Subgroups — #30593875

Order 15616.

10796 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460631	C₂	1	1	yes	maximal, characteristic, complemented
2	#21460629	C₂	1	1	yes	maximal, characteristic, complemented
3	#21460606	C₂	1	1	yes	maximal, characteristic, complemented
4	#21460602	C₂	1	6	yes	maximal, complemented
5	#21460601	C₂	1	8	yes	maximal, complemented
6	#21460599	C₂	1	1	yes	maximal, characteristic, complemented
7	#21460597	C₂	1	8	yes	maximal, complemented
8	#21460595	C₂	1	6	yes	maximal, complemented
9	#21460593	C₂	1	1	yes	maximal, characteristic, complemented
10	#21460591	C₂	1	8	yes	maximal, complemented
11	#21460588	C₂	1	6	yes	maximal, complemented
12	C₂×#16840568	C₂	1	6	yes	maximal, complemented
13	#577×D₆₁	C₂	1	8	yes	maximal, complemented
14	#21460530	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
16	#16840599	—	2	4	no	—
17	#16840599	C₂²	1	8	yes	complemented
18	#16840598	—	2	2	no	—
19	#16840598	—	2	6	no	—
20	#16840598	C₂²	1	1	yes	characteristic
21	#16840598	C₂²	1	1	yes	characteristic, complemented
22	#16840598	C₂²	1	1	yes	characteristic, complemented
23	#16840598	C₂²	1	6	yes	complemented
24	#16840598	C₂²	1	6	yes	complemented
25	#16840597	—	2	4	no	—
26	#16840597	C₂²	1	8	yes	complemented
27	C₂×#14519825	—	2	2	no	—
28	C₂×#14519825	C₂²	1	6	yes	complemented
29	2₋¹⁺⁴×D₆₁	—	2	4	no	—
30	2₋¹⁺⁴×D₆₁	C₂²	1	8	yes	complemented
31	C₂×#14519822	—	2	6	no	—
32	C₂×#14519822	C₂²	1	6	yes	complemented
33	H(5,𝔽₂)×D₆₁	—	2	4	no	—
34	H(5,𝔽₂)×D₆₁	C₂²	1	8	yes	complemented
35	#16840579	C₂²	1	4	yes	complemented
36	#16840578	C₂²	1	24	yes	complemented
37	#16840577	C₂²	1	8	yes	complemented
38	#16840576	C₂²	1	12	yes	complemented
39	#16840575	C₂²	1	12	yes	complemented
40	#16840574	C₂²	1	4	yes	complemented
41	#16840574	C₂²	1	4	yes	complemented
42	#16840573	C₂²	1	8	yes	complemented
43	#16840572	C₂²	1	24	yes	complemented
44	#16840571	C₂²	1	24	yes	complemented
45	#16840570	C₂²	1	8	yes	complemented
46	#16840569	C₂²	1	12	yes	complemented
47	#16840569	C₂²	1	12	yes	complemented
48	#16840568	C₂²	1	24	yes	complemented
49	#16840568	C₂²	1	12	yes	complemented
50	#16840568	C₂²	1	24	yes	complemented
51	#16840568	C₂²	1	24	yes	complemented
52	#16840568	C₂²	1	4	yes	complemented
53	#16840567	C₂²	1	4	yes	complemented
54	#16840566	C₂²	1	24	yes	complemented
55	#16840565	C₂²	1	8	yes	complemented
56	#16840564	C₂²	1	12	yes	complemented
57	#16840563	C₂²	1	12	yes	complemented
58	#16840562	C₂²	1	6	yes	complemented
59	#16840561	C₂²	1	24	yes	complemented
60	#16840560	C₂²	1	6	yes	complemented
61	#16840560	C₂²	1	6	yes	complemented
62	#16840559	C₂²	1	24	yes	complemented
63	#16840558	C₂²	1	24	yes	complemented
64	C₂×#14519808	C₂²	1	6	yes	complemented
65	C₂×#14519806	C₂²	1	12	yes	complemented
66	#137×D₆₁	C₂²	1	24	yes	complemented
67	C₂×#14519804	C₂²	1	12	yes	complemented
68	C₂×#14519803	C₂²	1	6	yes	complemented
69	AGL(1,ℤ/8)×D₆₁	C₂²	1	24	yes	complemented
70	C₂×#14519799	C₂²	1	6	yes	complemented
71	C₂×#14519798	C₂²	1	12	yes	complemented
72	#135×D₆₁	C₂²	1	24	yes	complemented
73	C₂×SD₁₆×D₆₁	C₂²	1	12	yes	complemented
74	#16840529	C₂²	1	1	yes	characteristic, complemented
75	#16840528	C₂²	1	6	yes	complemented
76	#16840527	C₂²	1	8	yes	complemented
77	C₂×#14519783	C₂²	1	6	yes	complemented
78	#131×D₆₁	C₂²	1	8	yes	complemented
79	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic, complemented
80	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#577	C₂²	1	8	yes	complemented
82	C₆₁×#577	C₂²	1	8	yes	complemented
83	C₂×#137×C₆₁	C₂²	1	3	yes	complemented
84	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	3	yes	complemented
85	C₂×#135×C₆₁	C₂²	1	3	yes	complemented
86	C₂²×SD₁₆×C₆₁	C₂²	1	3	yes	complemented
87	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic, complemented
88	#14519825	—	2	1	no	—
89	#14519825	—	2	1	no	—
90	#14519825	—	2	8	no	—
91	#14519825	—	2	8	no	—
92	#14519825	—	2	12	no	—
93	#14519825	—	2	12	no	—
94	#14519825	D₄	1	2	yes	—
95	#14519825	C₂³	1	4	yes	—
96	#14519825	C₂³	1	12	yes	complemented
97	#14519825	C₂³	1	24	yes	complemented
98	#14519824	—	2	8	no	—
99	#14519824	—	2	24	no	—
100	#14519824	—	2	6	no	—
101	#14519824	—	2	6	no	—
102	#14519824	D₄	1	4	yes	—
103	#14519824	C₂³	1	12	yes	—
104	#14519824	C₂³	1	4	yes	—
105	#14519824	C₂³	1	12	yes	complemented
106	#14519824	C₂³	1	4	yes	complemented
107	#14519823	—	2	8	no	—
108	#14519823	—	2	24	no	—
109	#14519823	—	2	6	no	—
110	#14519823	—	2	6	no	—
111	#14519823	D₄	1	4	yes	—
112	#14519823	C₂³	1	12	yes	—
113	#14519823	C₂³	1	4	yes	—
114	#14519823	C₂³	1	12	yes	complemented
115	#14519823	C₂³	1	4	yes	complemented
116	#14519822	—	2	3	no	—
117	#14519822	—	2	3	no	—
118	#14519822	—	2	12	no	—
119	#14519822	—	2	12	no	—
120	#14519822	—	2	24	no	—
121	#14519822	—	2	24	no	—
122	#14519822	—	2	12	no	—
123	#14519822	—	2	12	no	—
124	#14519822	D₄	1	6	yes	—
125	#14519822	C₂³	1	12	yes	—
126	#14519822	C₂³	1	24	yes	—
127	#14519822	C₂³	1	4	yes	complemented
128	C₂×#11758226	—	2	8	no	—
129	C₂×#11758226	—	2	6	no	—
130	C₂×#11758226	C₂³	1	12	yes	complemented
131	C₂×#11758222	—	2	12	no	—
132	C₂×#11758222	—	2	12	no	—
133	C₂×#11758222	—	2	12	no	—
134	C₂×#11758222	C₂³	1	6	yes	—
135	C₂×#11758222	C₂³	1	6	yes	—
136	C₂×#11758222	C₂³	1	6	yes	complemented
137	C₂×#11758224	—	2	24	no	—
138	C₂×#11758224	—	2	6	no	—
139	C₂×#11758224	C₂³	1	12	yes	—
140	#41×D₆₁	—	2	4	no	—
141	#41×D₆₁	—	2	4	no	—
142	#41×D₆₁	—	2	8	no	—
143	#41×D₆₁	—	2	8	no	—
144	#41×D₆₁	—	2	24	no	—
145	#41×D₆₁	—	2	24	no	—
146	#41×D₆₁	—	2	12	no	—
147	#41×D₆₁	—	2	12	no	—
148	#41×D₆₁	C₂³	1	24	yes	—
149	#41×D₆₁	C₂³	1	8	yes	—
150	#41×D₆₁	C₂³	1	24	yes	complemented
151	C₂×Q₈×D₆₁	—	2	8	no	—
152	C₂×Q₈×D₆₁	—	2	6	no	—
153	C₂×Q₈×D₆₁	C₂³	1	12	yes	complemented
154	C₂²×C₂²⋊D₆₁	—	2	12	no	—
155	C₂×D₄×D₆₁	—	2	24	no	—
156	C₂×D₄×D₆₁	—	2	6	no	—
157	C₂×D₄×D₆₁	C₂³	1	12	yes	—
158	#14519810	C₂³	1	12	yes	complemented
159	#14519810	C₂³	1	12	yes	complemented
160	#14519809	C₂³	1	24	yes	complemented
161	#14519809	C₂³	1	24	yes	complemented
162	#14519808	C₂³	1	24	yes	complemented
163	#14519808	C₂³	1	12	yes	complemented
164	#14519808	C₂³	1	4	yes	complemented
165	#14519807	C₂³	1	12	yes	complemented
166	#14519807	C₂³	1	12	yes	complemented
167	#14519806	C₂³	1	48	yes	complemented
168	#14519806	C₂³	1	24	yes	complemented
169	#14519806	C₂³	1	8	yes	complemented
170	#14519805	C₂³	1	12	yes	complemented
171	#14519805	C₂³	1	12	yes	complemented
172	#14519804	C₂³	1	48	yes	complemented
173	#14519804	C₂³	1	24	yes	complemented
174	#14519804	C₂³	1	8	yes	complemented
175	#14519803	C₂³	1	24	yes	complemented
176	#14519803	C₂³	1	12	yes	complemented
177	#14519803	C₂³	1	4	yes	complemented
178	#14519802	C₂³	1	12	yes	complemented
179	#14519802	C₂³	1	12	yes	complemented
180	#14519801	C₂³	1	24	yes	complemented
181	#14519801	C₂³	1	24	yes	complemented
182	#14519800	C₂³	1	24	yes	complemented
183	#14519799	C₂³	1	12	yes	complemented
184	#14519799	C₂³	1	4	yes	complemented
185	#14519799	C₂³	1	12	yes	complemented
186	#14519799	C₂³	1	12	yes	complemented
187	#14519798	C₂³	1	8	yes	complemented
188	#14519798	C₂³	1	24	yes	complemented
189	#14519798	C₂³	1	48	yes	complemented
190	#14519797	C₂³	1	24	yes	complemented
191	#14519797	C₂³	1	24	yes	complemented
192	#14519796	C₂³	1	24	yes	complemented
193	C₂×Dic₂₄₄	C₂³	1	6	yes	complemented
194	C₂×#11758202	C₂³	1	12	yes	complemented
195	Q₁₆×D₆₁	C₂³	1	24	yes	complemented
196	C₂×#11758190	C₂³	1	6	yes	complemented
197	C₂×#11758190	C₂³	1	6	yes	complemented
198	C₂×#11758200	C₂³	1	12	yes	complemented
199	C₂×#11758201	C₂³	1	12	yes	complemented
200	SD₁₆×D₆₁	C₂³	1	24	yes	complemented
201	SD₁₆×D₆₁	C₂³	1	48	yes	complemented
202	SD₁₆×D₆₁	C₂³	1	8	yes	complemented
203	C₂×D₄₈₈	C₂³	1	6	yes	complemented
204	C₂×#11758199	C₂³	1	12	yes	complemented
205	D₈×D₆₁	C₂³	1	24	yes	complemented
206	#14519785	C₂³	1	24	yes	complemented
207	#14519784	C₂³	1	8	yes	complemented
208	#14519783	C₂³	1	12	yes	complemented
209	#14519783	C₂³	1	4	yes	complemented
210	#14519783	C₂³	1	12	yes	complemented
211	#14519783	C₂³	1	12	yes	complemented
212	C₂×#11758194	C₂³	1	6	yes	complemented
213	C₂×#11758189	C₂³	1	12	yes	complemented
214	M₁₆×D₆₁	C₂³	1	24	yes	complemented
215	C₂×C₈×D₆₁	C₂³	1	12	yes	complemented
216	2₋¹⁺⁴×C₆₁	—	2	4	no	—
217	2₋¹⁺⁴×C₆₁	C₂³	1	8	yes	complemented
218	H(5,𝔽₂)×C₆₁	—	2	4	no	—
219	H(5,𝔽₂)×C₆₁	C₂³	1	8	yes	—
220	C₂×#41×C₆₁	—	2	1	no	—
221	C₂×#41×C₆₁	—	2	3	no	—
222	C₂×#41×C₆₁	C₂³	1	3	yes	—
223	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
224	C₂×#41×C₆₁	C₂³	1	3	yes	complemented
225	C₂²×Q₈×C₆₁	—	2	1	no	—
226	C₂²×Q₈×C₆₁	C₂³	1	3	yes	complemented
227	C₂²×D₄×C₆₁	—	2	3	no	—
228	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
229	#137×C₆₁	C₂³	1	24	yes	complemented
230	AGL(1,ℤ/8)×C₆₁	C₂³	1	24	yes	complemented
231	#135×C₆₁	C₂³	1	12	yes	complemented
232	#135×C₆₁	C₂³	1	12	yes	complemented
233	C₂×Q₁₆×C₆₁	C₂³	1	3	yes	complemented
234	C₂×SD₁₆×C₆₁	C₂³	1	3	yes	complemented
235	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	complemented
236	C₂×SD₁₆×C₆₁	C₂³	1	12	yes	complemented
237	C₂×SD₁₆×C₆₁	C₂³	1	12	yes	complemented
238	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic, complemented
239	C₂×D₈×C₆₁	C₂³	1	3	yes	complemented
240	#131×C₆₁	C₂³	1	4	yes	complemented
241	#131×C₆₁	C₂³	1	4	yes	complemented
242	C₂×M₁₆×C₆₁	C₂³	1	3	yes	complemented
243	C₂²×C₈×C₆₁	C₂³	1	3	yes	complemented
244	C₂⁴×C₆₁	—	2	3	no	—
245	C₂³×D₆₁	—	2	12	no	—
246	#41×C₆₁	—	2	8	no	—
247	#41×C₆₁	—	2	24	no	—
248	#41×C₆₁	—	2	6	no	—
249	#41×C₆₁	—	2	6	no	—
250	#41×C₆₁	C₂×D₄	1	4	yes	—
251	#41×C₆₁	C₂⁴	1	12	yes	—
252	#41×C₆₁	C₂⁴	1	12	yes	—
253	#41×C₆₁	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₆₁	—	2	8	no	—
255	C₂×Q₈×C₆₁	—	2	6	no	—
256	C₂×Q₈×C₆₁	—	2	3	no	—
257	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
258	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
259	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
260	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
261	C₂×D₄×C₆₁	—	2	3	no	—
262	C₂×D₄×C₆₁	—	2	3	no	—
263	C₂×D₄×C₆₁	—	2	24	no	—
264	C₂×D₄×C₆₁	—	2	6	no	—
265	C₂×D₄×C₆₁	—	2	3	no	—
266	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
267	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
268	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
269	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₁	—	2	3	no	—
271	C₂²×C₄×C₆₁	—	2	3	no	—
272	C₂²×C₄×C₆₁	—	2	3	no	—
273	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
274	C₂×C₂²⋊D₆₁	—	2	6	no	—
275	C₂×C₂²⋊D₆₁	—	2	6	no	—
276	C₂×C₂²⋊D₆₁	—	2	12	no	—
277	C₂×C₂²⋊D₆₁	—	2	48	no	—
278	C₂×C₂²⋊D₆₁	—	2	24	no	—
279	C₂×C₂²⋊D₆₁	—	2	8	no	—
280	C₂×C₂²⋊D₆₁	—	2	12	no	—
281	C₂×C₂²⋊D₆₁	C₂×D₄	1	12	yes	—
282	C₂²×Dic₆₁	—	2	12	no	—
283	#11758226	—	2	4	no	—
284	#11758226	—	2	4	no	—
285	#11758226	—	2	4	no	—
286	#11758226	—	2	24	no	—
287	#11758226	—	2	12	no	—
288	#11758226	—	2	24	no	—
289	#11758226	C₂×D₄	1	8	yes	—
290	#11758226	C₂⁴	1	8	yes	—
291	#11758226	C₂⁴	1	24	yes	—
292	Q₈×D₆₁	—	2	4	no	—
293	Q₈×D₆₁	—	2	4	no	—
294	Q₈×D₆₁	—	2	24	no	—
295	Q₈×D₆₁	—	2	24	no	—
296	Q₈×D₆₁	—	2	12	no	—
297	Q₈×D₆₁	—	2	4	no	—
298	Q₈×D₆₁	C₂×D₄	1	8	yes	—
299	Q₈×D₆₁	C₂⁴	1	8	yes	—
300	Q₈×D₆₁	C₂⁴	1	24	yes	—
301	#11758224	—	2	12	no	—
302	#11758224	—	2	12	no	—
303	#11758224	—	2	24	no	—
304	#11758224	—	2	24	no	—
305	#11758224	—	2	24	no	—
306	#11758224	—	2	24	no	—
307	#11758224	—	2	24	no	—
308	#11758224	—	2	4	no	—
309	#11758224	—	2	24	no	—
310	#11758224	—	2	12	no	—
311	#11758224	C₂×D₄	1	24	yes	—
312	#11758224	C₂⁴	1	24	yes	—
313	#11758224	C₂⁴	1	8	yes	—
314	D₄×D₆₁	—	2	24	no	—
315	D₄×D₆₁	—	2	24	no	—
316	D₄×D₆₁	—	2	12	no	—
317	D₄×D₆₁	—	2	12	no	—
318	D₄×D₆₁	—	2	24	no	—
319	D₄×D₆₁	—	2	24	no	—
320	D₄×D₆₁	—	2	24	no	—
321	D₄×D₆₁	—	2	12	no	—
322	D₄×D₆₁	—	2	4	no	—
323	D₄×D₆₁	—	2	24	no	—
324	D₄×D₆₁	C₂×D₄	1	24	yes	—
325	D₄×D₆₁	C₂⁴	1	24	yes	—
326	D₄×D₆₁	C₂⁴	1	8	yes	—
327	#11758222	—	2	6	no	—
328	#11758222	—	2	6	no	—
329	#11758222	—	2	6	no	—
330	#11758222	—	2	6	no	—
331	#11758222	—	2	48	no	—
332	#11758222	—	2	8	no	—
333	#11758222	—	2	24	no	—
334	#11758222	—	2	12	no	—
335	#11758222	—	2	12	no	—
336	#11758222	—	2	24	no	—
337	#11758222	—	2	24	no	—
338	#11758222	—	2	12	no	—
339	#11758222	—	2	12	no	—
340	#11758222	C₂×D₄	1	12	yes	—
341	#11758222	C₂×D₄	1	12	yes	—
342	#11758222	C₂⁴	1	12	yes	—
343	#11758222	C₂⁴	1	4	yes	—
344	#11758222	C₂⁴	1	4	yes	—
345	#11758222	C₂⁴	1	12	yes	—
346	#11758222	C₂⁴	1	4	yes	—
347	#11758222	C₂⁴	1	12	yes	—
348	C₂×D₂₄₄	—	2	12	no	—
349	C₂×D₂₄₄	—	2	12	no	—
350	C₂×D₂₄₄	—	2	12	no	—
351	C₂×D₂₄₄	C₂×D₄	1	6	yes	—
352	C₂×D₂₄₄	C₂⁴	1	6	yes	—
353	C₂×D₂₄₄	C₂⁴	1	6	yes	—
354	C₂×C₄×D₆₁	—	2	12	no	—
355	C₂×C₄×D₆₁	—	2	6	no	—
356	C₂×C₄×D₆₁	—	2	6	no	—
357	C₂×C₄×D₆₁	—	2	12	no	—
358	C₂×C₄×D₆₁	—	2	24	no	—
359	C₂×C₄×D₆₁	—	2	24	no	—
360	C₂×C₄×D₆₁	C₂⁴	1	12	yes	—
361	C₂×Dic₁₂₂	—	2	12	no	—
362	C₂×Dic₁₂₂	—	2	12	no	—
363	C₂×Dic₁₂₂	—	2	12	no	—
364	C₂×Dic₁₂₂	C₂×D₄	1	6	yes	—
365	C₂×Dic₁₂₂	C₂⁴	1	6	yes	—
366	C₂×Dic₁₂₂	C₂⁴	1	6	yes	—
367	Q₁₆×C₆₁	C₂⁴	1	12	yes	—
368	SD₁₆×C₆₁	C₂⁴	1	6	yes	—
369	SD₁₆×C₆₁	C₂⁴	1	6	yes	—
370	SD₁₆×C₆₁	C₂⁴	1	24	yes	—
371	SD₁₆×C₆₁	C₂⁴	1	2	yes	—
372	SD₁₆×C₆₁	C₂⁴	1	2	yes	—
373	D₈×C₆₁	C₂⁴	1	12	yes	—
374	M₁₆×C₆₁	C₂⁴	1	12	yes	—
375	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
377	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
378	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
379	#11758202	C₂⁴	1	24	yes	—
380	#11758202	C₂⁴	1	8	yes	—
381	#11758201	C₂⁴	1	24	yes	—
382	#11758201	C₂⁴	1	8	yes	—
383	#11758200	C₂⁴	1	24	yes	—
384	#11758200	C₂⁴	1	8	yes	—
385	#11758199	C₂⁴	1	8	yes	—
386	#11758199	C₂⁴	1	24	yes	—
387	#11758194	C₂⁴	1	4	yes	—
388	#11758194	C₂⁴	1	12	yes	—
389	C₂×#92418	C₂⁴	1	12	yes	—
390	Dic₂₄₄	C₂⁴	1	12	yes	—
391	Dic₂₄₄	C₂⁴	1	4	yes	—
392	D₄₈₈	C₂⁴	1	12	yes	—
393	D₄₈₈	C₂⁴	1	4	yes	—
394	#11758190	C₂⁴	1	12	yes	—
395	#11758190	C₂⁴	1	12	yes	—
396	#11758190	C₂⁴	1	4	yes	—
397	#11758190	C₂⁴	1	4	yes	—
398	#11758189	C₂⁴	1	24	yes	—
399	#11758189	C₂⁴	1	8	yes	—
400	C₈×D₆₁	C₂⁴	1	8	yes	—
401	C₈×D₆₁	C₂⁴	1	24	yes	—
402	C₂³×C₆₁	—	2	12	no	—
403	C₂³×C₆₁	—	2	1	no	—
404	C₂³×C₆₁	—	2	3	no	—
405	C₂³×C₆₁	—	16	3	no	—
406	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
407	C₂²×D₆₁	—	2	6	no	—
408	C₂²×D₆₁	—	2	6	no	—
409	C₂²×D₆₁	—	2	8	no	—
410	C₂²×D₆₁	—	2	24	no	—
411	C₂²×D₆₁	—	16	12	no	—
412	C₂²×D₆₁	C₂²×D₄	1	12	yes	—
413	Q₈×C₆₁	—	2	12	no	—
414	Q₈×C₆₁	—	2	3	no	—
415	Q₈×C₆₁	—	2	1	no	—
416	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
417	Q₈×C₆₁	C₂⁵	1	6	yes	—
418	Q₈×C₆₁	C₂⁵	1	2	yes	—
419	D₄×C₆₁	—	2	12	no	—
420	D₄×C₆₁	—	2	12	no	—
421	D₄×C₆₁	—	2	12	no	—
422	D₄×C₆₁	—	2	3	no	—
423	D₄×C₆₁	—	2	1	no	—
424	D₄×C₆₁	C₂²×D₄	1	12	yes	—
425	D₄×C₆₁	C₂⁵	1	2	yes	—
426	D₄×C₆₁	C₂⁵	1	6	yes	—
427	C₂×C₄×C₆₁	—	2	12	no	—
428	C₂×C₄×C₆₁	—	2	1	no	—
429	C₂×C₄×C₆₁	—	2	3	no	—
430	C₂×C₄×C₆₁	—	2	12	no	—
431	C₂×C₄×C₆₁	—	2	12	no	—
432	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
433	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
434	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
435	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
436	C₂²⋊D₆₁	—	2	4	no	—
437	C₂²⋊D₆₁	—	2	12	no	—
438	C₂²⋊D₆₁	—	2	4	no	—
439	C₂²⋊D₆₁	—	2	12	no	—
440	C₂²⋊D₆₁	—	2	8	no	—
441	C₂²⋊D₆₁	—	2	24	no	—
442	C₂²⋊D₆₁	—	2	8	no	—
443	C₂²⋊D₆₁	—	2	24	no	—
444	C₂²⋊D₆₁	C₂²×D₄	1	8	yes	—
445	C₂²⋊D₆₁	C₂²×D₄	1	24	yes	—
446	C₂×Dic₆₁	—	2	6	no	—
447	C₂×Dic₆₁	—	2	6	no	—
448	C₂×Dic₆₁	—	2	8	no	—
449	C₂×Dic₆₁	—	2	24	no	—
450	C₂×Dic₆₁	C₂²×D₄	1	12	yes	—
451	D₂₄₄	—	2	8	no	—
452	D₂₄₄	—	2	24	no	—
453	D₂₄₄	—	2	6	no	—
454	D₂₄₄	—	2	6	no	—
455	D₂₄₄	C₂²×D₄	1	12	yes	—
456	D₂₄₄	C₂²×D₄	1	4	yes	—
457	D₂₄₄	C₂⁵	1	4	yes	—
458	D₂₄₄	C₂⁵	1	4	yes	—
459	C₄×D₆₁	—	2	8	no	—
460	C₄×D₆₁	—	2	24	no	—
461	C₄×D₆₁	—	2	12	no	—
462	C₄×D₆₁	—	2	4	no	—
463	C₄×D₆₁	—	2	12	no	—
464	C₄×D₆₁	—	2	4	no	—
465	C₄×D₆₁	—	2	8	no	—
466	C₄×D₆₁	—	2	24	no	—
467	C₄×D₆₁	C₂²×D₄	1	24	yes	—
468	C₄×D₆₁	C₂⁵	1	8	yes	—
469	Dic₁₂₂	—	2	6	no	—
470	Dic₁₂₂	—	2	6	no	—
471	Dic₁₂₂	—	2	8	no	—
472	Dic₁₂₂	—	2	24	no	—
473	Dic₁₂₂	C₂²×D₄	1	12	yes	—
474	Dic₁₂₂	C₂²×D₄	1	4	yes	—
475	Dic₁₂₂	C₂⁵	1	4	yes	—
476	Dic₁₂₂	C₂⁵	1	4	yes	—
477	C₈×C₆₁	C₂⁵	1	1	yes	characteristic
478	C₈×C₆₁	C₂⁵	1	6	yes	—
479	C₈×C₆₁	C₂⁵	1	1	yes	characteristic
480	#92418	C₂⁵	1	8	yes	—
481	#63092	—	61	1	no	maximal, Sylow
482	C₂²×C₆₁	—	2	2	no	—
483	C₂²×C₆₁	—	2	6	no	—
484	C₂²×C₆₁	—	4	3	no	—
485	C₂²×C₆₁	—	8	12	no	—
486	C₂²×C₆₁	—	8	1	no	—
487	C₂²×C₆₁	—	8	3	no	—
488	C₂²×C₆₁	C₂³×D₄	1	6	yes	—
489	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
490	C₂×D₆₁	—	2	4	no	—
491	C₂×D₆₁	—	2	4	no	—
492	C₂×D₆₁	—	4	12	no	—
493	C₂×D₆₁	—	8	8	no	—
494	C₂×D₆₁	—	8	24	no	—
495	C₂×D₆₁	—	8	6	no	—
496	C₂×D₆₁	—	8	6	no	—
497	C₂×D₆₁	C₂³×D₄	1	8	yes	—
498	C₄×C₆₁	—	2	2	no	—
499	C₄×C₆₁	—	2	6	no	—
500	C₄×C₆₁	C₂³×D₄	1	6	yes	—
501	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
502	C₄×C₆₁	C₂⁶	1	1	yes	characteristic
503	Dic₆₁	—	2	4	no	—
504	Dic₆₁	—	2	4	no	—
505	Dic₆₁	C₂³×D₄	1	8	yes	—
506	2₋¹⁺⁶	—	61	1	no	—
507	H(7,𝔽₂)	—	61	1	no	—
508	#3586	—	61	1	no	—
509	#3586	—	61	8	no	—
510	#3586	—	61	6	no	—
511	#3585	—	61	1	no	—
512	#3585	—	61	8	no	—
513	#3585	—	61	6	no	—
514	#3584	—	61	8	no	—
515	#3584	—	61	6	no	—
516	#3584	—	61	1	no	—
517	C₂×#577	—	61	8	no	—
518	C₂×#577	—	61	6	no	—
519	C₂×#577	D₆₁	1	1	yes	characteristic, complemented
520	#3573	—	61	1	no	—
521	C₂×C₆₁	—	2	6	no	—
522	C₂×C₆₁	—	2	1	no	—
523	C₂×C₆₁	—	4	2	no	—
524	C₂×C₆₁	—	4	6	no	—
525	C₂×C₆₁	C₂⁴×D₄	1	1	yes	characteristic
526	D₆₁	—	2	8	no	—
527	D₆₁	—	4	4	no	—
528	D₆₁	—	4	4	no	—
529	#585	—	61	1	no	—
530	#585	—	61	8	no	—
531	#585	—	61	8	no	—
532	#585	—	61	6	no	—
533	#585	—	61	1	no	—
534	#585	—	61	1	no	—
535	#585	—	61	6	no	—
536	#585	—	122	6	no	—
537	#585	—	122	2	no	—
538	#585	—	122	4	no	—
539	#585	—	122	4	no	—
540	C₂×2₋¹⁺⁴	—	61	8	no	—
541	C₂×2₋¹⁺⁴	—	61	6	no	—
542	C₂×2₋¹⁺⁴	—	122	2	no	—
543	C₂×2₋¹⁺⁴	—	122	4	no	—
544	C₂×2₋¹⁺⁴	C₂×D₆₁	1	1	yes	characteristic, complemented
545	C₂×H(5,𝔽₂)	—	61	8	no	—
546	C₂×H(5,𝔽₂)	—	61	6	no	—
547	C₂×H(5,𝔽₂)	—	122	6	no	—
548	C₂×H(5,𝔽₂)	—	122	4	no	—
549	C₂×H(5,𝔽₂)	C₂×D₆₁	1	1	yes	characteristic, complemented
550	#578	—	61	8	no	—
551	#578	—	61	24	no	—
552	#578	—	61	12	no	—
553	#578	—	61	12	no	—
554	#578	—	61	4	no	—
555	#577	—	61	8	no	—
556	#577	—	61	8	no	—
557	#577	—	61	24	no	—
558	#577	—	61	24	no	—
559	#577	—	61	12	no	—
560	#577	—	61	12	no	—
561	#577	—	61	4	no	—
562	#577	—	61	24	no	—
563	#577	—	61	12	no	—
564	#577	—	61	24	no	—
565	#577	—	61	24	no	—
566	#577	—	61	4	no	—
567	#577	—	61	4	no	—
568	#577	C₂×D₆₁	1	8	yes	complemented
569	#577	C₂×D₆₁	1	8	yes	complemented
570	#576	—	61	8	no	—
571	#576	—	61	24	no	—
572	#576	—	61	12	no	—
573	#576	—	61	12	no	—
574	#576	—	61	4	no	—
575	#575	—	61	6	no	—
576	#575	—	61	6	no	—
577	#575	—	61	24	no	—
578	#575	—	61	24	no	—
579	#575	—	61	24	no	—
580	#575	—	61	6	no	—
581	C₂×#137	—	61	6	no	—
582	C₂×#137	—	61	24	no	—
583	C₂×#137	—	61	12	no	—
584	C₂×#137	C₂×D₆₁	1	3	yes	complemented
585	C₂×AGL(1,ℤ/8)	—	61	6	no	—
586	C₂×AGL(1,ℤ/8)	—	61	24	no	—
587	C₂×AGL(1,ℤ/8)	—	61	12	no	—
588	C₂×AGL(1,ℤ/8)	C₂×D₆₁	1	3	yes	complemented
589	C₂×#135	—	61	24	no	—
590	C₂×#135	—	61	12	no	—
591	C₂×#135	—	61	6	no	—
592	C₂×#135	C₂×D₆₁	1	3	yes	complemented
593	C₂²×SD₁₆	—	61	12	no	—
594	C₂²×SD₁₆	C₂×D₆₁	1	3	yes	complemented
595	#568	—	61	1	no	—
596	#568	—	61	8	no	—
597	#568	—	61	6	no	—
598	C₂×#131	—	61	8	no	—
599	C₂×#131	—	61	6	no	—
600	C₂×#131	C₂×D₆₁	1	1	yes	characteristic, complemented
601	C₆₁	#63092	1	1	yes	characteristic, complemented, Sylow
602	2₋¹⁺⁴	—	2	4	no	—
603	2₋¹⁺⁴	—	61	4	no	—
604	2₋¹⁺⁴	—	61	2	no	—
605	2₋¹⁺⁴	—	61	12	no	—
606	2₋¹⁺⁴	—	61	4	no	—
607	2₋¹⁺⁴	—	61	12	no	—
608	2₋¹⁺⁴	—	61	4	no	—
609	2₋¹⁺⁴	—	61	4	no	—
610	2₋¹⁺⁴	—	61	24	no	—
611	2₋¹⁺⁴	—	61	12	no	—
612	2₋¹⁺⁴	—	122	8	no	—
613	2₋¹⁺⁴	—	122	8	no	—
614	2₋¹⁺⁴	—	122	12	no	—
615	2₋¹⁺⁴	—	122	12	no	—
616	2₋¹⁺⁴	—	122	6	no	—
617	2₋¹⁺⁴	—	122	8	no	—
618	2₋¹⁺⁴	—	122	6	no	—
619	2₋¹⁺⁴	—	122	24	no	—
620	2₋¹⁺⁴	—	122	1	no	—
621	2₋¹⁺⁴	—	122	1	no	—
622	2₋¹⁺⁴	C₂²×D₆₁	1	8	yes	complemented
623	H(5,𝔽₂)	—	2	4	no	—
624	H(5,𝔽₂)	—	61	4	no	—
625	H(5,𝔽₂)	—	61	6	no	—
626	H(5,𝔽₂)	—	61	12	no	—
627	H(5,𝔽₂)	—	61	4	no	—
628	H(5,𝔽₂)	—	61	12	no	—
629	H(5,𝔽₂)	—	61	4	no	—
630	H(5,𝔽₂)	—	61	24	no	—
631	H(5,𝔽₂)	—	61	12	no	—
632	H(5,𝔽₂)	—	61	4	no	—
633	H(5,𝔽₂)	—	122	12	no	—
634	H(5,𝔽₂)	—	122	24	no	—
635	H(5,𝔽₂)	—	122	12	no	—
636	H(5,𝔽₂)	—	122	24	no	—
637	H(5,𝔽₂)	—	122	12	no	—
638	H(5,𝔽₂)	—	122	12	no	—
639	H(5,𝔽₂)	—	122	6	no	—
640	H(5,𝔽₂)	—	122	24	no	—
641	H(5,𝔽₂)	—	122	6	no	—
642	H(5,𝔽₂)	—	122	8	no	—
643	H(5,𝔽₂)	—	122	3	no	—
644	H(5,𝔽₂)	—	122	3	no	—
645	H(5,𝔽₂)	C₂²×D₆₁	1	8	yes	—
646	C₂×#41	—	2	1	no	—
647	C₂×#41	—	2	3	no	—
648	C₂×#41	—	61	8	no	—
649	C₂×#41	—	61	6	no	—
650	C₂×#41	—	61	24	no	—
651	C₂×#41	—	61	24	no	—
652	C₂×#41	—	61	12	no	—
653	C₂×#41	—	61	12	no	—
654	C₂×#41	—	61	6	no	—
655	C₂×#41	—	61	6	no	—
656	C₂×#41	—	122	12	no	—
657	C₂×#41	—	122	12	no	—
658	C₂×#41	—	122	12	no	—
659	C₂×#41	—	122	6	no	—
660	C₂×#41	—	122	24	no	—
661	C₂×#41	—	122	6	no	—
662	C₂×#41	—	122	24	no	—
663	C₂×#41	—	122	8	no	—
664	C₂×#41	—	122	8	no	—
665	C₂×#41	—	122	8	no	—
666	C₂×#41	—	122	12	no	—
667	C₂×#41	—	122	24	no	—
668	C₂×#41	—	122	12	no	—
669	C₂×#41	—	122	4	no	—
670	C₂×#41	—	122	4	no	—
671	C₂×#41	C₂²×D₆₁	1	3	yes	—
672	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
673	C₂×#41	C₂²×D₆₁	1	3	yes	complemented
674	C₂²×Q₈	—	2	1	no	—
675	C₂²×Q₈	—	61	12	no	—
676	C₂²×Q₈	—	122	8	no	—
677	C₂²×Q₈	—	122	6	no	—
678	C₂²×Q₈	C₂²×D₆₁	1	3	yes	complemented
679	C₂²×D₄	—	2	3	no	—
680	C₂²×D₄	—	61	12	no	—
681	C₂²×D₄	—	122	24	no	—
682	C₂²×D₄	—	122	6	no	—
683	C₂²×D₄	—	122	12	no	—
684	C₂²×D₄	C₂²×D₆₁	1	3	yes	—
685	#137	—	61	12	no	—
686	#137	—	61	12	no	—
687	#137	—	61	24	no	—
688	#137	—	61	12	no	—
689	#137	—	61	4	no	—
690	#137	—	61	24	no	—
691	#137	—	61	24	no	—
692	#137	—	61	48	no	—
693	#137	—	61	24	no	—
694	#137	—	61	8	no	—
695	#137	—	61	12	no	—
696	#137	—	61	12	no	—
697	#137	C₂²×D₆₁	1	24	yes	complemented
698	AGL(1,ℤ/8)	—	61	12	no	—
699	AGL(1,ℤ/8)	—	61	12	no	—
700	AGL(1,ℤ/8)	—	61	24	no	—
701	AGL(1,ℤ/8)	—	61	12	no	—
702	AGL(1,ℤ/8)	—	61	4	no	—
703	AGL(1,ℤ/8)	—	61	48	no	—
704	AGL(1,ℤ/8)	—	61	24	no	—
705	AGL(1,ℤ/8)	—	61	8	no	—
706	AGL(1,ℤ/8)	—	61	24	no	—
707	AGL(1,ℤ/8)	—	61	24	no	—
708	AGL(1,ℤ/8)	—	61	12	no	—
709	AGL(1,ℤ/8)	—	61	12	no	—
710	AGL(1,ℤ/8)	C₂²×D₆₁	1	24	yes	complemented
711	#135	—	61	24	no	—
712	#135	—	61	24	no	—
713	#135	—	61	24	no	—
714	#135	—	61	8	no	—
715	#135	—	61	24	no	—
716	#135	—	61	48	no	—
717	#135	—	61	24	no	—
718	#135	—	61	12	no	—
719	#135	—	61	4	no	—
720	#135	—	61	12	no	—
721	#135	—	61	12	no	—
722	#135	C₂²×D₆₁	1	12	yes	complemented
723	#135	C₂²×D₆₁	1	12	yes	complemented
724	C₂×Q₁₆	—	61	12	no	—
725	C₂×Q₁₆	—	61	24	no	—
726	C₂×Q₁₆	—	61	6	no	—
727	C₂×Q₁₆	C₂²×D₆₁	1	3	yes	complemented
728	C₂×SD₁₆	—	61	12	no	—
729	C₂×SD₁₆	—	61	12	no	—
730	C₂×SD₁₆	—	61	24	no	—
731	C₂×SD₁₆	—	61	48	no	—
732	C₂×SD₁₆	—	61	8	no	—
733	C₂×SD₁₆	—	61	6	no	—
734	C₂×SD₁₆	—	61	6	no	—
735	C₂×SD₁₆	C₂²×D₆₁	1	12	yes	complemented
736	C₂×SD₁₆	C₂²×D₆₁	1	3	yes	complemented
737	C₂×SD₁₆	C₂²×D₆₁	1	12	yes	complemented
738	C₂×SD₁₆	C₂²×D₆₁	1	6	yes	complemented
739	C₂×SD₁₆	C₂²×D₆₁	1	1	yes	characteristic, complemented
740	C₂×D₈	—	61	12	no	—
741	C₂×D₈	—	61	24	no	—
742	C₂×D₈	—	61	6	no	—
743	C₂×D₈	C₂²×D₆₁	1	3	yes	complemented
744	#131	—	61	8	no	—
745	#131	—	61	24	no	—
746	#131	—	61	12	no	—
747	#131	—	61	4	no	—
748	#131	—	61	12	no	—
749	#131	—	61	12	no	—
750	#131	C₂²×D₆₁	1	4	yes	complemented
751	#131	C₂²×D₆₁	1	4	yes	complemented
752	C₂×M₁₆	—	61	6	no	—
753	C₂×M₁₆	—	61	24	no	—
754	C₂×M₁₆	—	61	12	no	—
755	C₂×M₁₆	C₂²×D₆₁	1	3	yes	complemented
756	C₂²×C₈	—	61	12	no	—
757	C₂²×C₈	C₂²×D₆₁	1	3	yes	complemented
758	C₂⁴	—	2	3	no	—
759	C₂⁴	—	122	12	no	—
760	#41	—	2	8	no	—
761	#41	—	2	24	no	—
762	#41	—	2	6	no	—
763	#41	—	2	6	no	—
764	#41	—	61	8	no	—
765	#41	—	61	24	no	—
766	#41	—	61	12	no	—
767	#41	—	61	12	no	—
768	#41	—	61	12	no	—
769	#41	—	61	4	no	—
770	#41	—	61	24	no	—
771	#41	—	61	8	no	—
772	#41	—	61	8	no	—
773	#41	—	61	24	no	—
774	#41	—	61	12	no	—
775	#41	—	61	4	no	—
776	#41	—	61	12	no	—
777	#41	—	61	4	no	—
778	#41	—	122	24	no	—
779	#41	—	122	24	no	—
780	#41	—	122	8	no	—
781	#41	—	122	12	no	—
782	#41	—	122	24	no	—
783	#41	—	122	48	no	—
784	#41	—	122	12	no	—
785	#41	—	122	12	no	—
786	#41	—	122	12	no	—
787	#41	—	122	24	no	—
788	#41	—	122	24	no	—
789	#41	—	122	24	no	—
790	#41	—	122	24	no	—
791	#41	—	122	24	no	—
792	#41	—	122	24	no	—
793	#41	—	122	12	no	—
794	#41	—	122	24	no	—
795	#41	—	122	4	no	—
796	#41	—	122	4	no	—
797	#41	—	122	12	no	—
798	#41	—	122	24	no	—
799	#41	—	122	4	no	—
800	#41	—	122	4	no	—
801	#41	—	122	12	no	—
802	#41	—	122	12	no	—
803	#41	—	122	6	no	—
804	#41	—	122	6	no	—
805	#41	—	122	6	no	—
806	#41	—	122	6	no	—
807	#41	D₄×D₆₁	1	4	yes	—
808	#41	C₂³×D₆₁	1	12	yes	—
809	#41	C₂³×D₆₁	1	12	yes	—
810	#41	C₂³×D₆₁	1	4	yes	—
811	C₂×Q₈	—	2	8	no	—
812	C₂×Q₈	—	2	3	no	—
813	C₂×Q₈	—	2	6	no	—
814	C₂×Q₈	—	61	8	no	—
815	C₂×Q₈	—	61	6	no	—
816	C₂×Q₈	—	61	24	no	—
817	C₂×Q₈	—	61	8	no	—
818	C₂×Q₈	—	61	6	no	—
819	C₂×Q₈	—	61	6	no	—
820	C₂×Q₈	—	122	12	no	—
821	C₂×Q₈	—	122	12	no	—
822	C₂×Q₈	—	122	12	no	—
823	C₂×Q₈	—	122	24	no	—
824	C₂×Q₈	—	122	24	no	—
825	C₂×Q₈	—	122	12	no	—
826	C₂×Q₈	—	122	4	no	—
827	C₂×Q₈	—	122	4	no	—
828	C₂×Q₈	—	122	4	no	—
829	C₂×Q₈	D₄×D₆₁	1	1	yes	characteristic
830	C₂×Q₈	C₂³×D₆₁	1	12	yes	—
831	C₂×Q₈	C₂³×D₆₁	1	3	yes	—
832	C₂×Q₈	C₂³×D₆₁	1	1	yes	characteristic
833	C₂×D₄	—	2	3	no	—
834	C₂×D₄	—	2	3	no	—
835	C₂×D₄	—	2	24	no	—
836	C₂×D₄	—	2	3	no	—
837	C₂×D₄	—	2	6	no	—
838	C₂×D₄	—	61	12	no	—
839	C₂×D₄	—	61	24	no	—
840	C₂×D₄	—	61	8	no	—
841	C₂×D₄	—	61	24	no	—
842	C₂×D₄	—	61	6	no	—
843	C₂×D₄	—	61	6	no	—
844	C₂×D₄	—	61	6	no	—
845	C₂×D₄	—	122	12	no	—
846	C₂×D₄	—	122	12	no	—
847	C₂×D₄	—	122	12	no	—
848	C₂×D₄	—	122	24	no	—
849	C₂×D₄	—	122	12	no	—
850	C₂×D₄	—	122	24	no	—
851	C₂×D₄	—	122	24	no	—
852	C₂×D₄	—	122	12	no	—
853	C₂×D₄	—	122	24	no	—
854	C₂×D₄	—	122	4	no	—
855	C₂×D₄	—	122	24	no	—
856	C₂×D₄	—	122	24	no	—
857	C₂×D₄	—	122	24	no	—
858	C₂×D₄	—	122	48	no	—
859	C₂×D₄	—	122	8	no	—
860	C₂×D₄	—	122	12	no	—
861	C₂×D₄	—	122	6	no	—
862	C₂×D₄	—	122	6	no	—
863	C₂×D₄	—	122	12	no	—
864	C₂×D₄	—	122	12	no	—
865	C₂×D₄	D₄×D₆₁	1	3	yes	—
866	C₂×D₄	C₂³×D₆₁	1	12	yes	—
867	C₂×D₄	C₂³×D₆₁	1	1	yes	characteristic
868	C₂×D₄	C₂³×D₆₁	1	3	yes	—
869	C₂²×C₄	—	2	3	no	—
870	C₂²×C₄	—	2	3	no	—
871	C₂²×C₄	—	2	3	no	—
872	C₂²×C₄	—	61	12	no	—
873	C₂²×C₄	—	122	24	no	—
874	C₂²×C₄	—	122	12	no	—
875	C₂²×C₄	—	122	24	no	—
876	C₂²×C₄	—	122	12	no	—
877	C₂²×C₄	—	122	12	no	—
878	C₂²×C₄	—	122	6	no	—
879	C₂²×C₄	—	122	6	no	—
880	C₂²×C₄	C₂³×D₆₁	1	3	yes	—
881	Q₁₆	—	61	8	no	—
882	Q₁₆	—	61	24	no	—
883	Q₁₆	—	61	12	no	—
884	Q₁₆	—	61	4	no	—
885	Q₁₆	C₂³×D₆₁	1	12	yes	—
886	SD₁₆	—	61	24	no	—
887	SD₁₆	—	61	8	no	—
888	SD₁₆	—	61	24	no	—
889	SD₁₆	—	61	8	no	—
890	SD₁₆	—	61	4	no	—
891	SD₁₆	—	61	4	no	—
892	SD₁₆	—	61	12	no	—
893	SD₁₆	—	61	12	no	—
894	SD₁₆	C₂³×D₆₁	1	6	yes	—
895	SD₁₆	C₂³×D₆₁	1	2	yes	—
896	SD₁₆	C₂³×D₆₁	1	24	yes	—
897	SD₁₆	C₂³×D₆₁	1	6	yes	—
898	SD₁₆	C₂³×D₆₁	1	2	yes	—
899	D₈	—	61	24	no	—
900	D₈	—	61	8	no	—
901	D₈	—	61	12	no	—
902	D₈	—	61	4	no	—
903	D₈	C₂³×D₆₁	1	12	yes	—
904	M₁₆	—	61	12	no	—
905	M₁₆	—	61	4	no	—
906	M₁₆	—	61	24	no	—
907	M₁₆	—	61	8	no	—
908	M₁₆	C₂³×D₆₁	1	12	yes	—
909	C₂×C₈	—	61	12	no	—
910	C₂×C₈	—	61	8	no	—
911	C₂×C₈	—	61	24	no	—
912	C₂×C₈	C₂³×D₆₁	1	6	yes	—
913	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₆₁	1	6	yes	—
915	C₂×C₈	C₂³×D₆₁	1	3	yes	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	3	no	—
918	C₂³	—	2	12	no	—
919	C₂³	—	16	3	no	—
920	C₂³	—	61	12	no	—
921	C₂³	—	122	8	no	—
922	C₂³	—	122	24	no	—
923	C₂³	—	122	6	no	—
924	C₂³	—	122	6	no	—
925	C₂³	—	976	12	no	—
926	C₂³	C₂×D₄×D₆₁	1	3	yes	—
927	Q₈	—	2	12	no	—
928	Q₈	—	2	3	no	—
929	Q₈	—	2	1	no	—
930	Q₈	—	61	12	no	—
931	Q₈	—	61	4	no	—
932	Q₈	—	61	4	no	—
933	Q₈	—	61	4	no	—
934	Q₈	—	122	24	no	—
935	Q₈	—	122	8	no	—
936	Q₈	—	122	6	no	—
937	Q₈	—	122	6	no	—
938	Q₈	C₂×D₄×D₆₁	1	4	yes	—
939	Q₈	C₂⁴×D₆₁	1	6	yes	—
940	Q₈	C₂⁴×D₆₁	1	2	yes	—
941	D₄	—	2	12	no	—
942	D₄	—	2	12	no	—
943	D₄	—	2	12	no	—
944	D₄	—	2	3	no	—
945	D₄	—	2	1	no	—
946	D₄	—	61	8	no	—
947	D₄	—	61	24	no	—
948	D₄	—	61	12	no	—
949	D₄	—	61	4	no	—
950	D₄	—	61	4	no	—
951	D₄	—	61	4	no	—
952	D₄	—	122	8	no	—
953	D₄	—	122	24	no	—
954	D₄	—	122	24	no	—
955	D₄	—	122	8	no	—
956	D₄	—	122	24	no	—
957	D₄	—	122	8	no	—
958	D₄	—	122	4	no	—
959	D₄	—	122	12	no	—
960	D₄	—	122	4	no	—
961	D₄	—	122	12	no	—
962	D₄	—	122	6	no	—
963	D₄	—	122	6	no	—
964	D₄	C₂×D₄×D₆₁	1	12	yes	—
965	D₄	C₂⁴×D₆₁	1	2	yes	—
966	D₄	C₂⁴×D₆₁	1	6	yes	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	3	no	—
969	C₂×C₄	—	2	12	no	—
970	C₂×C₄	—	2	12	no	—
971	C₂×C₄	—	2	12	no	—
972	C₂×C₄	—	61	12	no	—
973	C₂×C₄	—	61	24	no	—
974	C₂×C₄	—	61	8	no	—
975	C₂×C₄	—	122	8	no	—
976	C₂×C₄	—	122	24	no	—
977	C₂×C₄	—	122	8	no	—
978	C₂×C₄	—	122	24	no	—
979	C₂×C₄	—	122	24	no	—
980	C₂×C₄	—	122	8	no	—
981	C₂×C₄	—	122	6	no	—
982	C₂×C₄	—	122	6	no	—
983	C₂×C₄	—	122	12	no	—
984	C₂×C₄	—	122	4	no	—
985	C₂×C₄	—	122	12	no	—
986	C₂×C₄	—	122	4	no	—
987	C₂×C₄	C₂×D₄×D₆₁	1	3	yes	—
988	C₂×C₄	C₂×D₄×D₆₁	1	6	yes	—
989	C₂×C₄	C₂⁴×D₆₁	1	6	yes	—
990	C₂×C₄	C₂⁴×D₆₁	1	1	yes	characteristic
991	C₈	—	61	8	no	—
992	C₈	C₂⁴×D₆₁	1	1	yes	characteristic
993	C₈	C₂⁴×D₆₁	1	6	yes	—
994	C₈	C₂⁴×D₆₁	1	1	yes	characteristic
995	C₂²	—	2	2	no	—
996	C₂²	—	2	6	no	—
997	C₂²	—	4	3	no	—
998	C₂²	—	8	1	no	—
999	C₂²	—	8	3	no	—
1000	C₂²	—	8	12	no	—
1001	C₂²	—	61	8	no	—
1002	C₂²	—	122	4	no	—
1003	C₂²	—	122	4	no	—
1004	C₂²	—	488	6	no	—
1005	C₂²	—	488	6	no	—
1006	C₂²	—	488	8	no	—
1007	C₂²	—	488	24	no	—
1008	C₂²	—	244	12	no	—
1009	C₂²	C₂²×D₄×D₆₁	1	1	yes	characteristic
1010	C₂²	C₂²×D₄×D₆₁	1	6	yes	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	6	no	—
1013	C₄	—	61	8	no	—
1014	C₄	—	122	4	no	—
1015	C₄	—	122	4	no	—
1016	C₄	C₂²×D₄×D₆₁	1	6	yes	—
1017	C₄	C₂²×D₄×D₆₁	1	1	yes	characteristic
1018	C₄	C₂⁵×D₆₁	1	1	yes	characteristic
1019	C₂	—	2	1	no	—
1020	C₂	—	2	6	no	—
1021	C₂	—	4	6	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	122	8	no	—
1024	C₂	—	244	4	no	—
1025	C₂	—	244	4	no	—
1026	C₂	C₂³×D₄×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₆₁
commutator, cosocle	C₄×C₆₁	C₂⁶
Frattini	C₄	C₂⁵×D₆₁
Fitting	C₂×C₆₁×#577	C₂
socle	C₂×C₆₁	C₂⁴×D₄
hypercenter	C₂×#577	D₆₁
hypocenter	C₆₁	#63092
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#577

Complements

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

N	H ≅ G/N	type
1. #21460631	C₂	semidirect
2. #21460629	C₂	semidirect
3. #21460606	C₂	semidirect
4. #21460602	C₂	semidirect
5. #21460601	C₂	semidirect
6. #21460599	C₂	semidirect
7. #21460597	C₂	semidirect
8. #21460595	C₂	semidirect
9. #21460593	C₂	semidirect
10. #21460591	C₂	semidirect
11. #21460588	C₂	semidirect
12. C₂×#16840568	C₂	semidirect
13. #577×D₆₁	C₂	semidirect
14. #21460530	C₂	semidirect
15. C₂×C₆₁×#577	C₂	semidirect
17. #16840599	C₂²	semidirect
21. #16840598	C₂²	semidirect
22. #16840598	C₂²	semidirect
23. #16840598	C₂²	semidirect
24. #16840598	C₂²	semidirect
26. #16840597	C₂²	semidirect
28. C₂×#14519825	C₂²	semidirect
30. 2₋¹⁺⁴×D₆₁	C₂²	semidirect
32. C₂×#14519822	C₂²	semidirect
34. H(5,𝔽₂)×D₆₁	C₂²	semidirect
35. #16840579	C₂²	semidirect
36. #16840578	C₂²	semidirect
37. #16840577	C₂²	semidirect
38. #16840576	C₂²	semidirect
39. #16840575	C₂²	semidirect
40. #16840574	C₂²	semidirect
41. #16840574	C₂²	semidirect
42. #16840573	C₂²	semidirect
43. #16840572	C₂²	semidirect
44. #16840571	C₂²	semidirect
45. #16840570	C₂²	semidirect
46. #16840569	C₂²	semidirect
47. #16840569	C₂²	semidirect
48. #16840568	C₂²	semidirect
49. #16840568	C₂²	semidirect
50. #16840568	C₂²	semidirect
51. #16840568	C₂²	semidirect
52. #16840568	C₂²	semidirect
53. #16840567	C₂²	semidirect
54. #16840566	C₂²	semidirect
55. #16840565	C₂²	semidirect
56. #16840564	C₂²	semidirect
57. #16840563	C₂²	semidirect
58. #16840562	C₂²	semidirect
59. #16840561	C₂²	semidirect
60. #16840560	C₂²	semidirect
61. #16840560	C₂²	semidirect
62. #16840559	C₂²	semidirect
63. #16840558	C₂²	semidirect
64. C₂×#14519808	C₂²	semidirect
65. C₂×#14519806	C₂²	semidirect
66. #137×D₆₁	C₂²	semidirect
67. C₂×#14519804	C₂²	semidirect
68. C₂×#14519803	C₂²	semidirect
69. AGL(1,ℤ/8)×D₆₁	C₂²	semidirect
70. C₂×#14519799	C₂²	semidirect
71. C₂×#14519798	C₂²	semidirect
72. #135×D₆₁	C₂²	semidirect
73. C₂×SD₁₆×D₆₁	C₂²	semidirect
74. #16840529	C₂²	semidirect
75. #16840528	C₂²	semidirect
76. #16840527	C₂²	semidirect
77. C₂×#14519783	C₂²	semidirect
78. #131×D₆₁	C₂²	semidirect
79. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
80. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
81. C₆₁×#577	C₂²	semidirect
82. C₆₁×#577	C₂²	semidirect
83. C₂×#137×C₆₁	C₂²	semidirect
84. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
85. C₂×#135×C₆₁	C₂²	semidirect
86. C₂²×SD₁₆×C₆₁	C₂²	semidirect
87. C₂×#131×C₆₁	C₂²	semidirect
96. #14519825	C₂³	semidirect
97. #14519825	C₂³	semidirect
105. #14519824	C₂³	semidirect
106. #14519824	C₂³	semidirect
114. #14519823	C₂³	semidirect
115. #14519823	C₂³	semidirect
127. #14519822	C₂³	semidirect
130. C₂×#11758226	C₂³	semidirect
136. C₂×#11758222	C₂³	semidirect
150. #41×D₆₁	C₂³	semidirect
153. C₂×Q₈×D₆₁	C₂³	semidirect
158. #14519810	C₂³	semidirect
159. #14519810	C₂³	semidirect
160. #14519809	C₂³	semidirect
161. #14519809	C₂³	semidirect
162. #14519808	C₂³	semidirect
163. #14519808	C₂³	semidirect
164. #14519808	C₂³	semidirect
165. #14519807	C₂³	semidirect
166. #14519807	C₂³	semidirect
167. #14519806	C₂³	semidirect
168. #14519806	C₂³	semidirect
169. #14519806	C₂³	semidirect
170. #14519805	C₂³	semidirect
171. #14519805	C₂³	semidirect
172. #14519804	C₂³	semidirect
173. #14519804	C₂³	semidirect
174. #14519804	C₂³	semidirect
175. #14519803	C₂³	semidirect
176. #14519803	C₂³	semidirect
177. #14519803	C₂³	semidirect
178. #14519802	C₂³	semidirect
179. #14519802	C₂³	semidirect
180. #14519801	C₂³	semidirect
181. #14519801	C₂³	semidirect
182. #14519800	C₂³	semidirect
183. #14519799	C₂³	semidirect
184. #14519799	C₂³	semidirect
185. #14519799	C₂³	semidirect
186. #14519799	C₂³	semidirect
187. #14519798	C₂³	semidirect
188. #14519798	C₂³	semidirect
189. #14519798	C₂³	semidirect
190. #14519797	C₂³	semidirect
191. #14519797	C₂³	semidirect
192. #14519796	C₂³	semidirect
193. C₂×Dic₂₄₄	C₂³	semidirect
194. C₂×#11758202	C₂³	semidirect
195. Q₁₆×D₆₁	C₂³	semidirect
196. C₂×#11758190	C₂³	semidirect
197. C₂×#11758190	C₂³	semidirect
198. C₂×#11758200	C₂³	semidirect
199. C₂×#11758201	C₂³	semidirect
200. SD₁₆×D₆₁	C₂³	semidirect
201. SD₁₆×D₆₁	C₂³	semidirect
202. SD₁₆×D₆₁	C₂³	semidirect
203. C₂×D₄₈₈	C₂³	semidirect
204. C₂×#11758199	C₂³	semidirect
205. D₈×D₆₁	C₂³	semidirect
206. #14519785	C₂³	semidirect
207. #14519784	C₂³	semidirect
208. #14519783	C₂³	semidirect
209. #14519783	C₂³	semidirect
210. #14519783	C₂³	semidirect
211. #14519783	C₂³	semidirect
212. C₂×#11758194	C₂³	semidirect
213. C₂×#11758189	C₂³	semidirect
214. M₁₆×D₆₁	C₂³	semidirect
215. C₂×C₈×D₆₁	C₂³	semidirect
217. 2₋¹⁺⁴×C₆₁	C₂³	semidirect
224. C₂×#41×C₆₁	C₂³	semidirect
226. C₂²×Q₈×C₆₁	C₂³	semidirect
229. #137×C₆₁	C₂³	semidirect
230. AGL(1,ℤ/8)×C₆₁	C₂³	semidirect
231. #135×C₆₁	C₂³	semidirect
232. #135×C₆₁	C₂³	semidirect
233. C₂×Q₁₆×C₆₁	C₂³	semidirect
234. C₂×SD₁₆×C₆₁	C₂³	semidirect
235. C₂×SD₁₆×C₆₁	C₂³	semidirect
236. C₂×SD₁₆×C₆₁	C₂³	semidirect
237. C₂×SD₁₆×C₆₁	C₂³	semidirect
238. C₂×SD₁₆×C₆₁	C₂³	semidirect
239. C₂×D₈×C₆₁	C₂³	semidirect
240. #131×C₆₁	C₂³	semidirect
241. #131×C₆₁	C₂³	semidirect
242. C₂×M₁₆×C₆₁	C₂³	semidirect
243. C₂²×C₈×C₆₁	C₂³	semidirect
519. C₂×#577	D₆₁	semidirect
544. C₂×2₋¹⁺⁴	C₂×D₆₁	semidirect
549. C₂×H(5,𝔽₂)	C₂×D₆₁	semidirect
568. #577	C₂×D₆₁	semidirect
569. #577	C₂×D₆₁	semidirect
584. C₂×#137	C₂×D₆₁	semidirect
588. C₂×AGL(1,ℤ/8)	C₂×D₆₁	semidirect
592. C₂×#135	C₂×D₆₁	semidirect
594. C₂²×SD₁₆	C₂×D₆₁	semidirect
600. C₂×#131	C₂×D₆₁	semidirect
601. C₆₁	#63092	semidirect
622. 2₋¹⁺⁴	C₂²×D₆₁	semidirect
673. C₂×#41	C₂²×D₆₁	semidirect
678. C₂²×Q₈	C₂²×D₆₁	semidirect
697. #137	C₂²×D₆₁	semidirect
710. AGL(1,ℤ/8)	C₂²×D₆₁	semidirect
722. #135	C₂²×D₆₁	semidirect
723. #135	C₂²×D₆₁	semidirect
727. C₂×Q₁₆	C₂²×D₆₁	semidirect
735. C₂×SD₁₆	C₂²×D₆₁	semidirect
736. C₂×SD₁₆	C₂²×D₆₁	semidirect
737. C₂×SD₁₆	C₂²×D₆₁	semidirect
738. C₂×SD₁₆	C₂²×D₆₁	semidirect
739. C₂×SD₁₆	C₂²×D₆₁	semidirect
743. C₂×D₈	C₂²×D₆₁	semidirect
750. #131	C₂²×D₆₁	semidirect
751. #131	C₂²×D₆₁	semidirect
755. C₂×M₁₆	C₂²×D₆₁	semidirect
757. C₂²×C₈	C₂²×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
#21460631	2
#21460629	2
#21460606	2
#21460602	2
#21460601	2
#21460599	2
#21460597	2
#21460595	2
#21460593	2
#21460591	2
#21460588	2
C₂×#16840568	2
#577×D₆₁	2
#21460530	2
C₂×C₆₁×#577	2
#63092	61