Subgroups — C₆₁×#11068 #29514501

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#104×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#424	—	2	2	no	—
16	C₆₁×#424	—	2	2	no	—
17	C₂×C₄⋊C₈×C₆₁	—	2	2	no	—
18	C₂×#104×C₆₁	—	2	2	no	—
19	C₂×#104×C₆₁	—	2	2	no	—
20	C₂×#104×C₆₁	—	2	2	no	—
21	C₆₁×#416	—	2	2	no	—
22	C₆₁×#416	—	2	2	no	—
23	C₂×#103×C₆₁	C₄	1	2	yes	complemented
24	C₂×#102×C₆₁	C₄	1	2	yes	complemented
25	C₆₁×#408	—	2	2	no	—
26	C₆₁×#408	—	2	2	no	—
27	C₂×C₂²⋊C₈×C₆₁	—	2	2	no	—
28	C₆₁×#341	—	2	2	no	—
29	C₆₁×#339	—	2	2	no	—
30	C₆₁×#336	—	2	2	no	—
31	C₂×#41×C₆₁	—	2	1	no	—
32	C₂×#41×C₆₁	—	2	1	no	—
33	C₂×#41×C₆₁	—	2	1	no	—
34	C₂×#41×C₆₁	—	2	1	no	—
35	C₂×#41×C₆₁	—	2	1	no	—
36	C₂×#41×C₆₁	—	2	1	no	—
37	C₂×#41×C₆₁	—	2	1	no	—
38	C₂×#41×C₆₁	—	2	1	no	—
39	C₂×#41×C₆₁	—	2	1	no	—
40	C₂×#41×C₆₁	—	2	1	no	—
41	C₂×#41×C₆₁	D₄	1	2	yes	—
42	C₂×#41×C₆₁	Q₈	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	—	2	1	no	—
45	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₆₁	—	2	1	no	—
50	C₂×M₁₆×C₆₁	—	2	1	no	—
51	C₂×M₁₆×C₆₁	—	2	1	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂×M₁₆×C₆₁	—	2	1	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	—	2	1	no	—
56	C₂×M₁₆×C₆₁	—	2	1	no	—
57	C₂×M₁₆×C₆₁	—	2	1	no	—
58	C₂×M₁₆×C₆₁	—	2	1	no	—
59	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
60	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
61	C₂²×C₈×C₆₁	—	2	1	no	—
62	C₂²×C₈×C₆₁	—	2	1	no	—
63	C₂²×C₈×C₆₁	—	2	1	no	—
64	C₂²×C₈×C₆₁	—	2	1	no	—
65	C₂²×C₈×C₆₁	—	2	1	no	—
66	C₂²×C₈×C₆₁	—	2	1	no	—
67	C₂²×C₈×C₆₁	—	2	1	no	—
68	C₂²×C₈×C₆₁	—	2	1	no	—
69	C₂²×C₈×C₆₁	—	2	1	no	—
70	C₂²×C₈×C₆₁	—	2	1	no	—
71	C₂²×C₈×C₆₁	—	2	1	no	—
72	C₂²×C₈×C₆₁	—	2	1	no	—
73	C₂²×C₈×C₆₁	—	2	1	no	—
74	C₂²×C₈×C₆₁	—	2	1	no	—
75	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₆₁	D₄	1	2	yes	—
77	#117×C₆₁	—	2	1	no	—
78	#117×C₆₁	—	2	1	no	—
79	#117×C₆₁	D₄	1	2	yes	—
80	#117×C₆₁	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄²×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	C₂×C₄²×C₆₁	D₄	1	2	yes	—
90	C₄⋊C₈×C₆₁	—	2	8	no	—
91	#104×C₆₁	—	2	8	no	—
92	#103×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	2	4	no	—
94	C₂²⋊C₈×C₆₁	—	2	8	no	—
95	C₂⁴×C₆₁	—	2	1	no	—
96	C₂⁴×C₆₁	#41	1	1	yes	characteristic
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	—	2	2	no	—
99	#41×C₆₁	—	2	2	no	—
100	#41×C₆₁	—	2	2	no	—
101	#41×C₆₁	—	2	2	no	—
102	#41×C₆₁	—	2	2	no	—
103	#41×C₆₁	—	2	2	no	—
104	#41×C₆₁	—	2	2	no	—
105	#41×C₆₁	—	4	1	no	—
106	#41×C₆₁	—	4	1	no	—
107	#41×C₆₁	—	4	1	no	—
108	#41×C₆₁	—	4	1	no	—
109	#41×C₆₁	—	4	1	no	—
110	#41×C₆₁	—	4	1	no	—
111	#41×C₆₁	—	4	1	no	—
112	#41×C₆₁	—	4	1	no	—
113	C₂×Q₈×C₆₁	—	2	1	no	—
114	C₂×Q₈×C₆₁	—	2	1	no	—
115	C₂×Q₈×C₆₁	—	2	1	no	—
116	C₂×Q₈×C₆₁	—	2	1	no	—
117	C₂×Q₈×C₆₁	—	2	1	no	—
118	C₂×Q₈×C₆₁	C₄⋊C₄	1	2	yes	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	—	2	1	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	2	1	no	—
126	C₂×D₄×C₆₁	—	4	1	no	—
127	C₂×D₄×C₆₁	—	4	1	no	—
128	C₂×D₄×C₆₁	—	4	1	no	—
129	C₂×D₄×C₆₁	—	4	1	no	—
130	C₂×D₄×C₆₁	C₄⋊C₄	1	2	yes	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	4	2	no	—
138	C₂²×C₄×C₆₁	—	4	1	no	—
139	C₂²×C₄×C₆₁	—	4	1	no	—
140	C₂²×C₄×C₆₁	—	4	1	no	—
141	C₂²×C₄×C₆₁	—	4	1	no	—
142	C₂²×C₄×C₆₁	—	4	1	no	—
143	C₂²×C₄×C₆₁	—	4	1	no	—
144	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
158	M₁₆×C₆₁	—	2	2	no	—
159	M₁₆×C₆₁	—	2	2	no	—
160	M₁₆×C₆₁	—	2	2	no	—
161	M₁₆×C₆₁	—	2	2	no	—
162	M₁₆×C₆₁	—	4	1	no	—
163	M₁₆×C₆₁	—	4	1	no	—
164	M₁₆×C₆₁	—	4	1	no	—
165	M₁₆×C₆₁	—	4	1	no	—
166	C₂×C₈×C₆₁	—	2	2	no	—
167	C₂×C₈×C₆₁	—	2	2	no	—
168	C₂×C₈×C₆₁	—	2	2	no	—
169	C₂×C₈×C₆₁	—	2	2	no	—
170	C₂×C₈×C₆₁	—	2	2	no	—
171	C₂×C₈×C₆₁	—	2	2	no	—
172	C₂×C₈×C₆₁	—	2	2	no	—
173	C₂×C₈×C₆₁	—	2	2	no	—
174	C₂×C₈×C₆₁	—	4	1	no	—
175	C₂×C₈×C₆₁	—	4	1	no	—
176	C₂×C₈×C₆₁	—	4	1	no	—
177	C₂×C₈×C₆₁	—	4	1	no	—
178	C₂×C₈×C₆₁	—	4	1	no	—
179	C₂×C₈×C₆₁	—	4	1	no	—
180	C₂×C₈×C₆₁	—	4	1	no	—
181	C₂×C₈×C₆₁	—	4	1	no	—
182	C₂×C₈×C₆₁	—	4	1	no	—
183	C₂×C₈×C₆₁	—	4	1	no	—
184	C₂×C₈×C₆₁	—	4	1	no	—
185	C₂×C₈×C₆₁	—	4	1	no	—
186	C₄⋊C₄×C₆₁	—	2	2	no	—
187	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
188	C₂²⋊C₄×C₆₁	—	2	2	no	—
189	C₂²⋊C₄×C₆₁	—	2	2	no	—
190	C₄²×C₆₁	—	2	2	no	—
191	C₄²×C₆₁	—	2	2	no	—
192	C₄²×C₆₁	—	2	2	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	—	4	1	no	—
195	C₄²×C₆₁	—	4	1	no	—
196	C₂³×C₆₁	—	2	2	no	—
197	C₂³×C₆₁	—	2	2	no	—
198	C₂³×C₆₁	—	2	2	no	—
199	C₂³×C₆₁	—	4	1	no	—
200	C₂³×C₆₁	—	4	1	no	—
201	C₂³×C₆₁	—	4	2	no	—
202	C₂³×C₆₁	—	4	2	no	—
203	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₆₁	#121	1	1	yes	characteristic
205	C₂³×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂³×C₆₁	#123	1	1	yes	characteristic
207	C₂³×C₆₁	#123	1	1	yes	characteristic
208	C₂³×C₆₁	#123	1	1	yes	characteristic
209	C₂³×C₆₁	#126	1	1	yes	characteristic
210	Q₈×C₆₁	—	2	2	no	—
211	Q₈×C₆₁	—	2	2	no	—
212	Q₈×C₆₁	—	4	1	no	—
213	Q₈×C₆₁	—	4	1	no	—
214	D₄×C₆₁	—	2	2	no	—
215	D₄×C₆₁	—	2	2	no	—
216	D₄×C₆₁	—	4	2	no	—
217	D₄×C₆₁	—	4	2	no	—
218	D₄×C₆₁	—	4	2	no	—
219	D₄×C₆₁	—	4	2	no	—
220	D₄×C₆₁	—	4	1	no	—
221	D₄×C₆₁	—	4	1	no	—
222	C₂×C₄×C₆₁	—	2	4	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	2	4	no	—
225	C₂×C₄×C₆₁	—	4	4	no	—
226	C₂×C₄×C₆₁	—	4	4	no	—
227	C₂×C₄×C₆₁	—	4	2	no	—
228	C₂×C₄×C₆₁	—	4	1	no	—
229	C₂×C₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	2	no	—
233	C₂×C₄×C₆₁	—	4	2	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	—	4	2	no	—
236	C₂×C₄×C₆₁	—	4	2	no	—
237	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
240	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
244	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
245	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
246	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
247	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
248	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
249	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
250	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
251	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
252	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
259	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
260	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
261	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
262	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
263	C₂×C₄×C₆₁	#126	1	1	yes	characteristic
264	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
265	C₈×C₆₁	—	4	2	no	—
266	C₈×C₆₁	—	4	2	no	—
267	C₈×C₆₁	—	4	2	no	—
268	C₈×C₆₁	—	4	2	no	—
269	#11068	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂²×C₆₁	—	2	2	no	—
271	C₂²×C₆₁	—	2	2	no	—
272	C₂²×C₆₁	—	2	2	no	—
273	C₂²×C₆₁	—	2	2	no	—
274	C₂²×C₆₁	—	2	1	no	—
275	C₂²×C₆₁	—	2	1	no	—
276	C₂²×C₆₁	—	2	1	no	—
277	C₂²×C₆₁	—	2	1	no	—
278	C₂²×C₆₁	—	4	4	no	—
279	C₂²×C₆₁	—	4	2	no	—
280	C₂²×C₆₁	—	8	2	no	—
281	C₂²×C₆₁	—	8	1	no	—
282	C₂²×C₆₁	—	8	1	no	—
283	C₂²×C₆₁	#385	1	1	yes	characteristic
284	C₂²×C₆₁	#386	1	1	yes	characteristic
285	C₂²×C₆₁	#388	1	1	yes	characteristic
286	C₂²×C₆₁	#394	1	1	yes	characteristic
287	C₂²×C₆₁	#396	1	1	yes	characteristic
288	C₂²×C₆₁	#397	1	1	yes	characteristic
289	C₂²×C₆₁	#399	1	1	yes	characteristic
290	C₂²×C₆₁	#443	1	2	yes	—
291	C₂²×C₆₁	#444	1	2	yes	—
292	C₄×C₆₁	—	4	4	no	—
293	C₄×C₆₁	—	4	4	no	—
294	C₄×C₆₁	—	4	2	no	—
295	C₄×C₆₁	#380	1	1	yes	characteristic
296	C₄×C₆₁	#385	1	1	yes	characteristic
297	C₄×C₆₁	#388	1	1	yes	characteristic
298	C₄×C₆₁	#390	1	1	yes	characteristic
299	C₄×C₆₁	#392	1	1	yes	characteristic
300	C₄×C₆₁	#393	1	1	yes	characteristic
301	C₄×C₆₁	#394	1	1	yes	characteristic
302	C₄×C₆₁	#396	1	1	yes	characteristic
303	C₂×#424	C₂×C₆₁	1	1	yes	characteristic, complemented
304	C₂²×#104	C₂×C₆₁	1	1	yes	characteristic
305	C₂×#416	C₂×C₆₁	1	1	yes	characteristic
306	C₂×#408	C₂×C₆₁	1	1	yes	characteristic
307	C₂×#341	C₂×C₆₁	1	1	yes	characteristic, complemented
308	C₂×#339	C₂×C₆₁	1	1	yes	characteristic, complemented
309	C₂×#336	C₂×C₆₁	1	1	yes	characteristic, complemented
310	C₂×C₆₁	—	2	1	no	—
311	C₂×C₆₁	—	2	1	no	—
312	C₂×C₆₁	—	2	1	no	—
313	C₂×C₆₁	—	2	1	no	—
314	C₂×C₆₁	—	8	2	no	—
315	C₂×C₆₁	#1439	1	1	yes	characteristic
316	C₂×C₆₁	#1866	1	2	yes	—
317	C₂×C₆₁	#1876	1	2	yes	—
318	C₂×C₆₁	#1937	1	1	yes	characteristic
319	C₂×C₆₁	#1938	1	1	yes	characteristic
320	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
321	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
322	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
323	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
324	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
325	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
326	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
327	#424	—	2	2	no	—
328	#424	—	2	2	no	—
329	C₂×C₄⋊C₈	—	2	2	no	—
330	C₂×#104	—	2	2	no	—
331	C₂×#104	—	2	2	no	—
332	C₂×#104	—	2	2	no	—
333	#416	—	2	2	no	—
334	#416	—	2	2	no	—
335	C₂×#103	C₄×C₆₁	1	2	yes	complemented
336	C₂×#102	C₄×C₆₁	1	2	yes	complemented
337	#408	—	2	2	no	—
338	#408	—	2	2	no	—
339	C₂×C₂²⋊C₈	—	2	2	no	—
340	#341	—	2	2	no	—
341	#339	—	2	2	no	—
342	#336	—	2	2	no	—
343	C₆₁	#11068	1	1	yes	characteristic, direct product factor, Sylow
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	D₄×C₆₁	1	2	yes	—
355	C₂×#41	Q₈×C₆₁	1	2	yes	—
356	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
373	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
389	C₂²×C₈	D₄×C₆₁	1	2	yes	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	D₄×C₆₁	1	2	yes	—
393	#117	D₄×C₆₁	1	2	yes	—
394	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	D₄×C₆₁	1	2	yes	—
403	C₄⋊C₈	—	2	8	no	—
404	#104	—	2	8	no	—
405	#103	—	2	4	no	—
406	#102	—	2	4	no	—
407	C₂²⋊C₈	—	2	8	no	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	#41×C₆₁	1	1	yes	characteristic
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	#41	—	4	1	no	—
423	#41	—	4	1	no	—
424	#41	—	4	1	no	—
425	#41	—	4	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	C₄⋊C₄×C₆₁	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	C₄⋊C₄×C₆₁	1	2	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
465	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
466	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
467	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
468	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
469	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
470	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	4	1	no	—
476	M₁₆	—	4	1	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	—	4	1	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	—	4	1	no	—
489	C₂×C₈	—	4	1	no	—
490	C₂×C₈	—	4	1	no	—
491	C₂×C₈	—	4	1	no	—
492	C₂×C₈	—	4	1	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	4	1	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
517	C₂³	#121×C₆₁	1	1	yes	characteristic
518	C₂³	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
519	C₂³	#123×C₆₁	1	1	yes	characteristic
520	C₂³	#123×C₆₁	1	1	yes	characteristic
521	C₂³	#123×C₆₁	1	1	yes	characteristic
522	C₂³	#126×C₆₁	1	1	yes	characteristic
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
551	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
552	C₂×C₄	#117×C₆₁	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
554	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
555	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
556	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
557	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
558	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
559	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
560	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
561	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
562	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
563	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
564	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
565	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
568	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
569	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
570	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
571	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
572	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
573	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
574	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
575	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
576	C₂×C₄	#126×C₆₁	1	1	yes	characteristic
577	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
578	C₈	—	4	2	no	—
579	C₈	—	4	2	no	—
580	C₈	—	4	2	no	—
581	C₈	—	4	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₆₁×#385	1	1	yes	characteristic
596	C₂²	C₆₁×#386	1	1	yes	characteristic
597	C₂²	C₆₁×#388	1	1	yes	characteristic
598	C₂²	C₆₁×#394	1	1	yes	characteristic
599	C₂²	C₆₁×#396	1	1	yes	characteristic
600	C₂²	C₆₁×#397	1	1	yes	characteristic
601	C₂²	C₆₁×#399	1	1	yes	characteristic
602	C₂²	C₆₁×#443	1	2	yes	—
603	C₂²	C₆₁×#444	1	2	yes	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	2	no	—
607	C₄	C₆₁×#380	1	1	yes	characteristic
608	C₄	C₆₁×#385	1	1	yes	characteristic
609	C₄	C₆₁×#388	1	1	yes	characteristic
610	C₄	C₆₁×#390	1	1	yes	characteristic
611	C₄	C₆₁×#392	1	1	yes	characteristic
612	C₄	C₆₁×#393	1	1	yes	characteristic
613	C₄	C₆₁×#394	1	1	yes	characteristic
614	C₄	C₆₁×#396	1	1	yes	characteristic
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	8	2	no	—
620	C₂	C₆₁×#1439	1	1	yes	characteristic
621	C₂	C₆₁×#1866	1	2	yes	—
622	C₂	C₆₁×#1876	1	2	yes	—
623	C₂	C₆₁×#1937	1	1	yes	characteristic
624	C₂	C₆₁×#1938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
socle	C₂³×C₆₁	C₄×D₄
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂³×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#424	C₂	semidirect
5. C₂×C₆₁×#341	C₂	semidirect
6. C₂×C₆₁×#339	C₂	semidirect
7. C₂×C₆₁×#336	C₂	semidirect
23. C₂×#103×C₆₁	C₄	semidirect
24. C₂×#102×C₆₁	C₄	semidirect
269. #11068	C₆₁	direct (N × H)
303. C₂×#424	C₂×C₆₁	semidirect
307. C₂×#341	C₂×C₆₁	semidirect
308. C₂×#339	C₂×C₆₁	semidirect
309. C₂×#336	C₂×C₆₁	semidirect
335. C₂×#103	C₄×C₆₁	semidirect
336. C₂×#102	C₄×C₆₁	semidirect
343. C₆₁	#11068	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×#424	2
C₂²×#104×C₆₁	2
C₂×C₆₁×#416	2
C₂×C₆₁×#408	2
C₂×C₆₁×#341	2
C₂×C₆₁×#339	2
C₂×C₆₁×#336	2
#11068	61

Subgroups — C61×#11068 #29514501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#11068 #29514501