Subgroups — #7804791

Order 512.

7016 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59820	C₂	1	4	yes	maximal, complemented
2	#59424	C₂	1	4	yes	maximal, complemented
3	#59147	C₂	1	4	yes	maximal, complemented
4	#59143	C₂	1	4	yes	maximal, complemented
5	#59006	C₂	1	8	yes	maximal, complemented
6	#47033	C₂	1	4	yes	maximal, complemented
7	#46452	C₂	1	4	yes	maximal, complemented
8	#42976	C₂	1	4	yes	maximal, complemented
9	#40546	C₂	1	4	yes	maximal, complemented
10	#40542	C₂	1	4	yes	maximal, complemented
11	#37451	C₂	1	1	yes	maximal, characteristic, complemented
12	#35808	C₂	1	4	yes	maximal, complemented
13	#35732	C₂	1	4	yes	maximal, complemented
14	#35695	C₂	1	4	yes	maximal, complemented
15	#34958	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#2435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#2433	C₂	1	1	yes	maximal, characteristic
18	#34246	C₂	1	1	yes	maximal, characteristic, complemented
19	#34245	C₂	1	1	yes	maximal, characteristic, complemented
20	#34171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁴×D₄	C₂²	1	1	yes	characteristic
22	C₂×#559	C₂²	1	4	yes	complemented
23	C₂×#551	C₂²	1	8	yes	complemented
24	C₂²×#127	C₂²	1	2	yes	—
25	C₂²×#124	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂²×#121	C₂²	1	1	yes	characteristic
28	C₂²×#120	C₂²	1	4	yes	—
29	C₂×#518	C₂²	1	2	yes	complemented
30	#2829	C₂²	1	8	yes	complemented
31	#2816	C₂²	1	2	yes	complemented
32	#2816	C₂²	1	2	yes	complemented
33	#2786	C₂²	1	8	yes	complemented
34	#2740	C₂²	1	8	yes	complemented
35	#2730	C₂²	1	8	yes	complemented
36	#2712	C₂²	1	8	yes	complemented
37	#2710	C₂²	1	8	yes	complemented
38	#2709	C₂²	1	8	yes	complemented
39	#2709	C₂²	1	8	yes	complemented
40	#2705	C₂²	1	8	yes	complemented
41	#2697	C₂²	1	8	yes	complemented
42	#2685	C₂²	1	8	yes	complemented
43	#2685	C₂²	1	8	yes	complemented
44	#2684	C₂²	1	8	yes	complemented
45	#2662	C₂²	1	8	yes	complemented
46	#2648	C₂²	1	8	yes	complemented
47	#2630	C₂²	1	8	yes	complemented
48	#2626	C₂²	1	4	yes	complemented
49	#2620	C₂²	1	4	yes	complemented
50	#2618	C₂²	1	4	yes	complemented
51	#2608	C₂²	1	2	yes	complemented
52	#2607	C₂²	1	2	yes	complemented
53	#2601	C₂²	1	8	yes	complemented
54	#2592	C₂²	1	4	yes	complemented
55	#2569	C₂²	1	2	yes	complemented
56	#2569	C₂²	1	2	yes	complemented
57	#2560	C₂²	1	8	yes	complemented
58	#2557	C₂²	1	8	yes	complemented
59	#2554	C₂²	1	8	yes	complemented
60	#2549	C₂²	1	2	yes	complemented
61	#2549	C₂²	1	2	yes	complemented
62	#2548	C₂²	1	4	yes	complemented
63	#2548	C₂²	1	4	yes	complemented
64	#2544	C₂²	1	4	yes	complemented
65	#2544	C₂²	1	4	yes	complemented
66	#2544	C₂²	1	8	yes	complemented
67	#2538	C₂²	1	4	yes	complemented
68	#2534	C₂²	1	8	yes	complemented
69	#2534	C₂²	1	8	yes	complemented
70	#2512	C₂²	1	4	yes	complemented
71	#2512	C₂²	1	4	yes	complemented
72	#2502	C₂²	1	2	yes	complemented
73	#2501	C₂²	1	2	yes	complemented
74	#2480	C₂²	1	8	yes	complemented
75	#2480	C₂²	1	8	yes	complemented
76	#2472	C₂²	1	8	yes	complemented
77	#2472	C₂²	1	8	yes	complemented
78	#2471	C₂²	1	8	yes	complemented
79	#2467	C₂²	1	8	yes	complemented
80	#2461	C₂²	1	8	yes	complemented
81	#2459	C₂²	1	8	yes	complemented
82	#2457	C₂²	1	8	yes	complemented
83	#2448	C₂²	1	4	yes	complemented
84	#2447	C₂²	1	4	yes	complemented
85	#2445	C₂²	1	4	yes	complemented
86	#2445	C₂²	1	8	yes	complemented
87	#2445	C₂²	1	4	yes	complemented
88	#2437	C₂²	1	4	yes	—
89	#2437	C₂²	1	8	yes	complemented
90	#2436	C₂²	1	2	yes	complemented
91	#2435	C₂²	1	4	yes	—
92	#2435	C₂²	1	2	yes	—
93	#2435	C₂²	1	2	yes	—
94	#2435	C₂²	1	4	yes	complemented
95	#2435	C₂²	1	2	yes	complemented
96	#2435	C₂²	1	2	yes	complemented
97	#2435	C₂²	1	2	yes	complemented
98	#2435	C₂²	1	8	yes	complemented
99	#2433	C₂²	1	4	yes	—
100	#2433	C₂²	1	2	yes	—
101	#2433	C₂²	1	4	yes	—
102	#2433	C₂²	1	2	yes	—
103	#2433	C₂²	1	2	yes	—
104	#2433	C₂²	1	2	yes	—
105	#2418	C₂²	1	8	yes	complemented
106	#2418	C₂²	1	8	yes	complemented
107	#2412	C₂²	1	8	yes	complemented
108	#2412	C₂²	1	8	yes	complemented
109	#2411	C₂²	1	8	yes	complemented
110	#2411	C₂²	1	8	yes	complemented
111	#2405	C₂²	1	4	yes	—
112	#2405	C₂²	1	8	yes	complemented
113	#2405	C₂²	1	8	yes	complemented
114	#2396	C₂²	1	4	yes	complemented
115	#2392	C₂²	1	8	yes	complemented
116	C₂×#394	C₂²	1	4	yes	complemented
117	C₂×#392	C₂²	1	4	yes	—
118	#2368	C₂²	1	4	yes	complemented
119	#2367	C₂²	1	4	yes	complemented
120	#2366	C₂²	1	4	yes	complemented
121	#2364	C₂²	1	4	yes	complemented
122	#2363	C₂²	1	4	yes	complemented
123	#2362	C₂²	1	4	yes	complemented
124	#2358	C₂²	1	8	yes	complemented
125	#2354	C₂²	1	4	yes	complemented
126	#2345	C₂²	1	2	yes	complemented
127	#2344	C₂²	1	2	yes	complemented
128	#2342	C₂²	1	4	yes	—
129	#2342	C₂²	1	8	yes	complemented
130	Q₈×C₂²⋊C₄	C₂²	1	2	yes	complemented
131	D₄×C₂²⋊C₄	C₂²	1	4	yes	—
132	D₄×C₂²⋊C₄	C₂²	1	4	yes	—
133	D₄×C₂²⋊C₄	C₂²	1	4	yes	—
134	D₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
135	D₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
136	D₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
137	D₄×C₂²⋊C₄	C₂²	1	8	yes	complemented
138	#2333	C₂²	1	4	yes	complemented
139	#2332	C₂²	1	4	yes	complemented
140	#2313	C₂²	1	2	yes	complemented
141	#2312	C₂²	1	2	yes	complemented
142	#2309	C₂²	1	2	yes	complemented
143	#2308	C₂²	1	2	yes	complemented
144	#2308	C₂²	1	2	yes	complemented
145	C₄×C₂²⋊Q₈	C₂²	1	4	yes	complemented
146	C₄×C₂²⋊Q₈	C₂²	1	4	yes	complemented
147	C₄×C₂²⋊Q₈	C₂²	1	4	yes	complemented
148	C₄×#121	C₂²	1	4	yes	complemented
149	C₂×#390	C₂²	1	2	yes	—
150	C₂×#390	C₂²	1	2	yes	complemented
151	#2280	C₂²	1	1	yes	characteristic
152	#2280	C₂²	1	1	yes	characteristic
153	C₂×#379	C₂²	1	4	yes	—
154	C₂×#379	C₂²	1	4	yes	—
155	#2274	C₂²	1	2	yes	complemented
156	#2273	C₂²	1	2	yes	complemented
157	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
159	C₂⁶	C₂³	1	2	yes	—
160	C₂³×Q₈	C₂³	1	1	yes	characteristic
161	C₂³×D₄	—	2	8	no	—
162	C₂³×D₄	—	4	8	no	—
163	C₂³×D₄	C₂³	1	1	yes	characteristic
164	C₂³×D₄	C₂³	1	2	yes	—
165	C₂³×D₄	C₂³	1	2	yes	—
166	C₂³×D₄	C₂³	1	2	yes	—
167	C₂³×D₄	C₂³	1	1	yes	characteristic
168	C₂³×D₄	C₂³	1	2	yes	—
169	C₂³×D₄	C₂³	1	2	yes	—
170	C₂³×D₄	C₂³	1	2	yes	—
171	C₂³×D₄	C₂³	1	1	yes	characteristic
172	C₂³×D₄	C₂³	1	8	yes	—
173	C₂⁴×C₄	C₂³	1	1	yes	characteristic
174	#559	—	4	16	no	—
175	#551	—	4	32	no	—
176	C₂×#127	—	4	8	no	—
177	C₂×#127	C₂³	1	4	yes	—
178	C₂×#127	C₂³	1	4	yes	—
179	C₂×#127	C₂³	1	4	yes	—
180	C₂×#127	C₂³	1	4	yes	—
181	C₂×#126	C₂³	1	8	yes	complemented
182	C₂×#126	C₂³	1	8	yes	complemented
183	C₂×#124	—	4	8	no	—
184	C₂×#124	C₂³	1	4	yes	—
185	C₂×#124	C₂³	1	4	yes	—
186	C₂×#124	C₂³	1	4	yes	—
187	C₂×#124	C₂³	1	4	yes	—
188	C₂×#124	C₂³	1	4	yes	complemented
189	C₂×#124	C₂³	1	8	yes	complemented
190	C₂×#124	C₂³	1	8	yes	complemented
191	C₂×#123	C₂³	1	8	yes	—
192	C₂×#123	C₂³	1	8	yes	complemented
193	C₂×#123	C₂³	1	8	yes	complemented
194	C₂×#123	C₂³	1	8	yes	complemented
195	C₂×#123	C₂³	1	8	yes	complemented
196	C₂×C₂²⋊Q₈	—	2	8	no	—
197	C₂×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
202	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₂×C₂²⋊Q₈	C₂³	1	8	yes	complemented
204	C₂×#121	—	2	8	no	—
205	C₂×#121	C₂³	1	2	yes	—
206	C₂×#121	C₂³	1	2	yes	—
207	C₂×#121	C₂³	1	2	yes	—
208	C₂×#121	C₂³	1	2	yes	—
209	C₂×#120	—	4	16	no	—
210	C₂×#120	C₂³	1	8	yes	—
211	C₂×#120	C₂³	1	8	yes	—
212	C₂×#120	C₂³	1	8	yes	—
213	C₂×#120	C₂³	1	8	yes	—
214	#518	—	4	8	no	—
215	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
216	C₂×C₄×Q₈	C₂³	1	4	yes	complemented
217	C₂×C₄×D₄	C₂³	1	4	yes	—
218	C₂×C₄×D₄	C₂³	1	4	yes	—
219	C₂×C₄×D₄	C₂³	1	8	yes	—
220	C₂×C₄×D₄	C₂³	1	8	yes	—
221	C₂×C₄×D₄	C₂³	1	8	yes	complemented
222	C₂×C₄×D₄	C₂³	1	4	yes	complemented
223	C₂×C₄×D₄	C₂³	1	8	yes	complemented
224	C₂×#117	C₂³	1	4	yes	—
225	C₂×#117	C₂³	1	2	yes	—
226	C₂×#117	C₂³	1	2	yes	—
227	C₂×#117	C₂³	1	8	yes	complemented
228	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
235	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
236	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
237	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
239	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
240	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
241	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
242	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
243	C₂²×C₄²	C₂³	1	2	yes	—
244	C₂²×C₄²	C₂³	1	2	yes	—
245	#400	C₂³	1	4	yes	complemented
246	#399	C₂³	1	4	yes	—
247	#399	C₂³	1	4	yes	complemented
248	#399	C₂³	1	4	yes	complemented
249	#399	C₂³	1	8	yes	complemented
250	#398	C₂³	1	4	yes	complemented
251	#398	C₂³	1	4	yes	complemented
252	#398	C₂³	1	4	yes	complemented
253	#398	C₂³	1	4	yes	complemented
254	#397	C₂³	1	8	yes	complemented
255	#397	C₂³	1	8	yes	complemented
256	#397	C₂³	1	8	yes	complemented
257	#397	C₂³	1	8	yes	complemented
258	#397	C₂³	1	8	yes	complemented
259	#397	C₂³	1	8	yes	complemented
260	#396	C₂³	1	4	yes	—
261	#396	C₂³	1	4	yes	—
262	#396	C₂³	1	8	yes	complemented
263	#396	C₂³	1	8	yes	complemented
264	#396	C₂³	1	8	yes	complemented
265	#396	C₂³	1	8	yes	complemented
266	#396	C₂³	1	8	yes	complemented
267	#396	C₂³	1	8	yes	complemented
268	#395	C₂³	1	4	yes	complemented
269	#394	C₂³	1	8	yes	—
270	#394	C₂³	1	8	yes	—
271	#394	C₂³	1	8	yes	—
272	#394	C₂³	1	4	yes	—
273	#394	C₂³	1	8	yes	—
274	#394	C₂³	1	4	yes	—
275	#394	C₂³	1	4	yes	—
276	#394	C₂³	1	4	yes	—
277	#394	C₂³	1	4	yes	complemented
278	#394	C₂³	1	4	yes	complemented
279	#394	C₂³	1	8	yes	complemented
280	#394	C₂³	1	8	yes	complemented
281	#394	C₂³	1	8	yes	complemented
282	#394	C₂³	1	8	yes	complemented
283	#394	C₂³	1	8	yes	complemented
284	#394	C₂³	1	8	yes	complemented
285	#394	C₂³	1	8	yes	complemented
286	#394	C₂³	1	8	yes	complemented
287	#394	C₂³	1	8	yes	complemented
288	#394	C₂³	1	8	yes	complemented
289	#394	C₂³	1	8	yes	complemented
290	#394	C₂³	1	8	yes	complemented
291	#393	C₂³	1	4	yes	—
292	#393	C₂³	1	8	yes	complemented
293	#393	C₂³	1	4	yes	complemented
294	#393	C₂³	1	4	yes	complemented
295	#392	C₂³	1	4	yes	—
296	#392	C₂³	1	4	yes	—
297	#392	C₂³	1	4	yes	—
298	#392	C₂³	1	4	yes	—
299	#392	C₂³	1	8	yes	—
300	#392	C₂³	1	8	yes	—
301	#391	C₂³	1	4	yes	complemented
302	#391	C₂³	1	8	yes	complemented
303	#391	C₂³	1	4	yes	complemented
304	#391	C₂³	1	4	yes	complemented
305	#391	C₂³	1	4	yes	complemented
306	#390	C₂³	1	4	yes	—
307	#390	C₂³	1	8	yes	—
308	#390	C₂³	1	4	yes	—
309	#390	C₂³	1	4	yes	—
310	#390	C₂³	1	8	yes	—
311	#390	C₂³	1	4	yes	—
312	#390	C₂³	1	4	yes	—
313	#390	C₂³	1	4	yes	—
314	#390	C₂³	1	4	yes	—
315	#390	C₂³	1	4	yes	—
316	#390	C₂³	1	4	yes	—
317	#390	C₂³	1	4	yes	—
318	#390	C₂³	1	4	yes	complemented
319	#390	C₂³	1	8	yes	complemented
320	#390	C₂³	1	8	yes	complemented
321	#390	C₂³	1	8	yes	complemented
322	#390	C₂³	1	4	yes	complemented
323	#390	C₂³	1	8	yes	complemented
324	#389	C₂³	1	4	yes	complemented
325	#389	C₂³	1	4	yes	complemented
326	#389	C₂³	1	4	yes	complemented
327	#389	C₂³	1	4	yes	complemented
328	#388	C₂³	1	8	yes	—
329	#388	C₂³	1	8	yes	—
330	#388	C₂³	1	8	yes	complemented
331	#388	C₂³	1	8	yes	complemented
332	#388	C₂³	1	8	yes	complemented
333	#388	C₂³	1	8	yes	complemented
334	#388	C₂³	1	8	yes	complemented
335	#388	C₂³	1	8	yes	complemented
336	#388	C₂³	1	8	yes	complemented
337	#388	C₂³	1	8	yes	complemented
338	#388	C₂³	1	8	yes	complemented
339	#388	C₂³	1	8	yes	complemented
340	#388	C₂³	1	8	yes	complemented
341	#388	C₂³	1	8	yes	complemented
342	#387	C₂³	1	8	yes	complemented
343	#387	C₂³	1	8	yes	complemented
344	#387	C₂³	1	8	yes	complemented
345	#387	C₂³	1	4	yes	complemented
346	#387	C₂³	1	4	yes	complemented
347	#387	C₂³	1	4	yes	complemented
348	#387	C₂³	1	4	yes	complemented
349	#387	C₂³	1	8	yes	complemented
350	#386	C₂³	1	8	yes	—
351	#386	C₂³	1	8	yes	—
352	#386	C₂³	1	8	yes	—
353	#386	C₂³	1	8	yes	—
354	#386	C₂³	1	8	yes	—
355	#386	C₂³	1	8	yes	—
356	#386	C₂³	1	8	yes	—
357	#386	C₂³	1	8	yes	complemented
358	#386	C₂³	1	8	yes	complemented
359	#386	C₂³	1	8	yes	complemented
360	#386	C₂³	1	8	yes	complemented
361	#386	C₂³	1	8	yes	complemented
362	#386	C₂³	1	8	yes	complemented
363	#386	C₂³	1	8	yes	complemented
364	#386	C₂³	1	8	yes	complemented
365	#386	C₂³	1	8	yes	complemented
366	#385	C₂³	1	4	yes	—
367	#385	C₂³	1	4	yes	—
368	#385	C₂³	1	8	yes	—
369	#385	C₂³	1	8	yes	—
370	#385	C₂³	1	4	yes	—
371	#385	C₂³	1	4	yes	—
372	#385	C₂³	1	8	yes	complemented
373	#385	C₂³	1	8	yes	complemented
374	#384	C₂³	1	4	yes	complemented
375	#381	C₂³	1	1	yes	characteristic
376	#381	C₂³	1	1	yes	characteristic
377	#381	C₂³	1	2	yes	—
378	#381	C₂³	1	4	yes	—
379	#381	C₂³	1	8	yes	complemented
380	#380	C₂³	1	4	yes	—
381	#380	C₂³	1	4	yes	—
382	#380	C₂³	1	2	yes	—
383	#380	C₂³	1	2	yes	—
384	#380	C₂³	1	4	yes	—
385	#380	C₂³	1	4	yes	—
386	#380	C₂³	1	2	yes	—
387	#380	C₂³	1	2	yes	—
388	#380	C₂³	1	8	yes	complemented
389	#380	C₂³	1	8	yes	complemented
390	#379	C₂³	1	4	yes	—
391	#379	C₂³	1	4	yes	—
392	#379	C₂³	1	4	yes	—
393	#379	C₂³	1	2	yes	—
394	#379	C₂³	1	8	yes	—
395	#379	C₂³	1	8	yes	—
396	#379	C₂³	1	8	yes	—
397	#379	C₂³	1	8	yes	—
398	#379	C₂³	1	2	yes	—
399	#379	C₂³	1	8	yes	—
400	#379	C₂³	1	8	yes	—
401	#379	C₂³	1	8	yes	—
402	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
403	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
404	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
405	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
406	C₄×C₄⋊C₄	C₂³	1	8	yes	complemented
407	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
408	C₄×C₄⋊C₄	C₂³	1	4	yes	complemented
409	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
414	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
416	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
418	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂³	1	8	yes	—
420	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂³	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
427	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
428	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
429	C₂×#95	C₂³	1	2	yes	—
430	C₂×#95	C₂³	1	2	yes	—
431	C₂⁵	—	2	8	no	—
432	C₂⁵	—	4	8	no	—
433	C₂⁵	—	4	8	no	—
434	C₂⁵	—	4	8	no	—
435	C₂⁵	C₂⁴	1	4	yes	—
436	C₂⁵	C₂⁴	1	4	yes	—
437	C₂⁵	C₂⁴	1	1	yes	characteristic
438	C₂⁵	C₂⁴	1	2	yes	—
439	C₂⁵	C₂⁴	1	2	yes	—
440	C₂⁵	C₂⁴	1	2	yes	—
441	C₂²×Q₈	—	2	4	no	—
442	C₂²×Q₈	—	4	4	no	—
443	C₂²×Q₈	C₂⁴	1	2	yes	—
444	C₂²×Q₈	C₂⁴	1	4	yes	—
445	C₂²×Q₈	C₂⁴	1	2	yes	—
446	C₂²×D₄	—	2	8	no	—
447	C₂²×D₄	—	2	8	no	—
448	C₂²×D₄	—	2	8	no	—
449	C₂²×D₄	—	2	8	no	—
450	C₂²×D₄	—	2	4	no	—
451	C₂²×D₄	—	2	8	no	—
452	C₂²×D₄	—	2	8	no	—
453	C₂²×D₄	—	2	4	no	—
454	C₂²×D₄	—	2	8	no	—
455	C₂²×D₄	—	2	8	no	—
456	C₂²×D₄	—	2	8	no	—
457	C₂²×D₄	—	2	4	no	—
458	C₂²×D₄	—	4	4	no	—
459	C₂²×D₄	—	4	4	no	—
460	C₂²×D₄	—	4	4	no	—
461	C₂²×D₄	—	4	16	no	—
462	C₂²×D₄	—	4	4	no	—
463	C₂²×D₄	—	4	16	no	—
464	C₂²×D₄	—	4	8	no	—
465	C₂²×D₄	—	4	8	no	—
466	C₂²×D₄	—	4	8	no	—
467	C₂²×D₄	—	4	8	no	—
468	C₂²×D₄	—	4	16	no	—
469	C₂²×D₄	—	4	64	no	—
470	C₂²×D₄	C₂⁴	1	2	yes	—
471	C₂²×D₄	C₂⁴	1	4	yes	—
472	C₂²×D₄	C₂⁴	1	2	yes	—
473	C₂²×D₄	C₂⁴	1	2	yes	—
474	C₂²×D₄	C₂⁴	1	8	yes	—
475	C₂²×D₄	C₂⁴	1	4	yes	—
476	C₂²×D₄	C₂⁴	1	4	yes	—
477	C₂²×D₄	C₂⁴	1	2	yes	—
478	C₂²×D₄	C₂⁴	1	4	yes	—
479	C₂²×D₄	C₂⁴	1	8	yes	—
480	C₂²×D₄	C₂⁴	1	8	yes	—
481	C₂²×D₄	C₂⁴	1	2	yes	—
482	C₂²×D₄	C₂⁴	1	2	yes	—
483	C₂²×D₄	C₂⁴	1	8	yes	—
484	C₂³×C₄	—	4	4	no	—
485	C₂³×C₄	#41	1	8	yes	—
486	C₂³×C₄	C₂⁴	1	2	yes	—
487	C₂³×C₄	C₂⁴	1	4	yes	—
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	2	yes	—
492	C₂³×C₄	C₂⁴	1	2	yes	—
493	C₂³×C₄	C₂⁴	1	4	yes	—
494	C₂³×C₄	C₂⁴	1	8	yes	—
495	C₂³×C₄	C₂⁴	1	8	yes	—
496	C₂³×C₄	C₂⁴	1	8	yes	—
497	C₂³×C₄	C₂⁴	1	1	yes	characteristic
498	C₂³×C₄	C₂⁴	1	1	yes	characteristic
499	C₂³×C₄	C₂⁴	1	1	yes	characteristic
500	#127	—	2	16	no	—
501	#127	—	4	8	no	—
502	#127	—	4	8	no	—
503	#127	—	4	8	no	—
504	#126	—	4	16	no	—
505	#126	—	4	16	no	—
506	#124	—	2	16	no	—
507	#124	—	4	8	no	—
508	#124	—	4	16	no	—
509	#124	—	4	8	no	—
510	#124	—	4	8	no	—
511	#124	—	4	8	no	—
512	#124	—	4	16	no	—
513	#123	—	4	16	no	—
514	#123	—	4	16	no	—
515	#123	—	4	16	no	—
516	#123	—	4	16	no	—
517	#123	—	4	16	no	—
518	C₂²⋊Q₈	—	2	8	no	—
519	C₂²⋊Q₈	—	2	8	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	—	2	8	no	—
522	C₂²⋊Q₈	—	2	16	no	—
523	C₂²⋊Q₈	—	4	8	no	—
524	C₂²⋊Q₈	—	4	16	no	—
525	#121	—	2	8	no	—
526	#121	—	2	8	no	—
527	#121	—	2	8	no	—
528	#121	—	2	8	no	—
529	#120	—	2	32	no	—
530	#120	—	4	16	no	—
531	#120	—	4	16	no	—
532	#120	—	4	16	no	—
533	C₄×Q₈	—	4	8	no	—
534	C₄×Q₈	—	4	8	no	—
535	C₄×D₄	—	2	16	no	—
536	C₄×D₄	—	4	8	no	—
537	C₄×D₄	—	4	16	no	—
538	C₄×D₄	—	4	8	no	—
539	C₄×D₄	—	4	16	no	—
540	C₄×D₄	—	4	16	no	—
541	C₄×D₄	—	4	16	no	—
542	#117	—	2	16	no	—
543	#117	—	4	4	no	—
544	#117	—	4	16	no	—
545	#117	—	4	4	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	8	no	—
549	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
550	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
551	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
552	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
553	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
554	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
555	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
556	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
557	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
558	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
559	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
560	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
561	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
562	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
563	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
564	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
565	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
566	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
567	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
568	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
569	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
570	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
571	C₂×C₂²⋊C₄	—	2	8	no	—
572	C₂×C₂²⋊C₄	—	2	8	no	—
573	C₂×C₂²⋊C₄	—	2	8	no	—
574	C₂×C₂²⋊C₄	—	4	16	no	—
575	C₂×C₂²⋊C₄	—	4	8	no	—
576	C₂×C₂²⋊C₄	—	4	16	no	—
577	C₂×C₂²⋊C₄	—	4	4	no	—
578	C₂×C₂²⋊C₄	—	4	8	no	—
579	C₂×C₂²⋊C₄	—	4	16	no	—
580	C₂×C₂²⋊C₄	—	4	16	no	—
581	C₂×C₂²⋊C₄	—	4	8	no	—
582	C₂×C₂²⋊C₄	—	4	16	no	—
583	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
589	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
590	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
591	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
594	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
600	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
604	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
605	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
606	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
607	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
608	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
609	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
610	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
611	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
612	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
613	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
614	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
615	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
616	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
617	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
618	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
619	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
620	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
621	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
622	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
623	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
624	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
625	C₂×C₄²	—	4	4	no	—
626	C₂×C₄²	—	4	4	no	—
627	C₂×C₄²	C₂⁴	1	8	yes	—
628	C₂×C₄²	C₂⁴	1	4	yes	—
629	C₂×C₄²	C₂⁴	1	4	yes	—
630	C₂×C₄²	C₂⁴	1	4	yes	—
631	C₂×C₄²	C₂⁴	1	4	yes	—
632	C₂×C₄²	C₂⁴	1	8	yes	—
633	C₂×C₄²	C₂⁴	1	8	yes	—
634	C₂×C₄²	C₂⁴	1	2	yes	—
635	C₂×C₄²	C₂⁴	1	2	yes	—
636	C₂×C₄²	C₂⁴	1	2	yes	—
637	C₂×C₄²	C₂⁴	1	2	yes	—
638	#95	C₂⁴	1	2	yes	—
639	#95	C₂⁴	1	2	yes	—
640	#95	C₂⁴	1	4	yes	—
641	#95	C₂⁴	1	4	yes	—
642	#95	C₂⁴	1	2	yes	—
643	#95	C₂⁴	1	2	yes	—
644	#95	C₂⁴	1	4	yes	—
645	#95	C₂⁴	1	8	yes	—
646	#95	C₂⁴	1	4	yes	—
647	#95	C₂⁴	1	8	yes	—
648	#95	C₂⁴	1	2	yes	—
649	#95	C₂⁴	1	2	yes	—
650	#95	C₂⁴	1	2	yes	—
651	#95	C₂⁴	1	2	yes	—
652	#95	C₂⁴	1	8	yes	—
653	#95	C₂⁴	1	8	yes	—
654	#95	C₂⁴	1	4	yes	—
655	#95	C₂⁴	1	8	yes	—
656	#95	C₂⁴	1	4	yes	—
657	#95	C₂⁴	1	8	yes	—
658	#95	C₂⁴	1	4	yes	—
659	#95	C₂⁴	1	4	yes	—
660	#95	C₂⁴	1	8	yes	—
661	#95	C₂⁴	1	4	yes	—
662	#95	C₂⁴	1	4	yes	—
663	#95	C₂⁴	1	8	yes	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	2	4	no	—
666	C₂⁴	—	2	4	no	—
667	C₂⁴	—	2	8	no	—
668	C₂⁴	—	2	8	no	—
669	C₂⁴	—	2	8	no	—
670	C₂⁴	—	2	8	no	—
671	C₂⁴	—	2	8	no	—
672	C₂⁴	—	2	16	no	—
673	C₂⁴	—	2	16	no	—
674	C₂⁴	—	2	4	no	—
675	C₂⁴	—	2	4	no	—
676	C₂⁴	—	2	8	no	—
677	C₂⁴	—	4	2	no	—
678	C₂⁴	—	4	8	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	4	4	no	—
681	C₂⁴	—	4	4	no	—
682	C₂⁴	—	4	8	no	—
683	C₂⁴	—	4	4	no	—
684	C₂⁴	—	4	4	no	—
685	C₂⁴	—	4	4	no	—
686	C₂⁴	—	4	4	no	—
687	C₂⁴	—	4	4	no	—
688	C₂⁴	—	4	4	no	—
689	C₂⁴	—	4	32	no	—
690	C₂⁴	—	8	16	no	—
691	C₂⁴	—	8	16	no	—
692	C₂⁴	—	8	64	no	—
693	C₂⁴	C₂×#41	1	4	yes	—
694	C₂⁴	C₂⁵	1	4	yes	—
695	C₂⁴	C₂⁵	1	4	yes	—
696	C₂⁴	C₂⁵	1	1	yes	characteristic
697	C₂⁴	C₂⁵	1	4	yes	—
698	C₂⁴	C₂⁵	1	1	yes	characteristic
699	C₂⁴	C₂⁵	1	1	yes	characteristic
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	2	8	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	4	4	no	—
705	C₂×Q₈	—	4	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	8	8	no	—
708	C₂×D₄	—	2	32	no	—
709	C₂×D₄	—	2	8	no	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	16	no	—
712	C₂×D₄	—	2	16	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	16	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	8	no	—
722	C₂×D₄	—	2	8	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	16	no	—
727	C₂×D₄	—	2	8	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	16	no	—
731	C₂×D₄	—	4	32	no	—
732	C₂×D₄	—	4	32	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	8	no	—
737	C₂×D₄	—	4	16	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	—	4	8	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	8	no	—
747	C₂×D₄	—	4	32	no	—
748	C₂×D₄	—	4	32	no	—
749	C₂×D₄	—	4	32	no	—
750	C₂×D₄	—	8	8	no	—
751	C₂×D₄	—	8	64	no	—
752	C₂×D₄	—	8	16	no	—
753	C₂×D₄	H(5,𝔽₂)	1	8	yes	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	8	no	—
759	C₂²×C₄	—	2	8	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	8	no	—
763	C₂²×C₄	—	2	16	no	—
764	C₂²×C₄	—	2	8	no	—
765	C₂²×C₄	—	4	16	no	—
766	C₂²×C₄	—	4	4	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	4	no	—
771	C₂²×C₄	—	4	4	no	—
772	C₂²×C₄	—	4	4	no	—
773	C₂²×C₄	—	4	8	no	—
774	C₂²×C₄	—	4	8	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	8	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	—	4	8	no	—
779	C₂²×C₄	—	4	8	no	—
780	C₂²×C₄	—	4	8	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	C₂×#41	1	4	yes	—
783	C₂²×C₄	C₂×#41	1	4	yes	—
784	C₂²×C₄	C₂×#41	1	4	yes	—
785	C₂²×C₄	C₂×#41	1	4	yes	—
786	C₂²×C₄	C₂×#41	1	4	yes	—
787	C₂²×C₄	C₂×#41	1	4	yes	—
788	C₂²×C₄	C₂⁵	1	4	yes	—
789	C₂²×C₄	C₂⁵	1	4	yes	—
790	C₂²×C₄	C₂⁵	1	8	yes	—
791	C₂²×C₄	C₂⁵	1	4	yes	—
792	C₂²×C₄	C₂⁵	1	4	yes	—
793	C₂²×C₄	C₂⁵	1	4	yes	—
794	C₂²×C₄	C₂⁵	1	4	yes	—
795	C₂²×C₄	C₂⁵	1	4	yes	—
796	C₂²×C₄	C₂⁵	1	4	yes	—
797	C₂²×C₄	C₂⁵	1	1	yes	characteristic
798	C₂²×C₄	C₂⁵	1	1	yes	characteristic
799	C₂²×C₄	C₂⁵	1	1	yes	characteristic
800	C₂²×C₄	C₂⁵	1	4	yes	—
801	C₂²×C₄	C₂⁵	1	1	yes	characteristic
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	8	no	—
807	C₄⋊C₄	—	2	8	no	—
808	C₄⋊C₄	—	2	16	no	—
809	C₄⋊C₄	—	2	8	no	—
810	C₄⋊C₄	—	2	8	no	—
811	C₄⋊C₄	—	2	8	no	—
812	C₄⋊C₄	—	2	8	no	—
813	C₄⋊C₄	—	4	4	no	—
814	C₄⋊C₄	—	4	8	no	—
815	C₄⋊C₄	—	4	4	no	—
816	C₄⋊C₄	—	4	8	no	—
817	C₄⋊C₄	—	4	4	no	—
818	C₄⋊C₄	—	4	4	no	—
819	C₄⋊C₄	—	4	8	no	—
820	C₄⋊C₄	—	4	4	no	—
821	C₄⋊C₄	—	4	4	no	—
822	C₄⋊C₄	—	4	4	no	—
823	C₄⋊C₄	—	4	8	no	—
824	C₂²⋊C₄	—	2	8	no	—
825	C₂²⋊C₄	—	2	8	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	8	no	—
828	C₂²⋊C₄	—	2	8	no	—
829	C₂²⋊C₄	—	2	16	no	—
830	C₂²⋊C₄	—	2	16	no	—
831	C₂²⋊C₄	—	2	16	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	8	no	—
834	C₂²⋊C₄	—	2	8	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	8	no	—
837	C₂²⋊C₄	—	2	8	no	—
838	C₂²⋊C₄	—	2	8	no	—
839	C₂²⋊C₄	—	2	16	no	—
840	C₂²⋊C₄	—	2	16	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	4	no	—
844	C₂²⋊C₄	—	4	8	no	—
845	C₂²⋊C₄	—	4	8	no	—
846	C₂²⋊C₄	—	4	8	no	—
847	C₂²⋊C₄	—	4	4	no	—
848	C₂²⋊C₄	—	4	8	no	—
849	C₂²⋊C₄	—	4	8	no	—
850	C₂²⋊C₄	—	4	8	no	—
851	C₂²⋊C₄	—	4	8	no	—
852	C₂²⋊C₄	—	4	8	no	—
853	C₂²⋊C₄	—	4	8	no	—
854	C₂²⋊C₄	—	4	8	no	—
855	C₂²⋊C₄	—	4	8	no	—
856	C₂²⋊C₄	—	4	8	no	—
857	C₂²⋊C₄	—	4	8	no	—
858	C₂²⋊C₄	—	4	8	no	—
859	C₂²⋊C₄	—	4	8	no	—
860	C₂²⋊C₄	—	4	8	no	—
861	C₂²⋊C₄	—	4	8	no	—
862	C₂²⋊C₄	—	4	8	no	—
863	C₂²⋊C₄	—	4	8	no	—
864	C₂²⋊C₄	—	4	8	no	—
865	C₂²⋊C₄	H(5,𝔽₂)	1	8	yes	—
866	C₄²	—	2	8	no	—
867	C₄²	—	2	8	no	—
868	C₄²	—	2	16	no	—
869	C₄²	—	2	8	no	—
870	C₄²	—	4	2	no	—
871	C₄²	—	4	2	no	—
872	C₄²	—	4	2	no	—
873	C₄²	—	4	2	no	—
874	C₄²	—	4	4	no	—
875	C₄²	—	4	8	no	—
876	C₄²	—	4	8	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	16	no	—
882	C₂³	—	2	4	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	8	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	4	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	8	no	—
889	C₂³	—	2	8	no	—
890	C₂³	—	2	8	no	—
891	C₂³	—	2	4	no	—
892	C₂³	—	2	4	no	—
893	C₂³	—	2	8	no	—
894	C₂³	—	2	4	no	—
895	C₂³	—	2	8	no	—
896	C₂³	—	2	8	no	—
897	C₂³	—	2	4	no	—
898	C₂³	—	2	4	no	—
899	C₂³	—	2	8	no	—
900	C₂³	—	2	4	no	—
901	C₂³	—	4	4	no	—
902	C₂³	—	4	16	no	—
903	C₂³	—	4	16	no	—
904	C₂³	—	4	16	no	—
905	C₂³	—	4	32	no	—
906	C₂³	—	4	32	no	—
907	C₂³	—	4	8	no	—
908	C₂³	—	4	16	no	—
909	C₂³	—	4	16	no	—
910	C₂³	—	4	8	no	—
911	C₂³	—	8	16	no	—
912	C₂³	—	8	16	no	—
913	C₂³	—	8	8	no	—
914	C₂³	—	8	8	no	—
915	C₂³	—	8	16	no	—
916	C₂³	—	8	4	no	—
917	C₂³	—	8	4	no	—
918	C₂³	—	8	4	no	—
919	C₂³	—	8	4	no	—
920	C₂³	—	8	16	no	—
921	C₂³	—	8	4	no	—
922	C₂³	—	8	4	no	—
923	C₂³	—	8	16	no	—
924	C₂³	—	8	128	no	—
925	C₂³	C₂²×#41	1	2	yes	—
926	C₂³	C₂²×#41	1	2	yes	—
927	C₂³	C₂²×#41	1	2	yes	—
928	C₂³	C₂×H(5,𝔽₂)	1	8	yes	—
929	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
930	C₂³	#585	1	4	yes	—
931	C₂³	C₂⁶	1	1	yes	characteristic
932	Q₈	—	4	8	no	—
933	Q₈	—	8	8	no	—
934	Q₈	—	8	4	no	—
935	D₄	—	2	16	no	—
936	D₄	—	2	16	no	—
937	D₄	—	4	16	no	—
938	D₄	—	4	16	no	—
939	D₄	—	4	32	no	—
940	D₄	—	4	8	no	—
941	D₄	—	4	16	no	—
942	D₄	—	4	8	no	—
943	D₄	—	4	8	no	—
944	D₄	—	8	16	no	—
945	D₄	—	8	4	no	—
946	D₄	—	8	16	no	—
947	D₄	—	8	8	no	—
948	D₄	—	8	16	no	—
949	C₂×C₄	—	2	4	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	4	no	—
954	C₂×C₄	—	2	8	no	—
955	C₂×C₄	—	2	8	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	4	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	8	no	—
964	C₂×C₄	—	2	4	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	8	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	8	no	—
970	C₂×C₄	—	2	8	no	—
971	C₂×C₄	—	2	4	no	—
972	C₂×C₄	—	2	4	no	—
973	C₂×C₄	—	2	4	no	—
974	C₂×C₄	—	2	4	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	4	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	4	no	—
979	C₂×C₄	—	2	4	no	—
980	C₂×C₄	—	2	4	no	—
981	C₂×C₄	—	2	4	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	16	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	8	16	no	—
988	C₂×C₄	—	8	8	no	—
989	C₂×C₄	—	8	4	no	—
990	C₂×C₄	—	8	4	no	—
991	C₂×C₄	—	16	8	no	—
992	C₂×C₄	—	16	8	no	—
993	C₂×C₄	C₂²×#41	1	2	yes	—
994	C₂×C₄	C₂²×#41	1	2	yes	—
995	C₂×C₄	C₂²×#41	1	2	yes	—
996	C₂×C₄	C₂²×#41	1	2	yes	—
997	C₂×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
998	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
999	C₂²	—	2	8	no	—
1000	C₂²	—	2	8	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	16	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	8	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	4	16	no	—
1011	C₂²	—	4	8	no	—
1012	C₂²	—	4	4	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	4	8	no	—
1016	C₂²	—	4	8	no	—
1017	C₂²	—	4	8	no	—
1018	C₂²	—	4	8	no	—
1019	C₂²	—	4	4	no	—
1020	C₂²	—	4	4	no	—
1021	C₂²	—	4	4	no	—
1022	C₂²	—	4	4	no	—
1023	C₂²	—	4	4	no	—
1024	C₂²	—	4	4	no	—
1025	C₂²	—	8	32	no	—
1026	C₂²	—	8	32	no	—
1027	C₂²	—	8	16	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	—	16	8	no	—
1030	C₂²	#3508	1	4	yes	—
1031	C₂²	#3510	1	4	yes	—
1032	C₂²	C₂³×#41	1	1	yes	characteristic
1033	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1034	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1035	C₂²	C₂×#585	1	2	yes	—
1036	C₄	—	2	8	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	4	4	no	—
1041	C₄	—	4	4	no	—
1042	C₄	—	4	4	no	—
1043	C₄	—	4	8	no	—
1044	C₄	—	4	4	no	—
1045	C₄	—	4	4	no	—
1046	C₄	—	4	4	no	—
1047	C₄	—	4	4	no	—
1048	C₄	—	4	4	no	—
1049	C₄	#3490	1	4	yes	—
1050	C₂	—	2	4	no	—
1051	C₂	—	2	4	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	4	8	no	—
1054	C₂	—	8	4	no	—
1055	C₂	—	8	4	no	—
1056	C₂	C₂×#3490	1	1	yes	characteristic
1057	C₂	C₂×#3508	1	1	yes	characteristic
1058	C₂	C₂×#3510	1	1	yes	characteristic
1059	C₂	#63012	1	4	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁶
prime radical	C₂×#2433	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #59820	C₂	semidirect
2. #59424	C₂	semidirect
3. #59147	C₂	semidirect
4. #59143	C₂	semidirect
5. #59006	C₂	semidirect
6. #47033	C₂	semidirect
7. #46452	C₂	semidirect
8. #42976	C₂	semidirect
9. #40546	C₂	semidirect
10. #40542	C₂	semidirect
11. #37451	C₂	semidirect
12. #35808	C₂	semidirect
13. #35732	C₂	semidirect
14. #35695	C₂	semidirect
15. #34958	C₂	semidirect
16. C₂×#2435	C₂	semidirect
18. #34246	C₂	semidirect
19. #34245	C₂	semidirect
20. #34171	C₂	semidirect
22. C₂×#559	C₂²	semidirect
23. C₂×#551	C₂²	semidirect
25. C₂²×#124	C₂²	semidirect
29. C₂×#518	C₂²	semidirect
30. #2829	C₂²	semidirect
31. #2816	C₂²	semidirect
32. #2816	C₂²	semidirect
33. #2786	C₂²	semidirect
34. #2740	C₂²	semidirect
35. #2730	C₂²	semidirect
36. #2712	C₂²	semidirect
37. #2710	C₂²	semidirect
38. #2709	C₂²	semidirect
39. #2709	C₂²	semidirect
40. #2705	C₂²	semidirect
41. #2697	C₂²	semidirect
42. #2685	C₂²	semidirect
43. #2685	C₂²	semidirect
44. #2684	C₂²	semidirect
45. #2662	C₂²	semidirect
46. #2648	C₂²	semidirect
47. #2630	C₂²	semidirect
48. #2626	C₂²	semidirect
49. #2620	C₂²	semidirect
50. #2618	C₂²	semidirect
51. #2608	C₂²	semidirect
52. #2607	C₂²	semidirect
53. #2601	C₂²	semidirect
54. #2592	C₂²	semidirect
55. #2569	C₂²	semidirect
56. #2569	C₂²	semidirect
57. #2560	C₂²	semidirect
58. #2557	C₂²	semidirect
59. #2554	C₂²	semidirect
60. #2549	C₂²	semidirect
61. #2549	C₂²	semidirect
62. #2548	C₂²	semidirect
63. #2548	C₂²	semidirect
64. #2544	C₂²	semidirect
65. #2544	C₂²	semidirect
66. #2544	C₂²	semidirect
67. #2538	C₂²	semidirect
68. #2534	C₂²	semidirect
69. #2534	C₂²	semidirect
70. #2512	C₂²	semidirect
71. #2512	C₂²	semidirect
72. #2502	C₂²	semidirect
73. #2501	C₂²	semidirect
74. #2480	C₂²	semidirect
75. #2480	C₂²	semidirect
76. #2472	C₂²	semidirect
77. #2472	C₂²	semidirect
78. #2471	C₂²	semidirect
79. #2467	C₂²	semidirect
80. #2461	C₂²	semidirect
81. #2459	C₂²	semidirect
82. #2457	C₂²	semidirect
83. #2448	C₂²	semidirect
84. #2447	C₂²	semidirect
85. #2445	C₂²	semidirect
86. #2445	C₂²	semidirect
87. #2445	C₂²	semidirect
89. #2437	C₂²	semidirect
90. #2436	C₂²	semidirect
94. #2435	C₂²	semidirect
95. #2435	C₂²	semidirect
96. #2435	C₂²	semidirect
97. #2435	C₂²	semidirect
98. #2435	C₂²	semidirect
105. #2418	C₂²	semidirect
106. #2418	C₂²	semidirect
107. #2412	C₂²	semidirect
108. #2412	C₂²	semidirect
109. #2411	C₂²	semidirect
110. #2411	C₂²	semidirect
112. #2405	C₂²	semidirect
113. #2405	C₂²	semidirect
114. #2396	C₂²	semidirect
115. #2392	C₂²	semidirect
116. C₂×#394	C₂²	semidirect
118. #2368	C₂²	semidirect
119. #2367	C₂²	semidirect
120. #2366	C₂²	semidirect
121. #2364	C₂²	semidirect
122. #2363	C₂²	semidirect
123. #2362	C₂²	semidirect
124. #2358	C₂²	semidirect
125. #2354	C₂²	semidirect
126. #2345	C₂²	semidirect
127. #2344	C₂²	semidirect
129. #2342	C₂²	semidirect
130. Q₈×C₂²⋊C₄	C₂²	semidirect
134. D₄×C₂²⋊C₄	C₂²	semidirect
135. D₄×C₂²⋊C₄	C₂²	semidirect
136. D₄×C₂²⋊C₄	C₂²	semidirect
137. D₄×C₂²⋊C₄	C₂²	semidirect
138. #2333	C₂²	semidirect
139. #2332	C₂²	semidirect
140. #2313	C₂²	semidirect
141. #2312	C₂²	semidirect
142. #2309	C₂²	semidirect
143. #2308	C₂²	semidirect
144. #2308	C₂²	semidirect
145. C₄×C₂²⋊Q₈	C₂²	semidirect
146. C₄×C₂²⋊Q₈	C₂²	semidirect
147. C₄×C₂²⋊Q₈	C₂²	semidirect
148. C₄×#121	C₂²	semidirect
150. C₂×#390	C₂²	semidirect
155. #2274	C₂²	semidirect
156. #2273	C₂²	semidirect
181. C₂×#126	C₂³	semidirect
182. C₂×#126	C₂³	semidirect
188. C₂×#124	C₂³	semidirect
189. C₂×#124	C₂³	semidirect
190. C₂×#124	C₂³	semidirect
192. C₂×#123	C₂³	semidirect
193. C₂×#123	C₂³	semidirect
194. C₂×#123	C₂³	semidirect
195. C₂×#123	C₂³	semidirect
203. C₂×C₂²⋊Q₈	C₂³	semidirect
215. C₂×C₄×Q₈	C₂³	semidirect
216. C₂×C₄×Q₈	C₂³	semidirect
221. C₂×C₄×D₄	C₂³	semidirect
222. C₂×C₄×D₄	C₂³	semidirect
223. C₂×C₄×D₄	C₂³	semidirect
227. C₂×#117	C₂³	semidirect
245. #400	C₂³	semidirect
247. #399	C₂³	semidirect
248. #399	C₂³	semidirect
249. #399	C₂³	semidirect
250. #398	C₂³	semidirect
251. #398	C₂³	semidirect
252. #398	C₂³	semidirect
253. #398	C₂³	semidirect
254. #397	C₂³	semidirect
255. #397	C₂³	semidirect
256. #397	C₂³	semidirect
257. #397	C₂³	semidirect
258. #397	C₂³	semidirect
259. #397	C₂³	semidirect
262. #396	C₂³	semidirect
263. #396	C₂³	semidirect
264. #396	C₂³	semidirect
265. #396	C₂³	semidirect
266. #396	C₂³	semidirect
267. #396	C₂³	semidirect
268. #395	C₂³	semidirect
277. #394	C₂³	semidirect
278. #394	C₂³	semidirect
279. #394	C₂³	semidirect
280. #394	C₂³	semidirect
281. #394	C₂³	semidirect
282. #394	C₂³	semidirect
283. #394	C₂³	semidirect
284. #394	C₂³	semidirect
285. #394	C₂³	semidirect
286. #394	C₂³	semidirect
287. #394	C₂³	semidirect
288. #394	C₂³	semidirect
289. #394	C₂³	semidirect
290. #394	C₂³	semidirect
292. #393	C₂³	semidirect
293. #393	C₂³	semidirect
294. #393	C₂³	semidirect
301. #391	C₂³	semidirect
302. #391	C₂³	semidirect
303. #391	C₂³	semidirect
304. #391	C₂³	semidirect
305. #391	C₂³	semidirect
318. #390	C₂³	semidirect
319. #390	C₂³	semidirect
320. #390	C₂³	semidirect
321. #390	C₂³	semidirect
322. #390	C₂³	semidirect
323. #390	C₂³	semidirect
324. #389	C₂³	semidirect
325. #389	C₂³	semidirect
326. #389	C₂³	semidirect
327. #389	C₂³	semidirect
330. #388	C₂³	semidirect
331. #388	C₂³	semidirect
332. #388	C₂³	semidirect
333. #388	C₂³	semidirect
334. #388	C₂³	semidirect
335. #388	C₂³	semidirect
336. #388	C₂³	semidirect
337. #388	C₂³	semidirect
338. #388	C₂³	semidirect
339. #388	C₂³	semidirect
340. #388	C₂³	semidirect
341. #388	C₂³	semidirect
342. #387	C₂³	semidirect
343. #387	C₂³	semidirect
344. #387	C₂³	semidirect
345. #387	C₂³	semidirect
346. #387	C₂³	semidirect
347. #387	C₂³	semidirect
348. #387	C₂³	semidirect
349. #387	C₂³	semidirect
357. #386	C₂³	semidirect
358. #386	C₂³	semidirect
359. #386	C₂³	semidirect
360. #386	C₂³	semidirect
361. #386	C₂³	semidirect
362. #386	C₂³	semidirect
363. #386	C₂³	semidirect
364. #386	C₂³	semidirect
365. #386	C₂³	semidirect
372. #385	C₂³	semidirect
373. #385	C₂³	semidirect
374. #384	C₂³	semidirect
379. #381	C₂³	semidirect
388. #380	C₂³	semidirect
389. #380	C₂³	semidirect
402. C₄×C₄⋊C₄	C₂³	semidirect
403. C₄×C₄⋊C₄	C₂³	semidirect
404. C₄×C₄⋊C₄	C₂³	semidirect
405. C₄×C₄⋊C₄	C₂³	semidirect
406. C₄×C₄⋊C₄	C₂³	semidirect
407. C₄×C₄⋊C₄	C₂³	semidirect
408. C₄×C₄⋊C₄	C₂³	semidirect
426. C₄×C₂²⋊C₄	C₂³	semidirect
427. C₄×C₂²⋊C₄	C₂³	semidirect
428. C₄×C₂²⋊C₄	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#59820	2
#59424	2
#59147	2
#59143	2
#59006	2
#47033	2
#46452	2
#42976	2
#40546	2
#40542	2
#37451	2
#35808	2
#35732	2
#35695	2
#34958	2
C₂×#2435	2
C₂×#2433	2
#34246	2
#34245	2
#34171	2