Subgroups — #8093832

Order 512.

6734 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#52925	C₂	1	4	yes	maximal, complemented
2	#52530	C₂	1	4	yes	maximal, complemented
3	#52395	C₂	1	4	yes	maximal, complemented
4	#52367	C₂	1	8	yes	maximal, complemented
5	#52310	C₂	1	4	yes	maximal, complemented
6	#46031	C₂	1	8	yes	maximal, complemented
7	#45568	C₂	1	8	yes	maximal, complemented
8	#45539	C₂	1	4	yes	maximal, complemented
9	#45458	C₂	1	4	yes	maximal, complemented
10	#35455	C₂	1	2	yes	maximal, complemented
11	#35377	C₂	1	2	yes	maximal, complemented
12	#35367	C₂	1	2	yes	maximal, complemented
13	#35088	C₂	1	2	yes	maximal, complemented
14	#34993	C₂	1	2	yes	maximal, complemented
15	#34980	C₂	1	2	yes	maximal, complemented
16	C₂×#2561	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#2404	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#2405	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂³×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×D₄	C₂²	1	1	yes	characteristic
21	C₂×#543	C₂²	1	2	yes	complemented
22	C₂×#534	C₂²	1	2	yes	—
23	C₂×#534	C₂²	1	2	yes	—
24	C₂²×#123	C₂²	1	2	yes	—
25	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#120	C₂²	1	2	yes	—
27	C₂³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	#2850	C₂²	1	8	yes	complemented
29	#2849	C₂²	1	4	yes	complemented
30	#2849	C₂²	1	4	yes	complemented
31	#2849	C₂²	1	4	yes	complemented
32	#2846	C₂²	1	4	yes	complemented
33	#2840	C₂²	1	4	yes	complemented
34	#2835	C₂²	1	4	yes	complemented
35	#2832	C₂²	1	8	yes	complemented
36	#2832	C₂²	1	8	yes	complemented
37	#2832	C₂²	1	8	yes	complemented
38	#2828	C₂²	1	8	yes	complemented
39	#2828	C₂²	1	8	yes	complemented
40	#2824	C₂²	1	4	yes	complemented
41	#2824	C₂²	1	8	yes	complemented
42	#2824	C₂²	1	8	yes	complemented
43	#2819	C₂²	1	8	yes	complemented
44	#2812	C₂²	1	4	yes	complemented
45	#2804	C₂²	1	8	yes	complemented
46	#2785	C₂²	1	8	yes	complemented
47	#2782	C₂²	1	8	yes	complemented
48	#2782	C₂²	1	8	yes	complemented
49	#2763	C₂²	1	4	yes	complemented
50	#2763	C₂²	1	8	yes	complemented
51	#2753	C₂²	1	8	yes	complemented
52	#2753	C₂²	1	8	yes	complemented
53	#2753	C₂²	1	8	yes	complemented
54	#2753	C₂²	1	8	yes	complemented
55	#2753	C₂²	1	8	yes	complemented
56	#2736	C₂²	1	4	yes	complemented
57	#2736	C₂²	1	8	yes	complemented
58	#2733	C₂²	1	8	yes	complemented
59	#2712	C₂²	1	4	yes	complemented
60	#2712	C₂²	1	8	yes	complemented
61	#2712	C₂²	1	8	yes	complemented
62	#2684	C₂²	1	8	yes	complemented
63	#2684	C₂²	1	8	yes	complemented
64	#2684	C₂²	1	8	yes	complemented
65	#2670	C₂²	1	8	yes	complemented
66	#2670	C₂²	1	4	yes	complemented
67	#2639	C₂²	1	8	yes	complemented
68	#2614	C₂²	1	4	yes	complemented
69	#2613	C₂²	1	4	yes	complemented
70	#2613	C₂²	1	4	yes	complemented
71	#2613	C₂²	1	4	yes	complemented
72	#2591	C₂²	1	4	yes	complemented
73	#2591	C₂²	1	4	yes	complemented
74	#2561	C₂²	1	4	yes	complemented
75	#2561	C₂²	1	4	yes	complemented
76	#2561	C₂²	1	8	yes	complemented
77	#2561	C₂²	1	4	yes	complemented
78	#2561	C₂²	1	8	yes	complemented
79	#2561	C₂²	1	4	yes	complemented
80	#2504	C₂²	1	4	yes	complemented
81	#2503	C₂²	1	8	yes	complemented
82	#2488	C₂²	1	8	yes	complemented
83	#2488	C₂²	1	8	yes	complemented
84	#2488	C₂²	1	8	yes	complemented
85	#2488	C₂²	1	8	yes	complemented
86	#2488	C₂²	1	8	yes	complemented
87	#2488	C₂²	1	8	yes	complemented
88	#2488	C₂²	1	8	yes	complemented
89	#2488	C₂²	1	8	yes	complemented
90	#2472	C₂²	1	8	yes	complemented
91	#2472	C₂²	1	8	yes	complemented
92	#2472	C₂²	1	8	yes	complemented
93	#2472	C₂²	1	8	yes	complemented
94	#2472	C₂²	1	8	yes	complemented
95	#2472	C₂²	1	8	yes	complemented
96	#2472	C₂²	1	8	yes	complemented
97	#2472	C₂²	1	8	yes	complemented
98	#2436	C₂²	1	4	yes	complemented
99	#2435	C₂²	1	8	yes	complemented
100	#2430	C₂²	1	8	yes	complemented
101	#2430	C₂²	1	8	yes	complemented
102	#2410	C₂²	1	8	yes	complemented
103	#2410	C₂²	1	8	yes	complemented
104	#2406	C₂²	1	8	yes	complemented
105	#2405	C₂²	1	4	yes	—
106	#2405	C₂²	1	8	yes	—
107	#2405	C₂²	1	4	yes	—
108	#2405	C₂²	1	4	yes	complemented
109	#2405	C₂²	1	4	yes	complemented
110	#2404	C₂²	1	4	yes	—
111	#2404	C₂²	1	8	yes	complemented
112	#2404	C₂²	1	4	yes	complemented
113	#2404	C₂²	1	4	yes	complemented
114	#2404	C₂²	1	4	yes	complemented
115	#2403	C₂²	1	8	yes	—
116	C₂×#397	C₂²	1	2	yes	complemented
117	C₂×#394	C₂²	1	4	yes	complemented
118	C₂×#393	C₂²	1	2	yes	complemented
119	C₂×#393	C₂²	1	2	yes	complemented
120	C₂×#392	C₂²	1	2	yes	complemented
121	#2379	C₂²	1	8	yes	complemented
122	#2375	C₂²	1	8	yes	complemented
123	#2308	C₂²	1	2	yes	—
124	#2308	C₂²	1	2	yes	—
125	#2308	C₂²	1	2	yes	complemented
126	#2308	C₂²	1	2	yes	complemented
127	C₂×#388	C₂²	1	4	yes	complemented
128	C₂×#386	C₂²	1	2	yes	—
129	C₂×#386	C₂²	1	4	yes	complemented
130	C₂×#386	C₂²	1	2	yes	complemented
131	C₂×#385	C₂²	1	2	yes	complemented
132	C₂×#381	C₂²	1	2	yes	complemented
133	C₂×#381	C₂²	1	1	yes	characteristic, complemented
134	C₂×#379	C₂²	1	2	yes	—
135	C₂×#379	C₂²	1	1	yes	characteristic
136	C₂×#379	C₂²	1	2	yes	complemented
137	#2273	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	C₂²×#41	—	4	4	no	—
142	C₂²×#41	—	4	8	no	—
143	C₂²×#41	C₂³	1	4	yes	—
144	C₂²×#41	C₂³	1	4	yes	complemented
145	C₂³×Q₈	C₂³	1	1	yes	characteristic, complemented
146	C₂³×Q₈	C₂³	1	1	yes	characteristic, complemented
147	C₂³×D₄	—	4	8	no	—
148	C₂³×D₄	—	4	4	no	—
149	C₂³×D₄	C₂³	1	2	yes	—
150	C₂³×D₄	C₂³	1	2	yes	—
151	C₂³×D₄	C₂³	1	2	yes	—
152	C₂³×D₄	C₂³	1	4	yes	—
153	C₂³×D₄	C₂³	1	4	yes	—
154	C₂³×D₄	C₂³	1	4	yes	—
155	C₂³×D₄	C₂³	1	1	yes	characteristic, complemented
156	C₂⁴×C₄	C₂³	1	1	yes	characteristic
157	C₂⁴×C₄	C₂³	1	1	yes	characteristic
158	C₂⁴×C₄	C₂³	1	1	yes	characteristic
159	C₂⁴×C₄	C₂³	1	2	yes	complemented
160	#543	—	4	8	no	—
161	#534	—	4	8	no	—
162	#534	—	4	8	no	—
163	C₂×#124	C₂³	1	8	yes	—
164	C₂×#124	C₂³	1	8	yes	complemented
165	C₂×#124	C₂³	1	8	yes	complemented
166	C₂×#124	C₂³	1	8	yes	complemented
167	C₂×#123	—	4	8	no	—
168	C₂×#123	C₂³	1	4	yes	—
169	C₂×#123	C₂³	1	4	yes	—
170	C₂×#123	C₂³	1	4	yes	—
171	C₂×#123	C₂³	1	4	yes	—
172	C₂×#123	C₂³	1	4	yes	—
173	C₂×#123	C₂³	1	4	yes	—
174	C₂×#123	C₂³	1	8	yes	—
175	C₂×C₂²⋊Q₈	—	4	4	no	—
176	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₂×C₂²⋊Q₈	C₂³	1	4	yes	complemented
179	C₂×C₂²⋊Q₈	C₂³	1	8	yes	complemented
180	C₂×C₂²⋊Q₈	C₂³	1	8	yes	complemented
181	C₂×#121	C₂³	1	4	yes	—
182	C₂×#121	C₂³	1	4	yes	—
183	C₂×#121	C₂³	1	8	yes	—
184	C₂×#120	—	4	8	no	—
185	C₂×#120	C₂³	1	4	yes	—
186	C₂×#120	C₂³	1	4	yes	—
187	C₂×#120	C₂³	1	4	yes	—
188	C₂×#120	C₂³	1	8	yes	—
189	C₂×#120	C₂³	1	4	yes	—
190	C₂×#120	C₂³	1	4	yes	—
191	C₂×#120	C₂³	1	4	yes	—
192	C₂×#120	C₂³	1	8	yes	—
193	C₂×#120	C₂³	1	8	yes	—
194	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
196	C₂²×C₄⋊C₄	C₂³	1	2	yes	complemented
197	C₂²×C₂²⋊C₄	—	4	4	no	—
198	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
213	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂²×C₂²⋊C₄	C₂³	1	4	yes	complemented
216	C₂²×C₄²	C₂³	1	2	yes	complemented
217	#400	C₂³	1	8	yes	complemented
218	#400	C₂³	1	8	yes	complemented
219	#400	C₂³	1	8	yes	complemented
220	#400	C₂³	1	8	yes	complemented
221	#400	C₂³	1	8	yes	complemented
222	#400	C₂³	1	8	yes	complemented
223	#400	C₂³	1	8	yes	complemented
224	#400	C₂³	1	8	yes	complemented
225	#397	C₂³	1	4	yes	—
226	#397	C₂³	1	4	yes	—
227	#397	C₂³	1	8	yes	—
228	#397	C₂³	1	4	yes	complemented
229	#397	C₂³	1	4	yes	complemented
230	#397	C₂³	1	8	yes	complemented
231	#397	C₂³	1	8	yes	complemented
232	#397	C₂³	1	8	yes	complemented
233	#397	C₂³	1	8	yes	complemented
234	#397	C₂³	1	8	yes	complemented
235	#397	C₂³	1	8	yes	complemented
236	#397	C₂³	1	8	yes	complemented
237	#395	C₂³	1	8	yes	complemented
238	#395	C₂³	1	8	yes	complemented
239	#394	C₂³	1	8	yes	—
240	#394	C₂³	1	8	yes	—
241	#394	C₂³	1	8	yes	—
242	#394	C₂³	1	8	yes	—
243	#394	C₂³	1	8	yes	—
244	#394	C₂³	1	8	yes	—
245	#394	C₂³	1	8	yes	—
246	#394	C₂³	1	8	yes	—
247	#394	C₂³	1	8	yes	—
248	#394	C₂³	1	8	yes	—
249	#394	C₂³	1	8	yes	complemented
250	#394	C₂³	1	8	yes	complemented
251	#394	C₂³	1	8	yes	complemented
252	#394	C₂³	1	8	yes	complemented
253	#394	C₂³	1	8	yes	complemented
254	#394	C₂³	1	8	yes	complemented
255	#394	C₂³	1	8	yes	complemented
256	#394	C₂³	1	8	yes	complemented
257	#393	C₂³	1	4	yes	—
258	#393	C₂³	1	4	yes	—
259	#393	C₂³	1	8	yes	—
260	#393	C₂³	1	4	yes	—
261	#393	C₂³	1	4	yes	—
262	#393	C₂³	1	4	yes	complemented
263	#393	C₂³	1	4	yes	complemented
264	#393	C₂³	1	8	yes	complemented
265	#393	C₂³	1	8	yes	complemented
266	#393	C₂³	1	8	yes	complemented
267	#393	C₂³	1	8	yes	complemented
268	#393	C₂³	1	8	yes	complemented
269	#393	C₂³	1	8	yes	complemented
270	#393	C₂³	1	4	yes	complemented
271	#393	C₂³	1	8	yes	complemented
272	#393	C₂³	1	4	yes	complemented
273	#393	C₂³	1	8	yes	complemented
274	#393	C₂³	1	8	yes	complemented
275	#392	C₂³	1	8	yes	—
276	#392	C₂³	1	8	yes	—
277	#392	C₂³	1	8	yes	—
278	#392	C₂³	1	4	yes	—
279	#392	C₂³	1	8	yes	—
280	#392	C₂³	1	4	yes	—
281	#392	C₂³	1	4	yes	complemented
282	#392	C₂³	1	8	yes	complemented
283	#392	C₂³	1	4	yes	complemented
284	#392	C₂³	1	8	yes	complemented
285	#391	C₂³	1	8	yes	complemented
286	#391	C₂³	1	8	yes	complemented
287	#391	C₂³	1	8	yes	complemented
288	#391	C₂³	1	8	yes	complemented
289	#390	C₂³	1	8	yes	—
290	#390	C₂³	1	8	yes	complemented
291	#390	C₂³	1	8	yes	complemented
292	#390	C₂³	1	8	yes	complemented
293	#388	C₂³	1	8	yes	—
294	#388	C₂³	1	8	yes	—
295	#388	C₂³	1	8	yes	—
296	#388	C₂³	1	8	yes	—
297	#388	C₂³	1	8	yes	complemented
298	#388	C₂³	1	8	yes	complemented
299	#388	C₂³	1	8	yes	complemented
300	#388	C₂³	1	8	yes	complemented
301	#388	C₂³	1	8	yes	complemented
302	#388	C₂³	1	8	yes	complemented
303	#388	C₂³	1	8	yes	complemented
304	#388	C₂³	1	8	yes	complemented
305	#388	C₂³	1	8	yes	complemented
306	#388	C₂³	1	8	yes	complemented
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	#386	C₂³	1	4	yes	—
314	#386	C₂³	1	8	yes	—
315	#386	C₂³	1	8	yes	—
316	#386	C₂³	1	8	yes	—
317	#386	C₂³	1	4	yes	—
318	#386	C₂³	1	8	yes	—
319	#386	C₂³	1	8	yes	—
320	#386	C₂³	1	8	yes	—
321	#386	C₂³	1	4	yes	—
322	#386	C₂³	1	4	yes	—
323	#386	C₂³	1	8	yes	—
324	#386	C₂³	1	8	yes	—
325	#386	C₂³	1	8	yes	—
326	#386	C₂³	1	8	yes	—
327	#386	C₂³	1	8	yes	—
328	#386	C₂³	1	4	yes	complemented
329	#386	C₂³	1	8	yes	complemented
330	#386	C₂³	1	4	yes	complemented
331	#386	C₂³	1	8	yes	complemented
332	#386	C₂³	1	8	yes	complemented
333	#386	C₂³	1	8	yes	complemented
334	#386	C₂³	1	4	yes	complemented
335	#386	C₂³	1	4	yes	complemented
336	#386	C₂³	1	8	yes	complemented
337	#386	C₂³	1	8	yes	complemented
338	#386	C₂³	1	8	yes	complemented
339	#385	C₂³	1	4	yes	—
340	#385	C₂³	1	8	yes	—
341	#385	C₂³	1	8	yes	—
342	#385	C₂³	1	4	yes	—
343	#385	C₂³	1	4	yes	—
344	#385	C₂³	1	4	yes	—
345	#385	C₂³	1	8	yes	complemented
346	#385	C₂³	1	8	yes	complemented
347	#385	C₂³	1	8	yes	complemented
348	#385	C₂³	1	8	yes	complemented
349	#382	C₂³	1	8	yes	complemented
350	#382	C₂³	1	8	yes	complemented
351	#382	C₂³	1	8	yes	complemented
352	#382	C₂³	1	8	yes	complemented
353	#381	C₂³	1	8	yes	—
354	#381	C₂³	1	4	yes	—
355	#381	C₂³	1	4	yes	—
356	#381	C₂³	1	4	yes	—
357	#381	C₂³	1	4	yes	complemented
358	#381	C₂³	1	4	yes	complemented
359	#381	C₂³	1	4	yes	complemented
360	#381	C₂³	1	4	yes	complemented
361	#381	C₂³	1	4	yes	complemented
362	#379	C₂³	1	8	yes	—
363	#379	C₂³	1	4	yes	—
364	#379	C₂³	1	4	yes	—
365	#379	C₂³	1	4	yes	—
366	#379	C₂³	1	4	yes	—
367	#379	C₂³	1	4	yes	—
368	#379	C₂³	1	8	yes	—
369	#379	C₂³	1	4	yes	—
370	#379	C₂³	1	8	yes	—
371	#379	C₂³	1	4	yes	—
372	#379	C₂³	1	4	yes	—
373	#379	C₂³	1	4	yes	—
374	#379	C₂³	1	4	yes	—
375	#379	C₂³	1	4	yes	complemented
376	#379	C₂³	1	4	yes	complemented
377	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
378	C₄×C₂²⋊C₄	C₂³	1	8	yes	—
379	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
380	C₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
381	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
382	C₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
383	C₂×#95	C₂³	1	4	yes	—
384	C₂×#95	C₂³	1	2	yes	complemented
385	C₂×#95	C₂³	1	2	yes	complemented
386	C₂×#95	C₂³	1	4	yes	complemented
387	C₂×#95	C₂³	1	4	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	C₂×#41	—	4	8	no	—
407	C₂×#41	—	4	16	no	—
408	C₂×#41	—	4	8	no	—
409	C₂×#41	—	4	16	no	—
410	C₂×#41	—	4	64	no	—
411	C₂²×Q₈	—	4	2	no	—
412	C₂²×Q₈	—	4	4	no	—
413	C₂²×Q₈	—	4	2	no	—
414	C₂²×Q₈	—	8	2	no	—
415	C₂²×Q₈	C₂⁴	1	8	yes	—
416	C₂²×Q₈	C₂⁴	1	4	yes	—
417	C₂²×Q₈	C₂⁴	1	4	yes	—
418	C₂²×D₄	—	2	8	no	—
419	C₂²×D₄	—	2	8	no	—
420	C₂²×D₄	—	2	8	no	—
421	C₂²×D₄	—	2	8	no	—
422	C₂²×D₄	—	2	8	no	—
423	C₂²×D₄	—	2	8	no	—
424	C₂²×D₄	—	4	4	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	—	4	4	no	—
427	C₂²×D₄	—	4	2	no	—
428	C₂²×D₄	—	4	4	no	—
429	C₂²×D₄	—	4	8	no	—
430	C₂²×D₄	—	4	8	no	—
431	C₂²×D₄	—	4	16	no	—
432	C₂²×D₄	—	4	8	no	—
433	C₂²×D₄	—	4	16	no	—
434	C₂²×D₄	—	4	8	no	—
435	C₂²×D₄	—	4	64	no	—
436	C₂²×D₄	—	8	4	no	—
437	C₂²×D₄	C₂⁴	1	4	yes	—
438	C₂²×D₄	C₂⁴	1	4	yes	—
439	C₂²×D₄	C₂⁴	1	4	yes	—
440	C₂²×D₄	C₂⁴	1	4	yes	—
441	C₂²×D₄	C₂⁴	1	8	yes	—
442	C₂²×D₄	C₂⁴	1	4	yes	—
443	C₂²×D₄	C₂⁴	1	8	yes	—
444	C₂²×D₄	C₂⁴	1	4	yes	—
445	C₂²×D₄	C₂⁴	1	8	yes	—
446	C₂²×D₄	C₂⁴	1	8	yes	—
447	C₂²×D₄	C₂⁴	1	4	yes	—
448	C₂³×C₄	—	2	4	no	—
449	C₂³×C₄	—	2	8	no	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	4	4	no	—
452	C₂³×C₄	—	4	2	no	—
453	C₂³×C₄	—	4	4	no	—
454	C₂³×C₄	—	4	4	no	—
455	C₂³×C₄	—	4	4	no	—
456	C₂³×C₄	—	8	2	no	—
457	C₂³×C₄	C₂⁴	1	2	yes	—
458	C₂³×C₄	C₂⁴	1	1	yes	characteristic
459	C₂³×C₄	C₂⁴	1	1	yes	characteristic
460	C₂³×C₄	C₂⁴	1	2	yes	—
461	C₂³×C₄	C₂⁴	1	2	yes	—
462	C₂³×C₄	C₂⁴	1	2	yes	—
463	C₂³×C₄	C₂⁴	1	4	yes	—
464	C₂³×C₄	C₂⁴	1	2	yes	—
465	C₂³×C₄	C₂⁴	1	2	yes	—
466	C₂³×C₄	C₂⁴	1	2	yes	—
467	C₂³×C₄	C₂⁴	1	4	yes	—
468	C₂³×C₄	C₂⁴	1	2	yes	—
469	C₂³×C₄	C₂⁴	1	4	yes	—
470	C₂³×C₄	C₂⁴	1	1	yes	characteristic
471	C₂³×C₄	C₂⁴	1	1	yes	characteristic
472	C₂³×C₄	C₂⁴	1	4	yes	—
473	C₂³×C₄	C₂⁴	1	8	yes	—
474	#124	—	4	16	no	—
475	#124	—	8	8	no	—
476	#124	—	8	8	no	—
477	#124	—	8	8	no	—
478	#123	—	4	8	no	—
479	#123	—	4	8	no	—
480	#123	—	4	16	no	—
481	#123	—	4	8	no	—
482	#123	—	4	8	no	—
483	#123	—	4	8	no	—
484	#123	—	4	8	no	—
485	C₂²⋊Q₈	—	4	8	no	—
486	C₂²⋊Q₈	—	4	8	no	—
487	C₂²⋊Q₈	—	4	16	no	—
488	C₂²⋊Q₈	—	4	16	no	—
489	C₂²⋊Q₈	—	4	16	no	—
490	#121	—	4	8	no	—
491	#121	—	4	8	no	—
492	#121	—	4	16	no	—
493	#120	—	4	8	no	—
494	#120	—	4	16	no	—
495	#120	—	4	8	no	—
496	#120	—	4	16	no	—
497	#120	—	4	8	no	—
498	#120	—	4	8	no	—
499	#120	—	4	8	no	—
500	#120	—	4	8	no	—
501	#120	—	8	8	no	—
502	C₂×C₄⋊C₄	—	4	8	no	—
503	C₂×C₄⋊C₄	—	4	4	no	—
504	C₂×C₄⋊C₄	—	4	2	no	—
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	4	yes	—
509	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
510	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
511	C₂×C₄⋊C₄	C₂⁴	1	4	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	4	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	8	no	—
528	C₂×C₂²⋊C₄	—	4	8	no	—
529	C₂×C₂²⋊C₄	—	8	4	no	—
530	C₂×C₂²⋊C₄	—	8	2	no	—
531	C₂×C₂²⋊C₄	—	8	4	no	—
532	C₂×C₂²⋊C₄	—	8	4	no	—
533	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
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	8	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	2	yes	—
544	C₂×C₂²⋊C₄	C₂⁴	1	2	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	8	yes	—
552	C₂×C₂²⋊C₄	C₂⁴	1	8	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	4	yes	—
561	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
562	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
563	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
564	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
566	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
569	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
571	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
572	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
573	C₂×C₂²⋊C₄	C₂⁴	1	8	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×C₄²	—	8	2	no	—
579	C₂×C₄²	C₂⁴	1	8	yes	—
580	C₂×C₄²	C₂⁴	1	8	yes	—
581	C₂×C₄²	C₂⁴	1	8	yes	—
582	#95	C₂⁴	1	8	yes	—
583	#95	C₂⁴	1	8	yes	—
584	#95	C₂⁴	1	4	yes	—
585	#95	C₂⁴	1	4	yes	—
586	#95	C₂⁴	1	4	yes	—
587	#95	C₂⁴	1	8	yes	—
588	#95	C₂⁴	1	8	yes	—
589	#95	C₂⁴	1	8	yes	—
590	#95	C₂⁴	1	8	yes	—
591	#95	C₂⁴	1	8	yes	—
592	#95	C₂⁴	1	4	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	#95	C₂⁴	1	8	yes	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	4	no	—
610	C₂⁴	—	2	4	no	—
611	C₂⁴	—	2	4	no	—
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	2	8	no	—
616	C₂⁴	—	2	8	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	4	no	—
620	C₂⁴	—	2	4	no	—
621	C₂⁴	—	2	4	no	—
622	C₂⁴	—	2	8	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	2	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	—	4	4	no	—
628	C₂⁴	—	4	4	no	—
629	C₂⁴	—	4	2	no	—
630	C₂⁴	—	4	4	no	—
631	C₂⁴	—	4	8	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	2	no	—
637	C₂⁴	—	4	4	no	—
638	C₂⁴	—	4	8	no	—
639	C₂⁴	—	4	4	no	—
640	C₂⁴	—	4	16	no	—
641	C₂⁴	—	4	16	no	—
642	C₂⁴	—	4	16	no	—
643	C₂⁴	—	8	8	no	—
644	C₂⁴	—	8	32	no	—
645	C₂⁴	—	8	8	no	—
646	C₂⁴	—	8	32	no	—
647	C₂⁴	—	8	8	no	—
648	C₂⁴	H(5,𝔽₂)	1	8	yes	—
649	C₂⁴	H(5,𝔽₂)	1	4	yes	—
650	C₂⁴	C₂⁵	1	4	yes	—
651	C₂⁴	C₂⁵	1	2	yes	—
652	C₂⁴	C₂⁵	1	4	yes	—
653	C₂⁴	C₂⁵	1	2	yes	—
654	C₂⁴	C₂⁵	1	1	yes	characteristic
655	C₂⁴	C₂⁵	1	1	yes	characteristic
656	C₂⁴	C₂⁵	1	1	yes	characteristic
657	#41	—	4	64	no	—
658	#41	—	4	64	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	—	4	8	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	8	no	—
663	C₂×Q₈	—	4	8	no	—
664	C₂×Q₈	—	4	8	no	—
665	C₂×Q₈	—	4	8	no	—
666	C₂×Q₈	—	4	16	no	—
667	C₂×Q₈	—	8	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	2	8	no	—
672	C₂×D₄	—	2	8	no	—
673	C₂×D₄	—	2	8	no	—
674	C₂×D₄	—	2	8	no	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	8	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	16	no	—
681	C₂×D₄	—	4	8	no	—
682	C₂×D₄	—	4	8	no	—
683	C₂×D₄	—	4	8	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	8	no	—
686	C₂×D₄	—	4	8	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	—	4	8	no	—
689	C₂×D₄	—	4	8	no	—
690	C₂×D₄	—	4	8	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	8	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	8	no	—
695	C₂×D₄	—	4	8	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	64	no	—
699	C₂×D₄	—	4	64	no	—
700	C₂×D₄	—	4	32	no	—
701	C₂×D₄	—	4	16	no	—
702	C₂×D₄	—	4	32	no	—
703	C₂×D₄	—	4	32	no	—
704	C₂×D₄	—	8	32	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	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	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	8	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	8	no	—
722	C₂²×C₄	—	2	8	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	8	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	2	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	8	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	—	4	4	no	—
743	C₂²×C₄	—	4	4	no	—
744	C₂²×C₄	—	4	4	no	—
745	C₂²×C₄	—	4	16	no	—
746	C₂²×C₄	—	4	32	no	—
747	C₂²×C₄	—	4	16	no	—
748	C₂²×C₄	—	8	8	no	—
749	C₂²×C₄	C₂⁵	1	8	yes	—
750	C₂²×C₄	C₂⁵	1	2	yes	—
751	C₂²×C₄	C₂⁵	1	2	yes	—
752	C₂²×C₄	C₂⁵	1	2	yes	—
753	C₂²×C₄	C₂⁵	1	4	yes	—
754	C₂²×C₄	C₂⁵	1	4	yes	—
755	C₂²×C₄	C₂⁵	1	4	yes	—
756	C₂²×C₄	C₂⁵	1	8	yes	—
757	C₂²×C₄	C₂⁵	1	4	yes	—
758	C₂²×C₄	C₂⁵	1	2	yes	—
759	C₂²×C₄	C₂⁵	1	8	yes	—
760	C₄⋊C₄	—	4	4	no	—
761	C₄⋊C₄	—	4	8	no	—
762	C₄⋊C₄	—	4	8	no	—
763	C₄⋊C₄	—	4	8	no	—
764	C₄⋊C₄	—	4	4	no	—
765	C₄⋊C₄	—	4	8	no	—
766	C₄⋊C₄	—	4	4	no	—
767	C₄⋊C₄	—	4	8	no	—
768	C₄⋊C₄	—	4	8	no	—
769	C₄⋊C₄	—	4	8	no	—
770	C₂²⋊C₄	—	2	8	no	—
771	C₂²⋊C₄	—	2	8	no	—
772	C₂²⋊C₄	—	2	8	no	—
773	C₂²⋊C₄	—	2	8	no	—
774	C₂²⋊C₄	—	2	8	no	—
775	C₂²⋊C₄	—	2	8	no	—
776	C₂²⋊C₄	—	2	8	no	—
777	C₂²⋊C₄	—	2	8	no	—
778	C₂²⋊C₄	—	2	16	no	—
779	C₂²⋊C₄	—	2	8	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	8	no	—
789	C₂²⋊C₄	—	4	4	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	8	no	—
800	C₂²⋊C₄	—	4	8	no	—
801	C₂²⋊C₄	—	4	8	no	—
802	C₂²⋊C₄	—	4	8	no	—
803	C₂²⋊C₄	—	4	4	no	—
804	C₂²⋊C₄	—	4	4	no	—
805	C₂²⋊C₄	—	4	8	no	—
806	C₂²⋊C₄	—	4	8	no	—
807	C₂²⋊C₄	—	4	4	no	—
808	C₂²⋊C₄	—	4	4	no	—
809	C₂²⋊C₄	—	4	8	no	—
810	C₂²⋊C₄	—	4	8	no	—
811	C₂²⋊C₄	—	4	8	no	—
812	C₂²⋊C₄	—	4	8	no	—
813	C₂²⋊C₄	—	4	8	no	—
814	C₂²⋊C₄	—	4	8	no	—
815	C₄²	—	4	8	no	—
816	C₄²	—	4	8	no	—
817	C₄²	—	4	8	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	8	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	4	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	4	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	4	no	—
834	C₂³	—	2	4	no	—
835	C₂³	—	2	4	no	—
836	C₂³	—	2	4	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	8	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	8	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	16	no	—
847	C₂³	—	4	16	no	—
848	C₂³	—	4	16	no	—
849	C₂³	—	4	8	no	—
850	C₂³	—	4	8	no	—
851	C₂³	—	4	16	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	16	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	4	no	—
856	C₂³	—	4	16	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	16	no	—
859	C₂³	—	4	8	no	—
860	C₂³	—	4	8	no	—
861	C₂³	—	4	8	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	8	no	—
864	C₂³	—	8	4	no	—
865	C₂³	—	8	4	no	—
866	C₂³	—	8	8	no	—
867	C₂³	—	8	4	no	—
868	C₂³	—	8	4	no	—
869	C₂³	—	8	4	no	—
870	C₂³	—	8	4	no	—
871	C₂³	—	8	8	no	—
872	C₂³	—	8	8	no	—
873	C₂³	—	8	8	no	—
874	C₂³	—	8	8	no	—
875	C₂³	—	8	8	no	—
876	C₂³	—	8	16	no	—
877	C₂³	—	8	8	no	—
878	C₂³	—	8	16	no	—
879	C₂³	—	8	64	no	—
880	C₂³	—	8	64	no	—
881	C₂³	H(3,𝔽₄)	1	16	yes	—
882	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
883	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
884	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
885	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
886	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
887	C₂³	C₂×H(5,𝔽₂)	1	2	yes	—
888	C₂³	#585	1	4	yes	—
889	C₂³	C₂⁶	1	1	yes	characteristic
890	Q₈	—	4	16	no	—
891	Q₈	—	8	8	no	—
892	Q₈	—	16	8	no	—
893	D₄	—	4	32	no	—
894	D₄	—	4	16	no	—
895	D₄	—	4	16	no	—
896	D₄	—	4	16	no	—
897	D₄	—	4	16	no	—
898	D₄	—	4	16	no	—
899	D₄	—	8	16	no	—
900	D₄	—	8	16	no	—
901	D₄	—	16	4	no	—
902	D₄	—	16	4	no	—
903	D₄	—	16	8	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	4	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	4	no	—
916	C₂×C₄	—	2	4	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	2	4	no	—
919	C₂×C₄	—	2	4	no	—
920	C₂×C₄	—	2	4	no	—
921	C₂×C₄	—	2	8	no	—
922	C₂×C₄	—	2	8	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	8	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	8	no	—
928	C₂×C₄	—	2	8	no	—
929	C₂×C₄	—	2	8	no	—
930	C₂×C₄	—	2	4	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	16	no	—
934	C₂×C₄	—	4	32	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	8	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	8	no	—
939	C₂×C₄	—	4	8	no	—
940	C₂×C₄	—	4	8	no	—
941	C₂×C₄	—	8	4	no	—
942	C₂×C₄	—	8	8	no	—
943	C₂×C₄	—	8	8	no	—
944	C₂×C₄	—	8	4	no	—
945	C₂×C₄	—	8	4	no	—
946	C₂×C₄	—	8	8	no	—
947	C₂×C₄	—	8	4	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	8	no	—
955	C₂²	—	2	8	no	—
956	C₂²	—	2	8	no	—
957	C₂²	—	2	4	no	—
958	C₂²	—	2	8	no	—
959	C₂²	—	4	16	no	—
960	C₂²	—	4	16	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	4	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	4	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	8	no	—
971	C₂²	—	4	4	no	—
972	C₂²	—	4	8	no	—
973	C₂²	—	4	8	no	—
974	C₂²	—	4	8	no	—
975	C₂²	—	4	4	no	—
976	C₂²	—	4	4	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	8	16	no	—
980	C₂²	—	8	16	no	—
981	C₂²	—	8	16	no	—
982	C₂²	—	8	8	no	—
983	C₂²	—	8	16	no	—
984	C₂²	—	8	32	no	—
985	C₂²	C₂×H(3,𝔽₄)	1	4	yes	—
986	C₂²	C₂×H(3,𝔽₄)	1	4	yes	—
987	C₂²	C₂×H(3,𝔽₄)	1	4	yes	—
988	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
989	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
990	C₂²	C₂×#585	1	2	yes	—
991	C₂²	H(7,𝔽₂)	1	2	yes	—
992	C₄	—	4	4	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	4	no	—
996	C₄	—	4	8	no	—
997	C₄	—	4	8	no	—
998	C₄	—	4	8	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	4	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	4	no	—
1003	C₂	—	2	4	no	—
1004	C₂	—	2	4	no	—
1005	C₂	—	2	4	no	—
1006	C₂	—	4	4	no	—
1007	C₂	—	8	4	no	—
1008	C₂	—	8	4	no	—
1009	C₂	—	8	2	no	—
1010	C₂	C₂²×H(3,𝔽₄)	1	1	yes	characteristic
1011	C₂	#62820	1	1	yes	characteristic
1012	C₂	#62862	1	1	yes	characteristic
1013	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. #52925	C₂	semidirect
2. #52530	C₂	semidirect
3. #52395	C₂	semidirect
4. #52367	C₂	semidirect
5. #52310	C₂	semidirect
6. #46031	C₂	semidirect
7. #45568	C₂	semidirect
8. #45539	C₂	semidirect
9. #45458	C₂	semidirect
10. #35455	C₂	semidirect
11. #35377	C₂	semidirect
12. #35367	C₂	semidirect
13. #35088	C₂	semidirect
14. #34993	C₂	semidirect
15. #34980	C₂	semidirect
16. C₂×#2561	C₂	semidirect
17. C₂×#2404	C₂	semidirect
18. C₂×#2405	C₂	semidirect
19. C₂³×#41	C₂²	semidirect
21. C₂×#543	C₂²	semidirect
25. C₂²×C₂²⋊Q₈	C₂²	semidirect
28. #2850	C₂²	semidirect
29. #2849	C₂²	semidirect
30. #2849	C₂²	semidirect
31. #2849	C₂²	semidirect
32. #2846	C₂²	semidirect
33. #2840	C₂²	semidirect
34. #2835	C₂²	semidirect
35. #2832	C₂²	semidirect
36. #2832	C₂²	semidirect
37. #2832	C₂²	semidirect
38. #2828	C₂²	semidirect
39. #2828	C₂²	semidirect
40. #2824	C₂²	semidirect
41. #2824	C₂²	semidirect
42. #2824	C₂²	semidirect
43. #2819	C₂²	semidirect
44. #2812	C₂²	semidirect
45. #2804	C₂²	semidirect
46. #2785	C₂²	semidirect
47. #2782	C₂²	semidirect
48. #2782	C₂²	semidirect
49. #2763	C₂²	semidirect
50. #2763	C₂²	semidirect
51. #2753	C₂²	semidirect
52. #2753	C₂²	semidirect
53. #2753	C₂²	semidirect
54. #2753	C₂²	semidirect
55. #2753	C₂²	semidirect
56. #2736	C₂²	semidirect
57. #2736	C₂²	semidirect
58. #2733	C₂²	semidirect
59. #2712	C₂²	semidirect
60. #2712	C₂²	semidirect
61. #2712	C₂²	semidirect
62. #2684	C₂²	semidirect
63. #2684	C₂²	semidirect
64. #2684	C₂²	semidirect
65. #2670	C₂²	semidirect
66. #2670	C₂²	semidirect
67. #2639	C₂²	semidirect
68. #2614	C₂²	semidirect
69. #2613	C₂²	semidirect
70. #2613	C₂²	semidirect
71. #2613	C₂²	semidirect
72. #2591	C₂²	semidirect
73. #2591	C₂²	semidirect
74. #2561	C₂²	semidirect
75. #2561	C₂²	semidirect
76. #2561	C₂²	semidirect
77. #2561	C₂²	semidirect
78. #2561	C₂²	semidirect
79. #2561	C₂²	semidirect
80. #2504	C₂²	semidirect
81. #2503	C₂²	semidirect
82. #2488	C₂²	semidirect
83. #2488	C₂²	semidirect
84. #2488	C₂²	semidirect
85. #2488	C₂²	semidirect
86. #2488	C₂²	semidirect
87. #2488	C₂²	semidirect
88. #2488	C₂²	semidirect
89. #2488	C₂²	semidirect
90. #2472	C₂²	semidirect
91. #2472	C₂²	semidirect
92. #2472	C₂²	semidirect
93. #2472	C₂²	semidirect
94. #2472	C₂²	semidirect
95. #2472	C₂²	semidirect
96. #2472	C₂²	semidirect
97. #2472	C₂²	semidirect
98. #2436	C₂²	semidirect
99. #2435	C₂²	semidirect
100. #2430	C₂²	semidirect
101. #2430	C₂²	semidirect
102. #2410	C₂²	semidirect
103. #2410	C₂²	semidirect
104. #2406	C₂²	semidirect
108. #2405	C₂²	semidirect
109. #2405	C₂²	semidirect
111. #2404	C₂²	semidirect
112. #2404	C₂²	semidirect
113. #2404	C₂²	semidirect
114. #2404	C₂²	semidirect
116. C₂×#397	C₂²	semidirect
117. C₂×#394	C₂²	semidirect
118. C₂×#393	C₂²	semidirect
119. C₂×#393	C₂²	semidirect
120. C₂×#392	C₂²	semidirect
121. #2379	C₂²	semidirect
122. #2375	C₂²	semidirect
125. #2308	C₂²	semidirect
126. #2308	C₂²	semidirect
127. C₂×#388	C₂²	semidirect
129. C₂×#386	C₂²	semidirect
130. C₂×#386	C₂²	semidirect
131. C₂×#385	C₂²	semidirect
132. C₂×#381	C₂²	semidirect
133. C₂×#381	C₂²	semidirect
136. C₂×#379	C₂²	semidirect
137. #2273	C₂²	semidirect
138. C₂×C₄×C₂²⋊C₄	C₂²	semidirect
144. C₂²×#41	C₂³	semidirect
145. C₂³×Q₈	C₂³	semidirect
146. C₂³×Q₈	C₂³	semidirect
155. C₂³×D₄	C₂³	semidirect
159. C₂⁴×C₄	C₂³	semidirect
164. C₂×#124	C₂³	semidirect
165. C₂×#124	C₂³	semidirect
166. C₂×#124	C₂³	semidirect
178. C₂×C₂²⋊Q₈	C₂³	semidirect
179. C₂×C₂²⋊Q₈	C₂³	semidirect
180. C₂×C₂²⋊Q₈	C₂³	semidirect
195. C₂²×C₄⋊C₄	C₂³	semidirect
196. C₂²×C₄⋊C₄	C₂³	semidirect
215. C₂²×C₂²⋊C₄	C₂³	semidirect
216. C₂²×C₄²	C₂³	semidirect
217. #400	C₂³	semidirect
218. #400	C₂³	semidirect
219. #400	C₂³	semidirect
220. #400	C₂³	semidirect
221. #400	C₂³	semidirect
222. #400	C₂³	semidirect
223. #400	C₂³	semidirect
224. #400	C₂³	semidirect
228. #397	C₂³	semidirect
229. #397	C₂³	semidirect
230. #397	C₂³	semidirect
231. #397	C₂³	semidirect
232. #397	C₂³	semidirect
233. #397	C₂³	semidirect
234. #397	C₂³	semidirect
235. #397	C₂³	semidirect
236. #397	C₂³	semidirect
237. #395	C₂³	semidirect
238. #395	C₂³	semidirect
249. #394	C₂³	semidirect
250. #394	C₂³	semidirect
251. #394	C₂³	semidirect
252. #394	C₂³	semidirect
253. #394	C₂³	semidirect
254. #394	C₂³	semidirect
255. #394	C₂³	semidirect
256. #394	C₂³	semidirect
262. #393	C₂³	semidirect
263. #393	C₂³	semidirect
264. #393	C₂³	semidirect
265. #393	C₂³	semidirect
266. #393	C₂³	semidirect
267. #393	C₂³	semidirect
268. #393	C₂³	semidirect
269. #393	C₂³	semidirect
270. #393	C₂³	semidirect
271. #393	C₂³	semidirect
272. #393	C₂³	semidirect
273. #393	C₂³	semidirect
274. #393	C₂³	semidirect
281. #392	C₂³	semidirect
282. #392	C₂³	semidirect
283. #392	C₂³	semidirect
284. #392	C₂³	semidirect
285. #391	C₂³	semidirect
286. #391	C₂³	semidirect
287. #391	C₂³	semidirect
288. #391	C₂³	semidirect
290. #390	C₂³	semidirect
291. #390	C₂³	semidirect
292. #390	C₂³	semidirect
297. #388	C₂³	semidirect
298. #388	C₂³	semidirect
299. #388	C₂³	semidirect
300. #388	C₂³	semidirect
301. #388	C₂³	semidirect
302. #388	C₂³	semidirect
303. #388	C₂³	semidirect
304. #388	C₂³	semidirect
305. #388	C₂³	semidirect
306. #388	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
328. #386	C₂³	semidirect
329. #386	C₂³	semidirect
330. #386	C₂³	semidirect
331. #386	C₂³	semidirect
332. #386	C₂³	semidirect
333. #386	C₂³	semidirect
334. #386	C₂³	semidirect
335. #386	C₂³	semidirect
336. #386	C₂³	semidirect
337. #386	C₂³	semidirect
338. #386	C₂³	semidirect
345. #385	C₂³	semidirect
346. #385	C₂³	semidirect
347. #385	C₂³	semidirect
348. #385	C₂³	semidirect
349. #382	C₂³	semidirect
350. #382	C₂³	semidirect
351. #382	C₂³	semidirect
352. #382	C₂³	semidirect
357. #381	C₂³	semidirect
358. #381	C₂³	semidirect
359. #381	C₂³	semidirect
360. #381	C₂³	semidirect
361. #381	C₂³	semidirect
375. #379	C₂³	semidirect
376. #379	C₂³	semidirect
379. C₄×C₂²⋊C₄	C₂³	semidirect
380. C₄×C₂²⋊C₄	C₂³	semidirect
381. C₄×C₂²⋊C₄	C₂³	semidirect
382. C₄×C₂²⋊C₄	C₂³	semidirect
384. C₂×#95	C₂³	semidirect
385. C₂×#95	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
#52925	2
#52530	2
#52395	2
#52367	2
#52310	2
#46031	2
#45568	2
#45539	2
#45458	2
#35455	2
#35377	2
#35367	2
#35088	2
#34993	2
#34980	2
C₂×#2561	2
C₂×#2404	2
C₂×#2405	2