Subgroups — C₂×C₆₁×#3173 #29564110

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#542	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3173	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#469	C₂	1	1	yes	maximal, characteristic
8	C₂×C₆₁×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#542	—	2	8	no	—
19	C₆₁×#542	C₂²	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×#126×C₆₁	—	2	2	no	—
22	C₂×#124×C₆₁	—	2	2	no	—
23	C₂×#124×C₆₁	C₂²	1	2	yes	—
24	C₂×#123×C₆₁	—	2	2	no	—
25	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
27	C₂×#121×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
30	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#498	C₂²	1	8	yes	complemented
32	C₆₁×#495	C₂²	1	8	yes	complemented
33	C₆₁×#489	C₂²	1	16	yes	complemented
34	C₆₁×#470	C₂²	1	8	yes	complemented
35	C₆₁×#469	C₂²	1	8	yes	—
36	C₆₁×#465	C₂²	1	16	yes	complemented
37	C₆₁×#442	C₂²	1	8	yes	complemented
38	C₆₁×#441	C₂²	1	8	yes	complemented
39	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
40	C₂×#106×C₆₁	C₂²	1	2	yes	—
41	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₁	C₂²	1	2	yes	—
44	C₂×#103×C₆₁	C₂²	1	2	yes	—
45	C₂×#102×C₆₁	C₂²	1	2	yes	—
46	C₂×#102×C₆₁	C₂²	1	2	yes	—
47	C₆₁×#405	C₂²	1	8	yes	complemented
48	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₆₁	—	2	2	no	—
53	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₆₁	—	2	2	no	—
55	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₁	—	2	2	no	—
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₆₁	—	2	4	no	—
59	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₆₁	—	2	8	no	—
61	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
62	C₂×D₈×C₆₁	—	2	4	no	—
63	C₂×D₈×C₆₁	C₂³	1	4	yes	—
64	C₂×M₁₆×C₆₁	—	2	4	no	—
65	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
66	C₂²×C₈×C₆₁	—	2	4	no	—
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₆₁	—	2	4	no	—
73	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
74	#126×C₆₁	—	2	16	no	—
75	#124×C₆₁	—	2	16	no	—
76	#124×C₆₁	—	2	4	no	—
77	#124×C₆₁	C₂³	1	8	yes	—
78	#123×C₆₁	—	2	16	no	—
79	C₂²⋊Q₈×C₆₁	—	2	4	no	—
80	C₂²⋊Q₈×C₆₁	—	2	16	no	—
81	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
82	#121×C₆₁	—	2	4	no	—
83	#121×C₆₁	C₂³	1	8	yes	—
84	C₄×Q₈×C₆₁	—	2	4	no	—
85	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
86	C₄×D₄×C₆₁	—	2	4	no	—
87	C₄×D₄×C₆₁	C₂³	1	8	yes	—
88	#117×C₆₁	D₄	1	4	yes	—
89	#117×C₆₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
102	C₂×C₄²×C₆₁	—	2	2	no	—
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	#106×C₆₁	C₂³	1	8	yes	—
106	#106×C₆₁	C₂³	1	4	yes	—
107	#106×C₆₁	C₂³	1	4	yes	—
108	#103×C₆₁	C₂³	1	8	yes	—
109	#103×C₆₁	C₂³	1	8	yes	—
110	#102×C₆₁	C₂³	1	8	yes	—
111	#102×C₆₁	C₂³	1	8	yes	—
112	#97×C₆₁	C₂³	1	4	yes	—
113	#97×C₆₁	C₂³	1	4	yes	—
114	C₄×C₈×C₆₁	C₂³	1	4	yes	—
115	C₄×C₈×C₆₁	C₂³	1	4	yes	—
116	C₂⁴×C₆₁	—	2	2	no	—
117	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	8	no	—
120	C₂×Q₈×C₆₁	—	2	4	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	8	4	no	—
123	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
124	C₂×D₄×C₆₁	—	2	8	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	2	4	no	—
127	C₂×D₄×C₆₁	—	2	4	no	—
128	C₂×D₄×C₆₁	—	8	4	no	—
129	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	8	no	—
136	C₂²×C₄×C₆₁	—	8	4	no	—
137	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₆₁	—	2	8	no	—
144	SD₁₆×C₆₁	—	2	16	no	—
145	D₈×C₆₁	—	2	8	no	—
146	M₁₆×C₆₁	—	2	8	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	8	no	—
150	C₂×C₈×C₆₁	#41	1	4	yes	—
151	C₂×C₈×C₆₁	#41	1	4	yes	—
152	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
153	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
154	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
155	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₆₁	—	2	8	no	—
157	C₄⋊C₄×C₆₁	—	2	8	no	—
158	C₄⋊C₄×C₆₁	—	2	8	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
162	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₆₁	—	2	8	no	—
165	C₂²⋊C₄×C₆₁	—	2	8	no	—
166	C₂²⋊C₄×C₆₁	—	2	8	no	—
167	C₂²⋊C₄×C₆₁	—	2	8	no	—
168	C₂²⋊C₄×C₆₁	—	2	8	no	—
169	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
170	C₄²×C₆₁	—	2	8	no	—
171	C₄²×C₆₁	C₂×D₄	1	2	yes	—
172	C₄²×C₆₁	C₂×D₄	1	2	yes	—
173	C₄²×C₆₁	C₂⁴	1	2	yes	—
174	C₄²×C₆₁	C₂⁴	1	2	yes	—
175	C₂³×C₆₁	—	2	2	no	—
176	C₂³×C₆₁	—	2	4	no	—
177	C₂³×C₆₁	—	2	4	no	—
178	C₂³×C₆₁	—	4	4	no	—
179	C₂³×C₆₁	—	4	4	no	—
180	C₂³×C₆₁	—	4	4	no	—
181	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
182	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₆₁	—	2	4	no	—
184	Q₈×C₆₁	—	2	4	no	—
185	Q₈×C₆₁	—	4	4	no	—
186	Q₈×C₆₁	—	8	8	no	—
187	D₄×C₆₁	—	2	4	no	—
188	D₄×C₆₁	—	2	4	no	—
189	D₄×C₆₁	—	4	4	no	—
190	D₄×C₆₁	—	8	8	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	4	no	—
193	C₂×C₄×C₆₁	—	2	4	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	4	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	4	4	no	—
201	C₂×C₄×C₆₁	—	4	4	no	—
202	C₂×C₄×C₆₁	—	4	4	no	—
203	C₂×C₄×C₆₁	—	8	8	no	—
204	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
209	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
210	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
211	C₈×C₆₁	—	2	2	no	—
212	C₈×C₆₁	—	2	2	no	—
213	C₈×C₆₁	C₂×#41	1	4	yes	—
214	C₈×C₆₁	C₂×#41	1	4	yes	—
215	C₂×#3173	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₆₁	—	2	2	no	—
217	C₂²×C₆₁	—	2	4	no	—
218	C₂²×C₆₁	—	4	4	no	—
219	C₂²×C₆₁	—	4	4	no	—
220	C₂²×C₆₁	—	4	4	no	—
221	C₂²×C₆₁	—	4	4	no	—
222	C₂²×C₆₁	—	8	8	no	—
223	C₂²×C₆₁	#532	1	2	yes	—
224	C₂²×C₆₁	#577	1	4	yes	—
225	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₆₁	—	2	2	no	—
227	C₄×C₆₁	—	2	4	no	—
228	C₄×C₆₁	—	2	4	no	—
229	C₄×C₆₁	—	4	4	no	—
230	C₄×C₆₁	—	4	4	no	—
231	C₄×C₆₁	—	4	4	no	—
232	C₄×C₆₁	#532	1	2	yes	—
233	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
234	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
235	C₂×#542	C₂×C₆₁	1	2	yes	complemented
236	#3173	C₂×C₆₁	1	16	yes	direct product factor
237	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
238	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
239	C₂×#489	C₂×C₆₁	1	2	yes	complemented
240	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
241	C₂×#469	C₂×C₆₁	1	1	yes	characteristic
242	C₂×#465	C₂×C₆₁	1	2	yes	complemented
243	C₂×#442	C₂×C₆₁	1	1	yes	characteristic, complemented
244	C₂×#441	C₂×C₆₁	1	1	yes	characteristic, complemented
245	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
246	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂×C₆₁	—	4	2	no	—
248	C₂×C₆₁	—	8	4	no	—
249	C₂×C₆₁	#3173	1	4	yes	direct product factor
250	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
251	C₂×C₆₁	C₂×#577	1	2	yes	—
252	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
253	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
254	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
256	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
257	#542	—	2	8	no	—
258	#542	C₂²×C₆₁	1	16	yes	complemented
259	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
260	C₂×#126	—	2	2	no	—
261	C₂×#124	—	2	2	no	—
262	C₂×#124	C₂²×C₆₁	1	2	yes	—
263	C₂×#123	—	2	2	no	—
264	C₂×C₂²⋊Q₈	—	2	2	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
266	C₂×#121	C₂²×C₆₁	1	2	yes	—
267	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
268	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
269	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
270	#498	C₂²×C₆₁	1	8	yes	complemented
271	#495	C₂²×C₆₁	1	8	yes	complemented
272	#489	C₂²×C₆₁	1	16	yes	complemented
273	#470	C₂²×C₆₁	1	8	yes	complemented
274	#469	C₂²×C₆₁	1	8	yes	—
275	#465	C₂²×C₆₁	1	16	yes	complemented
276	#442	C₂²×C₆₁	1	8	yes	complemented
277	#441	C₂²×C₆₁	1	8	yes	complemented
278	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
279	C₂×#106	C₂²×C₆₁	1	2	yes	—
280	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
281	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
282	C₂×#103	C₂²×C₆₁	1	2	yes	—
283	C₂×#103	C₂²×C₆₁	1	2	yes	—
284	C₂×#102	C₂²×C₆₁	1	2	yes	—
285	C₂×#102	C₂²×C₆₁	1	2	yes	—
286	#405	C₂²×C₆₁	1	8	yes	complemented
287	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
291	C₆₁	C₂×#3173	1	1	yes	characteristic, direct product factor, Sylow
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
300	C₂×SD₁₆	—	2	8	no	—
301	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
302	C₂×D₈	—	2	4	no	—
303	C₂×D₈	C₂³×C₆₁	1	4	yes	—
304	C₂×M₁₆	—	2	4	no	—
305	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
306	C₂²×C₈	—	2	4	no	—
307	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
309	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
314	#126	—	2	16	no	—
315	#124	—	2	16	no	—
316	#124	—	2	4	no	—
317	#124	C₂³×C₆₁	1	8	yes	—
318	#123	—	2	16	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	16	no	—
321	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
322	#121	—	2	4	no	—
323	#121	C₂³×C₆₁	1	8	yes	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	C₂³×C₆₁	1	8	yes	—
328	#117	D₄×C₆₁	1	4	yes	—
329	#117	C₂³×C₆₁	1	4	yes	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
345	#106	C₂³×C₆₁	1	8	yes	—
346	#106	C₂³×C₆₁	1	4	yes	—
347	#106	C₂³×C₆₁	1	4	yes	—
348	#103	C₂³×C₆₁	1	8	yes	—
349	#103	C₂³×C₆₁	1	8	yes	—
350	#102	C₂³×C₆₁	1	8	yes	—
351	#102	C₂³×C₆₁	1	8	yes	—
352	#97	C₂³×C₆₁	1	4	yes	—
353	#97	C₂³×C₆₁	1	4	yes	—
354	C₄×C₈	C₂³×C₆₁	1	4	yes	—
355	C₄×C₈	C₂³×C₆₁	1	4	yes	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	8	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	8	4	no	—
363	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	8	4	no	—
369	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	8	4	no	—
377	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
383	Q₁₆	—	2	8	no	—
384	SD₁₆	—	2	16	no	—
385	D₈	—	2	8	no	—
386	M₁₆	—	2	8	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	8	no	—
390	C₂×C₈	#41×C₆₁	1	4	yes	—
391	C₂×C₈	#41×C₆₁	1	4	yes	—
392	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
393	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
394	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
395	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
402	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
403	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
410	C₄²	—	2	8	no	—
411	C₄²	C₂×D₄×C₆₁	1	2	yes	—
412	C₄²	C₂×D₄×C₆₁	1	2	yes	—
413	C₄²	C₂⁴×C₆₁	1	2	yes	—
414	C₄²	C₂⁴×C₆₁	1	2	yes	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
422	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	4	no	—
426	Q₈	—	8	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
446	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
449	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
450	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	C₂×#41×C₆₁	1	4	yes	—
454	C₈	C₂×#41×C₆₁	1	4	yes	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₆₁×#532	1	2	yes	—
463	C₂²	C₆₁×#577	1	4	yes	—
464	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₆₁×#532	1	2	yes	—
472	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
473	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
474	C₂	—	4	2	no	—
475	C₂	—	8	4	no	—
476	C₂	C₆₁×#3173	1	4	yes	direct product factor
477	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
478	C₂	C₂×C₆₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#469	C₂
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. C₂×C₆₁×#542	C₂	semidirect
2. C₆₁×#3173	C₂	direct (N × H)
3. C₂×C₆₁×#498	C₂	semidirect
4. C₂×C₆₁×#495	C₂	semidirect
5. C₂×C₆₁×#489	C₂	semidirect
6. C₂×C₆₁×#470	C₂	semidirect
8. C₂×C₆₁×#465	C₂	semidirect
9. C₂×C₆₁×#442	C₂	semidirect
10. C₂×C₆₁×#441	C₂	semidirect
11. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
12. C₂×C₆₁×#405	C₂	semidirect
19. C₆₁×#542	C₂²	semidirect
31. C₆₁×#498	C₂²	semidirect
32. C₆₁×#495	C₂²	semidirect
33. C₆₁×#489	C₂²	semidirect
34. C₆₁×#470	C₂²	semidirect
36. C₆₁×#465	C₂²	semidirect
37. C₆₁×#442	C₂²	semidirect
38. C₆₁×#441	C₂²	semidirect
39. C₄×SD₁₆×C₆₁	C₂²	semidirect
47. C₆₁×#405	C₂²	semidirect
215. C₂×#3173	C₆₁	direct (N × H)
235. C₂×#542	C₂×C₆₁	semidirect
236. #3173	C₂×C₆₁	direct (N × H)
237. C₂×#498	C₂×C₆₁	semidirect
238. C₂×#495	C₂×C₆₁	semidirect
239. C₂×#489	C₂×C₆₁	semidirect
240. C₂×#470	C₂×C₆₁	semidirect
242. C₂×#465	C₂×C₆₁	semidirect
243. C₂×#442	C₂×C₆₁	semidirect
244. C₂×#441	C₂×C₆₁	semidirect
245. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
246. C₂×#405	C₂×C₆₁	semidirect
249. C₂×C₆₁	#3173	direct (N × H)
258. #542	C₂²×C₆₁	semidirect
270. #498	C₂²×C₆₁	semidirect
271. #495	C₂²×C₆₁	semidirect
272. #489	C₂²×C₆₁	semidirect
273. #470	C₂²×C₆₁	semidirect
275. #465	C₂²×C₆₁	semidirect
276. #442	C₂²×C₆₁	semidirect
277. #441	C₂²×C₆₁	semidirect
278. C₄×SD₁₆	C₂²×C₆₁	semidirect
286. #405	C₂²×C₆₁	semidirect
291. C₆₁	C₂×#3173	direct (N × H)
476. C₂	C₆₁×#3173	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#542	2
C₆₁×#3173	2
C₂×C₆₁×#498	2
C₂×C₆₁×#495	2
C₂×C₆₁×#489	2
C₂×C₆₁×#470	2
C₂×C₆₁×#469	2
C₂×C₆₁×#465	2
C₂×C₆₁×#442	2
C₂×C₆₁×#441	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₆₁×#405	2
C₂×#3173	61

Subgroups — C2×C61×#3173 #29564110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3173 #29564110