Subgroups — C₆₁×#62818 #29566251

Order 15616.

8042 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×#3542	C₂	1	8	yes	maximal, complemented
2	C₆₁×#3537	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3536	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3534	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3519	C₂	1	8	yes	maximal, complemented
6	C₆₁×#3505	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3496	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3494	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3492	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3490	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3488	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3484	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3484	C₂	1	2	yes	maximal, complemented
14	C₂×C₆₁×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×#121×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	complemented
17	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	4	yes	complemented
18	C₂²×#41×C₆₁	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₆₁	C₂²	1	2	yes	complemented
21	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₆₁×#562	C₂²	1	16	yes	complemented
23	C₆₁×#560	C₂²	1	16	yes	complemented
24	C₆₁×#555	C₂²	1	8	yes	complemented
25	C₆₁×#554	C₂²	1	8	yes	complemented
26	C₆₁×#553	C₂²	1	8	yes	complemented
27	C₆₁×#553	C₂²	1	8	yes	complemented
28	C₆₁×#553	C₂²	1	8	yes	complemented
29	C₆₁×#553	C₂²	1	16	yes	complemented
30	C₆₁×#552	C₂²	1	8	yes	complemented
31	C₆₁×#551	C₂²	1	16	yes	complemented
32	C₆₁×#551	C₂²	1	16	yes	complemented
33	C₆₁×#550	C₂²	1	8	yes	complemented
34	C₆₁×#548	C₂²	1	8	yes	complemented
35	C₆₁×#547	C₂²	1	8	yes	complemented
36	C₆₁×#547	C₂²	1	8	yes	complemented
37	C₆₁×#546	C₂²	1	16	yes	complemented
38	C₆₁×#546	C₂²	1	8	yes	complemented
39	C₆₁×#546	C₂²	1	8	yes	complemented
40	C₆₁×#546	C₂²	1	16	yes	complemented
41	C₆₁×#546	C₂²	1	16	yes	complemented
42	C₆₁×#546	C₂²	1	16	yes	complemented
43	C₆₁×#546	C₂²	1	8	yes	complemented
44	C₆₁×#546	C₂²	1	16	yes	complemented
45	D₄²×C₆₁	C₂²	1	16	yes	complemented
46	D₄²×C₆₁	C₂²	1	8	yes	complemented
47	D₄²×C₆₁	C₂²	1	16	yes	complemented
48	D₄²×C₆₁	C₂²	1	8	yes	complemented
49	D₄²×C₆₁	C₂²	1	8	yes	complemented
50	C₆₁×#544	C₂²	1	2	yes	complemented
51	C₆₁×#543	C₂²	1	4	yes	complemented
52	C₆₁×#542	C₂²	1	8	yes	complemented
53	C₆₁×#540	C₂²	1	8	yes	complemented
54	C₆₁×#540	C₂²	1	16	yes	complemented
55	C₆₁×#539	C₂²	1	8	yes	complemented
56	C₆₁×#539	C₂²	1	8	yes	complemented
57	C₆₁×#538	C₂²	1	8	yes	complemented
58	C₆₁×#538	C₂²	1	8	yes	complemented
59	C₆₁×#538	C₂²	1	8	yes	complemented
60	C₆₁×#538	C₂²	1	16	yes	complemented
61	C₆₁×#537	C₂²	1	2	yes	complemented
62	C₆₁×#537	C₂²	1	8	yes	complemented
63	C₆₁×#537	C₂²	1	8	yes	complemented
64	C₆₁×#535	C₂²	1	4	yes	complemented
65	C₆₁×#535	C₂²	1	8	yes	complemented
66	C₆₁×#535	C₂²	1	8	yes	complemented
67	C₆₁×#534	C₂²	1	8	yes	complemented
68	C₆₁×#534	C₂²	1	8	yes	complemented
69	C₆₁×#534	C₂²	1	8	yes	complemented
70	C₆₁×#534	C₂²	1	4	yes	complemented
71	C₆₁×#534	C₂²	1	8	yes	complemented
72	C₆₁×#532	C₂²	1	8	yes	complemented
73	C₆₁×#529	C₂²	1	8	yes	complemented
74	C₆₁×#525	C₂²	1	4	yes	complemented
75	C₆₁×#525	C₂²	1	4	yes	complemented
76	C₆₁×#525	C₂²	1	8	yes	complemented
77	C₆₁×#525	C₂²	1	4	yes	complemented
78	C₆₁×#525	C₂²	1	4	yes	complemented
79	C₆₁×#525	C₂²	1	4	yes	complemented
80	C₆₁×#525	C₂²	1	4	yes	complemented
81	C₆₁×#525	C₂²	1	4	yes	complemented
82	C₆₁×#525	C₂²	1	4	yes	complemented
83	C₆₁×#525	C₂²	1	8	yes	complemented
84	C₂×#123×C₆₁	C₂²	1	4	yes	complemented
85	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
87	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
88	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
89	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
90	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
91	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
92	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
93	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
94	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
95	C₂×#121×C₆₁	C₂²	1	8	yes	complemented
96	C₂×#120×C₆₁	C₂²	1	4	yes	complemented
97	C₂×#120×C₆₁	C₂²	1	8	yes	complemented
98	C₆₁×#520	C₂²	1	4	yes	complemented
99	C₆₁×#518	C₂²	1	2	yes	complemented
100	C₆₁×#518	C₂²	1	4	yes	complemented
101	C₆₁×#518	C₂²	1	8	yes	complemented
102	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
103	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
104	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
105	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
106	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
108	C₂⁵×C₆₁	C₂³	1	2	yes	—
109	H(5,𝔽₂)×C₆₁	—	4	16	no	—
110	H(5,𝔽₂)×C₆₁	—	4	8	no	—
111	C₂×#41×C₆₁	—	4	8	no	—
112	C₂×#41×C₆₁	C₂³	1	4	yes	—
113	C₂×#41×C₆₁	C₂³	1	8	yes	—
114	C₂×#41×C₆₁	C₂³	1	4	yes	—
115	C₂×#41×C₆₁	C₂³	1	16	yes	complemented
116	C₂×#41×C₆₁	C₂³	1	4	yes	complemented
117	C₂×#41×C₆₁	C₂³	1	8	yes	complemented
118	C₂×#41×C₆₁	C₂³	1	4	yes	complemented
119	C₂²×Q₈×C₆₁	C₂³	1	2	yes	complemented
120	C₂²×D₄×C₆₁	—	4	4	no	—
121	C₂²×D₄×C₆₁	—	4	8	no	—
122	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
123	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
124	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
127	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
128	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
129	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
130	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
131	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
132	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
133	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
134	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
135	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
136	C₂²×D₄×C₆₁	C₂³	1	16	yes	complemented
137	C₂²×D₄×C₆₁	C₂³	1	8	yes	complemented
138	C₂²×D₄×C₆₁	C₂³	1	2	yes	complemented
139	C₂³×C₄×C₆₁	—	4	4	no	—
140	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
148	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
149	C₂³×C₄×C₆₁	C₂³	1	4	yes	complemented
150	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	complemented
151	#127×C₆₁	C₂³	1	8	yes	complemented
152	#127×C₆₁	C₂³	1	16	yes	complemented
153	#126×C₆₁	C₂³	1	16	yes	complemented
154	#126×C₆₁	C₂³	1	16	yes	complemented
155	#126×C₆₁	C₂³	1	16	yes	complemented
156	#125×C₆₁	C₂³	1	16	yes	complemented
157	#125×C₆₁	C₂³	1	8	yes	complemented
158	#124×C₆₁	C₂³	1	16	yes	complemented
159	#124×C₆₁	C₂³	1	16	yes	complemented
160	#124×C₆₁	C₂³	1	16	yes	complemented
161	#124×C₆₁	C₂³	1	8	yes	complemented
162	#123×C₆₁	C₂³	1	8	yes	—
163	#123×C₆₁	C₂³	1	16	yes	—
164	#123×C₆₁	C₂³	1	8	yes	—
165	#123×C₆₁	C₂³	1	16	yes	complemented
166	#123×C₆₁	C₂³	1	16	yes	complemented
167	#123×C₆₁	C₂³	1	16	yes	complemented
168	#123×C₆₁	C₂³	1	16	yes	complemented
169	#123×C₆₁	C₂³	1	16	yes	complemented
170	#123×C₆₁	C₂³	1	16	yes	complemented
171	#123×C₆₁	C₂³	1	8	yes	complemented
172	#123×C₆₁	C₂³	1	16	yes	complemented
173	#123×C₆₁	C₂³	1	8	yes	complemented
174	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
181	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	complemented
182	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	complemented
183	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	complemented
184	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	complemented
185	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
186	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
187	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
188	#121×C₆₁	C₂³	1	8	yes	—
189	#121×C₆₁	C₂³	1	4	yes	—
190	#121×C₆₁	C₂³	1	8	yes	—
191	#121×C₆₁	C₂³	1	8	yes	—
192	#121×C₆₁	C₂³	1	8	yes	—
193	#121×C₆₁	C₂³	1	8	yes	—
194	#121×C₆₁	C₂³	1	8	yes	—
195	#121×C₆₁	C₂³	1	4	yes	—
196	#121×C₆₁	C₂³	1	4	yes	—
197	#121×C₆₁	C₂³	1	8	yes	—
198	#121×C₆₁	C₂³	1	4	yes	—
199	#121×C₆₁	C₂³	1	8	yes	—
200	#121×C₆₁	C₂³	1	8	yes	—
201	#121×C₆₁	C₂³	1	8	yes	—
202	#121×C₆₁	C₂³	1	4	yes	complemented
203	#121×C₆₁	C₂³	1	16	yes	complemented
204	#121×C₆₁	C₂³	1	4	yes	complemented
205	#121×C₆₁	C₂³	1	16	yes	complemented
206	#121×C₆₁	C₂³	1	16	yes	complemented
207	#121×C₆₁	C₂³	1	16	yes	complemented
208	#121×C₆₁	C₂³	1	16	yes	complemented
209	#121×C₆₁	C₂³	1	16	yes	complemented
210	#121×C₆₁	C₂³	1	4	yes	complemented
211	#121×C₆₁	C₂³	1	8	yes	complemented
212	#121×C₆₁	C₂³	1	16	yes	complemented
213	#121×C₆₁	C₂³	1	8	yes	complemented
214	#121×C₆₁	C₂³	1	8	yes	complemented
215	#121×C₆₁	C₂³	1	16	yes	complemented
216	#121×C₆₁	C₂³	1	16	yes	complemented
217	#121×C₆₁	C₂³	1	16	yes	complemented
218	#121×C₆₁	C₂³	1	4	yes	complemented
219	#120×C₆₁	C₂³	1	8	yes	—
220	#120×C₆₁	C₂³	1	16	yes	—
221	#120×C₆₁	C₂³	1	16	yes	—
222	#120×C₆₁	C₂³	1	16	yes	—
223	#120×C₆₁	C₂³	1	8	yes	—
224	#120×C₆₁	C₂³	1	8	yes	—
225	#120×C₆₁	C₂³	1	8	yes	—
226	#120×C₆₁	C₂³	1	16	yes	complemented
227	#120×C₆₁	C₂³	1	16	yes	complemented
228	#120×C₆₁	C₂³	1	16	yes	complemented
229	#120×C₆₁	C₂³	1	16	yes	complemented
230	C₄×Q₈×C₆₁	C₂³	1	8	yes	complemented
231	C₄×D₄×C₆₁	C₂³	1	8	yes	—
232	C₄×D₄×C₆₁	C₂³	1	16	yes	—
233	C₄×D₄×C₆₁	C₂³	1	16	yes	—
234	C₄×D₄×C₆₁	C₂³	1	8	yes	—
235	C₄×D₄×C₆₁	C₂³	1	8	yes	—
236	C₄×D₄×C₆₁	C₂³	1	8	yes	—
237	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
238	C₄×D₄×C₆₁	C₂³	1	16	yes	complemented
239	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
240	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
241	C₄×D₄×C₆₁	C₂³	1	16	yes	complemented
242	C₄×D₄×C₆₁	C₂³	1	16	yes	complemented
243	C₄×D₄×C₆₁	C₂³	1	16	yes	complemented
244	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
245	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
246	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
247	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
248	#117×C₆₁	C₂³	1	4	yes	—
249	#117×C₆₁	C₂³	1	8	yes	—
250	#117×C₆₁	C₂³	1	4	yes	—
251	#117×C₆₁	C₂³	1	8	yes	complemented
252	#117×C₆₁	C₂³	1	4	yes	complemented
253	#117×C₆₁	C₂³	1	16	yes	complemented
254	#117×C₆₁	C₂³	1	4	yes	complemented
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	complemented
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	complemented
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	complemented
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	complemented
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	complemented
264	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
265	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
266	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
267	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
268	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
269	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
270	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
271	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
272	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
274	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	complemented
275	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	complemented
276	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	complemented
277	C₂×C₄²×C₆₁	C₂³	1	4	yes	complemented
278	C₂⁴×C₆₁	—	2	4	no	—
279	C₂⁴×C₆₁	—	4	2	no	—
280	C₂⁴×C₆₁	—	4	2	no	—
281	C₂⁴×C₆₁	—	4	4	no	—
282	C₂⁴×C₆₁	—	4	4	no	—
283	C₂⁴×C₆₁	—	4	4	no	—
284	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
286	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
287	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
288	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
289	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
290	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
291	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
293	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
294	#41×C₆₁	—	2	16	no	—
295	#41×C₆₁	—	4	8	no	—
296	#41×C₆₁	—	4	8	no	—
297	#41×C₆₁	—	4	16	no	—
298	#41×C₆₁	—	4	32	no	—
299	#41×C₆₁	—	4	8	no	—
300	#41×C₆₁	—	4	16	no	—
301	C₂×Q₈×C₆₁	—	4	4	no	—
302	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
305	C₂×D₄×C₆₁	—	2	16	no	—
306	C₂×D₄×C₆₁	—	2	16	no	—
307	C₂×D₄×C₆₁	—	2	8	no	—
308	C₂×D₄×C₆₁	—	4	8	no	—
309	C₂×D₄×C₆₁	—	4	8	no	—
310	C₂×D₄×C₆₁	—	4	4	no	—
311	C₂×D₄×C₆₁	—	4	16	no	—
312	C₂×D₄×C₆₁	—	4	4	no	—
313	C₂×D₄×C₆₁	—	4	8	no	—
314	C₂×D₄×C₆₁	—	4	16	no	—
315	C₂×D₄×C₆₁	—	4	16	no	—
316	C₂×D₄×C₆₁	—	4	8	no	—
317	C₂×D₄×C₆₁	—	4	16	no	—
318	C₂×D₄×C₆₁	—	4	8	no	—
319	C₂×D₄×C₆₁	—	4	16	no	—
320	C₂×D₄×C₆₁	—	4	16	no	—
321	C₂×D₄×C₆₁	—	4	32	no	—
322	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
324	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
325	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
326	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
327	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
328	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
329	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
330	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
331	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
332	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
333	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
334	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
335	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
336	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
337	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
338	C₂²×C₄×C₆₁	—	2	4	no	—
339	C₂²×C₄×C₆₁	—	2	8	no	—
340	C₂²×C₄×C₆₁	—	4	4	no	—
341	C₂²×C₄×C₆₁	—	4	4	no	—
342	C₂²×C₄×C₆₁	—	4	4	no	—
343	C₂²×C₄×C₆₁	—	4	4	no	—
344	C₂²×C₄×C₆₁	—	4	8	no	—
345	C₂²×C₄×C₆₁	—	4	4	no	—
346	C₂²×C₄×C₆₁	—	4	2	no	—
347	C₂²×C₄×C₆₁	—	4	4	no	—
348	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
365	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
372	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
373	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
379	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
380	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
382	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
384	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
387	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
389	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
391	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
395	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
396	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
400	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
403	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
404	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
407	C₄²×C₆₁	C₂⁴	1	8	yes	—
408	C₄²×C₆₁	C₂⁴	1	8	yes	—
409	C₄²×C₆₁	C₂⁴	1	16	yes	—
410	C₂³×C₆₁	—	2	2	no	—
411	C₂³×C₆₁	—	2	2	no	—
412	C₂³×C₆₁	—	2	2	no	—
413	C₂³×C₆₁	—	2	4	no	—
414	C₂³×C₆₁	—	2	4	no	—
415	C₂³×C₆₁	—	2	4	no	—
416	C₂³×C₆₁	—	2	2	no	—
417	C₂³×C₆₁	—	2	4	no	—
418	C₂³×C₆₁	—	2	8	no	—
419	C₂³×C₆₁	—	2	8	no	—
420	C₂³×C₆₁	—	2	8	no	—
421	C₂³×C₆₁	—	2	8	no	—
422	C₂³×C₆₁	—	4	1	no	—
423	C₂³×C₆₁	—	4	2	no	—
424	C₂³×C₆₁	—	4	1	no	—
425	C₂³×C₆₁	—	4	1	no	—
426	C₂³×C₆₁	—	4	2	no	—
427	C₂³×C₆₁	—	4	1	no	—
428	C₂³×C₆₁	—	4	4	no	—
429	C₂³×C₆₁	—	4	4	no	—
430	C₂³×C₆₁	—	4	4	no	—
431	C₂³×C₆₁	—	4	4	no	—
432	C₂³×C₆₁	—	4	4	no	—
433	C₂³×C₆₁	—	4	4	no	—
434	C₂³×C₆₁	—	4	4	no	—
435	C₂³×C₆₁	—	4	4	no	—
436	C₂³×C₆₁	—	4	8	no	—
437	C₂³×C₆₁	—	4	8	no	—
438	C₂³×C₆₁	—	4	8	no	—
439	C₂³×C₆₁	—	4	16	no	—
440	C₂³×C₆₁	—	8	16	no	—
441	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	complemented
442	C₂³×C₆₁	C₂⁵	1	8	yes	—
443	C₂³×C₆₁	C₂⁵	1	2	yes	—
444	C₂³×C₆₁	C₂⁵	1	8	yes	—
445	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
446	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
447	C₂³×C₆₁	C₂⁵	1	2	yes	—
448	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
449	Q₈×C₆₁	—	2	8	no	—
450	Q₈×C₆₁	—	4	4	no	—
451	Q₈×C₆₁	—	4	8	no	—
452	D₄×C₆₁	—	2	32	no	—
453	D₄×C₆₁	—	2	16	no	—
454	D₄×C₆₁	—	2	16	no	—
455	D₄×C₆₁	—	2	16	no	—
456	D₄×C₆₁	—	2	16	no	—
457	D₄×C₆₁	—	2	16	no	—
458	D₄×C₆₁	—	2	8	no	—
459	D₄×C₆₁	—	4	8	no	—
460	D₄×C₆₁	—	4	16	no	—
461	D₄×C₆₁	—	4	8	no	—
462	D₄×C₆₁	—	4	16	no	—
463	D₄×C₆₁	—	4	16	no	—
464	D₄×C₆₁	—	4	16	no	—
465	D₄×C₆₁	—	4	8	no	—
466	D₄×C₆₁	—	4	4	no	—
467	D₄×C₆₁	—	4	8	no	—
468	C₂×C₄×C₆₁	—	2	2	no	—
469	C₂×C₄×C₆₁	—	2	4	no	—
470	C₂×C₄×C₆₁	—	2	8	no	—
471	C₂×C₄×C₆₁	—	2	8	no	—
472	C₂×C₄×C₆₁	—	2	4	no	—
473	C₂×C₄×C₆₁	—	2	4	no	—
474	C₂×C₄×C₆₁	—	2	4	no	—
475	C₂×C₄×C₆₁	—	2	4	no	—
476	C₂×C₄×C₆₁	—	2	4	no	—
477	C₂×C₄×C₆₁	—	2	4	no	—
478	C₂×C₄×C₆₁	—	2	16	no	—
479	C₂×C₄×C₆₁	—	4	1	no	—
480	C₂×C₄×C₆₁	—	4	2	no	—
481	C₂×C₄×C₆₁	—	4	2	no	—
482	C₂×C₄×C₆₁	—	4	2	no	—
483	C₂×C₄×C₆₁	—	4	2	no	—
484	C₂×C₄×C₆₁	—	4	2	no	—
485	C₂×C₄×C₆₁	—	4	1	no	—
486	C₂×C₄×C₆₁	—	4	4	no	—
487	C₂×C₄×C₆₁	—	4	4	no	—
488	C₂×C₄×C₆₁	—	4	4	no	—
489	C₂×C₄×C₆₁	—	4	8	no	—
490	C₂×C₄×C₆₁	—	4	4	no	—
491	C₂×C₄×C₆₁	—	4	8	no	—
492	C₂×C₄×C₆₁	—	4	16	no	—
493	C₂×C₄×C₆₁	—	4	8	no	—
494	C₂×C₄×C₆₁	—	4	8	no	—
495	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	complemented
496	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
497	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
498	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
499	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
500	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
501	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
502	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
503	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
504	#62818	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₆₁	—	2	8	no	—
506	C₂²×C₆₁	—	2	2	no	—
507	C₂²×C₆₁	—	2	1	no	—
508	C₂²×C₆₁	—	2	1	no	—
509	C₂²×C₆₁	—	2	1	no	—
510	C₂²×C₆₁	—	2	1	no	—
511	C₂²×C₆₁	—	2	2	no	—
512	C₂²×C₆₁	—	2	1	no	—
513	C₂²×C₆₁	—	2	1	no	—
514	C₂²×C₆₁	—	2	2	no	—
515	C₂²×C₆₁	—	2	8	no	—
516	C₂²×C₆₁	—	2	8	no	—
517	C₂²×C₆₁	—	2	8	no	—
518	C₂²×C₆₁	—	2	8	no	—
519	C₂²×C₆₁	—	2	2	no	—
520	C₂²×C₆₁	—	2	8	no	—
521	C₂²×C₆₁	—	2	8	no	—
522	C₂²×C₆₁	—	2	2	no	—
523	C₂²×C₆₁	—	4	4	no	—
524	C₂²×C₆₁	—	4	8	no	—
525	C₂²×C₆₁	—	4	8	no	—
526	C₂²×C₆₁	—	4	4	no	—
527	C₂²×C₆₁	—	8	8	no	—
528	C₂²×C₆₁	—	8	8	no	—
529	C₂²×C₆₁	—	8	8	no	—
530	C₂²×C₆₁	—	8	8	no	—
531	C₂²×C₆₁	—	16	8	no	—
532	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
533	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
534	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
535	C₂²×C₆₁	#585	1	2	yes	—
536	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
537	C₄×C₆₁	—	2	2	no	—
538	C₄×C₆₁	—	2	2	no	—
539	C₄×C₆₁	—	2	2	no	—
540	C₄×C₆₁	—	2	8	no	—
541	C₄×C₆₁	—	2	8	no	—
542	C₄×C₆₁	—	2	8	no	—
543	C₄×C₆₁	—	2	8	no	—
544	C₄×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
545	#3542	C₂×C₆₁	1	8	yes	complemented
546	#3537	C₂×C₆₁	1	4	yes	complemented
547	#3536	C₂×C₆₁	1	4	yes	complemented
548	#3534	C₂×C₆₁	1	8	yes	complemented
549	#3519	C₂×C₆₁	1	8	yes	complemented
550	#3505	C₂×C₆₁	1	4	yes	complemented
551	#3496	C₂×C₆₁	1	4	yes	complemented
552	#3494	C₂×C₆₁	1	4	yes	complemented
553	#3492	C₂×C₆₁	1	2	yes	complemented
554	#3490	C₂×C₆₁	1	4	yes	complemented
555	#3488	C₂×C₆₁	1	4	yes	complemented
556	#3484	C₂×C₆₁	1	2	yes	complemented
557	#3484	C₂×C₆₁	1	4	yes	complemented
558	C₂×#525	C₂×C₆₁	1	2	yes	complemented
559	C₂²×#121	C₂×C₆₁	1	1	yes	characteristic, complemented
560	C₂×C₆₁	—	2	2	no	—
561	C₂×C₆₁	—	2	2	no	—
562	C₂×C₆₁	—	2	2	no	—
563	C₂×C₆₁	—	2	4	no	—
564	C₂×C₆₁	—	4	2	no	—
565	C₂×C₆₁	—	4	8	no	—
566	C₂×C₆₁	—	4	8	no	—
567	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
570	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	complemented
571	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	4	yes	complemented
572	C₂²×#41	C₂²×C₆₁	1	2	yes	complemented
573	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
574	C₂³×D₄	C₂²×C₆₁	1	2	yes	complemented
575	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
576	#562	C₂²×C₆₁	1	16	yes	complemented
577	#560	C₂²×C₆₁	1	16	yes	complemented
578	#555	C₂²×C₆₁	1	8	yes	complemented
579	#554	C₂²×C₆₁	1	8	yes	complemented
580	#553	C₂²×C₆₁	1	8	yes	complemented
581	#553	C₂²×C₆₁	1	8	yes	complemented
582	#553	C₂²×C₆₁	1	8	yes	complemented
583	#553	C₂²×C₆₁	1	16	yes	complemented
584	#552	C₂²×C₆₁	1	8	yes	complemented
585	#551	C₂²×C₆₁	1	16	yes	complemented
586	#551	C₂²×C₆₁	1	16	yes	complemented
587	#550	C₂²×C₆₁	1	8	yes	complemented
588	#548	C₂²×C₆₁	1	8	yes	complemented
589	#547	C₂²×C₆₁	1	8	yes	complemented
590	#547	C₂²×C₆₁	1	8	yes	complemented
591	#546	C₂²×C₆₁	1	16	yes	complemented
592	#546	C₂²×C₆₁	1	8	yes	complemented
593	#546	C₂²×C₆₁	1	16	yes	complemented
594	#546	C₂²×C₆₁	1	8	yes	complemented
595	#546	C₂²×C₆₁	1	16	yes	complemented
596	#546	C₂²×C₆₁	1	16	yes	complemented
597	#546	C₂²×C₆₁	1	8	yes	complemented
598	#546	C₂²×C₆₁	1	16	yes	complemented
599	D₄²	C₂²×C₆₁	1	16	yes	complemented
600	D₄²	C₂²×C₆₁	1	8	yes	complemented
601	D₄²	C₂²×C₆₁	1	8	yes	complemented
602	D₄²	C₂²×C₆₁	1	16	yes	complemented
603	D₄²	C₂²×C₆₁	1	8	yes	complemented
604	#544	C₂²×C₆₁	1	2	yes	complemented
605	#543	C₂²×C₆₁	1	4	yes	complemented
606	#542	C₂²×C₆₁	1	8	yes	complemented
607	#540	C₂²×C₆₁	1	8	yes	complemented
608	#540	C₂²×C₆₁	1	16	yes	complemented
609	#539	C₂²×C₆₁	1	8	yes	complemented
610	#539	C₂²×C₆₁	1	8	yes	complemented
611	#538	C₂²×C₆₁	1	8	yes	complemented
612	#538	C₂²×C₆₁	1	8	yes	complemented
613	#538	C₂²×C₆₁	1	8	yes	complemented
614	#538	C₂²×C₆₁	1	16	yes	complemented
615	#537	C₂²×C₆₁	1	2	yes	complemented
616	#537	C₂²×C₆₁	1	8	yes	complemented
617	#537	C₂²×C₆₁	1	8	yes	complemented
618	#535	C₂²×C₆₁	1	4	yes	complemented
619	#535	C₂²×C₆₁	1	8	yes	complemented
620	#535	C₂²×C₆₁	1	8	yes	complemented
621	#534	C₂²×C₆₁	1	8	yes	complemented
622	#534	C₂²×C₆₁	1	8	yes	complemented
623	#534	C₂²×C₆₁	1	8	yes	complemented
624	#534	C₂²×C₆₁	1	4	yes	complemented
625	#534	C₂²×C₆₁	1	8	yes	complemented
626	#532	C₂²×C₆₁	1	8	yes	complemented
627	#529	C₂²×C₆₁	1	8	yes	complemented
628	#525	C₂²×C₆₁	1	4	yes	complemented
629	#525	C₂²×C₆₁	1	4	yes	complemented
630	#525	C₂²×C₆₁	1	8	yes	complemented
631	#525	C₂²×C₆₁	1	4	yes	complemented
632	#525	C₂²×C₆₁	1	4	yes	complemented
633	#525	C₂²×C₆₁	1	4	yes	complemented
634	#525	C₂²×C₆₁	1	4	yes	complemented
635	#525	C₂²×C₆₁	1	4	yes	complemented
636	#525	C₂²×C₆₁	1	4	yes	complemented
637	#525	C₂²×C₆₁	1	8	yes	complemented
638	C₂×#123	C₂²×C₆₁	1	4	yes	complemented
639	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
640	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
641	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
642	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
643	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
644	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
645	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
646	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
647	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
648	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
649	C₂×#121	C₂²×C₆₁	1	8	yes	complemented
650	C₂×#120	C₂²×C₆₁	1	4	yes	complemented
651	C₂×#120	C₂²×C₆₁	1	8	yes	complemented
652	#520	C₂²×C₆₁	1	4	yes	complemented
653	#518	C₂²×C₆₁	1	2	yes	complemented
654	#518	C₂²×C₆₁	1	4	yes	complemented
655	#518	C₂²×C₆₁	1	8	yes	complemented
656	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
657	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
658	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
659	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
661	C₆₁	#62818	1	1	yes	characteristic, direct product factor, Sylow
662	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
663	C₂⁵	C₂³×C₆₁	1	2	yes	—
664	H(5,𝔽₂)	—	4	16	no	—
665	H(5,𝔽₂)	—	4	8	no	—
666	C₂×#41	—	4	8	no	—
667	C₂×#41	C₂³×C₆₁	1	4	yes	—
668	C₂×#41	C₂³×C₆₁	1	4	yes	—
669	C₂×#41	C₂³×C₆₁	1	8	yes	—
670	C₂×#41	C₂³×C₆₁	1	4	yes	complemented
671	C₂×#41	C₂³×C₆₁	1	4	yes	complemented
672	C₂×#41	C₂³×C₆₁	1	8	yes	complemented
673	C₂×#41	C₂³×C₆₁	1	16	yes	complemented
674	C₂²×Q₈	C₂³×C₆₁	1	2	yes	complemented
675	C₂²×D₄	—	4	4	no	—
676	C₂²×D₄	—	4	8	no	—
677	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
678	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
679	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
680	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
681	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
682	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
683	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
684	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
685	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
686	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
687	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
688	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
689	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
690	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
691	C₂²×D₄	C₂³×C₆₁	1	2	yes	complemented
692	C₂²×D₄	C₂³×C₆₁	1	16	yes	complemented
693	C₂²×D₄	C₂³×C₆₁	1	8	yes	complemented
694	C₂³×C₄	—	4	4	no	—
695	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
697	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
699	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
700	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
701	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
702	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
703	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
704	C₂³×C₄	C₂³×C₆₁	1	4	yes	complemented
705	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	complemented
706	#127	C₂³×C₆₁	1	8	yes	complemented
707	#127	C₂³×C₆₁	1	16	yes	complemented
708	#126	C₂³×C₆₁	1	16	yes	complemented
709	#126	C₂³×C₆₁	1	16	yes	complemented
710	#126	C₂³×C₆₁	1	16	yes	complemented
711	#125	C₂³×C₆₁	1	8	yes	complemented
712	#125	C₂³×C₆₁	1	16	yes	complemented
713	#124	C₂³×C₆₁	1	8	yes	complemented
714	#124	C₂³×C₆₁	1	16	yes	complemented
715	#124	C₂³×C₆₁	1	16	yes	complemented
716	#124	C₂³×C₆₁	1	16	yes	complemented
717	#123	C₂³×C₆₁	1	8	yes	—
718	#123	C₂³×C₆₁	1	8	yes	—
719	#123	C₂³×C₆₁	1	16	yes	—
720	#123	C₂³×C₆₁	1	8	yes	complemented
721	#123	C₂³×C₆₁	1	8	yes	complemented
722	#123	C₂³×C₆₁	1	16	yes	complemented
723	#123	C₂³×C₆₁	1	16	yes	complemented
724	#123	C₂³×C₆₁	1	16	yes	complemented
725	#123	C₂³×C₆₁	1	16	yes	complemented
726	#123	C₂³×C₆₁	1	16	yes	complemented
727	#123	C₂³×C₆₁	1	16	yes	complemented
728	#123	C₂³×C₆₁	1	16	yes	complemented
729	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
730	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
731	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
732	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
733	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
734	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
735	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
736	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
737	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
738	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
739	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	complemented
740	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	complemented
741	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	complemented
742	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	complemented
743	#121	C₂³×C₆₁	1	8	yes	—
744	#121	C₂³×C₆₁	1	8	yes	—
745	#121	C₂³×C₆₁	1	8	yes	—
746	#121	C₂³×C₆₁	1	8	yes	—
747	#121	C₂³×C₆₁	1	8	yes	—
748	#121	C₂³×C₆₁	1	8	yes	—
749	#121	C₂³×C₆₁	1	8	yes	—
750	#121	C₂³×C₆₁	1	8	yes	—
751	#121	C₂³×C₆₁	1	4	yes	—
752	#121	C₂³×C₆₁	1	4	yes	—
753	#121	C₂³×C₆₁	1	4	yes	—
754	#121	C₂³×C₆₁	1	4	yes	—
755	#121	C₂³×C₆₁	1	8	yes	—
756	#121	C₂³×C₆₁	1	8	yes	—
757	#121	C₂³×C₆₁	1	4	yes	complemented
758	#121	C₂³×C₆₁	1	4	yes	complemented
759	#121	C₂³×C₆₁	1	4	yes	complemented
760	#121	C₂³×C₆₁	1	4	yes	complemented
761	#121	C₂³×C₆₁	1	16	yes	complemented
762	#121	C₂³×C₆₁	1	8	yes	complemented
763	#121	C₂³×C₆₁	1	8	yes	complemented
764	#121	C₂³×C₆₁	1	16	yes	complemented
765	#121	C₂³×C₆₁	1	8	yes	complemented
766	#121	C₂³×C₆₁	1	16	yes	complemented
767	#121	C₂³×C₆₁	1	16	yes	complemented
768	#121	C₂³×C₆₁	1	16	yes	complemented
769	#121	C₂³×C₆₁	1	16	yes	complemented
770	#121	C₂³×C₆₁	1	16	yes	complemented
771	#121	C₂³×C₆₁	1	16	yes	complemented
772	#121	C₂³×C₆₁	1	16	yes	complemented
773	#121	C₂³×C₆₁	1	16	yes	complemented
774	#120	C₂³×C₆₁	1	8	yes	—
775	#120	C₂³×C₆₁	1	8	yes	—
776	#120	C₂³×C₆₁	1	8	yes	—
777	#120	C₂³×C₆₁	1	8	yes	—
778	#120	C₂³×C₆₁	1	16	yes	—
779	#120	C₂³×C₆₁	1	16	yes	—
780	#120	C₂³×C₆₁	1	16	yes	—
781	#120	C₂³×C₆₁	1	16	yes	complemented
782	#120	C₂³×C₆₁	1	16	yes	complemented
783	#120	C₂³×C₆₁	1	16	yes	complemented
784	#120	C₂³×C₆₁	1	16	yes	complemented
785	C₄×Q₈	C₂³×C₆₁	1	8	yes	complemented
786	C₄×D₄	C₂³×C₆₁	1	8	yes	—
787	C₄×D₄	C₂³×C₆₁	1	8	yes	—
788	C₄×D₄	C₂³×C₆₁	1	8	yes	—
789	C₄×D₄	C₂³×C₆₁	1	8	yes	—
790	C₄×D₄	C₂³×C₆₁	1	16	yes	—
791	C₄×D₄	C₂³×C₆₁	1	16	yes	—
792	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
793	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
794	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
795	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
796	C₄×D₄	C₂³×C₆₁	1	16	yes	complemented
797	C₄×D₄	C₂³×C₆₁	1	16	yes	complemented
798	C₄×D₄	C₂³×C₆₁	1	16	yes	complemented
799	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
800	C₄×D₄	C₂³×C₆₁	1	16	yes	complemented
801	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
802	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
803	#117	C₂³×C₆₁	1	4	yes	—
804	#117	C₂³×C₆₁	1	4	yes	—
805	#117	C₂³×C₆₁	1	8	yes	—
806	#117	C₂³×C₆₁	1	4	yes	complemented
807	#117	C₂³×C₆₁	1	4	yes	complemented
808	#117	C₂³×C₆₁	1	16	yes	complemented
809	#117	C₂³×C₆₁	1	8	yes	complemented
810	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
812	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
813	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
814	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	complemented
815	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	complemented
816	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	complemented
817	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	complemented
818	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	complemented
819	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	complemented
830	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	complemented
831	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	complemented
832	C₂×C₄²	C₂³×C₆₁	1	4	yes	complemented
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	—	4	4	no	—
837	C₂⁴	—	4	4	no	—
838	C₂⁴	—	4	4	no	—
839	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
840	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
841	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
842	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
843	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
844	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
845	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
846	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
848	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
849	#41	—	2	16	no	—
850	#41	—	4	8	no	—
851	#41	—	4	8	no	—
852	#41	—	4	16	no	—
853	#41	—	4	32	no	—
854	#41	—	4	8	no	—
855	#41	—	4	16	no	—
856	C₂×Q₈	—	4	4	no	—
857	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
858	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
859	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
860	C₂×D₄	—	2	16	no	—
861	C₂×D₄	—	2	16	no	—
862	C₂×D₄	—	2	8	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	8	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	—	4	16	no	—
867	C₂×D₄	—	4	4	no	—
868	C₂×D₄	—	4	8	no	—
869	C₂×D₄	—	4	16	no	—
870	C₂×D₄	—	4	16	no	—
871	C₂×D₄	—	4	8	no	—
872	C₂×D₄	—	4	16	no	—
873	C₂×D₄	—	4	16	no	—
874	C₂×D₄	—	4	8	no	—
875	C₂×D₄	—	4	16	no	—
876	C₂×D₄	—	4	32	no	—
877	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
878	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
879	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
880	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
881	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
882	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
883	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
884	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
885	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
886	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
887	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
888	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
889	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
890	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
891	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
892	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	8	no	—
895	C₂²×C₄	—	4	4	no	—
896	C₂²×C₄	—	4	4	no	—
897	C₂²×C₄	—	4	4	no	—
898	C₂²×C₄	—	4	4	no	—
899	C₂²×C₄	—	4	8	no	—
900	C₂²×C₄	—	4	4	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	4	no	—
903	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
905	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
907	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
912	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
915	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
919	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
920	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
921	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
923	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
924	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
927	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
928	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
933	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
935	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
936	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
937	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
941	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
942	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
944	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
945	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
946	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
950	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
951	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
954	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
955	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
958	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
962	C₄²	C₂⁴×C₆₁	1	8	yes	—
963	C₄²	C₂⁴×C₆₁	1	8	yes	—
964	C₄²	C₂⁴×C₆₁	1	16	yes	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	4	no	—
969	C₂³	—	2	4	no	—
970	C₂³	—	2	4	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	4	no	—
973	C₂³	—	2	8	no	—
974	C₂³	—	2	8	no	—
975	C₂³	—	2	8	no	—
976	C₂³	—	2	8	no	—
977	C₂³	—	4	1	no	—
978	C₂³	—	4	2	no	—
979	C₂³	—	4	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	2	no	—
982	C₂³	—	4	1	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	4	4	no	—
985	C₂³	—	4	4	no	—
986	C₂³	—	4	4	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	4	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	8	no	—
994	C₂³	—	4	16	no	—
995	C₂³	—	8	16	no	—
996	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	complemented
997	C₂³	C₂⁵×C₆₁	1	8	yes	—
998	C₂³	C₂⁵×C₆₁	1	2	yes	—
999	C₂³	C₂⁵×C₆₁	1	8	yes	—
1000	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1001	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1002	C₂³	C₂⁵×C₆₁	1	2	yes	—
1003	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1004	Q₈	—	2	8	no	—
1005	Q₈	—	4	4	no	—
1006	Q₈	—	4	8	no	—
1007	D₄	—	2	32	no	—
1008	D₄	—	2	16	no	—
1009	D₄	—	2	16	no	—
1010	D₄	—	2	16	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	16	no	—
1013	D₄	—	2	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	16	no	—
1016	D₄	—	4	8	no	—
1017	D₄	—	4	16	no	—
1018	D₄	—	4	16	no	—
1019	D₄	—	4	16	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	4	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	4	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	4	no	—
1032	C₂×C₄	—	2	4	no	—
1033	C₂×C₄	—	2	16	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	8	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	16	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	complemented
1051	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1052	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1053	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1054	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1055	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
1056	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1058	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1059	C₂²	—	2	8	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	8	no	—
1070	C₂²	—	2	8	no	—
1071	C₂²	—	2	8	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	8	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	4	no	—
1078	C₂²	—	4	8	no	—
1079	C₂²	—	4	8	no	—
1080	C₂²	—	4	4	no	—
1081	C₂²	—	8	8	no	—
1082	C₂²	—	8	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	8	8	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
1087	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
1088	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
1089	C₂²	C₆₁×#585	1	2	yes	—
1090	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	8	no	—
1096	C₄	—	2	8	no	—
1097	C₄	—	2	8	no	—
1098	C₄	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
1099	C₂	—	2	2	no	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	2	no	—
1102	C₂	—	2	4	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	8	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	C₂×C₆₁×#585	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×#3542	C₂	semidirect
2. C₆₁×#3537	C₂	semidirect
3. C₆₁×#3536	C₂	semidirect
4. C₆₁×#3534	C₂	semidirect
5. C₆₁×#3519	C₂	semidirect
6. C₆₁×#3505	C₂	semidirect
7. C₆₁×#3496	C₂	semidirect
8. C₆₁×#3494	C₂	semidirect
9. C₆₁×#3492	C₂	semidirect
10. C₆₁×#3490	C₂	semidirect
11. C₆₁×#3488	C₂	semidirect
12. C₆₁×#3484	C₂	semidirect
13. C₆₁×#3484	C₂	semidirect
14. C₂×C₆₁×#525	C₂	semidirect
15. C₂²×#121×C₆₁	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
17. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
18. C₂²×#41×C₆₁	C₂²	semidirect
19. C₂³×D₄×C₆₁	C₂²	semidirect
20. C₂³×D₄×C₆₁	C₂²	semidirect
21. C₂⁴×C₄×C₆₁	C₂²	semidirect
22. C₆₁×#562	C₂²	semidirect
23. C₆₁×#560	C₂²	semidirect
24. C₆₁×#555	C₂²	semidirect
25. C₆₁×#554	C₂²	semidirect
26. C₆₁×#553	C₂²	semidirect
27. C₆₁×#553	C₂²	semidirect
28. C₆₁×#553	C₂²	semidirect
29. C₆₁×#553	C₂²	semidirect
30. C₆₁×#552	C₂²	semidirect
31. C₆₁×#551	C₂²	semidirect
32. C₆₁×#551	C₂²	semidirect
33. C₆₁×#550	C₂²	semidirect
34. C₆₁×#548	C₂²	semidirect
35. C₆₁×#547	C₂²	semidirect
36. C₆₁×#547	C₂²	semidirect
37. C₆₁×#546	C₂²	semidirect
38. C₆₁×#546	C₂²	semidirect
39. C₆₁×#546	C₂²	semidirect
40. C₆₁×#546	C₂²	semidirect
41. C₆₁×#546	C₂²	semidirect
42. C₆₁×#546	C₂²	semidirect
43. C₆₁×#546	C₂²	semidirect
44. C₆₁×#546	C₂²	semidirect
45. D₄²×C₆₁	C₂²	semidirect
46. D₄²×C₆₁	C₂²	semidirect
47. D₄²×C₆₁	C₂²	semidirect
48. D₄²×C₆₁	C₂²	semidirect
49. D₄²×C₆₁	C₂²	semidirect
50. C₆₁×#544	C₂²	semidirect
51. C₆₁×#543	C₂²	semidirect
52. C₆₁×#542	C₂²	semidirect
53. C₆₁×#540	C₂²	semidirect
54. C₆₁×#540	C₂²	semidirect
55. C₆₁×#539	C₂²	semidirect
56. C₆₁×#539	C₂²	semidirect
57. C₆₁×#538	C₂²	semidirect
58. C₆₁×#538	C₂²	semidirect
59. C₆₁×#538	C₂²	semidirect
60. C₆₁×#538	C₂²	semidirect
61. C₆₁×#537	C₂²	semidirect
62. C₆₁×#537	C₂²	semidirect
63. C₆₁×#537	C₂²	semidirect
64. C₆₁×#535	C₂²	semidirect
65. C₆₁×#535	C₂²	semidirect
66. C₆₁×#535	C₂²	semidirect
67. C₆₁×#534	C₂²	semidirect
68. C₆₁×#534	C₂²	semidirect
69. C₆₁×#534	C₂²	semidirect
70. C₆₁×#534	C₂²	semidirect
71. C₆₁×#534	C₂²	semidirect
72. C₆₁×#532	C₂²	semidirect
73. C₆₁×#529	C₂²	semidirect
74. C₆₁×#525	C₂²	semidirect
75. C₆₁×#525	C₂²	semidirect
76. C₆₁×#525	C₂²	semidirect
77. C₆₁×#525	C₂²	semidirect
78. C₆₁×#525	C₂²	semidirect
79. C₆₁×#525	C₂²	semidirect
80. C₆₁×#525	C₂²	semidirect
81. C₆₁×#525	C₂²	semidirect
82. C₆₁×#525	C₂²	semidirect
83. C₆₁×#525	C₂²	semidirect
84. C₂×#123×C₆₁	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
86. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
87. C₂×#121×C₆₁	C₂²	semidirect
88. C₂×#121×C₆₁	C₂²	semidirect
89. C₂×#121×C₆₁	C₂²	semidirect
90. C₂×#121×C₆₁	C₂²	semidirect
91. C₂×#121×C₆₁	C₂²	semidirect
92. C₂×#121×C₆₁	C₂²	semidirect
93. C₂×#121×C₆₁	C₂²	semidirect
94. C₂×#121×C₆₁	C₂²	semidirect
95. C₂×#121×C₆₁	C₂²	semidirect
96. C₂×#120×C₆₁	C₂²	semidirect
97. C₂×#120×C₆₁	C₂²	semidirect
98. C₆₁×#520	C₂²	semidirect
99. C₆₁×#518	C₂²	semidirect
100. C₆₁×#518	C₂²	semidirect
101. C₆₁×#518	C₂²	semidirect
102. C₂×C₄×D₄×C₆₁	C₂²	semidirect
103. C₂×C₄×D₄×C₆₁	C₂²	semidirect
104. C₂×#117×C₆₁	C₂²	semidirect
105. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
106. C₂²×C₂²⋊C₄×C₆₁	C₂²	semidirect
115. C₂×#41×C₆₁	C₂³	semidirect
116. C₂×#41×C₆₁	C₂³	semidirect
117. C₂×#41×C₆₁	C₂³	semidirect
118. C₂×#41×C₆₁	C₂³	semidirect
119. C₂²×Q₈×C₆₁	C₂³	semidirect
136. C₂²×D₄×C₆₁	C₂³	semidirect
137. C₂²×D₄×C₆₁	C₂³	semidirect
138. C₂²×D₄×C₆₁	C₂³	semidirect
149. C₂³×C₄×C₆₁	C₂³	semidirect
150. C₄⋊Q₈×C₆₁	C₂³	semidirect
151. #127×C₆₁	C₂³	semidirect
152. #127×C₆₁	C₂³	semidirect
153. #126×C₆₁	C₂³	semidirect
154. #126×C₆₁	C₂³	semidirect
155. #126×C₆₁	C₂³	semidirect
156. #125×C₆₁	C₂³	semidirect
157. #125×C₆₁	C₂³	semidirect
158. #124×C₆₁	C₂³	semidirect
159. #124×C₆₁	C₂³	semidirect
160. #124×C₆₁	C₂³	semidirect
161. #124×C₆₁	C₂³	semidirect
165. #123×C₆₁	C₂³	semidirect
166. #123×C₆₁	C₂³	semidirect
167. #123×C₆₁	C₂³	semidirect
168. #123×C₆₁	C₂³	semidirect
169. #123×C₆₁	C₂³	semidirect
170. #123×C₆₁	C₂³	semidirect
171. #123×C₆₁	C₂³	semidirect
172. #123×C₆₁	C₂³	semidirect
173. #123×C₆₁	C₂³	semidirect
180. C₂²⋊Q₈×C₆₁	C₂³	semidirect
181. C₂²⋊Q₈×C₆₁	C₂³	semidirect
182. C₂²⋊Q₈×C₆₁	C₂³	semidirect
183. C₂²⋊Q₈×C₆₁	C₂³	semidirect
184. C₂²⋊Q₈×C₆₁	C₂³	semidirect
185. C₂²⋊Q₈×C₆₁	C₂³	semidirect
186. C₂²⋊Q₈×C₆₁	C₂³	semidirect
187. C₂²⋊Q₈×C₆₁	C₂³	semidirect
202. #121×C₆₁	C₂³	semidirect
203. #121×C₆₁	C₂³	semidirect
204. #121×C₆₁	C₂³	semidirect
205. #121×C₆₁	C₂³	semidirect
206. #121×C₆₁	C₂³	semidirect
207. #121×C₆₁	C₂³	semidirect
208. #121×C₆₁	C₂³	semidirect
209. #121×C₆₁	C₂³	semidirect
210. #121×C₆₁	C₂³	semidirect
211. #121×C₆₁	C₂³	semidirect
212. #121×C₆₁	C₂³	semidirect
213. #121×C₆₁	C₂³	semidirect
214. #121×C₆₁	C₂³	semidirect
215. #121×C₆₁	C₂³	semidirect
216. #121×C₆₁	C₂³	semidirect
217. #121×C₆₁	C₂³	semidirect
218. #121×C₆₁	C₂³	semidirect
226. #120×C₆₁	C₂³	semidirect
227. #120×C₆₁	C₂³	semidirect
228. #120×C₆₁	C₂³	semidirect
229. #120×C₆₁	C₂³	semidirect
230. C₄×Q₈×C₆₁	C₂³	semidirect
237. C₄×D₄×C₆₁	C₂³	semidirect
238. C₄×D₄×C₆₁	C₂³	semidirect
239. C₄×D₄×C₆₁	C₂³	semidirect
240. C₄×D₄×C₆₁	C₂³	semidirect
241. C₄×D₄×C₆₁	C₂³	semidirect
242. C₄×D₄×C₆₁	C₂³	semidirect
243. C₄×D₄×C₆₁	C₂³	semidirect
244. C₄×D₄×C₆₁	C₂³	semidirect
245. C₄×D₄×C₆₁	C₂³	semidirect
246. C₄×D₄×C₆₁	C₂³	semidirect
247. C₄×D₄×C₆₁	C₂³	semidirect
251. #117×C₆₁	C₂³	semidirect
252. #117×C₆₁	C₂³	semidirect
253. #117×C₆₁	C₂³	semidirect
254. #117×C₆₁	C₂³	semidirect
259. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
260. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
261. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
262. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
263. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
274. C₂×C₂²⋊C₄×C₆₁	C₂³	semidirect
275. C₂×C₂²⋊C₄×C₆₁	C₂³	semidirect
276. C₂×C₂²⋊C₄×C₆₁	C₂³	semidirect
277. C₂×C₄²×C₆₁	C₂³	semidirect
441. C₂³×C₆₁	H(5,𝔽₂)	semidirect
495. C₂×C₄×C₆₁	H(5,𝔽₂)	semidirect
504. #62818	C₆₁	direct (N × H)
545. #3542	C₂×C₆₁	semidirect
546. #3537	C₂×C₆₁	semidirect
547. #3536	C₂×C₆₁	semidirect
548. #3534	C₂×C₆₁	semidirect
549. #3519	C₂×C₆₁	semidirect
550. #3505	C₂×C₆₁	semidirect
551. #3496	C₂×C₆₁	semidirect
552. #3494	C₂×C₆₁	semidirect
553. #3492	C₂×C₆₁	semidirect
554. #3490	C₂×C₆₁	semidirect
555. #3488	C₂×C₆₁	semidirect
556. #3484	C₂×C₆₁	semidirect
557. #3484	C₂×C₆₁	semidirect
558. C₂×#525	C₂×C₆₁	semidirect
559. C₂²×#121	C₂×C₆₁	semidirect
570. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
571. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
572. C₂²×#41	C₂²×C₆₁	semidirect
573. C₂³×D₄	C₂²×C₆₁	semidirect
574. C₂³×D₄	C₂²×C₆₁	semidirect
575. C₂⁴×C₄	C₂²×C₆₁	semidirect
576. #562	C₂²×C₆₁	semidirect
577. #560	C₂²×C₆₁	semidirect
578. #555	C₂²×C₆₁	semidirect
579. #554	C₂²×C₆₁	semidirect
580. #553	C₂²×C₆₁	semidirect
581. #553	C₂²×C₆₁	semidirect
582. #553	C₂²×C₆₁	semidirect
583. #553	C₂²×C₆₁	semidirect
584. #552	C₂²×C₆₁	semidirect
585. #551	C₂²×C₆₁	semidirect
586. #551	C₂²×C₆₁	semidirect
587. #550	C₂²×C₆₁	semidirect
588. #548	C₂²×C₆₁	semidirect
589. #547	C₂²×C₆₁	semidirect
590. #547	C₂²×C₆₁	semidirect
591. #546	C₂²×C₆₁	semidirect
592. #546	C₂²×C₆₁	semidirect
593. #546	C₂²×C₆₁	semidirect
594. #546	C₂²×C₆₁	semidirect
595. #546	C₂²×C₆₁	semidirect
596. #546	C₂²×C₆₁	semidirect
597. #546	C₂²×C₆₁	semidirect
598. #546	C₂²×C₆₁	semidirect
599. D₄²	C₂²×C₆₁	semidirect
600. D₄²	C₂²×C₆₁	semidirect
601. D₄²	C₂²×C₆₁	semidirect
602. D₄²	C₂²×C₆₁	semidirect
603. D₄²	C₂²×C₆₁	semidirect
604. #544	C₂²×C₆₁	semidirect
605. #543	C₂²×C₆₁	semidirect
606. #542	C₂²×C₆₁	semidirect
607. #540	C₂²×C₆₁	semidirect
608. #540	C₂²×C₆₁	semidirect
609. #539	C₂²×C₆₁	semidirect
610. #539	C₂²×C₆₁	semidirect
611. #538	C₂²×C₆₁	semidirect
612. #538	C₂²×C₆₁	semidirect
613. #538	C₂²×C₆₁	semidirect
614. #538	C₂²×C₆₁	semidirect
615. #537	C₂²×C₆₁	semidirect
616. #537	C₂²×C₆₁	semidirect
617. #537	C₂²×C₆₁	semidirect
618. #535	C₂²×C₆₁	semidirect
619. #535	C₂²×C₆₁	semidirect
620. #535	C₂²×C₆₁	semidirect
621. #534	C₂²×C₆₁	semidirect
622. #534	C₂²×C₆₁	semidirect
623. #534	C₂²×C₆₁	semidirect
624. #534	C₂²×C₆₁	semidirect
625. #534	C₂²×C₆₁	semidirect
626. #532	C₂²×C₆₁	semidirect
627. #529	C₂²×C₆₁	semidirect
628. #525	C₂²×C₆₁	semidirect
629. #525	C₂²×C₆₁	semidirect
630. #525	C₂²×C₆₁	semidirect
631. #525	C₂²×C₆₁	semidirect
632. #525	C₂²×C₆₁	semidirect
633. #525	C₂²×C₆₁	semidirect
634. #525	C₂²×C₆₁	semidirect
635. #525	C₂²×C₆₁	semidirect
636. #525	C₂²×C₆₁	semidirect
637. #525	C₂²×C₆₁	semidirect
638. C₂×#123	C₂²×C₆₁	semidirect
639. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
640. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
641. C₂×#121	C₂²×C₆₁	semidirect
642. C₂×#121	C₂²×C₆₁	semidirect
643. C₂×#121	C₂²×C₆₁	semidirect
644. C₂×#121	C₂²×C₆₁	semidirect
645. C₂×#121	C₂²×C₆₁	semidirect
646. C₂×#121	C₂²×C₆₁	semidirect
647. C₂×#121	C₂²×C₆₁	semidirect
648. C₂×#121	C₂²×C₆₁	semidirect
649. C₂×#121	C₂²×C₆₁	semidirect
650. C₂×#120	C₂²×C₆₁	semidirect
651. C₂×#120	C₂²×C₆₁	semidirect
652. #520	C₂²×C₆₁	semidirect
653. #518	C₂²×C₆₁	semidirect
654. #518	C₂²×C₆₁	semidirect
655. #518	C₂²×C₆₁	semidirect
656. C₂×C₄×D₄	C₂²×C₆₁	semidirect
657. C₂×C₄×D₄	C₂²×C₆₁	semidirect
658. C₂×#117	C₂²×C₆₁	semidirect
659. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
660. C₂²×C₂²⋊C₄	C₂²×C₆₁	semidirect
661. C₆₁	#62818	direct (N × H)
670. C₂×#41	C₂³×C₆₁	semidirect
671. C₂×#41	C₂³×C₆₁	semidirect
672. C₂×#41	C₂³×C₆₁	semidirect
673. C₂×#41	C₂³×C₆₁	semidirect
674. C₂²×Q₈	C₂³×C₆₁	semidirect
691. C₂²×D₄	C₂³×C₆₁	semidirect
692. C₂²×D₄	C₂³×C₆₁	semidirect
693. C₂²×D₄	C₂³×C₆₁	semidirect
704. C₂³×C₄	C₂³×C₆₁	semidirect
705. C₄⋊Q₈	C₂³×C₆₁	semidirect
706. #127	C₂³×C₆₁	semidirect
707. #127	C₂³×C₆₁	semidirect
708. #126	C₂³×C₆₁	semidirect
709. #126	C₂³×C₆₁	semidirect
710. #126	C₂³×C₆₁	semidirect
711. #125	C₂³×C₆₁	semidirect
712. #125	C₂³×C₆₁	semidirect
713. #124	C₂³×C₆₁	semidirect
714. #124	C₂³×C₆₁	semidirect
715. #124	C₂³×C₆₁	semidirect
716. #124	C₂³×C₆₁	semidirect
720. #123	C₂³×C₆₁	semidirect
721. #123	C₂³×C₆₁	semidirect
722. #123	C₂³×C₆₁	semidirect
723. #123	C₂³×C₆₁	semidirect
724. #123	C₂³×C₆₁	semidirect
725. #123	C₂³×C₆₁	semidirect
726. #123	C₂³×C₆₁	semidirect
727. #123	C₂³×C₆₁	semidirect
728. #123	C₂³×C₆₁	semidirect
735. C₂²⋊Q₈	C₂³×C₆₁	semidirect
736. C₂²⋊Q₈	C₂³×C₆₁	semidirect
737. C₂²⋊Q₈	C₂³×C₆₁	semidirect
738. C₂²⋊Q₈	C₂³×C₆₁	semidirect
739. C₂²⋊Q₈	C₂³×C₆₁	semidirect
740. C₂²⋊Q₈	C₂³×C₆₁	semidirect
741. C₂²⋊Q₈	C₂³×C₆₁	semidirect
742. C₂²⋊Q₈	C₂³×C₆₁	semidirect
757. #121	C₂³×C₆₁	semidirect
758. #121	C₂³×C₆₁	semidirect
759. #121	C₂³×C₆₁	semidirect
760. #121	C₂³×C₆₁	semidirect
761. #121	C₂³×C₆₁	semidirect
762. #121	C₂³×C₆₁	semidirect
763. #121	C₂³×C₆₁	semidirect
764. #121	C₂³×C₆₁	semidirect
765. #121	C₂³×C₆₁	semidirect
766. #121	C₂³×C₆₁	semidirect
767. #121	C₂³×C₆₁	semidirect
768. #121	C₂³×C₆₁	semidirect
769. #121	C₂³×C₆₁	semidirect
770. #121	C₂³×C₆₁	semidirect
771. #121	C₂³×C₆₁	semidirect
772. #121	C₂³×C₆₁	semidirect
773. #121	C₂³×C₆₁	semidirect
781. #120	C₂³×C₆₁	semidirect
782. #120	C₂³×C₆₁	semidirect
783. #120	C₂³×C₆₁	semidirect
784. #120	C₂³×C₆₁	semidirect
785. C₄×Q₈	C₂³×C₆₁	semidirect
792. C₄×D₄	C₂³×C₆₁	semidirect
793. C₄×D₄	C₂³×C₆₁	semidirect
794. C₄×D₄	C₂³×C₆₁	semidirect
795. C₄×D₄	C₂³×C₆₁	semidirect
796. C₄×D₄	C₂³×C₆₁	semidirect
797. C₄×D₄	C₂³×C₆₁	semidirect
798. C₄×D₄	C₂³×C₆₁	semidirect
799. C₄×D₄	C₂³×C₆₁	semidirect
800. C₄×D₄	C₂³×C₆₁	semidirect
801. C₄×D₄	C₂³×C₆₁	semidirect
802. C₄×D₄	C₂³×C₆₁	semidirect
806. #117	C₂³×C₆₁	semidirect
807. #117	C₂³×C₆₁	semidirect
808. #117	C₂³×C₆₁	semidirect
809. #117	C₂³×C₆₁	semidirect
814. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
815. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
816. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
817. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
818. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
829. C₂×C₂²⋊C₄	C₂³×C₆₁	semidirect
830. C₂×C₂²⋊C₄	C₂³×C₆₁	semidirect
831. C₂×C₂²⋊C₄	C₂³×C₆₁	semidirect
832. C₂×C₄²	C₂³×C₆₁	semidirect
996. C₂³	H(5,𝔽₂)×C₆₁	semidirect
1050. 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×#3542	2
C₆₁×#3537	2
C₆₁×#3536	2
C₆₁×#3534	2
C₆₁×#3519	2
C₆₁×#3505	2
C₆₁×#3496	2
C₆₁×#3494	2
C₆₁×#3492	2
C₆₁×#3490	2
C₆₁×#3488	2
C₆₁×#3484	2
C₂×C₆₁×#525	2
C₂²×#121×C₆₁	2
#62818	61

Subgroups — C61×#62818 #29566251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62818 #29566251