Subgroups — #30544920

Order 15616.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454895	C₂	1	2	yes	maximal, complemented
2	#21454890	C₂	1	2	yes	maximal, complemented
3	#21454881	C₂	1	2	yes	maximal, complemented
4	#21454875	C₂	1	2	yes	maximal, complemented
5	#21454867	C₂	1	2	yes	maximal, complemented
6	#21454867	C₂	1	2	yes	maximal, complemented
7	#21454854	C₂	1	2	yes	maximal, complemented
8	#21454848	C₂	1	2	yes	maximal, complemented
9	#21454563	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
11	#21454546	C₂	1	1	yes	maximal, characteristic, complemented
12	#21454546	C₂	1	1	yes	maximal, characteristic, complemented
13	#21454537	C₂	1	1	yes	maximal, characteristic, complemented
14	#21454523	C₂	1	1	yes	maximal, characteristic, complemented
15	#21454514	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16839834	C₂	1	1	yes	maximal, characteristic, complemented
17	#21454485	C₂	1	1	yes	maximal, characteristic, complemented
18	#21454470	C₂	1	1	yes	maximal, characteristic, complemented
19	#21454268	C₂	1	1	yes	maximal, characteristic, complemented
20	#21454268	C₂	1	1	yes	maximal, characteristic, complemented
21	#21454264	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16839729	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
24	C₂×#14519784	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14519784	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14519784	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14519784	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#11758194	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#11758194	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11758194	C₂²	1	1	yes	characteristic, complemented
31	C₂³×#92418	C₂²	1	1	yes	characteristic, complemented
32	#16839840	C₂²	1	2	yes	complemented
33	#16839840	C₂²	1	2	yes	complemented
34	#16839840	C₂²	1	2	yes	complemented
35	#16839840	C₂²	1	2	yes	complemented
36	#16839840	C₂²	1	2	yes	complemented
37	#16839840	C₂²	1	2	yes	complemented
38	#16839834	C₂²	1	1	yes	characteristic
39	#16839834	C₂²	1	2	yes	—
40	#16839834	C₂²	1	1	yes	characteristic
41	#16839834	C₂²	1	2	yes	complemented
42	#16839834	C₂²	1	2	yes	complemented
43	#16839834	C₂²	1	2	yes	complemented
44	#16839834	C₂²	1	2	yes	complemented
45	#16839834	C₂²	1	2	yes	complemented
46	#16839834	C₂²	1	2	yes	complemented
47	#16839834	C₂²	1	2	yes	complemented
48	#16839834	C₂²	1	2	yes	complemented
49	#16839834	C₂²	1	1	yes	characteristic, complemented
50	#16839834	C₂²	1	1	yes	characteristic, complemented
51	#16839834	C₂²	1	2	yes	complemented
52	#16839834	C₂²	1	2	yes	complemented
53	#16839834	C₂²	1	2	yes	complemented
54	#16839834	C₂²	1	1	yes	characteristic, complemented
55	#16839834	C₂²	1	2	yes	complemented
56	#16839834	C₂²	1	2	yes	complemented
57	#16839834	C₂²	1	1	yes	characteristic, complemented
58	#16839834	C₂²	1	2	yes	complemented
59	#16839834	C₂²	1	1	yes	characteristic, complemented
60	#16839834	C₂²	1	2	yes	complemented
61	#16839834	C₂²	1	1	yes	characteristic, complemented
62	D₄×#92418	C₂²	1	2	yes	complemented
63	D₄×#92418	C₂²	1	2	yes	complemented
64	D₄×#92418	C₂²	1	2	yes	complemented
65	D₄×#92418	C₂²	1	2	yes	complemented
66	D₄×#92418	C₂²	1	2	yes	complemented
67	D₄×#92418	C₂²	1	2	yes	complemented
68	#16839823	C₂²	1	2	yes	complemented
69	#16839823	C₂²	1	2	yes	complemented
70	#16839823	C₂²	1	2	yes	complemented
71	#16839823	C₂²	1	2	yes	complemented
72	#16839819	C₂²	1	2	yes	complemented
73	#16839819	C₂²	1	2	yes	complemented
74	#16839819	C₂²	1	2	yes	complemented
75	#16839815	C₂²	1	2	yes	complemented
76	#16839789	C₂²	1	1	yes	characteristic, complemented
77	#16839789	C₂²	1	1	yes	characteristic, complemented
78	#16839786	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic, complemented
80	#16839729	C₂²	1	1	yes	characteristic
81	#16839729	C₂²	1	1	yes	characteristic
82	#16839729	C₂²	1	1	yes	characteristic
83	#16839729	C₂²	1	1	yes	characteristic
84	#16839729	C₂²	1	2	yes	complemented
85	#16839729	C₂²	1	2	yes	complemented
86	#16839729	C₂²	1	2	yes	complemented
87	#16839729	C₂²	1	2	yes	complemented
88	#16839729	C₂²	1	2	yes	complemented
89	#16839729	C₂²	1	2	yes	complemented
90	#16839729	C₂²	1	2	yes	complemented
91	#16839729	C₂²	1	2	yes	complemented
92	#16839729	C₂²	1	1	yes	characteristic, complemented
93	#16839729	C₂²	1	1	yes	characteristic, complemented
94	#16839729	C₂²	1	1	yes	characteristic, complemented
95	#16839729	C₂²	1	1	yes	characteristic, complemented
96	#16839726	C₂²	1	2	yes	complemented
97	#16839726	C₂²	1	2	yes	complemented
98	#16839726	C₂²	1	2	yes	complemented
99	#16839726	C₂²	1	2	yes	complemented
100	#16839726	C₂²	1	1	yes	characteristic, complemented
101	#16839726	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₂²⋊#92418	C₂²	1	2	yes	complemented
103	C₂×C₂²⋊#92418	C₂²	1	2	yes	complemented
104	C₂×C₂²⋊#92418	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊#92418	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic, complemented
108	#16839718	C₂²	1	1	yes	characteristic, complemented
109	#16839718	C₂²	1	1	yes	characteristic, complemented
110	C₄×#11758194	C₂²	1	1	yes	characteristic, complemented
111	C₂×#14519688	C₂²	1	1	yes	characteristic, complemented
112	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
113	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
114	C₆₁×#550	C₄	1	1	yes	characteristic
115	D₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
116	C₆₁×#548	C₄	1	1	yes	characteristic
117	C₆₁×#548	C₄	1	1	yes	characteristic
118	C₆₁×#547	C₄	1	2	yes	—
119	C₆₁×#547	C₄	1	1	yes	characteristic
120	C₆₁×#546	C₄	1	2	yes	—
121	C₆₁×#546	C₄	1	2	yes	—
122	C₆₁×#546	C₄	1	1	yes	characteristic
123	C₆₁×#546	C₄	1	1	yes	characteristic
124	D₄²×C₆₁	C₄	1	1	yes	characteristic
125	D₄²×C₆₁	C₄	1	2	yes	—
126	C₆₁×#532	C₂²	1	2	yes	—
127	C₆₁×#532	C₂²	1	1	yes	characteristic
128	C₆₁×#525	C₂²	1	2	yes	—
129	C₆₁×#525	C₂²	1	2	yes	—
130	C₆₁×#525	C₂²	1	1	yes	characteristic
131	C₆₁×#525	C₂²	1	1	yes	characteristic
132	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
134	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
135	#14519784	—	4	2	no	—
136	#14519784	—	4	2	no	—
137	#14519784	—	4	2	no	—
138	#14519784	—	4	2	no	—
139	C₂×#11758194	—	4	2	no	—
140	C₂×#11758194	—	4	2	no	—
141	C₂×#11758194	—	4	2	no	—
142	C₂×#11758194	C₂³	1	1	yes	characteristic
143	C₂×#11758194	C₂³	1	1	yes	characteristic
144	C₂×#11758194	C₂³	1	1	yes	characteristic
145	C₂×#11758194	C₂³	1	1	yes	characteristic
146	C₂×#11758194	C₂³	1	1	yes	characteristic
147	C₂×#11758194	C₂³	1	1	yes	characteristic
148	C₂×#11758194	C₂³	1	2	yes	—
149	C₂×#11758194	C₂³	1	2	yes	—
150	C₂×#11758194	C₂³	1	2	yes	—
151	C₂×#11758194	C₂³	1	2	yes	—
152	C₂×#11758194	C₂³	1	2	yes	—
153	C₂×#11758194	C₂³	1	1	yes	characteristic
154	C₂×#11758194	C₂³	1	1	yes	characteristic
155	C₂×#11758194	C₂³	1	2	yes	—
156	C₂²×#92418	—	4	2	no	—
157	C₂²×#92418	C₂³	1	1	yes	characteristic
158	C₂²×#92418	C₂³	1	1	yes	characteristic
159	C₂²×#92418	C₂³	1	1	yes	characteristic
160	C₂²×#92418	C₂³	1	1	yes	characteristic
161	C₂²×#92418	C₂³	1	1	yes	characteristic
162	C₂²×#92418	C₂³	1	1	yes	characteristic
163	C₂²×#92418	C₂³	1	2	yes	—
164	C₂²×#92418	C₂³	1	2	yes	—
165	C₂²×#92418	C₂³	1	2	yes	—
166	C₂²×#92418	C₂³	1	2	yes	—
167	C₂²×#92418	C₂³	1	2	yes	—
168	C₂²×#92418	C₂³	1	1	yes	characteristic
169	C₂²×#92418	C₂³	1	1	yes	characteristic
170	C₂²×#92418	C₂³	1	2	yes	—
171	C₄⋊#92418	C₂³	1	1	yes	characteristic
172	C₄⋊#92418	C₂³	1	1	yes	characteristic
173	C₄⋊#92418	C₂³	1	1	yes	characteristic
174	C₄⋊#92418	C₂³	1	1	yes	characteristic
175	C₄⋊#92418	C₂³	1	2	yes	—
176	C₄⋊#92418	C₂³	1	2	yes	—
177	C₄⋊#92418	C₂³	1	2	yes	—
178	C₄⋊#92418	C₂³	1	2	yes	—
179	C₄⋊#92418	C₂³	1	2	yes	—
180	C₄⋊#92418	C₂³	1	2	yes	—
181	C₂²⋊#92418	C₂³	1	1	yes	characteristic
182	C₂²⋊#92418	C₂³	1	1	yes	characteristic
183	C₂²⋊#92418	C₂³	1	2	yes	—
184	C₂²⋊#92418	C₂³	1	1	yes	characteristic
185	C₂²⋊#92418	C₂³	1	2	yes	—
186	C₂²⋊#92418	C₂³	1	1	yes	characteristic
187	C₂²⋊#92418	C₂³	1	2	yes	—
188	C₂²⋊#92418	C₂³	1	2	yes	—
189	C₂²⋊#92418	C₂³	1	2	yes	—
190	C₂²⋊#92418	C₂³	1	2	yes	—
191	C₂²⋊#92418	C₂³	1	2	yes	—
192	C₂²⋊#92418	C₂³	1	2	yes	—
193	C₂²⋊#92418	C₂³	1	2	yes	—
194	C₂²⋊#92418	C₂³	1	1	yes	characteristic
195	C₂²⋊#92418	C₂³	1	2	yes	—
196	C₂²⋊#92418	C₂³	1	1	yes	characteristic
197	C₂²⋊#92418	C₂³	1	1	yes	characteristic
198	C₂²⋊#92418	C₂³	1	2	yes	—
199	C₂²⋊#92418	C₂³	1	2	yes	—
200	C₂²⋊#92418	C₂³	1	2	yes	—
201	C₂²⋊#92418	C₂³	1	1	yes	characteristic
202	C₂²⋊#92418	C₂³	1	2	yes	—
203	C₂²⋊#92418	C₂³	1	2	yes	—
204	C₂²⋊#92418	C₂³	1	2	yes	—
205	C₂²⋊#92418	C₂³	1	2	yes	—
206	C₂²⋊#92418	C₂³	1	2	yes	—
207	C₂²⋊#92418	C₂³	1	2	yes	—
208	C₂²⋊#92418	C₂³	1	2	yes	—
209	#14519688	C₂³	1	1	yes	characteristic
210	#14519688	C₂³	1	1	yes	characteristic
211	#14519688	C₂³	1	1	yes	characteristic
212	#14519688	C₂³	1	1	yes	characteristic
213	#14519688	C₂³	1	2	yes	—
214	#14519688	C₂³	1	2	yes	—
215	#14519688	C₂³	1	2	yes	—
216	C₄×#92418	C₂³	1	2	yes	—
217	C₄×#92418	C₂³	1	2	yes	—
218	C₄×#92418	C₂³	1	2	yes	—
219	C₂×#41×C₆₁	—	4	2	no	—
220	C₂×#41×C₆₁	—	4	2	no	—
221	C₂×#41×C₆₁	—	4	2	no	—
222	C₂×#41×C₆₁	—	4	2	no	—
223	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
224	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
225	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
226	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
227	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
228	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
229	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
230	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
231	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
232	C₂×#41×C₆₁	C₂³	1	2	yes	—
233	C₂×#41×C₆₁	C₂³	1	2	yes	—
234	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
235	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
236	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
237	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
238	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
239	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
240	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
241	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
242	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
243	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
245	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
246	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
247	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
248	#127×C₆₁	C₂×C₄	1	1	yes	characteristic
249	#127×C₆₁	C₂×C₄	1	2	yes	—
250	#124×C₆₁	C₂×C₄	1	1	yes	characteristic
251	#124×C₆₁	C₂×C₄	1	1	yes	characteristic
252	#124×C₆₁	C₂×C₄	1	2	yes	—
253	#124×C₆₁	C₂×C₄	1	2	yes	—
254	#123×C₆₁	C₂×C₄	1	2	yes	—
255	#123×C₆₁	C₂×C₄	1	2	yes	—
256	#123×C₆₁	C₂×C₄	1	2	yes	—
257	#123×C₆₁	C₂×C₄	1	2	yes	—
258	#123×C₆₁	C₂×C₄	1	2	yes	—
259	#123×C₆₁	C₂×C₄	1	2	yes	—
260	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
261	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
262	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
263	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
264	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
265	C₂²⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
267	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
268	#121×C₆₁	C₂×C₄	1	2	yes	—
269	#121×C₆₁	C₂×C₄	1	2	yes	—
270	#121×C₆₁	C₂×C₄	1	2	yes	—
271	#121×C₆₁	C₂×C₄	1	2	yes	—
272	#121×C₆₁	C₂×C₄	1	2	yes	—
273	#121×C₆₁	C₂×C₄	1	2	yes	—
274	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
275	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
276	#121×C₆₁	C₂×C₄	1	2	yes	—
277	#121×C₆₁	C₂×C₄	1	2	yes	—
278	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
279	#121×C₆₁	C₂×C₄	1	1	yes	characteristic
280	#121×C₆₁	C₂×C₄	1	2	yes	—
281	#121×C₆₁	C₂×C₄	1	2	yes	—
282	#120×C₆₁	C₂×C₄	1	2	yes	—
283	#120×C₆₁	C₂×C₄	1	2	yes	—
284	#120×C₆₁	C₂×C₄	1	2	yes	—
285	#120×C₆₁	C₂×C₄	1	2	yes	—
286	#120×C₆₁	C₂×C₄	1	2	yes	—
287	#120×C₆₁	C₂×C₄	1	2	yes	—
288	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
289	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
290	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
291	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
292	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
293	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
294	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
295	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
296	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
297	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
298	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
299	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
300	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
301	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
302	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
303	C₄×D₄×C₆₁	C₂³	1	2	yes	—
304	C₄×D₄×C₆₁	C₂³	1	2	yes	—
305	C₄×D₄×C₆₁	C₂³	1	2	yes	—
306	C₄×D₄×C₆₁	C₂³	1	2	yes	—
307	C₄×D₄×C₆₁	C₂³	1	2	yes	—
308	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×D₄×C₆₁	C₂³	1	2	yes	—
311	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
312	#117×C₆₁	C₂³	1	1	yes	characteristic
313	#117×C₆₁	C₂³	1	2	yes	—
314	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
316	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
319	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
320	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
322	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
323	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
325	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
326	#41×C₆₁	—	2	2	no	—
327	#41×C₆₁	—	2	2	no	—
328	#41×C₆₁	—	2	2	no	—
329	#41×C₆₁	—	2	2	no	—
330	#41×C₆₁	—	2	2	no	—
331	#41×C₆₁	—	2	2	no	—
332	#41×C₆₁	—	4	2	no	—
333	#41×C₆₁	—	4	2	no	—
334	#41×C₆₁	—	4	2	no	—
335	#41×C₆₁	—	4	2	no	—
336	#41×C₆₁	—	4	4	no	—
337	#41×C₆₁	—	4	4	no	—
338	#41×C₆₁	—	4	2	no	—
339	#41×C₆₁	—	4	2	no	—
340	#41×C₆₁	—	4	2	no	—
341	#41×C₆₁	—	4	2	no	—
342	C₂×Q₈×C₆₁	—	4	2	no	—
343	C₂×Q₈×C₆₁	—	4	2	no	—
344	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
345	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
348	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
349	C₂×D₄×C₆₁	—	4	2	no	—
350	C₂×D₄×C₆₁	—	4	2	no	—
351	C₂×D₄×C₆₁	—	4	2	no	—
352	C₂×D₄×C₆₁	—	4	4	no	—
353	C₂×D₄×C₆₁	—	4	4	no	—
354	C₂×D₄×C₆₁	—	4	4	no	—
355	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
356	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
357	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
358	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
360	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
361	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
366	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
368	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
373	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
374	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
375	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
376	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₆₁	—	2	2	no	—
378	C₂²×C₄×C₆₁	—	2	2	no	—
379	C₂²×C₄×C₆₁	—	2	2	no	—
380	C₂²×C₄×C₆₁	—	2	2	no	—
381	C₂²×C₄×C₆₁	—	4	2	no	—
382	C₂²×C₄×C₆₁	—	4	2	no	—
383	C₂²×C₄×C₆₁	—	4	2	no	—
384	C₂²×C₄×C₆₁	—	4	2	no	—
385	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
386	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
392	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
394	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
396	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
397	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
398	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
399	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
401	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
425	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
426	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
428	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
430	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
446	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
447	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
449	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	2	yes	—
453	#11758194	—	2	2	no	—
454	#11758194	—	2	2	no	—
455	#11758194	—	2	2	no	—
456	#11758194	—	2	2	no	—
457	#11758194	—	4	1	no	—
458	#11758194	—	4	1	no	—
459	#11758194	—	4	1	no	—
460	#11758194	—	4	1	no	—
461	#11758194	—	4	2	no	—
462	#11758194	—	4	2	no	—
463	#11758194	—	4	2	no	—
464	#11758194	—	4	2	no	—
465	#11758194	—	4	2	no	—
466	#11758194	—	4	2	no	—
467	C₂×#92418	—	2	2	no	—
468	C₂×#92418	—	2	2	no	—
469	C₂×#92418	—	2	2	no	—
470	C₂×#92418	—	2	2	no	—
471	C₂×#92418	—	4	1	no	—
472	C₂×#92418	—	4	1	no	—
473	C₂×#92418	—	4	1	no	—
474	C₂×#92418	—	4	1	no	—
475	C₂×#92418	—	4	2	no	—
476	C₂×#92418	—	4	2	no	—
477	C₂×#92418	—	4	2	no	—
478	C₂×#92418	—	4	2	no	—
479	C₂×#92418	—	4	2	no	—
480	C₂×#92418	—	4	2	no	—
481	C₂×#92418	C₂⁴	1	1	yes	characteristic
482	C₂×#92418	C₂⁴	1	1	yes	characteristic
483	C₂×#92418	C₂⁴	1	2	yes	—
484	C₂×#92418	C₂⁴	1	2	yes	—
485	C₂×#92418	C₂⁴	1	2	yes	—
486	C₂×#92418	C₂⁴	1	2	yes	—
487	C₂×#92418	C₂⁴	1	1	yes	characteristic
488	C₂×#92418	C₂⁴	1	1	yes	characteristic
489	C₂×#92418	C₂⁴	1	1	yes	characteristic
490	C₂×#92418	C₂⁴	1	1	yes	characteristic
491	C₂×#92418	C₂⁴	1	1	yes	characteristic
492	C₂×#92418	C₂⁴	1	1	yes	characteristic
493	C₂³×C₆₁	—	2	2	no	—
494	C₂³×C₆₁	—	2	2	no	—
495	C₂³×C₆₁	—	2	2	no	—
496	C₂³×C₆₁	—	2	4	no	—
497	C₂³×C₆₁	—	4	1	no	—
498	C₂³×C₆₁	—	4	2	no	—
499	C₂³×C₆₁	—	4	2	no	—
500	C₂³×C₆₁	—	4	1	no	—
501	C₂³×C₆₁	—	4	2	no	—
502	C₂³×C₆₁	—	4	1	no	—
503	C₂³×C₆₁	—	4	2	no	—
504	C₂³×C₆₁	—	4	2	no	—
505	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
506	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
507	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
508	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
509	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
510	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
511	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
512	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
513	Q₈×C₆₁	—	2	2	no	—
514	Q₈×C₆₁	—	2	2	no	—
515	Q₈×C₆₁	—	2	2	no	—
516	Q₈×C₆₁	—	4	2	no	—
517	Q₈×C₆₁	—	4	2	no	—
518	D₄×C₆₁	—	2	4	no	—
519	D₄×C₆₁	—	2	4	no	—
520	D₄×C₆₁	—	2	4	no	—
521	D₄×C₆₁	—	2	2	no	—
522	D₄×C₆₁	—	2	2	no	—
523	D₄×C₆₁	—	2	4	no	—
524	D₄×C₆₁	—	2	2	no	—
525	D₄×C₆₁	—	2	2	no	—
526	D₄×C₆₁	—	2	2	no	—
527	D₄×C₆₁	—	4	1	no	—
528	D₄×C₆₁	—	4	2	no	—
529	D₄×C₆₁	—	4	1	no	—
530	D₄×C₆₁	—	4	2	no	—
531	D₄×C₆₁	—	4	2	no	—
532	D₄×C₆₁	—	4	2	no	—
533	D₄×C₆₁	—	4	2	no	—
534	D₄×C₆₁	—	4	2	no	—
535	D₄×C₆₁	—	4	2	no	—
536	D₄×C₆₁	—	4	2	no	—
537	D₄×C₆₁	—	4	2	no	—
538	D₄×C₆₁	—	4	2	no	—
539	D₄×C₆₁	—	4	2	no	—
540	C₂×C₄×C₆₁	—	2	2	no	—
541	C₂×C₄×C₆₁	—	2	2	no	—
542	C₂×C₄×C₆₁	—	2	2	no	—
543	C₂×C₄×C₆₁	—	2	2	no	—
544	C₂×C₄×C₆₁	—	2	2	no	—
545	C₂×C₄×C₆₁	—	2	2	no	—
546	C₂×C₄×C₆₁	—	2	1	no	—
547	C₂×C₄×C₆₁	—	2	1	no	—
548	C₂×C₄×C₆₁	—	2	1	no	—
549	C₂×C₄×C₆₁	—	2	1	no	—
550	C₂×C₄×C₆₁	—	2	2	no	—
551	C₂×C₄×C₆₁	—	2	2	no	—
552	C₂×C₄×C₆₁	—	2	2	no	—
553	C₂×C₄×C₆₁	—	2	2	no	—
554	C₂×C₄×C₆₁	—	2	1	no	—
555	C₂×C₄×C₆₁	—	2	1	no	—
556	C₂×C₄×C₆₁	—	2	1	no	—
557	C₂×C₄×C₆₁	—	2	1	no	—
558	C₂×C₄×C₆₁	—	2	2	no	—
559	C₂×C₄×C₆₁	—	2	2	no	—
560	C₂×C₄×C₆₁	—	4	2	no	—
561	C₂×C₄×C₆₁	—	4	2	no	—
562	C₂×C₄×C₆₁	—	4	2	no	—
563	C₂×C₄×C₆₁	—	4	2	no	—
564	C₂×C₄×C₆₁	—	4	2	no	—
565	C₂×C₄×C₆₁	—	4	2	no	—
566	C₂×C₄×C₆₁	—	4	1	no	—
567	C₂×C₄×C₆₁	—	4	2	no	—
568	C₂×C₄×C₆₁	—	4	1	no	—
569	C₂×C₄×C₆₁	—	4	2	no	—
570	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
587	#92418	—	2	1	no	—
588	#92418	—	2	1	no	—
589	#92418	—	2	1	no	—
590	#92418	—	2	1	no	—
591	#92418	—	2	1	no	—
592	#92418	—	2	1	no	—
593	#92418	—	2	1	no	—
594	#92418	—	2	1	no	—
595	#92418	—	2	2	no	—
596	#92418	—	2	2	no	—
597	#92418	—	2	2	no	—
598	#92418	—	2	2	no	—
599	#60240	—	61	1	no	maximal, Sylow
600	C₂²×C₆₁	—	2	1	no	—
601	C₂²×C₆₁	—	2	1	no	—
602	C₂²×C₆₁	—	2	1	no	—
603	C₂²×C₆₁	—	2	1	no	—
604	C₂²×C₆₁	—	2	1	no	—
605	C₂²×C₆₁	—	2	1	no	—
606	C₂²×C₆₁	—	2	1	no	—
607	C₂²×C₆₁	—	2	2	no	—
608	C₂²×C₆₁	—	2	2	no	—
609	C₂²×C₆₁	—	2	2	no	—
610	C₂²×C₆₁	—	2	2	no	—
611	C₂²×C₆₁	—	2	1	no	—
612	C₂²×C₆₁	—	2	1	no	—
613	C₂²×C₆₁	—	2	2	no	—
614	C₂²×C₆₁	—	2	1	no	—
615	C₂²×C₆₁	—	2	2	no	—
616	C₂²×C₆₁	—	2	2	no	—
617	C₂²×C₆₁	—	2	1	no	—
618	C₂²×C₆₁	—	2	1	no	—
619	C₂²×C₆₁	—	2	2	no	—
620	C₂²×C₆₁	—	2	2	no	—
621	C₂²×C₆₁	—	2	1	no	—
622	C₂²×C₆₁	—	4	4	no	—
623	C₂²×C₆₁	—	8	4	no	—
624	C₂²×C₆₁	—	8	2	no	—
625	C₂²×C₆₁	—	8	4	no	—
626	C₂²×C₆₁	#518	1	2	yes	—
627	C₂²×C₆₁	#568	1	2	yes	—
628	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
629	C₄×C₆₁	—	2	1	no	—
630	C₄×C₆₁	—	2	1	no	—
631	C₄×C₆₁	—	2	1	no	—
632	C₄×C₆₁	—	2	1	no	—
633	C₄×C₆₁	—	2	2	no	—
634	C₄×C₆₁	—	2	2	no	—
635	C₄×C₆₁	—	2	2	no	—
636	C₄×C₆₁	—	2	1	no	—
637	C₄×C₆₁	—	2	1	no	—
638	C₄×C₆₁	—	2	2	no	—
639	C₄×C₆₁	—	2	1	no	—
640	C₄×C₆₁	—	2	1	no	—
641	C₄×C₆₁	—	2	2	no	—
642	C₄×C₆₁	#518	1	2	yes	—
643	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
644	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
645	D₄×#41	D₆₁	1	1	yes	characteristic
646	#2981	—	61	2	no	—
647	#2980	—	61	2	no	—
648	#2978	—	61	2	no	—
649	#2977	—	61	2	no	—
650	#2976	—	61	2	no	—
651	#2976	—	61	2	no	—
652	#2974	—	61	2	no	—
653	#2973	—	61	2	no	—
654	#2935	—	61	1	no	—
655	D₄×M₁₆	—	61	1	no	—
656	#2933	—	61	1	no	—
657	#2933	—	61	1	no	—
658	#2932	—	61	1	no	—
659	#2930	—	61	1	no	—
660	#2929	—	61	1	no	—
661	C₂×#435	—	61	1	no	—
662	#2925	—	61	1	no	—
663	#2923	—	61	1	no	—
664	#2880	—	61	1	no	—
665	#2880	—	61	1	no	—
666	#2879	—	61	1	no	—
667	C₂×#408	—	61	1	no	—
668	C₂×C₆₁	—	2	2	no	—
669	C₂×C₆₁	—	2	2	no	—
670	C₂×C₆₁	—	4	1	no	—
671	C₂×C₆₁	—	4	1	no	—
672	C₂×C₆₁	—	4	2	no	—
673	C₂×C₆₁	—	4	2	no	—
674	C₂×C₆₁	—	4	2	no	—
675	C₂×C₆₁	—	4	1	no	—
676	C₂×C₆₁	C₂×#518	1	1	yes	characteristic
677	C₂×C₆₁	C₂×#568	1	1	yes	characteristic
678	C₂×C₆₁	#3573	1	1	yes	characteristic
679	C₂²×#41	C₂×D₆₁	1	1	yes	characteristic
680	C₂²×#41	C₂×D₆₁	1	1	yes	characteristic
681	C₂×#131	—	61	1	no	—
682	C₂×#131	—	61	1	no	—
683	C₂×#131	—	61	1	no	—
684	C₂×#131	—	61	1	no	—
685	C₂²×M₁₆	—	61	1	no	—
686	C₂²×M₁₆	—	61	1	no	—
687	C₂²×M₁₆	—	61	1	no	—
688	C₂³×C₈	—	61	1	no	—
689	#550	Dic₆₁	1	1	yes	characteristic
690	D₄×Q₈	Dic₆₁	1	1	yes	characteristic
691	#548	Dic₆₁	1	1	yes	characteristic
692	#548	Dic₆₁	1	1	yes	characteristic
693	#547	Dic₆₁	1	2	yes	—
694	#547	Dic₆₁	1	1	yes	characteristic
695	#546	Dic₆₁	1	2	yes	—
696	#546	Dic₆₁	1	2	yes	—
697	#546	Dic₆₁	1	1	yes	characteristic
698	#546	Dic₆₁	1	1	yes	characteristic
699	D₄²	Dic₆₁	1	1	yes	characteristic
700	D₄²	Dic₆₁	1	2	yes	—
701	#532	C₂×D₆₁	1	1	yes	characteristic
702	#532	C₂×D₆₁	1	2	yes	—
703	#525	C₂×D₆₁	1	1	yes	characteristic
704	#525	C₂×D₆₁	1	1	yes	characteristic
705	#525	C₂×D₆₁	1	2	yes	—
706	#525	C₂×D₆₁	1	2	yes	—
707	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
708	C₂×C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
709	C₂×C₄×D₄	C₂×D₆₁	1	2	yes	—
710	#436	—	61	2	no	—
711	#436	—	61	2	no	—
712	#436	—	61	2	no	—
713	#436	—	61	2	no	—
714	#436	—	61	2	no	—
715	#436	—	61	2	no	—
716	#435	—	61	1	no	—
717	#435	—	61	1	no	—
718	#435	—	61	1	no	—
719	#435	—	61	1	no	—
720	#435	—	61	1	no	—
721	#435	—	61	1	no	—
722	#435	—	61	1	no	—
723	#435	—	61	1	no	—
724	#435	—	61	2	no	—
725	#435	—	61	2	no	—
726	#435	—	61	2	no	—
727	#435	—	61	2	no	—
728	#435	—	61	2	no	—
729	#435	—	61	2	no	—
730	#435	—	61	2	no	—
731	#435	—	61	2	no	—
732	#435	—	61	2	no	—
733	#435	—	61	2	no	—
734	#435	—	61	2	no	—
735	#435	—	61	2	no	—
736	#435	—	61	2	no	—
737	#435	—	61	2	no	—
738	#435	—	61	2	no	—
739	#435	—	61	2	no	—
740	C₈×D₄	—	61	2	no	—
741	C₈×D₄	—	61	2	no	—
742	C₈×D₄	—	61	2	no	—
743	C₈×D₄	—	61	2	no	—
744	C₈×D₄	—	61	2	no	—
745	C₈×D₄	—	61	2	no	—
746	#433	—	61	2	no	—
747	#433	—	61	2	no	—
748	#433	—	61	2	no	—
749	#433	—	61	2	no	—
750	#432	—	61	2	no	—
751	#432	—	61	2	no	—
752	#432	—	61	2	no	—
753	#431	—	61	2	no	—
754	#424	—	61	1	no	—
755	#424	—	61	1	no	—
756	#423	—	61	1	no	—
757	C₂×C₄⋊C₈	—	61	1	no	—
758	#408	—	61	1	no	—
759	#408	—	61	1	no	—
760	#408	—	61	1	no	—
761	#408	—	61	1	no	—
762	#408	—	61	1	no	—
763	#408	—	61	1	no	—
764	#408	—	61	2	no	—
765	#408	—	61	2	no	—
766	#408	—	61	1	no	—
767	#408	—	61	1	no	—
768	#408	—	61	2	no	—
769	#408	—	61	2	no	—
770	#408	—	61	2	no	—
771	#408	—	61	2	no	—
772	#408	—	61	2	no	—
773	#408	—	61	2	no	—
774	#407	—	61	2	no	—
775	#407	—	61	2	no	—
776	#407	—	61	1	no	—
777	#407	—	61	1	no	—
778	#407	—	61	2	no	—
779	#407	—	61	2	no	—
780	C₂×C₂²⋊C₈	—	61	2	no	—
781	C₂×C₂²⋊C₈	—	61	2	no	—
782	C₂×C₂²⋊C₈	—	61	1	no	—
783	C₂×C₂²⋊C₈	—	61	1	no	—
784	C₂×C₂²⋊C₈	—	61	2	no	—
785	C₂×C₂²⋊C₈	—	61	2	no	—
786	#405	—	61	1	no	—
787	#405	—	61	1	no	—
788	C₄×M₁₆	—	61	1	no	—
789	C₂×#97	—	61	1	no	—
790	C₆₁	#60240	1	1	yes	characteristic, complemented, Sylow
791	C₂×#41	—	4	2	no	—
792	C₂×#41	—	4	2	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	—	4	2	no	—
795	C₂×#41	C₂×Dic₆₁	1	2	yes	—
796	C₂×#41	C₂×Dic₆₁	1	2	yes	—
797	C₂×#41	C₂×Dic₆₁	1	1	yes	characteristic
798	C₂×#41	C₂×Dic₆₁	1	1	yes	characteristic
799	C₂×#41	C₂×Dic₆₁	1	1	yes	characteristic
800	C₂×#41	C₂×Dic₆₁	1	1	yes	characteristic
801	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
802	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
803	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
804	C₂×#41	C₂²×D₆₁	1	2	yes	—
805	C₂×#41	C₂²×D₆₁	1	2	yes	—
806	C₂²×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
807	C₂²×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
808	C₂²×D₄	C₂×Dic₆₁	1	1	yes	characteristic
809	C₂²×D₄	C₂×Dic₆₁	1	2	yes	—
810	C₂²×D₄	C₂×Dic₆₁	1	1	yes	characteristic
811	C₂²×D₄	C₂×Dic₆₁	1	1	yes	characteristic
812	C₂²×D₄	C₂×Dic₆₁	1	2	yes	—
813	C₂²×D₄	C₂×Dic₆₁	1	2	yes	—
814	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
815	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
816	C₂³×C₄	C₂²×D₆₁	1	2	yes	—
817	C₂³×C₄	C₂²×D₆₁	1	2	yes	—
818	#131	—	244	2	no	—
819	#131	—	244	2	no	—
820	#131	—	244	2	no	—
821	#131	—	244	2	no	—
822	C₂×M₁₆	—	61	1	no	—
823	C₂×M₁₆	—	61	1	no	—
824	C₂×M₁₆	—	61	1	no	—
825	C₂×M₁₆	—	61	1	no	—
826	C₂×M₁₆	—	61	1	no	—
827	C₂×M₁₆	—	61	1	no	—
828	C₂×M₁₆	—	61	2	no	—
829	C₂×M₁₆	—	61	1	no	—
830	C₂×M₁₆	—	61	1	no	—
831	C₂×M₁₆	—	61	2	no	—
832	C₂×M₁₆	—	61	2	no	—
833	C₂×M₁₆	—	61	2	no	—
834	C₂×M₁₆	—	61	2	no	—
835	C₂×M₁₆	—	61	2	no	—
836	C₂×M₁₆	—	244	2	no	—
837	C₂×M₁₆	—	244	2	no	—
838	C₂×M₁₆	—	244	2	no	—
839	C₂²×C₈	—	61	1	no	—
840	C₂²×C₈	—	61	1	no	—
841	C₂²×C₈	—	61	1	no	—
842	C₂²×C₈	—	61	1	no	—
843	C₂²×C₈	—	61	1	no	—
844	C₂²×C₈	—	61	1	no	—
845	C₂²×C₈	—	61	1	no	—
846	C₂²×C₈	—	61	1	no	—
847	C₂²×C₈	—	61	2	no	—
848	C₂²×C₈	—	61	2	no	—
849	C₂²×C₈	—	61	2	no	—
850	C₂²×C₈	—	61	2	no	—
851	C₂²×C₈	—	61	2	no	—
852	C₂²×C₈	—	61	2	no	—
853	C₂²×C₈	—	244	2	no	—
854	C₄⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
855	C₄⋊Q₈	C₂×Dic₆₁	1	2	yes	—
856	#127	C₂×Dic₆₁	1	1	yes	characteristic
857	#127	C₂×Dic₆₁	1	2	yes	—
858	#124	C₂×Dic₆₁	1	1	yes	characteristic
859	#124	C₂×Dic₆₁	1	1	yes	characteristic
860	#124	C₂×Dic₆₁	1	2	yes	—
861	#124	C₂×Dic₆₁	1	2	yes	—
862	#123	C₂×Dic₆₁	1	2	yes	—
863	#123	C₂×Dic₆₁	1	2	yes	—
864	#123	C₂×Dic₆₁	1	2	yes	—
865	#123	C₂×Dic₆₁	1	2	yes	—
866	#123	C₂×Dic₆₁	1	2	yes	—
867	#123	C₂×Dic₆₁	1	2	yes	—
868	C₂²⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
871	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
872	C₂²⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
875	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
876	#121	C₂×Dic₆₁	1	1	yes	characteristic
877	#121	C₂×Dic₆₁	1	1	yes	characteristic
878	#121	C₂×Dic₆₁	1	2	yes	—
879	#121	C₂×Dic₆₁	1	2	yes	—
880	#121	C₂×Dic₆₁	1	1	yes	characteristic
881	#121	C₂×Dic₆₁	1	1	yes	characteristic
882	#121	C₂×Dic₆₁	1	2	yes	—
883	#121	C₂×Dic₆₁	1	2	yes	—
884	#121	C₂×Dic₆₁	1	2	yes	—
885	#121	C₂×Dic₆₁	1	2	yes	—
886	#121	C₂×Dic₆₁	1	2	yes	—
887	#121	C₂×Dic₆₁	1	2	yes	—
888	#121	C₂×Dic₆₁	1	2	yes	—
889	#121	C₂×Dic₆₁	1	2	yes	—
890	#120	C₂×Dic₆₁	1	2	yes	—
891	#120	C₂×Dic₆₁	1	2	yes	—
892	#120	C₂×Dic₆₁	1	2	yes	—
893	#120	C₂×Dic₆₁	1	2	yes	—
894	#120	C₂×Dic₆₁	1	2	yes	—
895	#120	C₂×Dic₆₁	1	2	yes	—
896	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
897	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
898	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
899	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
900	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
901	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
902	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
903	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
904	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
905	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
906	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
907	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
908	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
909	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
910	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
911	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
912	C₄×D₄	C₂²×D₆₁	1	2	yes	—
913	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
914	C₄×D₄	C₂²×D₆₁	1	2	yes	—
915	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
916	C₄×D₄	C₂²×D₆₁	1	2	yes	—
917	C₄×D₄	C₂²×D₆₁	1	2	yes	—
918	C₄×D₄	C₂²×D₆₁	1	2	yes	—
919	C₄×D₄	C₂²×D₆₁	1	2	yes	—
920	#117	C₂²×D₆₁	1	1	yes	characteristic
921	#117	C₂²×D₆₁	1	2	yes	—
922	C₂×C₄⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂×Dic₆₁	1	2	yes	—
928	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
929	C₂×C₄²	C₂²×D₆₁	1	2	yes	—
930	C₄⋊C₈	—	61	1	no	—
931	C₄⋊C₈	—	61	1	no	—
932	C₄⋊C₈	—	61	1	no	—
933	C₄⋊C₈	—	61	1	no	—
934	C₄⋊C₈	—	61	2	no	—
935	C₄⋊C₈	—	61	2	no	—
936	C₄⋊C₈	—	61	2	no	—
937	C₄⋊C₈	—	61	2	no	—
938	C₄⋊C₈	—	61	2	no	—
939	C₄⋊C₈	—	61	2	no	—
940	C₂²⋊C₈	—	61	1	no	—
941	C₂²⋊C₈	—	61	1	no	—
942	C₂²⋊C₈	—	61	2	no	—
943	C₂²⋊C₈	—	61	1	no	—
944	C₂²⋊C₈	—	61	2	no	—
945	C₂²⋊C₈	—	61	1	no	—
946	C₂²⋊C₈	—	61	2	no	—
947	C₂²⋊C₈	—	61	2	no	—
948	C₂²⋊C₈	—	61	2	no	—
949	C₂²⋊C₈	—	61	2	no	—
950	C₂²⋊C₈	—	61	2	no	—
951	C₂²⋊C₈	—	61	2	no	—
952	C₂²⋊C₈	—	61	2	no	—
953	C₂²⋊C₈	—	61	1	no	—
954	C₂²⋊C₈	—	61	2	no	—
955	C₂²⋊C₈	—	61	1	no	—
956	C₂²⋊C₈	—	61	1	no	—
957	C₂²⋊C₈	—	61	2	no	—
958	C₂²⋊C₈	—	61	2	no	—
959	C₂²⋊C₈	—	61	2	no	—
960	C₂²⋊C₈	—	61	1	no	—
961	C₂²⋊C₈	—	61	2	no	—
962	C₂²⋊C₈	—	61	2	no	—
963	C₂²⋊C₈	—	61	2	no	—
964	C₂²⋊C₈	—	61	2	no	—
965	C₂²⋊C₈	—	61	2	no	—
966	C₂²⋊C₈	—	61	2	no	—
967	C₂²⋊C₈	—	61	2	no	—
968	#97	—	61	1	no	—
969	#97	—	61	1	no	—
970	#97	—	61	1	no	—
971	#97	—	61	1	no	—
972	#97	—	61	2	no	—
973	#97	—	61	2	no	—
974	#97	—	61	2	no	—
975	C₄×C₈	—	61	2	no	—
976	C₄×C₈	—	61	2	no	—
977	C₄×C₈	—	61	2	no	—
978	C₂⁴	C₂²×Dic₆₁	1	1	yes	characteristic
979	C₂⁴	C₂²×Dic₆₁	1	1	yes	characteristic
980	C₂⁴	C₂²×Dic₆₁	1	2	yes	—
981	C₂⁴	C₂²×Dic₆₁	1	2	yes	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	2	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	2	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	C₂²×Dic₆₁	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×Dic₆₁	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×Dic₆₁	1	1	yes	characteristic
1003	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
1004	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	4	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	4	no	—
1011	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1012	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1013	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1014	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1015	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1016	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1017	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1018	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1019	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1020	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1021	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1022	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
1023	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1024	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1025	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1026	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1027	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1028	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1029	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1030	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1031	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1032	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1048	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1050	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1051	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1052	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1053	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1054	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1055	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1056	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
1057	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
1058	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
1059	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
1060	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
1062	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
1063	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
1065	M₁₆	—	122	2	no	—
1066	M₁₆	—	122	2	no	—
1067	M₁₆	—	122	2	no	—
1068	M₁₆	—	122	2	no	—
1069	M₁₆	—	244	1	no	—
1070	M₁₆	—	244	1	no	—
1071	M₁₆	—	244	1	no	—
1072	M₁₆	—	244	1	no	—
1073	M₁₆	—	244	2	no	—
1074	M₁₆	—	244	2	no	—
1075	M₁₆	—	244	2	no	—
1076	M₁₆	—	244	2	no	—
1077	M₁₆	—	244	2	no	—
1078	M₁₆	—	244	2	no	—
1079	C₂×C₈	—	61	1	no	—
1080	C₂×C₈	—	61	1	no	—
1081	C₂×C₈	—	61	2	no	—
1082	C₂×C₈	—	61	2	no	—
1083	C₂×C₈	—	61	2	no	—
1084	C₂×C₈	—	61	2	no	—
1085	C₂×C₈	—	61	1	no	—
1086	C₂×C₈	—	61	1	no	—
1087	C₂×C₈	—	61	1	no	—
1088	C₂×C₈	—	61	1	no	—
1089	C₂×C₈	—	61	1	no	—
1090	C₂×C₈	—	61	1	no	—
1091	C₂×C₈	—	122	2	no	—
1092	C₂×C₈	—	122	2	no	—
1093	C₂×C₈	—	122	2	no	—
1094	C₂×C₈	—	122	2	no	—
1095	C₂×C₈	—	244	1	no	—
1096	C₂×C₈	—	244	1	no	—
1097	C₂×C₈	—	244	1	no	—
1098	C₂×C₈	—	244	1	no	—
1099	C₂×C₈	—	244	2	no	—
1100	C₂×C₈	—	244	2	no	—
1101	C₂×C₈	—	244	2	no	—
1102	C₂×C₈	—	244	2	no	—
1103	C₂×C₈	—	244	2	no	—
1104	C₂×C₈	—	244	2	no	—
1105	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1107	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1108	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1109	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1110	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1111	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1112	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1113	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1114	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1117	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1118	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1119	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1123	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1125	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1127	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1129	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1132	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1133	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1134	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1135	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1136	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1137	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1138	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1139	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1140	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1141	C₂²⋊C₄	C₂²×Dic₆₁	1	2	yes	—
1142	C₄²	C₂²×Dic₆₁	1	2	yes	—
1143	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
1144	C₄²	C₂²×Dic₆₁	1	2	yes	—
1145	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
1146	C₄²	C₂³×D₆₁	1	1	yes	characteristic
1147	C₄²	C₂³×D₆₁	1	2	yes	—
1148	C₄²	C₂³×D₆₁	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	4	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
1162	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
1163	C₂³	C₂³×Dic₆₁	1	2	yes	—
1164	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
1165	C₂³	C₂³×Dic₆₁	1	2	yes	—
1166	C₂³	C₂³×Dic₆₁	1	2	yes	—
1167	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
1168	C₂³	C₂³×Dic₆₁	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	1	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	1	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	2	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1227	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1228	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
1229	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
1230	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1231	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
1232	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1233	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1234	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1235	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1236	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1237	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
1238	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
1239	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
1240	C₂×C₄	#14519822	1	2	yes	—
1241	C₂×C₄	#14519822	1	2	yes	—
1242	C₂×C₄	C₂⁴×D₆₁	1	1	yes	characteristic
1243	C₈	—	122	1	no	—
1244	C₈	—	122	1	no	—
1245	C₈	—	122	1	no	—
1246	C₈	—	122	1	no	—
1247	C₈	—	122	1	no	—
1248	C₈	—	122	1	no	—
1249	C₈	—	122	1	no	—
1250	C₈	—	122	1	no	—
1251	C₈	—	122	2	no	—
1252	C₈	—	122	2	no	—
1253	C₈	—	122	2	no	—
1254	C₈	—	122	2	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	#16840237	1	2	yes	—
1282	C₂²	#16840529	1	2	yes	—
1283	C₂²	C₂⁴×Dic₆₁	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	2	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	2	no	—
1297	C₄	#16840237	1	2	yes	—
1298	C₄	C₂×#14519822	1	1	yes	characteristic
1299	C₄	C₂×#14519822	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×#16840237	1	1	yes	characteristic
1309	C₂	C₂×#16840529	1	1	yes	characteristic
1310	C₂	#21460531	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁴×C₄
Fitting, prime radical	D₄×#41×C₆₁	C₂
cosocle	C₂×C₄×C₆₁	C₂⁵
hypercenter	D₄×#41	D₆₁
hypocenter	C₆₁	#60240
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #21454895	C₂	semidirect
2. #21454890	C₂	semidirect
3. #21454881	C₂	semidirect
4. #21454875	C₂	semidirect
5. #21454867	C₂	semidirect
6. #21454867	C₂	semidirect
7. #21454854	C₂	semidirect
8. #21454848	C₂	semidirect
9. #21454563	C₂	semidirect
10. D₄×#11758194	C₂	semidirect
11. #21454546	C₂	semidirect
12. #21454546	C₂	semidirect
13. #21454537	C₂	semidirect
14. #21454523	C₂	semidirect
15. #21454514	C₂	semidirect
16. C₂×#16839834	C₂	semidirect
17. #21454485	C₂	semidirect
18. #21454470	C₂	semidirect
19. #21454268	C₂	semidirect
20. #21454268	C₂	semidirect
21. #21454264	C₂	semidirect
22. C₂×#16839729	C₂	semidirect
24. C₂×#14519784	C₂²	semidirect
25. C₂×#14519784	C₂²	semidirect
26. C₂×#14519784	C₂²	semidirect
27. C₂×#14519784	C₂²	semidirect
28. C₂²×#11758194	C₂²	semidirect
29. C₂²×#11758194	C₂²	semidirect
30. C₂²×#11758194	C₂²	semidirect
31. C₂³×#92418	C₂²	semidirect
32. #16839840	C₂²	semidirect
33. #16839840	C₂²	semidirect
34. #16839840	C₂²	semidirect
35. #16839840	C₂²	semidirect
36. #16839840	C₂²	semidirect
37. #16839840	C₂²	semidirect
41. #16839834	C₂²	semidirect
42. #16839834	C₂²	semidirect
43. #16839834	C₂²	semidirect
44. #16839834	C₂²	semidirect
45. #16839834	C₂²	semidirect
46. #16839834	C₂²	semidirect
47. #16839834	C₂²	semidirect
48. #16839834	C₂²	semidirect
49. #16839834	C₂²	semidirect
50. #16839834	C₂²	semidirect
51. #16839834	C₂²	semidirect
52. #16839834	C₂²	semidirect
53. #16839834	C₂²	semidirect
54. #16839834	C₂²	semidirect
55. #16839834	C₂²	semidirect
56. #16839834	C₂²	semidirect
57. #16839834	C₂²	semidirect
58. #16839834	C₂²	semidirect
59. #16839834	C₂²	semidirect
60. #16839834	C₂²	semidirect
61. #16839834	C₂²	semidirect
62. D₄×#92418	C₂²	semidirect
63. D₄×#92418	C₂²	semidirect
64. D₄×#92418	C₂²	semidirect
65. D₄×#92418	C₂²	semidirect
66. D₄×#92418	C₂²	semidirect
67. D₄×#92418	C₂²	semidirect
68. #16839823	C₂²	semidirect
69. #16839823	C₂²	semidirect
70. #16839823	C₂²	semidirect
71. #16839823	C₂²	semidirect
72. #16839819	C₂²	semidirect
73. #16839819	C₂²	semidirect
74. #16839819	C₂²	semidirect
75. #16839815	C₂²	semidirect
76. #16839789	C₂²	semidirect
77. #16839789	C₂²	semidirect
78. #16839786	C₂²	semidirect
79. C₂×C₄⋊#92418	C₂²	semidirect
84. #16839729	C₂²	semidirect
85. #16839729	C₂²	semidirect
86. #16839729	C₂²	semidirect
87. #16839729	C₂²	semidirect
88. #16839729	C₂²	semidirect
89. #16839729	C₂²	semidirect
90. #16839729	C₂²	semidirect
91. #16839729	C₂²	semidirect
92. #16839729	C₂²	semidirect
93. #16839729	C₂²	semidirect
94. #16839729	C₂²	semidirect
95. #16839729	C₂²	semidirect
96. #16839726	C₂²	semidirect
97. #16839726	C₂²	semidirect
98. #16839726	C₂²	semidirect
99. #16839726	C₂²	semidirect
100. #16839726	C₂²	semidirect
101. #16839726	C₂²	semidirect
102. C₂×C₂²⋊#92418	C₂²	semidirect
103. C₂×C₂²⋊#92418	C₂²	semidirect
104. C₂×C₂²⋊#92418	C₂²	semidirect
105. C₂×C₂²⋊#92418	C₂²	semidirect
106. C₂×C₂²⋊#92418	C₂²	semidirect
107. C₂×C₂²⋊#92418	C₂²	semidirect
108. #16839718	C₂²	semidirect
109. #16839718	C₂²	semidirect
110. C₄×#11758194	C₂²	semidirect
111. C₂×#14519688	C₂²	semidirect
790. C₆₁	#60240	semidirect

Maximal subgroups

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

subgroup	index
#21454895	2
#21454890	2
#21454881	2
#21454875	2
#21454867	2
#21454854	2
#21454848	2
#21454563	2
D₄×#11758194	2
#21454546	2
#21454537	2
#21454523	2
#21454514	2
C₂×#16839834	2
#21454485	2
#21454470	2
#21454268	2
#21454264	2
C₂×#16839729	2
D₄×#41×C₆₁	2
#60240	61