Subgroups — #10579247

Order 512.

6876 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62824	C₂	1	2	yes	maximal, complemented
2	#62437	C₂	1	4	yes	maximal, complemented
3	#62436	C₂	1	4	yes	maximal, complemented
4	#62435	C₂	1	8	yes	maximal, complemented
5	#62428	C₂	1	8	yes	maximal, complemented
6	#62419	C₂	1	8	yes	maximal, complemented
7	#61413	C₂	1	2	yes	maximal, complemented
8	#61412	C₂	1	2	yes	maximal, complemented
9	#61090	C₂	1	2	yes	maximal, complemented
10	#61088	C₂	1	2	yes	maximal, complemented
11	#61053	C₂	1	2	yes	maximal, complemented
12	#61050	C₂	1	4	yes	maximal, complemented
13	#61049	C₂	1	2	yes	maximal, complemented
14	#60819	C₂	1	4	yes	maximal, complemented
15	#60799	C₂	1	2	yes	maximal, complemented
16	#60713	C₂	1	2	yes	maximal, complemented
17	#60673	C₂	1	1	yes	maximal, characteristic, complemented
18	#60649	C₂	1	2	yes	maximal, complemented
19	C₂²×#495	C₂	1	1	yes	maximal, characteristic, complemented
20	#60204	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#578	C₂²	1	2	yes	complemented
22	C₂×#577	C₂²	1	4	yes	complemented
23	C₂×#576	C₂²	1	2	yes	complemented
24	C₂³×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂³×SD₁₆	C₂²	1	2	yes	complemented
26	C₂³×D₈	C₂²	1	1	yes	characteristic
27	#3561	—	2	4	no	—
28	#3561	C₂²	1	8	yes	complemented
29	#3558	—	2	4	no	—
30	#3558	C₂²	1	8	yes	complemented
31	#3545	—	2	8	no	—
32	#3514	—	2	8	no	—
33	#3514	C₂²	1	16	yes	complemented
34	#3510	C₂²	1	4	yes	complemented
35	#3510	C₂²	1	4	yes	complemented
36	#3500	C₂²	1	4	yes	complemented
37	#3500	C₂²	1	4	yes	complemented
38	#3490	—	2	8	no	—
39	#3486	C₂²	1	4	yes	complemented
40	#3484	C₂²	1	4	yes	complemented
41	#3444	C₂²	1	1	yes	characteristic
42	#3444	C₂²	1	2	yes	complemented
43	C₂²×#124	C₂²	1	2	yes	complemented
44	#3403	C₂²	1	8	yes	complemented
45	#3402	C₂²	1	8	yes	complemented
46	#3401	C₂²	1	16	yes	complemented
47	#3396	C₂²	1	8	yes	complemented
48	#3394	C₂²	1	16	yes	complemented
49	#3393	C₂²	1	8	yes	complemented
50	D₄×Q₁₆	C₂²	1	8	yes	complemented
51	#3285	C₂²	1	8	yes	complemented
52	#3285	C₂²	1	8	yes	complemented
53	#3282	C₂²	1	16	yes	complemented
54	#3282	C₂²	1	16	yes	complemented
55	D₄×SD₁₆	C₂²	1	16	yes	complemented
56	#3280	C₂²	1	8	yes	complemented
57	#3280	C₂²	1	8	yes	complemented
58	D₄×D₈	C₂²	1	8	yes	complemented
59	#3277	C₂²	1	8	yes	complemented
60	#3275	C₂²	1	16	yes	complemented
61	#3273	C₂²	1	8	yes	complemented
62	#3270	C₂²	1	16	yes	complemented
63	#3266	C₂²	1	16	yes	complemented
64	#3265	C₂²	1	16	yes	complemented
65	#3264	C₂²	1	16	yes	complemented
66	#3225	C₂²	1	16	yes	complemented
67	#3224	C₂²	1	16	yes	complemented
68	#3215	C₂²	1	8	yes	complemented
69	#3213	C₂²	1	8	yes	complemented
70	#3212	C₂²	1	16	yes	complemented
71	#3211	C₂²	1	16	yes	complemented
72	#3211	C₂²	1	16	yes	complemented
73	#3183	C₂²	1	8	yes	complemented
74	#3175	C₂²	1	8	yes	complemented
75	#3173	C₂²	1	8	yes	complemented
76	#3170	C₂²	1	2	yes	complemented
77	#3169	C₂²	1	2	yes	complemented
78	#3168	C₂²	1	4	yes	complemented
79	#3168	C₂²	1	4	yes	complemented
80	#3168	C₂²	1	8	yes	complemented
81	#3167	C₂²	1	4	yes	complemented
82	#3160	C₂²	1	1	yes	characteristic, complemented
83	#3156	C₂²	1	2	yes	complemented
84	#3156	C₂²	1	4	yes	complemented
85	#3155	C₂²	1	2	yes	—
86	#3155	C₂²	1	4	yes	complemented
87	#3154	C₂²	1	4	yes	complemented
88	#3154	C₂²	1	8	yes	complemented
89	#3153	C₂²	1	4	yes	complemented
90	#3153	C₂²	1	8	yes	complemented
91	#3147	C₂²	1	1	yes	characteristic, complemented
92	#3147	C₂²	1	4	yes	complemented
93	C₂×#495	C₂²	1	2	yes	complemented
94	C₂×#495	C₂²	1	2	yes	complemented
95	C₂×#495	C₂²	1	2	yes	complemented
96	C₂×#495	C₂²	1	2	yes	complemented
97	C₂×#495	C₂²	1	4	yes	complemented
98	C₂×#495	C₂²	1	4	yes	complemented
99	C₂×#495	C₂²	1	4	yes	complemented
100	C₂×#495	C₂²	1	4	yes	complemented
101	C₂×#495	C₂²	1	4	yes	complemented
102	#3140	C₂²	1	4	yes	complemented
103	#3131	C₂²	1	2	yes	complemented
104	#3059	C₂²	1	2	yes	complemented
105	#3058	C₂²	1	2	yes	—
106	#3057	C₂²	1	4	yes	complemented
107	#3050	C₂²	1	2	yes	complemented
108	#3050	C₂²	1	2	yes	complemented
109	#3044	C₂²	1	4	yes	complemented
110	#3043	C₂²	1	4	yes	complemented
111	#3042	C₂²	1	4	yes	complemented
112	#3041	C₂²	1	4	yes	complemented
113	#3040	C₂²	1	4	yes	complemented
114	#3040	C₂²	1	4	yes	complemented
115	#3011	C₂²	1	4	yes	complemented
116	#3010	C₂²	1	4	yes	complemented
117	#3009	C₂²	1	4	yes	complemented
118	#3008	C₂²	1	4	yes	complemented
119	#3004	C₂²	1	4	yes	complemented
120	#3003	C₂²	1	4	yes	complemented
121	#2966	C₂²	1	4	yes	complemented
122	#2966	C₂²	1	4	yes	complemented
123	#2965	C₂²	1	4	yes	complemented
124	C₈×#41	C₂²	1	4	yes	complemented
125	#2960	C₂²	1	1	yes	characteristic, complemented
126	#2960	C₂²	1	1	yes	characteristic, complemented
127	#2950	C₂²	1	2	yes	complemented
128	#2949	C₂²	1	4	yes	complemented
129	#2948	C₂²	1	2	yes	complemented
130	C₄×#135	C₂²	1	2	yes	complemented
131	C₄×#135	C₂²	1	2	yes	complemented
132	#2931	C₂²	1	1	yes	characteristic, complemented
133	#2931	C₂²	1	1	yes	characteristic, complemented
134	#2929	C₂²	1	2	yes	complemented
135	#2929	C₂²	1	2	yes	complemented
136	#2922	C₂²	1	2	yes	complemented
137	#2920	C₂²	1	1	yes	characteristic, complemented
138	C₄×#131	C₂²	1	2	yes	complemented
139	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
140	C₂×2₋¹⁺⁴	C₂³	1	4	yes	—
141	C₂×H(5,𝔽₂)	C₂³	1	4	yes	—
142	C₂³×Q₈	C₂³	1	2	yes	—
143	C₂³×D₄	C₂³	1	2	yes	—
144	#578	—	4	8	no	—
145	#577	—	4	16	no	—
146	#576	—	4	8	no	—
147	C₂×#137	C₂³	1	4	yes	—
148	C₂×#137	C₂³	1	4	yes	—
149	C₂×#137	C₂³	1	8	yes	complemented
150	C₂×#137	C₂³	1	8	yes	complemented
151	C₂×AGL(1,ℤ/8)	C₂³	1	4	yes	—
152	C₂×AGL(1,ℤ/8)	C₂³	1	8	yes	—
153	C₂×AGL(1,ℤ/8)	C₂³	1	4	yes	—
154	C₂×AGL(1,ℤ/8)	C₂³	1	8	yes	complemented
155	C₂×#135	C₂³	1	2	yes	—
156	C₂×#135	C₂³	1	2	yes	—
157	C₂×#135	C₂³	1	4	yes	—
158	C₂×#135	C₂³	1	8	yes	complemented
159	C₂×#135	C₂³	1	4	yes	complemented
160	C₂²×Q₁₆	—	4	4	no	—
161	C₂²×Q₁₆	C₂³	1	2	yes	—
162	C₂²×Q₁₆	C₂³	1	2	yes	—
163	C₂²×Q₁₆	C₂³	1	4	yes	—
164	C₂²×Q₁₆	C₂³	1	4	yes	—
165	C₂²×Q₁₆	C₂³	1	4	yes	complemented
166	C₂²×SD₁₆	—	4	8	no	—
167	C₂²×SD₁₆	C₂³	1	4	yes	—
168	C₂²×SD₁₆	C₂³	1	4	yes	—
169	C₂²×SD₁₆	C₂³	1	8	yes	—
170	C₂²×SD₁₆	C₂³	1	8	yes	—
171	C₂²×SD₁₆	C₂³	1	8	yes	complemented
172	C₂²×D₈	—	4	4	no	—
173	C₂²×D₈	C₂³	1	2	yes	—
174	C₂²×D₈	C₂³	1	2	yes	—
175	C₂²×D₈	C₂³	1	4	yes	—
176	C₂²×D₈	C₂³	1	4	yes	—
177	C₂²×D₈	C₂³	1	4	yes	—
178	C₂×#131	C₂³	1	2	yes	—
179	C₂×#131	C₂³	1	2	yes	—
180	C₂³×C₈	C₂³	1	1	yes	characteristic
181	C₂³×C₈	C₂³	1	1	yes	characteristic
182	#563	—	2	8	no	—
183	#562	—	2	8	no	—
184	#562	—	2	8	no	—
185	H(3,𝔽₄)	—	2	8	no	—
186	#559	—	2	8	no	—
187	#559	C₂³	1	16	yes	complemented
188	#556	—	2	8	no	—
189	#556	C₂³	1	16	yes	complemented
190	#555	—	2	16	no	—
191	#551	—	2	16	no	—
192	#551	—	2	16	no	—
193	#551	—	2	16	no	—
194	#551	—	2	16	no	—
195	#551	—	2	16	no	—
196	D₄×Q₈	—	2	8	no	—
197	D₄×Q₈	C₂³	1	16	yes	—
198	#548	—	2	8	no	—
199	#548	—	2	8	no	—
200	#548	C₂³	1	16	yes	—
201	#548	C₂³	1	16	yes	complemented
202	#546	—	2	16	no	—
203	#546	—	2	16	no	—
204	#546	—	2	8	no	—
205	#546	—	2	16	no	—
206	#546	—	2	16	no	—
207	#546	—	2	8	no	—
208	#546	C₂³	1	16	yes	—
209	#546	C₂³	1	16	yes	complemented
210	D₄²	—	2	8	no	—
211	D₄²	C₂³	1	16	yes	—
212	#543	—	2	8	no	—
213	#542	—	2	8	no	—
214	#542	—	2	16	no	—
215	#542	—	2	16	no	—
216	#542	C₂³	1	16	yes	complemented
217	#538	—	2	16	no	—
218	#538	—	2	8	no	—
219	#538	—	2	8	no	—
220	#538	—	2	16	no	—
221	#538	—	2	16	no	—
222	#536	—	2	4	no	—
223	#536	—	2	8	no	—
224	#536	C₂³	1	4	yes	—
225	#536	C₂³	1	4	yes	—
226	#536	C₂³	1	8	yes	complemented
227	#535	—	2	4	no	—
228	#535	C₂³	1	4	yes	—
229	#535	C₂³	1	4	yes	—
230	#535	C₂³	1	8	yes	complemented
231	#534	—	2	8	no	—
232	#534	—	2	8	no	—
233	#533	D₄	1	2	yes	—
234	#533	C₂³	1	4	yes	—
235	#533	C₂³	1	2	yes	—
236	#533	C₂³	1	1	yes	characteristic
237	#532	—	2	4	no	—
238	#532	D₄	1	2	yes	—
239	#532	C₂³	1	2	yes	—
240	#532	C₂³	1	4	yes	—
241	#532	C₂³	1	1	yes	characteristic
242	#532	C₂³	1	8	yes	complemented
243	#529	—	2	8	no	—
244	#529	—	2	4	no	—
245	#529	—	2	4	no	—
246	#529	D₄	1	4	yes	—
247	#529	D₄	1	4	yes	—
248	#529	C₂³	1	8	yes	—
249	#529	C₂³	1	4	yes	—
250	#529	C₂³	1	16	yes	complemented
251	C₂×#124	—	2	4	no	—
252	C₂×#124	—	2	4	no	—
253	C₂×#124	—	2	4	no	—
254	C₂×#124	—	2	4	no	—
255	C₂×#124	C₂³	1	4	yes	—
256	C₂×#124	C₂³	1	8	yes	—
257	C₂×#124	C₂³	1	8	yes	—
258	C₂×#124	C₂³	1	4	yes	—
259	C₂×#124	C₂³	1	8	yes	complemented
260	#525	—	2	4	no	—
261	#525	—	2	8	no	—
262	#525	D₄	1	4	yes	—
263	#525	C₂³	1	4	yes	—
264	#525	C₂³	1	2	yes	—
265	C₂×#120	—	2	8	no	—
266	#519	C₂³	1	4	yes	—
267	#518	—	2	16	no	—
268	#518	C₂³	1	4	yes	—
269	C₄×#41	—	2	4	no	—
270	C₄×#41	C₂³	1	4	yes	—
271	C₄×#41	C₂³	1	4	yes	—
272	C₄×#41	C₂³	1	2	yes	—
273	C₂²×C₂²⋊C₄	—	2	4	no	—
274	C₂²×C₄²	C₂³	1	1	yes	characteristic
275	#500	C₂³	1	2	yes	complemented
276	#499	C₂³	1	2	yes	complemented
277	#499	C₂³	1	2	yes	complemented
278	#498	C₂³	1	2	yes	complemented
279	#497	C₂³	1	8	yes	complemented
280	#497	C₂³	1	8	yes	complemented
281	#497	C₂³	1	8	yes	complemented
282	#496	C₂³	1	8	yes	—
283	#496	C₂³	1	8	yes	complemented
284	#496	C₂³	1	8	yes	complemented
285	#495	C₂³	1	4	yes	—
286	#495	C₂³	1	8	yes	—
287	#495	C₂³	1	8	yes	—
288	#495	C₂³	1	8	yes	—
289	#495	C₂³	1	4	yes	—
290	#495	C₂³	1	8	yes	—
291	#495	C₂³	1	4	yes	—
292	#495	C₂³	1	4	yes	—
293	#495	C₂³	1	4	yes	—
294	#495	C₂³	1	8	yes	—
295	#495	C₂³	1	8	yes	—
296	#495	C₂³	1	8	yes	complemented
297	#495	C₂³	1	4	yes	complemented
298	#495	C₂³	1	2	yes	complemented
299	#495	C₂³	1	8	yes	complemented
300	#495	C₂³	1	2	yes	complemented
301	#495	C₂³	1	8	yes	complemented
302	#494	C₂³	1	4	yes	complemented
303	#494	C₂³	1	1	yes	characteristic, complemented
304	#493	C₂³	1	4	yes	—
305	#493	C₂³	1	1	yes	characteristic, complemented
306	#492	C₂³	1	8	yes	complemented
307	#492	C₂³	1	2	yes	complemented
308	#489	C₂³	1	16	yes	complemented
309	#488	C₂³	1	8	yes	complemented
310	#488	C₂³	1	16	yes	complemented
311	#487	C₂³	1	4	yes	complemented
312	#486	C₂³	1	4	yes	complemented
313	#470	C₂³	1	8	yes	complemented
314	#469	C₂³	1	8	yes	—
315	#468	C₂³	1	16	yes	complemented
316	#467	C₂³	1	4	yes	—
317	#467	C₂³	1	4	yes	—
318	#467	C₂³	1	8	yes	complemented
319	#466	C₂³	1	4	yes	—
320	#466	C₂³	1	4	yes	—
321	#466	C₂³	1	8	yes	—
322	#465	C₂³	1	8	yes	—
323	#465	C₂³	1	8	yes	—
324	#465	C₂³	1	16	yes	complemented
325	#464	C₂³	1	16	yes	complemented
326	#464	C₂³	1	16	yes	complemented
327	#464	C₂³	1	16	yes	complemented
328	#464	C₂³	1	16	yes	complemented
329	#463	C₂³	1	16	yes	—
330	#463	C₂³	1	16	yes	complemented
331	#463	C₂³	1	16	yes	complemented
332	#463	C₂³	1	16	yes	complemented
333	#462	C₂³	1	16	yes	complemented
334	#461	C₂³	1	16	yes	complemented
335	#460	C₂³	1	16	yes	complemented
336	#459	C₂³	1	16	yes	—
337	#452	C₂³	1	16	yes	complemented
338	#452	C₂³	1	16	yes	complemented
339	#451	C₂³	1	16	yes	—
340	#451	C₂³	1	16	yes	complemented
341	#450	C₂³	1	16	yes	—
342	#450	C₂³	1	16	yes	complemented
343	#449	C₂³	1	16	yes	—
344	#449	C₂³	1	16	yes	complemented
345	#448	C₂³	1	16	yes	—
346	#448	C₂³	1	16	yes	complemented
347	#447	C₂³	1	16	yes	—
348	#447	C₂³	1	16	yes	—
349	#446	C₂³	1	4	yes	complemented
350	#446	C₂³	1	4	yes	complemented
351	C₈×Q₈	C₂³	1	4	yes	complemented
352	C₈×Q₈	C₂³	1	4	yes	complemented
353	#442	C₂³	1	8	yes	—
354	#441	C₂³	1	8	yes	complemented
355	#440	C₂³	1	16	yes	complemented
356	C₄×Q₁₆	C₂³	1	4	yes	complemented
357	C₄×Q₁₆	C₂³	1	8	yes	complemented
358	C₄×Q₁₆	C₂³	1	4	yes	complemented
359	C₄×SD₁₆	C₂³	1	8	yes	complemented
360	C₄×SD₁₆	C₂³	1	16	yes	complemented
361	C₄×SD₁₆	C₂³	1	8	yes	complemented
362	C₄×D₈	C₂³	1	8	yes	—
363	C₄×D₈	C₂³	1	4	yes	complemented
364	C₄×D₈	C₂³	1	4	yes	complemented
365	#436	C₂³	1	4	yes	complemented
366	#436	C₂³	1	4	yes	complemented
367	#435	C₂³	1	8	yes	—
368	#435	C₂³	1	8	yes	—
369	C₈×D₄	C₂³	1	8	yes	—
370	C₈×D₄	C₂³	1	8	yes	—
371	C₈×D₄	C₂³	1	4	yes	complemented
372	C₈×D₄	C₂³	1	4	yes	complemented
373	#433	C₂³	1	8	yes	complemented
374	#432	C₂³	1	4	yes	—
375	#431	C₂³	1	4	yes	—
376	#431	C₂³	1	8	yes	complemented
377	#427	C₂³	1	2	yes	—
378	#427	C₂³	1	2	yes	—
379	#424	C₂³	1	2	yes	—
380	#424	C₂³	1	2	yes	—
381	#423	C₂³	1	1	yes	characteristic
382	#423	C₂³	1	1	yes	characteristic
383	#419	C₂³	1	4	yes	—
384	#419	C₂³	1	4	yes	—
385	#418	C₂³	1	4	yes	—
386	#418	C₂³	1	4	yes	—
387	#416	C₂³	1	4	yes	—
388	#416	C₂³	1	4	yes	—
389	#408	C₂³	1	2	yes	—
390	#408	C₂³	1	2	yes	—
391	#407	C₂³	1	2	yes	—
392	#405	C₂³	1	2	yes	—
393	#405	C₂³	1	2	yes	—
394	#405	C₂³	1	4	yes	complemented
395	#405	C₂³	1	4	yes	complemented
396	C₄×M₁₆	C₂³	1	2	yes	—
397	C₄×M₁₆	C₂³	1	4	yes	complemented
398	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
399	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
400	C₂×C₄×C₈	C₂³	1	2	yes	—
401	C₂×C₄×C₈	C₂³	1	2	yes	—
402	C₂×C₄×C₈	C₂³	1	2	yes	—
403	C₂×C₄×C₈	C₂³	1	2	yes	—
404	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
405	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
406	C₂×C₄×C₈	C₂³	1	4	yes	complemented
407	C₂⁵	—	2	2	no	—
408	2₋¹⁺⁴	—	4	8	no	—
409	2₋¹⁺⁴	—	4	8	no	—
410	H(5,𝔽₂)	—	4	8	no	—
411	H(5,𝔽₂)	—	4	8	no	—
412	C₂×#41	—	2	4	no	—
413	C₂×#41	—	2	8	no	—
414	C₂×#41	—	2	4	no	—
415	C₂×#41	—	2	4	no	—
416	C₂×#41	C₂×D₄	1	4	yes	—
417	C₂×#41	C₂⁴	1	4	yes	—
418	C₂×#41	C₂⁴	1	8	yes	—
419	C₂×#41	C₂⁴	1	8	yes	—
420	C₂×#41	C₂⁴	1	2	yes	—
421	C₂²×Q₈	—	2	4	no	—
422	C₂²×Q₈	—	2	2	no	—
423	C₂²×Q₈	—	2	4	no	—
424	C₂²×Q₈	—	4	4	no	—
425	C₂²×Q₈	—	4	4	no	—
426	C₂²×Q₈	C₂⁴	1	4	yes	—
427	C₂²×Q₈	C₂⁴	1	8	yes	—
428	C₂²×Q₈	C₂⁴	1	8	yes	—
429	C₂²×D₄	—	2	16	no	—
430	C₂²×D₄	—	2	8	no	—
431	C₂²×D₄	—	2	4	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	4	no	—
434	C₂²×D₄	—	4	4	no	—
435	C₂²×D₄	—	4	4	no	—
436	C₂²×D₄	C₂⁴	1	4	yes	—
437	C₂²×D₄	C₂⁴	1	8	yes	—
438	C₂²×D₄	C₂⁴	1	8	yes	—
439	C₂³×C₄	—	2	2	no	—
440	C₂³×C₄	C₂×D₄	1	2	yes	—
441	C₂³×C₄	C₂⁴	1	1	yes	characteristic
442	#137	—	4	16	no	—
443	#137	—	4	16	no	—
444	#137	—	4	8	no	—
445	#137	—	4	8	no	—
446	AGL(1,ℤ/8)	—	4	16	no	—
447	AGL(1,ℤ/8)	—	4	16	no	—
448	AGL(1,ℤ/8)	—	4	8	no	—
449	AGL(1,ℤ/8)	—	4	8	no	—
450	#135	—	2	8	no	—
451	#135	—	2	8	no	—
452	#135	—	4	8	no	—
453	#135	—	4	8	no	—
454	#135	—	4	16	no	—
455	C₂×Q₁₆	—	2	8	no	—
456	C₂×Q₁₆	—	4	8	no	—
457	C₂×Q₁₆	—	4	8	no	—
458	C₂×Q₁₆	—	4	8	no	—
459	C₂×Q₁₆	—	4	4	no	—
460	C₂×Q₁₆	C₂⁴	1	4	yes	—
461	C₂×Q₁₆	C₂⁴	1	4	yes	—
462	C₂×Q₁₆	C₂⁴	1	2	yes	—
463	C₂×Q₁₆	C₂⁴	1	2	yes	—
464	C₂×Q₁₆	C₂⁴	1	8	yes	—
465	C₂×Q₁₆	C₂⁴	1	8	yes	—
466	C₂×Q₁₆	C₂⁴	1	8	yes	—
467	C₂×SD₁₆	—	2	16	no	—
468	C₂×SD₁₆	—	4	16	no	—
469	C₂×SD₁₆	—	4	16	no	—
470	C₂×SD₁₆	—	4	16	no	—
471	C₂×SD₁₆	—	4	8	no	—
472	C₂×SD₁₆	C₂⁴	1	8	yes	—
473	C₂×SD₁₆	C₂⁴	1	8	yes	—
474	C₂×SD₁₆	C₂⁴	1	4	yes	—
475	C₂×SD₁₆	C₂⁴	1	4	yes	—
476	C₂×SD₁₆	C₂⁴	1	16	yes	—
477	C₂×SD₁₆	C₂⁴	1	8	yes	—
478	C₂×SD₁₆	C₂⁴	1	8	yes	—
479	C₂×SD₁₆	C₂⁴	1	8	yes	—
480	C₂×SD₁₆	C₂⁴	1	8	yes	—
481	C₂×D₈	—	2	8	no	—
482	C₂×D₈	—	4	8	no	—
483	C₂×D₈	—	4	8	no	—
484	C₂×D₈	—	4	8	no	—
485	C₂×D₈	—	4	4	no	—
486	C₂×D₈	C₂⁴	1	4	yes	—
487	C₂×D₈	C₂⁴	1	4	yes	—
488	C₂×D₈	C₂⁴	1	2	yes	—
489	C₂×D₈	C₂⁴	1	2	yes	—
490	C₂×D₈	C₂⁴	1	8	yes	—
491	C₂×D₈	C₂⁴	1	8	yes	—
492	C₂×D₈	C₂⁴	1	8	yes	—
493	#131	—	2	8	no	—
494	#131	—	2	8	no	—
495	C₂×M₁₆	C₂⁴	1	2	yes	—
496	C₂×M₁₆	C₂⁴	1	2	yes	—
497	C₂×M₁₆	C₂⁴	1	4	yes	—
498	C₂×M₁₆	C₂⁴	1	4	yes	—
499	C₂²×C₈	—	2	4	no	—
500	C₂²×C₈	—	2	4	no	—
501	C₂²×C₈	C₂⁴	1	1	yes	characteristic
502	C₂²×C₈	C₂⁴	1	2	yes	—
503	C₂²×C₈	C₂⁴	1	2	yes	—
504	C₂²×C₈	C₂⁴	1	1	yes	characteristic
505	C₂²×C₈	C₂⁴	1	2	yes	—
506	C₂²×C₈	C₂⁴	1	2	yes	—
507	C₂²×C₈	C₂⁴	1	4	yes	—
508	C₂²×C₈	C₂⁴	1	4	yes	—
509	C₂²×C₈	C₂⁴	1	1	yes	characteristic
510	C₂²×C₈	C₂⁴	1	1	yes	characteristic
511	C₄⋊Q₈	—	2	4	no	—
512	C₄⋊Q₈	—	2	16	no	—
513	C₄⋊Q₈	C₂×D₄	1	2	yes	—
514	C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
515	C₄⋊Q₈	C₂⁴	1	2	yes	—
516	C₄⋊Q₈	C₂⁴	1	8	yes	—
517	C₄⋊Q₈	C₂⁴	1	4	yes	—
518	#127	—	2	4	no	—
519	#127	C₂×D₄	1	1	yes	characteristic
520	#127	C₂⁴	1	2	yes	—
521	#127	C₂⁴	1	8	yes	—
522	#126	—	2	16	no	—
523	#126	—	2	16	no	—
524	#126	—	2	16	no	—
525	#126	—	2	8	no	—
526	#126	—	2	16	no	—
527	#126	C₂×D₄	1	8	yes	—
528	#125	—	2	4	no	—
529	#125	C₂×D₄	1	2	yes	—
530	#125	C₂×D₄	1	4	yes	—
531	#125	C₂⁴	1	4	yes	—
532	#124	—	2	4	no	—
533	#124	—	2	16	no	—
534	#124	—	2	4	no	—
535	#124	—	2	16	no	—
536	#124	—	2	16	no	—
537	#124	—	2	16	no	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	8	no	—
541	#124	—	2	8	no	—
542	#124	—	2	8	no	—
543	#124	—	2	8	no	—
544	#124	—	2	8	no	—
545	#124	—	2	16	no	—
546	#124	—	2	4	no	—
547	#124	C₂×D₄	1	2	yes	—
548	#124	C₂×D₄	1	4	yes	—
549	#124	C₂⁴	1	8	yes	—
550	#124	C₂⁴	1	8	yes	—
551	#124	C₂⁴	1	16	yes	—
552	#124	C₂⁴	1	4	yes	—
553	#124	C₂⁴	1	8	yes	—
554	#124	C₂⁴	1	8	yes	—
555	#123	—	2	8	no	—
556	#123	—	2	8	no	—
557	#123	—	2	4	no	—
558	#123	—	2	16	no	—
559	#123	—	2	16	no	—
560	#123	—	2	16	no	—
561	#123	—	2	16	no	—
562	#123	—	2	16	no	—
563	#123	—	2	8	no	—
564	#123	—	2	16	no	—
565	#123	—	2	16	no	—
566	#123	C₂×D₄	1	8	yes	—
567	#123	C₂×D₄	1	4	yes	—
568	C₂²⋊Q₈	—	2	16	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	8	no	—
572	C₂²⋊Q₈	—	2	16	no	—
573	C₂²⋊Q₈	—	2	16	no	—
574	C₂²⋊Q₈	—	2	16	no	—
575	C₂²⋊Q₈	—	2	16	no	—
576	C₂²⋊Q₈	—	2	16	no	—
577	C₂²⋊Q₈	—	2	16	no	—
578	C₂²⋊Q₈	C₂×D₄	1	4	yes	—
579	C₂²⋊Q₈	C₂×D₄	1	4	yes	—
580	C₂²⋊Q₈	C₂×D₄	1	4	yes	—
581	C₂²⋊Q₈	C₂⁴	1	8	yes	—
582	C₂²⋊Q₈	C₂⁴	1	16	yes	—
583	#121	—	2	16	no	—
584	#121	—	2	16	no	—
585	#121	—	2	4	no	—
586	#121	—	2	4	no	—
587	#121	—	2	16	no	—
588	#121	—	2	8	no	—
589	#121	—	2	16	no	—
590	#121	—	2	16	no	—
591	#121	—	2	16	no	—
592	#121	—	2	16	no	—
593	#121	C₂×D₄	1	4	yes	—
594	#121	C₂×D₄	1	4	yes	—
595	#121	C₂×D₄	1	4	yes	—
596	#121	C₂⁴	1	8	yes	—
597	#121	C₂⁴	1	16	yes	—
598	#120	—	2	4	no	—
599	#120	—	2	8	no	—
600	#120	—	2	16	no	—
601	#120	—	2	16	no	—
602	#120	—	2	8	no	—
603	#120	—	2	16	no	—
604	#120	—	2	16	no	—
605	#120	—	2	16	no	—
606	#120	C₂×D₄	1	4	yes	—
607	C₄×Q₈	—	2	8	no	—
608	C₄×Q₈	—	2	4	no	—
609	C₄×Q₈	—	2	4	no	—
610	C₄×Q₈	C₂×D₄	1	4	yes	—
611	C₄×Q₈	C₂×D₄	1	4	yes	—
612	C₄×Q₈	C₂⁴	1	8	yes	—
613	C₄×Q₈	C₂⁴	1	16	yes	—
614	C₄×Q₈	C₂⁴	1	4	yes	—
615	C₄×D₄	—	2	16	no	—
616	C₄×D₄	—	2	8	no	—
617	C₄×D₄	—	2	8	no	—
618	C₄×D₄	—	2	8	no	—
619	C₄×D₄	—	2	16	no	—
620	C₄×D₄	—	2	16	no	—
621	C₄×D₄	—	2	8	no	—
622	C₄×D₄	—	2	16	no	—
623	C₄×D₄	—	2	16	no	—
624	C₄×D₄	—	2	4	no	—
625	C₄×D₄	—	2	4	no	—
626	C₄×D₄	—	2	16	no	—
627	C₄×D₄	C₂×D₄	1	8	yes	—
628	C₄×D₄	C₂×D₄	1	8	yes	—
629	C₄×D₄	C₂×D₄	1	4	yes	—
630	C₄×D₄	C₂×D₄	1	4	yes	—
631	C₄×D₄	C₂⁴	1	8	yes	—
632	C₄×D₄	C₂⁴	1	16	yes	—
633	C₄×D₄	C₂⁴	1	8	yes	—
634	C₄×D₄	C₂⁴	1	4	yes	—
635	#117	—	2	4	no	—
636	#117	—	2	16	no	—
637	#117	—	2	8	no	—
638	#117	—	2	8	no	—
639	#117	—	2	4	no	—
640	#117	—	2	16	no	—
641	#117	C₂×D₄	1	4	yes	—
642	#117	C₂×D₄	1	8	yes	—
643	#117	C₂⁴	1	4	yes	—
644	#117	C₂⁴	1	2	yes	—
645	#117	C₂⁴	1	4	yes	—
646	C₂×C₂²⋊C₄	—	2	8	no	—
647	C₂×C₂²⋊C₄	—	2	8	no	—
648	C₂×C₂²⋊C₄	—	2	8	no	—
649	C₂×C₂²⋊C₄	—	2	8	no	—
650	C₂×C₂²⋊C₄	—	2	8	no	—
651	C₂×C₂²⋊C₄	—	2	8	no	—
652	C₂×C₂²⋊C₄	—	2	16	no	—
653	C₂×C₂²⋊C₄	—	2	16	no	—
654	C₂×C₂²⋊C₄	—	2	16	no	—
655	C₂×C₂²⋊C₄	—	2	8	no	—
656	C₂×C₄²	—	2	4	no	—
657	C₂×C₄²	C₂×D₄	1	2	yes	—
658	C₂×C₄²	C₂×D₄	1	2	yes	—
659	C₂×C₄²	C₂×D₄	1	2	yes	—
660	C₂×C₄²	C₂⁴	1	1	yes	characteristic
661	C₂×C₄²	C₂⁴	1	4	yes	—
662	C₂×C₄²	C₂⁴	1	2	yes	—
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	2	yes	—
665	#107	C₂⁴	1	4	yes	—
666	#107	C₂⁴	1	4	yes	—
667	#106	C₂⁴	1	4	yes	—
668	#106	C₂⁴	1	4	yes	—
669	C₄⋊C₈	C₂⁴	1	4	yes	—
670	C₄⋊C₈	C₂⁴	1	4	yes	—
671	C₄⋊C₈	C₂⁴	1	8	yes	—
672	C₄⋊C₈	C₂⁴	1	8	yes	—
673	#103	C₂⁴	1	8	yes	—
674	#103	C₂⁴	1	8	yes	—
675	#103	C₂⁴	1	16	yes	—
676	#103	C₂⁴	1	16	yes	—
677	#102	C₂⁴	1	8	yes	—
678	#102	C₂⁴	1	8	yes	—
679	#102	C₂⁴	1	16	yes	—
680	#102	C₂⁴	1	16	yes	—
681	C₂²⋊C₈	C₂⁴	1	8	yes	—
682	C₂²⋊C₈	C₂⁴	1	8	yes	—
683	C₂²⋊C₈	C₂⁴	1	8	yes	—
684	#97	C₂⁴	1	4	yes	—
685	#97	C₂⁴	1	4	yes	—
686	#97	C₂⁴	1	4	yes	—
687	C₄×C₈	C₂⁴	1	1	yes	characteristic
688	C₄×C₈	C₂⁴	1	1	yes	characteristic
689	C₄×C₈	C₂⁴	1	1	yes	characteristic
690	C₄×C₈	C₂⁴	1	1	yes	characteristic
691	C₄×C₈	C₂⁴	1	2	yes	—
692	C₄×C₈	C₂⁴	1	2	yes	—
693	C₄×C₈	C₂⁴	1	2	yes	—
694	C₄×C₈	C₂⁴	1	2	yes	—
695	C₄×C₈	C₂⁴	1	2	yes	—
696	C₄×C₈	C₂⁴	1	2	yes	—
697	C₄×C₈	C₂⁴	1	4	yes	—
698	C₄×C₈	C₂⁴	1	4	yes	—
699	C₄×C₈	C₂⁴	1	4	yes	—
700	C₂⁴	—	2	8	no	—
701	C₂⁴	—	2	4	no	—
702	C₂⁴	—	2	8	no	—
703	C₂⁴	—	8	4	no	—
704	C₂⁴	—	8	8	no	—
705	C₂⁴	C₂²×D₄	1	1	yes	characteristic
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	2	8	no	—
709	#41	—	2	8	no	—
710	#41	—	4	8	no	—
711	#41	—	4	8	no	—
712	#41	—	4	8	no	—
713	#41	—	4	8	no	—
714	#41	—	4	8	no	—
715	#41	—	8	8	no	—
716	#41	—	8	16	no	—
717	#41	—	8	8	no	—
718	#41	—	8	8	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	2	8	no	—
722	C₂×Q₈	—	2	8	no	—
723	C₂×Q₈	—	2	8	no	—
724	C₂×Q₈	—	2	8	no	—
725	C₂×Q₈	—	4	8	no	—
726	C₂×Q₈	—	4	8	no	—
727	C₂×Q₈	—	4	8	no	—
728	C₂×Q₈	—	4	8	no	—
729	C₂×Q₈	—	8	4	no	—
730	C₂×Q₈	—	8	8	no	—
731	C₂×Q₈	—	8	8	no	—
732	C₂×Q₈	C₂²×D₄	1	2	yes	—
733	C₂×Q₈	C₂²×D₄	1	4	yes	—
734	C₂×Q₈	C₂⁵	1	8	yes	—
735	C₂×Q₈	C₂⁵	1	4	yes	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	16	no	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	8	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	16	no	—
744	C₂×D₄	—	2	8	no	—
745	C₂×D₄	—	2	8	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	4	8	no	—
749	C₂×D₄	—	4	8	no	—
750	C₂×D₄	—	4	8	no	—
751	C₂×D₄	—	4	8	no	—
752	C₂×D₄	—	8	8	no	—
753	C₂×D₄	—	8	4	no	—
754	C₂×D₄	—	8	8	no	—
755	C₂×D₄	—	8	32	no	—
756	C₂×D₄	—	8	16	no	—
757	C₂×D₄	C₂²×D₄	1	8	yes	—
758	C₂×D₄	C₂²×D₄	1	4	yes	—
759	C₂×D₄	C₂²×D₄	1	2	yes	—
760	C₂×D₄	C₂²×D₄	1	4	yes	—
761	C₂×D₄	C₂⁵	1	8	yes	—
762	C₂×D₄	C₂⁵	1	4	yes	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	8	no	—
767	C₂²×C₄	—	2	8	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	8	no	—
770	C₂²×C₄	—	2	16	no	—
771	C₂²×C₄	—	2	8	no	—
772	C₂²×C₄	—	2	8	no	—
773	C₂²×C₄	—	4	4	no	—
774	C₂²×C₄	—	8	4	no	—
775	C₂²×C₄	C₂²×D₄	1	2	yes	—
776	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
777	C₂²×C₄	C₂²×D₄	1	2	yes	—
778	C₂²×C₄	C₂²×D₄	1	2	yes	—
779	C₂²×C₄	C₂²×D₄	1	2	yes	—
780	C₂²×C₄	C₂²×D₄	1	2	yes	—
781	C₂²×C₄	C₂²×D₄	1	2	yes	—
782	C₂²×C₄	C₂²×D₄	1	2	yes	—
783	C₂²×C₄	C₂²×D₄	1	8	yes	—
784	C₂²×C₄	C₂⁵	1	2	yes	—
785	C₂²×C₄	C₂⁵	1	4	yes	—
786	C₂²×C₄	C₂⁵	1	1	yes	characteristic
787	Q₁₆	—	2	8	no	—
788	Q₁₆	—	2	8	no	—
789	Q₁₆	—	2	4	no	—
790	Q₁₆	—	2	4	no	—
791	Q₁₆	—	4	8	no	—
792	Q₁₆	—	4	8	no	—
793	Q₁₆	—	4	8	no	—
794	SD₁₆	—	2	16	no	—
795	SD₁₆	—	2	16	no	—
796	SD₁₆	—	2	8	no	—
797	SD₁₆	—	2	8	no	—
798	SD₁₆	—	4	16	no	—
799	SD₁₆	—	4	8	no	—
800	SD₁₆	—	4	8	no	—
801	SD₁₆	—	4	8	no	—
802	SD₁₆	—	4	8	no	—
803	D₈	—	2	8	no	—
804	D₈	—	2	8	no	—
805	D₈	—	2	4	no	—
806	D₈	—	2	4	no	—
807	D₈	—	4	8	no	—
808	D₈	—	4	8	no	—
809	D₈	—	4	8	no	—
810	M₁₆	—	2	4	no	—
811	M₁₆	—	2	4	no	—
812	M₁₆	—	2	8	no	—
813	M₁₆	—	2	8	no	—
814	C₂×C₈	—	2	2	no	—
815	C₂×C₈	—	2	2	no	—
816	C₂×C₈	—	2	4	no	—
817	C₂×C₈	—	2	4	no	—
818	C₂×C₈	—	2	4	no	—
819	C₂×C₈	—	2	4	no	—
820	C₂×C₈	—	2	8	no	—
821	C₂×C₈	—	2	8	no	—
822	C₂×C₈	H(5,𝔽₂)	1	4	yes	—
823	C₂×C₈	H(5,𝔽₂)	1	4	yes	—
824	C₂×C₈	C₂⁵	1	2	yes	—
825	C₂×C₈	C₂⁵	1	2	yes	—
826	C₂×C₈	C₂⁵	1	4	yes	—
827	C₂×C₈	C₂⁵	1	4	yes	—
828	C₂×C₈	C₂⁵	1	1	yes	characteristic
829	C₂×C₈	C₂⁵	1	1	yes	characteristic
830	C₂×C₈	C₂⁵	1	1	yes	characteristic
831	C₂×C₈	C₂⁵	1	1	yes	characteristic
832	C₄⋊C₄	—	2	8	no	—
833	C₄⋊C₄	—	2	16	no	—
834	C₄⋊C₄	—	2	16	no	—
835	C₄⋊C₄	—	2	8	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	8	no	—
839	C₄⋊C₄	—	2	16	no	—
840	C₄⋊C₄	C₂²×D₄	1	8	yes	—
841	C₄⋊C₄	C₂²×D₄	1	4	yes	—
842	C₄⋊C₄	C₂²×D₄	1	8	yes	—
843	C₄⋊C₄	C₂²×D₄	1	4	yes	—
844	C₄⋊C₄	C₂²×D₄	1	4	yes	—
845	C₄⋊C₄	C₂²×D₄	1	8	yes	—
846	C₄⋊C₄	C₂⁵	1	8	yes	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	8	no	—
849	C₂²⋊C₄	—	2	16	no	—
850	C₂²⋊C₄	—	2	16	no	—
851	C₂²⋊C₄	—	2	16	no	—
852	C₂²⋊C₄	—	2	16	no	—
853	C₂²⋊C₄	—	2	16	no	—
854	C₂²⋊C₄	—	2	8	no	—
855	C₂²⋊C₄	—	2	16	no	—
856	C₂²⋊C₄	—	2	16	no	—
857	C₂²⋊C₄	—	2	16	no	—
858	C₂²⋊C₄	—	2	16	no	—
859	C₂²⋊C₄	—	2	8	no	—
860	C₂²⋊C₄	—	2	8	no	—
861	C₂²⋊C₄	C₂²×D₄	1	4	yes	—
862	C₂²⋊C₄	C₂²×D₄	1	8	yes	—
863	C₂²⋊C₄	C₂²×D₄	1	8	yes	—
864	C₂²⋊C₄	C₂²×D₄	1	8	yes	—
865	C₂²⋊C₄	C₂²×D₄	1	8	yes	—
866	C₄²	—	2	8	no	—
867	C₄²	—	2	4	no	—
868	C₄²	—	2	16	no	—
869	C₄²	C₂²×D₄	1	1	yes	characteristic
870	C₄²	C₂²×D₄	1	2	yes	—
871	C₄²	C₂²×D₄	1	1	yes	characteristic
872	C₄²	C₂²×D₄	1	2	yes	—
873	C₄²	C₂²×D₄	1	2	yes	—
874	C₄²	C₂²×D₄	1	2	yes	—
875	C₄²	C₂²×D₄	1	2	yes	—
876	C₄²	C₂²×D₄	1	8	yes	—
877	C₄²	C₂⁵	1	1	yes	characteristic
878	C₄²	C₂⁵	1	1	yes	characteristic
879	C₄²	C₂⁵	1	2	yes	—
880	C₄²	C₂⁵	1	4	yes	—
881	C₂³	—	2	4	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	8	no	—
884	C₂³	—	2	4	no	—
885	C₂³	—	4	16	no	—
886	C₂³	—	4	8	no	—
887	C₂³	—	8	8	no	—
888	C₂³	—	8	8	no	—
889	C₂³	—	8	8	no	—
890	C₂³	—	8	8	no	—
891	C₂³	—	8	16	no	—
892	C₂³	—	16	16	no	—
893	C₂³	C₂³×D₄	1	4	yes	—
894	C₂³	C₂³×D₄	1	2	yes	—
895	C₂³	C₂³×D₄	1	1	yes	characteristic
896	Q₈	—	2	4	no	—
897	Q₈	—	2	8	no	—
898	Q₈	—	2	4	no	—
899	Q₈	—	2	4	no	—
900	Q₈	—	2	8	no	—
901	Q₈	—	4	4	no	—
902	Q₈	—	4	8	no	—
903	Q₈	—	8	8	no	—
904	Q₈	—	8	8	no	—
905	Q₈	—	8	4	no	—
906	D₄	—	2	16	no	—
907	D₄	—	2	8	no	—
908	D₄	—	2	8	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	4	no	—
911	D₄	—	2	8	no	—
912	D₄	—	2	4	no	—
913	D₄	—	4	4	no	—
914	D₄	—	4	16	no	—
915	D₄	—	4	8	no	—
916	D₄	—	4	8	no	—
917	D₄	—	8	8	no	—
918	D₄	—	8	8	no	—
919	D₄	—	8	16	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	16	no	—
922	D₄	—	8	8	no	—
923	D₄	—	8	8	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	2	4	no	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	4	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	8	no	—
940	C₂×C₄	—	4	8	no	—
941	C₂×C₄	—	4	8	no	—
942	C₂×C₄	—	8	16	no	—
943	C₂×C₄	—	8	8	no	—
944	C₂×C₄	—	8	8	no	—
945	C₂×C₄	—	8	8	no	—
946	C₂×C₄	—	8	8	no	—
947	C₂×C₄	—	8	8	no	—
948	C₂×C₄	C₂³×D₄	1	2	yes	—
949	C₂×C₄	C₂³×D₄	1	8	yes	—
950	C₂×C₄	C₂³×D₄	1	2	yes	—
951	C₂×C₄	C₂³×D₄	1	2	yes	—
952	C₂×C₄	C₂³×D₄	1	2	yes	—
953	C₂×C₄	C₂³×D₄	1	2	yes	—
954	C₂×C₄	C₂³×D₄	1	4	yes	—
955	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
956	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
957	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
958	C₂×C₄	C₂⁶	1	1	yes	characteristic
959	C₈	—	2	2	no	—
960	C₈	—	2	2	no	—
961	C₈	—	2	4	no	—
962	C₈	—	2	4	no	—
963	C₈	C₂×H(5,𝔽₂)	1	2	yes	—
964	C₈	C₂×H(5,𝔽₂)	1	2	yes	—
965	C₈	C₂×H(5,𝔽₂)	1	2	yes	—
966	C₈	C₂×H(5,𝔽₂)	1	2	yes	—
967	C₂²	—	2	8	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	8	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	8	no	—
975	C₂²	—	4	8	no	—
976	C₂²	—	4	16	no	—
977	C₂²	—	16	16	no	—
978	C₂²	—	16	8	no	—
979	C₂²	—	32	8	no	—
980	C₂²	#3498	1	2	yes	—
981	C₂²	#3584	1	4	yes	—
982	C₂²	C₂⁴×D₄	1	1	yes	characteristic
983	C₄	—	2	2	no	—
984	C₄	—	2	4	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	8	no	—
990	C₄	—	4	4	no	—
991	C₄	—	4	8	no	—
992	C₄	—	4	8	no	—
993	C₄	#3498	1	2	yes	—
994	C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
995	C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
996	C₂	—	2	4	no	—
997	C₂	—	2	2	no	—
998	C₂	—	4	4	no	—
999	C₂	—	8	8	no	—
1000	C₂	—	8	4	no	—
1001	C₂	C₂×#3498	1	1	yes	characteristic
1002	C₂	C₂×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂⁴×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁶
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #3444 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62824	C₂	semidirect
2. #62437	C₂	semidirect
3. #62436	C₂	semidirect
4. #62435	C₂	semidirect
5. #62428	C₂	semidirect
6. #62419	C₂	semidirect
7. #61413	C₂	semidirect
8. #61412	C₂	semidirect
9. #61090	C₂	semidirect
10. #61088	C₂	semidirect
11. #61053	C₂	semidirect
12. #61050	C₂	semidirect
13. #61049	C₂	semidirect
14. #60819	C₂	semidirect
15. #60799	C₂	semidirect
16. #60713	C₂	semidirect
17. #60673	C₂	semidirect
18. #60649	C₂	semidirect
19. C₂²×#495	C₂	semidirect
20. #60204	C₂	semidirect
21. C₂×#578	C₂²	semidirect
22. C₂×#577	C₂²	semidirect
23. C₂×#576	C₂²	semidirect
24. C₂³×Q₁₆	C₂²	semidirect
25. C₂³×SD₁₆	C₂²	semidirect
28. #3561	C₂²	semidirect
30. #3558	C₂²	semidirect
33. #3514	C₂²	semidirect
34. #3510	C₂²	semidirect
35. #3510	C₂²	semidirect
36. #3500	C₂²	semidirect
37. #3500	C₂²	semidirect
39. #3486	C₂²	semidirect
40. #3484	C₂²	semidirect
42. #3444	C₂²	semidirect
43. C₂²×#124	C₂²	semidirect
44. #3403	C₂²	semidirect
45. #3402	C₂²	semidirect
46. #3401	C₂²	semidirect
47. #3396	C₂²	semidirect
48. #3394	C₂²	semidirect
49. #3393	C₂²	semidirect
50. D₄×Q₁₆	C₂²	semidirect
51. #3285	C₂²	semidirect
52. #3285	C₂²	semidirect
53. #3282	C₂²	semidirect
54. #3282	C₂²	semidirect
55. D₄×SD₁₆	C₂²	semidirect
56. #3280	C₂²	semidirect
57. #3280	C₂²	semidirect
58. D₄×D₈	C₂²	semidirect
59. #3277	C₂²	semidirect
60. #3275	C₂²	semidirect
61. #3273	C₂²	semidirect
62. #3270	C₂²	semidirect
63. #3266	C₂²	semidirect
64. #3265	C₂²	semidirect
65. #3264	C₂²	semidirect
66. #3225	C₂²	semidirect
67. #3224	C₂²	semidirect
68. #3215	C₂²	semidirect
69. #3213	C₂²	semidirect
70. #3212	C₂²	semidirect
71. #3211	C₂²	semidirect
72. #3211	C₂²	semidirect
73. #3183	C₂²	semidirect
74. #3175	C₂²	semidirect
75. #3173	C₂²	semidirect
76. #3170	C₂²	semidirect
77. #3169	C₂²	semidirect
78. #3168	C₂²	semidirect
79. #3168	C₂²	semidirect
80. #3168	C₂²	semidirect
81. #3167	C₂²	semidirect
82. #3160	C₂²	semidirect
83. #3156	C₂²	semidirect
84. #3156	C₂²	semidirect
86. #3155	C₂²	semidirect
87. #3154	C₂²	semidirect
88. #3154	C₂²	semidirect
89. #3153	C₂²	semidirect
90. #3153	C₂²	semidirect
91. #3147	C₂²	semidirect
92. #3147	C₂²	semidirect
93. C₂×#495	C₂²	semidirect
94. C₂×#495	C₂²	semidirect
95. C₂×#495	C₂²	semidirect
96. C₂×#495	C₂²	semidirect
97. C₂×#495	C₂²	semidirect
98. C₂×#495	C₂²	semidirect
99. C₂×#495	C₂²	semidirect
100. C₂×#495	C₂²	semidirect
101. C₂×#495	C₂²	semidirect
102. #3140	C₂²	semidirect
103. #3131	C₂²	semidirect
104. #3059	C₂²	semidirect
106. #3057	C₂²	semidirect
107. #3050	C₂²	semidirect
108. #3050	C₂²	semidirect
109. #3044	C₂²	semidirect
110. #3043	C₂²	semidirect
111. #3042	C₂²	semidirect
112. #3041	C₂²	semidirect
113. #3040	C₂²	semidirect
114. #3040	C₂²	semidirect
115. #3011	C₂²	semidirect
116. #3010	C₂²	semidirect
117. #3009	C₂²	semidirect
118. #3008	C₂²	semidirect
119. #3004	C₂²	semidirect
120. #3003	C₂²	semidirect
121. #2966	C₂²	semidirect
122. #2966	C₂²	semidirect
123. #2965	C₂²	semidirect
124. C₈×#41	C₂²	semidirect
125. #2960	C₂²	semidirect
126. #2960	C₂²	semidirect
127. #2950	C₂²	semidirect
128. #2949	C₂²	semidirect
129. #2948	C₂²	semidirect
130. C₄×#135	C₂²	semidirect
131. C₄×#135	C₂²	semidirect
132. #2931	C₂²	semidirect
133. #2931	C₂²	semidirect
134. #2929	C₂²	semidirect
135. #2929	C₂²	semidirect
136. #2922	C₂²	semidirect
137. #2920	C₂²	semidirect
138. C₄×#131	C₂²	semidirect
139. C₂²×C₄×C₈	C₂²	semidirect
149. C₂×#137	C₂³	semidirect
150. C₂×#137	C₂³	semidirect
154. C₂×AGL(1,ℤ/8)	C₂³	semidirect
158. C₂×#135	C₂³	semidirect
159. C₂×#135	C₂³	semidirect
165. C₂²×Q₁₆	C₂³	semidirect
171. C₂²×SD₁₆	C₂³	semidirect
187. #559	C₂³	semidirect
189. #556	C₂³	semidirect
201. #548	C₂³	semidirect
209. #546	C₂³	semidirect
216. #542	C₂³	semidirect
226. #536	C₂³	semidirect
230. #535	C₂³	semidirect
242. #532	C₂³	semidirect
250. #529	C₂³	semidirect
259. C₂×#124	C₂³	semidirect
275. #500	C₂³	semidirect
276. #499	C₂³	semidirect
277. #499	C₂³	semidirect
278. #498	C₂³	semidirect
279. #497	C₂³	semidirect
280. #497	C₂³	semidirect
281. #497	C₂³	semidirect
283. #496	C₂³	semidirect
284. #496	C₂³	semidirect
296. #495	C₂³	semidirect
297. #495	C₂³	semidirect
298. #495	C₂³	semidirect
299. #495	C₂³	semidirect
300. #495	C₂³	semidirect
301. #495	C₂³	semidirect
302. #494	C₂³	semidirect
303. #494	C₂³	semidirect
305. #493	C₂³	semidirect
306. #492	C₂³	semidirect
307. #492	C₂³	semidirect
308. #489	C₂³	semidirect
309. #488	C₂³	semidirect
310. #488	C₂³	semidirect
311. #487	C₂³	semidirect
312. #486	C₂³	semidirect
313. #470	C₂³	semidirect
315. #468	C₂³	semidirect
318. #467	C₂³	semidirect
324. #465	C₂³	semidirect
325. #464	C₂³	semidirect
326. #464	C₂³	semidirect
327. #464	C₂³	semidirect
328. #464	C₂³	semidirect
330. #463	C₂³	semidirect
331. #463	C₂³	semidirect
332. #463	C₂³	semidirect
333. #462	C₂³	semidirect
334. #461	C₂³	semidirect
335. #460	C₂³	semidirect
337. #452	C₂³	semidirect
338. #452	C₂³	semidirect
340. #451	C₂³	semidirect
342. #450	C₂³	semidirect
344. #449	C₂³	semidirect
346. #448	C₂³	semidirect
349. #446	C₂³	semidirect
350. #446	C₂³	semidirect
351. C₈×Q₈	C₂³	semidirect
352. C₈×Q₈	C₂³	semidirect
354. #441	C₂³	semidirect
355. #440	C₂³	semidirect
356. C₄×Q₁₆	C₂³	semidirect
357. C₄×Q₁₆	C₂³	semidirect
358. C₄×Q₁₆	C₂³	semidirect
359. C₄×SD₁₆	C₂³	semidirect
360. C₄×SD₁₆	C₂³	semidirect
361. C₄×SD₁₆	C₂³	semidirect
363. C₄×D₈	C₂³	semidirect
364. C₄×D₈	C₂³	semidirect
365. #436	C₂³	semidirect
366. #436	C₂³	semidirect
371. C₈×D₄	C₂³	semidirect
372. C₈×D₄	C₂³	semidirect
373. #433	C₂³	semidirect
376. #431	C₂³	semidirect
394. #405	C₂³	semidirect
395. #405	C₂³	semidirect
397. C₄×M₁₆	C₂³	semidirect
406. C₂×C₄×C₈	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#62824	2
#62437	2
#62436	2
#62435	2
#62428	2
#62419	2
#61413	2
#61412	2
#61090	2
#61088	2
#61053	2
#61050	2
#61049	2
#60819	2
#60799	2
#60713	2
#60673	2
#60649	2
C₂²×#495	2
#60204	2