Subgroups — C₆₁×#60455 #29563888

Order 15616.

2678 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3449	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3063	C₂	1	8	yes	maximal, complemented
6	C₆₁×#3059	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3057	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3056	C₂	1	8	yes	maximal, complemented
9	C₆₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#137×C₆₁	—	2	8	no	—
16	C₂×#137×C₆₁	C₂²	1	4	yes	—
17	C₂×#137×C₆₁	C₂²	1	4	yes	complemented
18	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
19	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
20	C₆₁×#568	—	2	8	no	—
21	C₂×#131×C₆₁	C₂²	1	4	yes	—
22	C₂×#131×C₆₁	C₂²	1	4	yes	complemented
23	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₆₁	C₂²	1	4	yes	complemented
26	C₆₁×#537	C₂²	1	4	yes	—
27	C₆₁×#536	—	2	2	no	—
28	C₆₁×#536	—	2	2	no	—
29	C₆₁×#536	—	2	1	no	—
30	C₆₁×#536	C₂²	1	4	yes	—
31	C₆₁×#536	C₂²	1	2	yes	—
32	C₆₁×#536	C₂²	1	4	yes	complemented
33	C₆₁×#535	—	2	1	no	—
34	C₆₁×#535	C₂²	1	2	yes	—
35	C₆₁×#534	—	2	2	no	—
36	C₆₁×#532	—	2	2	no	—
37	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
38	C₂×#124×C₆₁	—	2	1	no	—
39	C₆₁×#525	—	2	2	no	—
40	C₆₁×#525	C₂²	1	4	yes	—
41	C₂×#123×C₆₁	—	2	2	no	—
42	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
43	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#470	C₂²	1	16	yes	complemented
46	C₆₁×#468	C₂²	1	16	yes	complemented
47	C₆₁×#467	C₂²	1	16	yes	complemented
48	C₆₁×#465	C₂²	1	16	yes	complemented
49	C₆₁×#428	C₂²	1	4	yes	complemented
50	C₆₁×#428	C₂²	1	4	yes	complemented
51	C₆₁×#427	C₂²	1	4	yes	complemented
52	C₆₁×#419	C₂²	1	4	yes	complemented
53	C₆₁×#419	C₂²	1	4	yes	complemented
54	C₆₁×#419	C₂²	1	2	yes	complemented
55	C₆₁×#418	C₂²	1	2	yes	complemented
56	C₆₁×#417	C₂²	1	4	yes	—
57	C₆₁×#416	C₂²	1	4	yes	complemented
58	C₂×#103×C₆₁	C₂²	1	4	yes	complemented
59	C₂×#41×C₆₁	—	2	4	no	—
60	C₂×#41×C₆₁	—	2	1	no	—
61	C₂×#41×C₆₁	—	2	1	no	—
62	C₂×#41×C₆₁	—	2	4	no	—
63	C₂×#41×C₆₁	—	2	4	no	—
64	C₂×#41×C₆₁	—	2	4	no	—
65	C₂×#41×C₆₁	D₄	1	2	yes	—
66	C₂×#41×C₆₁	D₄	1	2	yes	—
67	C₂×#41×C₆₁	C₂³	1	2	yes	—
68	C₂×#41×C₆₁	C₂³	1	2	yes	—
69	C₂×#41×C₆₁	C₂³	1	2	yes	—
70	C₂×#41×C₆₁	C₂³	1	2	yes	—
71	C₂²×Q₈×C₆₁	—	2	1	no	—
72	C₂²×Q₈×C₆₁	—	2	1	no	—
73	C₂²×Q₈×C₆₁	—	2	1	no	—
74	C₂²×Q₈×C₆₁	—	2	4	no	—
75	C₂²×Q₈×C₆₁	—	2	4	no	—
76	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
77	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
78	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
80	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₁	—	2	1	no	—
82	C₂²×D₄×C₆₁	D₄	1	2	yes	—
83	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₁	—	2	1	no	—
86	C₂³×C₄×C₆₁	—	2	1	no	—
87	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
89	#137×C₆₁	—	2	16	no	—
90	#137×C₆₁	—	2	16	no	—
91	C₂×Q₁₆×C₆₁	—	2	8	no	—
92	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
93	C₂×SD₁₆×C₆₁	—	2	8	no	—
94	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
95	#131×C₆₁	—	2	16	no	—
96	#131×C₆₁	—	2	16	no	—
97	C₂×M₁₆×C₆₁	—	2	4	no	—
98	C₂×M₁₆×C₆₁	—	2	16	no	—
99	C₂×M₁₆×C₆₁	D₄	1	8	yes	complemented
100	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
103	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
107	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
108	C₄⋊Q₈×C₆₁	—	2	4	no	—
109	C₄⋊Q₈×C₆₁	—	2	4	no	—
110	C₄⋊Q₈×C₆₁	—	2	2	no	—
111	#127×C₆₁	—	2	2	no	—
112	#124×C₆₁	—	2	2	no	—
113	#124×C₆₁	—	2	2	no	—
114	#124×C₆₁	—	2	4	no	—
115	#124×C₆₁	—	2	4	no	—
116	#123×C₆₁	—	2	4	no	—
117	#123×C₆₁	—	2	8	no	—
118	#123×C₆₁	—	2	8	no	—
119	#123×C₆₁	—	2	4	no	—
120	C₂²⋊Q₈×C₆₁	—	2	4	no	—
121	C₂²⋊Q₈×C₆₁	—	2	8	no	—
122	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
123	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
124	#121×C₆₁	—	2	8	no	—
125	#121×C₆₁	—	2	4	no	—
126	#121×C₆₁	C₂³	1	8	yes	—
127	#120×C₆₁	—	2	4	no	—
128	#120×C₆₁	—	2	4	no	—
129	C₄×D₄×C₆₁	—	2	8	no	—
130	#117×C₆₁	—	2	1	no	—
131	#117×C₆₁	—	2	1	no	—
132	#117×C₆₁	—	2	1	no	—
133	#117×C₆₁	—	2	1	no	—
134	#117×C₆₁	C₂³	1	2	yes	—
135	#117×C₆₁	C₂³	1	2	yes	—
136	#117×C₆₁	C₂³	1	2	yes	—
137	#117×C₆₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
144	C₂×C₄²×C₆₁	—	2	1	no	—
145	C₂×C₄²×C₆₁	—	2	1	no	—
146	#107×C₆₁	C₂³	1	8	yes	—
147	#106×C₆₁	C₂³	1	8	yes	—
148	#103×C₆₁	C₂³	1	16	yes	—
149	#103×C₆₁	C₂³	1	8	yes	—
150	#102×C₆₁	C₂³	1	8	yes	—
151	C₂⁴×C₆₁	—	2	1	no	—
152	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
153	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
154	#41×C₆₁	—	2	8	no	—
155	#41×C₆₁	—	2	8	no	—
156	#41×C₆₁	—	2	4	no	—
157	#41×C₆₁	—	2	4	no	—
158	#41×C₆₁	—	2	4	no	—
159	#41×C₆₁	—	2	4	no	—
160	#41×C₆₁	—	2	4	no	—
161	#41×C₆₁	—	2	4	no	—
162	#41×C₆₁	—	2	4	no	—
163	#41×C₆₁	—	2	4	no	—
164	#41×C₆₁	—	4	4	no	—
165	#41×C₆₁	—	4	4	no	—
166	C₂×Q₈×C₆₁	—	2	4	no	—
167	C₂×Q₈×C₆₁	—	2	2	no	—
168	C₂×Q₈×C₆₁	—	2	2	no	—
169	C₂×Q₈×C₆₁	—	2	2	no	—
170	C₂×Q₈×C₆₁	—	2	1	no	—
171	C₂×Q₈×C₆₁	—	2	4	no	—
172	C₂×Q₈×C₆₁	—	2	2	no	—
173	C₂×Q₈×C₆₁	—	2	4	no	—
174	C₂×Q₈×C₆₁	—	2	4	no	—
175	C₂×Q₈×C₆₁	—	2	4	no	—
176	C₂×Q₈×C₆₁	—	2	4	no	—
177	C₂×Q₈×C₆₁	—	2	4	no	—
178	C₂×Q₈×C₆₁	—	2	2	no	—
179	C₂×Q₈×C₆₁	—	4	4	no	—
180	C₂×Q₈×C₆₁	—	4	4	no	—
181	C₂×Q₈×C₆₁	—	4	4	no	—
182	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
183	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
185	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
186	C₂×D₄×C₆₁	—	2	8	no	—
187	C₂×D₄×C₆₁	—	2	2	no	—
188	C₂×D₄×C₆₁	—	2	2	no	—
189	C₂×D₄×C₆₁	—	2	8	no	—
190	C₂×D₄×C₆₁	—	2	4	no	—
191	C₂×D₄×C₆₁	—	2	2	no	—
192	C₂×D₄×C₆₁	—	2	1	no	—
193	C₂×D₄×C₆₁	—	2	2	no	—
194	C₂×D₄×C₆₁	—	4	4	no	—
195	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
196	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
197	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₁	—	2	4	no	—
201	C₂²×C₄×C₆₁	—	2	4	no	—
202	C₂²×C₄×C₆₁	—	2	2	no	—
203	C₂²×C₄×C₆₁	—	2	2	no	—
204	C₂²×C₄×C₆₁	—	2	1	no	—
205	C₂²×C₄×C₆₁	—	2	2	no	—
206	C₂²×C₄×C₆₁	—	2	2	no	—
207	C₂²×C₄×C₆₁	—	2	2	no	—
208	C₂²×C₄×C₆₁	—	2	2	no	—
209	C₂²×C₄×C₆₁	—	2	2	no	—
210	C₂²×C₄×C₆₁	—	4	4	no	—
211	C₂²×C₄×C₆₁	—	4	4	no	—
212	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₆₁	#41	1	4	yes	—
219	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
223	Q₁₆×C₆₁	—	2	16	no	—
224	SD₁₆×C₆₁	—	2	16	no	—
225	M₁₆×C₆₁	—	2	4	no	—
226	M₁₆×C₆₁	—	2	4	no	—
227	M₁₆×C₆₁	—	2	16	no	—
228	M₁₆×C₆₁	C₂×D₄	1	8	yes	—
229	M₁₆×C₆₁	C₂×D₄	1	8	yes	—
230	C₂×C₈×C₆₁	—	2	4	no	—
231	C₂×C₈×C₆₁	—	2	16	no	—
232	C₂×C₈×C₆₁	C₂×D₄	1	8	yes	—
233	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
234	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
235	C₄⋊C₄×C₆₁	—	2	16	no	—
236	C₄⋊C₄×C₆₁	—	2	2	no	—
237	C₄⋊C₄×C₆₁	—	2	2	no	—
238	C₄⋊C₄×C₆₁	—	2	8	no	—
239	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
240	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
241	C₂²⋊C₄×C₆₁	—	2	2	no	—
242	C₂²⋊C₄×C₆₁	—	2	2	no	—
243	C₂²⋊C₄×C₆₁	—	2	2	no	—
244	C₂²⋊C₄×C₆₁	—	2	2	no	—
245	C₂²⋊C₄×C₆₁	—	2	16	no	—
246	C₂²⋊C₄×C₆₁	—	2	8	no	—
247	C₂²⋊C₄×C₆₁	—	2	8	no	—
248	C₄²×C₆₁	—	2	2	no	—
249	C₄²×C₆₁	—	2	2	no	—
250	C₄²×C₆₁	—	2	2	no	—
251	C₄²×C₆₁	—	2	2	no	—
252	C₂³×C₆₁	—	2	4	no	—
253	C₂³×C₆₁	—	2	2	no	—
254	C₂³×C₆₁	—	4	2	no	—
255	C₂³×C₆₁	—	4	4	no	—
256	C₂³×C₆₁	—	4	2	no	—
257	C₂³×C₆₁	—	8	2	no	—
258	C₂³×C₆₁	#121	1	4	yes	—
259	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
260	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
261	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
262	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
263	Q₈×C₆₁	—	2	4	no	—
264	Q₈×C₆₁	—	2	4	no	—
265	Q₈×C₆₁	—	2	4	no	—
266	Q₈×C₆₁	—	2	2	no	—
267	Q₈×C₆₁	—	2	4	no	—
268	Q₈×C₆₁	—	2	2	no	—
269	Q₈×C₆₁	—	4	4	no	—
270	Q₈×C₆₁	—	4	4	no	—
271	Q₈×C₆₁	—	4	4	no	—
272	Q₈×C₆₁	—	4	2	no	—
273	D₄×C₆₁	—	2	8	no	—
274	D₄×C₆₁	—	2	8	no	—
275	D₄×C₆₁	—	2	4	no	—
276	D₄×C₆₁	—	2	4	no	—
277	D₄×C₆₁	—	2	2	no	—
278	D₄×C₆₁	—	2	2	no	—
279	D₄×C₆₁	—	4	4	no	—
280	D₄×C₆₁	—	4	4	no	—
281	D₄×C₆₁	—	4	2	no	—
282	D₄×C₆₁	—	8	8	no	—
283	C₂×C₄×C₆₁	—	2	4	no	—
284	C₂×C₄×C₆₁	—	2	8	no	—
285	C₂×C₄×C₆₁	—	2	4	no	—
286	C₂×C₄×C₆₁	—	2	4	no	—
287	C₂×C₄×C₆₁	—	2	4	no	—
288	C₂×C₄×C₆₁	—	2	4	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	4	no	—
291	C₂×C₄×C₆₁	—	4	4	no	—
292	C₂×C₄×C₆₁	—	4	2	no	—
293	C₂×C₄×C₆₁	—	4	4	no	—
294	C₂×C₄×C₆₁	—	4	4	no	—
295	C₂×C₄×C₆₁	—	4	4	no	—
296	C₂×C₄×C₆₁	—	4	4	no	—
297	C₂×C₄×C₆₁	—	4	4	no	—
298	C₂×C₄×C₆₁	—	8	2	no	—
299	C₂×C₄×C₆₁	#121	1	4	yes	—
300	C₂×C₄×C₆₁	#121	1	4	yes	—
301	C₂×C₄×C₆₁	#121	1	4	yes	—
302	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
310	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
312	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
313	C₈×C₆₁	—	2	4	no	—
314	C₈×C₆₁	C₂²×D₄	1	8	yes	—
315	#60455	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂²×C₆₁	—	2	2	no	—
317	C₂²×C₆₁	—	2	2	no	—
318	C₂²×C₆₁	—	2	2	no	—
319	C₂²×C₆₁	—	2	8	no	—
320	C₂²×C₆₁	—	2	4	no	—
321	C₂²×C₆₁	—	4	4	no	—
322	C₂²×C₆₁	—	4	4	no	—
323	C₂²×C₆₁	—	4	2	no	—
324	C₂²×C₆₁	—	8	4	no	—
325	C₂²×C₆₁	—	8	4	no	—
326	C₂²×C₆₁	C₂×#121	1	2	yes	—
327	C₂²×C₆₁	C₂×#121	1	2	yes	—
328	C₂²×C₆₁	C₂×#121	1	2	yes	—
329	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₆₁	—	2	4	no	—
331	C₄×C₆₁	—	4	4	no	—
332	C₄×C₆₁	—	4	4	no	—
333	C₄×C₆₁	—	4	2	no	—
334	C₄×C₆₁	—	4	4	no	—
335	C₄×C₆₁	C₂×#121	1	2	yes	—
336	C₄×C₆₁	C₂×#121	1	2	yes	—
337	C₄×C₆₁	C₂×#121	1	2	yes	—
338	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
339	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
340	C₂²×#137	C₂×C₆₁	1	1	yes	characteristic, complemented
341	C₂×#568	C₂×C₆₁	1	1	yes	characteristic, complemented
342	#3449	C₂×C₆₁	1	1	yes	characteristic
343	C₂×#536	C₂×C₆₁	1	1	yes	characteristic, complemented
344	#3063	C₂×C₆₁	1	8	yes	complemented
345	#3059	C₂×C₆₁	1	4	yes	complemented
346	#3057	C₂×C₆₁	1	4	yes	complemented
347	#3056	C₂×C₆₁	1	8	yes	complemented
348	#2911	C₂×C₆₁	1	1	yes	characteristic, complemented
349	#2896	C₂×C₆₁	1	1	yes	characteristic, complemented
350	C₂×#419	C₂×C₆₁	1	1	yes	characteristic, complemented
351	C₂×C₆₁	—	2	2	no	—
352	C₂×C₆₁	—	2	2	no	—
353	C₂×C₆₁	—	2	2	no	—
354	C₂×C₆₁	—	4	4	no	—
355	C₂×C₆₁	—	8	2	no	—
356	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
357	C₂×C₆₁	#3586	1	2	yes	—
358	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
359	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
360	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×#137	—	2	8	no	—
362	C₂×#137	C₂²×C₆₁	1	4	yes	—
363	C₂×#137	C₂²×C₆₁	1	4	yes	complemented
364	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
365	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
366	#568	—	2	8	no	—
367	C₂×#131	C₂²×C₆₁	1	4	yes	—
368	C₂×#131	C₂²×C₆₁	1	4	yes	complemented
369	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
370	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
371	C₂²×M₁₆	C₂²×C₆₁	1	4	yes	complemented
372	#537	C₂²×C₆₁	1	4	yes	—
373	#536	—	2	2	no	—
374	#536	—	2	2	no	—
375	#536	—	2	1	no	—
376	#536	C₂²×C₆₁	1	4	yes	—
377	#536	C₂²×C₆₁	1	2	yes	—
378	#536	C₂²×C₆₁	1	4	yes	complemented
379	#535	—	2	1	no	—
380	#535	C₂²×C₆₁	1	2	yes	—
381	#534	—	2	2	no	—
382	#532	—	2	2	no	—
383	C₂×C₄⋊Q₈	—	2	1	no	—
384	C₂×#124	—	2	1	no	—
385	#525	—	2	2	no	—
386	#525	C₂²×C₆₁	1	4	yes	—
387	C₂×#123	—	2	2	no	—
388	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
389	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
390	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
391	#470	C₂²×C₆₁	1	16	yes	complemented
392	#468	C₂²×C₆₁	1	16	yes	complemented
393	#467	C₂²×C₆₁	1	16	yes	complemented
394	#465	C₂²×C₆₁	1	16	yes	complemented
395	#428	C₂²×C₆₁	1	4	yes	complemented
396	#428	C₂²×C₆₁	1	4	yes	complemented
397	#427	C₂²×C₆₁	1	4	yes	complemented
398	#419	C₂²×C₆₁	1	4	yes	complemented
399	#419	C₂²×C₆₁	1	4	yes	complemented
400	#419	C₂²×C₆₁	1	2	yes	complemented
401	#418	C₂²×C₆₁	1	2	yes	complemented
402	#417	C₂²×C₆₁	1	4	yes	—
403	#416	C₂²×C₆₁	1	4	yes	complemented
404	C₂×#103	C₂²×C₆₁	1	4	yes	complemented
405	C₆₁	#60455	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×#41	—	2	4	no	—
407	C₂×#41	—	2	1	no	—
408	C₂×#41	—	2	1	no	—
409	C₂×#41	—	2	4	no	—
410	C₂×#41	—	2	4	no	—
411	C₂×#41	—	2	4	no	—
412	C₂×#41	D₄×C₆₁	1	2	yes	—
413	C₂×#41	D₄×C₆₁	1	2	yes	—
414	C₂×#41	C₂³×C₆₁	1	2	yes	—
415	C₂×#41	C₂³×C₆₁	1	2	yes	—
416	C₂×#41	C₂³×C₆₁	1	2	yes	—
417	C₂×#41	C₂³×C₆₁	1	2	yes	—
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	—	2	1	no	—
420	C₂²×Q₈	—	2	1	no	—
421	C₂²×Q₈	—	2	4	no	—
422	C₂²×Q₈	—	2	4	no	—
423	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
425	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
426	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	D₄×C₆₁	1	2	yes	—
430	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
435	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
436	#137	—	2	16	no	—
437	#137	—	2	16	no	—
438	C₂×Q₁₆	—	2	8	no	—
439	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
440	C₂×SD₁₆	—	2	8	no	—
441	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
442	#131	—	2	16	no	—
443	#131	—	2	16	no	—
444	C₂×M₁₆	—	2	4	no	—
445	C₂×M₁₆	—	2	16	no	—
446	C₂×M₁₆	D₄×C₆₁	1	8	yes	complemented
447	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
448	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
449	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
450	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
451	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
452	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
453	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
454	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	4	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	#127	—	2	2	no	—
459	#124	—	2	2	no	—
460	#124	—	2	4	no	—
461	#124	—	2	4	no	—
462	#124	—	2	2	no	—
463	#123	—	2	8	no	—
464	#123	—	2	8	no	—
465	#123	—	2	4	no	—
466	#123	—	2	4	no	—
467	C₂²⋊Q₈	—	2	4	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
470	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
471	#121	—	2	4	no	—
472	#121	—	2	8	no	—
473	#121	C₂³×C₆₁	1	8	yes	—
474	#120	—	2	4	no	—
475	#120	—	2	4	no	—
476	C₄×D₄	—	2	8	no	—
477	#117	—	2	1	no	—
478	#117	—	2	1	no	—
479	#117	—	2	1	no	—
480	#117	—	2	1	no	—
481	#117	C₂³×C₆₁	1	2	yes	—
482	#117	C₂³×C₆₁	1	2	yes	—
483	#117	C₂³×C₆₁	1	2	yes	—
484	#117	C₂³×C₆₁	1	2	yes	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	#107	C₂³×C₆₁	1	8	yes	—
494	#106	C₂³×C₆₁	1	8	yes	—
495	#103	C₂³×C₆₁	1	16	yes	—
496	#103	C₂³×C₆₁	1	8	yes	—
497	#102	C₂³×C₆₁	1	8	yes	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
500	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
501	#41	—	2	8	no	—
502	#41	—	2	8	no	—
503	#41	—	2	4	no	—
504	#41	—	2	4	no	—
505	#41	—	2	4	no	—
506	#41	—	2	4	no	—
507	#41	—	2	4	no	—
508	#41	—	2	4	no	—
509	#41	—	2	4	no	—
510	#41	—	2	4	no	—
511	#41	—	4	4	no	—
512	#41	—	4	4	no	—
513	C₂×Q₈	—	2	4	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	4	4	no	—
527	C₂×Q₈	—	4	4	no	—
528	C₂×Q₈	—	4	4	no	—
529	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
530	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
531	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
532	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
543	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
544	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
545	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
546	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
560	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
561	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
565	C₂²×C₄	#41×C₆₁	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
570	Q₁₆	—	2	16	no	—
571	SD₁₆	—	2	16	no	—
572	M₁₆	—	2	4	no	—
573	M₁₆	—	2	4	no	—
574	M₁₆	—	2	16	no	—
575	M₁₆	C₂×D₄×C₆₁	1	8	yes	—
576	M₁₆	C₂×D₄×C₆₁	1	8	yes	—
577	C₂×C₈	—	2	4	no	—
578	C₂×C₈	—	2	16	no	—
579	C₂×C₈	C₂×D₄×C₆₁	1	8	yes	—
580	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
581	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
582	C₄⋊C₄	—	2	16	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
587	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	16	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	2	no	—
604	C₂³	—	8	2	no	—
605	C₂³	#121×C₆₁	1	4	yes	—
606	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
607	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
608	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
609	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
610	Q₈	—	2	4	no	—
611	Q₈	—	2	4	no	—
612	Q₈	—	2	4	no	—
613	Q₈	—	2	2	no	—
614	Q₈	—	2	4	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	4	4	no	—
617	Q₈	—	4	4	no	—
618	Q₈	—	4	4	no	—
619	Q₈	—	4	2	no	—
620	D₄	—	2	8	no	—
621	D₄	—	2	8	no	—
622	D₄	—	2	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	2	4	no	—
625	D₄	—	2	4	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	D₄	—	4	2	no	—
629	D₄	—	8	8	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	8	2	no	—
646	C₂×C₄	#121×C₆₁	1	4	yes	—
647	C₂×C₄	#121×C₆₁	1	4	yes	—
648	C₂×C₄	#121×C₆₁	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
655	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
656	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
657	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
658	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
659	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
660	C₈	—	2	4	no	—
661	C₈	C₂²×D₄×C₆₁	1	8	yes	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	4	no	—
672	C₂²	C₂×#121×C₆₁	1	2	yes	—
673	C₂²	C₂×#121×C₆₁	1	2	yes	—
674	C₂²	C₂×#121×C₆₁	1	2	yes	—
675	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
676	C₄	—	2	4	no	—
677	C₄	—	4	4	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	4	no	—
681	C₄	C₂×#121×C₆₁	1	2	yes	—
682	C₄	C₂×#121×C₆₁	1	2	yes	—
683	C₄	C₂×#121×C₆₁	1	2	yes	—
684	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
685	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
686	C₂	—	2	2	no	—
687	C₂	—	2	2	no	—
688	C₂	—	2	2	no	—
689	C₂	—	4	4	no	—
690	C₂	—	8	2	no	—
691	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
692	C₂	C₆₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₆₁	C₂	semidirect
2. C₂×C₆₁×#568	C₂	semidirect
4. C₂×C₆₁×#536	C₂	semidirect
5. C₆₁×#3063	C₂	semidirect
6. C₆₁×#3059	C₂	semidirect
7. C₆₁×#3057	C₂	semidirect
8. C₆₁×#3056	C₂	semidirect
9. C₆₁×#2911	C₂	semidirect
10. C₆₁×#2896	C₂	semidirect
11. C₂×C₆₁×#419	C₂	semidirect
17. C₂×#137×C₆₁	C₂²	semidirect
18. C₂²×Q₁₆×C₆₁	C₂²	semidirect
19. C₂²×SD₁₆×C₆₁	C₂²	semidirect
22. C₂×#131×C₆₁	C₂²	semidirect
25. C₂²×M₁₆×C₆₁	C₂²	semidirect
32. C₆₁×#536	C₂²	semidirect
42. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
45. C₆₁×#470	C₂²	semidirect
46. C₆₁×#468	C₂²	semidirect
47. C₆₁×#467	C₂²	semidirect
48. C₆₁×#465	C₂²	semidirect
49. C₆₁×#428	C₂²	semidirect
50. C₆₁×#428	C₂²	semidirect
51. C₆₁×#427	C₂²	semidirect
52. C₆₁×#419	C₂²	semidirect
53. C₆₁×#419	C₂²	semidirect
54. C₆₁×#419	C₂²	semidirect
55. C₆₁×#418	C₂²	semidirect
57. C₆₁×#416	C₂²	semidirect
58. C₂×#103×C₆₁	C₂²	semidirect
99. C₂×M₁₆×C₆₁	D₄	semidirect
315. #60455	C₆₁	direct (N × H)
340. C₂²×#137	C₂×C₆₁	semidirect
341. C₂×#568	C₂×C₆₁	semidirect
343. C₂×#536	C₂×C₆₁	semidirect
344. #3063	C₂×C₆₁	semidirect
345. #3059	C₂×C₆₁	semidirect
346. #3057	C₂×C₆₁	semidirect
347. #3056	C₂×C₆₁	semidirect
348. #2911	C₂×C₆₁	semidirect
349. #2896	C₂×C₆₁	semidirect
350. C₂×#419	C₂×C₆₁	semidirect
363. C₂×#137	C₂²×C₆₁	semidirect
364. C₂²×Q₁₆	C₂²×C₆₁	semidirect
365. C₂²×SD₁₆	C₂²×C₆₁	semidirect
368. C₂×#131	C₂²×C₆₁	semidirect
371. C₂²×M₁₆	C₂²×C₆₁	semidirect
378. #536	C₂²×C₆₁	semidirect
388. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
391. #470	C₂²×C₆₁	semidirect
392. #468	C₂²×C₆₁	semidirect
393. #467	C₂²×C₆₁	semidirect
394. #465	C₂²×C₆₁	semidirect
395. #428	C₂²×C₆₁	semidirect
396. #428	C₂²×C₆₁	semidirect
397. #427	C₂²×C₆₁	semidirect
398. #419	C₂²×C₆₁	semidirect
399. #419	C₂²×C₆₁	semidirect
400. #419	C₂²×C₆₁	semidirect
401. #418	C₂²×C₆₁	semidirect
403. #416	C₂²×C₆₁	semidirect
404. C₂×#103	C₂²×C₆₁	semidirect
405. C₆₁	#60455	direct (N × H)
446. C₂×M₁₆	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₆₁	2
C₂×C₆₁×#568	2
C₆₁×#3449	2
C₂×C₆₁×#536	2
C₆₁×#3063	2
C₆₁×#3059	2
C₆₁×#3057	2
C₆₁×#3056	2
C₆₁×#2911	2
C₆₁×#2896	2
C₂×C₆₁×#419	2
#60455	61

Subgroups — C61×#60455 #29563888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60455 #29563888