Subgroups — C₂×C₆₁×#3274 #29564466

Order 15616.

3278 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3274	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#447	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₁	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₆₁	—	2	1	no	—
15	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₆₁	—	2	16	no	—
17	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	16	yes	complemented
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
20	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
21	C₂²×D₈×C₆₁	C₂²	1	2	yes	complemented
22	C₂²×D₈×C₆₁	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	complemented
24	C₆₁×#550	—	2	4	no	—
25	C₆₁×#550	C₂²	1	8	yes	complemented
26	D₄²×C₆₁	—	2	4	no	—
27	D₄²×C₆₁	C₂²	1	8	yes	complemented
28	C₂×#127×C₆₁	—	2	1	no	—
29	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#121×C₆₁	—	2	1	no	—
32	C₂×#121×C₆₁	—	2	2	no	—
33	C₂×#121×C₆₁	C₂²	1	2	yes	—
34	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
35	C₂×#120×C₆₁	—	2	2	no	—
36	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₆₁	—	2	1	no	—
38	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#493	C₂²	1	8	yes	complemented
41	C₆₁×#469	C₂²	1	16	yes	complemented
42	C₆₁×#460	C₂²	1	8	yes	complemented
43	C₆₁×#459	C₂²	1	8	yes	complemented
44	C₆₁×#449	C₂²	1	16	yes	complemented
45	C₆₁×#447	C₂²	1	16	yes	complemented
46	C₄×SD₁₆×C₆₁	C₂²	1	8	yes	complemented
47	C₆₁×#436	C₂²	1	8	yes	complemented
48	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
53	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
54	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₆₁	—	2	2	no	—
57	C₂×#41×C₆₁	—	2	4	no	—
58	C₂×#41×C₆₁	—	2	8	no	—
59	C₂×#41×C₆₁	—	4	4	no	—
60	C₂×#41×C₆₁	C₂³	1	8	yes	complemented
61	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₆₁	—	2	8	no	—
63	C₂²×D₄×C₆₁	—	2	2	no	—
64	C₂²×D₄×C₆₁	—	2	2	no	—
65	C₂²×D₄×C₆₁	—	2	2	no	—
66	C₂²×D₄×C₆₁	—	2	8	no	—
67	C₂²×D₄×C₆₁	—	2	1	no	—
68	C₂²×D₄×C₆₁	—	2	1	no	—
69	C₂²×D₄×C₆₁	—	2	4	no	—
70	C₂²×D₄×C₆₁	—	2	2	no	—
71	C₂²×D₄×C₆₁	—	2	1	no	—
72	C₂²×D₄×C₆₁	—	2	1	no	—
73	C₂²×D₄×C₆₁	—	4	4	no	—
74	C₂²×D₄×C₆₁	—	4	8	no	—
75	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
77	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
79	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₁	—	2	1	no	—
81	C₂³×C₄×C₆₁	—	2	2	no	—
82	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
83	AGL(1,ℤ/8)×C₆₁	—	2	64	no	—
84	C₂×SD₁₆×C₆₁	—	2	8	no	—
85	C₂×SD₁₆×C₆₁	D₄	1	8	yes	complemented
86	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
87	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	complemented
88	C₂×D₈×C₆₁	—	2	8	no	—
89	C₂×D₈×C₆₁	—	2	8	no	—
90	C₂×D₈×C₆₁	—	4	4	no	—
91	C₂×D₈×C₆₁	C₂³	1	8	yes	—
92	C₂×D₈×C₆₁	C₂³	1	8	yes	complemented
93	C₂×D₈×C₆₁	C₂³	1	8	yes	complemented
94	C₂×M₁₆×C₆₁	—	2	8	no	—
95	C₂×M₁₆×C₆₁	C₂³	1	8	yes	complemented
96	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
97	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
99	#127×C₆₁	—	2	8	no	—
100	#127×C₆₁	—	2	2	no	—
101	#127×C₆₁	—	2	2	no	—
102	#127×C₆₁	C₂³	1	4	yes	—
103	#127×C₆₁	C₂³	1	4	yes	complemented
104	#121×C₆₁	—	2	4	no	—
105	#121×C₆₁	—	2	4	no	—
106	#121×C₆₁	—	2	8	no	—
107	#121×C₆₁	—	2	16	no	—
108	#121×C₆₁	C₂³	1	8	yes	—
109	#121×C₆₁	C₂³	1	8	yes	complemented
110	#120×C₆₁	—	2	16	no	—
111	C₄×Q₈×C₆₁	—	2	2	no	—
112	C₄×Q₈×C₆₁	C₂³	1	4	yes	complemented
113	C₄×D₄×C₆₁	—	2	8	no	—
114	C₄×D₄×C₆₁	—	2	2	no	—
115	C₄×D₄×C₆₁	D₄	1	4	yes	—
116	C₄×D₄×C₆₁	C₂³	1	4	yes	—
117	C₄×D₄×C₆₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
126	C₂×C₄²×C₆₁	—	2	1	no	—
127	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
128	#106×C₆₁	C₂³	1	4	yes	complemented
129	C₄⋊C₈×C₆₁	C₂³	1	4	yes	complemented
130	#103×C₆₁	C₂³	1	4	yes	complemented
131	#102×C₆₁	C₂³	1	4	yes	—
132	#102×C₆₁	C₂³	1	8	yes	complemented
133	#102×C₆₁	C₂³	1	8	yes	complemented
134	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	complemented
135	C₄×C₈×C₆₁	C₂³	1	4	yes	complemented
136	C₂⁴×C₆₁	—	2	1	no	—
137	C₂⁴×C₆₁	—	2	2	no	—
138	C₂⁴×C₆₁	—	2	2	no	—
139	C₂⁴×C₆₁	—	2	8	no	—
140	C₂⁴×C₆₁	—	4	8	no	—
141	C₂⁴×C₆₁	—	4	8	no	—
142	C₂⁴×C₆₁	—	8	4	no	—
143	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
144	#41×C₆₁	—	2	16	no	—
145	#41×C₆₁	—	4	8	no	—
146	#41×C₆₁	—	4	16	no	—
147	C₂×Q₈×C₆₁	—	2	1	no	—
148	C₂×Q₈×C₆₁	—	2	2	no	—
149	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	complemented
150	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
151	C₂×D₄×C₆₁	—	2	16	no	—
152	C₂×D₄×C₆₁	—	2	8	no	—
153	C₂×D₄×C₆₁	—	2	8	no	—
154	C₂×D₄×C₆₁	—	2	8	no	—
155	C₂×D₄×C₆₁	—	2	4	no	—
156	C₂×D₄×C₆₁	—	2	1	no	—
157	C₂×D₄×C₆₁	—	2	4	no	—
158	C₂×D₄×C₆₁	—	2	4	no	—
159	C₂×D₄×C₆₁	—	2	4	no	—
160	C₂×D₄×C₆₁	—	2	8	no	—
161	C₂×D₄×C₆₁	—	2	2	no	—
162	C₂×D₄×C₆₁	—	2	2	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	4	no	—
165	C₂×D₄×C₆₁	—	2	4	no	—
166	C₂×D₄×C₆₁	—	2	2	no	—
167	C₂×D₄×C₆₁	—	2	4	no	—
168	C₂×D₄×C₆₁	—	2	4	no	—
169	C₂×D₄×C₆₁	—	4	8	no	—
170	C₂×D₄×C₆₁	—	4	16	no	—
171	C₂×D₄×C₆₁	—	4	8	no	—
172	C₂×D₄×C₆₁	—	4	8	no	—
173	C₂×D₄×C₆₁	—	4	32	no	—
174	C₂×D₄×C₆₁	—	4	8	no	—
175	C₂×D₄×C₆₁	—	4	4	no	—
176	C₂×D₄×C₆₁	—	4	4	no	—
177	C₂×D₄×C₆₁	—	8	2	no	—
178	C₂×D₄×C₆₁	—	8	2	no	—
179	C₂×D₄×C₆₁	—	8	4	no	—
180	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
181	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
183	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
184	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₆₁	—	2	1	no	—
186	C₂²×C₄×C₆₁	—	2	4	no	—
187	C₂²×C₄×C₆₁	—	2	4	no	—
188	C₂²×C₄×C₆₁	—	2	1	no	—
189	C₂²×C₄×C₆₁	—	2	1	no	—
190	C₂²×C₄×C₆₁	—	2	8	no	—
191	C₂²×C₄×C₆₁	—	2	4	no	—
192	C₂²×C₄×C₆₁	—	4	8	no	—
193	C₂²×C₄×C₆₁	—	4	4	no	—
194	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
200	SD₁₆×C₆₁	—	2	16	no	—
201	SD₁₆×C₆₁	C₂×D₄	1	16	yes	complemented
202	D₈×C₆₁	—	2	16	no	—
203	D₈×C₆₁	—	2	16	no	—
204	D₈×C₆₁	—	4	8	no	—
205	M₁₆×C₆₁	—	2	16	no	—
206	C₂×C₈×C₆₁	—	2	4	no	—
207	C₂×C₈×C₆₁	—	2	2	no	—
208	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	complemented
209	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
210	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
211	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
212	C₄⋊C₄×C₆₁	—	2	4	no	—
213	C₄⋊C₄×C₆₁	—	2	1	no	—
214	C₄⋊C₄×C₆₁	—	2	1	no	—
215	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
216	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
218	C₂²⋊C₄×C₆₁	—	2	8	no	—
219	C₂²⋊C₄×C₆₁	—	2	4	no	—
220	C₂²⋊C₄×C₆₁	—	2	8	no	—
221	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
222	C₄²×C₆₁	—	2	4	no	—
223	C₄²×C₆₁	C₂×D₄	1	2	yes	—
224	C₄²×C₆₁	C₂⁴	1	2	yes	—
225	C₂³×C₆₁	—	2	4	no	—
226	C₂³×C₆₁	—	2	4	no	—
227	C₂³×C₆₁	—	2	4	no	—
228	C₂³×C₆₁	—	2	4	no	—
229	C₂³×C₆₁	—	2	2	no	—
230	C₂³×C₆₁	—	2	4	no	—
231	C₂³×C₆₁	—	2	4	no	—
232	C₂³×C₆₁	—	4	16	no	—
233	C₂³×C₆₁	—	4	16	no	—
234	C₂³×C₆₁	—	4	2	no	—
235	C₂³×C₆₁	—	4	2	no	—
236	C₂³×C₆₁	—	4	4	no	—
237	C₂³×C₆₁	—	4	4	no	—
238	C₂³×C₆₁	—	4	4	no	—
239	C₂³×C₆₁	—	4	4	no	—
240	C₂³×C₆₁	—	4	4	no	—
241	C₂³×C₆₁	—	4	4	no	—
242	C₂³×C₆₁	—	8	8	no	—
243	C₂³×C₆₁	—	8	32	no	—
244	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
245	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₆₁	—	2	4	no	—
247	Q₈×C₆₁	—	2	2	no	—
248	Q₈×C₆₁	C₂²×D₄	1	4	yes	complemented
249	D₄×C₆₁	—	2	4	no	—
250	D₄×C₆₁	—	2	8	no	—
251	D₄×C₆₁	—	2	4	no	—
252	D₄×C₆₁	—	2	4	no	—
253	D₄×C₆₁	—	2	2	no	—
254	D₄×C₆₁	—	2	4	no	—
255	D₄×C₆₁	—	2	4	no	—
256	D₄×C₆₁	—	4	16	no	—
257	D₄×C₆₁	—	4	16	no	—
258	D₄×C₆₁	—	4	16	no	—
259	D₄×C₆₁	—	4	4	no	—
260	D₄×C₆₁	—	4	4	no	—
261	D₄×C₆₁	—	4	8	no	—
262	D₄×C₆₁	—	4	8	no	—
263	D₄×C₆₁	—	8	4	no	—
264	D₄×C₆₁	—	8	4	no	—
265	D₄×C₆₁	—	8	8	no	—
266	D₄×C₆₁	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₆₁	—	2	4	no	—
268	C₂×C₄×C₆₁	—	2	4	no	—
269	C₂×C₄×C₆₁	—	2	2	no	—
270	C₂×C₄×C₆₁	—	2	2	no	—
271	C₂×C₄×C₆₁	—	2	8	no	—
272	C₂×C₄×C₆₁	—	2	4	no	—
273	C₂×C₄×C₆₁	—	2	4	no	—
274	C₂×C₄×C₆₁	—	2	2	no	—
275	C₂×C₄×C₆₁	—	2	2	no	—
276	C₂×C₄×C₆₁	—	4	16	no	—
277	C₂×C₄×C₆₁	—	4	2	no	—
278	C₂×C₄×C₆₁	—	4	2	no	—
279	C₂×C₄×C₆₁	—	4	8	no	—
280	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
281	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
287	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
288	C₈×C₆₁	—	2	4	no	—
289	C₈×C₆₁	—	2	2	no	—
290	C₈×C₆₁	C₂²×D₄	1	4	yes	complemented
291	C₂×#3274	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₆₁	—	2	4	no	—
293	C₂²×C₆₁	—	2	4	no	—
294	C₂²×C₆₁	—	2	4	no	—
295	C₂²×C₆₁	—	2	4	no	—
296	C₂²×C₆₁	—	4	8	no	—
297	C₂²×C₆₁	—	4	8	no	—
298	C₂²×C₆₁	—	4	2	no	—
299	C₂²×C₆₁	—	4	2	no	—
300	C₂²×C₆₁	—	4	4	no	—
301	C₂²×C₆₁	—	4	4	no	—
302	C₂²×C₆₁	—	4	4	no	—
303	C₂²×C₆₁	—	4	4	no	—
304	C₂²×C₆₁	—	4	4	no	—
305	C₂²×C₆₁	—	4	4	no	—
306	C₂²×C₆₁	—	8	32	no	—
307	C₂²×C₆₁	—	8	8	no	—
308	C₂²×C₆₁	—	8	8	no	—
309	C₂²×C₆₁	D₄²	1	2	yes	—
310	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
311	C₂²×C₆₁	#576	1	2	yes	—
312	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
313	C₄×C₆₁	—	2	4	no	—
314	C₄×C₆₁	—	2	4	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	4	2	no	—
317	C₄×C₆₁	—	4	2	no	—
318	C₄×C₆₁	D₄²	1	2	yes	—
319	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
320	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	2	yes	complemented
323	C₂×#550	C₂×C₆₁	1	1	yes	characteristic, complemented
324	C₂×D₄²	C₂×C₆₁	1	1	yes	characteristic, complemented
325	#3274	C₂×C₆₁	1	16	yes	direct product factor
326	C₂×#493	C₂×C₆₁	1	1	yes	characteristic, complemented
327	C₂×#469	C₂×C₆₁	1	2	yes	complemented
328	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
329	C₂×#459	C₂×C₆₁	1	1	yes	characteristic, complemented
330	C₂×#449	C₂×C₆₁	1	2	yes	complemented
331	C₂×#447	C₂×C₆₁	1	2	yes	complemented
332	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
333	C₂×#436	C₂×C₆₁	1	1	yes	characteristic, complemented
334	C₂×C₆₁	—	4	4	no	—
335	C₂×C₆₁	—	4	4	no	—
336	C₂×C₆₁	—	8	4	no	—
337	C₂×C₆₁	—	8	4	no	—
338	C₂×C₆₁	#3274	1	4	yes	direct product factor
339	C₂×C₆₁	C₂×D₄²	1	1	yes	characteristic
340	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
342	C₂²×#41	C₂²×C₆₁	1	2	yes	complemented
343	C₂³×D₄	—	2	1	no	—
344	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
345	C₂×AGL(1,ℤ/8)	—	2	16	no	—
346	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	16	yes	complemented
347	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
348	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
349	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
350	C₂²×D₈	C₂²×C₆₁	1	2	yes	complemented
351	C₂²×D₈	C₂²×C₆₁	1	2	yes	complemented
352	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	complemented
353	#550	—	2	4	no	—
354	#550	C₂²×C₆₁	1	8	yes	complemented
355	D₄²	—	2	4	no	—
356	D₄²	C₂²×C₆₁	1	8	yes	complemented
357	C₂×#127	—	2	1	no	—
358	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
360	C₂×#121	—	2	1	no	—
361	C₂×#121	—	2	2	no	—
362	C₂×#121	C₂²×C₆₁	1	2	yes	—
363	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
364	C₂×#120	—	2	2	no	—
365	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
369	#493	C₂²×C₆₁	1	8	yes	complemented
370	#469	C₂²×C₆₁	1	16	yes	complemented
371	#460	C₂²×C₆₁	1	8	yes	complemented
372	#459	C₂²×C₆₁	1	8	yes	complemented
373	#449	C₂²×C₆₁	1	16	yes	complemented
374	#447	C₂²×C₆₁	1	16	yes	complemented
375	C₄×SD₁₆	C₂²×C₆₁	1	8	yes	complemented
376	#436	C₂²×C₆₁	1	8	yes	complemented
377	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
378	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
379	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
380	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
381	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
382	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
383	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	complemented
384	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
385	C₆₁	C₂×#3274	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁵	—	2	2	no	—
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	8	no	—
389	C₂×#41	—	4	4	no	—
390	C₂×#41	C₂³×C₆₁	1	8	yes	complemented
391	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
392	C₂²×D₄	—	2	8	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	2	2	no	—
396	C₂²×D₄	—	2	8	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	—	2	2	no	—
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	4	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	—	4	4	no	—
404	C₂²×D₄	—	4	8	no	—
405	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
406	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
407	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
408	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
409	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
410	C₂³×C₄	—	2	2	no	—
411	C₂³×C₄	—	2	1	no	—
412	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
413	AGL(1,ℤ/8)	—	2	64	no	—
414	C₂×SD₁₆	—	2	8	no	—
415	C₂×SD₁₆	D₄×C₆₁	1	8	yes	complemented
416	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
417	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	complemented
418	C₂×D₈	—	2	8	no	—
419	C₂×D₈	—	2	8	no	—
420	C₂×D₈	—	4	4	no	—
421	C₂×D₈	C₂³×C₆₁	1	8	yes	—
422	C₂×D₈	C₂³×C₆₁	1	8	yes	complemented
423	C₂×D₈	C₂³×C₆₁	1	8	yes	complemented
424	C₂×M₁₆	—	2	8	no	—
425	C₂×M₁₆	C₂³×C₆₁	1	8	yes	complemented
426	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
427	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
429	#127	—	2	8	no	—
430	#127	—	2	2	no	—
431	#127	—	2	2	no	—
432	#127	C₂³×C₆₁	1	4	yes	—
433	#127	C₂³×C₆₁	1	4	yes	complemented
434	#121	—	2	4	no	—
435	#121	—	2	4	no	—
436	#121	—	2	8	no	—
437	#121	—	2	16	no	—
438	#121	C₂³×C₆₁	1	8	yes	—
439	#121	C₂³×C₆₁	1	8	yes	complemented
440	#120	—	2	16	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	C₂³×C₆₁	1	4	yes	complemented
443	C₄×D₄	—	2	8	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	D₄×C₆₁	1	4	yes	—
446	C₄×D₄	C₂³×C₆₁	1	4	yes	—
447	C₄×D₄	C₂³×C₆₁	1	4	yes	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	2	no	—
455	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
458	#106	C₂³×C₆₁	1	4	yes	complemented
459	C₄⋊C₈	C₂³×C₆₁	1	4	yes	complemented
460	#103	C₂³×C₆₁	1	4	yes	complemented
461	#102	C₂³×C₆₁	1	4	yes	—
462	#102	C₂³×C₆₁	1	8	yes	complemented
463	#102	C₂³×C₆₁	1	8	yes	complemented
464	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	complemented
465	C₄×C₈	C₂³×C₆₁	1	4	yes	complemented
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	2	no	—
469	C₂⁴	—	2	8	no	—
470	C₂⁴	—	4	8	no	—
471	C₂⁴	—	4	8	no	—
472	C₂⁴	—	8	4	no	—
473	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
474	#41	—	2	16	no	—
475	#41	—	4	8	no	—
476	#41	—	4	16	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	complemented
480	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
481	C₂×D₄	—	2	16	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	8	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	4	8	no	—
500	C₂×D₄	—	4	16	no	—
501	C₂×D₄	—	4	8	no	—
502	C₂×D₄	—	4	8	no	—
503	C₂×D₄	—	4	32	no	—
504	C₂×D₄	—	4	8	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	8	2	no	—
508	C₂×D₄	—	8	2	no	—
509	C₂×D₄	—	8	4	no	—
510	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
511	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
512	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
513	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
514	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	8	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
527	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
530	SD₁₆	—	2	16	no	—
531	SD₁₆	C₂×D₄×C₆₁	1	16	yes	complemented
532	D₈	—	2	16	no	—
533	D₈	—	2	16	no	—
534	D₈	—	4	8	no	—
535	M₁₆	—	2	16	no	—
536	C₂×C₈	—	2	4	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	complemented
539	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
540	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
541	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
546	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
547	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
552	C₄²	—	2	4	no	—
553	C₄²	C₂×D₄×C₆₁	1	2	yes	—
554	C₄²	C₂⁴×C₆₁	1	2	yes	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	16	no	—
563	C₂³	—	4	16	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	4	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	8	8	no	—
573	C₂³	—	8	32	no	—
574	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
575	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
576	Q₈	—	2	4	no	—
577	Q₈	—	2	2	no	—
578	Q₈	C₂²×D₄×C₆₁	1	4	yes	complemented
579	D₄	—	2	4	no	—
580	D₄	—	2	8	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	4	16	no	—
587	D₄	—	4	16	no	—
588	D₄	—	4	16	no	—
589	D₄	—	4	4	no	—
590	D₄	—	4	4	no	—
591	D₄	—	4	8	no	—
592	D₄	—	4	8	no	—
593	D₄	—	8	4	no	—
594	D₄	—	8	4	no	—
595	D₄	—	8	8	no	—
596	D₄	C₂²×D₄×C₆₁	1	4	yes	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	16	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
611	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
612	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
613	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
616	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
617	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
618	C₈	—	2	4	no	—
619	C₈	—	2	2	no	—
620	C₈	C₂²×D₄×C₆₁	1	4	yes	complemented
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	8	no	—
628	C₂²	—	4	8	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	8	32	no	—
636	C₂²	—	8	8	no	—
637	C₂²	—	8	8	no	—
638	C₂²	D₄²×C₆₁	1	2	yes	—
639	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
640	C₂²	C₆₁×#576	1	2	yes	—
641	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	4	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	D₄²×C₆₁	1	2	yes	—
648	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
649	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
650	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
651	C₂	—	4	4	no	—
652	C₂	—	4	4	no	—
653	C₂	—	8	4	no	—
654	C₂	—	8	4	no	—
655	C₂	C₆₁×#3274	1	4	yes	direct product factor
656	C₂	C₂×D₄²×C₆₁	1	1	yes	characteristic
657	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
658	C₂	C₂×C₆₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₂×C₆₁×#550	C₂	semidirect
3. C₂×D₄²×C₆₁	C₂	semidirect
4. C₆₁×#3274	C₂	direct (N × H)
5. C₂×C₆₁×#493	C₂	semidirect
6. C₂×C₆₁×#469	C₂	semidirect
7. C₂×C₆₁×#460	C₂	semidirect
8. C₂×C₆₁×#459	C₂	semidirect
9. C₂×C₆₁×#449	C₂	semidirect
10. C₂×C₆₁×#447	C₂	semidirect
11. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
12. C₂×C₆₁×#436	C₂	semidirect
13. C₂²×#41×C₆₁	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
19. C₂²×SD₁₆×C₆₁	C₂²	semidirect
21. C₂²×D₈×C₆₁	C₂²	semidirect
22. C₂²×D₈×C₆₁	C₂²	semidirect
23. C₂²×M₁₆×C₆₁	C₂²	semidirect
25. C₆₁×#550	C₂²	semidirect
27. D₄²×C₆₁	C₂²	semidirect
30. C₂×#127×C₆₁	C₂²	semidirect
34. C₂×#121×C₆₁	C₂²	semidirect
36. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
40. C₆₁×#493	C₂²	semidirect
41. C₆₁×#469	C₂²	semidirect
42. C₆₁×#460	C₂²	semidirect
43. C₆₁×#459	C₂²	semidirect
44. C₆₁×#449	C₂²	semidirect
45. C₆₁×#447	C₂²	semidirect
46. C₄×SD₁₆×C₆₁	C₂²	semidirect
47. C₆₁×#436	C₂²	semidirect
48. C₂×#106×C₆₁	C₂²	semidirect
49. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
50. C₂×#103×C₆₁	C₂²	semidirect
52. C₂×#102×C₆₁	C₂²	semidirect
53. C₂×#102×C₆₁	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₆₁	C₂²	semidirect
55. C₂×C₄×C₈×C₆₁	C₂²	semidirect
60. C₂×#41×C₆₁	C₂³	semidirect
85. C₂×SD₁₆×C₆₁	D₄	semidirect
87. C₂×SD₁₆×C₆₁	C₂³	semidirect
92. C₂×D₈×C₆₁	C₂³	semidirect
93. C₂×D₈×C₆₁	C₂³	semidirect
95. C₂×M₁₆×C₆₁	C₂³	semidirect
103. #127×C₆₁	C₂³	semidirect
109. #121×C₆₁	C₂³	semidirect
112. C₄×Q₈×C₆₁	C₂³	semidirect
128. #106×C₆₁	C₂³	semidirect
129. C₄⋊C₈×C₆₁	C₂³	semidirect
130. #103×C₆₁	C₂³	semidirect
132. #102×C₆₁	C₂³	semidirect
133. #102×C₆₁	C₂³	semidirect
134. C₂²⋊C₈×C₆₁	C₂³	semidirect
135. C₄×C₈×C₆₁	C₂³	semidirect
149. C₂×Q₈×C₆₁	C₂×D₄	semidirect
201. SD₁₆×C₆₁	C₂×D₄	semidirect
208. C₂×C₈×C₆₁	C₂×D₄	semidirect
248. Q₈×C₆₁	C₂²×D₄	semidirect
280. C₂×C₄×C₆₁	AGL(1,ℤ/8)	semidirect
290. C₈×C₆₁	C₂²×D₄	semidirect
291. C₂×#3274	C₆₁	direct (N × H)
319. C₄×C₆₁	C₂×AGL(1,ℤ/8)	semidirect
322. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
323. C₂×#550	C₂×C₆₁	semidirect
324. C₂×D₄²	C₂×C₆₁	semidirect
325. #3274	C₂×C₆₁	direct (N × H)
326. C₂×#493	C₂×C₆₁	semidirect
327. C₂×#469	C₂×C₆₁	semidirect
328. C₂×#460	C₂×C₆₁	semidirect
329. C₂×#459	C₂×C₆₁	semidirect
330. C₂×#449	C₂×C₆₁	semidirect
331. C₂×#447	C₂×C₆₁	semidirect
332. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
333. C₂×#436	C₂×C₆₁	semidirect
338. C₂×C₆₁	#3274	direct (N × H)
342. C₂²×#41	C₂²×C₆₁	semidirect
346. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
348. C₂²×SD₁₆	C₂²×C₆₁	semidirect
350. C₂²×D₈	C₂²×C₆₁	semidirect
351. C₂²×D₈	C₂²×C₆₁	semidirect
352. C₂²×M₁₆	C₂²×C₆₁	semidirect
354. #550	C₂²×C₆₁	semidirect
356. D₄²	C₂²×C₆₁	semidirect
359. C₂×#127	C₂²×C₆₁	semidirect
363. C₂×#121	C₂²×C₆₁	semidirect
365. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
369. #493	C₂²×C₆₁	semidirect
370. #469	C₂²×C₆₁	semidirect
371. #460	C₂²×C₆₁	semidirect
372. #459	C₂²×C₆₁	semidirect
373. #449	C₂²×C₆₁	semidirect
374. #447	C₂²×C₆₁	semidirect
375. C₄×SD₁₆	C₂²×C₆₁	semidirect
376. #436	C₂²×C₆₁	semidirect
377. C₂×#106	C₂²×C₆₁	semidirect
378. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
379. C₂×#103	C₂²×C₆₁	semidirect
381. C₂×#102	C₂²×C₆₁	semidirect
382. C₂×#102	C₂²×C₆₁	semidirect
383. C₂×C₂²⋊C₈	C₂²×C₆₁	semidirect
384. C₂×C₄×C₈	C₂²×C₆₁	semidirect
385. C₆₁	C₂×#3274	direct (N × H)
390. C₂×#41	C₂³×C₆₁	semidirect
415. C₂×SD₁₆	D₄×C₆₁	semidirect
417. C₂×SD₁₆	C₂³×C₆₁	semidirect
422. C₂×D₈	C₂³×C₆₁	semidirect
423. C₂×D₈	C₂³×C₆₁	semidirect
425. C₂×M₁₆	C₂³×C₆₁	semidirect
433. #127	C₂³×C₆₁	semidirect
439. #121	C₂³×C₆₁	semidirect
442. C₄×Q₈	C₂³×C₆₁	semidirect
458. #106	C₂³×C₆₁	semidirect
459. C₄⋊C₈	C₂³×C₆₁	semidirect
460. #103	C₂³×C₆₁	semidirect
462. #102	C₂³×C₆₁	semidirect
463. #102	C₂³×C₆₁	semidirect
464. C₂²⋊C₈	C₂³×C₆₁	semidirect
465. C₄×C₈	C₂³×C₆₁	semidirect
479. C₂×Q₈	C₂×D₄×C₆₁	semidirect
531. SD₁₆	C₂×D₄×C₆₁	semidirect
538. C₂×C₈	C₂×D₄×C₆₁	semidirect
578. Q₈	C₂²×D₄×C₆₁	semidirect
610. C₂×C₄	AGL(1,ℤ/8)×C₆₁	semidirect
620. C₈	C₂²×D₄×C₆₁	semidirect
648. C₄	C₂×AGL(1,ℤ/8)×C₆₁	semidirect
655. C₂	C₆₁×#3274	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#550	2
C₂×D₄²×C₆₁	2
C₆₁×#3274	2
C₂×C₆₁×#493	2
C₂×C₆₁×#469	2
C₂×C₆₁×#460	2
C₂×C₆₁×#459	2
C₂×C₆₁×#449	2
C₂×C₆₁×#447	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₆₁×#436	2
C₂×#3274	61

Subgroups — C2×C61×#3274 #29564466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3274 #29564466