Subgroups — C₆₁×#62914 #29566347

Order 15616.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3546	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3542	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3536	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3536	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3534	C₂	1	8	yes	maximal, complemented
7	C₆₁×#3520	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3511	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3496	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3492	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3488	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3488	C₂	1	4	yes	maximal, complemented
14	D₄×#41×C₆₁	C₂	1	2	yes	maximal, complemented
15	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₆₁×#537	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	4	yes	complemented
20	C₂²×#41×C₆₁	C₂²	1	4	yes	complemented
21	C₂²×#41×C₆₁	C₂²	1	2	yes	complemented
22	C₆₁×#562	C₂²	1	16	yes	complemented
23	C₆₁×#562	C₂²	1	16	yes	complemented
24	C₆₁×#560	C₂²	1	16	yes	complemented
25	C₆₁×#556	C₂²	1	4	yes	complemented
26	C₆₁×#555	C₂²	1	4	yes	complemented
27	C₆₁×#554	C₂²	1	8	yes	complemented
28	C₆₁×#554	C₂²	1	8	yes	complemented
29	C₆₁×#554	C₂²	1	4	yes	complemented
30	C₆₁×#553	C₂²	1	8	yes	complemented
31	C₆₁×#553	C₂²	1	8	yes	complemented
32	C₆₁×#552	C₂²	1	8	yes	complemented
33	C₆₁×#551	C₂²	1	16	yes	complemented
34	C₆₁×#550	C₂²	1	2	yes	complemented
35	C₆₁×#550	C₂²	1	8	yes	complemented
36	C₆₁×#550	C₂²	1	8	yes	complemented
37	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
38	C₆₁×#548	C₂²	1	4	yes	complemented
39	C₆₁×#548	C₂²	1	8	yes	complemented
40	C₆₁×#548	C₂²	1	8	yes	complemented
41	C₆₁×#547	C₂²	1	4	yes	complemented
42	C₆₁×#547	C₂²	1	2	yes	complemented
43	C₆₁×#547	C₂²	1	4	yes	complemented
44	C₆₁×#547	C₂²	1	4	yes	complemented
45	C₆₁×#547	C₂²	1	4	yes	complemented
46	C₆₁×#547	C₂²	1	8	yes	complemented
47	C₆₁×#547	C₂²	1	4	yes	complemented
48	C₆₁×#547	C₂²	1	8	yes	complemented
49	C₆₁×#546	C₂²	1	8	yes	complemented
50	C₆₁×#546	C₂²	1	8	yes	complemented
51	C₆₁×#546	C₂²	1	8	yes	complemented
52	C₆₁×#546	C₂²	1	4	yes	complemented
53	C₆₁×#546	C₂²	1	8	yes	complemented
54	C₆₁×#546	C₂²	1	16	yes	complemented
55	C₆₁×#546	C₂²	1	16	yes	complemented
56	C₆₁×#546	C₂²	1	16	yes	complemented
57	C₆₁×#546	C₂²	1	8	yes	complemented
58	D₄²×C₆₁	C₂²	1	4	yes	complemented
59	D₄²×C₆₁	C₂²	1	4	yes	complemented
60	D₄²×C₆₁	C₂²	1	2	yes	complemented
61	D₄²×C₆₁	C₂²	1	16	yes	complemented
62	D₄²×C₆₁	C₂²	1	8	yes	complemented
63	C₆₁×#544	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#543	C₂²	1	8	yes	complemented
65	C₆₁×#542	C₂²	1	8	yes	complemented
66	C₆₁×#542	C₂²	1	4	yes	complemented
67	C₆₁×#542	C₂²	1	8	yes	complemented
68	C₆₁×#540	C₂²	1	16	yes	complemented
69	C₆₁×#540	C₂²	1	4	yes	complemented
70	C₆₁×#539	C₂²	1	8	yes	complemented
71	C₆₁×#539	C₂²	1	16	yes	complemented
72	C₆₁×#538	C₂²	1	16	yes	complemented
73	C₆₁×#538	C₂²	1	4	yes	complemented
74	C₆₁×#538	C₂²	1	8	yes	complemented
75	C₆₁×#537	C₂²	1	8	yes	complemented
76	C₆₁×#537	C₂²	1	4	yes	complemented
77	C₆₁×#537	C₂²	1	8	yes	complemented
78	C₆₁×#537	C₂²	1	8	yes	complemented
79	C₆₁×#537	C₂²	1	8	yes	complemented
80	C₆₁×#537	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#537	C₂²	1	4	yes	complemented
82	C₆₁×#537	C₂²	1	2	yes	complemented
83	C₆₁×#537	C₂²	1	8	yes	complemented
84	C₆₁×#537	C₂²	1	8	yes	complemented
85	C₆₁×#535	C₂²	1	4	yes	complemented
86	C₆₁×#535	C₂²	1	8	yes	complemented
87	C₆₁×#535	C₂²	1	2	yes	complemented
88	C₆₁×#535	C₂²	1	8	yes	complemented
89	C₆₁×#534	C₂²	1	4	yes	complemented
90	C₆₁×#534	C₂²	1	16	yes	complemented
91	C₆₁×#533	C₂²	1	4	yes	complemented
92	C₆₁×#532	C₂²	1	4	yes	complemented
93	C₆₁×#532	C₂²	1	4	yes	complemented
94	C₆₁×#532	C₂²	1	4	yes	complemented
95	C₆₁×#532	C₂²	1	2	yes	complemented
96	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#529	C₂²	1	4	yes	complemented
98	C₆₁×#525	C₂²	1	4	yes	complemented
99	C₆₁×#525	C₂²	1	4	yes	complemented
100	C₆₁×#525	C₂²	1	8	yes	complemented
101	C₆₁×#525	C₂²	1	8	yes	complemented
102	C₆₁×#525	C₂²	1	8	yes	complemented
103	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
104	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
105	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
106	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
107	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
108	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
109	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
110	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
111	C₆₁×#520	C₂²	1	4	yes	complemented
112	C₆₁×#520	C₂²	1	4	yes	complemented
113	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
117	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
118	H(5,𝔽₂)×C₆₁	—	4	16	no	—
119	H(5,𝔽₂)×C₆₁	—	4	8	no	—
120	C₂×#41×C₆₁	—	4	16	no	—
121	C₂×#41×C₆₁	—	4	8	no	—
122	C₂×#41×C₆₁	C₂³	1	4	yes	—
123	C₂×#41×C₆₁	C₂³	1	2	yes	—
124	C₂×#41×C₆₁	C₂³	1	4	yes	—
125	C₂×#41×C₆₁	C₂³	1	4	yes	—
126	C₂×#41×C₆₁	C₂³	1	8	yes	—
127	C₂×#41×C₆₁	C₂³	1	8	yes	—
128	C₂×#41×C₆₁	C₂³	1	8	yes	—
129	C₂×#41×C₆₁	C₂³	1	4	yes	—
130	C₂×#41×C₆₁	C₂³	1	8	yes	—
131	C₂×#41×C₆₁	C₂³	1	4	yes	—
132	C₂×#41×C₆₁	C₂³	1	4	yes	—
133	C₂×#41×C₆₁	C₂³	1	8	yes	—
134	C₂×#41×C₆₁	C₂³	1	8	yes	—
135	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
137	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
140	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
141	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
142	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
143	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
144	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
145	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
146	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
147	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
148	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
149	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
150	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
152	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
153	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
154	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
156	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
157	#127×C₆₁	C₂³	1	2	yes	—
158	#127×C₆₁	C₂³	1	4	yes	—
159	#127×C₆₁	C₂³	1	4	yes	—
160	#127×C₆₁	C₂³	1	16	yes	—
161	#126×C₆₁	C₂³	1	8	yes	—
162	#126×C₆₁	C₂³	1	16	yes	—
163	#126×C₆₁	C₂³	1	16	yes	—
164	#125×C₆₁	C₂³	1	8	yes	—
165	#125×C₆₁	C₂³	1	16	yes	—
166	#125×C₆₁	C₂³	1	4	yes	—
167	#124×C₆₁	C₂³	1	8	yes	—
168	#124×C₆₁	C₂³	1	8	yes	—
169	#124×C₆₁	C₂³	1	8	yes	—
170	#124×C₆₁	C₂³	1	4	yes	—
171	#124×C₆₁	C₂³	1	16	yes	—
172	#124×C₆₁	C₂³	1	16	yes	—
173	#124×C₆₁	C₂³	1	4	yes	—
174	#123×C₆₁	C₂³	1	16	yes	—
175	#123×C₆₁	C₂³	1	16	yes	—
176	#123×C₆₁	C₂³	1	16	yes	—
177	#123×C₆₁	C₂³	1	16	yes	—
178	#123×C₆₁	C₂³	1	16	yes	—
179	#123×C₆₁	C₂³	1	8	yes	—
180	#123×C₆₁	C₂³	1	16	yes	—
181	#123×C₆₁	C₂³	1	8	yes	—
182	#123×C₆₁	C₂³	1	8	yes	—
183	#123×C₆₁	C₂³	1	16	yes	—
184	#123×C₆₁	C₂³	1	8	yes	—
185	#123×C₆₁	C₂³	1	8	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
205	#121×C₆₁	C₂³	1	8	yes	—
206	#121×C₆₁	C₂³	1	4	yes	—
207	#121×C₆₁	C₂³	1	8	yes	—
208	#121×C₆₁	C₂³	1	8	yes	—
209	#121×C₆₁	C₂³	1	4	yes	—
210	#121×C₆₁	C₂³	1	4	yes	—
211	#121×C₆₁	C₂³	1	4	yes	—
212	#121×C₆₁	C₂³	1	4	yes	—
213	#121×C₆₁	C₂³	1	8	yes	—
214	#121×C₆₁	C₂³	1	4	yes	—
215	#121×C₆₁	C₂³	1	16	yes	—
216	#121×C₆₁	C₂³	1	8	yes	—
217	#121×C₆₁	C₂³	1	16	yes	—
218	#121×C₆₁	C₂³	1	4	yes	—
219	#121×C₆₁	C₂³	1	4	yes	—
220	#121×C₆₁	C₂³	1	4	yes	—
221	#121×C₆₁	C₂³	1	8	yes	—
222	#121×C₆₁	C₂³	1	8	yes	—
223	#121×C₆₁	C₂³	1	8	yes	—
224	#121×C₆₁	C₂³	1	8	yes	—
225	#121×C₆₁	C₂³	1	8	yes	—
226	#121×C₆₁	C₂³	1	4	yes	—
227	#121×C₆₁	C₂³	1	16	yes	—
228	#121×C₆₁	C₂³	1	16	yes	—
229	#121×C₆₁	C₂³	1	16	yes	—
230	#121×C₆₁	C₂³	1	8	yes	—
231	#121×C₆₁	C₂³	1	8	yes	—
232	#121×C₆₁	C₂³	1	16	yes	—
233	#121×C₆₁	C₂³	1	8	yes	—
234	#121×C₆₁	C₂³	1	16	yes	—
235	#121×C₆₁	C₂³	1	16	yes	—
236	#121×C₆₁	C₂³	1	16	yes	—
237	#121×C₆₁	C₂³	1	8	yes	—
238	#121×C₆₁	C₂³	1	8	yes	—
239	#121×C₆₁	C₂³	1	4	yes	—
240	#121×C₆₁	C₂³	1	8	yes	—
241	#120×C₆₁	C₂³	1	16	yes	—
242	#120×C₆₁	C₂³	1	8	yes	—
243	#120×C₆₁	C₂³	1	16	yes	—
244	#120×C₆₁	C₂³	1	16	yes	—
245	#120×C₆₁	C₂³	1	16	yes	—
246	#120×C₆₁	C₂³	1	8	yes	—
247	#120×C₆₁	C₂³	1	8	yes	—
248	#120×C₆₁	C₂³	1	8	yes	—
249	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
250	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
251	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
252	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
253	C₄×D₄×C₆₁	C₂³	1	2	yes	—
254	C₄×D₄×C₆₁	C₂³	1	4	yes	—
255	C₄×D₄×C₆₁	C₂³	1	2	yes	—
256	C₄×D₄×C₆₁	C₂³	1	8	yes	—
257	C₄×D₄×C₆₁	C₂³	1	8	yes	—
258	C₄×D₄×C₆₁	C₂³	1	4	yes	—
259	C₄×D₄×C₆₁	C₂³	1	8	yes	—
260	C₄×D₄×C₆₁	C₂³	1	4	yes	—
261	C₄×D₄×C₆₁	C₂³	1	8	yes	—
262	C₄×D₄×C₆₁	C₂³	1	4	yes	—
263	C₄×D₄×C₆₁	C₂³	1	16	yes	—
264	C₄×D₄×C₆₁	C₂³	1	16	yes	—
265	C₄×D₄×C₆₁	C₂³	1	8	yes	—
266	C₄×D₄×C₆₁	C₂³	1	16	yes	—
267	C₄×D₄×C₆₁	C₂³	1	16	yes	—
268	C₄×D₄×C₆₁	C₂³	1	2	yes	—
269	C₄×D₄×C₆₁	C₂³	1	4	yes	—
270	C₄×D₄×C₆₁	C₂³	1	4	yes	—
271	C₄×D₄×C₆₁	C₂³	1	4	yes	—
272	C₄×D₄×C₆₁	C₂³	1	2	yes	—
273	C₄×D₄×C₆₁	C₂³	1	4	yes	—
274	C₄×D₄×C₆₁	C₂³	1	8	yes	—
275	C₄×D₄×C₆₁	C₂³	1	4	yes	—
276	#117×C₆₁	C₂³	1	8	yes	—
277	#117×C₆₁	C₂³	1	4	yes	—
278	#117×C₆₁	C₂³	1	2	yes	—
279	#117×C₆₁	C₂³	1	8	yes	—
280	#117×C₆₁	C₂³	1	8	yes	—
281	#117×C₆₁	C₂³	1	4	yes	—
282	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
286	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
289	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
290	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
291	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
295	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
296	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
297	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
299	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
300	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
302	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
303	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
304	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
305	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
306	#41×C₆₁	—	2	16	no	—
307	#41×C₆₁	—	2	8	no	—
308	#41×C₆₁	—	2	16	no	—
309	#41×C₆₁	—	4	16	no	—
310	#41×C₆₁	—	4	8	no	—
311	#41×C₆₁	—	4	16	no	—
312	#41×C₆₁	—	4	16	no	—
313	#41×C₆₁	—	4	16	no	—
314	#41×C₆₁	—	4	8	no	—
315	#41×C₆₁	—	4	8	no	—
316	#41×C₆₁	—	4	8	no	—
317	#41×C₆₁	—	4	16	no	—
318	#41×C₆₁	—	4	16	no	—
319	C₂×Q₈×C₆₁	—	4	8	no	—
320	C₂×Q₈×C₆₁	—	4	4	no	—
321	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
323	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
324	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
325	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
327	C₂×D₄×C₆₁	—	2	4	no	—
328	C₂×D₄×C₆₁	—	2	16	no	—
329	C₂×D₄×C₆₁	—	2	4	no	—
330	C₂×D₄×C₆₁	—	4	8	no	—
331	C₂×D₄×C₆₁	—	4	8	no	—
332	C₂×D₄×C₆₁	—	4	16	no	—
333	C₂×D₄×C₆₁	—	4	16	no	—
334	C₂×D₄×C₆₁	—	4	8	no	—
335	C₂×D₄×C₆₁	—	4	16	no	—
336	C₂×D₄×C₆₁	—	4	32	no	—
337	C₂×D₄×C₆₁	—	4	16	no	—
338	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
339	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
340	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
341	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
342	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
343	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
344	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
345	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
346	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
347	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
349	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
350	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
351	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
352	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
353	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
354	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
355	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
356	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
357	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
358	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
359	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
360	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₆₁	—	2	8	no	—
362	C₂²×C₄×C₆₁	—	4	16	no	—
363	C₂²×C₄×C₆₁	—	4	4	no	—
364	C₂²×C₄×C₆₁	—	4	8	no	—
365	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
370	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
371	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
372	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
374	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
377	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
378	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
379	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
382	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
384	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
387	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
391	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
392	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
393	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
394	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
395	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
396	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
398	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
399	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
401	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
403	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
407	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
408	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
410	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
411	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
412	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
416	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
420	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
421	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
422	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
423	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
424	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
425	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
426	C₄²×C₆₁	C₂⁴	1	2	yes	—
427	C₄²×C₆₁	C₂⁴	1	2	yes	—
428	C₄²×C₆₁	C₂⁴	1	4	yes	—
429	C₄²×C₆₁	C₂⁴	1	4	yes	—
430	C₄²×C₆₁	C₂⁴	1	4	yes	—
431	C₄²×C₆₁	C₂⁴	1	16	yes	—
432	C₂³×C₆₁	—	2	4	no	—
433	C₂³×C₆₁	—	2	4	no	—
434	C₂³×C₆₁	—	2	16	no	—
435	C₂³×C₆₁	—	2	4	no	—
436	C₂³×C₆₁	—	4	2	no	—
437	C₂³×C₆₁	—	4	8	no	—
438	C₂³×C₆₁	—	4	2	no	—
439	C₂³×C₆₁	—	4	2	no	—
440	C₂³×C₆₁	—	4	8	no	—
441	C₂³×C₆₁	—	4	8	no	—
442	C₂³×C₆₁	—	4	8	no	—
443	C₂³×C₆₁	—	4	8	no	—
444	C₂³×C₆₁	C₂⁵	1	8	yes	—
445	C₂³×C₆₁	C₂⁵	1	4	yes	—
446	C₂³×C₆₁	C₂⁵	1	4	yes	—
447	C₂³×C₆₁	C₂⁵	1	2	yes	—
448	C₂³×C₆₁	C₂⁵	1	2	yes	—
449	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
450	Q₈×C₆₁	—	2	4	no	—
451	Q₈×C₆₁	—	2	8	no	—
452	Q₈×C₆₁	—	2	8	no	—
453	Q₈×C₆₁	—	4	8	no	—
454	Q₈×C₆₁	—	4	4	no	—
455	Q₈×C₆₁	—	4	4	no	—
456	D₄×C₆₁	—	2	16	no	—
457	D₄×C₆₁	—	2	4	no	—
458	D₄×C₆₁	—	2	16	no	—
459	D₄×C₆₁	—	2	16	no	—
460	D₄×C₆₁	—	2	8	no	—
461	D₄×C₆₁	—	2	8	no	—
462	D₄×C₆₁	—	2	8	no	—
463	D₄×C₆₁	—	2	2	no	—
464	D₄×C₆₁	—	2	8	no	—
465	D₄×C₆₁	—	2	4	no	—
466	D₄×C₆₁	—	4	4	no	—
467	D₄×C₆₁	—	4	8	no	—
468	D₄×C₆₁	—	4	8	no	—
469	D₄×C₆₁	—	4	16	no	—
470	D₄×C₆₁	—	4	16	no	—
471	D₄×C₆₁	—	4	8	no	—
472	D₄×C₆₁	—	4	8	no	—
473	D₄×C₆₁	—	4	8	no	—
474	D₄×C₆₁	—	4	8	no	—
475	D₄×C₆₁	—	4	4	no	—
476	D₄×C₆₁	—	4	8	no	—
477	D₄×C₆₁	—	4	8	no	—
478	D₄×C₆₁	H(5,𝔽₂)	1	4	yes	complemented
479	C₂×C₄×C₆₁	—	2	4	no	—
480	C₂×C₄×C₆₁	—	2	16	no	—
481	C₂×C₄×C₆₁	—	2	8	no	—
482	C₂×C₄×C₆₁	—	2	8	no	—
483	C₂×C₄×C₆₁	—	2	2	no	—
484	C₂×C₄×C₆₁	—	2	8	no	—
485	C₂×C₄×C₆₁	—	2	8	no	—
486	C₂×C₄×C₆₁	—	2	16	no	—
487	C₂×C₄×C₆₁	—	2	8	no	—
488	C₂×C₄×C₆₁	—	4	2	no	—
489	C₂×C₄×C₆₁	—	4	4	no	—
490	C₂×C₄×C₆₁	—	4	8	no	—
491	C₂×C₄×C₆₁	—	4	4	no	—
492	C₂×C₄×C₆₁	—	4	8	no	—
493	C₂×C₄×C₆₁	—	4	8	no	—
494	C₂×C₄×C₆₁	—	4	8	no	—
495	C₂×C₄×C₆₁	—	4	1	no	—
496	C₂×C₄×C₆₁	—	4	4	no	—
497	C₂×C₄×C₆₁	—	4	16	no	—
498	C₂×C₄×C₆₁	—	4	8	no	—
499	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	complemented
500	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
501	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
502	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
503	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
504	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
505	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
506	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
507	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
508	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
509	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
511	#62914	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂²×C₆₁	—	2	2	no	—
513	C₂²×C₆₁	—	2	1	no	—
514	C₂²×C₆₁	—	2	1	no	—
515	C₂²×C₆₁	—	2	2	no	—
516	C₂²×C₆₁	—	2	2	no	—
517	C₂²×C₆₁	—	2	4	no	—
518	C₂²×C₆₁	—	2	4	no	—
519	C₂²×C₆₁	—	2	8	no	—
520	C₂²×C₆₁	—	2	4	no	—
521	C₂²×C₆₁	—	2	2	no	—
522	C₂²×C₆₁	—	2	8	no	—
523	C₂²×C₆₁	—	2	4	no	—
524	C₂²×C₆₁	—	2	4	no	—
525	C₂²×C₆₁	—	2	2	no	—
526	C₂²×C₆₁	—	2	8	no	—
527	C₂²×C₆₁	—	2	4	no	—
528	C₂²×C₆₁	—	4	8	no	—
529	C₂²×C₆₁	—	8	4	no	—
530	C₂²×C₆₁	—	8	16	no	—
531	C₂²×C₆₁	—	16	8	no	—
532	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
533	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
534	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
535	C₄×C₆₁	—	2	4	no	—
536	C₄×C₆₁	—	2	4	no	—
537	C₄×C₆₁	—	2	4	no	—
538	C₄×C₆₁	—	2	1	no	—
539	C₄×C₆₁	—	2	8	no	—
540	C₄×C₆₁	—	2	8	no	—
541	C₄×C₆₁	—	2	4	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	2	4	no	—
544	C₄×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
545	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
546	#3548	C₂×C₆₁	1	4	yes	complemented
547	#3546	C₂×C₆₁	1	4	yes	complemented
548	#3542	C₂×C₆₁	1	8	yes	complemented
549	#3536	C₂×C₆₁	1	8	yes	complemented
550	#3536	C₂×C₆₁	1	4	yes	complemented
551	#3534	C₂×C₆₁	1	8	yes	complemented
552	#3520	C₂×C₆₁	1	4	yes	complemented
553	#3511	C₂×C₆₁	1	2	yes	complemented
554	#3496	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#3496	C₂×C₆₁	1	4	yes	complemented
556	#3492	C₂×C₆₁	1	2	yes	complemented
557	#3488	C₂×C₆₁	1	4	yes	complemented
558	#3488	C₂×C₆₁	1	4	yes	complemented
559	D₄×#41	C₂×C₆₁	1	2	yes	complemented
560	C₂×#547	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3460	C₂×C₆₁	1	1	yes	characteristic, complemented
562	C₂×#537	C₂×C₆₁	1	2	yes	complemented
563	C₂×C₆₁	—	2	2	no	—
564	C₂×C₆₁	—	2	4	no	—
565	C₂×C₆₁	—	4	2	no	—
566	C₂×C₆₁	—	4	4	no	—
567	C₂×C₆₁	—	4	4	no	—
568	C₂×C₆₁	—	4	8	no	—
569	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
572	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	complemented
573	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	4	yes	complemented
574	C₂²×#41	C₂²×C₆₁	1	4	yes	complemented
575	C₂²×#41	C₂²×C₆₁	1	2	yes	complemented
576	#562	C₂²×C₆₁	1	16	yes	complemented
577	#562	C₂²×C₆₁	1	16	yes	complemented
578	#560	C₂²×C₆₁	1	16	yes	complemented
579	#556	C₂²×C₆₁	1	4	yes	complemented
580	#555	C₂²×C₆₁	1	4	yes	complemented
581	#554	C₂²×C₆₁	1	8	yes	complemented
582	#554	C₂²×C₆₁	1	4	yes	complemented
583	#554	C₂²×C₆₁	1	8	yes	complemented
584	#553	C₂²×C₆₁	1	8	yes	complemented
585	#553	C₂²×C₆₁	1	8	yes	complemented
586	#552	C₂²×C₆₁	1	8	yes	complemented
587	#551	C₂²×C₆₁	1	16	yes	complemented
588	#550	C₂²×C₆₁	1	2	yes	complemented
589	#550	C₂²×C₆₁	1	8	yes	complemented
590	#550	C₂²×C₆₁	1	8	yes	complemented
591	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
592	#548	C₂²×C₆₁	1	4	yes	complemented
593	#548	C₂²×C₆₁	1	8	yes	complemented
594	#548	C₂²×C₆₁	1	8	yes	complemented
595	#547	C₂²×C₆₁	1	4	yes	complemented
596	#547	C₂²×C₆₁	1	8	yes	complemented
597	#547	C₂²×C₆₁	1	4	yes	complemented
598	#547	C₂²×C₆₁	1	4	yes	complemented
599	#547	C₂²×C₆₁	1	2	yes	complemented
600	#547	C₂²×C₆₁	1	8	yes	complemented
601	#547	C₂²×C₆₁	1	4	yes	complemented
602	#547	C₂²×C₆₁	1	4	yes	complemented
603	#546	C₂²×C₆₁	1	8	yes	complemented
604	#546	C₂²×C₆₁	1	4	yes	complemented
605	#546	C₂²×C₆₁	1	8	yes	complemented
606	#546	C₂²×C₆₁	1	16	yes	complemented
607	#546	C₂²×C₆₁	1	16	yes	complemented
608	#546	C₂²×C₆₁	1	8	yes	complemented
609	#546	C₂²×C₆₁	1	16	yes	complemented
610	#546	C₂²×C₆₁	1	8	yes	complemented
611	#546	C₂²×C₆₁	1	8	yes	complemented
612	D₄²	C₂²×C₆₁	1	4	yes	complemented
613	D₄²	C₂²×C₆₁	1	2	yes	complemented
614	D₄²	C₂²×C₆₁	1	16	yes	complemented
615	D₄²	C₂²×C₆₁	1	8	yes	complemented
616	D₄²	C₂²×C₆₁	1	4	yes	complemented
617	#544	C₂²×C₆₁	1	1	yes	characteristic, complemented
618	#543	C₂²×C₆₁	1	8	yes	complemented
619	#542	C₂²×C₆₁	1	4	yes	complemented
620	#542	C₂²×C₆₁	1	8	yes	complemented
621	#542	C₂²×C₆₁	1	8	yes	complemented
622	#540	C₂²×C₆₁	1	4	yes	complemented
623	#540	C₂²×C₆₁	1	16	yes	complemented
624	#539	C₂²×C₆₁	1	8	yes	complemented
625	#539	C₂²×C₆₁	1	16	yes	complemented
626	#538	C₂²×C₆₁	1	4	yes	complemented
627	#538	C₂²×C₆₁	1	16	yes	complemented
628	#538	C₂²×C₆₁	1	8	yes	complemented
629	#537	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#537	C₂²×C₆₁	1	4	yes	complemented
631	#537	C₂²×C₆₁	1	2	yes	complemented
632	#537	C₂²×C₆₁	1	8	yes	complemented
633	#537	C₂²×C₆₁	1	8	yes	complemented
634	#537	C₂²×C₆₁	1	8	yes	complemented
635	#537	C₂²×C₆₁	1	8	yes	complemented
636	#537	C₂²×C₆₁	1	8	yes	complemented
637	#537	C₂²×C₆₁	1	4	yes	complemented
638	#537	C₂²×C₆₁	1	8	yes	complemented
639	#535	C₂²×C₆₁	1	2	yes	complemented
640	#535	C₂²×C₆₁	1	8	yes	complemented
641	#535	C₂²×C₆₁	1	8	yes	complemented
642	#535	C₂²×C₆₁	1	4	yes	complemented
643	#534	C₂²×C₆₁	1	4	yes	complemented
644	#534	C₂²×C₆₁	1	16	yes	complemented
645	#533	C₂²×C₆₁	1	4	yes	complemented
646	#532	C₂²×C₆₁	1	4	yes	complemented
647	#532	C₂²×C₆₁	1	2	yes	complemented
648	#532	C₂²×C₆₁	1	4	yes	complemented
649	#532	C₂²×C₆₁	1	4	yes	complemented
650	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
651	#529	C₂²×C₆₁	1	4	yes	complemented
652	#525	C₂²×C₆₁	1	4	yes	complemented
653	#525	C₂²×C₆₁	1	4	yes	complemented
654	#525	C₂²×C₆₁	1	8	yes	complemented
655	#525	C₂²×C₆₁	1	8	yes	complemented
656	#525	C₂²×C₆₁	1	8	yes	complemented
657	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
658	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
659	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
660	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
661	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
662	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
663	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
664	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
665	#520	C₂²×C₆₁	1	4	yes	complemented
666	#520	C₂²×C₆₁	1	4	yes	complemented
667	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
668	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
670	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
671	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
672	C₆₁	#62914	1	1	yes	characteristic, direct product factor, Sylow
673	H(5,𝔽₂)	—	4	16	no	—
674	H(5,𝔽₂)	—	4	8	no	—
675	C₂×#41	—	4	16	no	—
676	C₂×#41	—	4	8	no	—
677	C₂×#41	C₂³×C₆₁	1	2	yes	—
678	C₂×#41	C₂³×C₆₁	1	4	yes	—
679	C₂×#41	C₂³×C₆₁	1	4	yes	—
680	C₂×#41	C₂³×C₆₁	1	4	yes	—
681	C₂×#41	C₂³×C₆₁	1	8	yes	—
682	C₂×#41	C₂³×C₆₁	1	8	yes	—
683	C₂×#41	C₂³×C₆₁	1	8	yes	—
684	C₂×#41	C₂³×C₆₁	1	8	yes	—
685	C₂×#41	C₂³×C₆₁	1	8	yes	—
686	C₂×#41	C₂³×C₆₁	1	4	yes	—
687	C₂×#41	C₂³×C₆₁	1	8	yes	—
688	C₂×#41	C₂³×C₆₁	1	4	yes	—
689	C₂×#41	C₂³×C₆₁	1	4	yes	—
690	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
691	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
692	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
695	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
696	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
697	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
698	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
699	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
700	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
701	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
702	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
703	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
704	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
705	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
706	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
707	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
708	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
709	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
710	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
711	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
712	#127	C₂³×C₆₁	1	2	yes	—
713	#127	C₂³×C₆₁	1	4	yes	—
714	#127	C₂³×C₆₁	1	4	yes	—
715	#127	C₂³×C₆₁	1	16	yes	—
716	#126	C₂³×C₆₁	1	8	yes	—
717	#126	C₂³×C₆₁	1	16	yes	—
718	#126	C₂³×C₆₁	1	16	yes	—
719	#125	C₂³×C₆₁	1	4	yes	—
720	#125	C₂³×C₆₁	1	8	yes	—
721	#125	C₂³×C₆₁	1	16	yes	—
722	#124	C₂³×C₆₁	1	4	yes	—
723	#124	C₂³×C₆₁	1	8	yes	—
724	#124	C₂³×C₆₁	1	8	yes	—
725	#124	C₂³×C₆₁	1	8	yes	—
726	#124	C₂³×C₆₁	1	4	yes	—
727	#124	C₂³×C₆₁	1	16	yes	—
728	#124	C₂³×C₆₁	1	16	yes	—
729	#123	C₂³×C₆₁	1	16	yes	—
730	#123	C₂³×C₆₁	1	16	yes	—
731	#123	C₂³×C₆₁	1	16	yes	—
732	#123	C₂³×C₆₁	1	8	yes	—
733	#123	C₂³×C₆₁	1	8	yes	—
734	#123	C₂³×C₆₁	1	16	yes	—
735	#123	C₂³×C₆₁	1	8	yes	—
736	#123	C₂³×C₆₁	1	8	yes	—
737	#123	C₂³×C₆₁	1	8	yes	—
738	#123	C₂³×C₆₁	1	16	yes	—
739	#123	C₂³×C₆₁	1	16	yes	—
740	#123	C₂³×C₆₁	1	16	yes	—
741	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
742	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
743	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
744	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
745	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
746	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
747	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
748	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
749	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
750	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
751	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
752	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
753	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
754	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
755	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
756	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
757	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
758	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
759	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
760	#121	C₂³×C₆₁	1	8	yes	—
761	#121	C₂³×C₆₁	1	4	yes	—
762	#121	C₂³×C₆₁	1	8	yes	—
763	#121	C₂³×C₆₁	1	4	yes	—
764	#121	C₂³×C₆₁	1	8	yes	—
765	#121	C₂³×C₆₁	1	4	yes	—
766	#121	C₂³×C₆₁	1	4	yes	—
767	#121	C₂³×C₆₁	1	4	yes	—
768	#121	C₂³×C₆₁	1	16	yes	—
769	#121	C₂³×C₆₁	1	16	yes	—
770	#121	C₂³×C₆₁	1	8	yes	—
771	#121	C₂³×C₆₁	1	8	yes	—
772	#121	C₂³×C₆₁	1	8	yes	—
773	#121	C₂³×C₆₁	1	8	yes	—
774	#121	C₂³×C₆₁	1	8	yes	—
775	#121	C₂³×C₆₁	1	16	yes	—
776	#121	C₂³×C₆₁	1	8	yes	—
777	#121	C₂³×C₆₁	1	16	yes	—
778	#121	C₂³×C₆₁	1	16	yes	—
779	#121	C₂³×C₆₁	1	16	yes	—
780	#121	C₂³×C₆₁	1	8	yes	—
781	#121	C₂³×C₆₁	1	4	yes	—
782	#121	C₂³×C₆₁	1	4	yes	—
783	#121	C₂³×C₆₁	1	4	yes	—
784	#121	C₂³×C₆₁	1	8	yes	—
785	#121	C₂³×C₆₁	1	8	yes	—
786	#121	C₂³×C₆₁	1	8	yes	—
787	#121	C₂³×C₆₁	1	8	yes	—
788	#121	C₂³×C₆₁	1	4	yes	—
789	#121	C₂³×C₆₁	1	8	yes	—
790	#121	C₂³×C₆₁	1	4	yes	—
791	#121	C₂³×C₆₁	1	4	yes	—
792	#121	C₂³×C₆₁	1	8	yes	—
793	#121	C₂³×C₆₁	1	16	yes	—
794	#121	C₂³×C₆₁	1	16	yes	—
795	#121	C₂³×C₆₁	1	16	yes	—
796	#120	C₂³×C₆₁	1	8	yes	—
797	#120	C₂³×C₆₁	1	8	yes	—
798	#120	C₂³×C₆₁	1	16	yes	—
799	#120	C₂³×C₆₁	1	8	yes	—
800	#120	C₂³×C₆₁	1	8	yes	—
801	#120	C₂³×C₆₁	1	16	yes	—
802	#120	C₂³×C₆₁	1	16	yes	—
803	#120	C₂³×C₆₁	1	16	yes	—
804	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
806	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
807	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
808	C₄×D₄	C₂³×C₆₁	1	2	yes	—
809	C₄×D₄	C₂³×C₆₁	1	4	yes	—
810	C₄×D₄	C₂³×C₆₁	1	8	yes	—
811	C₄×D₄	C₂³×C₆₁	1	4	yes	—
812	C₄×D₄	C₂³×C₆₁	1	4	yes	—
813	C₄×D₄	C₂³×C₆₁	1	4	yes	—
814	C₄×D₄	C₂³×C₆₁	1	2	yes	—
815	C₄×D₄	C₂³×C₆₁	1	8	yes	—
816	C₄×D₄	C₂³×C₆₁	1	4	yes	—
817	C₄×D₄	C₂³×C₆₁	1	4	yes	—
818	C₄×D₄	C₂³×C₆₁	1	4	yes	—
819	C₄×D₄	C₂³×C₆₁	1	2	yes	—
820	C₄×D₄	C₂³×C₆₁	1	4	yes	—
821	C₄×D₄	C₂³×C₆₁	1	2	yes	—
822	C₄×D₄	C₂³×C₆₁	1	16	yes	—
823	C₄×D₄	C₂³×C₆₁	1	16	yes	—
824	C₄×D₄	C₂³×C₆₁	1	8	yes	—
825	C₄×D₄	C₂³×C₆₁	1	4	yes	—
826	C₄×D₄	C₂³×C₆₁	1	8	yes	—
827	C₄×D₄	C₂³×C₆₁	1	8	yes	—
828	C₄×D₄	C₂³×C₆₁	1	16	yes	—
829	C₄×D₄	C₂³×C₆₁	1	16	yes	—
830	C₄×D₄	C₂³×C₆₁	1	8	yes	—
831	#117	C₂³×C₆₁	1	2	yes	—
832	#117	C₂³×C₆₁	1	4	yes	—
833	#117	C₂³×C₆₁	1	4	yes	—
834	#117	C₂³×C₆₁	1	8	yes	—
835	#117	C₂³×C₆₁	1	8	yes	—
836	#117	C₂³×C₆₁	1	8	yes	—
837	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
839	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
840	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
841	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
842	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
844	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
845	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
846	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
847	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
848	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
849	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
850	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
851	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
852	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
853	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
854	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
855	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
856	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
857	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
858	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
859	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
860	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
861	#41	—	2	16	no	—
862	#41	—	2	8	no	—
863	#41	—	2	16	no	—
864	#41	—	4	16	no	—
865	#41	—	4	8	no	—
866	#41	—	4	16	no	—
867	#41	—	4	16	no	—
868	#41	—	4	16	no	—
869	#41	—	4	8	no	—
870	#41	—	4	8	no	—
871	#41	—	4	8	no	—
872	#41	—	4	16	no	—
873	#41	—	4	16	no	—
874	C₂×Q₈	—	4	8	no	—
875	C₂×Q₈	—	4	4	no	—
876	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
877	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
878	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
879	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
880	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
881	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	16	no	—
884	C₂×D₄	—	2	4	no	—
885	C₂×D₄	—	4	8	no	—
886	C₂×D₄	—	4	8	no	—
887	C₂×D₄	—	4	16	no	—
888	C₂×D₄	—	4	16	no	—
889	C₂×D₄	—	4	8	no	—
890	C₂×D₄	—	4	16	no	—
891	C₂×D₄	—	4	32	no	—
892	C₂×D₄	—	4	16	no	—
893	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
894	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
895	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
896	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
897	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
898	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
899	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
900	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
901	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
902	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
904	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
905	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
906	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
907	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
908	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
909	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
910	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
911	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
912	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
913	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
914	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
915	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂²×C₄	—	2	8	no	—
917	C₂²×C₄	—	4	16	no	—
918	C₂²×C₄	—	4	4	no	—
919	C₂²×C₄	—	4	8	no	—
920	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
922	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
923	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
925	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
926	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
927	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
928	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
929	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
931	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
932	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
933	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
934	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
935	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
936	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
937	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
938	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
939	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
940	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
942	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
946	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
947	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
948	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
949	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
950	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
951	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
953	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
954	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
956	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
957	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
958	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
959	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
960	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
962	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
963	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
964	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
965	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
966	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
967	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
968	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
969	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
970	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
971	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
972	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
973	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
974	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
975	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
976	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
977	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
978	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
979	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
980	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
981	C₄²	C₂⁴×C₆₁	1	2	yes	—
982	C₄²	C₂⁴×C₆₁	1	2	yes	—
983	C₄²	C₂⁴×C₆₁	1	4	yes	—
984	C₄²	C₂⁴×C₆₁	1	4	yes	—
985	C₄²	C₂⁴×C₆₁	1	4	yes	—
986	C₄²	C₂⁴×C₆₁	1	16	yes	—
987	C₂³	—	2	4	no	—
988	C₂³	—	2	4	no	—
989	C₂³	—	2	16	no	—
990	C₂³	—	2	4	no	—
991	C₂³	—	4	2	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	2	no	—
994	C₂³	—	4	2	no	—
995	C₂³	—	4	8	no	—
996	C₂³	—	4	8	no	—
997	C₂³	—	4	8	no	—
998	C₂³	—	4	8	no	—
999	C₂³	C₂⁵×C₆₁	1	8	yes	—
1000	C₂³	C₂⁵×C₆₁	1	4	yes	—
1001	C₂³	C₂⁵×C₆₁	1	4	yes	—
1002	C₂³	C₂⁵×C₆₁	1	2	yes	—
1003	C₂³	C₂⁵×C₆₁	1	2	yes	—
1004	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1005	Q₈	—	2	4	no	—
1006	Q₈	—	2	8	no	—
1007	Q₈	—	2	8	no	—
1008	Q₈	—	4	8	no	—
1009	Q₈	—	4	4	no	—
1010	Q₈	—	4	4	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	4	no	—
1013	D₄	—	2	16	no	—
1014	D₄	—	2	16	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	8	no	—
1020	D₄	—	2	4	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	D₄	—	4	8	no	—
1024	D₄	—	4	16	no	—
1025	D₄	—	4	16	no	—
1026	D₄	—	4	8	no	—
1027	D₄	—	4	8	no	—
1028	D₄	—	4	8	no	—
1029	D₄	—	4	8	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	8	no	—
1032	D₄	—	4	8	no	—
1033	D₄	H(5,𝔽₂)×C₆₁	1	4	yes	complemented
1034	C₂×C₄	—	2	4	no	—
1035	C₂×C₄	—	2	16	no	—
1036	C₂×C₄	—	2	8	no	—
1037	C₂×C₄	—	2	8	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	8	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	16	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	8	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	16	no	—
1053	C₂×C₄	—	4	8	no	—
1054	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	complemented
1055	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1056	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1058	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1059	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1060	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1061	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1062	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1063	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
1064	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	4	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	8	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	2	4	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	8	no	—
1081	C₂²	—	2	4	no	—
1082	C₂²	—	4	8	no	—
1083	C₂²	—	8	4	no	—
1084	C₂²	—	8	16	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
1087	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
1088	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1089	C₄	—	2	4	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	8	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	4	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
1099	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	4	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	4	4	no	—
1104	C₂	—	4	4	no	—
1105	C₂	—	4	8	no	—
1106	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1107	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1108	C₂	C₆₁×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3546	C₂	semidirect
3. C₆₁×#3542	C₂	semidirect
4. C₆₁×#3536	C₂	semidirect
5. C₆₁×#3536	C₂	semidirect
6. C₆₁×#3534	C₂	semidirect
7. C₆₁×#3520	C₂	semidirect
8. C₆₁×#3511	C₂	semidirect
9. C₆₁×#3496	C₂	semidirect
10. C₆₁×#3496	C₂	semidirect
11. C₆₁×#3492	C₂	semidirect
12. C₆₁×#3488	C₂	semidirect
13. C₆₁×#3488	C₂	semidirect
14. D₄×#41×C₆₁	C₂	semidirect
15. C₂×C₆₁×#547	C₂	semidirect
16. C₆₁×#3460	C₂	semidirect
17. C₂×C₆₁×#537	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
19. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
20. C₂²×#41×C₆₁	C₂²	semidirect
21. C₂²×#41×C₆₁	C₂²	semidirect
22. C₆₁×#562	C₂²	semidirect
23. C₆₁×#562	C₂²	semidirect
24. C₆₁×#560	C₂²	semidirect
25. C₆₁×#556	C₂²	semidirect
26. C₆₁×#555	C₂²	semidirect
27. C₆₁×#554	C₂²	semidirect
28. C₆₁×#554	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
30. C₆₁×#553	C₂²	semidirect
31. C₆₁×#553	C₂²	semidirect
32. C₆₁×#552	C₂²	semidirect
33. C₆₁×#551	C₂²	semidirect
34. C₆₁×#550	C₂²	semidirect
35. C₆₁×#550	C₂²	semidirect
36. C₆₁×#550	C₂²	semidirect
37. D₄×Q₈×C₆₁	C₂²	semidirect
38. C₆₁×#548	C₂²	semidirect
39. C₆₁×#548	C₂²	semidirect
40. C₆₁×#548	C₂²	semidirect
41. C₆₁×#547	C₂²	semidirect
42. C₆₁×#547	C₂²	semidirect
43. C₆₁×#547	C₂²	semidirect
44. C₆₁×#547	C₂²	semidirect
45. C₆₁×#547	C₂²	semidirect
46. C₆₁×#547	C₂²	semidirect
47. C₆₁×#547	C₂²	semidirect
48. C₆₁×#547	C₂²	semidirect
49. C₆₁×#546	C₂²	semidirect
50. C₆₁×#546	C₂²	semidirect
51. C₆₁×#546	C₂²	semidirect
52. C₆₁×#546	C₂²	semidirect
53. C₆₁×#546	C₂²	semidirect
54. C₆₁×#546	C₂²	semidirect
55. C₆₁×#546	C₂²	semidirect
56. C₆₁×#546	C₂²	semidirect
57. C₆₁×#546	C₂²	semidirect
58. D₄²×C₆₁	C₂²	semidirect
59. D₄²×C₆₁	C₂²	semidirect
60. D₄²×C₆₁	C₂²	semidirect
61. D₄²×C₆₁	C₂²	semidirect
62. D₄²×C₆₁	C₂²	semidirect
63. C₆₁×#544	C₂²	semidirect
64. C₆₁×#543	C₂²	semidirect
65. C₆₁×#542	C₂²	semidirect
66. C₆₁×#542	C₂²	semidirect
67. C₆₁×#542	C₂²	semidirect
68. C₆₁×#540	C₂²	semidirect
69. C₆₁×#540	C₂²	semidirect
70. C₆₁×#539	C₂²	semidirect
71. C₆₁×#539	C₂²	semidirect
72. C₆₁×#538	C₂²	semidirect
73. C₆₁×#538	C₂²	semidirect
74. C₆₁×#538	C₂²	semidirect
75. C₆₁×#537	C₂²	semidirect
76. C₆₁×#537	C₂²	semidirect
77. C₆₁×#537	C₂²	semidirect
78. C₆₁×#537	C₂²	semidirect
79. C₆₁×#537	C₂²	semidirect
80. C₆₁×#537	C₂²	semidirect
81. C₆₁×#537	C₂²	semidirect
82. C₆₁×#537	C₂²	semidirect
83. C₆₁×#537	C₂²	semidirect
84. C₆₁×#537	C₂²	semidirect
85. C₆₁×#535	C₂²	semidirect
86. C₆₁×#535	C₂²	semidirect
87. C₆₁×#535	C₂²	semidirect
88. C₆₁×#535	C₂²	semidirect
89. C₆₁×#534	C₂²	semidirect
90. C₆₁×#534	C₂²	semidirect
91. C₆₁×#533	C₂²	semidirect
92. C₆₁×#532	C₂²	semidirect
93. C₆₁×#532	C₂²	semidirect
94. C₆₁×#532	C₂²	semidirect
95. C₆₁×#532	C₂²	semidirect
96. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
97. C₆₁×#529	C₂²	semidirect
98. C₆₁×#525	C₂²	semidirect
99. C₆₁×#525	C₂²	semidirect
100. C₆₁×#525	C₂²	semidirect
101. C₆₁×#525	C₂²	semidirect
102. C₆₁×#525	C₂²	semidirect
103. C₂×#123×C₆₁	C₂²	semidirect
104. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
105. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
106. C₂×#121×C₆₁	C₂²	semidirect
107. C₂×#121×C₆₁	C₂²	semidirect
108. C₂×#121×C₆₁	C₂²	semidirect
109. C₂×#121×C₆₁	C₂²	semidirect
110. C₂×#121×C₆₁	C₂²	semidirect
111. C₆₁×#520	C₂²	semidirect
112. C₆₁×#520	C₂²	semidirect
113. C₄×#41×C₆₁	C₂²	semidirect
114. C₂×C₄×D₄×C₆₁	C₂²	semidirect
115. C₂×C₄×D₄×C₆₁	C₂²	semidirect
116. C₂×C₄×D₄×C₆₁	C₂²	semidirect
117. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
478. D₄×C₆₁	H(5,𝔽₂)	semidirect
499. C₂×C₄×C₆₁	H(5,𝔽₂)	semidirect
511. #62914	C₆₁	direct (N × H)
546. #3548	C₂×C₆₁	semidirect
547. #3546	C₂×C₆₁	semidirect
548. #3542	C₂×C₆₁	semidirect
549. #3536	C₂×C₆₁	semidirect
550. #3536	C₂×C₆₁	semidirect
551. #3534	C₂×C₆₁	semidirect
552. #3520	C₂×C₆₁	semidirect
553. #3511	C₂×C₆₁	semidirect
554. #3496	C₂×C₆₁	semidirect
555. #3496	C₂×C₆₁	semidirect
556. #3492	C₂×C₆₁	semidirect
557. #3488	C₂×C₆₁	semidirect
558. #3488	C₂×C₆₁	semidirect
559. D₄×#41	C₂×C₆₁	semidirect
560. C₂×#547	C₂×C₆₁	semidirect
561. #3460	C₂×C₆₁	semidirect
562. C₂×#537	C₂×C₆₁	semidirect
572. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
573. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
574. C₂²×#41	C₂²×C₆₁	semidirect
575. C₂²×#41	C₂²×C₆₁	semidirect
576. #562	C₂²×C₆₁	semidirect
577. #562	C₂²×C₆₁	semidirect
578. #560	C₂²×C₆₁	semidirect
579. #556	C₂²×C₆₁	semidirect
580. #555	C₂²×C₆₁	semidirect
581. #554	C₂²×C₆₁	semidirect
582. #554	C₂²×C₆₁	semidirect
583. #554	C₂²×C₆₁	semidirect
584. #553	C₂²×C₆₁	semidirect
585. #553	C₂²×C₆₁	semidirect
586. #552	C₂²×C₆₁	semidirect
587. #551	C₂²×C₆₁	semidirect
588. #550	C₂²×C₆₁	semidirect
589. #550	C₂²×C₆₁	semidirect
590. #550	C₂²×C₆₁	semidirect
591. D₄×Q₈	C₂²×C₆₁	semidirect
592. #548	C₂²×C₆₁	semidirect
593. #548	C₂²×C₆₁	semidirect
594. #548	C₂²×C₆₁	semidirect
595. #547	C₂²×C₆₁	semidirect
596. #547	C₂²×C₆₁	semidirect
597. #547	C₂²×C₆₁	semidirect
598. #547	C₂²×C₆₁	semidirect
599. #547	C₂²×C₆₁	semidirect
600. #547	C₂²×C₆₁	semidirect
601. #547	C₂²×C₆₁	semidirect
602. #547	C₂²×C₆₁	semidirect
603. #546	C₂²×C₆₁	semidirect
604. #546	C₂²×C₆₁	semidirect
605. #546	C₂²×C₆₁	semidirect
606. #546	C₂²×C₆₁	semidirect
607. #546	C₂²×C₆₁	semidirect
608. #546	C₂²×C₆₁	semidirect
609. #546	C₂²×C₆₁	semidirect
610. #546	C₂²×C₆₁	semidirect
611. #546	C₂²×C₆₁	semidirect
612. D₄²	C₂²×C₆₁	semidirect
613. D₄²	C₂²×C₆₁	semidirect
614. D₄²	C₂²×C₆₁	semidirect
615. D₄²	C₂²×C₆₁	semidirect
616. D₄²	C₂²×C₆₁	semidirect
617. #544	C₂²×C₆₁	semidirect
618. #543	C₂²×C₆₁	semidirect
619. #542	C₂²×C₆₁	semidirect
620. #542	C₂²×C₆₁	semidirect
621. #542	C₂²×C₆₁	semidirect
622. #540	C₂²×C₆₁	semidirect
623. #540	C₂²×C₆₁	semidirect
624. #539	C₂²×C₆₁	semidirect
625. #539	C₂²×C₆₁	semidirect
626. #538	C₂²×C₆₁	semidirect
627. #538	C₂²×C₆₁	semidirect
628. #538	C₂²×C₆₁	semidirect
629. #537	C₂²×C₆₁	semidirect
630. #537	C₂²×C₆₁	semidirect
631. #537	C₂²×C₆₁	semidirect
632. #537	C₂²×C₆₁	semidirect
633. #537	C₂²×C₆₁	semidirect
634. #537	C₂²×C₆₁	semidirect
635. #537	C₂²×C₆₁	semidirect
636. #537	C₂²×C₆₁	semidirect
637. #537	C₂²×C₆₁	semidirect
638. #537	C₂²×C₆₁	semidirect
639. #535	C₂²×C₆₁	semidirect
640. #535	C₂²×C₆₁	semidirect
641. #535	C₂²×C₆₁	semidirect
642. #535	C₂²×C₆₁	semidirect
643. #534	C₂²×C₆₁	semidirect
644. #534	C₂²×C₆₁	semidirect
645. #533	C₂²×C₆₁	semidirect
646. #532	C₂²×C₆₁	semidirect
647. #532	C₂²×C₆₁	semidirect
648. #532	C₂²×C₆₁	semidirect
649. #532	C₂²×C₆₁	semidirect
650. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
651. #529	C₂²×C₆₁	semidirect
652. #525	C₂²×C₆₁	semidirect
653. #525	C₂²×C₆₁	semidirect
654. #525	C₂²×C₆₁	semidirect
655. #525	C₂²×C₆₁	semidirect
656. #525	C₂²×C₆₁	semidirect
657. C₂×#123	C₂²×C₆₁	semidirect
658. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
659. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
660. C₂×#121	C₂²×C₆₁	semidirect
661. C₂×#121	C₂²×C₆₁	semidirect
662. C₂×#121	C₂²×C₆₁	semidirect
663. C₂×#121	C₂²×C₆₁	semidirect
664. C₂×#121	C₂²×C₆₁	semidirect
665. #520	C₂²×C₆₁	semidirect
666. #520	C₂²×C₆₁	semidirect
667. C₄×#41	C₂²×C₆₁	semidirect
668. C₂×C₄×D₄	C₂²×C₆₁	semidirect
669. C₂×C₄×D₄	C₂²×C₆₁	semidirect
670. C₂×C₄×D₄	C₂²×C₆₁	semidirect
671. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
672. C₆₁	#62914	direct (N × H)
1033. D₄	H(5,𝔽₂)×C₆₁	semidirect
1054. C₂×C₄	H(5,𝔽₂)×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3548	2
C₆₁×#3546	2
C₆₁×#3542	2
C₆₁×#3536	2
C₆₁×#3534	2
C₆₁×#3520	2
C₆₁×#3511	2
C₆₁×#3496	2
C₆₁×#3492	2
C₆₁×#3488	2
D₄×#41×C₆₁	2
C₂×C₆₁×#547	2
C₆₁×#3460	2
C₂×C₆₁×#537	2
#62914	61

Subgroups — C61×#62914 #29566347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62914 #29566347