Subgroups — C₆₁×#62834 #29566267

Order 15616.

7900 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3558	C₂	1	8	yes	maximal, complemented
2	C₆₁×#3549	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3548	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3546	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3537	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3519	C₂	1	8	yes	maximal, complemented
7	C₆₁×#3511	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3508	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3506	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3498	C₂	1	4	yes	maximal, complemented
11	C₆₁×#3496	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3488	C₂	1	8	yes	maximal, complemented
13	C₆₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#532	C₂	1	2	yes	maximal, complemented
15	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	8	yes	complemented
16	C₂²×#41×C₆₁	C₂²	1	4	yes	complemented
17	C₆₁×#562	C₂²	1	8	yes	complemented
18	C₆₁×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₆₁×#560	C₂²	1	16	yes	complemented
20	C₆₁×#559	C₂²	1	16	yes	complemented
21	C₆₁×#556	C₂²	1	8	yes	complemented
22	C₆₁×#555	C₂²	1	4	yes	complemented
23	C₆₁×#555	C₂²	1	8	yes	complemented
24	C₆₁×#554	C₂²	1	8	yes	complemented
25	C₆₁×#553	C₂²	1	16	yes	complemented
26	C₆₁×#553	C₂²	1	16	yes	complemented
27	C₆₁×#550	C₂²	1	16	yes	complemented
28	C₆₁×#550	C₂²	1	8	yes	complemented
29	C₆₁×#550	C₂²	1	8	yes	complemented
30	C₆₁×#548	C₂²	1	16	yes	complemented
31	C₆₁×#547	C₂²	1	8	yes	complemented
32	C₆₁×#547	C₂²	1	8	yes	complemented
33	C₆₁×#546	C₂²	1	16	yes	complemented
34	C₆₁×#546	C₂²	1	16	yes	complemented
35	C₆₁×#546	C₂²	1	32	yes	complemented
36	C₆₁×#546	C₂²	1	16	yes	complemented
37	D₄²×C₆₁	C₂²	1	8	yes	complemented
38	D₄²×C₆₁	C₂²	1	4	yes	complemented
39	D₄²×C₆₁	C₂²	1	8	yes	complemented
40	D₄²×C₆₁	C₂²	1	16	yes	complemented
41	D₄²×C₆₁	C₂²	1	16	yes	complemented
42	D₄²×C₆₁	C₂²	1	16	yes	complemented
43	C₆₁×#542	C₂²	1	16	yes	complemented
44	C₆₁×#540	C₂²	1	8	yes	complemented
45	C₆₁×#540	C₂²	1	8	yes	complemented
46	C₆₁×#538	C₂²	1	32	yes	complemented
47	C₆₁×#538	C₂²	1	16	yes	complemented
48	C₆₁×#537	C₂²	1	16	yes	complemented
49	C₆₁×#537	C₂²	1	8	yes	complemented
50	C₆₁×#535	C₂²	1	16	yes	complemented
51	C₆₁×#535	C₂²	1	16	yes	complemented
52	C₆₁×#535	C₂²	1	8	yes	complemented
53	C₆₁×#535	C₂²	1	8	yes	complemented
54	C₆₁×#534	C₂²	1	16	yes	complemented
55	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#533	C₂²	1	2	yes	complemented
57	C₆₁×#533	C₂²	1	4	yes	complemented
58	C₆₁×#532	C₂²	1	4	yes	complemented
59	C₆₁×#532	C₂²	1	4	yes	complemented
60	C₆₁×#532	C₂²	1	4	yes	complemented
61	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#532	C₂²	1	4	yes	complemented
63	C₆₁×#532	C₂²	1	4	yes	complemented
64	C₆₁×#532	C₂²	1	4	yes	complemented
65	C₆₁×#532	C₂²	1	4	yes	complemented
66	C₆₁×#532	C₂²	1	4	yes	complemented
67	C₆₁×#532	C₂²	1	2	yes	complemented
68	C₆₁×#532	C₂²	1	8	yes	complemented
69	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
70	C₂×#127×C₆₁	C₂²	1	2	yes	complemented
71	C₂×#127×C₆₁	C₂²	1	4	yes	complemented
72	C₆₁×#529	C₂²	1	4	yes	complemented
73	C₆₁×#529	C₂²	1	4	yes	complemented
74	C₆₁×#529	C₂²	1	4	yes	complemented
75	C₂×#124×C₆₁	C₂²	1	4	yes	complemented
76	C₆₁×#525	C₂²	1	4	yes	complemented
77	C₆₁×#525	C₂²	1	2	yes	complemented
78	C₆₁×#525	C₂²	1	16	yes	complemented
79	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
80	C₂×#121×C₆₁	C₂²	1	4	yes	complemented
81	C₂×#121×C₆₁	C₂²	1	16	yes	complemented
82	C₆₁×#520	C₂²	1	8	yes	complemented
83	C₆₁×#518	C₂²	1	8	yes	complemented
84	C₄×#41×C₆₁	C₂²	1	4	yes	complemented
85	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
86	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
87	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	complemented
88	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
89	H(5,𝔽₂)×C₆₁	—	4	32	no	—
90	C₂×#41×C₆₁	—	4	16	no	—
91	C₂×#41×C₆₁	C₂³	1	8	yes	—
92	C₂×#41×C₆₁	C₂³	1	4	yes	—
93	C₂×#41×C₆₁	C₂³	1	8	yes	—
94	C₂×#41×C₆₁	C₂³	1	8	yes	—
95	C₂×#41×C₆₁	C₂³	1	8	yes	—
96	C₂×#41×C₆₁	C₂³	1	2	yes	—
97	C₂×#41×C₆₁	C₂³	1	16	yes	—
98	C₂×#41×C₆₁	C₂³	1	16	yes	—
99	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
100	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
101	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
102	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
103	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
104	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
105	C₂²×D₄×C₆₁	C₂³	1	32	yes	—
106	C₂²×D₄×C₆₁	C₂³	1	16	yes	—
107	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
108	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
109	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
110	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
117	#127×C₆₁	C₂³	1	4	yes	—
118	#127×C₆₁	C₂³	1	4	yes	—
119	#127×C₆₁	C₂³	1	4	yes	—
120	#127×C₆₁	C₂³	1	4	yes	—
121	#127×C₆₁	C₂³	1	16	yes	—
122	#127×C₆₁	C₂³	1	8	yes	—
123	#127×C₆₁	C₂³	1	1	yes	characteristic
124	#127×C₆₁	C₂³	1	16	yes	—
125	#126×C₆₁	C₂³	1	8	yes	—
126	#126×C₆₁	C₂³	1	32	yes	—
127	#125×C₆₁	C₂³	1	8	yes	—
128	#125×C₆₁	C₂³	1	4	yes	—
129	#125×C₆₁	C₂³	1	2	yes	—
130	#124×C₆₁	C₂³	1	8	yes	—
131	#124×C₆₁	C₂³	1	8	yes	—
132	#124×C₆₁	C₂³	1	8	yes	—
133	#124×C₆₁	C₂³	1	8	yes	—
134	#124×C₆₁	C₂³	1	16	yes	—
135	#124×C₆₁	C₂³	1	4	yes	—
136	#124×C₆₁	C₂³	1	2	yes	—
137	#124×C₆₁	C₂³	1	16	yes	—
138	#124×C₆₁	C₂³	1	32	yes	—
139	#123×C₆₁	C₂³	1	32	yes	—
140	#123×C₆₁	C₂³	1	32	yes	—
141	#123×C₆₁	C₂³	1	32	yes	—
142	#123×C₆₁	C₂³	1	8	yes	—
143	#123×C₆₁	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
146	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
148	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
149	C₂²⋊Q₈×C₆₁	C₂³	1	32	yes	—
150	#121×C₆₁	C₂³	1	8	yes	—
151	#121×C₆₁	C₂³	1	8	yes	—
152	#121×C₆₁	C₂³	1	8	yes	—
153	#121×C₆₁	C₂³	1	8	yes	—
154	#121×C₆₁	C₂³	1	8	yes	—
155	#121×C₆₁	C₂³	1	8	yes	—
156	#121×C₆₁	C₂³	1	8	yes	—
157	#121×C₆₁	C₂³	1	8	yes	—
158	#121×C₆₁	C₂³	1	4	yes	—
159	#121×C₆₁	C₂³	1	4	yes	—
160	#121×C₆₁	C₂³	1	16	yes	—
161	#121×C₆₁	C₂³	1	16	yes	—
162	#121×C₆₁	C₂³	1	4	yes	—
163	#121×C₆₁	C₂³	1	32	yes	—
164	#121×C₆₁	C₂³	1	16	yes	—
165	#121×C₆₁	C₂³	1	32	yes	—
166	#121×C₆₁	C₂³	1	16	yes	—
167	#121×C₆₁	C₂³	1	16	yes	—
168	#121×C₆₁	C₂³	1	32	yes	—
169	#121×C₆₁	C₂³	1	32	yes	—
170	#121×C₆₁	C₂³	1	32	yes	—
171	#120×C₆₁	C₂³	1	16	yes	—
172	#120×C₆₁	C₂³	1	32	yes	—
173	#120×C₆₁	C₂³	1	16	yes	—
174	#120×C₆₁	C₂³	1	32	yes	—
175	#120×C₆₁	C₂³	1	32	yes	—
176	#120×C₆₁	C₂³	1	4	yes	—
177	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
178	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
179	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
180	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
181	C₄×D₄×C₆₁	C₂³	1	8	yes	—
182	C₄×D₄×C₆₁	C₂³	1	8	yes	—
183	C₄×D₄×C₆₁	C₂³	1	8	yes	—
184	C₄×D₄×C₆₁	C₂³	1	8	yes	—
185	C₄×D₄×C₆₁	C₂³	1	8	yes	—
186	C₄×D₄×C₆₁	C₂³	1	8	yes	—
187	C₄×D₄×C₆₁	C₂³	1	8	yes	—
188	C₄×D₄×C₆₁	C₂³	1	8	yes	—
189	C₄×D₄×C₆₁	C₂³	1	16	yes	—
190	C₄×D₄×C₆₁	C₂³	1	16	yes	—
191	C₄×D₄×C₆₁	C₂³	1	4	yes	—
192	C₄×D₄×C₆₁	C₂³	1	4	yes	—
193	C₄×D₄×C₆₁	C₂³	1	4	yes	—
194	C₄×D₄×C₆₁	C₂³	1	32	yes	—
195	C₄×D₄×C₆₁	C₂³	1	32	yes	—
196	C₄×D₄×C₆₁	C₂³	1	8	yes	—
197	C₄×D₄×C₆₁	C₂³	1	8	yes	—
198	C₄×D₄×C₆₁	C₂³	1	8	yes	—
199	#117×C₆₁	C₂³	1	4	yes	—
200	#117×C₆₁	C₂³	1	8	yes	—
201	#117×C₆₁	C₂³	1	2	yes	—
202	#117×C₆₁	C₂³	1	8	yes	—
203	#117×C₆₁	C₂³	1	16	yes	—
204	#117×C₆₁	C₂³	1	4	yes	—
205	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
206	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
208	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
209	C₂×C₂²⋊C₄×C₆₁	C₂³	1	32	yes	—
210	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
211	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
213	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
216	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
219	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₆₁	C₂⁴	1	8	yes	—
221	C₂⁴×C₆₁	C₂⁴	1	16	yes	—
222	#41×C₆₁	—	2	32	no	—
223	#41×C₆₁	—	2	16	no	—
224	#41×C₆₁	—	4	16	no	—
225	#41×C₆₁	—	4	4	no	—
226	#41×C₆₁	—	4	16	no	—
227	#41×C₆₁	—	4	16	no	—
228	#41×C₆₁	—	4	32	no	—
229	#41×C₆₁	—	4	32	no	—
230	C₂×Q₈×C₆₁	—	4	8	no	—
231	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
235	C₂×D₄×C₆₁	—	2	16	no	—
236	C₂×D₄×C₆₁	—	4	8	no	—
237	C₂×D₄×C₆₁	—	4	16	no	—
238	C₂×D₄×C₆₁	—	4	8	no	—
239	C₂×D₄×C₆₁	—	4	32	no	—
240	C₂×D₄×C₆₁	—	4	32	no	—
241	C₂×D₄×C₆₁	—	4	16	no	—
242	C₂×D₄×C₆₁	—	4	64	no	—
243	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
244	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
245	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
246	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
247	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
248	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
249	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
250	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
251	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
252	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
253	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
254	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
255	C₂×D₄×C₆₁	C₂⁴	1	32	yes	—
256	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
257	C₂×D₄×C₆₁	C₂⁴	1	32	yes	—
258	C₂²×C₄×C₆₁	—	2	8	no	—
259	C₂²×C₄×C₆₁	—	4	2	no	—
260	C₂²×C₄×C₆₁	—	4	16	no	—
261	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
270	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
271	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
274	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
275	C₂²×C₄×C₆₁	C₂⁴	1	32	yes	—
276	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	32	yes	—
283	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
285	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
286	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
287	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
288	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
289	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
290	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
291	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
292	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
293	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
294	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
295	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
296	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
297	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
298	C₂²⋊C₄×C₆₁	C₂⁴	1	32	yes	—
299	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
300	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
301	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₁	C₂⁴	1	2	yes	—
303	C₄²×C₆₁	C₂⁴	1	2	yes	—
304	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₆₁	C₂⁴	1	2	yes	—
306	C₄²×C₆₁	C₂⁴	1	2	yes	—
307	C₄²×C₆₁	C₂⁴	1	2	yes	—
308	C₄²×C₆₁	C₂⁴	1	2	yes	—
309	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₆₁	C₂⁴	1	4	yes	—
311	C₄²×C₆₁	C₂⁴	1	8	yes	—
312	C₄²×C₆₁	C₂⁴	1	16	yes	—
313	C₂³×C₆₁	—	2	4	no	—
314	C₂³×C₆₁	—	2	16	no	—
315	C₂³×C₆₁	—	4	1	no	—
316	C₂³×C₆₁	—	4	8	no	—
317	C₂³×C₆₁	—	4	8	no	—
318	C₂³×C₆₁	—	4	32	no	—
319	C₂³×C₆₁	—	4	16	no	—
320	C₂³×C₆₁	C₂⁵	1	4	yes	—
321	C₂³×C₆₁	C₂⁵	1	16	yes	—
322	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
323	C₂³×C₆₁	C₂⁵	1	2	yes	—
324	Q₈×C₆₁	—	2	16	no	—
325	Q₈×C₆₁	—	2	8	no	—
326	Q₈×C₆₁	—	4	8	no	—
327	Q₈×C₆₁	—	4	2	no	—
328	D₄×C₆₁	—	2	16	no	—
329	D₄×C₆₁	—	2	32	no	—
330	D₄×C₆₁	—	2	16	no	—
331	D₄×C₆₁	—	2	16	no	—
332	D₄×C₆₁	—	2	8	no	—
333	D₄×C₆₁	—	2	16	no	—
334	D₄×C₆₁	—	2	16	no	—
335	D₄×C₆₁	—	4	32	no	—
336	D₄×C₆₁	—	4	32	no	—
337	D₄×C₆₁	—	4	8	no	—
338	D₄×C₆₁	—	4	16	no	—
339	D₄×C₆₁	—	4	8	no	—
340	D₄×C₆₁	—	4	16	no	—
341	D₄×C₆₁	—	4	2	no	—
342	D₄×C₆₁	—	4	4	no	—
343	C₂×C₄×C₆₁	—	2	4	no	—
344	C₂×C₄×C₆₁	—	2	4	no	—
345	C₂×C₄×C₆₁	—	2	4	no	—
346	C₂×C₄×C₆₁	—	2	4	no	—
347	C₂×C₄×C₆₁	—	2	4	no	—
348	C₂×C₄×C₆₁	—	2	32	no	—
349	C₂×C₄×C₆₁	—	2	16	no	—
350	C₂×C₄×C₆₁	—	2	4	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	8	no	—
353	C₂×C₄×C₆₁	—	4	1	no	—
354	C₂×C₄×C₆₁	—	4	2	no	—
355	C₂×C₄×C₆₁	—	4	8	no	—
356	C₂×C₄×C₆₁	—	4	16	no	—
357	C₂×C₄×C₆₁	—	4	32	no	—
358	C₂×C₄×C₆₁	H(5,𝔽₂)	1	8	yes	complemented
359	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
360	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
361	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
362	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
363	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
364	C₂×C₄×C₆₁	C₂⁵	1	16	yes	—
365	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
366	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
367	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
368	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
369	#62834	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂²×C₆₁	—	2	2	no	—
371	C₂²×C₆₁	—	2	2	no	—
372	C₂²×C₆₁	—	2	2	no	—
373	C₂²×C₆₁	—	2	16	no	—
374	C₂²×C₆₁	—	2	8	no	—
375	C₂²×C₆₁	—	2	16	no	—
376	C₂²×C₆₁	—	2	1	no	—
377	C₂²×C₆₁	—	2	4	no	—
378	C₂²×C₆₁	—	2	16	no	—
379	C₂²×C₆₁	—	4	4	no	—
380	C₂²×C₆₁	—	8	16	no	—
381	C₂²×C₆₁	—	16	16	no	—
382	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
383	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
384	C₄×C₆₁	—	2	2	no	—
385	C₄×C₆₁	—	2	2	no	—
386	C₄×C₆₁	—	2	8	no	—
387	C₄×C₆₁	—	2	16	no	—
388	C₄×C₆₁	—	2	2	no	—
389	C₄×C₆₁	—	2	1	no	—
390	C₄×C₆₁	—	2	4	no	—
391	C₄×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
392	C₄×C₆₁	C₂×H(5,𝔽₂)	1	4	yes	—
393	C₄×C₆₁	#585	1	2	yes	—
394	#3558	C₂×C₆₁	1	8	yes	complemented
395	#3549	C₂×C₆₁	1	2	yes	complemented
396	#3548	C₂×C₆₁	1	2	yes	complemented
397	#3546	C₂×C₆₁	1	8	yes	complemented
398	#3537	C₂×C₆₁	1	4	yes	complemented
399	#3519	C₂×C₆₁	1	8	yes	complemented
400	#3511	C₂×C₆₁	1	4	yes	complemented
401	#3508	C₂×C₆₁	1	4	yes	complemented
402	#3506	C₂×C₆₁	1	4	yes	complemented
403	#3498	C₂×C₆₁	1	4	yes	complemented
404	#3496	C₂×C₆₁	1	4	yes	complemented
405	#3488	C₂×C₆₁	1	8	yes	complemented
406	#3444	C₂×C₆₁	1	1	yes	characteristic, complemented
407	C₂×#532	C₂×C₆₁	1	2	yes	complemented
408	C₂×C₆₁	—	2	4	no	—
409	C₂×C₆₁	—	4	1	no	—
410	C₂×C₆₁	—	4	16	no	—
411	C₂×C₆₁	—	4	4	no	—
412	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	2	yes	—
413	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
414	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	8	yes	complemented
415	C₂²×#41	C₂²×C₆₁	1	4	yes	complemented
416	#562	C₂²×C₆₁	1	8	yes	complemented
417	H(3,𝔽₄)	C₂²×C₆₁	1	8	yes	complemented
418	#560	C₂²×C₆₁	1	16	yes	complemented
419	#559	C₂²×C₆₁	1	16	yes	complemented
420	#556	C₂²×C₆₁	1	8	yes	complemented
421	#555	C₂²×C₆₁	1	4	yes	complemented
422	#555	C₂²×C₆₁	1	8	yes	complemented
423	#554	C₂²×C₆₁	1	8	yes	complemented
424	#553	C₂²×C₆₁	1	16	yes	complemented
425	#553	C₂²×C₆₁	1	16	yes	complemented
426	#550	C₂²×C₆₁	1	16	yes	complemented
427	#550	C₂²×C₆₁	1	8	yes	complemented
428	#550	C₂²×C₆₁	1	8	yes	complemented
429	#548	C₂²×C₆₁	1	16	yes	complemented
430	#547	C₂²×C₆₁	1	8	yes	complemented
431	#547	C₂²×C₆₁	1	8	yes	complemented
432	#546	C₂²×C₆₁	1	16	yes	complemented
433	#546	C₂²×C₆₁	1	32	yes	complemented
434	#546	C₂²×C₆₁	1	16	yes	complemented
435	#546	C₂²×C₆₁	1	16	yes	complemented
436	D₄²	C₂²×C₆₁	1	16	yes	complemented
437	D₄²	C₂²×C₆₁	1	16	yes	complemented
438	D₄²	C₂²×C₆₁	1	4	yes	complemented
439	D₄²	C₂²×C₆₁	1	8	yes	complemented
440	D₄²	C₂²×C₆₁	1	16	yes	complemented
441	D₄²	C₂²×C₆₁	1	8	yes	complemented
442	#542	C₂²×C₆₁	1	16	yes	complemented
443	#540	C₂²×C₆₁	1	8	yes	complemented
444	#540	C₂²×C₆₁	1	8	yes	complemented
445	#538	C₂²×C₆₁	1	16	yes	complemented
446	#538	C₂²×C₆₁	1	32	yes	complemented
447	#537	C₂²×C₆₁	1	8	yes	complemented
448	#537	C₂²×C₆₁	1	16	yes	complemented
449	#535	C₂²×C₆₁	1	8	yes	complemented
450	#535	C₂²×C₆₁	1	16	yes	complemented
451	#535	C₂²×C₆₁	1	16	yes	complemented
452	#535	C₂²×C₆₁	1	8	yes	complemented
453	#534	C₂²×C₆₁	1	16	yes	complemented
454	#533	C₂²×C₆₁	1	2	yes	complemented
455	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
456	#533	C₂²×C₆₁	1	4	yes	complemented
457	#532	C₂²×C₆₁	1	4	yes	complemented
458	#532	C₂²×C₆₁	1	4	yes	complemented
459	#532	C₂²×C₆₁	1	4	yes	complemented
460	#532	C₂²×C₆₁	1	4	yes	complemented
461	#532	C₂²×C₆₁	1	4	yes	complemented
462	#532	C₂²×C₆₁	1	4	yes	complemented
463	#532	C₂²×C₆₁	1	4	yes	complemented
464	#532	C₂²×C₆₁	1	4	yes	complemented
465	#532	C₂²×C₆₁	1	2	yes	complemented
466	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
467	#532	C₂²×C₆₁	1	8	yes	complemented
468	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
469	C₂×#127	C₂²×C₆₁	1	2	yes	complemented
470	C₂×#127	C₂²×C₆₁	1	4	yes	complemented
471	#529	C₂²×C₆₁	1	4	yes	complemented
472	#529	C₂²×C₆₁	1	4	yes	complemented
473	#529	C₂²×C₆₁	1	4	yes	complemented
474	C₂×#124	C₂²×C₆₁	1	4	yes	complemented
475	#525	C₂²×C₆₁	1	4	yes	complemented
476	#525	C₂²×C₆₁	1	2	yes	complemented
477	#525	C₂²×C₆₁	1	16	yes	complemented
478	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
479	C₂×#121	C₂²×C₆₁	1	4	yes	complemented
480	C₂×#121	C₂²×C₆₁	1	16	yes	complemented
481	#520	C₂²×C₆₁	1	8	yes	complemented
482	#518	C₂²×C₆₁	1	8	yes	complemented
483	C₄×#41	C₂²×C₆₁	1	4	yes	complemented
484	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
485	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
486	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	complemented
487	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
488	C₆₁	#62834	1	1	yes	characteristic, direct product factor, Sylow
489	H(5,𝔽₂)	—	4	32	no	—
490	C₂×#41	—	4	16	no	—
491	C₂×#41	C₂³×C₆₁	1	4	yes	—
492	C₂×#41	C₂³×C₆₁	1	8	yes	—
493	C₂×#41	C₂³×C₆₁	1	2	yes	—
494	C₂×#41	C₂³×C₆₁	1	16	yes	—
495	C₂×#41	C₂³×C₆₁	1	8	yes	—
496	C₂×#41	C₂³×C₆₁	1	8	yes	—
497	C₂×#41	C₂³×C₆₁	1	8	yes	—
498	C₂×#41	C₂³×C₆₁	1	16	yes	—
499	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
500	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
501	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
502	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
503	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
504	C₂²×D₄	C₂³×C₆₁	1	32	yes	—
505	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
506	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
507	C₂²×D₄	C₂³×C₆₁	1	16	yes	—
508	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
509	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
510	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
513	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
514	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
515	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
517	#127	C₂³×C₆₁	1	4	yes	—
518	#127	C₂³×C₆₁	1	4	yes	—
519	#127	C₂³×C₆₁	1	4	yes	—
520	#127	C₂³×C₆₁	1	4	yes	—
521	#127	C₂³×C₆₁	1	16	yes	—
522	#127	C₂³×C₆₁	1	8	yes	—
523	#127	C₂³×C₆₁	1	1	yes	characteristic
524	#127	C₂³×C₆₁	1	16	yes	—
525	#126	C₂³×C₆₁	1	8	yes	—
526	#126	C₂³×C₆₁	1	32	yes	—
527	#125	C₂³×C₆₁	1	4	yes	—
528	#125	C₂³×C₆₁	1	2	yes	—
529	#125	C₂³×C₆₁	1	8	yes	—
530	#124	C₂³×C₆₁	1	8	yes	—
531	#124	C₂³×C₆₁	1	8	yes	—
532	#124	C₂³×C₆₁	1	8	yes	—
533	#124	C₂³×C₆₁	1	8	yes	—
534	#124	C₂³×C₆₁	1	4	yes	—
535	#124	C₂³×C₆₁	1	2	yes	—
536	#124	C₂³×C₆₁	1	16	yes	—
537	#124	C₂³×C₆₁	1	16	yes	—
538	#124	C₂³×C₆₁	1	32	yes	—
539	#123	C₂³×C₆₁	1	8	yes	—
540	#123	C₂³×C₆₁	1	4	yes	—
541	#123	C₂³×C₆₁	1	32	yes	—
542	#123	C₂³×C₆₁	1	32	yes	—
543	#123	C₂³×C₆₁	1	32	yes	—
544	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
546	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
547	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
548	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
549	C₂²⋊Q₈	C₂³×C₆₁	1	32	yes	—
550	#121	C₂³×C₆₁	1	4	yes	—
551	#121	C₂³×C₆₁	1	8	yes	—
552	#121	C₂³×C₆₁	1	8	yes	—
553	#121	C₂³×C₆₁	1	8	yes	—
554	#121	C₂³×C₆₁	1	8	yes	—
555	#121	C₂³×C₆₁	1	8	yes	—
556	#121	C₂³×C₆₁	1	8	yes	—
557	#121	C₂³×C₆₁	1	8	yes	—
558	#121	C₂³×C₆₁	1	8	yes	—
559	#121	C₂³×C₆₁	1	32	yes	—
560	#121	C₂³×C₆₁	1	16	yes	—
561	#121	C₂³×C₆₁	1	16	yes	—
562	#121	C₂³×C₆₁	1	32	yes	—
563	#121	C₂³×C₆₁	1	4	yes	—
564	#121	C₂³×C₆₁	1	4	yes	—
565	#121	C₂³×C₆₁	1	16	yes	—
566	#121	C₂³×C₆₁	1	16	yes	—
567	#121	C₂³×C₆₁	1	16	yes	—
568	#121	C₂³×C₆₁	1	32	yes	—
569	#121	C₂³×C₆₁	1	32	yes	—
570	#121	C₂³×C₆₁	1	32	yes	—
571	#120	C₂³×C₆₁	1	4	yes	—
572	#120	C₂³×C₆₁	1	32	yes	—
573	#120	C₂³×C₆₁	1	16	yes	—
574	#120	C₂³×C₆₁	1	32	yes	—
575	#120	C₂³×C₆₁	1	16	yes	—
576	#120	C₂³×C₆₁	1	32	yes	—
577	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
578	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
579	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
580	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
581	C₄×D₄	C₂³×C₆₁	1	8	yes	—
582	C₄×D₄	C₂³×C₆₁	1	8	yes	—
583	C₄×D₄	C₂³×C₆₁	1	8	yes	—
584	C₄×D₄	C₂³×C₆₁	1	8	yes	—
585	C₄×D₄	C₂³×C₆₁	1	8	yes	—
586	C₄×D₄	C₂³×C₆₁	1	8	yes	—
587	C₄×D₄	C₂³×C₆₁	1	8	yes	—
588	C₄×D₄	C₂³×C₆₁	1	8	yes	—
589	C₄×D₄	C₂³×C₆₁	1	8	yes	—
590	C₄×D₄	C₂³×C₆₁	1	8	yes	—
591	C₄×D₄	C₂³×C₆₁	1	8	yes	—
592	C₄×D₄	C₂³×C₆₁	1	4	yes	—
593	C₄×D₄	C₂³×C₆₁	1	4	yes	—
594	C₄×D₄	C₂³×C₆₁	1	4	yes	—
595	C₄×D₄	C₂³×C₆₁	1	32	yes	—
596	C₄×D₄	C₂³×C₆₁	1	16	yes	—
597	C₄×D₄	C₂³×C₆₁	1	32	yes	—
598	C₄×D₄	C₂³×C₆₁	1	16	yes	—
599	#117	C₂³×C₆₁	1	4	yes	—
600	#117	C₂³×C₆₁	1	4	yes	—
601	#117	C₂³×C₆₁	1	2	yes	—
602	#117	C₂³×C₆₁	1	8	yes	—
603	#117	C₂³×C₆₁	1	8	yes	—
604	#117	C₂³×C₆₁	1	16	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₁	1	32	yes	—
611	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
612	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
613	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
614	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
617	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
618	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
619	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₆₁	1	8	yes	—
621	C₂⁴	C₂⁴×C₆₁	1	16	yes	—
622	#41	—	2	32	no	—
623	#41	—	2	16	no	—
624	#41	—	4	16	no	—
625	#41	—	4	4	no	—
626	#41	—	4	16	no	—
627	#41	—	4	16	no	—
628	#41	—	4	32	no	—
629	#41	—	4	32	no	—
630	C₂×Q₈	—	4	8	no	—
631	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
632	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
633	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
635	C₂×D₄	—	2	16	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	32	no	—
638	C₂×D₄	—	4	32	no	—
639	C₂×D₄	—	4	8	no	—
640	C₂×D₄	—	4	16	no	—
641	C₂×D₄	—	4	16	no	—
642	C₂×D₄	—	4	64	no	—
643	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
644	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
645	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
646	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
647	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
648	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
649	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
650	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
651	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
652	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
653	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
654	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
655	C₂×D₄	C₂⁴×C₆₁	1	32	yes	—
656	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
657	C₂×D₄	C₂⁴×C₆₁	1	32	yes	—
658	C₂²×C₄	—	2	8	no	—
659	C₂²×C₄	—	4	16	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
670	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
671	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
674	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
675	C₂²×C₄	C₂⁴×C₆₁	1	32	yes	—
676	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
678	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
682	C₄⋊C₄	C₂⁴×C₆₁	1	32	yes	—
683	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
688	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
689	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
690	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
691	C₂²⋊C₄	C₂⁴×C₆₁	1	32	yes	—
692	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
693	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
694	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
695	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
697	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
698	C₂²⋊C₄	C₂⁴×C₆₁	1	32	yes	—
699	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
700	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
701	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
702	C₄²	C₂⁴×C₆₁	1	2	yes	—
703	C₄²	C₂⁴×C₆₁	1	2	yes	—
704	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
705	C₄²	C₂⁴×C₆₁	1	2	yes	—
706	C₄²	C₂⁴×C₆₁	1	2	yes	—
707	C₄²	C₂⁴×C₆₁	1	2	yes	—
708	C₄²	C₂⁴×C₆₁	1	2	yes	—
709	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
710	C₄²	C₂⁴×C₆₁	1	4	yes	—
711	C₄²	C₂⁴×C₆₁	1	8	yes	—
712	C₄²	C₂⁴×C₆₁	1	16	yes	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	16	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	32	no	—
719	C₂³	—	4	16	no	—
720	C₂³	C₂⁵×C₆₁	1	4	yes	—
721	C₂³	C₂⁵×C₆₁	1	16	yes	—
722	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
723	C₂³	C₂⁵×C₆₁	1	2	yes	—
724	Q₈	—	2	16	no	—
725	Q₈	—	2	8	no	—
726	Q₈	—	4	8	no	—
727	Q₈	—	4	2	no	—
728	D₄	—	2	16	no	—
729	D₄	—	2	32	no	—
730	D₄	—	2	16	no	—
731	D₄	—	2	16	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	16	no	—
734	D₄	—	2	16	no	—
735	D₄	—	4	32	no	—
736	D₄	—	4	32	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	16	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	16	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	32	no	—
749	C₂×C₄	—	2	16	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	8	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	16	no	—
757	C₂×C₄	—	4	32	no	—
758	C₂×C₄	H(5,𝔽₂)×C₆₁	1	8	yes	complemented
759	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
760	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
761	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
762	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
763	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
764	C₂×C₄	C₂⁵×C₆₁	1	16	yes	—
765	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
766	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
767	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
768	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	16	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	2	16	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	16	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	8	16	no	—
780	C₂²	—	16	16	no	—
781	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
782	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	16	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
791	C₄	C₂×H(5,𝔽₂)×C₆₁	1	4	yes	—
792	C₄	C₆₁×#585	1	2	yes	—
793	C₂	—	2	4	no	—
794	C₂	—	4	1	no	—
795	C₂	—	4	16	no	—
796	C₂	—	4	4	no	—
797	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	2	yes	—
798	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×#3558	C₂	semidirect
2. C₆₁×#3549	C₂	semidirect
3. C₆₁×#3548	C₂	semidirect
4. C₆₁×#3546	C₂	semidirect
5. C₆₁×#3537	C₂	semidirect
6. C₆₁×#3519	C₂	semidirect
7. C₆₁×#3511	C₂	semidirect
8. C₆₁×#3508	C₂	semidirect
9. C₆₁×#3506	C₂	semidirect
10. C₆₁×#3498	C₂	semidirect
11. C₆₁×#3496	C₂	semidirect
12. C₆₁×#3488	C₂	semidirect
13. C₆₁×#3444	C₂	semidirect
14. C₂×C₆₁×#532	C₂	semidirect
15. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
16. C₂²×#41×C₆₁	C₂²	semidirect
17. C₆₁×#562	C₂²	semidirect
18. C₆₁×H(3,𝔽₄)	C₂²	semidirect
19. C₆₁×#560	C₂²	semidirect
20. C₆₁×#559	C₂²	semidirect
21. C₆₁×#556	C₂²	semidirect
22. C₆₁×#555	C₂²	semidirect
23. C₆₁×#555	C₂²	semidirect
24. C₆₁×#554	C₂²	semidirect
25. C₆₁×#553	C₂²	semidirect
26. C₆₁×#553	C₂²	semidirect
27. C₆₁×#550	C₂²	semidirect
28. C₆₁×#550	C₂²	semidirect
29. C₆₁×#550	C₂²	semidirect
30. C₆₁×#548	C₂²	semidirect
31. C₆₁×#547	C₂²	semidirect
32. C₆₁×#547	C₂²	semidirect
33. C₆₁×#546	C₂²	semidirect
34. C₆₁×#546	C₂²	semidirect
35. C₆₁×#546	C₂²	semidirect
36. C₆₁×#546	C₂²	semidirect
37. D₄²×C₆₁	C₂²	semidirect
38. D₄²×C₆₁	C₂²	semidirect
39. D₄²×C₆₁	C₂²	semidirect
40. D₄²×C₆₁	C₂²	semidirect
41. D₄²×C₆₁	C₂²	semidirect
42. D₄²×C₆₁	C₂²	semidirect
43. C₆₁×#542	C₂²	semidirect
44. C₆₁×#540	C₂²	semidirect
45. C₆₁×#540	C₂²	semidirect
46. C₆₁×#538	C₂²	semidirect
47. C₆₁×#538	C₂²	semidirect
48. C₆₁×#537	C₂²	semidirect
49. C₆₁×#537	C₂²	semidirect
50. C₆₁×#535	C₂²	semidirect
51. C₆₁×#535	C₂²	semidirect
52. C₆₁×#535	C₂²	semidirect
53. C₆₁×#535	C₂²	semidirect
54. C₆₁×#534	C₂²	semidirect
55. C₆₁×#533	C₂²	semidirect
56. C₆₁×#533	C₂²	semidirect
57. C₆₁×#533	C₂²	semidirect
58. C₆₁×#532	C₂²	semidirect
59. C₆₁×#532	C₂²	semidirect
60. C₆₁×#532	C₂²	semidirect
61. C₆₁×#532	C₂²	semidirect
62. C₆₁×#532	C₂²	semidirect
63. C₆₁×#532	C₂²	semidirect
64. C₆₁×#532	C₂²	semidirect
65. C₆₁×#532	C₂²	semidirect
66. C₆₁×#532	C₂²	semidirect
67. C₆₁×#532	C₂²	semidirect
68. C₆₁×#532	C₂²	semidirect
69. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
70. C₂×#127×C₆₁	C₂²	semidirect
71. C₂×#127×C₆₁	C₂²	semidirect
72. C₆₁×#529	C₂²	semidirect
73. C₆₁×#529	C₂²	semidirect
74. C₆₁×#529	C₂²	semidirect
75. C₂×#124×C₆₁	C₂²	semidirect
76. C₆₁×#525	C₂²	semidirect
77. C₆₁×#525	C₂²	semidirect
78. C₆₁×#525	C₂²	semidirect
79. C₂×#121×C₆₁	C₂²	semidirect
80. C₂×#121×C₆₁	C₂²	semidirect
81. C₂×#121×C₆₁	C₂²	semidirect
82. C₆₁×#520	C₂²	semidirect
83. C₆₁×#518	C₂²	semidirect
84. C₄×#41×C₆₁	C₂²	semidirect
85. C₄×#41×C₆₁	C₂²	semidirect
86. C₂×C₄×D₄×C₆₁	C₂²	semidirect
87. C₂×C₄×D₄×C₆₁	C₂²	semidirect
88. C₂²×C₄²×C₆₁	C₂²	semidirect
358. C₂×C₄×C₆₁	H(5,𝔽₂)	semidirect
369. #62834	C₆₁	direct (N × H)
394. #3558	C₂×C₆₁	semidirect
395. #3549	C₂×C₆₁	semidirect
396. #3548	C₂×C₆₁	semidirect
397. #3546	C₂×C₆₁	semidirect
398. #3537	C₂×C₆₁	semidirect
399. #3519	C₂×C₆₁	semidirect
400. #3511	C₂×C₆₁	semidirect
401. #3508	C₂×C₆₁	semidirect
402. #3506	C₂×C₆₁	semidirect
403. #3498	C₂×C₆₁	semidirect
404. #3496	C₂×C₆₁	semidirect
405. #3488	C₂×C₆₁	semidirect
406. #3444	C₂×C₆₁	semidirect
407. C₂×#532	C₂×C₆₁	semidirect
414. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
415. C₂²×#41	C₂²×C₆₁	semidirect
416. #562	C₂²×C₆₁	semidirect
417. H(3,𝔽₄)	C₂²×C₆₁	semidirect
418. #560	C₂²×C₆₁	semidirect
419. #559	C₂²×C₆₁	semidirect
420. #556	C₂²×C₆₁	semidirect
421. #555	C₂²×C₆₁	semidirect
422. #555	C₂²×C₆₁	semidirect
423. #554	C₂²×C₆₁	semidirect
424. #553	C₂²×C₆₁	semidirect
425. #553	C₂²×C₆₁	semidirect
426. #550	C₂²×C₆₁	semidirect
427. #550	C₂²×C₆₁	semidirect
428. #550	C₂²×C₆₁	semidirect
429. #548	C₂²×C₆₁	semidirect
430. #547	C₂²×C₆₁	semidirect
431. #547	C₂²×C₆₁	semidirect
432. #546	C₂²×C₆₁	semidirect
433. #546	C₂²×C₆₁	semidirect
434. #546	C₂²×C₆₁	semidirect
435. #546	C₂²×C₆₁	semidirect
436. D₄²	C₂²×C₆₁	semidirect
437. D₄²	C₂²×C₆₁	semidirect
438. D₄²	C₂²×C₆₁	semidirect
439. D₄²	C₂²×C₆₁	semidirect
440. D₄²	C₂²×C₆₁	semidirect
441. D₄²	C₂²×C₆₁	semidirect
442. #542	C₂²×C₆₁	semidirect
443. #540	C₂²×C₆₁	semidirect
444. #540	C₂²×C₆₁	semidirect
445. #538	C₂²×C₆₁	semidirect
446. #538	C₂²×C₆₁	semidirect
447. #537	C₂²×C₆₁	semidirect
448. #537	C₂²×C₆₁	semidirect
449. #535	C₂²×C₆₁	semidirect
450. #535	C₂²×C₆₁	semidirect
451. #535	C₂²×C₆₁	semidirect
452. #535	C₂²×C₆₁	semidirect
453. #534	C₂²×C₆₁	semidirect
454. #533	C₂²×C₆₁	semidirect
455. #533	C₂²×C₆₁	semidirect
456. #533	C₂²×C₆₁	semidirect
457. #532	C₂²×C₆₁	semidirect
458. #532	C₂²×C₆₁	semidirect
459. #532	C₂²×C₆₁	semidirect
460. #532	C₂²×C₆₁	semidirect
461. #532	C₂²×C₆₁	semidirect
462. #532	C₂²×C₆₁	semidirect
463. #532	C₂²×C₆₁	semidirect
464. #532	C₂²×C₆₁	semidirect
465. #532	C₂²×C₆₁	semidirect
466. #532	C₂²×C₆₁	semidirect
467. #532	C₂²×C₆₁	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
469. C₂×#127	C₂²×C₆₁	semidirect
470. C₂×#127	C₂²×C₆₁	semidirect
471. #529	C₂²×C₆₁	semidirect
472. #529	C₂²×C₆₁	semidirect
473. #529	C₂²×C₆₁	semidirect
474. C₂×#124	C₂²×C₆₁	semidirect
475. #525	C₂²×C₆₁	semidirect
476. #525	C₂²×C₆₁	semidirect
477. #525	C₂²×C₆₁	semidirect
478. C₂×#121	C₂²×C₆₁	semidirect
479. C₂×#121	C₂²×C₆₁	semidirect
480. C₂×#121	C₂²×C₆₁	semidirect
481. #520	C₂²×C₆₁	semidirect
482. #518	C₂²×C₆₁	semidirect
483. C₄×#41	C₂²×C₆₁	semidirect
484. C₄×#41	C₂²×C₆₁	semidirect
485. C₂×C₄×D₄	C₂²×C₆₁	semidirect
486. C₂×C₄×D₄	C₂²×C₆₁	semidirect
487. C₂²×C₄²	C₂²×C₆₁	semidirect
488. C₆₁	#62834	direct (N × H)
758. 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×#3558	2
C₆₁×#3549	2
C₆₁×#3548	2
C₆₁×#3546	2
C₆₁×#3537	2
C₆₁×#3519	2
C₆₁×#3511	2
C₆₁×#3508	2
C₆₁×#3506	2
C₆₁×#3498	2
C₆₁×#3496	2
C₆₁×#3488	2
C₆₁×#3444	2
C₂×C₆₁×#532	2
#62834	61

Subgroups — C61×#62834 #29566267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62834 #29566267