Subgroups — #6370488

Order 512.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1183 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2981	C₂	1	1	yes	maximal, characteristic
2	C₂×#2935	C₂	1	1	yes	maximal, characteristic
3	#34346	C₂	1	1	yes	maximal, characteristic
4	#20564	C₂	1	1	yes	maximal, characteristic, complemented
5	#20564	C₂	1	1	yes	maximal, characteristic, complemented
6	#20561	C₂	1	1	yes	maximal, characteristic, complemented
7	#20561	C₂	1	1	yes	maximal, characteristic, complemented
8	#20560	C₂	1	1	yes	maximal, characteristic, complemented
9	#20560	C₂	1	1	yes	maximal, characteristic, complemented
10	#20557	C₂	1	1	yes	maximal, characteristic, complemented
11	#20557	C₂	1	1	yes	maximal, characteristic, complemented
12	#20545	C₂	1	1	yes	maximal, characteristic, complemented
13	#20544	C₂	1	1	yes	maximal, characteristic, complemented
14	#20532	C₂	1	1	yes	maximal, characteristic, complemented
15	#20531	C₂	1	1	yes	maximal, characteristic, complemented
16	#20531	C₂	1	1	yes	maximal, characteristic, complemented
17	#20530	C₂	1	1	yes	maximal, characteristic, complemented
18	#20493	C₂	1	1	yes	maximal, characteristic, complemented
19	#20493	C₂	1	1	yes	maximal, characteristic, complemented
20	#20490	C₂	1	1	yes	maximal, characteristic, complemented
21	#20490	C₂	1	1	yes	maximal, characteristic, complemented
22	#20487	C₂	1	1	yes	maximal, characteristic, complemented
23	#20487	C₂	1	1	yes	maximal, characteristic, complemented
24	#20484	C₂	1	1	yes	maximal, characteristic, complemented
25	#20484	C₂	1	1	yes	maximal, characteristic, complemented
26	#20482	C₂	1	1	yes	maximal, characteristic, complemented
27	#20477	C₂	1	1	yes	maximal, characteristic, complemented
28	#20387	C₂	1	1	yes	maximal, characteristic, complemented
29	#20387	C₂	1	1	yes	maximal, characteristic, complemented
30	#20384	C₂	1	1	yes	maximal, characteristic, complemented
31	#20383	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#131	C₂²	1	1	yes	characteristic
33	C₂²×#131	C₂²	1	1	yes	characteristic
34	C₂×#532	C₂²	1	1	yes	characteristic
35	#2981	C₄	1	16	yes	complemented
36	#2935	C₄	1	16	yes	complemented
37	C₂×#436	C₂²	1	1	yes	characteristic
38	C₂×#436	C₂²	1	1	yes	characteristic
39	C₂×#436	C₂²	1	1	yes	characteristic
40	C₂×#436	C₂²	1	1	yes	characteristic
41	C₂×#435	C₂²	1	1	yes	characteristic
42	C₂×#435	C₂²	1	1	yes	characteristic
43	C₂×#435	C₂²	1	1	yes	characteristic
44	C₂×#435	C₂²	1	1	yes	characteristic
45	C₂×#435	C₂²	1	1	yes	characteristic
46	C₂×#435	C₂²	1	1	yes	characteristic
47	C₂×#435	C₂²	1	1	yes	characteristic
48	C₂×#435	C₂²	1	1	yes	characteristic
49	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
53	C₂×#432	C₂²	1	1	yes	characteristic
54	C₂×#431	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×#408	C₂²	1	1	yes	characteristic
57	C₂×#408	C₂²	1	1	yes	characteristic
58	C₂×#408	C₂²	1	1	yes	characteristic
59	C₂×#408	C₂²	1	1	yes	characteristic
60	C₂×#408	C₂²	1	1	yes	characteristic
61	C₂×#408	C₂²	1	1	yes	characteristic
62	C₂×#405	C₂²	1	1	yes	characteristic
63	C₂×#405	C₂²	1	1	yes	characteristic
64	C₂×#405	C₂²	1	1	yes	characteristic
65	C₂×#405	C₂²	1	1	yes	characteristic
66	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
67	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
68	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
69	C₂²×#97	C₂²	1	1	yes	characteristic
70	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
71	#2381	C₄	1	2	yes	—
72	#2380	C₄	1	2	yes	—
73	#2379	C₄	1	2	yes	—
74	#2379	C₄	1	2	yes	—
75	#2377	C₄	1	2	yes	—
76	#2377	C₄	1	2	yes	—
77	#2377	C₄	1	2	yes	—
78	#2377	C₄	1	2	yes	—
79	#2297	C₂²	1	1	yes	characteristic
80	#2297	C₂²	1	1	yes	characteristic
81	#2297	C₂²	1	1	yes	characteristic
82	#2297	C₂²	1	1	yes	characteristic
83	#2290	C₂²	1	1	yes	characteristic
84	#2290	C₂²	1	1	yes	characteristic
85	#2290	C₂²	1	1	yes	characteristic
86	#2290	C₂²	1	1	yes	characteristic
87	#2290	C₂²	1	1	yes	characteristic
88	#2290	C₂²	1	1	yes	characteristic
89	#2290	C₂²	1	1	yes	characteristic
90	#2290	C₂²	1	1	yes	characteristic
91	#2283	C₂²	1	1	yes	characteristic
92	#2283	C₂²	1	1	yes	characteristic
93	#1771	C₂²	1	1	yes	characteristic
94	#1771	C₂²	1	1	yes	characteristic
95	#1771	C₂²	1	1	yes	characteristic
96	#1771	C₂²	1	1	yes	characteristic
97	#1771	C₂²	1	1	yes	characteristic
98	#1771	C₂²	1	1	yes	characteristic
99	#1771	C₂²	1	1	yes	characteristic
100	#1771	C₂²	1	1	yes	characteristic
101	#1770	C₂²	1	1	yes	characteristic
102	#1770	C₂²	1	1	yes	characteristic
103	#1770	C₂²	1	1	yes	characteristic
104	#1770	C₂²	1	1	yes	characteristic
105	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	#1768	C₂²	1	1	yes	characteristic
110	#1768	C₂²	1	1	yes	characteristic
111	#1768	C₂²	1	1	yes	characteristic
112	#1768	C₂²	1	1	yes	characteristic
113	#1768	C₂²	1	1	yes	characteristic
114	#1768	C₂²	1	1	yes	characteristic
115	#1768	C₂²	1	1	yes	characteristic
116	#1768	C₂²	1	1	yes	characteristic
117	#1753	C₂²	1	1	yes	characteristic
118	#1753	C₂²	1	1	yes	characteristic
119	#1753	C₂²	1	1	yes	characteristic
120	#1753	C₂²	1	1	yes	characteristic
121	#1753	C₂²	1	1	yes	characteristic
122	#1753	C₂²	1	1	yes	characteristic
123	#1753	C₂²	1	1	yes	characteristic
124	#1753	C₂²	1	1	yes	characteristic
125	#1753	C₂²	1	1	yes	characteristic
126	#1753	C₂²	1	1	yes	characteristic
127	#1753	C₂²	1	1	yes	characteristic
128	#1753	C₂²	1	1	yes	characteristic
129	#1753	C₂²	1	1	yes	characteristic
130	#1753	C₂²	1	1	yes	characteristic
131	#1753	C₂²	1	1	yes	characteristic
132	#1753	C₂²	1	1	yes	characteristic
133	#1753	C₂²	1	1	yes	characteristic
134	#1753	C₂²	1	1	yes	characteristic
135	#1753	C₂²	1	1	yes	characteristic
136	#1753	C₂²	1	1	yes	characteristic
137	#1753	C₂²	1	1	yes	characteristic
138	#1753	C₂²	1	1	yes	characteristic
139	#1753	C₂²	1	1	yes	characteristic
140	#1753	C₂²	1	1	yes	characteristic
141	#1752	C₂²	1	1	yes	characteristic
142	#1752	C₂²	1	1	yes	characteristic
143	#1752	C₂²	1	1	yes	characteristic
144	#1752	C₂²	1	1	yes	characteristic
145	#1752	C₂²	1	1	yes	characteristic
146	#1752	C₂²	1	1	yes	characteristic
147	#1752	C₂²	1	1	yes	characteristic
148	#1752	C₂²	1	1	yes	characteristic
149	#1752	C₂²	1	1	yes	characteristic
150	#1752	C₂²	1	1	yes	characteristic
151	#1752	C₂²	1	1	yes	characteristic
152	#1752	C₂²	1	1	yes	characteristic
153	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
156	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
157	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
159	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
160	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
161	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
162	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
164	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
165	#1750	C₂²	1	1	yes	characteristic
166	#1750	C₂²	1	1	yes	characteristic
167	#1750	C₂²	1	1	yes	characteristic
168	#1750	C₂²	1	1	yes	characteristic
169	#1750	C₂²	1	1	yes	characteristic
170	#1750	C₂²	1	1	yes	characteristic
171	#1750	C₂²	1	1	yes	characteristic
172	#1750	C₂²	1	1	yes	characteristic
173	#1749	C₂²	1	1	yes	characteristic
174	#1749	C₂²	1	1	yes	characteristic
175	#1749	C₂²	1	1	yes	characteristic
176	#1749	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
181	#1746	C₂²	1	1	yes	characteristic
182	#1746	C₂²	1	1	yes	characteristic
183	#1746	C₂²	1	1	yes	characteristic
184	#1746	C₂²	1	1	yes	characteristic
185	#1729	C₂²	1	1	yes	characteristic
186	#1729	C₂²	1	1	yes	characteristic
187	#1729	C₂²	1	1	yes	characteristic
188	#1729	C₂²	1	1	yes	characteristic
189	#1728	C₂²	1	1	yes	characteristic
190	#1728	C₂²	1	1	yes	characteristic
191	C₂×#336	C₂²	1	1	yes	characteristic
192	C₂×#336	C₂²	1	1	yes	characteristic
193	#1726	C₂²	1	1	yes	characteristic
194	#1726	C₂²	1	1	yes	characteristic
195	#1726	C₂²	1	1	yes	characteristic
196	#1726	C₂²	1	1	yes	characteristic
197	C₂²×#41	C₂³	1	1	yes	characteristic
198	C₂²×#41	C₂³	1	1	yes	characteristic
199	C₂×#131	—	4	2	no	—
200	C₂×#131	—	4	2	no	—
201	C₂×#131	—	4	2	no	—
202	C₂×#131	—	4	2	no	—
203	C₂×#131	C₂×C₄	1	8	yes	complemented
204	C₂×#131	C₂×C₄	1	8	yes	complemented
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂²×M₁₆	C₂³	1	1	yes	characteristic
209	C₂²×M₁₆	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	C₂²×M₁₆	C₂³	1	1	yes	characteristic
213	C₂²×M₁₆	C₂³	1	1	yes	characteristic
214	C₂²×M₁₆	C₂³	1	1	yes	characteristic
215	C₂³×C₈	C₂³	1	1	yes	characteristic
216	C₂³×C₈	C₂³	1	1	yes	characteristic
217	C₂³×C₈	C₂³	1	1	yes	characteristic
218	C₂³×C₈	C₂³	1	1	yes	characteristic
219	C₂³×C₈	C₂³	1	1	yes	characteristic
220	C₂³×C₈	C₂³	1	1	yes	characteristic
221	C₂³×C₈	C₂³	1	1	yes	characteristic
222	C₂³×C₈	C₂³	1	1	yes	characteristic
223	C₂³×C₈	C₂³	1	1	yes	characteristic
224	C₂³×C₈	C₂³	1	1	yes	characteristic
225	#532	C₂×C₄	1	8	yes	—
226	#532	C₂×C₄	1	8	yes	—
227	C₂×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
228	C₂×#127	C₂×C₄	1	1	yes	characteristic
229	C₂×#124	C₂×C₄	1	1	yes	characteristic
230	C₂×#124	C₂×C₄	1	1	yes	characteristic
231	C₂×#121	C₂×C₄	1	1	yes	characteristic
232	C₂×#121	C₂×C₄	1	1	yes	characteristic
233	C₂×#121	C₂×C₄	1	1	yes	characteristic
234	C₂×#121	C₂×C₄	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×#117	C₂³	1	1	yes	characteristic
240	C₂×#117	C₂³	1	1	yes	characteristic
241	C₂×#117	C₂³	1	1	yes	characteristic
242	C₂×#117	C₂³	1	1	yes	characteristic
243	C₂²×C₄²	C₂³	1	1	yes	characteristic
244	C₂²×C₄²	C₂³	1	1	yes	characteristic
245	C₂²×C₄²	C₂³	1	1	yes	characteristic
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	C₂²×C₄²	C₂³	1	1	yes	characteristic
248	#436	C₂×C₄	1	8	yes	complemented
249	#436	C₂×C₄	1	8	yes	complemented
250	#436	C₂×C₄	1	8	yes	complemented
251	#436	C₂×C₄	1	8	yes	complemented
252	#435	C₂×C₄	1	8	yes	complemented
253	#435	C₂×C₄	1	8	yes	complemented
254	#435	C₂×C₄	1	8	yes	complemented
255	#435	C₂×C₄	1	8	yes	complemented
256	#435	C₂×C₄	1	8	yes	complemented
257	#435	C₂×C₄	1	8	yes	complemented
258	#435	C₂×C₄	1	8	yes	complemented
259	#435	C₂×C₄	1	8	yes	complemented
260	C₈×D₄	C₂×C₄	1	8	yes	complemented
261	C₈×D₄	C₂×C₄	1	8	yes	complemented
262	C₈×D₄	C₂×C₄	1	8	yes	complemented
263	C₈×D₄	C₂×C₄	1	8	yes	complemented
264	#432	C₂×C₄	1	8	yes	complemented
265	#431	C₂×C₄	1	8	yes	complemented
266	C₂×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	#408	C₂×C₄	1	8	yes	complemented
276	#408	C₂×C₄	1	8	yes	complemented
277	#408	C₂×C₄	1	8	yes	complemented
278	#408	C₂×C₄	1	8	yes	complemented
279	#408	C₂×C₄	1	8	yes	complemented
280	#408	C₂×C₄	1	8	yes	complemented
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	#405	—	4	2	no	—
302	#405	—	4	2	no	—
303	#405	—	4	2	no	—
304	#405	—	4	2	no	—
305	C₄×M₁₆	—	4	2	no	—
306	C₄×M₁₆	—	4	2	no	—
307	C₄×M₁₆	C₂×C₄	1	8	yes	complemented
308	C₂×#97	—	4	2	no	—
309	C₂×#97	C₂³	1	1	yes	characteristic
310	C₂×#97	C₂³	1	1	yes	characteristic
311	C₂×#97	C₂³	1	1	yes	characteristic
312	C₂×#97	C₂³	1	1	yes	characteristic
313	C₂×#97	C₂³	1	1	yes	characteristic
314	C₂×#97	C₂³	1	1	yes	characteristic
315	C₂×#97	C₂³	1	1	yes	characteristic
316	C₂×#97	C₂³	1	1	yes	characteristic
317	C₂×#97	C₂³	1	1	yes	characteristic
318	C₂×#97	C₂³	1	1	yes	characteristic
319	C₂×#97	C₂³	1	1	yes	characteristic
320	C₂×#97	C₂³	1	1	yes	characteristic
321	C₂×#97	C₂³	1	1	yes	characteristic
322	C₂×#97	C₂³	1	1	yes	characteristic
323	C₂×#97	C₂³	1	1	yes	characteristic
324	C₂×#97	C₂³	1	1	yes	characteristic
325	C₂×#97	C₂³	1	1	yes	characteristic
326	C₂×#97	C₂³	1	1	yes	characteristic
327	C₂×#97	C₂³	1	1	yes	characteristic
328	C₂×#97	C₂³	1	1	yes	characteristic
329	C₂×C₄×C₈	—	4	2	no	—
330	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
337	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
346	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
347	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
348	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
349	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
350	#391	C₂×C₄	1	2	yes	—
351	#391	C₂×C₄	1	2	yes	—
352	#391	C₂×C₄	1	2	yes	—
353	#391	C₂×C₄	1	2	yes	—
354	#390	C₂×C₄	1	2	yes	—
355	#390	C₂×C₄	1	2	yes	—
356	#390	C₂×C₄	1	2	yes	—
357	#390	C₂×C₄	1	2	yes	—
358	#388	C₂×C₄	1	2	yes	—
359	#388	C₂×C₄	1	2	yes	—
360	#388	C₂×C₄	1	2	yes	—
361	#388	C₂×C₄	1	2	yes	—
362	#388	C₂×C₄	1	2	yes	—
363	#388	C₂×C₄	1	2	yes	—
364	#388	C₂×C₄	1	2	yes	—
365	#388	C₂×C₄	1	2	yes	—
366	#387	C₂×C₄	1	2	yes	—
367	#387	C₂×C₄	1	2	yes	—
368	#387	C₂×C₄	1	2	yes	—
369	#387	C₂×C₄	1	2	yes	—
370	#387	C₂×C₄	1	2	yes	—
371	#387	C₂×C₄	1	2	yes	—
372	#387	C₂×C₄	1	2	yes	—
373	#387	C₂×C₄	1	2	yes	—
374	#386	C₂×C₄	1	2	yes	—
375	#386	C₂×C₄	1	2	yes	—
376	#386	C₂×C₄	1	2	yes	—
377	#386	C₂×C₄	1	2	yes	—
378	#386	C₂×C₄	1	2	yes	—
379	#386	C₂×C₄	1	2	yes	—
380	#386	C₂×C₄	1	2	yes	—
381	#386	C₂×C₄	1	2	yes	—
382	#386	C₂×C₄	1	2	yes	—
383	#386	C₂×C₄	1	2	yes	—
384	#386	C₂×C₄	1	2	yes	—
385	#386	C₂×C₄	1	2	yes	—
386	#386	C₂×C₄	1	2	yes	—
387	#386	C₂×C₄	1	2	yes	—
388	#386	C₂×C₄	1	2	yes	—
389	#386	C₂×C₄	1	2	yes	—
390	#385	C₂×C₄	1	2	yes	—
391	#385	C₂×C₄	1	2	yes	—
392	#385	C₂×C₄	1	2	yes	—
393	#385	C₂×C₄	1	2	yes	—
394	#385	C₂×C₄	1	2	yes	—
395	#385	C₂×C₄	1	2	yes	—
396	#385	C₂×C₄	1	2	yes	—
397	#385	C₂×C₄	1	2	yes	—
398	#383	C₂×C₄	1	2	yes	—
399	#383	C₂×C₄	1	2	yes	—
400	#382	C₂×C₄	1	2	yes	—
401	#382	C₂×C₄	1	2	yes	—
402	#381	C₂×C₄	1	2	yes	—
403	#381	C₂×C₄	1	2	yes	—
404	#380	C₂×C₄	1	2	yes	—
405	#380	C₂×C₄	1	2	yes	—
406	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
414	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
415	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
417	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
418	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
422	#376	C₂³	1	1	yes	characteristic
423	#376	C₂³	1	1	yes	characteristic
424	#376	C₂³	1	1	yes	characteristic
425	#376	C₂³	1	1	yes	characteristic
426	#336	C₂³	1	1	yes	characteristic
427	#336	C₂³	1	1	yes	characteristic
428	#336	C₂³	1	1	yes	characteristic
429	#336	C₂³	1	1	yes	characteristic
430	#336	C₂³	1	1	yes	characteristic
431	#336	C₂³	1	1	yes	characteristic
432	#336	C₂³	1	1	yes	characteristic
433	#336	C₂³	1	1	yes	characteristic
434	#336	C₂³	1	1	yes	characteristic
435	#336	C₂³	1	1	yes	characteristic
436	#336	C₂³	1	1	yes	characteristic
437	#336	C₂³	1	1	yes	characteristic
438	#336	C₂³	1	1	yes	characteristic
439	#336	C₂³	1	1	yes	characteristic
440	#336	C₂³	1	1	yes	characteristic
441	#336	C₂³	1	1	yes	characteristic
442	#336	C₂³	1	1	yes	characteristic
443	#336	C₂³	1	1	yes	characteristic
444	#336	C₂³	1	1	yes	characteristic
445	#336	C₂³	1	1	yes	characteristic
446	#336	C₂³	1	1	yes	characteristic
447	#336	C₂³	1	1	yes	characteristic
448	#336	C₂³	1	1	yes	characteristic
449	#336	C₂³	1	1	yes	characteristic
450	#336	C₂³	1	1	yes	characteristic
451	#336	C₂³	1	1	yes	characteristic
452	#336	C₂³	1	1	yes	characteristic
453	#336	C₂³	1	1	yes	characteristic
454	#336	C₂³	1	1	yes	characteristic
455	#336	C₂³	1	1	yes	characteristic
456	#336	C₂³	1	1	yes	characteristic
457	#336	C₂³	1	1	yes	characteristic
458	C₂×#41	—	4	1	no	—
459	C₂×#41	—	4	1	no	—
460	C₂×#41	—	4	1	no	—
461	C₂×#41	—	4	1	no	—
462	C₂×#41	—	4	1	no	—
463	C₂×#41	—	4	1	no	—
464	C₂×#41	—	4	1	no	—
465	C₂×#41	—	4	1	no	—
466	C₂×#41	C₂²×C₄	1	4	yes	—
467	C₂×#41	C₂²×C₄	1	4	yes	—
468	C₂×#41	C₂²×C₄	1	4	yes	—
469	C₂×#41	C₂²×C₄	1	4	yes	—
470	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
471	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
472	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
473	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
474	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
475	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
476	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
477	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
478	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
479	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
480	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
481	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
482	C₂³×C₄	C₂²×C₄	1	2	yes	—
483	C₂³×C₄	C₂²×C₄	1	2	yes	—
484	C₂³×C₄	C₂²×C₄	1	2	yes	—
485	C₂³×C₄	C₂²×C₄	1	2	yes	—
486	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
487	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
488	C₂³×C₄	C₂⁴	1	1	yes	characteristic
489	C₂³×C₄	C₂⁴	1	1	yes	characteristic
490	C₂³×C₄	C₂⁴	1	1	yes	characteristic
491	C₂³×C₄	C₂⁴	1	1	yes	characteristic
492	C₂³×C₄	C₂⁴	1	1	yes	characteristic
493	#131	—	4	16	no	—
494	#131	—	4	16	no	—
495	C₂×M₁₆	—	2	2	no	—
496	C₂×M₁₆	—	2	2	no	—
497	C₂×M₁₆	—	2	2	no	—
498	C₂×M₁₆	—	2	2	no	—
499	C₂×M₁₆	—	2	2	no	—
500	C₂×M₁₆	—	2	2	no	—
501	C₂×M₁₆	—	4	1	no	—
502	C₂×M₁₆	—	4	1	no	—
503	C₂×M₁₆	—	4	1	no	—
504	C₂×M₁₆	—	4	1	no	—
505	C₂×M₁₆	—	4	1	no	—
506	C₂×M₁₆	—	4	1	no	—
507	C₂×M₁₆	—	4	1	no	—
508	C₂×M₁₆	—	4	1	no	—
509	C₂×M₁₆	—	4	1	no	—
510	C₂×M₁₆	—	4	1	no	—
511	C₂×M₁₆	—	4	1	no	—
512	C₂×M₁₆	—	4	1	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂×M₁₆	C₂²×C₄	1	4	yes	—
516	C₂×M₁₆	C₂²×C₄	1	4	yes	—
517	C₂×M₁₆	C₂²×C₄	1	4	yes	—
518	C₂×M₁₆	C₂²×C₄	1	4	yes	—
519	C₂×M₁₆	C₂²×C₄	1	4	yes	—
520	C₂×M₁₆	C₂²×C₄	1	4	yes	—
521	C₂×M₁₆	C₂²×C₄	1	4	yes	—
522	C₂×M₁₆	C₂²×C₄	1	4	yes	—
523	C₂×M₁₆	C₂²×C₄	1	4	yes	—
524	C₂×M₁₆	C₂²×C₄	1	4	yes	—
525	C₂²×C₈	—	2	2	no	—
526	C₂²×C₈	—	2	2	no	—
527	C₂²×C₈	—	2	2	no	—
528	C₂²×C₈	—	2	2	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	—	4	1	no	—
532	C₂²×C₈	—	4	1	no	—
533	C₂²×C₈	—	4	1	no	—
534	C₂²×C₈	—	4	1	no	—
535	C₂²×C₈	—	4	1	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	—	4	1	no	—
538	C₂²×C₈	—	4	1	no	—
539	C₂²×C₈	—	4	1	no	—
540	C₂²×C₈	—	4	1	no	—
541	C₂²×C₈	—	4	1	no	—
542	C₂²×C₈	—	4	1	no	—
543	C₂²×C₈	—	4	1	no	—
544	C₂²×C₈	—	4	1	no	—
545	C₂²×C₈	C₂²×C₄	1	4	yes	—
546	C₂²×C₈	C₂²×C₄	1	4	yes	—
547	C₂²×C₈	C₂²×C₄	1	4	yes	—
548	C₂²×C₈	C₂²×C₄	1	4	yes	—
549	C₂²×C₈	C₂²×C₄	1	4	yes	—
550	C₂²×C₈	C₂²×C₄	1	4	yes	—
551	C₂²×C₈	C₂²×C₄	1	4	yes	—
552	C₂²×C₈	C₂²×C₄	1	4	yes	—
553	C₂²×C₈	C₂²×C₄	1	4	yes	—
554	C₂²×C₈	C₂²×C₄	1	4	yes	—
555	C₂²×C₈	C₂⁴	1	1	yes	characteristic
556	C₂²×C₈	C₂⁴	1	1	yes	characteristic
557	C₂²×C₈	C₂⁴	1	1	yes	characteristic
558	C₂²×C₈	C₂⁴	1	1	yes	characteristic
559	C₂²×C₈	C₂⁴	1	1	yes	characteristic
560	C₂²×C₈	C₂⁴	1	1	yes	characteristic
561	C₂²×C₈	C₂⁴	1	1	yes	characteristic
562	C₂²×C₈	C₂⁴	1	1	yes	characteristic
563	C₂²×C₈	C₂⁴	1	1	yes	characteristic
564	C₂²×C₈	C₂⁴	1	1	yes	characteristic
565	C₂²×C₈	C₂⁴	1	1	yes	characteristic
566	C₂²×C₈	C₂⁴	1	1	yes	characteristic
567	C₂²×C₈	C₂⁴	1	1	yes	characteristic
568	C₂²×C₈	C₂⁴	1	1	yes	characteristic
569	C₂²×C₈	C₂⁴	1	1	yes	characteristic
570	C₂²×C₈	C₂⁴	1	1	yes	characteristic
571	C₄⋊Q₈	C₄²	1	8	yes	—
572	#127	C₄²	1	8	yes	—
573	#124	C₄²	1	8	yes	—
574	#124	C₄²	1	8	yes	—
575	#121	C₄²	1	8	yes	—
576	#121	C₄²	1	8	yes	—
577	#121	C₄²	1	8	yes	—
578	#121	C₄²	1	8	yes	—
579	C₄×D₄	C₂²×C₄	1	4	yes	—
580	C₄×D₄	C₂²×C₄	1	4	yes	—
581	C₄×D₄	C₂²×C₄	1	4	yes	—
582	C₄×D₄	C₂²×C₄	1	4	yes	—
583	C₄×D₄	C₂²×C₄	1	4	yes	—
584	C₄×D₄	C₂²×C₄	1	4	yes	—
585	C₄×D₄	C₂²×C₄	1	4	yes	—
586	C₄×D₄	C₂²×C₄	1	4	yes	—
587	#117	—	4	1	no	—
588	#117	—	4	1	no	—
589	#117	—	4	1	no	—
590	#117	—	4	1	no	—
591	#117	—	4	1	no	—
592	#117	—	4	1	no	—
593	#117	—	4	1	no	—
594	#117	—	4	1	no	—
595	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
596	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
597	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
598	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
599	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
600	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
601	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
602	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
603	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
631	C₂×C₄²	—	4	1	no	—
632	C₂×C₄²	—	4	1	no	—
633	C₂×C₄²	—	4	1	no	—
634	C₂×C₄²	—	4	1	no	—
635	C₂×C₄²	—	4	1	no	—
636	C₂×C₄²	—	4	1	no	—
637	C₂×C₄²	—	4	1	no	—
638	C₂×C₄²	—	4	1	no	—
639	C₂×C₄²	C₂²×C₄	1	2	yes	—
640	C₂×C₄²	C₂²×C₄	1	2	yes	—
641	C₂×C₄²	C₂²×C₄	1	2	yes	—
642	C₂×C₄²	C₂²×C₄	1	2	yes	—
643	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
644	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
645	C₂×C₄²	C₂²×C₄	1	4	yes	—
646	C₂×C₄²	C₂²×C₄	1	4	yes	—
647	C₂×C₄²	C₂⁴	1	1	yes	characteristic
648	C₂×C₄²	C₂⁴	1	1	yes	characteristic
649	C₂×C₄²	C₂⁴	1	1	yes	characteristic
650	C₂×C₄²	C₂⁴	1	1	yes	characteristic
651	C₂×C₄²	C₂⁴	1	1	yes	characteristic
652	C₂×C₄²	C₂⁴	1	1	yes	characteristic
653	C₂×C₄²	C₂⁴	1	1	yes	characteristic
654	C₂×C₄²	C₂⁴	1	1	yes	characteristic
655	C₂×C₄²	C₂⁴	1	1	yes	characteristic
656	C₂×C₄²	C₂⁴	1	1	yes	characteristic
657	C₄⋊C₈	C₂²×C₄	1	4	yes	—
658	C₄⋊C₈	C₂²×C₄	1	4	yes	—
659	C₄⋊C₈	C₂²×C₄	1	4	yes	—
660	C₄⋊C₈	C₂²×C₄	1	4	yes	—
661	C₄⋊C₈	C₂²×C₄	1	4	yes	—
662	C₄⋊C₈	C₂²×C₄	1	4	yes	—
663	C₄⋊C₈	C₂²×C₄	1	4	yes	—
664	C₄⋊C₈	C₂²×C₄	1	4	yes	—
665	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
666	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
667	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
668	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
669	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
670	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
671	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
672	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
673	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
674	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
675	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
676	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
677	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
678	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
679	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
680	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
681	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
682	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
683	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
684	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
685	#97	—	2	2	no	—
686	#97	—	2	2	no	—
687	#97	—	2	2	no	—
688	#97	—	2	2	no	—
689	#97	—	4	1	no	—
690	#97	—	4	1	no	—
691	#97	—	4	1	no	—
692	#97	—	4	1	no	—
693	#97	—	4	1	no	—
694	#97	—	4	1	no	—
695	#97	—	4	1	no	—
696	#97	—	4	1	no	—
697	#97	—	4	1	no	—
698	#97	—	4	1	no	—
699	#97	—	4	1	no	—
700	#97	—	4	1	no	—
701	#97	C₂²×C₄	1	4	yes	—
702	#97	C₂²×C₄	1	4	yes	—
703	#97	C₂²×C₄	1	4	yes	—
704	#97	C₂²×C₄	1	4	yes	—
705	C₄×C₈	—	2	2	no	—
706	C₄×C₈	—	2	2	no	—
707	C₄×C₈	—	2	2	no	—
708	C₄×C₈	—	2	2	no	—
709	C₄×C₈	—	4	1	no	—
710	C₄×C₈	—	4	1	no	—
711	C₄×C₈	—	4	1	no	—
712	C₄×C₈	—	4	1	no	—
713	C₄×C₈	—	4	1	no	—
714	C₄×C₈	—	4	1	no	—
715	C₄×C₈	—	4	1	no	—
716	C₄×C₈	—	4	1	no	—
717	C₄×C₈	—	4	1	no	—
718	C₄×C₈	—	4	1	no	—
719	C₄×C₈	—	4	1	no	—
720	C₄×C₈	—	4	1	no	—
721	C₄×C₈	C₂²×C₄	1	4	yes	—
722	C₄×C₈	C₂²×C₄	1	4	yes	—
723	C₄×C₈	C₂²×C₄	1	4	yes	—
724	C₄×C₈	C₂²×C₄	1	4	yes	—
725	#95	C₂²×C₄	1	2	yes	—
726	#95	C₂²×C₄	1	2	yes	—
727	#95	C₂²×C₄	1	2	yes	—
728	#95	C₂²×C₄	1	2	yes	—
729	#95	C₂²×C₄	1	2	yes	—
730	#95	C₂²×C₄	1	2	yes	—
731	#95	C₂²×C₄	1	2	yes	—
732	#95	C₂²×C₄	1	2	yes	—
733	#95	C₂²×C₄	1	2	yes	—
734	#95	C₂²×C₄	1	2	yes	—
735	#95	C₂²×C₄	1	2	yes	—
736	#95	C₂²×C₄	1	2	yes	—
737	#95	C₂²×C₄	1	2	yes	—
738	#95	C₂²×C₄	1	2	yes	—
739	#95	C₂²×C₄	1	2	yes	—
740	#95	C₂²×C₄	1	2	yes	—
741	#95	C₂²×C₄	1	2	yes	—
742	#95	C₂²×C₄	1	2	yes	—
743	#95	C₂²×C₄	1	2	yes	—
744	#95	C₂²×C₄	1	2	yes	—
745	#95	C₂²×C₄	1	2	yes	—
746	#95	C₂²×C₄	1	2	yes	—
747	#95	C₂²×C₄	1	2	yes	—
748	#95	C₂²×C₄	1	2	yes	—
749	C₂⁴	C₂³×C₄	1	1	yes	characteristic
750	C₂⁴	C₂³×C₄	1	1	yes	characteristic
751	C₂⁴	C₂³×C₄	1	1	yes	characteristic
752	C₂⁴	C₂³×C₄	1	1	yes	characteristic
753	C₂⁴	C₂³×C₄	1	1	yes	characteristic
754	#41	—	4	4	no	—
755	#41	—	4	4	no	—
756	#41	—	4	4	no	—
757	#41	—	4	4	no	—
758	#41	—	4	4	no	—
759	#41	—	4	4	no	—
760	#41	—	4	4	no	—
761	#41	—	4	4	no	—
762	C₂×Q₈	—	4	1	no	—
763	C₂×Q₈	—	4	1	no	—
764	C₂×Q₈	—	4	1	no	—
765	C₂×Q₈	—	4	1	no	—
766	C₂×Q₈	C₂×C₄²	1	4	yes	—
767	C₂×Q₈	C₂×C₄²	1	4	yes	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	1	no	—
773	C₂×D₄	—	4	1	no	—
774	C₂×D₄	—	4	1	no	—
775	C₂×D₄	—	4	1	no	—
776	C₂×D₄	—	4	1	no	—
777	C₂×D₄	—	4	1	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	1	no	—
783	C₂×D₄	—	4	1	no	—
784	C₂×D₄	C₂×C₄²	1	4	yes	—
785	C₂×D₄	C₂×C₄²	1	4	yes	—
786	C₂×D₄	C₂×C₄²	1	4	yes	—
787	C₂×D₄	C₂×C₄²	1	4	yes	—
788	C₂×D₄	C₂×C₄²	1	4	yes	—
789	C₂×D₄	C₂×C₄²	1	4	yes	—
790	C₂×D₄	C₂×C₄²	1	4	yes	—
791	C₂×D₄	C₂×C₄²	1	4	yes	—
792	C₂×D₄	C₂×C₄²	1	4	yes	—
793	C₂×D₄	C₂×C₄²	1	4	yes	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	C₂×C₄²	1	4	yes	—
829	C₂²×C₄	C₂×C₄²	1	4	yes	—
830	C₂²×C₄	C₂³×C₄	1	2	yes	—
831	C₂²×C₄	C₂³×C₄	1	2	yes	—
832	C₂²×C₄	C₂³×C₄	1	2	yes	—
833	C₂²×C₄	C₂³×C₄	1	2	yes	—
834	C₂²×C₄	C₂³×C₄	1	2	yes	—
835	C₂²×C₄	C₂³×C₄	1	2	yes	—
836	C₂²×C₄	C₂³×C₄	1	2	yes	—
837	C₂²×C₄	C₂³×C₄	1	2	yes	—
838	C₂²×C₄	C₂³×C₄	1	2	yes	—
839	C₂²×C₄	C₂³×C₄	1	2	yes	—
840	C₂²×C₄	C₂³×C₄	1	2	yes	—
841	C₂²×C₄	C₂³×C₄	1	2	yes	—
842	C₂²×C₄	C₂³×C₄	1	2	yes	—
843	C₂²×C₄	C₂³×C₄	1	2	yes	—
844	C₂²×C₄	C₂³×C₄	1	2	yes	—
845	C₂²×C₄	C₂³×C₄	1	2	yes	—
846	C₂²×C₄	C₂³×C₄	1	2	yes	—
847	C₂²×C₄	C₂³×C₄	1	2	yes	—
848	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
849	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
850	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
851	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
852	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
853	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
854	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
855	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
856	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
857	C₂²×C₄	C₂⁵	1	1	yes	characteristic
858	M₁₆	—	2	8	no	—
859	M₁₆	—	2	8	no	—
860	M₁₆	—	2	8	no	—
861	M₁₆	—	4	4	no	—
862	M₁₆	—	4	4	no	—
863	M₁₆	—	4	4	no	—
864	M₁₆	—	4	4	no	—
865	M₁₆	—	4	4	no	—
866	M₁₆	—	4	4	no	—
867	M₁₆	—	4	4	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	8	no	—
899	C₂×C₈	—	2	8	no	—
900	C₂×C₈	—	4	4	no	—
901	C₂×C₈	—	4	4	no	—
902	C₂×C₈	—	4	4	no	—
903	C₂×C₈	—	4	4	no	—
904	C₂×C₈	—	4	4	no	—
905	C₂×C₈	—	4	4	no	—
906	C₂×C₈	—	4	4	no	—
907	C₂×C₈	—	4	4	no	—
908	C₂×C₈	C₂³×C₄	1	2	yes	—
909	C₂×C₈	C₂³×C₄	1	2	yes	—
910	C₂×C₈	C₂³×C₄	1	2	yes	—
911	C₂×C₈	C₂³×C₄	1	2	yes	—
912	C₂×C₈	C₂³×C₄	1	2	yes	—
913	C₂×C₈	C₂³×C₄	1	2	yes	—
914	C₂×C₈	C₂³×C₄	1	2	yes	—
915	C₂×C₈	C₂³×C₄	1	2	yes	—
916	C₂×C₈	C₂³×C₄	1	2	yes	—
917	C₂×C₈	C₂³×C₄	1	2	yes	—
918	C₂×C₈	C₂³×C₄	1	2	yes	—
919	C₂×C₈	C₂³×C₄	1	2	yes	—
920	C₂×C₈	C₂³×C₄	1	2	yes	—
921	C₂×C₈	C₂³×C₄	1	2	yes	—
922	C₂×C₈	C₂³×C₄	1	2	yes	—
923	C₂×C₈	C₂³×C₄	1	2	yes	—
924	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
925	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	C₂×C₄²	1	4	yes	—
935	C₄⋊C₄	C₂×C₄²	1	4	yes	—
936	C₄⋊C₄	C₂×C₄²	1	4	yes	—
937	C₄⋊C₄	C₂×C₄²	1	4	yes	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
955	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
956	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
957	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
958	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
959	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
960	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
961	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	4	2	no	—
979	C₄²	—	4	2	no	—
980	C₄²	—	4	2	no	—
981	C₄²	—	4	2	no	—
982	C₄²	C₂×C₄²	1	4	yes	—
983	C₄²	C₂×C₄²	1	4	yes	—
984	C₄²	C₂³×C₄	1	2	yes	—
985	C₄²	C₂³×C₄	1	2	yes	—
986	C₄²	C₂³×C₄	1	2	yes	—
987	C₄²	C₂³×C₄	1	2	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	C₂²×C₄²	1	2	yes	—
1009	C₂³	C₂²×C₄²	1	2	yes	—
1010	C₂³	C₂²×C₄²	1	2	yes	—
1011	C₂³	C₂²×C₄²	1	2	yes	—
1012	C₂³	C₂²×C₄²	1	2	yes	—
1013	C₂³	C₂⁴×C₄	1	1	yes	characteristic
1014	Q₈	—	4	4	no	—
1015	Q₈	—	4	4	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	4	no	—
1018	D₄	—	4	4	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	4	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	4	no	—
1023	D₄	—	4	4	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	4	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	8	no	—
1087	C₂×C₄	—	8	4	no	—
1088	C₂×C₄	—	8	4	no	—
1089	C₂×C₄	—	8	4	no	—
1090	C₂×C₄	C₂²×C₄²	1	2	yes	—
1091	C₂×C₄	C₂²×C₄²	1	2	yes	—
1092	C₂×C₄	C₂²×C₄²	1	2	yes	—
1093	C₂×C₄	C₂²×C₄²	1	2	yes	—
1094	C₂×C₄	C₂²×C₄²	1	2	yes	—
1095	C₂×C₄	C₂²×C₄²	1	2	yes	—
1096	C₂×C₄	C₂²×C₄²	1	2	yes	—
1097	C₂×C₄	C₂²×C₄²	1	2	yes	—
1098	C₂×C₄	C₂²×C₄²	1	2	yes	—
1099	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1100	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1101	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1102	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1103	C₂×C₄	#585	1	1	yes	characteristic
1104	C₂×C₄	#585	1	1	yes	characteristic
1105	C₈	—	2	2	no	—
1106	C₈	—	2	2	no	—
1107	C₈	—	2	2	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	2	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	2	no	—
1120	C₈	#518	1	4	yes	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	C₂³×C₄²	1	1	yes	characteristic
1147	C₂²	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1148	C₂²	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1149	C₂²	#3573	1	2	yes	—
1150	C₂²	#3573	1	2	yes	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	C₂×#518	1	1	yes	characteristic
1169	C₄	#3428	1	1	yes	characteristic
1170	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1171	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	C₄×#518	1	1	yes	characteristic
1178	C₂	#60058	1	1	yes	characteristic
1179	C₂	#60058	1	1	yes	characteristic
1180	C₂	#60315	1	2	yes	—
1181	C₂	#60327	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₄	C₂⁵
commutator	C₂²	C₂³×C₄²
socle	C₂³	C₂⁴×C₄
prime radical	C₂×#532	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #20564	C₂	semidirect
5. #20564	C₂	semidirect
6. #20561	C₂	semidirect
7. #20561	C₂	semidirect
8. #20560	C₂	semidirect
9. #20560	C₂	semidirect
10. #20557	C₂	semidirect
11. #20557	C₂	semidirect
12. #20545	C₂	semidirect
13. #20544	C₂	semidirect
14. #20532	C₂	semidirect
15. #20531	C₂	semidirect
16. #20531	C₂	semidirect
17. #20530	C₂	semidirect
18. #20493	C₂	semidirect
19. #20493	C₂	semidirect
20. #20490	C₂	semidirect
21. #20490	C₂	semidirect
22. #20487	C₂	semidirect
23. #20487	C₂	semidirect
24. #20484	C₂	semidirect
25. #20484	C₂	semidirect
26. #20482	C₂	semidirect
27. #20477	C₂	semidirect
28. #20387	C₂	semidirect
29. #20387	C₂	semidirect
30. #20384	C₂	semidirect
31. #20383	C₂	semidirect
35. #2981	C₄	semidirect
36. #2935	C₄	semidirect
203. C₂×#131	C₂×C₄	semidirect
204. C₂×#131	C₂×C₄	semidirect
248. #436	C₂×C₄	semidirect
249. #436	C₂×C₄	semidirect
250. #436	C₂×C₄	semidirect
251. #436	C₂×C₄	semidirect
252. #435	C₂×C₄	semidirect
253. #435	C₂×C₄	semidirect
254. #435	C₂×C₄	semidirect
255. #435	C₂×C₄	semidirect
256. #435	C₂×C₄	semidirect
257. #435	C₂×C₄	semidirect
258. #435	C₂×C₄	semidirect
259. #435	C₂×C₄	semidirect
260. C₈×D₄	C₂×C₄	semidirect
261. C₈×D₄	C₂×C₄	semidirect
262. C₈×D₄	C₂×C₄	semidirect
263. C₈×D₄	C₂×C₄	semidirect
264. #432	C₂×C₄	semidirect
265. #431	C₂×C₄	semidirect
266. C₂×C₄⋊C₈	C₂×C₄	semidirect
275. #408	C₂×C₄	semidirect
276. #408	C₂×C₄	semidirect
277. #408	C₂×C₄	semidirect
278. #408	C₂×C₄	semidirect
279. #408	C₂×C₄	semidirect
280. #408	C₂×C₄	semidirect
307. C₄×M₁₆	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2981	2
C₂×#2935	2
#34346	2
#20564	2
#20561	2
#20560	2
#20557	2
#20545	2
#20544	2
#20532	2
#20531	2
#20530	2
#20493	2
#20490	2
#20487	2
#20484	2
#20482	2
#20477	2
#20387	2
#20384	2
#20383	2