Subgroups — #6370665

Order 512.

1944 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2985	C₂	1	1	yes	maximal, characteristic
2	C₂×#2961	C₂	1	1	yes	maximal, characteristic
3	#34085	C₂	1	1	yes	maximal, characteristic
4	#20576	C₂	1	1	yes	maximal, characteristic, complemented
5	#20576	C₂	1	1	yes	maximal, characteristic, complemented
6	#20575	C₂	1	1	yes	maximal, characteristic, complemented
7	#20575	C₂	1	1	yes	maximal, characteristic, complemented
8	#20574	C₂	1	1	yes	maximal, characteristic, complemented
9	#20573	C₂	1	1	yes	maximal, characteristic, complemented
10	#20571	C₂	1	1	yes	maximal, characteristic, complemented
11	#20570	C₂	1	1	yes	maximal, characteristic, complemented
12	#20554	C₂	1	1	yes	maximal, characteristic
13	#20553	C₂	1	1	yes	maximal, characteristic
14	#20553	C₂	1	1	yes	maximal, characteristic
15	#20552	C₂	1	1	yes	maximal, characteristic
16	#20551	C₂	1	1	yes	maximal, characteristic
17	#20550	C₂	1	1	yes	maximal, characteristic
18	#20521	C₂	1	1	yes	maximal, characteristic, complemented
19	#20520	C₂	1	1	yes	maximal, characteristic, complemented
20	#20519	C₂	1	1	yes	maximal, characteristic, complemented
21	#20519	C₂	1	1	yes	maximal, characteristic, complemented
22	#20518	C₂	1	1	yes	maximal, characteristic, complemented
23	#20518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#446	C₂	1	1	yes	maximal, characteristic, complemented
25	#20516	C₂	1	1	yes	maximal, characteristic, complemented
26	#20481	C₂	1	1	yes	maximal, characteristic
27	#20479	C₂	1	1	yes	maximal, characteristic
28	#20478	C₂	1	1	yes	maximal, characteristic
29	#20478	C₂	1	1	yes	maximal, characteristic
30	#20475	C₂	1	1	yes	maximal, characteristic
31	#20474	C₂	1	1	yes	maximal, characteristic
32	C₂×#533	C₂²	1	1	yes	characteristic
33	#2985	C₄	1	16	yes	complemented
34	#2961	C₄	1	16	yes	complemented
35	C₂×#446	C₂²	1	1	yes	characteristic
36	C₂×#446	C₂²	1	1	yes	characteristic
37	C₂×#446	C₂²	1	1	yes	characteristic
38	C₂×#446	C₂²	1	1	yes	characteristic
39	C₂×#446	C₂²	1	1	yes	characteristic
40	C₂×#446	C₂²	1	1	yes	characteristic
41	C₂×#446	C₂²	1	1	yes	characteristic
42	C₂×#446	C₂²	1	1	yes	characteristic
43	C₂×#446	C₂²	1	1	yes	characteristic
44	C₂×#446	C₂²	1	1	yes	characteristic
45	C₂×#446	C₂²	1	1	yes	characteristic
46	C₂×#446	C₂²	1	1	yes	characteristic
47	C₂×#446	C₂²	1	1	yes	characteristic
48	C₂×#446	C₂²	1	1	yes	characteristic
49	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
51	C₂×#433	C₂²	1	1	yes	characteristic
52	C₂×#433	C₂²	1	1	yes	characteristic
53	C₂×#433	C₂²	1	1	yes	characteristic
54	C₂×#433	C₂²	1	1	yes	characteristic
55	C₂×#432	C₂²	1	1	yes	characteristic
56	C₂×#431	C₂²	1	1	yes	characteristic
57	C₂×#424	C₂²	1	1	yes	characteristic
58	C₂×#424	C₂²	1	1	yes	characteristic
59	C₂×#423	C₂²	1	1	yes	characteristic
60	C₂×#405	C₂²	1	1	yes	characteristic
61	C₂×#405	C₂²	1	1	yes	characteristic
62	C₂²×#97	C₂²	1	1	yes	characteristic
63	#2336	C₄	1	2	yes	—
64	#2336	C₄	1	2	yes	—
65	#2332	C₄	1	2	yes	—
66	#2332	C₄	1	2	yes	—
67	#2331	C₄	1	2	yes	—
68	#2327	C₄	1	2	yes	—
69	#2323	C₄	1	2	yes	—
70	#2323	C₄	1	2	yes	—
71	#2298	C₂²	1	1	yes	characteristic
72	#2298	C₂²	1	1	yes	characteristic
73	#2298	C₂²	1	1	yes	characteristic
74	#2298	C₂²	1	1	yes	characteristic
75	#2295	C₂²	1	1	yes	characteristic
76	#2295	C₂²	1	1	yes	characteristic
77	#2295	C₂²	1	1	yes	characteristic
78	#2295	C₂²	1	1	yes	characteristic
79	#2295	C₂²	1	1	yes	characteristic
80	#2295	C₂²	1	1	yes	characteristic
81	#2283	C₂²	1	1	yes	characteristic
82	C₄²×Q₈	C₂²	1	1	yes	characteristic
83	C₄²×Q₈	C₂²	1	1	yes	characteristic
84	C₄×#117	C₂²	1	1	yes	characteristic
85	#1771	C₂²	1	1	yes	characteristic
86	#1771	C₂²	1	1	yes	characteristic
87	#1771	C₂²	1	1	yes	characteristic
88	#1771	C₂²	1	1	yes	characteristic
89	#1771	C₂²	1	1	yes	characteristic
90	#1771	C₂²	1	1	yes	characteristic
91	#1771	C₂²	1	1	yes	characteristic
92	#1771	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	#1771	C₂²	1	1	yes	characteristic
102	#1771	C₂²	1	1	yes	characteristic
103	#1771	C₂²	1	1	yes	characteristic
104	#1771	C₂²	1	1	yes	characteristic
105	#1771	C₂²	1	1	yes	characteristic
106	#1771	C₂²	1	1	yes	characteristic
107	#1771	C₂²	1	1	yes	characteristic
108	#1771	C₂²	1	1	yes	characteristic
109	#1771	C₂²	1	1	yes	characteristic
110	#1771	C₂²	1	1	yes	characteristic
111	#1771	C₂²	1	1	yes	characteristic
112	#1771	C₂²	1	1	yes	characteristic
113	#1770	C₂²	1	1	yes	characteristic
114	#1770	C₂²	1	1	yes	characteristic
115	#1770	C₂²	1	1	yes	characteristic
116	#1770	C₂²	1	1	yes	characteristic
117	#1770	C₂²	1	1	yes	characteristic
118	#1770	C₂²	1	1	yes	characteristic
119	#1770	C₂²	1	1	yes	characteristic
120	#1770	C₂²	1	1	yes	characteristic
121	#1770	C₂²	1	1	yes	characteristic
122	#1770	C₂²	1	1	yes	characteristic
123	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
124	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
125	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
126	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
127	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
128	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
129	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
130	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
131	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
132	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
133	#1768	C₂²	1	1	yes	characteristic
134	#1768	C₂²	1	1	yes	characteristic
135	#1768	C₂²	1	1	yes	characteristic
136	#1768	C₂²	1	1	yes	characteristic
137	#1768	C₂²	1	1	yes	characteristic
138	#1768	C₂²	1	1	yes	characteristic
139	#1768	C₂²	1	1	yes	characteristic
140	#1768	C₂²	1	1	yes	characteristic
141	#1768	C₂²	1	1	yes	characteristic
142	#1768	C₂²	1	1	yes	characteristic
143	#1768	C₂²	1	1	yes	characteristic
144	#1768	C₂²	1	1	yes	characteristic
145	#1767	C₂²	1	1	yes	characteristic
146	#1767	C₂²	1	1	yes	characteristic
147	#1767	C₂²	1	1	yes	characteristic
148	#1767	C₂²	1	1	yes	characteristic
149	#1767	C₂²	1	1	yes	characteristic
150	#1767	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
157	#1753	C₂²	1	1	yes	characteristic
158	#1753	C₂²	1	1	yes	characteristic
159	#1753	C₂²	1	1	yes	characteristic
160	#1753	C₂²	1	1	yes	characteristic
161	#1753	C₂²	1	1	yes	characteristic
162	#1753	C₂²	1	1	yes	characteristic
163	#1753	C₂²	1	1	yes	characteristic
164	#1753	C₂²	1	1	yes	characteristic
165	#1752	C₂²	1	1	yes	characteristic
166	#1752	C₂²	1	1	yes	characteristic
167	#1752	C₂²	1	1	yes	characteristic
168	#1752	C₂²	1	1	yes	characteristic
169	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
170	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
172	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
173	#1746	C₂²	1	1	yes	characteristic
174	#1746	C₂²	1	1	yes	characteristic
175	#1746	C₂²	1	1	yes	characteristic
176	#1746	C₂²	1	1	yes	characteristic
177	#1746	C₂²	1	1	yes	characteristic
178	#1746	C₂²	1	1	yes	characteristic
179	#1745	C₂²	1	1	yes	characteristic
180	#1745	C₂²	1	1	yes	characteristic
181	#1745	C₂²	1	1	yes	characteristic
182	#1745	C₂²	1	1	yes	characteristic
183	#1744	C₂²	1	1	yes	characteristic
184	#1744	C₂²	1	1	yes	characteristic
185	#1726	C₂²	1	1	yes	characteristic
186	#1726	C₂²	1	1	yes	characteristic
187	#1726	C₂²	1	1	yes	characteristic
188	#1726	C₂²	1	1	yes	characteristic
189	#1726	C₂²	1	1	yes	characteristic
190	#1726	C₂²	1	1	yes	characteristic
191	C₄×#97	C₂²	1	1	yes	characteristic
192	C₄×#97	C₂²	1	1	yes	characteristic
193	C₄×#97	C₂²	1	1	yes	characteristic
194	C₄×#97	C₂²	1	1	yes	characteristic
195	C₄×#97	C₂²	1	1	yes	characteristic
196	C₄²×C₈	C₂²	1	1	yes	characteristic
197	C₂²×M₁₆	C₂³	1	1	yes	characteristic
198	C₂²×M₁₆	C₂³	1	1	yes	characteristic
199	C₂³×C₈	C₂³	1	1	yes	characteristic
200	C₂³×C₈	C₂³	1	1	yes	characteristic
201	#533	C₂×C₄	1	8	yes	—
202	#533	C₂×C₄	1	8	yes	—
203	C₂×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
205	C₂×#125	C₂×C₄	1	1	yes	characteristic
206	C₂×#125	C₂×C₄	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
208	C₂×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
211	C₂×C₄×Q₈	C₂×C₄	1	2	yes	—
212	C₂×C₄×Q₈	C₂×C₄	1	2	yes	—
213	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₂×#117	C₂×C₄	1	2	yes	—
218	C₂×#117	C₂³	1	1	yes	characteristic
219	C₂×#117	C₂³	1	1	yes	characteristic
220	C₂²×C₄²	C₂³	1	1	yes	characteristic
221	#446	C₂×C₄	1	8	yes	—
222	#446	C₂×C₄	1	8	yes	—
223	#446	C₂×C₄	1	8	yes	—
224	#446	C₂×C₄	1	8	yes	—
225	#446	C₂×C₄	1	8	yes	—
226	#446	C₂×C₄	1	8	yes	—
227	#446	C₂×C₄	1	8	yes	—
228	#446	C₂×C₄	1	8	yes	—
229	#446	C₂×C₄	1	8	yes	—
230	#446	C₂×C₄	1	8	yes	—
231	#446	C₂×C₄	1	8	yes	—
232	#446	C₂×C₄	1	8	yes	—
233	#446	C₂×C₄	1	8	yes	—
234	#446	C₂×C₄	1	8	yes	—
235	C₈×Q₈	C₂×C₄	1	8	yes	—
236	C₈×Q₈	C₂×C₄	1	8	yes	—
237	#433	C₂×C₄	1	8	yes	—
238	#433	C₂×C₄	1	8	yes	—
239	#433	C₂×C₄	1	8	yes	—
240	#433	C₂×C₄	1	8	yes	—
241	#432	C₂×C₄	1	8	yes	—
242	#431	C₂×C₄	1	8	yes	—
243	#424	C₂×C₄	1	8	yes	—
244	#424	C₂×C₄	1	8	yes	—
245	#423	C₂×C₄	1	8	yes	—
246	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	#405	C₂×C₄	1	8	yes	—
275	#405	C₂×C₄	1	8	yes	—
276	C₂×#97	C₂×C₄	1	8	yes	—
277	C₂×#97	C₂³	1	1	yes	characteristic
278	C₂×#97	C₂³	1	1	yes	characteristic
279	C₂×#97	C₂³	1	1	yes	characteristic
280	C₂×#97	C₂³	1	1	yes	characteristic
281	C₂×#97	C₂³	1	1	yes	characteristic
282	C₂×#97	C₂³	1	1	yes	characteristic
283	C₂×#97	C₂³	1	1	yes	characteristic
284	C₂×#97	C₂³	1	1	yes	characteristic
285	C₂×#97	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×#97	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×#97	C₂³	1	1	yes	characteristic
294	C₂×#97	C₂³	1	1	yes	characteristic
295	C₂×#97	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×#97	C₂³	1	1	yes	characteristic
301	C₂×#97	C₂³	1	1	yes	characteristic
302	C₂×#97	C₂³	1	1	yes	characteristic
303	C₂×#97	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×#97	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
320	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
329	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
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	#391	C₂×C₄	1	2	yes	—
334	#391	C₂×C₄	1	2	yes	—
335	#391	C₂×C₄	1	2	yes	—
336	#391	C₂×C₄	1	2	yes	—
337	#391	C₂×C₄	1	2	yes	—
338	#391	C₂×C₄	1	2	yes	—
339	#389	C₂×C₄	1	2	yes	—
340	#389	C₂×C₄	1	2	yes	—
341	#389	C₂×C₄	1	2	yes	—
342	#389	C₂×C₄	1	2	yes	—
343	#389	C₂×C₄	1	2	yes	—
344	#389	C₂×C₄	1	2	yes	—
345	#388	C₂×C₄	1	2	yes	—
346	#388	C₂×C₄	1	2	yes	—
347	#388	C₂×C₄	1	2	yes	—
348	#388	C₂×C₄	1	2	yes	—
349	#388	C₂×C₄	1	2	yes	—
350	#388	C₂×C₄	1	2	yes	—
351	#388	C₂×C₄	1	2	yes	—
352	#388	C₂×C₄	1	2	yes	—
353	#387	C₂×C₄	1	2	yes	—
354	#387	C₂×C₄	1	2	yes	—
355	#387	C₂×C₄	1	2	yes	—
356	#387	C₂×C₄	1	2	yes	—
357	#387	C₂×C₄	1	2	yes	—
358	#387	C₂×C₄	1	2	yes	—
359	#387	C₂×C₄	1	2	yes	—
360	#387	C₂×C₄	1	2	yes	—
361	#387	C₂×C₄	1	2	yes	—
362	#387	C₂×C₄	1	2	yes	—
363	#387	C₂×C₄	1	2	yes	—
364	#387	C₂×C₄	1	2	yes	—
365	#387	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	#383	C₂×C₄	1	2	yes	—
374	#382	C₂×C₄	1	2	yes	—
375	#381	C₂×C₄	1	2	yes	—
376	#380	C₂×C₄	1	2	yes	—
377	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
378	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
379	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
380	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
381	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
382	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
383	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
384	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
385	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
386	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
387	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
388	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
389	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
391	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
392	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
393	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
395	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
396	C₄×C₂²⋊C₄	C₂×C₄	1	2	yes	—
397	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
398	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
399	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
401	#376	C₂×C₄	1	2	yes	—
402	#376	C₂³	1	1	yes	characteristic
403	#376	C₂³	1	1	yes	characteristic
404	#376	C₂³	1	1	yes	characteristic
405	#376	C₂³	1	1	yes	characteristic
406	#376	C₂³	1	1	yes	characteristic
407	#376	C₂³	1	1	yes	characteristic
408	C₄³	C₂³	1	1	yes	characteristic
409	C₄³	C₂³	1	1	yes	characteristic
410	C₄³	C₂³	1	1	yes	characteristic
411	C₄³	C₂³	1	1	yes	characteristic
412	C₄³	C₂³	1	1	yes	characteristic
413	C₄³	C₂³	1	1	yes	characteristic
414	#336	C₂³	1	1	yes	characteristic
415	#336	C₂³	1	1	yes	characteristic
416	#336	C₂³	1	1	yes	characteristic
417	#336	C₂³	1	1	yes	characteristic
418	#336	C₂³	1	1	yes	characteristic
419	#336	C₂³	1	1	yes	characteristic
420	#336	C₂³	1	1	yes	characteristic
421	#336	C₂³	1	1	yes	characteristic
422	#336	C₂³	1	1	yes	characteristic
423	#336	C₂³	1	1	yes	characteristic
424	#336	C₂³	1	1	yes	characteristic
425	#336	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	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
447	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
448	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
449	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
450	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
451	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
452	C₂³×C₄	C₂⁴	1	1	yes	characteristic
453	C₂×M₁₆	—	4	1	no	—
454	C₂×M₁₆	—	4	1	no	—
455	C₂×M₁₆	—	4	1	no	—
456	C₂×M₁₆	—	4	1	no	—
457	C₂×M₁₆	C₂²×C₄	1	4	yes	—
458	C₂×M₁₆	C₂²×C₄	1	4	yes	—
459	C₂²×C₈	—	2	2	no	—
460	C₂²×C₈	—	2	2	no	—
461	C₂²×C₈	—	4	1	no	—
462	C₂²×C₈	—	4	1	no	—
463	C₂²×C₈	C₂²×C₄	1	4	yes	—
464	C₂²×C₈	C₂²×C₄	1	4	yes	—
465	C₂²×C₈	C₂⁴	1	1	yes	characteristic
466	C₂²×C₈	C₂⁴	1	1	yes	characteristic
467	C₂²×C₈	C₂⁴	1	1	yes	characteristic
468	C₂²×C₈	C₂⁴	1	1	yes	characteristic
469	C₂²×C₈	C₂⁴	1	1	yes	characteristic
470	C₂²×C₈	C₂⁴	1	1	yes	characteristic
471	C₂²×C₈	C₂⁴	1	1	yes	characteristic
472	C₂²×C₈	C₂⁴	1	1	yes	characteristic
473	C₂²×C₈	C₂⁴	1	1	yes	characteristic
474	C₂²×C₈	C₂⁴	1	1	yes	characteristic
475	C₂²×C₈	C₂⁴	1	1	yes	characteristic
476	C₂²×C₈	C₂⁴	1	1	yes	characteristic
477	C₂²×C₈	C₂⁴	1	1	yes	characteristic
478	C₂²×C₈	C₂⁴	1	1	yes	characteristic
479	C₂²×C₈	C₂⁴	1	1	yes	characteristic
480	C₂²×C₈	C₂⁴	1	1	yes	characteristic
481	C₄⋊Q₈	C₄²	1	8	yes	—
482	C₄⋊Q₈	C₄²	1	8	yes	—
483	#125	C₄²	1	8	yes	—
484	#125	C₄²	1	8	yes	—
485	C₂²⋊Q₈	C₄²	1	8	yes	—
486	C₂²⋊Q₈	C₄²	1	8	yes	—
487	C₂²⋊Q₈	C₄²	1	8	yes	—
488	C₂²⋊Q₈	C₄²	1	8	yes	—
489	C₄×Q₈	—	4	4	no	—
490	C₄×Q₈	—	4	4	no	—
491	C₄×Q₈	C₂²×C₄	1	4	yes	—
492	C₄×Q₈	C₂²×C₄	1	4	yes	—
493	C₄×Q₈	C₂²×C₄	1	4	yes	—
494	C₄×Q₈	C₂²×C₄	1	4	yes	—
495	C₄×Q₈	C₂²×C₄	1	4	yes	—
496	C₄×Q₈	C₂²×C₄	1	4	yes	—
497	C₄×Q₈	C₂²×C₄	1	4	yes	—
498	C₄×Q₈	C₂²×C₄	1	4	yes	—
499	#117	—	4	4	no	—
500	#117	C₂²×C₄	1	4	yes	—
501	#117	C₂²×C₄	1	4	yes	—
502	#117	C₂²×C₄	1	4	yes	—
503	#117	C₂²×C₄	1	4	yes	—
504	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
505	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
506	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
507	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
508	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
509	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
510	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
511	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
512	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
513	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
514	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
515	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
516	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
540	C₂×C₄²	C₂²×C₄	1	2	yes	—
541	C₂×C₄²	C₂²×C₄	1	2	yes	—
542	C₂×C₄²	C₂²×C₄	1	2	yes	—
543	C₂×C₄²	C₂²×C₄	1	2	yes	—
544	C₂×C₄²	C₂²×C₄	1	2	yes	—
545	C₂×C₄²	C₂²×C₄	1	2	yes	—
546	C₂×C₄²	C₂²×C₄	1	2	yes	—
547	C₂×C₄²	C₂²×C₄	1	2	yes	—
548	C₂×C₄²	C₂²×C₄	1	2	yes	—
549	C₂×C₄²	C₂²×C₄	1	2	yes	—
550	C₂×C₄²	C₂²×C₄	1	2	yes	—
551	C₂×C₄²	C₂²×C₄	1	2	yes	—
552	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
553	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
554	C₂×C₄²	C₂²×C₄	1	4	yes	—
555	C₂×C₄²	C₂²×C₄	1	4	yes	—
556	C₂×C₄²	C₂⁴	1	1	yes	characteristic
557	C₂×C₄²	C₂⁴	1	1	yes	characteristic
558	C₂×C₄²	C₂⁴	1	1	yes	characteristic
559	C₂×C₄²	C₂⁴	1	1	yes	characteristic
560	C₂×C₄²	C₂⁴	1	1	yes	characteristic
561	C₂×C₄²	C₂⁴	1	1	yes	characteristic
562	C₂×C₄²	C₂⁴	1	1	yes	characteristic
563	C₂×C₄²	C₂⁴	1	1	yes	characteristic
564	C₂×C₄²	C₂⁴	1	1	yes	characteristic
565	C₂×C₄²	C₂⁴	1	1	yes	characteristic
566	C₂×C₄²	C₂⁴	1	1	yes	characteristic
567	C₂×C₄²	C₂⁴	1	1	yes	characteristic
568	C₂×C₄²	C₂⁴	1	1	yes	characteristic
569	C₂×C₄²	C₂⁴	1	1	yes	characteristic
570	C₄⋊C₈	C₂²×C₄	1	4	yes	—
571	C₄⋊C₈	C₂²×C₄	1	4	yes	—
572	C₄⋊C₈	C₂²×C₄	1	4	yes	—
573	C₄⋊C₈	C₂²×C₄	1	4	yes	—
574	C₄⋊C₈	C₂²×C₄	1	4	yes	—
575	C₄⋊C₈	C₂²×C₄	1	4	yes	—
576	C₄⋊C₈	C₂²×C₄	1	4	yes	—
577	C₄⋊C₈	C₂²×C₄	1	4	yes	—
578	C₄⋊C₈	C₂²×C₄	1	4	yes	—
579	C₄⋊C₈	C₂²×C₄	1	4	yes	—
580	C₄⋊C₈	C₂²×C₄	1	4	yes	—
581	C₄⋊C₈	C₂²×C₄	1	4	yes	—
582	C₄⋊C₈	C₂²×C₄	1	4	yes	—
583	C₄⋊C₈	C₂²×C₄	1	4	yes	—
584	C₄⋊C₈	C₂²×C₄	1	4	yes	—
585	C₄⋊C₈	C₂²×C₄	1	4	yes	—
586	C₄⋊C₈	C₂²×C₄	1	4	yes	—
587	C₄⋊C₈	C₂²×C₄	1	4	yes	—
588	C₄⋊C₈	C₂²×C₄	1	4	yes	—
589	C₄⋊C₈	C₂²×C₄	1	4	yes	—
590	C₄⋊C₈	C₂²×C₄	1	4	yes	—
591	C₄⋊C₈	C₂²×C₄	1	4	yes	—
592	C₄⋊C₈	C₂²×C₄	1	4	yes	—
593	C₄⋊C₈	C₂²×C₄	1	4	yes	—
594	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
595	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
596	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
597	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
598	#97	—	2	2	no	—
599	#97	—	2	2	no	—
600	#97	—	2	2	no	—
601	#97	—	2	2	no	—
602	#97	—	4	1	no	—
603	#97	—	4	1	no	—
604	#97	—	4	1	no	—
605	#97	—	4	1	no	—
606	#97	—	4	1	no	—
607	#97	—	4	1	no	—
608	#97	—	4	1	no	—
609	#97	—	4	1	no	—
610	#97	—	4	1	no	—
611	#97	—	4	1	no	—
612	#97	—	4	1	no	—
613	#97	—	4	1	no	—
614	#97	C₂²×C₄	1	4	yes	—
615	#97	C₂²×C₄	1	4	yes	—
616	#97	C₂²×C₄	1	4	yes	—
617	#97	C₂²×C₄	1	4	yes	—
618	#97	C₂²×C₄	1	4	yes	—
619	#97	C₂²×C₄	1	4	yes	—
620	#97	C₂²×C₄	1	4	yes	—
621	#97	C₂²×C₄	1	4	yes	—
622	#97	C₂²×C₄	1	4	yes	—
623	#97	C₂²×C₄	1	4	yes	—
624	#97	C₂²×C₄	1	4	yes	—
625	#97	C₂²×C₄	1	4	yes	—
626	#97	C₂²×C₄	1	4	yes	—
627	#97	C₂²×C₄	1	4	yes	—
628	C₄×C₈	—	2	2	no	—
629	C₄×C₈	—	2	2	no	—
630	C₄×C₈	—	2	2	no	—
631	C₄×C₈	—	2	2	no	—
632	C₄×C₈	—	4	1	no	—
633	C₄×C₈	—	4	1	no	—
634	C₄×C₈	—	4	1	no	—
635	C₄×C₈	—	4	1	no	—
636	C₄×C₈	—	4	1	no	—
637	C₄×C₈	—	4	1	no	—
638	C₄×C₈	—	4	1	no	—
639	C₄×C₈	—	4	1	no	—
640	C₄×C₈	—	4	1	no	—
641	C₄×C₈	—	4	1	no	—
642	C₄×C₈	—	4	1	no	—
643	C₄×C₈	—	4	1	no	—
644	C₄×C₈	C₂²×C₄	1	4	yes	—
645	C₄×C₈	C₂²×C₄	1	4	yes	—
646	C₄×C₈	C₂²×C₄	1	4	yes	—
647	C₄×C₈	C₂²×C₄	1	4	yes	—
648	C₄×C₈	C₂²×C₄	1	4	yes	—
649	C₄×C₈	C₂²×C₄	1	4	yes	—
650	C₄×C₈	C₂²×C₄	1	4	yes	—
651	C₄×C₈	C₂²×C₄	1	4	yes	—
652	C₄×C₈	C₂²×C₄	1	4	yes	—
653	C₄×C₈	C₂²×C₄	1	4	yes	—
654	#95	C₂²×C₄	1	2	yes	—
655	#95	C₂²×C₄	1	2	yes	—
656	#95	C₂²×C₄	1	2	yes	—
657	#95	C₂²×C₄	1	2	yes	—
658	#95	C₂²×C₄	1	2	yes	—
659	#95	C₂²×C₄	1	2	yes	—
660	#95	C₂²×C₄	1	2	yes	—
661	#95	C₂²×C₄	1	2	yes	—
662	#95	C₂²×C₄	1	2	yes	—
663	#95	C₂²×C₄	1	2	yes	—
664	#95	C₂²×C₄	1	2	yes	—
665	#95	C₂²×C₄	1	2	yes	—
666	#95	C₂²×C₄	1	2	yes	—
667	#95	C₂²×C₄	1	2	yes	—
668	#95	C₂²×C₄	1	2	yes	—
669	#95	C₂²×C₄	1	2	yes	—
670	#95	C₂²×C₄	1	2	yes	—
671	#95	C₂²×C₄	1	2	yes	—
672	#95	C₂²×C₄	1	2	yes	—
673	#95	C₂²×C₄	1	2	yes	—
674	#95	C₂²×C₄	1	2	yes	—
675	#95	C₂²×C₄	1	2	yes	—
676	#95	C₂²×C₄	1	2	yes	—
677	#95	C₂²×C₄	1	2	yes	—
678	#95	C₂²×C₄	1	2	yes	—
679	#95	C₂²×C₄	1	2	yes	—
680	#95	C₂²×C₄	1	2	yes	—
681	#95	C₂²×C₄	1	2	yes	—
682	C₂⁴	C₂³×C₄	1	1	yes	characteristic
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	C₂×C₄²	1	4	yes	—
688	C₂×Q₈	C₂×C₄²	1	4	yes	—
689	C₂×Q₈	C₂×C₄²	1	4	yes	—
690	C₂×Q₈	C₂×C₄²	1	4	yes	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	C₂×C₄²	1	4	yes	—
698	C₂²×C₄	C₂×C₄²	1	4	yes	—
699	C₂²×C₄	C₂³×C₄	1	2	yes	—
700	C₂²×C₄	C₂³×C₄	1	2	yes	—
701	C₂²×C₄	C₂³×C₄	1	2	yes	—
702	C₂²×C₄	C₂³×C₄	1	2	yes	—
703	C₂²×C₄	C₂³×C₄	1	2	yes	—
704	C₂²×C₄	C₂³×C₄	1	2	yes	—
705	C₂²×C₄	C₂³×C₄	1	2	yes	—
706	C₂²×C₄	C₂³×C₄	1	2	yes	—
707	C₂²×C₄	C₂³×C₄	1	2	yes	—
708	C₂²×C₄	C₂³×C₄	1	2	yes	—
709	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
710	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
711	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
712	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
713	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
714	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
715	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
716	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
717	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
718	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
719	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
720	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
721	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
722	C₂²×C₄	C₂⁵	1	1	yes	characteristic
723	M₁₆	—	4	4	no	—
724	M₁₆	—	4	4	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₂×C₈	—	2	1	no	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	2	1	no	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	8	no	—
756	C₂×C₈	—	4	4	no	—
757	C₂×C₈	C₂³×C₄	1	2	yes	—
758	C₂×C₈	C₂³×C₄	1	2	yes	—
759	C₂×C₈	C₂³×C₄	1	2	yes	—
760	C₂×C₈	C₂³×C₄	1	2	yes	—
761	C₂×C₈	C₂³×C₄	1	2	yes	—
762	C₂×C₈	C₂³×C₄	1	2	yes	—
763	C₂×C₈	C₂³×C₄	1	2	yes	—
764	C₂×C₈	C₂³×C₄	1	2	yes	—
765	C₂×C₈	C₂³×C₄	1	2	yes	—
766	C₂×C₈	C₂³×C₄	1	2	yes	—
767	C₂×C₈	C₂³×C₄	1	2	yes	—
768	C₂×C₈	C₂³×C₄	1	2	yes	—
769	C₂×C₈	C₂³×C₄	1	2	yes	—
770	C₂×C₈	C₂³×C₄	1	2	yes	—
771	C₂×C₈	C₂³×C₄	1	2	yes	—
772	C₂×C₈	C₂³×C₄	1	2	yes	—
773	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
774	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	C₂×C₄²	1	4	yes	—
788	C₄⋊C₄	C₂×C₄²	1	4	yes	—
789	C₄⋊C₄	C₂×C₄²	1	4	yes	—
790	C₄⋊C₄	C₂×C₄²	1	4	yes	—
791	C₄⋊C₄	C₂×C₄²	1	4	yes	—
792	C₄⋊C₄	C₂×C₄²	1	4	yes	—
793	C₄⋊C₄	C₂×C₄²	1	4	yes	—
794	C₄⋊C₄	C₂×C₄²	1	4	yes	—
795	C₄⋊C₄	C₂×C₄²	1	4	yes	—
796	C₄⋊C₄	C₂×C₄²	1	4	yes	—
797	C₄⋊C₄	C₂×C₄²	1	4	yes	—
798	C₄⋊C₄	C₂×C₄²	1	4	yes	—
799	C₄⋊C₄	C₂×C₄²	1	4	yes	—
800	C₄⋊C₄	C₂×C₄²	1	4	yes	—
801	C₄⋊C₄	C₂×C₄²	1	4	yes	—
802	C₄⋊C₄	C₂×C₄²	1	4	yes	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
808	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
809	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
810	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
811	C₄²	—	2	4	no	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	4	no	—
814	C₄²	—	2	1	no	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	—	2	1	no	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	1	no	—
820	C₄²	—	2	1	no	—
821	C₄²	—	2	1	no	—
822	C₄²	—	2	1	no	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	1	no	—
825	C₄²	—	2	1	no	—
826	C₄²	—	2	1	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	1	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	2	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	2	no	—
839	C₄²	C₂×C₄²	1	4	yes	—
840	C₄²	C₂×C₄²	1	4	yes	—
841	C₄²	C₂³×C₄	1	2	yes	—
842	C₄²	C₂³×C₄	1	2	yes	—
843	C₄²	C₂³×C₄	1	2	yes	—
844	C₄²	C₂³×C₄	1	2	yes	—
845	C₄²	C₂³×C₄	1	2	yes	—
846	C₄²	C₂³×C₄	1	2	yes	—
847	C₄²	C₂³×C₄	1	2	yes	—
848	C₄²	C₂³×C₄	1	2	yes	—
849	C₄²	C₂³×C₄	1	2	yes	—
850	C₄²	C₂³×C₄	1	2	yes	—
851	C₄²	C₂³×C₄	1	2	yes	—
852	C₄²	C₂³×C₄	1	2	yes	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	C₂²×C₄²	1	2	yes	—
858	C₂³	C₂⁴×C₄	1	1	yes	characteristic
859	Q₈	—	4	4	no	—
860	Q₈	—	4	4	no	—
861	Q₈	—	4	4	no	—
862	Q₈	—	4	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	C₂²×C₄²	1	2	yes	—
907	C₂×C₄	C₂²×C₄²	1	2	yes	—
908	C₂×C₄	C₂²×C₄²	1	2	yes	—
909	C₂×C₄	C₂²×C₄²	1	2	yes	—
910	C₂×C₄	C₂²×C₄²	1	2	yes	—
911	C₂×C₄	C₂²×C₄²	1	2	yes	—
912	C₂×C₄	C₂²×C₄²	1	2	yes	—
913	C₂×C₄	C₂²×C₄²	1	2	yes	—
914	C₂×C₄	C₂²×C₄²	1	2	yes	—
915	C₂×C₄	C₂²×C₄²	1	2	yes	—
916	C₂×C₄	C₂²×C₄²	1	2	yes	—
917	C₂×C₄	C₂²×C₄²	1	2	yes	—
918	C₂×C₄	C₂²×C₄²	1	2	yes	—
919	C₂×C₄	#568	1	4	yes	—
920	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
921	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
922	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
923	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
924	C₂×C₄	#585	1	1	yes	characteristic
925	C₂×C₄	#585	1	1	yes	characteristic
926	C₈	—	2	2	no	—
927	C₈	—	2	2	no	—
928	C₈	—	2	2	no	—
929	C₈	—	2	2	no	—
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	#519	1	4	yes	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	C₂³×C₄²	1	1	yes	characteristic
948	C₂²	C₄×2₋¹⁺⁴	1	1	yes	characteristic
949	C₂²	C₄×2₋¹⁺⁴	1	1	yes	characteristic
950	C₂²	C₂×#568	1	2	yes	—
951	C₂²	#3573	1	2	yes	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	4	no	—
965	C₄	—	2	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	C₂×#519	1	1	yes	characteristic
974	C₄	#3428	1	1	yes	characteristic
975	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
976	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
977	C₂	—	4	2	no	—
978	C₂	C₄×#519	1	1	yes	characteristic
979	C₂	C₄×#568	1	1	yes	characteristic
980	C₂	#60058	1	1	yes	characteristic
981	C₂	#60340	1	2	yes	—
982	C₂	#60344	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₄	C₂⁵
commutator	C₂²	C₂³×C₄²
socle	C₂³	C₂⁴×C₄
prime radical	C₂⁴	C₂³×C₄
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. #20576	C₂	semidirect
5. #20576	C₂	semidirect
6. #20575	C₂	semidirect
7. #20575	C₂	semidirect
8. #20574	C₂	semidirect
9. #20573	C₂	semidirect
10. #20571	C₂	semidirect
11. #20570	C₂	semidirect
18. #20521	C₂	semidirect
19. #20520	C₂	semidirect
20. #20519	C₂	semidirect
21. #20519	C₂	semidirect
22. #20518	C₂	semidirect
23. #20518	C₂	semidirect
24. C₄×#446	C₂	semidirect
25. #20516	C₂	semidirect
33. #2985	C₄	semidirect
34. #2961	C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2985	2
C₂×#2961	2
#34085	2
#20576	2
#20575	2
#20574	2
#20573	2
#20571	2
#20570	2
#20554	2
#20553	2
#20552	2
#20551	2
#20550	2
#20521	2
#20520	2
#20519	2
#20518	2
C₄×#446	2
#20516	2
#20481	2
#20479	2
#20478	2
#20475	2
#20474	2