Subgroups — C₂×C₆₁×#3175 #29564112

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 512 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×#3175	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#500	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×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic
9	C₂×C₆₁×#440	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, 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×#500	C₂²	1	8	yes	complemented
32	C₆₁×#495	C₂²	1	8	yes	complemented
33	C₆₁×#489	C₂²	1	16	yes	complemented
34	C₆₁×#468	C₂²	1	16	yes	complemented
35	C₆₁×#467	C₂²	1	8	yes	complemented
36	C₆₁×#466	C₂²	1	8	yes	—
37	C₆₁×#440	C₂²	1	16	yes	complemented
38	C₄×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
39	C₄×D₈×C₆₁	C₂²	1	8	yes	complemented
40	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#107×C₆₁	C₂²	1	2	yes	—
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	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	—	2	2	no	—
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	#107×C₆₁	C₂³	1	4	yes	—
108	#107×C₆₁	C₂³	1	4	yes	—
109	#107×C₆₁	C₂³	1	8	yes	—
110	#103×C₆₁	C₂³	1	8	yes	—
111	#103×C₆₁	C₂³	1	8	yes	—
112	#102×C₆₁	C₂³	1	8	yes	—
113	#102×C₆₁	C₂³	1	8	yes	—
114	#97×C₆₁	C₂³	1	4	yes	—
115	#97×C₆₁	C₂³	1	4	yes	—
116	C₄×C₈×C₆₁	C₂³	1	4	yes	—
117	C₄×C₈×C₆₁	C₂³	1	4	yes	—
118	C₂⁴×C₆₁	—	2	2	no	—
119	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₆₁	—	2	2	no	—
121	C₂×Q₈×C₆₁	—	2	8	no	—
122	C₂×Q₈×C₆₁	—	2	4	no	—
123	C₂×Q₈×C₆₁	—	2	4	no	—
124	C₂×Q₈×C₆₁	—	8	4	no	—
125	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
126	C₂×D₄×C₆₁	—	2	8	no	—
127	C₂×D₄×C₆₁	—	2	2	no	—
128	C₂×D₄×C₆₁	—	2	4	no	—
129	C₂×D₄×C₆₁	—	2	4	no	—
130	C₂×D₄×C₆₁	—	8	4	no	—
131	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
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	2	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	—	8	4	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₆₁	—	2	8	no	—
148	SD₁₆×C₆₁	—	2	16	no	—
149	D₈×C₆₁	—	2	8	no	—
150	M₁₆×C₆₁	—	2	8	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	8	no	—
154	C₂×C₈×C₆₁	#41	1	4	yes	—
155	C₂×C₈×C₆₁	#41	1	4	yes	—
156	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
157	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
158	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
159	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
160	C₄⋊C₄×C₆₁	—	2	8	no	—
161	C₄⋊C₄×C₆₁	—	2	8	no	—
162	C₄⋊C₄×C₆₁	—	2	8	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₆₁	—	2	8	no	—
170	C₂²⋊C₄×C₆₁	—	2	8	no	—
171	C₂²⋊C₄×C₆₁	—	2	8	no	—
172	C₂²⋊C₄×C₆₁	—	2	8	no	—
173	C₂²⋊C₄×C₆₁	—	2	8	no	—
174	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
175	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
176	C₄²×C₆₁	—	2	8	no	—
177	C₄²×C₆₁	C₂×D₄	1	2	yes	—
178	C₄²×C₆₁	C₂×D₄	1	2	yes	—
179	C₄²×C₆₁	C₂⁴	1	2	yes	—
180	C₄²×C₆₁	C₂⁴	1	2	yes	—
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	2	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	4	no	—
187	C₂³×C₆₁	—	4	4	no	—
188	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
189	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₆₁	—	2	4	no	—
191	Q₈×C₆₁	—	2	4	no	—
192	Q₈×C₆₁	—	4	4	no	—
193	Q₈×C₆₁	—	8	8	no	—
194	D₄×C₆₁	—	2	4	no	—
195	D₄×C₆₁	—	2	4	no	—
196	D₄×C₆₁	—	4	4	no	—
197	D₄×C₆₁	—	8	8	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	4	no	—
207	C₂×C₄×C₆₁	—	2	4	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	4	4	no	—
210	C₂×C₄×C₆₁	—	4	4	no	—
211	C₂×C₄×C₆₁	—	4	4	no	—
212	C₂×C₄×C₆₁	—	8	8	no	—
213	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
220	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
221	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
222	C₈×C₆₁	—	2	2	no	—
223	C₈×C₆₁	—	2	2	no	—
224	C₈×C₆₁	C₂×#41	1	4	yes	—
225	C₈×C₆₁	C₂×#41	1	4	yes	—
226	C₂×#3175	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₆₁	—	2	2	no	—
228	C₂²×C₆₁	—	2	2	no	—
229	C₂²×C₆₁	—	2	2	no	—
230	C₂²×C₆₁	—	4	4	no	—
231	C₂²×C₆₁	—	4	4	no	—
232	C₂²×C₆₁	—	4	4	no	—
233	C₂²×C₆₁	—	4	4	no	—
234	C₂²×C₆₁	—	8	8	no	—
235	C₂²×C₆₁	#532	1	2	yes	—
236	C₂²×C₆₁	#576	1	2	yes	—
237	C₂²×C₆₁	#578	1	2	yes	—
238	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₆₁	—	2	2	no	—
240	C₄×C₆₁	—	2	2	no	—
241	C₄×C₆₁	—	2	2	no	—
242	C₄×C₆₁	—	2	2	no	—
243	C₄×C₆₁	—	2	2	no	—
244	C₄×C₆₁	—	4	4	no	—
245	C₄×C₆₁	—	4	4	no	—
246	C₄×C₆₁	—	4	4	no	—
247	C₄×C₆₁	#532	1	2	yes	—
248	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
249	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
250	C₂×#542	C₂×C₆₁	1	2	yes	complemented
251	#3175	C₂×C₆₁	1	16	yes	direct product factor
252	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
253	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
254	C₂×#489	C₂×C₆₁	1	2	yes	complemented
255	C₂×#468	C₂×C₆₁	1	2	yes	complemented
256	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
257	C₂×#466	C₂×C₆₁	1	1	yes	characteristic
258	C₂×#440	C₂×C₆₁	1	2	yes	complemented
259	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
260	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
262	C₂×C₆₁	—	4	2	no	—
263	C₂×C₆₁	—	8	4	no	—
264	C₂×C₆₁	#3175	1	4	yes	direct product factor
265	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
266	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
267	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
268	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
269	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
270	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
271	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
273	#542	—	2	8	no	—
274	#542	C₂²×C₆₁	1	16	yes	complemented
275	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
276	C₂×#126	—	2	2	no	—
277	C₂×#124	—	2	2	no	—
278	C₂×#124	C₂²×C₆₁	1	2	yes	—
279	C₂×#123	—	2	2	no	—
280	C₂×C₂²⋊Q₈	—	2	2	no	—
281	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
282	C₂×#121	C₂²×C₆₁	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
284	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
285	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
286	#500	C₂²×C₆₁	1	8	yes	complemented
287	#495	C₂²×C₆₁	1	8	yes	complemented
288	#489	C₂²×C₆₁	1	16	yes	complemented
289	#468	C₂²×C₆₁	1	16	yes	complemented
290	#467	C₂²×C₆₁	1	8	yes	complemented
291	#466	C₂²×C₆₁	1	8	yes	—
292	#440	C₂²×C₆₁	1	16	yes	complemented
293	C₄×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
294	C₄×D₈	C₂²×C₆₁	1	8	yes	complemented
295	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
296	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
297	C₂×#107	C₂²×C₆₁	1	2	yes	—
298	C₂×#103	C₂²×C₆₁	1	2	yes	—
299	C₂×#103	C₂²×C₆₁	1	2	yes	—
300	C₂×#102	C₂²×C₆₁	1	2	yes	—
301	C₂×#102	C₂²×C₆₁	1	2	yes	—
302	#405	C₂²×C₆₁	1	8	yes	complemented
303	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
304	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
306	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
307	C₆₁	C₂×#3175	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
314	C₂×Q₁₆	—	2	4	no	—
315	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
316	C₂×SD₁₆	—	2	8	no	—
317	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	C₂³×C₆₁	1	4	yes	—
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
322	C₂²×C₈	—	2	4	no	—
323	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
325	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
328	C₄⋊Q₈	—	2	4	no	—
329	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
330	#126	—	2	16	no	—
331	#124	—	2	16	no	—
332	#124	—	2	4	no	—
333	#124	C₂³×C₆₁	1	8	yes	—
334	#123	—	2	16	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	16	no	—
337	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
338	#121	—	2	4	no	—
339	#121	C₂³×C₆₁	1	8	yes	—
340	C₄×Q₈	—	2	4	no	—
341	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	C₂³×C₆₁	1	8	yes	—
344	#117	D₄×C₆₁	1	4	yes	—
345	#117	C₂³×C₆₁	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
363	#107	C₂³×C₆₁	1	4	yes	—
364	#107	C₂³×C₆₁	1	4	yes	—
365	#107	C₂³×C₆₁	1	8	yes	—
366	#103	C₂³×C₆₁	1	8	yes	—
367	#103	C₂³×C₆₁	1	8	yes	—
368	#102	C₂³×C₆₁	1	8	yes	—
369	#102	C₂³×C₆₁	1	8	yes	—
370	#97	C₂³×C₆₁	1	4	yes	—
371	#97	C₂³×C₆₁	1	4	yes	—
372	C₄×C₈	C₂³×C₆₁	1	4	yes	—
373	C₄×C₈	C₂³×C₆₁	1	4	yes	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	8	4	no	—
381	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	8	4	no	—
387	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	8	4	no	—
395	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	8	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	8	no	—
410	C₂×C₈	#41×C₆₁	1	4	yes	—
411	C₂×C₈	#41×C₆₁	1	4	yes	—
412	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
413	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
414	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
415	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
422	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
424	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
431	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
432	C₄²	—	2	8	no	—
433	C₄²	C₂×D₄×C₆₁	1	2	yes	—
434	C₄²	C₂×D₄×C₆₁	1	2	yes	—
435	C₄²	C₂⁴×C₆₁	1	2	yes	—
436	C₄²	C₂⁴×C₆₁	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
445	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	4	no	—
449	Q₈	—	8	8	no	—
450	D₄	—	2	4	no	—
451	D₄	—	2	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	8	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
476	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
477	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	C₂×#41×C₆₁	1	4	yes	—
481	C₈	C₂×#41×C₆₁	1	4	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	8	no	—
490	C₂²	C₆₁×#532	1	2	yes	—
491	C₂²	C₆₁×#576	1	2	yes	—
492	C₂²	C₆₁×#578	1	2	yes	—
493	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₆₁×#532	1	2	yes	—
503	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
504	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	—	8	4	no	—
507	C₂	C₆₁×#3175	1	4	yes	direct product factor
508	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
509	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
510	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#466	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×#3175	C₂	direct (N × H)
3. C₂×C₆₁×#500	C₂	semidirect
4. C₂×C₆₁×#495	C₂	semidirect
5. C₂×C₆₁×#489	C₂	semidirect
6. C₂×C₆₁×#468	C₂	semidirect
7. C₂×C₆₁×#467	C₂	semidirect
9. C₂×C₆₁×#440	C₂	semidirect
10. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
11. C₂×C₄×D₈×C₆₁	C₂	semidirect
12. C₂×C₆₁×#405	C₂	semidirect
19. C₆₁×#542	C₂²	semidirect
31. C₆₁×#500	C₂²	semidirect
32. C₆₁×#495	C₂²	semidirect
33. C₆₁×#489	C₂²	semidirect
34. C₆₁×#468	C₂²	semidirect
35. C₆₁×#467	C₂²	semidirect
37. C₆₁×#440	C₂²	semidirect
38. C₄×Q₁₆×C₆₁	C₂²	semidirect
39. C₄×D₈×C₆₁	C₂²	semidirect
47. C₆₁×#405	C₂²	semidirect
226. C₂×#3175	C₆₁	direct (N × H)
250. C₂×#542	C₂×C₆₁	semidirect
251. #3175	C₂×C₆₁	direct (N × H)
252. C₂×#500	C₂×C₆₁	semidirect
253. C₂×#495	C₂×C₆₁	semidirect
254. C₂×#489	C₂×C₆₁	semidirect
255. C₂×#468	C₂×C₆₁	semidirect
256. C₂×#467	C₂×C₆₁	semidirect
258. C₂×#440	C₂×C₆₁	semidirect
259. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
260. C₂×C₄×D₈	C₂×C₆₁	semidirect
261. C₂×#405	C₂×C₆₁	semidirect
264. C₂×C₆₁	#3175	direct (N × H)
274. #542	C₂²×C₆₁	semidirect
286. #500	C₂²×C₆₁	semidirect
287. #495	C₂²×C₆₁	semidirect
288. #489	C₂²×C₆₁	semidirect
289. #468	C₂²×C₆₁	semidirect
290. #467	C₂²×C₆₁	semidirect
292. #440	C₂²×C₆₁	semidirect
293. C₄×Q₁₆	C₂²×C₆₁	semidirect
294. C₄×D₈	C₂²×C₆₁	semidirect
302. #405	C₂²×C₆₁	semidirect
307. C₆₁	C₂×#3175	direct (N × H)
507. C₂	C₆₁×#3175	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×#3175	2
C₂×C₆₁×#500	2
C₂×C₆₁×#495	2
C₂×C₆₁×#489	2
C₂×C₆₁×#468	2
C₂×C₆₁×#467	2
C₂×C₆₁×#466	2
C₂×C₆₁×#440	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₂×C₆₁×#405	2
C₂×#3175	61

Subgroups — C2×C61×#3175 #29564112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3175 #29564112