Subgroups — C₂×C₆₁×#3035 #29563842

Order 15616.

2874 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3035	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#464	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#416	C₂	1	2	yes	maximal, complemented
13	C₂²×#41×C₆₁	C₂²	1	2	yes	—
14	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#135×C₆₁	—	2	16	no	—
16	C₂×#135×C₆₁	C₂²	1	16	yes	complemented
17	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
20	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
21	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#532	—	2	4	no	—
23	C₆₁×#532	C₂²	1	8	yes	complemented
24	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#124×C₆₁	C₂²	1	2	yes	—
27	C₂×#121×C₆₁	—	2	1	no	—
28	C₂×#121×C₆₁	—	2	1	no	—
29	C₄×#41×C₆₁	—	2	4	no	—
30	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
31	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₁	—	2	1	no	—
34	C₂×C₄×D₄×C₆₁	—	2	1	no	—
35	C₂×C₄×D₄×C₆₁	—	2	1	no	—
36	C₂×C₄×D₄×C₆₁	—	2	1	no	—
37	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₁	—	2	1	no	—
40	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₁	—	2	1	no	—
42	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#464	C₂²	1	16	yes	complemented
44	C₆₁×#463	C₂²	1	16	yes	complemented
45	C₆₁×#462	C₂²	1	8	yes	complemented
46	C₆₁×#461	C₂²	1	8	yes	complemented
47	C₆₁×#460	C₂²	1	8	yes	complemented
48	C₆₁×#459	C₂²	1	8	yes	complemented
49	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
50	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₆₁	C₂²	1	8	yes	complemented
53	C₆₁×#416	C₂²	1	16	yes	complemented
54	C₂×#103×C₆₁	C₂²	1	2	yes	—
55	C₂×#103×C₆₁	C₂²	1	2	yes	—
56	C₂×#102×C₆₁	C₂²	1	2	yes	—
57	C₂×#102×C₆₁	C₂²	1	2	yes	—
58	C₂×#41×C₆₁	—	2	2	no	—
59	C₂×#41×C₆₁	—	2	4	no	—
60	C₂×#41×C₆₁	—	2	4	no	—
61	C₂×#41×C₆₁	—	2	8	no	—
62	C₂×#41×C₆₁	—	2	8	no	—
63	C₂×#41×C₆₁	D₄	1	8	yes	complemented
64	C₂×#41×C₆₁	C₂³	1	8	yes	—
65	C₂×#41×C₆₁	C₂³	1	4	yes	—
66	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
67	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₆₁	—	2	1	no	—
69	C₂²×D₄×C₆₁	—	2	2	no	—
70	C₂²×D₄×C₆₁	—	2	1	no	—
71	C₂²×D₄×C₆₁	—	2	1	no	—
72	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₁	—	2	1	no	—
75	C₂³×C₄×C₆₁	—	2	1	no	—
76	C₂³×C₄×C₆₁	—	2	1	no	—
77	C₂³×C₄×C₆₁	—	2	2	no	—
78	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
79	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
80	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
81	#135×C₆₁	—	2	64	no	—
82	C₂×Q₁₆×C₆₁	—	2	8	no	—
83	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
84	C₂×SD₁₆×C₆₁	—	2	8	no	—
85	C₂×SD₁₆×C₆₁	—	2	8	no	—
86	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
87	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
88	C₂×D₈×C₆₁	—	2	8	no	—
89	C₂×D₈×C₆₁	C₂³	1	8	yes	—
90	C₂²×C₈×C₆₁	—	2	8	no	—
91	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
94	C₄⋊Q₈×C₆₁	—	2	2	no	—
95	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
96	#127×C₆₁	—	2	2	no	—
97	#127×C₆₁	C₂³	1	4	yes	—
98	#124×C₆₁	—	2	4	no	—
99	#124×C₆₁	C₂³	1	8	yes	—
100	#121×C₆₁	—	2	8	no	—
101	#121×C₆₁	—	2	8	no	—
102	C₄×Q₈×C₆₁	—	2	2	no	—
103	C₄×Q₈×C₆₁	—	2	2	no	—
104	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
105	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
106	C₄×D₄×C₆₁	—	2	8	no	—
107	C₄×D₄×C₆₁	—	2	8	no	—
108	C₄×D₄×C₆₁	—	2	8	no	—
109	C₄×D₄×C₆₁	—	2	8	no	—
110	C₄×D₄×C₆₁	—	2	2	no	—
111	C₄×D₄×C₆₁	—	2	2	no	—
112	C₄×D₄×C₆₁	C₂³	1	4	yes	—
113	C₄×D₄×C₆₁	C₂³	1	4	yes	—
114	#117×C₆₁	—	2	2	no	—
115	#117×C₆₁	—	2	8	no	—
116	#117×C₆₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
118	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
120	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
128	C₂×C₄²×C₆₁	—	2	1	no	—
129	C₂×C₄²×C₆₁	—	2	1	no	—
130	C₂×C₄²×C₆₁	—	2	1	no	—
131	C₂×C₄²×C₆₁	—	2	8	no	—
132	C₂×C₄²×C₆₁	D₄	1	4	yes	—
133	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
135	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
139	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
140	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
141	#103×C₆₁	C₂³	1	8	yes	—
142	#103×C₆₁	C₂³	1	8	yes	—
143	#102×C₆₁	C₂³	1	8	yes	—
144	#102×C₆₁	C₂³	1	8	yes	—
145	C₂⁴×C₆₁	—	2	1	no	—
146	C₂⁴×C₆₁	—	2	2	no	—
147	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
148	#41×C₆₁	—	2	16	no	—
149	#41×C₆₁	—	2	8	no	—
150	#41×C₆₁	—	2	16	no	—
151	#41×C₆₁	—	2	16	no	—
152	#41×C₆₁	—	4	16	no	—
153	#41×C₆₁	C₂×D₄	1	16	yes	complemented
154	C₂×Q₈×C₆₁	—	2	1	no	—
155	C₂×Q₈×C₆₁	—	2	2	no	—
156	C₂×Q₈×C₆₁	—	2	2	no	—
157	C₂×Q₈×C₆₁	—	2	4	no	—
158	C₂×Q₈×C₆₁	—	2	4	no	—
159	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
160	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
161	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
162	C₂×D₄×C₆₁	—	2	8	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	8	no	—
165	C₂×D₄×C₆₁	—	2	1	no	—
166	C₂×D₄×C₆₁	—	2	4	no	—
167	C₂×D₄×C₆₁	—	2	4	no	—
168	C₂×D₄×C₆₁	—	2	4	no	—
169	C₂×D₄×C₆₁	—	2	2	no	—
170	C₂×D₄×C₆₁	—	2	2	no	—
171	C₂×D₄×C₆₁	—	2	4	no	—
172	C₂×D₄×C₆₁	—	4	4	no	—
173	C₂×D₄×C₆₁	—	4	8	no	—
174	C₂×D₄×C₆₁	—	4	4	no	—
175	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
177	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₆₁	—	2	1	no	—
179	C₂²×C₄×C₆₁	—	2	8	no	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	2	4	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	1	no	—
184	C₂²×C₄×C₆₁	—	2	2	no	—
185	C₂²×C₄×C₆₁	—	2	4	no	—
186	C₂²×C₄×C₆₁	—	2	4	no	—
187	C₂²×C₄×C₆₁	—	2	8	no	—
188	C₂²×C₄×C₆₁	—	4	2	no	—
189	C₂²×C₄×C₆₁	—	4	4	no	—
190	C₂²×C₄×C₆₁	—	4	8	no	—
191	C₂²×C₄×C₆₁	—	4	4	no	—
192	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₁	#41	1	4	yes	—
202	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
204	Q₁₆×C₆₁	—	2	16	no	—
205	SD₁₆×C₆₁	—	2	16	no	—
206	SD₁₆×C₆₁	—	2	16	no	—
207	D₈×C₆₁	—	2	16	no	—
208	C₂×C₈×C₆₁	—	2	4	no	—
209	C₂×C₈×C₆₁	—	2	4	no	—
210	C₂×C₈×C₆₁	—	2	16	no	—
211	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
212	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
213	C₄⋊C₄×C₆₁	—	2	4	no	—
214	C₄⋊C₄×C₆₁	—	2	4	no	—
215	C₄⋊C₄×C₆₁	—	2	4	no	—
216	C₄⋊C₄×C₆₁	—	2	4	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	2	1	no	—
219	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
220	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂²⋊C₄×C₆₁	—	2	4	no	—
222	C₂²⋊C₄×C₆₁	—	2	4	no	—
223	C₂²⋊C₄×C₆₁	—	2	4	no	—
224	C₂²⋊C₄×C₆₁	—	2	8	no	—
225	C₂²⋊C₄×C₆₁	—	2	8	no	—
226	C₄²×C₆₁	—	2	4	no	—
227	C₄²×C₆₁	—	2	4	no	—
228	C₄²×C₆₁	—	2	4	no	—
229	C₄²×C₆₁	C₂×D₄	1	4	yes	—
230	C₄²×C₆₁	C₂×D₄	1	4	yes	—
231	C₄²×C₆₁	C₂×D₄	1	2	yes	—
232	C₄²×C₆₁	C₂×D₄	1	2	yes	—
233	C₄²×C₆₁	C₂⁴	1	2	yes	—
234	C₄²×C₆₁	C₂⁴	1	2	yes	—
235	C₂³×C₆₁	—	2	2	no	—
236	C₂³×C₆₁	—	2	2	no	—
237	C₂³×C₆₁	—	2	4	no	—
238	C₂³×C₆₁	—	2	2	no	—
239	C₂³×C₆₁	—	2	4	no	—
240	C₂³×C₆₁	—	4	2	no	—
241	C₂³×C₆₁	—	4	2	no	—
242	C₂³×C₆₁	—	4	4	no	—
243	C₂³×C₆₁	—	4	4	no	—
244	C₂³×C₆₁	—	4	4	no	—
245	C₂³×C₆₁	#121	1	4	yes	—
246	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
247	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₆₁	—	2	4	no	—
249	Q₈×C₆₁	—	2	2	no	—
250	Q₈×C₆₁	—	2	4	no	—
251	Q₈×C₆₁	—	2	4	no	—
252	Q₈×C₆₁	—	4	4	no	—
253	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
254	D₄×C₆₁	—	2	16	no	—
255	D₄×C₆₁	—	2	4	no	—
256	D₄×C₆₁	—	2	4	no	—
257	D₄×C₆₁	—	2	2	no	—
258	D₄×C₆₁	—	2	4	no	—
259	D₄×C₆₁	—	4	8	no	—
260	D₄×C₆₁	—	4	16	no	—
261	D₄×C₆₁	—	4	4	no	—
262	D₄×C₆₁	—	4	8	no	—
263	D₄×C₆₁	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₆₁	—	2	4	no	—
265	C₂×C₄×C₆₁	—	2	2	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	2	no	—
268	C₂×C₄×C₆₁	—	2	2	no	—
269	C₂×C₄×C₆₁	—	2	16	no	—
270	C₂×C₄×C₆₁	—	2	8	no	—
271	C₂×C₄×C₆₁	—	2	2	no	—
272	C₂×C₄×C₆₁	—	2	2	no	—
273	C₂×C₄×C₆₁	—	2	4	no	—
274	C₂×C₄×C₆₁	—	4	4	no	—
275	C₂×C₄×C₆₁	—	4	8	no	—
276	C₂×C₄×C₆₁	—	4	4	no	—
277	C₂×C₄×C₆₁	—	4	2	no	—
278	C₂×C₄×C₆₁	—	4	2	no	—
279	C₂×C₄×C₆₁	—	4	16	no	—
280	C₂×C₄×C₆₁	—	4	8	no	—
281	C₂×C₄×C₆₁	#121	1	4	yes	—
282	C₂×C₄×C₆₁	#121	1	8	yes	—
283	C₂×C₄×C₆₁	#135	1	4	yes	complemented
284	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
293	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
294	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
295	C₈×C₆₁	—	2	4	no	—
296	C₈×C₆₁	—	2	4	no	—
297	C₂×#3035	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂²×C₆₁	—	2	8	no	—
299	C₂²×C₆₁	—	2	2	no	—
300	C₂²×C₆₁	—	2	2	no	—
301	C₂²×C₆₁	—	2	4	no	—
302	C₂²×C₆₁	—	4	8	no	—
303	C₂²×C₆₁	—	4	2	no	—
304	C₂²×C₆₁	—	4	2	no	—
305	C₂²×C₆₁	—	4	4	no	—
306	C₂²×C₆₁	—	4	4	no	—
307	C₂²×C₆₁	—	4	4	no	—
308	C₂²×C₆₁	—	8	8	no	—
309	C₂²×C₆₁	C₂×#121	1	4	yes	—
310	C₂²×C₆₁	C₂×#121	1	2	yes	—
311	C₂²×C₆₁	C₂×#135	1	2	yes	—
312	C₂²×C₆₁	#575	1	2	yes	—
313	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
314	C₄×C₆₁	—	2	4	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	2	2	no	—
317	C₄×C₆₁	—	2	2	no	—
318	C₄×C₆₁	—	4	4	no	—
319	C₄×C₆₁	—	4	2	no	—
320	C₄×C₆₁	—	4	2	no	—
321	C₄×C₆₁	C₂×#121	1	4	yes	—
322	C₄×C₆₁	C₂×#121	1	2	yes	—
323	C₄×C₆₁	C₂×#135	1	4	yes	complemented
324	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
325	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
326	C₂²×#135	C₂×C₆₁	1	2	yes	complemented
327	C₂×#532	C₂×C₆₁	1	1	yes	characteristic, complemented
328	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
329	#3035	C₂×C₆₁	1	16	yes	direct product factor
330	C₂×#464	C₂×C₆₁	1	2	yes	complemented
331	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
332	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
333	C₂×#463	C₂×C₆₁	1	2	yes	complemented
334	C₂×#461	C₂×C₆₁	1	1	yes	characteristic, complemented
335	C₂×#459	C₂×C₆₁	1	1	yes	characteristic, complemented
336	C₂²×C₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
337	C₂×#416	C₂×C₆₁	1	2	yes	complemented
338	C₂×C₆₁	—	2	4	no	—
339	C₂×C₆₁	—	4	4	no	—
340	C₂×C₆₁	—	8	4	no	—
341	C₂×C₆₁	#3035	1	4	yes	direct product factor
342	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
343	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
344	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
345	C₂²×#41	C₂²×C₆₁	1	2	yes	—
346	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×#135	—	2	16	no	—
348	C₂×#135	C₂²×C₆₁	1	16	yes	complemented
349	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
350	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
351	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
352	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
353	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
354	#532	—	2	4	no	—
355	#532	C₂²×C₆₁	1	8	yes	complemented
356	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#124	C₂²×C₆₁	1	2	yes	—
359	C₂×#121	—	2	1	no	—
360	C₂×#121	—	2	1	no	—
361	C₄×#41	—	2	4	no	—
362	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
363	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×C₄×D₄	—	2	1	no	—
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	—	2	1	no	—
368	C₂×C₄×D₄	—	2	1	no	—
369	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×#117	—	2	1	no	—
372	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
373	C₂²×C₄²	—	2	1	no	—
374	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
375	#464	C₂²×C₆₁	1	16	yes	complemented
376	#463	C₂²×C₆₁	1	16	yes	complemented
377	#462	C₂²×C₆₁	1	8	yes	complemented
378	#461	C₂²×C₆₁	1	8	yes	complemented
379	#460	C₂²×C₆₁	1	8	yes	complemented
380	#459	C₂²×C₆₁	1	8	yes	complemented
381	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
382	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
383	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
384	C₂×C₄⋊C₈	C₂²×C₆₁	1	8	yes	complemented
385	#416	C₂²×C₆₁	1	16	yes	complemented
386	C₂×#103	C₂²×C₆₁	1	2	yes	—
387	C₂×#103	C₂²×C₆₁	1	2	yes	—
388	C₂×#102	C₂²×C₆₁	1	2	yes	—
389	C₂×#102	C₂²×C₆₁	1	2	yes	—
390	C₆₁	C₂×#3035	1	1	yes	characteristic, direct product factor, Sylow
391	C₂×#41	—	2	2	no	—
392	C₂×#41	—	2	4	no	—
393	C₂×#41	—	2	4	no	—
394	C₂×#41	—	2	8	no	—
395	C₂×#41	—	2	8	no	—
396	C₂×#41	D₄×C₆₁	1	8	yes	complemented
397	C₂×#41	C₂³×C₆₁	1	8	yes	—
398	C₂×#41	C₂³×C₆₁	1	4	yes	—
399	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
400	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	2	no	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
406	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	2	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
412	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
414	#135	—	2	64	no	—
415	C₂×Q₁₆	—	2	8	no	—
416	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
417	C₂×SD₁₆	—	2	8	no	—
418	C₂×SD₁₆	—	2	8	no	—
419	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
420	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
421	C₂×D₈	—	2	8	no	—
422	C₂×D₈	C₂³×C₆₁	1	8	yes	—
423	C₂²×C₈	—	2	8	no	—
424	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
425	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
426	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
427	C₄⋊Q₈	—	2	2	no	—
428	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
429	#127	—	2	2	no	—
430	#127	C₂³×C₆₁	1	4	yes	—
431	#124	—	2	4	no	—
432	#124	C₂³×C₆₁	1	8	yes	—
433	#121	—	2	8	no	—
434	#121	—	2	8	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
438	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
439	C₄×D₄	—	2	8	no	—
440	C₄×D₄	—	2	8	no	—
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	—	2	8	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	C₂³×C₆₁	1	4	yes	—
446	C₄×D₄	C₂³×C₆₁	1	4	yes	—
447	#117	—	2	2	no	—
448	#117	—	2	8	no	—
449	#117	C₂³×C₆₁	1	4	yes	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	2	no	—
460	C₂×C₂²⋊C₄	—	2	2	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	—	2	8	no	—
465	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
466	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄²	D₄×C₆₁	1	4	yes	—
468	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
471	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
472	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
473	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
474	#103	C₂³×C₆₁	1	8	yes	—
475	#103	C₂³×C₆₁	1	8	yes	—
476	#102	C₂³×C₆₁	1	8	yes	—
477	#102	C₂³×C₆₁	1	8	yes	—
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	2	no	—
480	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
481	#41	—	2	16	no	—
482	#41	—	2	8	no	—
483	#41	—	2	16	no	—
484	#41	—	2	16	no	—
485	#41	—	4	16	no	—
486	#41	C₂×D₄×C₆₁	1	16	yes	complemented
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
493	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
494	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
495	C₂×D₄	—	2	8	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	8	no	—
507	C₂×D₄	—	4	4	no	—
508	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
509	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
510	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	—	4	8	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
529	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
532	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
533	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
534	C₂²×C₄	#41×C₆₁	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
537	Q₁₆	—	2	16	no	—
538	SD₁₆	—	2	16	no	—
539	SD₁₆	—	2	16	no	—
540	D₈	—	2	16	no	—
541	C₂×C₈	—	2	4	no	—
542	C₂×C₈	—	2	4	no	—
543	C₂×C₈	—	2	16	no	—
544	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
545	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
553	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	4	no	—
562	C₄²	C₂×D₄×C₆₁	1	4	yes	—
563	C₄²	C₂×D₄×C₆₁	1	4	yes	—
564	C₄²	C₂×D₄×C₆₁	1	2	yes	—
565	C₄²	C₂×D₄×C₆₁	1	2	yes	—
566	C₄²	C₂⁴×C₆₁	1	2	yes	—
567	C₄²	C₂⁴×C₆₁	1	2	yes	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	4	no	—
576	C₂³	—	4	4	no	—
577	C₂³	—	4	4	no	—
578	C₂³	#121×C₆₁	1	4	yes	—
579	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
580	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
581	Q₈	—	2	2	no	—
582	Q₈	—	2	4	no	—
583	Q₈	—	2	4	no	—
584	Q₈	—	2	4	no	—
585	Q₈	—	4	4	no	—
586	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
587	D₄	—	2	16	no	—
588	D₄	—	2	4	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	4	no	—
592	D₄	—	4	8	no	—
593	D₄	—	4	16	no	—
594	D₄	—	4	8	no	—
595	D₄	—	4	4	no	—
596	D₄	C₂²×D₄×C₆₁	1	4	yes	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	8	no	—
603	C₂×C₄	—	2	16	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	8	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	16	no	—
614	C₂×C₄	#121×C₆₁	1	4	yes	—
615	C₂×C₄	#121×C₆₁	1	8	yes	—
616	C₂×C₄	#135×C₆₁	1	4	yes	complemented
617	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
618	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
620	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
621	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
623	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
626	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
627	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
628	C₈	—	2	4	no	—
629	C₈	—	2	4	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	8	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	8	8	no	—
641	C₂²	C₂×#121×C₆₁	1	4	yes	—
642	C₂²	C₂×#121×C₆₁	1	2	yes	—
643	C₂²	C₂×#135×C₆₁	1	2	yes	—
644	C₂²	C₆₁×#575	1	2	yes	—
645	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	4	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	4	no	—
653	C₄	C₂×#121×C₆₁	1	4	yes	—
654	C₄	C₂×#121×C₆₁	1	2	yes	—
655	C₄	C₂×#135×C₆₁	1	4	yes	complemented
656	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
657	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
658	C₂	—	2	4	no	—
659	C₂	—	4	4	no	—
660	C₂	—	8	4	no	—
661	C₂	C₆₁×#3035	1	4	yes	direct product factor
662	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
663	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
664	C₂	C₂×C₆₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₆₁	C₂	semidirect
2. C₂×C₆₁×#532	C₂	semidirect
3. C₂×C₄×#41×C₆₁	C₂	semidirect
4. C₆₁×#3035	C₂	direct (N × H)
5. C₂×C₆₁×#464	C₂	semidirect
6. C₂×C₆₁×#462	C₂	semidirect
7. C₂×C₆₁×#460	C₂	semidirect
8. C₂×C₆₁×#463	C₂	semidirect
9. C₂×C₆₁×#461	C₂	semidirect
10. C₂×C₆₁×#459	C₂	semidirect
11. C₂²×C₄⋊C₈×C₆₁	C₂	semidirect
12. C₂×C₆₁×#416	C₂	semidirect
16. C₂×#135×C₆₁	C₂²	semidirect
23. C₆₁×#532	C₂²	semidirect
30. C₄×#41×C₆₁	C₂²	semidirect
43. C₆₁×#464	C₂²	semidirect
44. C₆₁×#463	C₂²	semidirect
45. C₆₁×#462	C₂²	semidirect
46. C₆₁×#461	C₂²	semidirect
47. C₆₁×#460	C₂²	semidirect
48. C₆₁×#459	C₂²	semidirect
52. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
53. C₆₁×#416	C₂²	semidirect
63. C₂×#41×C₆₁	D₄	semidirect
153. #41×C₆₁	C₂×D₄	semidirect
283. C₂×C₄×C₆₁	#135	semidirect
297. C₂×#3035	C₆₁	direct (N × H)
323. C₄×C₆₁	C₂×#135	semidirect
326. C₂²×#135	C₂×C₆₁	semidirect
327. C₂×#532	C₂×C₆₁	semidirect
328. C₂×C₄×#41	C₂×C₆₁	semidirect
329. #3035	C₂×C₆₁	direct (N × H)
330. C₂×#464	C₂×C₆₁	semidirect
331. C₂×#462	C₂×C₆₁	semidirect
332. C₂×#460	C₂×C₆₁	semidirect
333. C₂×#463	C₂×C₆₁	semidirect
334. C₂×#461	C₂×C₆₁	semidirect
335. C₂×#459	C₂×C₆₁	semidirect
336. C₂²×C₄⋊C₈	C₂×C₆₁	semidirect
337. C₂×#416	C₂×C₆₁	semidirect
341. C₂×C₆₁	#3035	direct (N × H)
348. C₂×#135	C₂²×C₆₁	semidirect
355. #532	C₂²×C₆₁	semidirect
362. C₄×#41	C₂²×C₆₁	semidirect
375. #464	C₂²×C₆₁	semidirect
376. #463	C₂²×C₆₁	semidirect
377. #462	C₂²×C₆₁	semidirect
378. #461	C₂²×C₆₁	semidirect
379. #460	C₂²×C₆₁	semidirect
380. #459	C₂²×C₆₁	semidirect
384. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
385. #416	C₂²×C₆₁	semidirect
390. C₆₁	C₂×#3035	direct (N × H)
396. C₂×#41	D₄×C₆₁	semidirect
486. #41	C₂×D₄×C₆₁	semidirect
616. C₂×C₄	#135×C₆₁	semidirect
655. C₄	C₂×#135×C₆₁	semidirect
661. C₂	C₆₁×#3035	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×#135×C₆₁	2
C₂×C₆₁×#532	2
C₂×C₄×#41×C₆₁	2
C₆₁×#3035	2
C₂×C₆₁×#464	2
C₂×C₆₁×#462	2
C₂×C₆₁×#460	2
C₂×C₆₁×#463	2
C₂×C₆₁×#461	2
C₂×C₆₁×#459	2
C₂²×C₄⋊C₈×C₆₁	2
C₂×C₆₁×#416	2
C₂×#3035	61

Subgroups — C2×C61×#3035 #29563842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3035 #29563842