Subgroups — C₂×C₆₁×#3045 #29563853

Order 15616.

2934 conjugacy classes of subgroups.

The subgroup lattice has 680 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	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3045	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₆₁×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#460	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#459	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
17	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	complemented
18	C₂×#135×C₆₁	—	2	8	no	—
19	C₂×#135×C₆₁	C₂²	1	8	yes	complemented
20	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
25	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#535	—	2	4	no	—
29	C₆₁×#535	C₂²	1	8	yes	complemented
30	C₂×#127×C₆₁	C₂²	1	2	yes	—
31	C₂×#124×C₆₁	C₂²	1	2	yes	—
32	C₂×#121×C₆₁	—	2	1	no	—
33	C₂×#121×C₆₁	—	2	1	no	—
34	C₂×#120×C₆₁	—	2	2	no	—
35	C₆₁×#520	—	2	4	no	—
36	C₆₁×#520	C₂²	1	8	yes	complemented
37	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₁	—	2	2	no	—
39	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
40	C₂×#117×C₆₁	—	2	1	no	—
41	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
43	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#464	C₂²	1	16	yes	complemented
45	C₆₁×#463	C₂²	1	16	yes	complemented
46	C₆₁×#460	C₂²	1	16	yes	complemented
47	C₆₁×#459	C₂²	1	16	yes	complemented
48	C₆₁×#424	C₂²	1	8	yes	complemented
49	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
50	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
51	C₆₁×#417	C₂²	1	8	yes	complemented
52	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
53	C₂×#102×C₆₁	C₂²	1	2	yes	—
54	C₂×#102×C₆₁	C₂²	1	2	yes	—
55	C₂×#102×C₆₁	C₂²	1	8	yes	complemented
56	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
57	C₂⁵×C₆₁	—	2	1	no	—
58	C₂×#41×C₆₁	—	2	2	no	—
59	C₂×#41×C₆₁	—	2	2	no	—
60	C₂×#41×C₆₁	—	2	4	no	—
61	C₂×#41×C₆₁	—	2	4	no	—
62	C₂×#41×C₆₁	—	2	4	no	—
63	C₂×#41×C₆₁	D₄	1	8	yes	complemented
64	C₂×#41×C₆₁	C₂³	1	4	yes	—
65	C₂×#41×C₆₁	C₂³	1	4	yes	—
66	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₆₁	—	2	1	no	—
69	C₂²×D₄×C₆₁	—	2	1	no	—
70	C₂²×D₄×C₆₁	—	2	4	no	—
71	C₂²×D₄×C₆₁	—	2	2	no	—
72	C₂²×D₄×C₆₁	—	2	1	no	—
73	C₂²×D₄×C₆₁	—	2	2	no	—
74	C₂²×D₄×C₆₁	—	2	2	no	—
75	C₂²×D₄×C₆₁	—	2	4	no	—
76	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
79	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₁	—	2	1	no	—
81	C₂³×C₄×C₆₁	—	2	1	no	—
82	C₂³×C₄×C₆₁	—	2	1	no	—
83	C₂³×C₄×C₆₁	—	2	2	no	—
84	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
85	AGL(1,ℤ/8)×C₆₁	—	2	32	no	—
86	#135×C₆₁	—	2	32	no	—
87	C₂×Q₁₆×C₆₁	—	2	4	no	—
88	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	complemented
89	C₂×SD₁₆×C₆₁	—	2	8	no	—
90	C₂×SD₁₆×C₆₁	—	2	4	no	—
91	C₂×SD₁₆×C₆₁	—	2	4	no	—
92	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
93	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	complemented
94	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	complemented
95	C₂×D₈×C₆₁	—	2	8	no	—
96	C₂×D₈×C₆₁	—	2	4	no	—
97	C₂×D₈×C₆₁	C₂³	1	8	yes	—
98	C₂×D₈×C₆₁	C₂³	1	4	yes	complemented
99	C₂×M₁₆×C₆₁	—	2	4	no	—
100	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
101	C₂²×C₈×C₆₁	—	2	4	no	—
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
106	#127×C₆₁	—	2	4	no	—
107	#127×C₆₁	C₂³	1	8	yes	—
108	#124×C₆₁	—	2	4	no	—
109	#124×C₆₁	C₂³	1	8	yes	—
110	#121×C₆₁	—	2	8	no	—
111	#121×C₆₁	—	2	8	no	—
112	#120×C₆₁	—	2	16	no	—
113	C₄×Q₈×C₆₁	—	2	4	no	—
114	C₄×Q₈×C₆₁	C₂³	1	8	yes	complemented
115	C₄×D₄×C₆₁	—	2	16	no	—
116	C₄×D₄×C₆₁	—	2	4	no	—
117	C₄×D₄×C₆₁	C₂³	1	8	yes	complemented
118	#117×C₆₁	—	2	8	no	—
119	#117×C₆₁	D₄	1	4	yes	—
120	#117×C₆₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
122	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
125	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
133	C₂×C₄²×C₆₁	—	2	2	no	—
134	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
135	C₄⋊C₈×C₆₁	C₂³	1	8	yes	complemented
136	C₄⋊C₈×C₆₁	C₂³	1	8	yes	complemented
137	#103×C₆₁	C₂³	1	8	yes	complemented
138	#102×C₆₁	C₂³	1	8	yes	—
139	#102×C₆₁	C₂³	1	8	yes	—
140	#102×C₆₁	C₂³	1	8	yes	complemented
141	C₂⁴×C₆₁	—	2	1	no	—
142	C₂⁴×C₆₁	—	2	2	no	—
143	C₂⁴×C₆₁	—	2	1	no	—
144	C₂⁴×C₆₁	—	2	4	no	—
145	C₂⁴×C₆₁	—	4	4	no	—
146	C₂⁴×C₆₁	—	8	2	no	—
147	C₂⁴×C₆₁	—	8	2	no	—
148	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
149	#41×C₆₁	—	2	16	no	—
150	#41×C₆₁	—	2	8	no	—
151	#41×C₆₁	—	2	8	no	—
152	#41×C₆₁	—	2	8	no	—
153	#41×C₆₁	—	4	8	no	—
154	#41×C₆₁	C₂×D₄	1	16	yes	complemented
155	C₂×Q₈×C₆₁	—	2	1	no	—
156	C₂×Q₈×C₆₁	—	2	1	no	—
157	C₂×Q₈×C₆₁	—	2	2	no	—
158	C₂×Q₈×C₆₁	—	2	2	no	—
159	C₂×Q₈×C₆₁	—	2	2	no	—
160	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
161	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
162	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
163	C₂×D₄×C₆₁	—	2	8	no	—
164	C₂×D₄×C₆₁	—	2	4	no	—
165	C₂×D₄×C₆₁	—	2	4	no	—
166	C₂×D₄×C₆₁	—	2	1	no	—
167	C₂×D₄×C₆₁	—	2	4	no	—
168	C₂×D₄×C₆₁	—	2	2	no	—
169	C₂×D₄×C₆₁	—	2	8	no	—
170	C₂×D₄×C₆₁	—	2	4	no	—
171	C₂×D₄×C₆₁	—	2	2	no	—
172	C₂×D₄×C₆₁	—	2	1	no	—
173	C₂×D₄×C₆₁	—	2	8	no	—
174	C₂×D₄×C₆₁	—	2	8	no	—
175	C₂×D₄×C₆₁	—	2	2	no	—
176	C₂×D₄×C₆₁	—	2	4	no	—
177	C₂×D₄×C₆₁	—	2	8	no	—
178	C₂×D₄×C₆₁	—	2	2	no	—
179	C₂×D₄×C₆₁	—	4	4	no	—
180	C₂×D₄×C₆₁	—	4	4	no	—
181	C₂×D₄×C₆₁	—	4	8	no	—
182	C₂×D₄×C₆₁	—	8	4	no	—
183	C₂×D₄×C₆₁	—	8	4	no	—
184	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
185	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
186	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
187	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₁	—	2	1	no	—
189	C₂²×C₄×C₆₁	—	2	8	no	—
190	C₂²×C₄×C₆₁	—	2	4	no	—
191	C₂²×C₄×C₆₁	—	2	2	no	—
192	C₂²×C₄×C₆₁	—	2	1	no	—
193	C₂²×C₄×C₆₁	—	2	4	no	—
194	C₂²×C₄×C₆₁	—	2	4	no	—
195	C₂²×C₄×C₆₁	—	2	8	no	—
196	C₂²×C₄×C₆₁	—	4	4	no	—
197	C₂²×C₄×C₆₁	—	8	4	no	—
198	C₂²×C₄×C₆₁	—	8	2	no	—
199	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₆₁	#41	1	4	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
207	Q₁₆×C₆₁	—	2	8	no	—
208	SD₁₆×C₆₁	—	2	16	no	—
209	SD₁₆×C₆₁	—	2	8	no	—
210	SD₁₆×C₆₁	—	2	8	no	—
211	D₈×C₆₁	—	2	16	no	—
212	D₈×C₆₁	—	2	8	no	—
213	M₁₆×C₆₁	—	2	8	no	—
214	C₂×C₈×C₆₁	—	2	2	no	—
215	C₂×C₈×C₆₁	—	2	2	no	—
216	C₂×C₈×C₆₁	—	2	8	no	—
217	C₂×C₈×C₆₁	—	2	4	no	—
218	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
219	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
220	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
221	C₄⋊C₄×C₆₁	—	2	4	no	—
222	C₄⋊C₄×C₆₁	—	2	8	no	—
223	C₄⋊C₄×C₆₁	—	2	2	no	—
224	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
225	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
226	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
227	C₂²⋊C₄×C₆₁	—	2	8	no	—
228	C₂²⋊C₄×C₆₁	—	2	8	no	—
229	C₂²⋊C₄×C₆₁	—	2	8	no	—
230	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
231	C₄²×C₆₁	—	2	8	no	—
232	C₄²×C₆₁	C₂×D₄	1	4	yes	—
233	C₄²×C₆₁	C₂⁴	1	4	yes	—
234	C₂³×C₆₁	—	2	2	no	—
235	C₂³×C₆₁	—	2	2	no	—
236	C₂³×C₆₁	—	2	4	no	—
237	C₂³×C₆₁	—	2	2	no	—
238	C₂³×C₆₁	—	2	4	no	—
239	C₂³×C₆₁	—	2	2	no	—
240	C₂³×C₆₁	—	4	2	no	—
241	C₂³×C₆₁	—	4	2	no	—
242	C₂³×C₆₁	—	4	2	no	—
243	C₂³×C₆₁	—	4	8	no	—
244	C₂³×C₆₁	—	4	4	no	—
245	C₂³×C₆₁	—	4	2	no	—
246	C₂³×C₆₁	—	4	4	no	—
247	C₂³×C₆₁	—	4	2	no	—
248	C₂³×C₆₁	—	4	4	no	—
249	C₂³×C₆₁	—	8	4	no	—
250	C₂³×C₆₁	—	8	4	no	—
251	C₂³×C₆₁	—	8	16	no	—
252	C₂³×C₆₁	#121	1	4	yes	—
253	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
254	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₆₁	—	2	4	no	—
256	Q₈×C₆₁	—	2	2	no	—
257	Q₈×C₆₁	—	2	2	no	—
258	Q₈×C₆₁	—	2	2	no	—
259	Q₈×C₆₁	—	4	2	no	—
260	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
261	D₄×C₆₁	—	2	16	no	—
262	D₄×C₆₁	—	2	4	no	—
263	D₄×C₆₁	—	2	4	no	—
264	D₄×C₆₁	—	2	2	no	—
265	D₄×C₆₁	—	2	2	no	—
266	D₄×C₆₁	—	2	4	no	—
267	D₄×C₆₁	—	2	2	no	—
268	D₄×C₆₁	—	4	8	no	—
269	D₄×C₆₁	—	4	8	no	—
270	D₄×C₆₁	—	4	4	no	—
271	D₄×C₆₁	—	4	2	no	—
272	D₄×C₆₁	—	8	8	no	—
273	D₄×C₆₁	—	8	8	no	—
274	D₄×C₆₁	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₆₁	—	2	4	no	—
276	C₂×C₄×C₆₁	—	2	4	no	—
277	C₂×C₄×C₆₁	—	2	4	no	—
278	C₂×C₄×C₆₁	—	2	2	no	—
279	C₂×C₄×C₆₁	—	2	16	no	—
280	C₂×C₄×C₆₁	—	2	4	no	—
281	C₂×C₄×C₆₁	—	2	2	no	—
282	C₂×C₄×C₆₁	—	4	2	no	—
283	C₂×C₄×C₆₁	—	4	4	no	—
284	C₂×C₄×C₆₁	—	4	8	no	—
285	C₂×C₄×C₆₁	—	8	8	no	—
286	C₂×C₄×C₆₁	—	8	4	no	—
287	C₂×C₄×C₆₁	#121	1	4	yes	—
288	C₂×C₄×C₆₁	#121	1	8	yes	—
289	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
290	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
296	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
297	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
298	C₈×C₆₁	—	2	2	no	—
299	C₈×C₆₁	—	2	2	no	—
300	C₈×C₆₁	—	2	4	no	—
301	C₂×#3045	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂²×C₆₁	—	2	8	no	—
303	C₂²×C₆₁	—	2	2	no	—
304	C₂²×C₆₁	—	2	2	no	—
305	C₂²×C₆₁	—	2	4	no	—
306	C₂²×C₆₁	—	4	8	no	—
307	C₂²×C₆₁	—	4	2	no	—
308	C₂²×C₆₁	—	4	2	no	—
309	C₂²×C₆₁	—	4	2	no	—
310	C₂²×C₆₁	—	4	4	no	—
311	C₂²×C₆₁	—	4	2	no	—
312	C₂²×C₆₁	—	4	4	no	—
313	C₂²×C₆₁	—	4	2	no	—
314	C₂²×C₆₁	—	4	4	no	—
315	C₂²×C₆₁	—	8	16	no	—
316	C₂²×C₆₁	—	8	4	no	—
317	C₂²×C₆₁	—	8	8	no	—
318	C₂²×C₆₁	C₂×#121	1	4	yes	—
319	C₂²×C₆₁	C₂×#121	1	2	yes	—
320	C₂²×C₆₁	#576	1	2	yes	—
321	C₂²×C₆₁	#577	1	2	yes	—
322	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
323	C₄×C₆₁	—	2	4	no	—
324	C₄×C₆₁	—	2	4	no	—
325	C₄×C₆₁	—	2	4	no	—
326	C₄×C₆₁	—	4	2	no	—
327	C₄×C₆₁	—	4	4	no	—
328	C₄×C₆₁	C₂×#121	1	4	yes	—
329	C₄×C₆₁	C₂×#121	1	2	yes	—
330	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
331	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
332	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
333	C₂²×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
334	C₂×#535	C₂×C₆₁	1	1	yes	characteristic, complemented
335	C₂×#520	C₂×C₆₁	1	1	yes	characteristic, complemented
336	#3045	C₂×C₆₁	1	16	yes	direct product factor
337	C₂×#464	C₂×C₆₁	1	2	yes	complemented
338	C₂×#460	C₂×C₆₁	1	2	yes	complemented
339	C₂×#463	C₂×C₆₁	1	2	yes	complemented
340	C₂×#459	C₂×C₆₁	1	2	yes	complemented
341	C₂×#424	C₂×C₆₁	1	1	yes	characteristic, complemented
342	C₂×#417	C₂×C₆₁	1	1	yes	characteristic, complemented
343	C₂²×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
344	C₂×C₆₁	—	2	4	no	—
345	C₂×C₆₁	—	4	4	no	—
346	C₂×C₆₁	—	8	2	no	—
347	C₂×C₆₁	—	8	4	no	—
348	C₂×C₆₁	#3045	1	4	yes	direct product factor
349	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
350	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
351	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
352	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
353	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
354	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×AGL(1,ℤ/8)	—	2	8	no	—
356	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	complemented
357	C₂×#135	—	2	8	no	—
358	C₂×#135	C₂²×C₆₁	1	8	yes	complemented
359	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
360	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
361	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
362	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
363	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
364	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
365	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
366	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
367	#535	—	2	4	no	—
368	#535	C₂²×C₆₁	1	8	yes	complemented
369	C₂×#127	C₂²×C₆₁	1	2	yes	—
370	C₂×#124	C₂²×C₆₁	1	2	yes	—
371	C₂×#121	—	2	1	no	—
372	C₂×#121	—	2	1	no	—
373	C₂×#120	—	2	2	no	—
374	#520	—	2	4	no	—
375	#520	C₂²×C₆₁	1	8	yes	complemented
376	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
377	C₂×C₄×D₄	—	2	2	no	—
378	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
379	C₂×#117	—	2	1	no	—
380	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
381	C₂²×C₄⋊C₄	—	2	1	no	—
382	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
383	#464	C₂²×C₆₁	1	16	yes	complemented
384	#463	C₂²×C₆₁	1	16	yes	complemented
385	#460	C₂²×C₆₁	1	16	yes	complemented
386	#459	C₂²×C₆₁	1	16	yes	complemented
387	#424	C₂²×C₆₁	1	8	yes	complemented
388	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
389	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
390	#417	C₂²×C₆₁	1	8	yes	complemented
391	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
392	C₂×#102	C₂²×C₆₁	1	2	yes	—
393	C₂×#102	C₂²×C₆₁	1	2	yes	—
394	C₂×#102	C₂²×C₆₁	1	8	yes	complemented
395	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
396	C₆₁	C₂×#3045	1	1	yes	characteristic, direct product factor, Sylow
397	C₂⁵	—	2	1	no	—
398	C₂×#41	—	2	2	no	—
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	2	4	no	—
401	C₂×#41	—	2	4	no	—
402	C₂×#41	—	2	4	no	—
403	C₂×#41	D₄×C₆₁	1	8	yes	complemented
404	C₂×#41	C₂³×C₆₁	1	4	yes	—
405	C₂×#41	C₂³×C₆₁	1	4	yes	—
406	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	—	2	4	no	—
411	C₂²×D₄	—	2	1	no	—
412	C₂²×D₄	—	2	2	no	—
413	C₂²×D₄	—	2	2	no	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
417	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
419	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	—	2	1	no	—
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	—	2	2	no	—
424	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
425	AGL(1,ℤ/8)	—	2	32	no	—
426	#135	—	2	32	no	—
427	C₂×Q₁₆	—	2	4	no	—
428	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	complemented
429	C₂×SD₁₆	—	2	8	no	—
430	C₂×SD₁₆	—	2	4	no	—
431	C₂×SD₁₆	—	2	4	no	—
432	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
433	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	complemented
434	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	complemented
435	C₂×D₈	—	2	8	no	—
436	C₂×D₈	—	2	4	no	—
437	C₂×D₈	C₂³×C₆₁	1	8	yes	—
438	C₂×D₈	C₂³×C₆₁	1	4	yes	complemented
439	C₂×M₁₆	—	2	4	no	—
440	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
441	C₂²×C₈	—	2	4	no	—
442	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
445	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
446	#127	—	2	4	no	—
447	#127	C₂³×C₆₁	1	8	yes	—
448	#124	—	2	4	no	—
449	#124	C₂³×C₆₁	1	8	yes	—
450	#121	—	2	8	no	—
451	#121	—	2	8	no	—
452	#120	—	2	16	no	—
453	C₄×Q₈	—	2	4	no	—
454	C₄×Q₈	C₂³×C₆₁	1	8	yes	complemented
455	C₄×D₄	—	2	16	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	C₂³×C₆₁	1	8	yes	complemented
458	#117	—	2	8	no	—
459	#117	D₄×C₆₁	1	4	yes	—
460	#117	C₂³×C₆₁	1	4	yes	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	—	2	2	no	—
464	C₂×C₄⋊C₄	—	2	8	no	—
465	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
466	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₂²⋊C₄	—	2	2	no	—
472	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
473	C₂×C₄²	—	2	2	no	—
474	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
475	C₄⋊C₈	C₂³×C₆₁	1	8	yes	complemented
476	C₄⋊C₈	C₂³×C₆₁	1	8	yes	complemented
477	#103	C₂³×C₆₁	1	8	yes	complemented
478	#102	C₂³×C₆₁	1	8	yes	—
479	#102	C₂³×C₆₁	1	8	yes	—
480	#102	C₂³×C₆₁	1	8	yes	complemented
481	C₂⁴	—	2	1	no	—
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	4	no	—
485	C₂⁴	—	4	4	no	—
486	C₂⁴	—	8	2	no	—
487	C₂⁴	—	8	2	no	—
488	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
489	#41	—	2	16	no	—
490	#41	—	2	8	no	—
491	#41	—	2	8	no	—
492	#41	—	2	8	no	—
493	#41	—	4	8	no	—
494	#41	C₂×D₄×C₆₁	1	16	yes	complemented
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
501	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
502	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
503	C₂×D₄	—	2	8	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	4	8	no	—
522	C₂×D₄	—	8	4	no	—
523	C₂×D₄	—	8	4	no	—
524	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
525	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
526	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
527	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	8	4	no	—
538	C₂²×C₄	—	8	2	no	—
539	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
540	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
541	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
543	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
544	C₂²×C₄	#41×C₆₁	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
547	Q₁₆	—	2	8	no	—
548	SD₁₆	—	2	16	no	—
549	SD₁₆	—	2	8	no	—
550	SD₁₆	—	2	8	no	—
551	D₈	—	2	16	no	—
552	D₈	—	2	8	no	—
553	M₁₆	—	2	8	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	—	2	8	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
559	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
560	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
565	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
566	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
571	C₄²	—	2	8	no	—
572	C₄²	C₂×D₄×C₆₁	1	4	yes	—
573	C₄²	C₂⁴×C₆₁	1	4	yes	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	2	no	—
582	C₂³	—	4	2	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	4	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	8	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	8	4	no	—
590	C₂³	—	8	4	no	—
591	C₂³	—	8	16	no	—
592	C₂³	#121×C₆₁	1	4	yes	—
593	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
594	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
595	Q₈	—	2	2	no	—
596	Q₈	—	2	4	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	4	2	no	—
600	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
601	D₄	—	2	16	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	4	8	no	—
609	D₄	—	4	8	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	8	8	no	—
613	D₄	—	8	8	no	—
614	D₄	C₂²×D₄×C₆₁	1	4	yes	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	16	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	8	no	—
625	C₂×C₄	—	8	8	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	#121×C₆₁	1	4	yes	—
628	C₂×C₄	#121×C₆₁	1	8	yes	—
629	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
630	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
631	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
633	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
635	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
636	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
637	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	2	4	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	4	8	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	8	16	no	—
655	C₂²	—	8	4	no	—
656	C₂²	—	8	8	no	—
657	C₂²	C₂×#121×C₆₁	1	4	yes	—
658	C₂²	C₂×#121×C₆₁	1	2	yes	—
659	C₂²	C₆₁×#576	1	2	yes	—
660	C₂²	C₆₁×#577	1	2	yes	—
661	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
662	C₄	—	2	4	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	4	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	C₂×#121×C₆₁	1	4	yes	—
668	C₄	C₂×#121×C₆₁	1	2	yes	—
669	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
670	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
671	C₂	—	2	4	no	—
672	C₂	—	4	4	no	—
673	C₂	—	8	4	no	—
674	C₂	—	8	2	no	—
675	C₂	C₆₁×#3045	1	4	yes	direct product factor
676	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
677	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
678	C₂	C₂×C₆₁×#577	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×#117×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. C₂²×#135×C₆₁	C₂	semidirect
3. C₂×C₆₁×#535	C₂	semidirect
4. C₂×C₆₁×#520	C₂	semidirect
5. C₆₁×#3045	C₂	direct (N × H)
6. C₂×C₆₁×#464	C₂	semidirect
7. C₂×C₆₁×#460	C₂	semidirect
8. C₂×C₆₁×#463	C₂	semidirect
9. C₂×C₆₁×#459	C₂	semidirect
10. C₂×C₆₁×#424	C₂	semidirect
11. C₂×C₆₁×#417	C₂	semidirect
12. C₂²×#102×C₆₁	C₂	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
19. C₂×#135×C₆₁	C₂²	semidirect
20. C₂²×Q₁₆×C₆₁	C₂²	semidirect
22. C₂²×SD₁₆×C₆₁	C₂²	semidirect
23. C₂²×SD₁₆×C₆₁	C₂²	semidirect
25. C₂²×D₈×C₆₁	C₂²	semidirect
29. C₆₁×#535	C₂²	semidirect
36. C₆₁×#520	C₂²	semidirect
37. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
39. C₂×C₄×D₄×C₆₁	C₂²	semidirect
44. C₆₁×#464	C₂²	semidirect
45. C₆₁×#463	C₂²	semidirect
46. C₆₁×#460	C₂²	semidirect
47. C₆₁×#459	C₂²	semidirect
48. C₆₁×#424	C₂²	semidirect
49. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
50. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
51. C₆₁×#417	C₂²	semidirect
52. C₂×#103×C₆₁	C₂²	semidirect
55. C₂×#102×C₆₁	C₂²	semidirect
56. C₂×#102×C₆₁	C₂²	semidirect
63. C₂×#41×C₆₁	D₄	semidirect
88. C₂×Q₁₆×C₆₁	C₂³	semidirect
93. C₂×SD₁₆×C₆₁	C₂³	semidirect
94. C₂×SD₁₆×C₆₁	C₂³	semidirect
98. C₂×D₈×C₆₁	C₂³	semidirect
114. C₄×Q₈×C₆₁	C₂³	semidirect
117. C₄×D₄×C₆₁	C₂³	semidirect
135. C₄⋊C₈×C₆₁	C₂³	semidirect
136. C₄⋊C₈×C₆₁	C₂³	semidirect
137. #103×C₆₁	C₂³	semidirect
140. #102×C₆₁	C₂³	semidirect
154. #41×C₆₁	C₂×D₄	semidirect
301. C₂×#3045	C₆₁	direct (N × H)
332. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
333. C₂²×#135	C₂×C₆₁	semidirect
334. C₂×#535	C₂×C₆₁	semidirect
335. C₂×#520	C₂×C₆₁	semidirect
336. #3045	C₂×C₆₁	direct (N × H)
337. C₂×#464	C₂×C₆₁	semidirect
338. C₂×#460	C₂×C₆₁	semidirect
339. C₂×#463	C₂×C₆₁	semidirect
340. C₂×#459	C₂×C₆₁	semidirect
341. C₂×#424	C₂×C₆₁	semidirect
342. C₂×#417	C₂×C₆₁	semidirect
343. C₂²×#102	C₂×C₆₁	semidirect
348. C₂×C₆₁	#3045	direct (N × H)
356. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
358. C₂×#135	C₂²×C₆₁	semidirect
359. C₂²×Q₁₆	C₂²×C₆₁	semidirect
361. C₂²×SD₁₆	C₂²×C₆₁	semidirect
362. C₂²×SD₁₆	C₂²×C₆₁	semidirect
364. C₂²×D₈	C₂²×C₆₁	semidirect
368. #535	C₂²×C₆₁	semidirect
375. #520	C₂²×C₆₁	semidirect
376. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
378. C₂×C₄×D₄	C₂²×C₆₁	semidirect
383. #464	C₂²×C₆₁	semidirect
384. #463	C₂²×C₆₁	semidirect
385. #460	C₂²×C₆₁	semidirect
386. #459	C₂²×C₆₁	semidirect
387. #424	C₂²×C₆₁	semidirect
388. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
389. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
390. #417	C₂²×C₆₁	semidirect
391. C₂×#103	C₂²×C₆₁	semidirect
394. C₂×#102	C₂²×C₆₁	semidirect
395. C₂×#102	C₂²×C₆₁	semidirect
396. C₆₁	C₂×#3045	direct (N × H)
403. C₂×#41	D₄×C₆₁	semidirect
428. C₂×Q₁₆	C₂³×C₆₁	semidirect
433. C₂×SD₁₆	C₂³×C₆₁	semidirect
434. C₂×SD₁₆	C₂³×C₆₁	semidirect
438. C₂×D₈	C₂³×C₆₁	semidirect
454. C₄×Q₈	C₂³×C₆₁	semidirect
457. C₄×D₄	C₂³×C₆₁	semidirect
475. C₄⋊C₈	C₂³×C₆₁	semidirect
476. C₄⋊C₈	C₂³×C₆₁	semidirect
477. #103	C₂³×C₆₁	semidirect
480. #102	C₂³×C₆₁	semidirect
494. #41	C₂×D₄×C₆₁	semidirect
675. C₂	C₆₁×#3045	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
C₂²×#135×C₆₁	2
C₂×C₆₁×#535	2
C₂×C₆₁×#520	2
C₆₁×#3045	2
C₂×C₆₁×#464	2
C₂×C₆₁×#460	2
C₂×C₆₁×#463	2
C₂×C₆₁×#459	2
C₂×C₆₁×#424	2
C₂×C₆₁×#417	2
C₂²×#102×C₆₁	2
C₂×#3045	61

Subgroups — C2×C61×#3045 #29563853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3045 #29563853