Subgroups — C₂×C₆₁×#1628 #29521925

Order 15616.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#459	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1628	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₆₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₆₁	—	2	1	no	—
10	C₂²×D₈×C₆₁	—	2	1	no	—
11	C₆₁×#556	—	2	2	no	—
12	C₆₁×#556	—	2	2	no	—
13	C₆₁×#556	—	2	2	no	—
14	C₆₁×#556	C₂²	1	4	yes	complemented
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₆₁	—	2	2	no	—
18	C₂×#124×C₆₁	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₁	—	2	1	no	—
24	C₆₁×#486	—	2	2	no	—
25	C₆₁×#486	C₂²	1	4	yes	complemented
26	C₆₁×#460	—	2	2	no	—
27	C₆₁×#460	C₂²	1	4	yes	complemented
28	C₆₁×#459	—	2	2	no	—
29	C₆₁×#459	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×C₆₁	—	2	1	no	—
33	C₂×#102×C₆₁	—	2	2	no	—
34	C₂×#102×C₆₁	—	2	1	no	—
35	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#332	C₂²	1	4	yes	complemented
37	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₆₁×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂²×Q₈×C₆₁	—	2	1	no	—
40	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₆₁	—	2	1	no	—
42	C₂²×D₄×C₆₁	—	2	1	no	—
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂×SD₁₆×C₆₁	—	2	4	no	—
47	C₂×SD₁₆×C₆₁	—	4	4	no	—
48	C₂×D₈×C₆₁	—	2	4	no	—
49	C₂×D₈×C₆₁	—	4	4	no	—
50	C₂²×C₈×C₆₁	—	2	1	no	—
51	C₂²×C₈×C₆₁	—	2	1	no	—
52	C₂²×C₈×C₆₁	—	2	1	no	—
53	C₄⋊Q₈×C₆₁	—	2	1	no	—
54	C₄⋊Q₈×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
56	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
57	#127×C₆₁	—	2	1	no	—
58	#127×C₆₁	—	2	1	no	—
59	#127×C₆₁	—	2	1	no	—
60	#127×C₆₁	C₂³	1	2	yes	—
61	#126×C₆₁	—	2	8	no	—
62	#126×C₆₁	—	2	8	no	—
63	#124×C₆₁	—	2	4	no	—
64	#124×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	4	no	—
66	C₂²⋊Q₈×C₆₁	—	2	4	no	—
67	C₄×Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	—	2	4	no	—
69	C₄×Q₈×C₆₁	—	2	1	no	—
70	C₄×Q₈×C₆₁	—	2	1	no	—
71	C₄×Q₈×C₆₁	D₄	1	2	yes	—
72	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
73	C₄×D₄×C₆₁	—	2	1	no	—
74	C₄×D₄×C₆₁	—	2	1	no	—
75	C₄×D₄×C₆₁	D₄	1	2	yes	—
76	C₄×D₄×C₆₁	C₂³	1	2	yes	—
77	#117×C₆₁	—	2	4	no	—
78	#117×C₆₁	—	2	4	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	2	no	—
89	C₂×C₄²×C₆₁	—	2	1	no	—
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₁	—	2	1	no	—
92	C₄⋊C₈×C₆₁	—	2	1	no	—
93	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
94	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
95	#102×C₆₁	—	2	4	no	—
96	#102×C₆₁	—	2	4	no	—
97	#102×C₆₁	—	2	8	no	—
98	C₄×C₈×C₆₁	—	2	1	no	—
99	C₄×C₈×C₆₁	C₂³	1	2	yes	—
100	C₂⁴×C₆₁	—	2	1	no	—
101	C₂⁴×C₆₁	—	4	1	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	4	2	no	—
108	C₂×Q₈×C₆₁	—	4	2	no	—
109	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₆₁	—	2	1	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	4	4	no	—
117	C₂×D₄×C₆₁	—	4	1	no	—
118	C₂×D₄×C₆₁	—	4	1	no	—
119	C₂×D₄×C₆₁	—	4	1	no	—
120	C₂×D₄×C₆₁	—	4	2	no	—
121	C₂×D₄×C₆₁	—	4	2	no	—
122	C₂×D₄×C₆₁	—	4	2	no	—
123	C₂×D₄×C₆₁	—	4	2	no	—
124	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	4	2	no	—
132	C₂²×C₄×C₆₁	—	4	2	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	SD₁₆×C₆₁	—	4	8	no	—
137	D₈×C₆₁	—	4	8	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	2	no	—
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	4	2	no	—
142	C₂×C₈×C₆₁	—	4	2	no	—
143	C₂×C₈×C₆₁	—	4	2	no	—
144	C₄⋊C₄×C₆₁	—	2	8	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	—	2	8	no	—
157	C₂²⋊C₄×C₆₁	—	2	2	no	—
158	C₂²⋊C₄×C₆₁	—	2	2	no	—
159	C₄²×C₆₁	—	2	8	no	—
160	C₄²×C₆₁	—	2	2	no	—
161	C₄²×C₆₁	—	2	2	no	—
162	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
166	C₂³×C₆₁	—	2	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	—	4	2	no	—
171	C₂³×C₆₁	—	8	2	no	—
172	C₂³×C₆₁	—	8	2	no	—
173	C₂³×C₆₁	—	8	2	no	—
174	C₂³×C₆₁	#120	1	1	yes	characteristic
175	Q₈×C₆₁	—	2	2	no	—
176	Q₈×C₆₁	—	2	2	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	Q₈×C₆₁	—	4	2	no	—
179	Q₈×C₆₁	—	4	2	no	—
180	Q₈×C₆₁	—	4	4	no	—
181	D₄×C₆₁	—	2	2	no	—
182	D₄×C₆₁	—	2	2	no	—
183	D₄×C₆₁	—	4	4	no	—
184	D₄×C₆₁	—	4	2	no	—
185	D₄×C₆₁	—	4	2	no	—
186	D₄×C₆₁	—	4	2	no	—
187	D₄×C₆₁	—	4	2	no	—
188	D₄×C₆₁	—	4	2	no	—
189	D₄×C₆₁	—	8	2	no	—
190	D₄×C₆₁	—	8	2	no	—
191	D₄×C₆₁	—	8	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	4	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	4	no	—
204	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
205	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
206	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
207	C₂×C₄×C₆₁	#135	1	2	yes	—
208	C₂×C₄×C₆₁	#135	1	2	yes	—
209	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₈×C₆₁	—	4	2	no	—
215	C₈×C₆₁	—	4	2	no	—
216	C₈×C₆₁	—	4	2	no	—
217	C₂×#1628	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	2	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	8	4	no	—
222	C₂²×C₆₁	—	8	2	no	—
223	C₂²×C₆₁	—	8	2	no	—
224	C₂²×C₆₁	—	8	2	no	—
225	C₂²×C₆₁	—	16	4	no	—
226	C₂²×C₆₁	#449	1	2	yes	—
227	C₂²×C₆₁	#449	1	2	yes	—
228	C₂²×C₆₁	#454	1	2	yes	—
229	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	2	1	no	—
232	C₄×C₆₁	—	4	2	no	—
233	C₄×C₆₁	—	4	2	no	—
234	C₄×C₆₁	—	4	4	no	—
235	C₄×C₆₁	—	4	2	no	—
236	C₄×C₆₁	#449	1	2	yes	—
237	C₄×C₆₁	#449	1	2	yes	—
238	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
239	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
240	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
243	C₂×#486	C₂×C₆₁	1	1	yes	characteristic, complemented
244	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
245	C₂×#459	C₂×C₆₁	1	1	yes	characteristic
246	#1628	C₂×C₆₁	1	8	yes	direct product factor
247	C₂×#332	C₂×C₆₁	1	1	yes	characteristic, complemented
248	C₂×Q₈⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
249	C₂×D₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×C₆₁	—	8	2	no	—
251	C₂×C₆₁	—	16	2	no	—
252	C₂×C₆₁	#1628	1	4	yes	direct product factor
253	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
254	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
255	C₂×C₆₁	C₂×#454	1	1	yes	characteristic
256	C₂²×SD₁₆	—	2	1	no	—
257	C₂²×D₈	—	2	1	no	—
258	#556	—	2	2	no	—
259	#556	—	2	2	no	—
260	#556	—	2	2	no	—
261	#556	C₂²×C₆₁	1	4	yes	complemented
262	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#126	—	2	2	no	—
265	C₂×#124	—	2	1	no	—
266	C₂×C₂²⋊Q₈	—	2	1	no	—
267	C₂×C₄×Q₈	—	2	1	no	—
268	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#117	—	2	1	no	—
271	#486	—	2	2	no	—
272	#486	C₂²×C₆₁	1	4	yes	complemented
273	#460	—	2	2	no	—
274	#460	C₂²×C₆₁	1	4	yes	complemented
275	#459	—	2	2	no	—
276	#459	C₂²×C₆₁	1	4	yes	—
277	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
279	C₂×#102	—	2	2	no	—
280	C₂×#102	—	2	1	no	—
281	C₂×#102	—	2	1	no	—
282	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
283	#332	C₂²×C₆₁	1	4	yes	complemented
284	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	complemented
285	D₄⋊C₈	C₂²×C₆₁	1	4	yes	complemented
286	C₆₁	C₂×#1628	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	4	4	no	—
296	C₂×D₈	—	2	4	no	—
297	C₂×D₈	—	4	4	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
304	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
305	#127	—	2	1	no	—
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	C₂³×C₆₁	1	2	yes	—
309	#126	—	2	8	no	—
310	#126	—	2	8	no	—
311	#124	—	2	4	no	—
312	#124	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	4	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	D₄×C₆₁	1	2	yes	—
320	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	D₄×C₆₁	1	2	yes	—
324	C₄×D₄	C₂³×C₆₁	1	2	yes	—
325	#117	—	2	4	no	—
326	#117	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
342	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	#102	—	2	8	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	C₂³×C₆₁	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	4	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
384	SD₁₆	—	4	8	no	—
385	D₈	—	4	8	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	2	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
401	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
411	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
413	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	8	2	no	—
420	C₂³	—	8	2	no	—
421	C₂³	—	8	2	no	—
422	C₂³	#120×C₆₁	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	4	no	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	2	no	—
438	D₄	—	8	2	no	—
439	D₄	—	8	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
453	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
454	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
455	C₂×C₄	#135×C₆₁	1	2	yes	—
456	C₂×C₄	#135×C₆₁	1	2	yes	—
457	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
458	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	8	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	16	4	no	—
473	C₂²	C₆₁×#449	1	2	yes	—
474	C₂²	C₆₁×#449	1	2	yes	—
475	C₂²	C₆₁×#454	1	2	yes	—
476	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	2	no	—
483	C₄	C₆₁×#449	1	2	yes	—
484	C₄	C₆₁×#449	1	2	yes	—
485	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
486	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
487	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
488	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
489	C₂	—	8	2	no	—
490	C₂	—	16	2	no	—
491	C₂	C₆₁×#1628	1	4	yes	direct product factor
492	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
493	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
494	C₂	C₂×C₆₁×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#556	C₂	semidirect
2. C₂×C₆₁×#486	C₂	semidirect
3. C₂×C₆₁×#460	C₂	semidirect
5. C₆₁×#1628	C₂	direct (N × H)
6. C₂×C₆₁×#332	C₂	semidirect
7. C₂×C₆₁×Q₈⋊C₈	C₂	semidirect
8. C₂×C₆₁×D₄⋊C₈	C₂	semidirect
14. C₆₁×#556	C₂²	semidirect
25. C₆₁×#486	C₂²	semidirect
27. C₆₁×#460	C₂²	semidirect
36. C₆₁×#332	C₂²	semidirect
37. C₆₁×Q₈⋊C₈	C₂²	semidirect
38. C₆₁×D₄⋊C₈	C₂²	semidirect
217. C₂×#1628	C₆₁	direct (N × H)
242. C₂×#556	C₂×C₆₁	semidirect
243. C₂×#486	C₂×C₆₁	semidirect
244. C₂×#460	C₂×C₆₁	semidirect
246. #1628	C₂×C₆₁	direct (N × H)
247. C₂×#332	C₂×C₆₁	semidirect
248. C₂×Q₈⋊C₈	C₂×C₆₁	semidirect
249. C₂×D₄⋊C₈	C₂×C₆₁	semidirect
252. C₂×C₆₁	#1628	direct (N × H)
261. #556	C₂²×C₆₁	semidirect
272. #486	C₂²×C₆₁	semidirect
274. #460	C₂²×C₆₁	semidirect
283. #332	C₂²×C₆₁	semidirect
284. Q₈⋊C₈	C₂²×C₆₁	semidirect
285. D₄⋊C₈	C₂²×C₆₁	semidirect
286. C₆₁	C₂×#1628	direct (N × H)
491. C₂	C₆₁×#1628	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×#556	2
C₂×C₆₁×#486	2
C₂×C₆₁×#460	2
C₂×C₆₁×#459	2
C₆₁×#1628	2
C₂×C₆₁×#332	2
C₂×C₆₁×Q₈⋊C₈	2
C₂×C₆₁×D₄⋊C₈	2
C₂×#1628	61

Subgroups — C2×C61×#1628 #29521925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1628 #29521925