Subgroups — #8093867

Order 512.

6406 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#52742	C₂	1	4	yes	maximal, complemented
2	#52586	C₂	1	4	yes	maximal, complemented
3	#52548	C₂	1	4	yes	maximal, complemented
4	#52397	C₂	1	4	yes	maximal, complemented
5	#52340	C₂	1	8	yes	maximal, complemented
6	#46334	C₂	1	8	yes	maximal, complemented
7	#45578	C₂	1	8	yes	maximal, complemented
8	#45569	C₂	1	4	yes	maximal, complemented
9	#45457	C₂	1	4	yes	maximal, complemented
10	#35447	C₂	1	2	yes	maximal, complemented
11	#35358	C₂	1	2	yes	maximal, complemented
12	#35350	C₂	1	2	yes	maximal, complemented
13	#35089	C₂	1	2	yes	maximal, complemented
14	#34995	C₂	1	2	yes	maximal, complemented
15	#34980	C₂	1	2	yes	maximal, complemented
16	C₂×#2539	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#2482	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#2405	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂⁴×D₄	C₂²	1	1	yes	characteristic
20	C₂×#534	C₂²	1	2	yes	—
21	C₂×#534	C₂²	1	2	yes	—
22	C₂²×#123	C₂²	1	2	yes	—
23	C₂²×#123	C₂²	1	2	yes	complemented
24	C₂²×#121	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#120	C₂²	1	2	yes	—
26	C₂×#518	C₂²	1	2	yes	complemented
27	C₂²×#117	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	#2854	C₂²	1	4	yes	complemented
30	#2854	C₂²	1	4	yes	complemented
31	#2852	C₂²	1	8	yes	complemented
32	#2849	C₂²	1	4	yes	complemented
33	#2846	C₂²	1	4	yes	complemented
34	#2842	C₂²	1	4	yes	complemented
35	#2837	C₂²	1	8	yes	complemented
36	#2837	C₂²	1	8	yes	complemented
37	#2837	C₂²	1	8	yes	complemented
38	#2834	C₂²	1	4	yes	complemented
39	#2829	C₂²	1	8	yes	complemented
40	#2829	C₂²	1	8	yes	complemented
41	#2828	C₂²	1	8	yes	complemented
42	#2826	C₂²	1	4	yes	complemented
43	#2825	C₂²	1	8	yes	complemented
44	#2813	C₂²	1	8	yes	complemented
45	#2812	C₂²	1	4	yes	complemented
46	#2807	C₂²	1	8	yes	complemented
47	#2807	C₂²	1	4	yes	complemented
48	#2803	C₂²	1	8	yes	complemented
49	#2803	C₂²	1	8	yes	complemented
50	#2801	C₂²	1	8	yes	complemented
51	#2778	C₂²	1	8	yes	complemented
52	#2757	C₂²	1	8	yes	complemented
53	#2757	C₂²	1	8	yes	complemented
54	#2756	C₂²	1	8	yes	complemented
55	#2756	C₂²	1	8	yes	complemented
56	#2748	C₂²	1	8	yes	complemented
57	#2735	C₂²	1	8	yes	complemented
58	#2735	C₂²	1	4	yes	complemented
59	#2705	C₂²	1	8	yes	complemented
60	#2705	C₂²	1	8	yes	complemented
61	#2703	C₂²	1	8	yes	complemented
62	#2697	C₂²	1	8	yes	complemented
63	#2693	C₂²	1	4	yes	complemented
64	#2685	C₂²	1	8	yes	complemented
65	#2685	C₂²	1	8	yes	complemented
66	#2678	C₂²	1	8	yes	complemented
67	#2668	C₂²	1	4	yes	complemented
68	#2643	C₂²	1	8	yes	complemented
69	#2618	C₂²	1	4	yes	complemented
70	#2618	C₂²	1	4	yes	complemented
71	#2613	C₂²	1	4	yes	complemented
72	#2613	C₂²	1	4	yes	complemented
73	#2543	C₂²	1	8	yes	complemented
74	#2539	C₂²	1	4	yes	—
75	#2539	C₂²	1	4	yes	complemented
76	#2539	C₂²	1	4	yes	complemented
77	#2539	C₂²	1	4	yes	complemented
78	#2534	C₂²	1	8	yes	complemented
79	#2510	C₂²	1	8	yes	complemented
80	#2493	C₂²	1	8	yes	complemented
81	#2486	C₂²	1	8	yes	complemented
82	#2482	C₂²	1	4	yes	complemented
83	#2482	C₂²	1	4	yes	complemented
84	#2482	C₂²	1	8	yes	complemented
85	#2482	C₂²	1	4	yes	complemented
86	#2482	C₂²	1	4	yes	complemented
87	#2481	C₂²	1	8	yes	complemented
88	#2480	C₂²	1	8	yes	complemented
89	#2425	C₂²	1	8	yes	complemented
90	#2425	C₂²	1	8	yes	complemented
91	#2425	C₂²	1	8	yes	complemented
92	#2424	C₂²	1	8	yes	complemented
93	#2418	C₂²	1	8	yes	complemented
94	#2418	C₂²	1	8	yes	complemented
95	#2418	C₂²	1	8	yes	complemented
96	#2418	C₂²	1	8	yes	complemented
97	#2416	C₂²	1	8	yes	complemented
98	#2413	C₂²	1	8	yes	complemented
99	#2413	C₂²	1	4	yes	complemented
100	#2413	C₂²	1	8	yes	complemented
101	#2413	C₂²	1	8	yes	complemented
102	#2412	C₂²	1	4	yes	complemented
103	#2412	C₂²	1	8	yes	complemented
104	#2411	C₂²	1	8	yes	complemented
105	#2411	C₂²	1	8	yes	complemented
106	#2411	C₂²	1	4	yes	complemented
107	#2410	C₂²	1	8	yes	complemented
108	#2410	C₂²	1	8	yes	complemented
109	#2410	C₂²	1	4	yes	complemented
110	#2405	C₂²	1	4	yes	—
111	#2405	C₂²	1	8	yes	—
112	#2405	C₂²	1	4	yes	—
113	#2405	C₂²	1	4	yes	complemented
114	#2405	C₂²	1	4	yes	complemented
115	#2405	C₂²	1	8	yes	complemented
116	#2403	C₂²	1	8	yes	—
117	C₂×#399	C₂²	1	2	yes	complemented
118	C₂×#399	C₂²	1	2	yes	complemented
119	C₂×#397	C₂²	1	2	yes	complemented
120	C₂×#394	C₂²	1	4	yes	complemented
121	C₂×#392	C₂²	1	2	yes	complemented
122	#2376	C₂²	1	8	yes	complemented
123	#2375	C₂²	1	8	yes	complemented
124	#2315	C₂²	1	2	yes	complemented
125	#2315	C₂²	1	2	yes	complemented
126	#2308	C₂²	1	2	yes	—
127	#2308	C₂²	1	2	yes	—
128	#2308	C₂²	1	2	yes	complemented
129	C₂×#390	C₂²	1	4	yes	complemented
130	C₂×#388	C₂²	1	4	yes	complemented
131	C₂×#386	C₂²	1	2	yes	—
132	C₂×#385	C₂²	1	2	yes	complemented
133	C₂×#385	C₂²	1	2	yes	complemented
134	C₂×#381	C₂²	1	1	yes	characteristic, complemented
135	C₂×#379	C₂²	1	1	yes	characteristic
136	C₂×#379	C₂²	1	2	yes	—
137	C₂×#379	C₂²	1	2	yes	complemented
138	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
139	C₂⁶	C₂³	1	1	yes	characteristic
140	C₂⁶	C₂³	1	1	yes	characteristic
141	C₂³×D₄	—	4	8	no	—
142	C₂³×D₄	—	4	4	no	—
143	C₂³×D₄	C₂³	1	2	yes	—
144	C₂³×D₄	C₂³	1	2	yes	—
145	C₂³×D₄	C₂³	1	2	yes	—
146	C₂³×D₄	C₂³	1	4	yes	—
147	C₂³×D₄	C₂³	1	4	yes	—
148	C₂³×D₄	C₂³	1	4	yes	—
149	C₂³×D₄	C₂³	1	1	yes	characteristic, complemented
150	C₂⁴×C₄	C₂³	1	1	yes	characteristic
151	C₂⁴×C₄	C₂³	1	1	yes	characteristic
152	C₂⁴×C₄	C₂³	1	1	yes	characteristic
153	#534	—	4	8	no	—
154	#534	—	4	8	no	—
155	C₂×#126	C₂³	1	8	yes	complemented
156	C₂×#123	—	4	8	no	—
157	C₂×#123	—	4	8	no	—
158	C₂×#123	C₂³	1	4	yes	—
159	C₂×#123	C₂³	1	4	yes	—
160	C₂×#123	C₂³	1	4	yes	—
161	C₂×#123	C₂³	1	4	yes	—
162	C₂×#123	C₂³	1	8	yes	—
163	C₂×#123	C₂³	1	8	yes	—
164	C₂×#123	C₂³	1	4	yes	—
165	C₂×#123	C₂³	1	4	yes	—
166	C₂×#123	C₂³	1	8	yes	—
167	C₂×#123	C₂³	1	4	yes	complemented
168	C₂×#123	C₂³	1	4	yes	complemented
169	C₂×#123	C₂³	1	8	yes	complemented
170	C₂×#121	—	4	4	no	—
171	C₂×#121	C₂³	1	4	yes	—
172	C₂×#121	C₂³	1	4	yes	—
173	C₂×#121	C₂³	1	4	yes	—
174	C₂×#121	C₂³	1	8	yes	—
175	C₂×#121	C₂³	1	4	yes	complemented
176	C₂×#121	C₂³	1	8	yes	complemented
177	C₂×#120	—	4	8	no	—
178	C₂×#120	C₂³	1	4	yes	—
179	C₂×#120	C₂³	1	4	yes	—
180	C₂×#120	C₂³	1	4	yes	—
181	C₂×#120	C₂³	1	8	yes	—
182	C₂×#120	C₂³	1	4	yes	—
183	C₂×#120	C₂³	1	4	yes	—
184	C₂×#120	C₂³	1	4	yes	—
185	C₂×#120	C₂³	1	8	yes	—
186	C₂×#120	C₂³	1	8	yes	—
187	#518	—	4	8	no	—
188	C₂×C₄×D₄	C₂³	1	8	yes	—
189	C₂×C₄×D₄	C₂³	1	8	yes	complemented
190	C₂×#117	—	4	4	no	—
191	C₂×#117	C₂³	1	4	yes	—
192	C₂×#117	C₂³	1	4	yes	complemented
193	C₂×#117	C₂³	1	4	yes	complemented
194	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
196	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
197	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
198	C₂²×C₄⋊C₄	C₂³	1	4	yes	complemented
199	C₂²×C₄⋊C₄	C₂³	1	4	yes	complemented
200	C₂²×C₂²⋊C₄	—	4	4	no	—
201	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂³	1	4	yes	complemented
219	C₂²×C₂²⋊C₄	C₂³	1	4	yes	complemented
220	C₂²×C₂²⋊C₄	C₂³	1	2	yes	complemented
221	C₂²×C₄²	C₂³	1	2	yes	complemented
222	C₂²×C₄²	C₂³	1	2	yes	complemented
223	#401	C₂³	1	8	yes	complemented
224	#400	C₂³	1	8	yes	complemented
225	#400	C₂³	1	8	yes	complemented
226	#400	C₂³	1	8	yes	complemented
227	#399	C₂³	1	4	yes	—
228	#399	C₂³	1	4	yes	—
229	#399	C₂³	1	8	yes	—
230	#399	C₂³	1	4	yes	—
231	#399	C₂³	1	4	yes	—
232	#399	C₂³	1	4	yes	complemented
233	#399	C₂³	1	8	yes	complemented
234	#399	C₂³	1	4	yes	complemented
235	#399	C₂³	1	4	yes	complemented
236	#399	C₂³	1	4	yes	complemented
237	#398	C₂³	1	8	yes	complemented
238	#398	C₂³	1	8	yes	complemented
239	#398	C₂³	1	8	yes	complemented
240	#398	C₂³	1	8	yes	complemented
241	#398	C₂³	1	8	yes	complemented
242	#397	C₂³	1	4	yes	—
243	#397	C₂³	1	8	yes	—
244	#397	C₂³	1	4	yes	—
245	#397	C₂³	1	4	yes	complemented
246	#397	C₂³	1	8	yes	complemented
247	#397	C₂³	1	8	yes	complemented
248	#397	C₂³	1	8	yes	complemented
249	#397	C₂³	1	8	yes	complemented
250	#397	C₂³	1	4	yes	complemented
251	#397	C₂³	1	8	yes	complemented
252	#397	C₂³	1	8	yes	complemented
253	#397	C₂³	1	8	yes	complemented
254	#396	C₂³	1	8	yes	complemented
255	#396	C₂³	1	8	yes	complemented
256	#396	C₂³	1	8	yes	complemented
257	#396	C₂³	1	8	yes	complemented
258	#396	C₂³	1	8	yes	complemented
259	#396	C₂³	1	8	yes	complemented
260	#396	C₂³	1	8	yes	complemented
261	#396	C₂³	1	8	yes	complemented
262	#396	C₂³	1	8	yes	complemented
263	#394	C₂³	1	8	yes	—
264	#394	C₂³	1	8	yes	—
265	#394	C₂³	1	8	yes	—
266	#394	C₂³	1	8	yes	—
267	#394	C₂³	1	8	yes	—
268	#394	C₂³	1	8	yes	—
269	#394	C₂³	1	8	yes	—
270	#394	C₂³	1	8	yes	—
271	#394	C₂³	1	8	yes	—
272	#394	C₂³	1	8	yes	—
273	#394	C₂³	1	8	yes	complemented
274	#394	C₂³	1	8	yes	complemented
275	#394	C₂³	1	8	yes	complemented
276	#394	C₂³	1	8	yes	complemented
277	#394	C₂³	1	8	yes	complemented
278	#394	C₂³	1	8	yes	complemented
279	#394	C₂³	1	8	yes	complemented
280	#394	C₂³	1	8	yes	complemented
281	#394	C₂³	1	8	yes	complemented
282	#392	C₂³	1	8	yes	—
283	#392	C₂³	1	8	yes	—
284	#392	C₂³	1	4	yes	—
285	#392	C₂³	1	8	yes	—
286	#392	C₂³	1	8	yes	—
287	#392	C₂³	1	4	yes	—
288	#392	C₂³	1	4	yes	complemented
289	#392	C₂³	1	8	yes	complemented
290	#392	C₂³	1	4	yes	complemented
291	#390	C₂³	1	8	yes	—
292	#390	C₂³	1	8	yes	—
293	#390	C₂³	1	8	yes	complemented
294	#390	C₂³	1	8	yes	complemented
295	#390	C₂³	1	8	yes	complemented
296	#390	C₂³	1	8	yes	complemented
297	#390	C₂³	1	8	yes	complemented
298	#389	C₂³	1	8	yes	complemented
299	#389	C₂³	1	8	yes	complemented
300	#389	C₂³	1	8	yes	complemented
301	#389	C₂³	1	8	yes	complemented
302	#389	C₂³	1	8	yes	complemented
303	#388	C₂³	1	8	yes	—
304	#388	C₂³	1	8	yes	—
305	#388	C₂³	1	8	yes	—
306	#388	C₂³	1	8	yes	—
307	#388	C₂³	1	8	yes	complemented
308	#388	C₂³	1	8	yes	complemented
309	#388	C₂³	1	8	yes	complemented
310	#388	C₂³	1	8	yes	complemented
311	#388	C₂³	1	8	yes	complemented
312	#388	C₂³	1	8	yes	complemented
313	#388	C₂³	1	8	yes	complemented
314	#388	C₂³	1	8	yes	complemented
315	#388	C₂³	1	8	yes	complemented
316	#388	C₂³	1	8	yes	complemented
317	#388	C₂³	1	8	yes	complemented
318	#388	C₂³	1	8	yes	complemented
319	#388	C₂³	1	8	yes	complemented
320	#388	C₂³	1	8	yes	complemented
321	#388	C₂³	1	8	yes	complemented
322	#387	C₂³	1	8	yes	complemented
323	#387	C₂³	1	8	yes	complemented
324	#387	C₂³	1	8	yes	complemented
325	#386	C₂³	1	8	yes	—
326	#386	C₂³	1	8	yes	—
327	#386	C₂³	1	4	yes	—
328	#386	C₂³	1	4	yes	—
329	#386	C₂³	1	8	yes	—
330	#386	C₂³	1	8	yes	—
331	#386	C₂³	1	8	yes	—
332	#386	C₂³	1	8	yes	—
333	#386	C₂³	1	4	yes	—
334	#386	C₂³	1	8	yes	—
335	#386	C₂³	1	4	yes	—
336	#386	C₂³	1	8	yes	—
337	#386	C₂³	1	4	yes	complemented
338	#386	C₂³	1	4	yes	complemented
339	#386	C₂³	1	8	yes	complemented
340	#386	C₂³	1	8	yes	complemented
341	#386	C₂³	1	8	yes	complemented
342	#386	C₂³	1	8	yes	complemented
343	#386	C₂³	1	8	yes	complemented
344	#385	C₂³	1	4	yes	—
345	#385	C₂³	1	8	yes	—
346	#385	C₂³	1	8	yes	—
347	#385	C₂³	1	8	yes	—
348	#385	C₂³	1	4	yes	—
349	#385	C₂³	1	4	yes	—
350	#385	C₂³	1	4	yes	—
351	#385	C₂³	1	8	yes	—
352	#385	C₂³	1	8	yes	complemented
353	#385	C₂³	1	8	yes	complemented
354	#385	C₂³	1	8	yes	complemented
355	#385	C₂³	1	4	yes	complemented
356	#385	C₂³	1	4	yes	complemented
357	#383	C₂³	1	8	yes	complemented
358	#381	C₂³	1	4	yes	—
359	#381	C₂³	1	4	yes	—
360	#381	C₂³	1	4	yes	—
361	#381	C₂³	1	4	yes	complemented
362	#381	C₂³	1	4	yes	complemented
363	#380	C₂³	1	8	yes	—
364	#380	C₂³	1	4	yes	complemented
365	#380	C₂³	1	4	yes	complemented
366	#380	C₂³	1	8	yes	complemented
367	#380	C₂³	1	8	yes	complemented
368	#380	C₂³	1	8	yes	complemented
369	#379	C₂³	1	4	yes	—
370	#379	C₂³	1	4	yes	—
371	#379	C₂³	1	8	yes	—
372	#379	C₂³	1	4	yes	—
373	#379	C₂³	1	4	yes	—
374	#379	C₂³	1	8	yes	—
375	#379	C₂³	1	4	yes	—
376	#379	C₂³	1	4	yes	—
377	#379	C₂³	1	8	yes	—
378	#379	C₂³	1	4	yes	—
379	#379	C₂³	1	4	yes	—
380	#379	C₂³	1	4	yes	—
381	#379	C₂³	1	4	yes	—
382	#379	C₂³	1	4	yes	complemented
383	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
384	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
385	C₂×#95	C₂³	1	4	yes	—
386	C₂×#95	C₂³	1	2	yes	complemented
387	C₂×#95	C₂³	1	2	yes	complemented
388	C₂×#95	C₂³	1	4	yes	complemented
389	C₂×#95	C₂³	1	2	yes	complemented
390	C₂⁵	—	2	4	no	—
391	C₂⁵	—	2	8	no	—
392	C₂⁵	—	4	2	no	—
393	C₂⁵	—	4	4	no	—
394	C₂⁵	—	4	4	no	—
395	C₂⁵	—	4	4	no	—
396	C₂⁵	—	8	2	no	—
397	C₂⁵	—	8	2	no	—
398	C₂⁵	C₂⁴	1	1	yes	characteristic
399	C₂⁵	C₂⁴	1	2	yes	—
400	C₂⁵	C₂⁴	1	2	yes	—
401	C₂⁵	C₂⁴	1	2	yes	—
402	C₂⁵	C₂⁴	1	1	yes	characteristic
403	C₂⁵	C₂⁴	1	2	yes	—
404	C₂⁵	C₂⁴	1	4	yes	—
405	C₂⁵	C₂⁴	1	1	yes	characteristic
406	C₂²×D₄	—	2	8	no	—
407	C₂²×D₄	—	2	8	no	—
408	C₂²×D₄	—	2	8	no	—
409	C₂²×D₄	—	2	8	no	—
410	C₂²×D₄	—	2	8	no	—
411	C₂²×D₄	—	2	8	no	—
412	C₂²×D₄	—	4	4	no	—
413	C₂²×D₄	—	4	4	no	—
414	C₂²×D₄	—	4	4	no	—
415	C₂²×D₄	—	4	8	no	—
416	C₂²×D₄	—	4	2	no	—
417	C₂²×D₄	—	4	8	no	—
418	C₂²×D₄	—	4	16	no	—
419	C₂²×D₄	—	4	8	no	—
420	C₂²×D₄	—	4	16	no	—
421	C₂²×D₄	—	4	8	no	—
422	C₂²×D₄	—	4	64	no	—
423	C₂²×D₄	—	8	4	no	—
424	C₂²×D₄	—	8	2	no	—
425	C₂²×D₄	C₂⁴	1	4	yes	—
426	C₂²×D₄	C₂⁴	1	4	yes	—
427	C₂²×D₄	C₂⁴	1	4	yes	—
428	C₂²×D₄	C₂⁴	1	4	yes	—
429	C₂²×D₄	C₂⁴	1	8	yes	—
430	C₂²×D₄	C₂⁴	1	4	yes	—
431	C₂²×D₄	C₂⁴	1	8	yes	—
432	C₂²×D₄	C₂⁴	1	4	yes	—
433	C₂²×D₄	C₂⁴	1	8	yes	—
434	C₂²×D₄	C₂⁴	1	4	yes	—
435	C₂²×D₄	C₂⁴	1	8	yes	—
436	C₂³×C₄	—	2	4	no	—
437	C₂³×C₄	—	2	8	no	—
438	C₂³×C₄	—	2	4	no	—
439	C₂³×C₄	—	4	4	no	—
440	C₂³×C₄	—	4	2	no	—
441	C₂³×C₄	—	8	2	no	—
442	C₂³×C₄	C₂⁴	1	2	yes	—
443	C₂³×C₄	C₂⁴	1	2	yes	—
444	C₂³×C₄	C₂⁴	1	2	yes	—
445	C₂³×C₄	C₂⁴	1	1	yes	characteristic
446	C₂³×C₄	C₂⁴	1	1	yes	characteristic
447	C₂³×C₄	C₂⁴	1	2	yes	—
448	C₂³×C₄	C₂⁴	1	4	yes	—
449	C₂³×C₄	C₂⁴	1	2	yes	—
450	C₂³×C₄	C₂⁴	1	2	yes	—
451	C₂³×C₄	C₂⁴	1	4	yes	—
452	C₂³×C₄	C₂⁴	1	2	yes	—
453	C₂³×C₄	C₂⁴	1	1	yes	characteristic
454	C₂³×C₄	C₂⁴	1	4	yes	—
455	C₂³×C₄	C₂⁴	1	2	yes	—
456	C₂³×C₄	C₂⁴	1	1	yes	characteristic
457	C₂³×C₄	C₂⁴	1	8	yes	—
458	C₂³×C₄	C₂⁴	1	4	yes	—
459	#126	—	8	8	no	—
460	#123	—	4	16	no	—
461	#123	—	4	16	no	—
462	#123	—	4	8	no	—
463	#123	—	4	8	no	—
464	#123	—	4	16	no	—
465	#123	—	4	8	no	—
466	#123	—	4	8	no	—
467	#123	—	4	8	no	—
468	#123	—	4	8	no	—
469	#123	—	4	8	no	—
470	#123	—	4	8	no	—
471	#123	—	8	8	no	—
472	#121	—	4	8	no	—
473	#121	—	4	8	no	—
474	#121	—	4	8	no	—
475	#121	—	4	8	no	—
476	#121	—	4	16	no	—
477	#121	—	8	8	no	—
478	#120	—	4	8	no	—
479	#120	—	4	16	no	—
480	#120	—	4	8	no	—
481	#120	—	4	16	no	—
482	#120	—	4	8	no	—
483	#120	—	4	8	no	—
484	#120	—	4	8	no	—
485	#120	—	4	8	no	—
486	#120	—	8	8	no	—
487	C₄×D₄	—	4	16	no	—
488	C₄×D₄	—	4	16	no	—
489	#117	—	4	8	no	—
490	#117	—	4	8	no	—
491	#117	—	4	8	no	—
492	C₂×C₄⋊C₄	—	4	8	no	—
493	C₂×C₄⋊C₄	—	4	2	no	—
494	C₂×C₄⋊C₄	—	4	2	no	—
495	C₂×C₄⋊C₄	—	4	2	no	—
496	C₂×C₄⋊C₄	—	4	8	no	—
497	C₂×C₄⋊C₄	—	8	4	no	—
498	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
499	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
500	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
501	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
502	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
503	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
504	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
505	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
506	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
507	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
508	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
509	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
510	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
511	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
512	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
513	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
514	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
515	C₂×C₂²⋊C₄	—	2	8	no	—
516	C₂×C₂²⋊C₄	—	2	8	no	—
517	C₂×C₂²⋊C₄	—	2	8	no	—
518	C₂×C₂²⋊C₄	—	2	8	no	—
519	C₂×C₂²⋊C₄	—	4	8	no	—
520	C₂×C₂²⋊C₄	—	4	4	no	—
521	C₂×C₂²⋊C₄	—	4	8	no	—
522	C₂×C₂²⋊C₄	—	4	4	no	—
523	C₂×C₂²⋊C₄	—	4	4	no	—
524	C₂×C₂²⋊C₄	—	4	4	no	—
525	C₂×C₂²⋊C₄	—	4	4	no	—
526	C₂×C₂²⋊C₄	—	4	4	no	—
527	C₂×C₂²⋊C₄	—	4	4	no	—
528	C₂×C₂²⋊C₄	—	4	8	no	—
529	C₂×C₂²⋊C₄	—	4	8	no	—
530	C₂×C₂²⋊C₄	—	4	4	no	—
531	C₂×C₂²⋊C₄	—	4	8	no	—
532	C₂×C₂²⋊C₄	—	8	4	no	—
533	C₂×C₂²⋊C₄	—	8	4	no	—
534	C₂×C₂²⋊C₄	—	8	2	no	—
535	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
544	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
554	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
555	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
556	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
557	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
558	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
559	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
560	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
561	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
562	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
564	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
565	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
566	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
567	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
568	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
569	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
572	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
575	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
576	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
577	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
578	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
579	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
580	C₂×C₄²	—	4	4	no	—
581	C₂×C₄²	—	8	2	no	—
582	C₂×C₄²	C₂⁴	1	8	yes	—
583	C₂×C₄²	C₂⁴	1	8	yes	—
584	C₂×C₄²	C₂⁴	1	8	yes	—
585	#95	C₂⁴	1	8	yes	—
586	#95	C₂⁴	1	8	yes	—
587	#95	C₂⁴	1	4	yes	—
588	#95	C₂⁴	1	4	yes	—
589	#95	C₂⁴	1	4	yes	—
590	#95	C₂⁴	1	8	yes	—
591	#95	C₂⁴	1	4	yes	—
592	#95	C₂⁴	1	8	yes	—
593	#95	C₂⁴	1	8	yes	—
594	#95	C₂⁴	1	8	yes	—
595	#95	C₂⁴	1	8	yes	—
596	#95	C₂⁴	1	8	yes	—
597	#95	C₂⁴	1	8	yes	—
598	#95	C₂⁴	1	8	yes	—
599	#95	C₂⁴	1	8	yes	—
600	#95	C₂⁴	1	8	yes	—
601	#95	C₂⁴	1	8	yes	—
602	#95	C₂⁴	1	8	yes	—
603	#95	C₂⁴	1	8	yes	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	4	no	—
609	C₂⁴	—	2	4	no	—
610	C₂⁴	—	2	4	no	—
611	C₂⁴	—	2	4	no	—
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	8	no	—
614	C₂⁴	—	2	8	no	—
615	C₂⁴	—	2	4	no	—
616	C₂⁴	—	2	4	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	4	no	—
620	C₂⁴	—	2	4	no	—
621	C₂⁴	—	2	8	no	—
622	C₂⁴	—	4	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	4	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	—	4	2	no	—
628	C₂⁴	—	4	4	no	—
629	C₂⁴	—	4	8	no	—
630	C₂⁴	—	4	4	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	—	4	8	no	—
636	C₂⁴	—	4	4	no	—
637	C₂⁴	—	4	4	no	—
638	C₂⁴	—	4	4	no	—
639	C₂⁴	—	4	16	no	—
640	C₂⁴	—	4	16	no	—
641	C₂⁴	—	4	16	no	—
642	C₂⁴	—	8	8	no	—
643	C₂⁴	—	8	32	no	—
644	C₂⁴	—	8	8	no	—
645	C₂⁴	—	8	32	no	—
646	C₂⁴	—	8	8	no	—
647	C₂⁴	H(5,𝔽₂)	1	8	yes	—
648	C₂⁴	H(5,𝔽₂)	1	4	yes	—
649	C₂⁴	C₂⁵	1	4	yes	—
650	C₂⁴	C₂⁵	1	2	yes	—
651	C₂⁴	C₂⁵	1	4	yes	—
652	C₂⁴	C₂⁵	1	2	yes	—
653	C₂⁴	C₂⁵	1	1	yes	characteristic
654	C₂⁴	C₂⁵	1	1	yes	characteristic
655	C₂⁴	C₂⁵	1	1	yes	characteristic
656	C₂×D₄	—	2	8	no	—
657	C₂×D₄	—	2	8	no	—
658	C₂×D₄	—	2	8	no	—
659	C₂×D₄	—	2	8	no	—
660	C₂×D₄	—	2	8	no	—
661	C₂×D₄	—	2	8	no	—
662	C₂×D₄	—	2	8	no	—
663	C₂×D₄	—	2	8	no	—
664	C₂×D₄	—	2	8	no	—
665	C₂×D₄	—	2	8	no	—
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	16	no	—
669	C₂×D₄	—	4	8	no	—
670	C₂×D₄	—	4	8	no	—
671	C₂×D₄	—	4	8	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	8	no	—
674	C₂×D₄	—	4	8	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	4	8	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	8	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	8	no	—
682	C₂×D₄	—	4	8	no	—
683	C₂×D₄	—	4	8	no	—
684	C₂×D₄	—	4	8	no	—
685	C₂×D₄	—	4	8	no	—
686	C₂×D₄	—	4	64	no	—
687	C₂×D₄	—	4	64	no	—
688	C₂×D₄	—	4	32	no	—
689	C₂×D₄	—	4	32	no	—
690	C₂×D₄	—	4	32	no	—
691	C₂×D₄	—	8	32	no	—
692	C₂×D₄	—	8	8	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	8	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	8	no	—
702	C₂²×C₄	—	2	8	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	8	no	—
713	C₂²×C₄	—	2	8	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	4	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	—	4	8	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	—	4	4	no	—
727	C₂²×C₄	—	4	4	no	—
728	C₂²×C₄	—	4	4	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	8	no	—
731	C₂²×C₄	—	4	8	no	—
732	C₂²×C₄	—	4	8	no	—
733	C₂²×C₄	—	4	16	no	—
734	C₂²×C₄	—	4	16	no	—
735	C₂²×C₄	—	8	8	no	—
736	C₂²×C₄	C₂⁵	1	2	yes	—
737	C₂²×C₄	C₂⁵	1	4	yes	—
738	C₂²×C₄	C₂⁵	1	4	yes	—
739	C₂²×C₄	C₂⁵	1	8	yes	—
740	C₂²×C₄	C₂⁵	1	8	yes	—
741	C₂²×C₄	C₂⁵	1	2	yes	—
742	C₂²×C₄	C₂⁵	1	8	yes	—
743	C₂²×C₄	C₂⁵	1	4	yes	—
744	C₂²×C₄	C₂⁵	1	2	yes	—
745	C₂²×C₄	C₂⁵	1	4	yes	—
746	C₂²×C₄	C₂⁵	1	2	yes	—
747	C₄⋊C₄	—	4	4	no	—
748	C₄⋊C₄	—	4	4	no	—
749	C₄⋊C₄	—	4	4	no	—
750	C₄⋊C₄	—	4	8	no	—
751	C₄⋊C₄	—	4	8	no	—
752	C₄⋊C₄	—	4	8	no	—
753	C₄⋊C₄	—	4	8	no	—
754	C₄⋊C₄	—	4	8	no	—
755	C₄⋊C₄	—	4	8	no	—
756	C₄⋊C₄	—	4	8	no	—
757	C₄⋊C₄	—	4	4	no	—
758	C₄⋊C₄	—	4	4	no	—
759	C₄⋊C₄	—	4	8	no	—
760	C₄⋊C₄	—	4	8	no	—
761	C₄⋊C₄	—	4	8	no	—
762	C₄⋊C₄	—	4	8	no	—
763	C₄⋊C₄	—	4	8	no	—
764	C₂²⋊C₄	—	2	8	no	—
765	C₂²⋊C₄	—	2	8	no	—
766	C₂²⋊C₄	—	2	8	no	—
767	C₂²⋊C₄	—	2	8	no	—
768	C₂²⋊C₄	—	2	8	no	—
769	C₂²⋊C₄	—	2	8	no	—
770	C₂²⋊C₄	—	2	8	no	—
771	C₂²⋊C₄	—	2	8	no	—
772	C₂²⋊C₄	—	2	16	no	—
773	C₂²⋊C₄	—	2	8	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	8	no	—
783	C₂²⋊C₄	—	4	4	no	—
784	C₂²⋊C₄	—	4	8	no	—
785	C₂²⋊C₄	—	4	8	no	—
786	C₂²⋊C₄	—	4	8	no	—
787	C₂²⋊C₄	—	4	8	no	—
788	C₂²⋊C₄	—	4	8	no	—
789	C₂²⋊C₄	—	4	8	no	—
790	C₂²⋊C₄	—	4	8	no	—
791	C₂²⋊C₄	—	4	8	no	—
792	C₂²⋊C₄	—	4	8	no	—
793	C₂²⋊C₄	—	4	8	no	—
794	C₂²⋊C₄	—	4	8	no	—
795	C₂²⋊C₄	—	4	8	no	—
796	C₂²⋊C₄	—	4	8	no	—
797	C₂²⋊C₄	—	4	8	no	—
798	C₂²⋊C₄	—	4	8	no	—
799	C₂²⋊C₄	—	4	4	no	—
800	C₂²⋊C₄	—	4	4	no	—
801	C₂²⋊C₄	—	4	4	no	—
802	C₂²⋊C₄	—	4	4	no	—
803	C₂²⋊C₄	—	4	8	no	—
804	C₂²⋊C₄	—	4	8	no	—
805	C₂²⋊C₄	—	4	8	no	—
806	C₂²⋊C₄	—	4	8	no	—
807	C₂²⋊C₄	—	4	8	no	—
808	C₂²⋊C₄	—	4	8	no	—
809	C₄²	—	4	8	no	—
810	C₄²	—	4	8	no	—
811	C₄²	—	4	8	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	8	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	4	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	4	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	4	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	4	no	—
830	C₂³	—	2	4	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	8	no	—
833	C₂³	—	2	8	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	8	no	—
836	C₂³	—	2	4	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	16	no	—
841	C₂³	—	4	16	no	—
842	C₂³	—	4	16	no	—
843	C₂³	—	4	8	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	4	16	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	4	16	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	16	no	—
852	C₂³	—	4	8	no	—
853	C₂³	—	4	8	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	8	no	—
856	C₂³	—	4	8	no	—
857	C₂³	—	8	4	no	—
858	C₂³	—	8	4	no	—
859	C₂³	—	8	4	no	—
860	C₂³	—	8	4	no	—
861	C₂³	—	8	8	no	—
862	C₂³	—	8	8	no	—
863	C₂³	—	8	8	no	—
864	C₂³	—	8	8	no	—
865	C₂³	—	8	8	no	—
866	C₂³	—	8	16	no	—
867	C₂³	—	8	4	no	—
868	C₂³	—	8	8	no	—
869	C₂³	—	8	4	no	—
870	C₂³	—	8	8	no	—
871	C₂³	—	8	8	no	—
872	C₂³	—	8	16	no	—
873	C₂³	—	8	64	no	—
874	C₂³	—	8	64	no	—
875	C₂³	#560	1	16	yes	—
876	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
877	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
878	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
879	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
880	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
881	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
882	C₂³	#585	1	4	yes	—
883	C₂³	C₂⁶	1	1	yes	characteristic
884	D₄	—	4	32	no	—
885	D₄	—	4	16	no	—
886	D₄	—	4	16	no	—
887	D₄	—	4	16	no	—
888	D₄	—	4	16	no	—
889	D₄	—	8	16	no	—
890	D₄	—	8	8	no	—
891	D₄	—	8	16	no	—
892	D₄	—	16	4	no	—
893	D₄	—	16	4	no	—
894	D₄	—	16	8	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	4	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	8	no	—
901	C₂×C₄	—	2	8	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	4	no	—
910	C₂×C₄	—	2	4	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	8	no	—
913	C₂×C₄	—	2	8	no	—
914	C₂×C₄	—	2	8	no	—
915	C₂×C₄	—	2	8	no	—
916	C₂×C₄	—	2	4	no	—
917	C₂×C₄	—	2	8	no	—
918	C₂×C₄	—	2	8	no	—
919	C₂×C₄	—	2	8	no	—
920	C₂×C₄	—	2	8	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	16	no	—
925	C₂×C₄	—	4	16	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	8	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	—	8	4	no	—
934	C₂×C₄	—	8	8	no	—
935	C₂×C₄	—	8	8	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	4	no	—
938	C₂×C₄	—	16	8	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	8	no	—
946	C₂²	—	2	8	no	—
947	C₂²	—	2	8	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	8	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	4	16	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	4	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	4	no	—
956	C₂²	—	4	4	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	4	no	—
959	C₂²	—	4	4	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	8	no	—
962	C₂²	—	4	4	no	—
963	C₂²	—	4	8	no	—
964	C₂²	—	4	8	no	—
965	C₂²	—	4	8	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	8	16	no	—
971	C₂²	—	8	16	no	—
972	C₂²	—	8	8	no	—
973	C₂²	—	8	16	no	—
974	C₂²	—	8	32	no	—
975	C₂²	—	16	8	no	—
976	C₂²	C₂×#560	1	4	yes	—
977	C₂²	C₂×#560	1	4	yes	—
978	C₂²	C₂×#560	1	4	yes	—
979	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
980	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
981	C₂²	C₂×#585	1	2	yes	—
982	C₂²	H(7,𝔽₂)	1	2	yes	—
983	C₄	—	4	4	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	4	no	—
987	C₄	—	4	8	no	—
988	C₄	—	4	8	no	—
989	C₄	—	4	8	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	4	no	—
993	C₄	—	4	4	no	—
994	C₂	—	2	4	no	—
995	C₂	—	2	4	no	—
996	C₂	—	2	4	no	—
997	C₂	—	4	4	no	—
998	C₂	—	8	4	no	—
999	C₂	—	8	2	no	—
1000	C₂	—	8	4	no	—
1001	C₂	C₂²×#560	1	1	yes	characteristic
1002	C₂	#62820	1	1	yes	characteristic
1003	C₂	#62862	1	1	yes	characteristic
1004	C₂	#62900	1	4	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁶
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. #52742	C₂	semidirect
2. #52586	C₂	semidirect
3. #52548	C₂	semidirect
4. #52397	C₂	semidirect
5. #52340	C₂	semidirect
6. #46334	C₂	semidirect
7. #45578	C₂	semidirect
8. #45569	C₂	semidirect
9. #45457	C₂	semidirect
10. #35447	C₂	semidirect
11. #35358	C₂	semidirect
12. #35350	C₂	semidirect
13. #35089	C₂	semidirect
14. #34995	C₂	semidirect
15. #34980	C₂	semidirect
16. C₂×#2539	C₂	semidirect
17. C₂×#2482	C₂	semidirect
18. C₂×#2405	C₂	semidirect
23. C₂²×#123	C₂²	semidirect
24. C₂²×#121	C₂²	semidirect
26. C₂×#518	C₂²	semidirect
27. C₂²×#117	C₂²	semidirect
29. #2854	C₂²	semidirect
30. #2854	C₂²	semidirect
31. #2852	C₂²	semidirect
32. #2849	C₂²	semidirect
33. #2846	C₂²	semidirect
34. #2842	C₂²	semidirect
35. #2837	C₂²	semidirect
36. #2837	C₂²	semidirect
37. #2837	C₂²	semidirect
38. #2834	C₂²	semidirect
39. #2829	C₂²	semidirect
40. #2829	C₂²	semidirect
41. #2828	C₂²	semidirect
42. #2826	C₂²	semidirect
43. #2825	C₂²	semidirect
44. #2813	C₂²	semidirect
45. #2812	C₂²	semidirect
46. #2807	C₂²	semidirect
47. #2807	C₂²	semidirect
48. #2803	C₂²	semidirect
49. #2803	C₂²	semidirect
50. #2801	C₂²	semidirect
51. #2778	C₂²	semidirect
52. #2757	C₂²	semidirect
53. #2757	C₂²	semidirect
54. #2756	C₂²	semidirect
55. #2756	C₂²	semidirect
56. #2748	C₂²	semidirect
57. #2735	C₂²	semidirect
58. #2735	C₂²	semidirect
59. #2705	C₂²	semidirect
60. #2705	C₂²	semidirect
61. #2703	C₂²	semidirect
62. #2697	C₂²	semidirect
63. #2693	C₂²	semidirect
64. #2685	C₂²	semidirect
65. #2685	C₂²	semidirect
66. #2678	C₂²	semidirect
67. #2668	C₂²	semidirect
68. #2643	C₂²	semidirect
69. #2618	C₂²	semidirect
70. #2618	C₂²	semidirect
71. #2613	C₂²	semidirect
72. #2613	C₂²	semidirect
73. #2543	C₂²	semidirect
75. #2539	C₂²	semidirect
76. #2539	C₂²	semidirect
77. #2539	C₂²	semidirect
78. #2534	C₂²	semidirect
79. #2510	C₂²	semidirect
80. #2493	C₂²	semidirect
81. #2486	C₂²	semidirect
82. #2482	C₂²	semidirect
83. #2482	C₂²	semidirect
84. #2482	C₂²	semidirect
85. #2482	C₂²	semidirect
86. #2482	C₂²	semidirect
87. #2481	C₂²	semidirect
88. #2480	C₂²	semidirect
89. #2425	C₂²	semidirect
90. #2425	C₂²	semidirect
91. #2425	C₂²	semidirect
92. #2424	C₂²	semidirect
93. #2418	C₂²	semidirect
94. #2418	C₂²	semidirect
95. #2418	C₂²	semidirect
96. #2418	C₂²	semidirect
97. #2416	C₂²	semidirect
98. #2413	C₂²	semidirect
99. #2413	C₂²	semidirect
100. #2413	C₂²	semidirect
101. #2413	C₂²	semidirect
102. #2412	C₂²	semidirect
103. #2412	C₂²	semidirect
104. #2411	C₂²	semidirect
105. #2411	C₂²	semidirect
106. #2411	C₂²	semidirect
107. #2410	C₂²	semidirect
108. #2410	C₂²	semidirect
109. #2410	C₂²	semidirect
113. #2405	C₂²	semidirect
114. #2405	C₂²	semidirect
115. #2405	C₂²	semidirect
117. C₂×#399	C₂²	semidirect
118. C₂×#399	C₂²	semidirect
119. C₂×#397	C₂²	semidirect
120. C₂×#394	C₂²	semidirect
121. C₂×#392	C₂²	semidirect
122. #2376	C₂²	semidirect
123. #2375	C₂²	semidirect
124. #2315	C₂²	semidirect
125. #2315	C₂²	semidirect
128. #2308	C₂²	semidirect
129. C₂×#390	C₂²	semidirect
130. C₂×#388	C₂²	semidirect
132. C₂×#385	C₂²	semidirect
133. C₂×#385	C₂²	semidirect
134. C₂×#381	C₂²	semidirect
137. C₂×#379	C₂²	semidirect
138. C₂×C₄×C₂²⋊C₄	C₂²	semidirect
149. C₂³×D₄	C₂³	semidirect
155. C₂×#126	C₂³	semidirect
167. C₂×#123	C₂³	semidirect
168. C₂×#123	C₂³	semidirect
169. C₂×#123	C₂³	semidirect
175. C₂×#121	C₂³	semidirect
176. C₂×#121	C₂³	semidirect
189. C₂×C₄×D₄	C₂³	semidirect
192. C₂×#117	C₂³	semidirect
193. C₂×#117	C₂³	semidirect
195. C₂²×C₄⋊C₄	C₂³	semidirect
196. C₂²×C₄⋊C₄	C₂³	semidirect
197. C₂²×C₄⋊C₄	C₂³	semidirect
198. C₂²×C₄⋊C₄	C₂³	semidirect
199. C₂²×C₄⋊C₄	C₂³	semidirect
218. C₂²×C₂²⋊C₄	C₂³	semidirect
219. C₂²×C₂²⋊C₄	C₂³	semidirect
220. C₂²×C₂²⋊C₄	C₂³	semidirect
221. C₂²×C₄²	C₂³	semidirect
222. C₂²×C₄²	C₂³	semidirect
223. #401	C₂³	semidirect
224. #400	C₂³	semidirect
225. #400	C₂³	semidirect
226. #400	C₂³	semidirect
232. #399	C₂³	semidirect
233. #399	C₂³	semidirect
234. #399	C₂³	semidirect
235. #399	C₂³	semidirect
236. #399	C₂³	semidirect
237. #398	C₂³	semidirect
238. #398	C₂³	semidirect
239. #398	C₂³	semidirect
240. #398	C₂³	semidirect
241. #398	C₂³	semidirect
245. #397	C₂³	semidirect
246. #397	C₂³	semidirect
247. #397	C₂³	semidirect
248. #397	C₂³	semidirect
249. #397	C₂³	semidirect
250. #397	C₂³	semidirect
251. #397	C₂³	semidirect
252. #397	C₂³	semidirect
253. #397	C₂³	semidirect
254. #396	C₂³	semidirect
255. #396	C₂³	semidirect
256. #396	C₂³	semidirect
257. #396	C₂³	semidirect
258. #396	C₂³	semidirect
259. #396	C₂³	semidirect
260. #396	C₂³	semidirect
261. #396	C₂³	semidirect
262. #396	C₂³	semidirect
273. #394	C₂³	semidirect
274. #394	C₂³	semidirect
275. #394	C₂³	semidirect
276. #394	C₂³	semidirect
277. #394	C₂³	semidirect
278. #394	C₂³	semidirect
279. #394	C₂³	semidirect
280. #394	C₂³	semidirect
281. #394	C₂³	semidirect
288. #392	C₂³	semidirect
289. #392	C₂³	semidirect
290. #392	C₂³	semidirect
293. #390	C₂³	semidirect
294. #390	C₂³	semidirect
295. #390	C₂³	semidirect
296. #390	C₂³	semidirect
297. #390	C₂³	semidirect
298. #389	C₂³	semidirect
299. #389	C₂³	semidirect
300. #389	C₂³	semidirect
301. #389	C₂³	semidirect
302. #389	C₂³	semidirect
307. #388	C₂³	semidirect
308. #388	C₂³	semidirect
309. #388	C₂³	semidirect
310. #388	C₂³	semidirect
311. #388	C₂³	semidirect
312. #388	C₂³	semidirect
313. #388	C₂³	semidirect
314. #388	C₂³	semidirect
315. #388	C₂³	semidirect
316. #388	C₂³	semidirect
317. #388	C₂³	semidirect
318. #388	C₂³	semidirect
319. #388	C₂³	semidirect
320. #388	C₂³	semidirect
321. #388	C₂³	semidirect
322. #387	C₂³	semidirect
323. #387	C₂³	semidirect
324. #387	C₂³	semidirect
337. #386	C₂³	semidirect
338. #386	C₂³	semidirect
339. #386	C₂³	semidirect
340. #386	C₂³	semidirect
341. #386	C₂³	semidirect
342. #386	C₂³	semidirect
343. #386	C₂³	semidirect
352. #385	C₂³	semidirect
353. #385	C₂³	semidirect
354. #385	C₂³	semidirect
355. #385	C₂³	semidirect
356. #385	C₂³	semidirect
357. #383	C₂³	semidirect
361. #381	C₂³	semidirect
362. #381	C₂³	semidirect
364. #380	C₂³	semidirect
365. #380	C₂³	semidirect
366. #380	C₂³	semidirect
367. #380	C₂³	semidirect
368. #380	C₂³	semidirect
382. #379	C₂³	semidirect
384. C₄×C₂²⋊C₄	C₂³	semidirect
386. C₂×#95	C₂³	semidirect
387. C₂×#95	C₂³	semidirect
388. C₂×#95	C₂³	semidirect
389. C₂×#95	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#52742	2
#52586	2
#52548	2
#52397	2
#52340	2
#46334	2
#45578	2
#45569	2
#45457	2
#35447	2
#35358	2
#35350	2
#35089	2
#34995	2
#34980	2
C₂×#2539	2
C₂×#2482	2
C₂×#2405	2