806	C₂×C₄×D₄	—	43	1	no	—
807	C₂×C₄×D₄	—	43	2	no	—
808	C₂×C₄×D₄	—	43	2	no	—
809	C₂×C₄×D₄	—	43	2	no	—
810	C₂×C₄×D₄	—	43	1	no	—
811	C₂×C₄×D₄	—	43	2	no	—
812	C₂×C₄×D₄	—	43	2	no	—
813	C₂×C₄×D₄	—	43	2	no	—
814	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
815	C₂×#117	—	43	2	no	—
816	C₂×#117	—	43	2	no	—
817	C₂×#117	—	43	1	no	—
818	C₂×#117	—	43	2	no	—
819	C₂×#117	C₂×D₄₃	1	2	yes	complemented
820	C₂×#117	C₂×D₄₃	1	1	yes	characteristic, complemented
821	C₂²×C₄⋊C₄	—	43	2	no	—
822	C₂²×C₄⋊C₄	—	43	1	no	—
823	C₂²×C₄⋊C₄	—	43	2	no	—
824	C₂²×C₄⋊C₄	—	43	2	no	—
825	C₂²×C₄⋊C₄	—	43	1	no	—
826	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
827	C₂²×C₂²⋊C₄	—	43	2	no	—
828	C₂²×C₂²⋊C₄	—	43	1	no	—
829	C₂²×C₂²⋊C₄	—	43	1	no	—
830	C₂²×C₂²⋊C₄	—	43	2	no	—
831	C₂²×C₄²	—	43	1	no	—
832	C₄₃	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
833	C₂⁵	—	43	1	no	—
834	C₂⁵	—	43	1	no	—
835	C₂×#41	—	43	8	no	—
836	C₂×#41	—	43	16	no	—
837	C₂×#41	—	43	8	no	—
838	C₂×#41	—	86	16	no	—
839	C₂×#41	—	172	4	no	—
840	C₂×#41	—	172	4	no	—
841	C₂²×Q₈	—	43	8	no	—
842	C₂²×Q₈	—	43	2	no	—
843	C₂²×Q₈	—	43	1	no	—
844	C₂²×Q₈	—	43	1	no	—
845	C₂²×Q₈	—	43	2	no	—
846	C₂²×Q₈	—	43	2	no	—
847	C₂²×Q₈	—	43	8	no	—
848	C₂²×Q₈	—	172	4	no	—
849	C₂²×Q₈	—	172	4	no	—
850	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
851	C₂²×D₄	—	43	1	no	—
852	C₂²×D₄	—	43	2	no	—
853	C₂²×D₄	—	43	1	no	—
854	C₂²×D₄	—	43	2	no	—
855	C₂²×D₄	—	43	8	no	—
856	C₂²×D₄	—	43	2	no	—
857	C₂²×D₄	—	43	2	no	—
858	C₂²×D₄	—	43	1	no	—
859	C₂²×D₄	—	43	1	no	—
860	C₂²×D₄	—	43	2	no	—
861	C₂²×D₄	—	86	8	no	—
862	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
863	C₂³×C₄	—	43	2	no	—
864	C₂³×C₄	—	43	1	no	—
865	C₂³×C₄	—	43	1	no	—
866	C₂³×C₄	—	43	1	no	—
867	C₂³×C₄	—	43	2	no	—
868	C₂³×C₄	—	43	2	no	—
869	C₂³×C₄	—	43	1	no	—
870	C₂³×C₄	—	43	1	no	—
871	C₂³×C₄	—	43	1	no	—
872	C₂³×C₄	—	43	1	no	—
873	C₂³×C₄	—	43	2	no	—
874	C₂³×C₄	—	43	1	no	—
875	C₂³×C₄	—	43	1	no	—
876	C₂³×C₄	—	43	1	no	—
877	C₂³×C₄	—	43	2	no	—
878	C₂³×C₄	—	43	2	no	—
879	C₂³×C₄	—	43	1	no	—
880	C₂³×C₄	—	43	8	no	—
881	C₂³×C₄	—	43	8	no	—
882	C₂³×C₄	—	172	4	no	—
883	C₂³×C₄	—	172	4	no	—
884	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
885	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
886	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
887	C₄⋊Q₈	—	43	8	no	—
888	C₄⋊Q₈	—	43	8	no	—
889	C₄⋊Q₈	—	43	16	no	—
890	#126	—	43	16	no	—
891	#126	—	43	16	no	—
892	#126	—	43	16	no	—
893	#126	—	43	16	no	—
894	#126	C₂²×D₄₃	1	16	yes	complemented
895	#125	—	43	16	no	—
896	#125	—	43	16	no	—
897	#125	C₂²×D₄₃	1	8	yes	complemented
898	#125	C₂²×D₄₃	1	16	yes	complemented
899	#124	—	43	16	no	—
900	#124	—	43	16	no	—
901	#124	—	43	8	no	—
902	#124	—	43	16	no	—
903	#123	—	43	16	no	—
904	#123	—	43	16	no	—
905	#123	—	43	16	no	—
906	#123	—	43	16	no	—
907	#123	—	43	16	no	—
908	#123	—	43	16	no	—
909	#123	—	43	16	no	—
910	#123	—	43	16	no	—
911	#123	C₂²×D₄₃	1	16	yes	—
912	C₂²⋊Q₈	—	43	8	no	—
913	C₂²⋊Q₈	—	43	8	no	—
914	C₂²⋊Q₈	—	43	8	no	—
915	C₂²⋊Q₈	—	43	8	no	—
916	C₂²⋊Q₈	—	43	16	no	—
917	C₂²⋊Q₈	—	43	8	no	—
918	C₂²⋊Q₈	—	43	8	no	—
919	C₂²⋊Q₈	—	43	16	no	—
920	C₂²⋊Q₈	—	43	16	no	—
921	C₂²⋊Q₈	—	43	8	no	—
922	C₂²⋊Q₈	—	43	16	no	—
923	C₂²⋊Q₈	—	43	16	no	—
924	C₂²⋊Q₈	—	43	16	no	—
925	C₂²⋊Q₈	—	43	16	no	—
926	C₂²⋊Q₈	—	43	16	no	—
927	C₂²⋊Q₈	—	43	16	no	—
928	C₂²⋊Q₈	—	43	16	no	—
929	C₂²⋊Q₈	C₂²×D₄₃	1	8	yes	complemented
930	C₂²⋊Q₈	C₂²×D₄₃	1	8	yes	complemented
931	#121	—	43	16	no	—
932	#121	—	43	8	no	—
933	#121	—	43	8	no	—
934	#121	—	43	8	no	—
935	#121	—	43	16	no	—
936	#121	—	43	16	no	—
937	#120	—	43	16	no	—
938	#120	—	43	16	no	—
939	C₄×Q₈	—	43	8	no	—
940	C₄×Q₈	—	43	16	no	—
941	C₄×Q₈	—	43	16	no	—
942	C₄×Q₈	—	43	8	no	—
943	C₄×Q₈	C₂²×D₄₃	1	8	yes	complemented
944	C₄×D₄	—	43	8	no	—
945	C₄×D₄	—	43	8	no	—
946	C₄×D₄	—	43	8	no	—
947	C₄×D₄	—	43	8	no	—
948	C₄×D₄	—	43	16	no	—
949	C₄×D₄	—	43	16	no	—
950	C₄×D₄	—	43	8	no	—
951	C₄×D₄	—	43	8	no	—
952	C₄×D₄	—	43	8	no	—
953	C₄×D₄	—	43	16	no	—
954	C₄×D₄	—	43	16	no	—
955	C₄×D₄	—	43	16	no	—
956	C₄×D₄	—	43	8	no	—
957	C₄×D₄	—	43	16	no	—
958	C₄×D₄	—	43	16	no	—
959	C₄×D₄	—	43	16	no	—
960	C₄×D₄	C₂²×D₄₃	1	8	yes	—
961	#117	—	43	16	no	—
962	#117	—	43	16	no	—
963	#117	—	43	8	no	—
964	#117	—	43	16	no	—
965	#117	C₂²×D₄₃	1	16	yes	complemented
966	#117	C₂²×D₄₃	1	8	yes	complemented
967	C₂×C₄⋊C₄	—	43	1	no	—
968	C₂×C₄⋊C₄	—	43	2	no	—
969	C₂×C₄⋊C₄	—	43	2	no	—
970	C₂×C₄⋊C₄	—	43	1	no	—
971	C₂×C₄⋊C₄	—	43	1	no	—
972	C₂×C₄⋊C₄	—	43	1	no	—
973	C₂×C₄⋊C₄	—	43	2	no	—
974	C₂×C₄⋊C₄	—	43	2	no	—
975	C₂×C₄⋊C₄	—	43	2	no	—
976	C₂×C₄⋊C₄	—	43	2	no	—
977	C₂×C₄⋊C₄	—	43	2	no	—
978	C₂×C₄⋊C₄	—	43	16	no	—
979	C₂×C₄⋊C₄	—	43	2	no	—
980	C₂×C₄⋊C₄	—	43	2	no	—
981	C₂×C₄⋊C₄	—	43	2	no	—
982	C₂×C₄⋊C₄	—	43	2	no	—
983	C₂×C₄⋊C₄	—	43	2	no	—
984	C₂×C₄⋊C₄	—	43	2	no	—
985	C₂×C₄⋊C₄	—	43	8	no	—
986	C₂×C₄⋊C₄	—	43	16	no	—
987	C₂×C₄⋊C₄	—	43	16	no	—
988	C₂×C₄⋊C₄	—	43	8	no	—
989	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
990	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
994	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
995	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
997	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
998	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
999	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	complemented
1000	C₂×C₂²⋊C₄	—	43	1	no	—
1001	C₂×C₂²⋊C₄	—	43	1	no	—
1002	C₂×C₂²⋊C₄	—	43	2	no	—
1003	C₂×C₂²⋊C₄	—	43	2	no	—
1004	C₂×C₂²⋊C₄	—	43	1	no	—
1005	C₂×C₂²⋊C₄	—	43	2	no	—
1006	C₂×C₂²⋊C₄	—	43	2	no	—
1007	C₂×C₂²⋊C₄	—	43	1	no	—
1008	C₂×C₂²⋊C₄	—	43	1	no	—
1009	C₂×C₂²⋊C₄	—	43	1	no	—
1010	C₂×C₂²⋊C₄	—	43	2	no	—
1011	C₂×C₂²⋊C₄	—	43	2	no	—
1012	C₂×C₂²⋊C₄	—	43	16	no	—
1013	C₂×C₂²⋊C₄	—	43	2	no	—
1014	C₂×C₂²⋊C₄	—	43	2	no	—
1015	C₂×C₂²⋊C₄	—	43	2	no	—
1016	C₂×C₂²⋊C₄	—	43	2	no	—
1017	C₂×C₂²⋊C₄	—	43	2	no	—
1018	C₂×C₂²⋊C₄	—	43	2	no	—
1019	C₂×C₂²⋊C₄	—	43	2	no	—
1020	C₂×C₂²⋊C₄	—	43	2	no	—
1021	C₂×C₂²⋊C₄	—	43	8	no	—
1022	C₂×C₂²⋊C₄	—	43	8	no	—
1023	C₂×C₂²⋊C₄	—	43	16	no	—
1024	C₂×C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
1027	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
1028	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
1029	C₂×C₄²	—	43	1	no	—
1030	C₂×C₄²	—	43	2	no	—
1031	C₂×C₄²	—	43	2	no	—
1032	C₂×C₄²	—	43	2	no	—
1033	C₂×C₄²	—	43	1	no	—
1034	C₂×C₄²	—	43	1	no	—
1035	C₂×C₄²	—	43	8	no	—
1036	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
1037	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
1038	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
1039	C₂⁴	—	43	1	no	—
1040	C₂⁴	—	43	1	no	—
1041	C₂⁴	—	43	1	no	—
1042	C₂⁴	—	43	2	no	—
1043	C₂⁴	—	43	4	no	—
1044	C₂⁴	—	43	4	no	—
1045	C₂⁴	—	86	4	no	—
1046	C₂⁴	—	86	4	no	—
1047	C₂⁴	—	86	4	no	—
1048	C₂⁴	—	86	4	no	—
1049	C₂⁴	—	172	2	no	—
1050	C₂⁴	—	172	2	no	—
1051	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
1052	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
1053	#41	—	86	64	no	—
1054	#41	—	172	16	no	—
1055	#41	—	172	16	no	—
1056	C₂×Q₈	—	2	4	no	—
1057	C₂×Q₈	—	43	8	no	—
1058	C₂×Q₈	—	43	4	no	—
1059	C₂×Q₈	—	43	4	no	—
1060	C₂×Q₈	—	43	8	no	—
1061	C₂×Q₈	—	43	8	no	—
1062	C₂×Q₈	—	86	8	no	—
1063	C₂×Q₈	—	86	4	no	—
1064	C₂×Q₈	—	86	4	no	—
1065	C₂×Q₈	—	172	4	no	—
1066	C₂×Q₈	—	172	4	no	—
1067	C₂×Q₈	—	172	16	no	—
1068	C₂×Q₈	—	172	16	no	—
1069	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
1070	C₂×D₄	—	2	4	no	—
1071	C₂×D₄	—	43	8	no	—
1072	C₂×D₄	—	43	4	no	—
1073	C₂×D₄	—	43	8	no	—
1074	C₂×D₄	—	43	4	no	—
1075	C₂×D₄	—	43	8	no	—
1076	C₂×D₄	—	43	8	no	—
1077	C₂×D₄	—	43	8	no	—
1078	C₂×D₄	—	43	4	no	—
1079	C₂×D₄	—	43	4	no	—
1080	C₂×D₄	—	43	8	no	—
1081	C₂×D₄	—	86	4	no	—
1082	C₂×D₄	—	86	8	no	—
1083	C₂×D₄	—	86	8	no	—
1084	C₂×D₄	—	86	4	no	—
1085	C₂×D₄	—	86	32	no	—
1086	C₂×D₄	—	86	8	no	—
1087	C₂×D₄	—	86	4	no	—
1088	C₂×D₄	—	172	4	no	—
1089	C₂×D₄	—	172	4	no	—
1090	C₂×D₄	C₂³×D₄₃	1	4	yes	—
1091	C₂²×C₄	—	2	8	no	—
1092	C₂²×C₄	—	2	4	no	—
1093	C₂²×C₄	—	2	4	no	—
1094	C₂²×C₄	—	43	1	no	—
1095	C₂²×C₄	—	43	1	no	—
1096	C₂²×C₄	—	43	2	no	—
1097	C₂²×C₄	—	43	1	no	—
1098	C₂²×C₄	—	43	1	no	—
1099	C₂²×C₄	—	43	2	no	—
1100	C₂²×C₄	—	43	2	no	—
1101	C₂²×C₄	—	43	1	no	—
1102	C₂²×C₄	—	43	8	no	—
1103	C₂²×C₄	—	43	4	no	—
1104	C₂²×C₄	—	43	4	no	—
1105	C₂²×C₄	—	43	4	no	—
1106	C₂²×C₄	—	43	4	no	—
1107	C₂²×C₄	—	43	4	no	—
1108	C₂²×C₄	—	43	8	no	—
1109	C₂²×C₄	—	43	8	no	—
1110	C₂²×C₄	—	43	4	no	—
1111	C₂²×C₄	—	43	4	no	—
1112	C₂²×C₄	—	43	8	no	—
1113	C₂²×C₄	—	43	4	no	—
1114	C₂²×C₄	—	43	4	no	—
1115	C₂²×C₄	—	43	4	no	—
1116	C₂²×C₄	—	43	8	no	—
1117	C₂²×C₄	—	43	8	no	—
1118	C₂²×C₄	—	43	4	no	—
1119	C₂²×C₄	—	86	4	no	—
1120	C₂²×C₄	—	86	8	no	—
1121	C₂²×C₄	—	86	8	no	—
1122	C₂²×C₄	—	86	4	no	—
1123	C₂²×C₄	—	86	4	no	—
1124	C₂²×C₄	—	86	4	no	—
1125	C₂²×C₄	—	86	4	no	—
1126	C₂²×C₄	—	172	16	no	—
1127	C₂²×C₄	—	172	16	no	—
1128	C₂²×C₄	—	172	2	no	—
1129	C₂²×C₄	—	172	2	no	—
1130	C₂²×C₄	—	172	2	no	—
1131	C₂²×C₄	—	172	2	no	—
1132	C₂²×C₄	—	172	4	no	—
1133	C₂²×C₄	—	172	4	no	—
1134	C₂²×C₄	—	172	4	no	—
1135	C₂²×C₄	—	172	2	no	—
1136	C₂²×C₄	—	172	2	no	—
1137	C₂²×C₄	—	172	4	no	—
1138	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
1139	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
1140	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
1141	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1143	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1145	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1147	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1148	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1150	C₄⋊C₄	—	43	4	no	—
1151	C₄⋊C₄	—	43	8	no	—
1152	C₄⋊C₄	—	43	8	no	—
1153	C₄⋊C₄	—	43	4	no	—
1154	C₄⋊C₄	—	43	4	no	—
1155	C₄⋊C₄	—	43	4	no	—
1156	C₄⋊C₄	—	43	8	no	—
1157	C₄⋊C₄	—	43	8	no	—
1158	C₄⋊C₄	—	43	8	no	—
1159	C₄⋊C₄	—	43	8	no	—
1160	C₄⋊C₄	—	43	8	no	—
1161	C₄⋊C₄	—	43	8	no	—
1162	C₄⋊C₄	—	43	8	no	—
1163	C₄⋊C₄	—	43	8	no	—
1164	C₄⋊C₄	—	43	8	no	—
1165	C₄⋊C₄	—	43	8	no	—
1166	C₄⋊C₄	—	43	8	no	—
1167	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1168	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
1169	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
1170	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
1171	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1172	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1173	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
1174	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1175	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1176	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
1177	C₂²⋊C₄	—	43	4	no	—
1178	C₂²⋊C₄	—	43	4	no	—
1179	C₂²⋊C₄	—	43	8	no	—
1180	C₂²⋊C₄	—	43	8	no	—
1181	C₂²⋊C₄	—	43	4	no	—
1182	C₂²⋊C₄	—	43	8	no	—
1183	C₂²⋊C₄	—	43	8	no	—
1184	C₂²⋊C₄	—	43	4	no	—
1185	C₂²⋊C₄	—	43	4	no	—
1186	C₂²⋊C₄	—	43	4	no	—
1187	C₂²⋊C₄	—	43	8	no	—
1188	C₂²⋊C₄	—	43	8	no	—
1189	C₂²⋊C₄	—	43	8	no	—
1190	C₂²⋊C₄	—	43	8	no	—
1191	C₂²⋊C₄	—	43	8	no	—
1192	C₂²⋊C₄	—	43	8	no	—
1193	C₂²⋊C₄	—	43	8	no	—
1194	C₂²⋊C₄	—	43	8	no	—
1195	C₂²⋊C₄	—	43	8	no	—
1196	C₂²⋊C₄	—	43	8	no	—
1197	C₂²⋊C₄	C₂³×D₄₃	1	4	yes	—
1198	C₂²⋊C₄	C₂³×D₄₃	1	4	yes	—
1199	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
1200	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
1201	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
1202	C₄²	—	43	4	no	—
1203	C₄²	—	43	4	no	—
1204	C₄²	—	43	4	no	—
1205	C₄²	—	43	8	no	—
1206	C₄²	—	43	8	no	—
1207	C₄²	—	43	8	no	—
1208	C₄²	C₂³×D₄₃	1	4	yes	—
1209	C₄²	C₂³×D₄₃	1	8	yes	—
1210	C₄²	C₂³×D₄₃	1	8	yes	—
1211	C₂³	—	2	2	no	—
1212	C₂³	—	2	2	no	—
1213	C₂³	—	2	2	no	—
1214	C₂³	—	2	2	no	—
1215	C₂³	—	2	2	no	—
1216	C₂³	—	43	4	no	—
1217	C₂³	—	43	4	no	—
1218	C₂³	—	43	2	no	—
1219	C₂³	—	43	2	no	—
1220	C₂³	—	43	2	no	—
1221	C₂³	—	43	4	no	—
1222	C₂³	—	86	8	no	—
1223	C₂³	—	86	8	no	—
1224	C₂³	—	86	8	no	—
1225	C₂³	—	86	2	no	—
1226	C₂³	—	86	2	no	—
1227	C₂³	—	86	2	no	—
1228	C₂³	—	86	2	no	—
1229	C₂³	—	86	4	no	—
1230	C₂³	—	86	8	no	—
1231	C₂³	—	86	2	no	—
1232	C₂³	—	86	2	no	—
1233	C₂³	—	86	4	no	—
1234	C₂³	—	86	4	no	—
1235	C₂³	—	86	2	no	—
1236	C₂³	—	172	4	no	—
1237	C₂³	—	172	4	no	—
1238	C₂³	—	172	16	no	—
1239	C₂³	—	172	16	no	—
1240	C₂³	#41×D₄₃	1	4	yes	—
1241	C₂³	C₂⁴×D₄₃	1	2	yes	—
1242	C₂³	C₂⁴×D₄₃	1	2	yes	—
1243	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
1244	Q₈	—	2	8	no	—
1245	Q₈	—	86	16	no	—
1246	Q₈	—	86	8	no	—
1247	Q₈	—	86	8	no	—
1248	Q₈	—	172	8	no	—
1249	Q₈	—	172	8	no	—
1250	D₄	—	2	8	no	—
1251	D₄	—	43	16	no	—
1252	D₄	—	86	8	no	—
1253	D₄	—	86	16	no	—
1254	D₄	—	86	16	no	—
1255	D₄	—	86	8	no	—
1256	D₄	—	86	16	no	—
1257	D₄	—	86	8	no	—
1258	D₄	—	172	8	no	—
1259	D₄	—	172	8	no	—
1260	C₂×C₄	—	2	4	no	—
1261	C₂×C₄	—	2	4	no	—
1262	C₂×C₄	—	2	16	no	—
1263	C₂×C₄	—	2	2	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	4	no	—
1267	C₂×C₄	—	2	2	no	—
1268	C₂×C₄	—	2	4	no	—
1269	C₂×C₄	—	2	8	no	—
1270	C₂×C₄	—	2	8	no	—
1271	C₂×C₄	—	43	4	no	—
1272	C₂×C₄	—	43	2	no	—
1273	C₂×C₄	—	43	2	no	—
1274	C₂×C₄	—	43	4	no	—
1275	C₂×C₄	—	43	2	no	—
1276	C₂×C₄	—	43	2	no	—
1277	C₂×C₄	—	43	4	no	—
1278	C₂×C₄	—	43	4	no	—
1279	C₂×C₄	—	43	2	no	—
1280	C₂×C₄	—	86	8	no	—
1281	C₂×C₄	—	86	16	no	—
1282	C₂×C₄	—	86	16	no	—
1283	C₂×C₄	—	86	8	no	—
1284	C₂×C₄	—	86	4	no	—
1285	C₂×C₄	—	86	2	no	—
1286	C₂×C₄	—	86	2	no	—
1287	C₂×C₄	—	86	2	no	—
1288	C₂×C₄	—	86	4	no	—
1289	C₂×C₄	—	86	4	no	—
1290	C₂×C₄	—	86	2	no	—
1291	C₂×C₄	—	86	8	no	—
1292	C₂×C₄	—	86	8	no	—
1293	C₂×C₄	—	86	8	no	—
1294	C₂×C₄	—	172	4	no	—
1295	C₂×C₄	—	172	4	no	—
1296	C₂×C₄	—	172	4	no	—
1297	C₂×C₄	—	172	4	no	—
1298	C₂×C₄	—	172	8	no	—
1299	C₂×C₄	—	172	8	no	—
1300	C₂×C₄	—	172	8	no	—
1301	C₂×C₄	—	172	4	no	—
1302	C₂×C₄	—	172	4	no	—
1303	C₂×C₄	—	172	8	no	—
1304	C₂×C₄	#13063371	1	4	yes	—
1305	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
1306	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
1307	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
1308	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
1309	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
1310	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
1311	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
1312	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
1313	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	2	2	no	—
1316	C₂²	—	2	8	no	—
1317	C₂²	—	2	2	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	2	no	—
1320	C₂²	—	4	4	no	—
1321	C₂²	—	43	4	no	—
1322	C₂²	—	43	4	no	—
1323	C₂²	—	86	2	no	—
1324	C₂²	—	86	2	no	—
1325	C₂²	—	86	2	no	—
1326	C₂²	—	86	2	no	—
1327	C₂²	—	86	8	no	—
1328	C₂²	—	86	8	no	—
1329	C₂²	—	86	4	no	—
1330	C₂²	—	86	2	no	—
1331	C₂²	—	86	2	no	—
1332	C₂²	—	86	4	no	—
1333	C₂²	—	86	4	no	—
1334	C₂²	—	86	2	no	—
1335	C₂²	—	172	16	no	—
1336	C₂²	—	172	16	no	—
1337	C₂²	—	172	4	no	—
1338	C₂²	—	172	8	no	—
1339	C₂²	C₂×#41×D₄₃	1	4	yes	—
1340	C₂²	C₂×#41×D₄₃	1	2	yes	—
1341	C₂²	C₂×#13063371	1	2	yes	—
1342	C₂²	2₋¹⁺⁴×D₄₃	1	2	yes	—
1343	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
1344	C₄	—	2	4	no	—
1345	C₄	—	2	4	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	4	no	—
1350	C₄	—	2	2	no	—
1351	C₄	—	2	4	no	—
1352	C₄	—	43	4	no	—
1353	C₄	—	86	4	no	—
1354	C₄	—	86	2	no	—
1355	C₄	—	86	2	no	—
1356	C₄	—	86	2	no	—
1357	C₄	—	86	4	no	—
1358	C₄	—	86	4	no	—
1359	C₄	—	86	2	no	—
1360	C₄	C₂×#13063371	1	4	yes	—
1361	C₂	—	2	4	no	—
1362	C₂	—	4	2	no	—
1363	C₂	—	86	4	no	—
1364	C₂	—	86	4	no	—
1365	C₂	—	172	2	no	—
1366	C₂	—	172	4	no	—
1367	C₂	#19148641	1	4	yes	direct product factor
1368	C₂	C₂²×#41×D₄₃	1	1	yes	characteristic
1369	C₂	C₂²×#13063371	1	1	yes	characteristic
1370	C₂	C₂×2₋¹⁺⁴×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#552	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#552	D₄₃
hypocenter	C₄₃	C₂×#3520
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#552

Complements

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

N	H ≅ G/N	type
1. #19148641	C₂	direct (N × H)
2. C₂×#14583617	C₂	semidirect
3. C₂×#14583605	C₂	semidirect
4. C₂×#14583587	C₂	semidirect
5. C₂×#14583574	C₂	semidirect
6. C₂×#14583573	C₂	semidirect
7. C₂×#14583562	C₂	semidirect
8. C₂×#14583561	C₂	semidirect
9. C₂×#14583558	C₂	semidirect
10. C₂×#14583551	C₂	semidirect
11. C₂×#14583550	C₂	semidirect
12. C₂×#14583541	C₂	semidirect
13. C₂×#14583515	C₂	semidirect
14. C₂×#14583497	C₂	semidirect
15. C₂×#14583493	C₂	semidirect
16. C₂×#14583453	C₂	semidirect
17. C₂×#14583434	C₂	semidirect
18. C₂×#14583412	C₂	semidirect
19. C₂×#14583411	C₂	semidirect
20. C₂²×#13063305	C₂	semidirect
21. C₂×C₂²⋊Q₈×D₄₃	C₂	semidirect
22. C₂×#14583379	C₂	semidirect
23. C₂×C₄×D₄×D₄₃	C₂	semidirect
24. C₂×C₄₃×#552	C₂	semidirect
25. C₂²×#10621902	C₂²	semidirect
27. C₂²×#10621898	C₂²	semidirect
28. C₂³×Dic₈₆	C₂²	semidirect
29. C₂²×Q₈×D₄₃	C₂²	semidirect
33. #14583617	C₂²	semidirect
34. #14583605	C₂²	semidirect
35. #14583587	C₂²	semidirect
36. #14583574	C₂²	semidirect
37. #14583573	C₂²	semidirect
38. #14583562	C₂²	semidirect
39. #14583561	C₂²	semidirect
40. #14583558	C₂²	semidirect
41. #14583551	C₂²	semidirect
42. #14583550	C₂²	semidirect
43. #14583541	C₂²	semidirect
44. #14583515	C₂²	semidirect
45. #14583497	C₂²	semidirect
46. #14583493	C₂²	semidirect
47. #14583453	C₂²	semidirect
48. C₂×#13063324	C₂²	semidirect
49. C₂×#13063324	C₂²	semidirect
50. C₂×#13063323	C₂²	semidirect
51. #14583434	C₂²	semidirect
52. C₂×#13063320	C₂²	semidirect
53. C₂×#13063320	C₂²	semidirect
54. C₂×#13063319	C₂²	semidirect
55. C₂×#13063318	C₂²	semidirect
56. C₂×#13063316	C₂²	semidirect
57. C₂×#13063315	C₂²	semidirect
58. C₂×#13063313	C₂²	semidirect
59. C₂×#13063313	C₂²	semidirect
61. C₂×#13063311	C₂²	semidirect
62. #14583412	C₂²	semidirect
63. #14583411	C₂²	semidirect
66. C₂×#13063310	C₂²	semidirect
67. C₂×#13063310	C₂²	semidirect
68. C₂×#13063310	C₂²	semidirect
69. C₂×#13063309	C₂²	semidirect
70. C₂×#13063308	C₂²	semidirect
71. C₂×#13063307	C₂²	semidirect
75. C₂×#13063305	C₂²	semidirect
76. C₂×#13063305	C₂²	semidirect
77. C₂×#13063305	C₂²	semidirect
78. C₂×#13063305	C₂²	semidirect
79. C₂×#13063305	C₂²	semidirect
80. C₂×#13063305	C₂²	semidirect
81. C₂×#13063304	C₂²	semidirect
84. C₂×#13063303	C₂²	semidirect
85. C₂×#13063303	C₂²	semidirect
86. C₂×#13063303	C₂²	semidirect
87. C₂×#13063302	C₂²	semidirect
88. C₂×#13063302	C₂²	semidirect
90. C₂²⋊Q₈×D₄₃	C₂²	semidirect
93. C₂×#13063300	C₂²	semidirect
94. C₂×#13063299	C₂²	semidirect
99. #14583379	C₂²	semidirect
100. C₂×C₄×Dic₈₆	C₂²	semidirect
101. C₂×C₄×Dic₈₆	C₂²	semidirect
102. C₂×C₄×Dic₈₆	C₂²	semidirect
103. C₂×#13063290	C₂²	semidirect
106. C₂×C₄×D₁₇₂	C₂²	semidirect
107. C₂×C₄×D₁₇₂	C₂²	semidirect
112. C₂×#13063287	C₂²	semidirect
118. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
119. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
120. C₄×D₄×D₄₃	C₂²	semidirect
121. C₂×#13063283	C₂²	semidirect
122. C₂×#13063283	C₂²	semidirect
123. C₂×#13063283	C₂²	semidirect
125. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
127. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
128. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
129. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
135. C₄₃×#552	C₂²	semidirect
136. C₂×#126×C₄₃	C₂²	semidirect
137. C₂×#125×C₄₃	C₂²	semidirect
138. C₂×#125×C₄₃	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
142. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
144. C₂×#117×C₄₃	C₂²	semidirect
145. C₂×#117×C₄₃	C₂²	semidirect
146. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
150. C₂×#10621902	C₂³	semidirect
154. C₂×#10621898	C₂³	semidirect
161. C₂²×Dic₈₆	C₂³	semidirect
163. C₂×Q₈×D₄₃	C₂³	semidirect
196. #13063324	C₂³	semidirect
197. #13063324	C₂³	semidirect
198. #13063323	C₂³	semidirect
199. #13063320	C₂³	semidirect
200. #13063320	C₂³	semidirect
201. #13063319	C₂³	semidirect
202. #13063318	C₂³	semidirect
203. #13063316	C₂³	semidirect
204. #13063315	C₂³	semidirect
205. #13063313	C₂³	semidirect
206. #13063313	C₂³	semidirect
208. #13063311	C₂³	semidirect
211. #13063310	C₂³	semidirect
212. #13063310	C₂³	semidirect
213. #13063310	C₂³	semidirect
214. #13063309	C₂³	semidirect
215. #13063308	C₂³	semidirect
216. #13063307	C₂³	semidirect
220. #13063305	C₂³	semidirect
221. #13063305	C₂³	semidirect
222. #13063305	C₂³	semidirect
223. #13063305	C₂³	semidirect
224. #13063305	C₂³	semidirect
225. #13063304	C₂³	semidirect
228. #13063303	C₂³	semidirect
229. #13063303	C₂³	semidirect
230. #13063303	C₂³	semidirect
231. #13063302	C₂³	semidirect
232. #13063302	C₂³	semidirect
236. #13063300	C₂³	semidirect
237. #13063299	C₂³	semidirect
242. C₄×Dic₈₆	C₂³	semidirect
243. C₄×Dic₈₆	C₂³	semidirect
244. C₄×Dic₈₆	C₂³	semidirect
245. #13063290	C₂³	semidirect
248. C₄×D₁₇₂	C₂³	semidirect
249. C₄×D₁₇₂	C₂³	semidirect
254. #13063287	C₂³	semidirect
260. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
261. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
262. #13063283	C₂³	semidirect
263. #13063283	C₂³	semidirect
264. #13063283	C₂³	semidirect
273. C₂×C₄⋊Dic₄₃	C₂³	semidirect
285. C₄⋊C₄×D₄₃	C₂³	semidirect
286. C₄⋊C₄×D₄₃	C₂³	semidirect
287. C₄⋊C₄×D₄₃	C₂³	semidirect
324. #126×C₄₃	C₂³	semidirect
325. #125×C₄₃	C₂³	semidirect
326. #125×C₄₃	C₂³	semidirect
328. C₂²⋊Q₈×C₄₃	C₂³	semidirect
329. C₂²⋊Q₈×C₄₃	C₂³	semidirect
330. C₄×Q₈×C₄₃	C₂³	semidirect
332. #117×C₄₃	C₂³	semidirect
333. #117×C₄₃	C₂³	semidirect
344. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
389. C₂×C₂²⋊D₄₃	#41	semidirect
584. C₂²⋊D₄₃	C₂×#41	semidirect
680. C₂×#552	D₄₃	semidirect
702. C₂×C₄₃	#3520	semidirect
721. #552	C₂×D₄₃	semidirect
742. C₂×#126	C₂×D₄₃	semidirect
745. C₂×#125	C₂×D₄₃	semidirect
746. C₂×#125	C₂×D₄₃	semidirect
781. C₂×C₂²⋊Q₈	C₂×D₄₃	semidirect
782. C₂×C₂²⋊Q₈	C₂×D₄₃	semidirect
796. C₂×C₄×Q₈	C₂×D₄₃	semidirect
819. C₂×#117	C₂×D₄₃	semidirect
820. C₂×#117	C₂×D₄₃	semidirect
826. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
832. C₄₃	C₂×#3520	semidirect
894. #126	C₂²×D₄₃	semidirect
897. #125	C₂²×D₄₃	semidirect
898. #125	C₂²×D₄₃	semidirect
929. C₂²⋊Q₈	C₂²×D₄₃	semidirect
930. C₂²⋊Q₈	C₂²×D₄₃	semidirect
943. C₄×Q₈	C₂²×D₄₃	semidirect
965. #117	C₂²×D₄₃	semidirect
966. #117	C₂²×D₄₃	semidirect
999. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
1367. C₂	#19148641	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148641	2
C₂×#14583617	2
C₂×#14583605	2
C₂×#14583587	2
C₂×#14583574	2
C₂×#14583573	2
C₂×#14583562	2
C₂×#14583561	2
C₂×#14583558	2
C₂×#14583551	2
C₂×#14583550	2
C₂×#14583541	2
C₂×#14583515	2
C₂×#14583497	2
C₂×#14583493	2
C₂×#14583453	2
C₂×#14583434	2
C₂×#14583412	2
C₂×#14583411	2
C₂²×#13063305	2
C₂×C₂²⋊Q₈×D₄₃	2
C₂×#14583379	2
C₂×C₄×D₄×D₄₃	2
C₂×C₄₃×#552	2
C₂×#3520	43

Subgroups — C2×#19148641 #26004599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148641 #26004599