Subgroups — C₆₁×#21474 #29524907

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×H(5,𝔽₂)×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#455	C₂	1	1	yes	maximal, characteristic
3	C₄×#137×C₆₁	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1885	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1882	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1859	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1856	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1792	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#100×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#137×C₆₁	C₂²	1	2	yes	—
14	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#520	—	2	2	no	—
16	C₆₁×#520	C₂²	1	2	yes	—
17	C₆₁×#518	—	2	2	no	—
18	C₆₁×#518	—	2	2	no	—
19	C₆₁×#518	C₂²	1	1	yes	characteristic
20	C₄×#41×C₆₁	—	2	2	no	—
21	C₄×#41×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₆₁	—	2	2	no	—
24	C₂×C₄×D₄×C₆₁	—	2	2	no	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#455	C₄	1	8	yes	complemented
27	C₆₁×#441	—	2	2	no	—
28	C₆₁×#440	—	2	2	no	—
29	C₄×Q₁₆×C₆₁	—	2	2	no	—
30	C₄×SD₁₆×C₆₁	—	2	2	no	—
31	C₆₁×#428	C₂²	1	2	yes	complemented
32	C₂×#104×C₆₁	C₂²	1	2	yes	—
33	C₂×#104×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#419	C₂²	1	2	yes	complemented
35	C₆₁×#417	C₂²	1	2	yes	—
36	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₆₁	C₂²	1	2	yes	complemented
39	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#390	C₂²	1	1	yes	characteristic
41	C₆₁×#388	—	2	2	no	—
42	C₆₁×#385	—	2	2	no	—
43	C₆₁×#384	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#376	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#343	C₂²	1	2	yes	complemented
46	C₆₁×#339	C₂²	1	2	yes	complemented
47	C₆₁×#339	C₂²	1	2	yes	complemented
48	H(5,𝔽₂)×C₆₁	—	2	4	no	—
49	H(5,𝔽₂)×C₆₁	—	2	2	no	—
50	H(5,𝔽₂)×C₆₁	C₂×C₄	1	4	yes	—
51	C₂×#41×C₆₁	—	2	2	no	—
52	C₂×#41×C₆₁	C₂³	1	2	yes	—
53	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₆₁	—	2	2	no	—
55	C₂²×D₄×C₆₁	—	2	2	no	—
56	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	—	2	2	no	—
58	C₂³×C₄×C₆₁	D₄	1	2	yes	—
59	#137×C₆₁	—	2	4	no	—
60	#137×C₆₁	C₂×C₄	1	8	yes	complemented
61	C₂×Q₁₆×C₆₁	—	2	2	no	—
62	C₂×SD₁₆×C₆₁	—	2	2	no	—
63	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
64	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
65	#124×C₆₁	—	2	2	no	—
66	#124×C₆₁	C₂×C₄	1	4	yes	complemented
67	C₄×Q₈×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	—	2	2	no	—
69	C₄×Q₈×C₆₁	—	2	2	no	—
70	C₄×Q₈×C₆₁	D₄	1	2	yes	—
71	C₄×Q₈×C₆₁	D₄	1	2	yes	—
72	C₄×D₄×C₆₁	—	2	4	no	—
73	C₄×D₄×C₆₁	—	2	4	no	—
74	C₄×D₄×C₆₁	—	2	4	no	—
75	C₄×D₄×C₆₁	—	2	4	no	—
76	C₄×D₄×C₆₁	—	2	2	no	—
77	C₄×D₄×C₆₁	—	2	2	no	—
78	C₄×D₄×C₆₁	—	2	4	no	—
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	2	2	no	—
81	C₄×D₄×C₆₁	—	2	2	no	—
82	C₄×D₄×C₆₁	—	2	2	no	—
83	C₄×D₄×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	D₄	1	2	yes	—
85	C₄×D₄×C₆₁	D₄	1	2	yes	—
86	#117×C₆₁	—	2	4	no	—
87	#117×C₆₁	—	2	2	no	—
88	#117×C₆₁	—	2	2	no	—
89	#117×C₆₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	4	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	D₄	1	2	yes	—
102	C₂×C₄²×C₆₁	—	2	2	no	—
103	C₂×C₄²×C₆₁	—	2	2	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	#107×C₆₁	—	2	2	no	—
109	#106×C₆₁	—	2	2	no	—
110	#104×C₆₁	—	2	4	no	—
111	#104×C₆₁	C₂×C₄	1	8	yes	complemented
112	#103×C₆₁	—	2	2	no	—
113	#103×C₆₁	—	2	2	no	—
114	#103×C₆₁	—	2	2	no	—
115	#102×C₆₁	—	2	2	no	—
116	#100×C₆₁	—	2	2	no	—
117	#100×C₆₁	C₂×C₄	1	4	yes	complemented
118	#97×C₆₁	—	2	2	no	—
119	C₄×C₈×C₆₁	—	2	2	no	—
120	#95×C₆₁	—	2	1	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	2	no	—
123	C₂⁴×C₆₁	—	2	2	no	—
124	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
125	#41×C₆₁	—	2	8	no	—
126	#41×C₆₁	—	2	8	no	—
127	#41×C₆₁	—	2	2	no	—
128	#41×C₆₁	—	2	2	no	—
129	#41×C₆₁	C₂²×C₄	1	4	yes	—
130	#41×C₆₁	#41	1	4	yes	—
131	C₂×Q₈×C₆₁	—	2	1	no	—
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	2	2	no	—
134	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	complemented
135	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₆₁	—	2	4	no	—
137	C₂×D₄×C₆₁	—	2	8	no	—
138	C₂×D₄×C₆₁	—	2	8	no	—
139	C₂×D₄×C₆₁	—	2	8	no	—
140	C₂×D₄×C₆₁	—	2	2	no	—
141	C₂×D₄×C₆₁	—	2	8	no	—
142	C₂×D₄×C₆₁	—	2	2	no	—
143	C₂×D₄×C₆₁	—	2	2	no	—
144	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₆₁	#41	1	2	yes	—
147	C₂²×C₄×C₆₁	—	2	2	no	—
148	C₂²×C₄×C₆₁	—	2	2	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	1	no	—
151	C₂²×C₄×C₆₁	—	2	2	no	—
152	C₂²×C₄×C₆₁	—	2	4	no	—
153	C₂²×C₄×C₆₁	—	2	2	no	—
154	C₂²×C₄×C₆₁	—	2	2	no	—
155	C₂²×C₄×C₆₁	—	2	2	no	—
156	C₂²×C₄×C₆₁	—	2	2	no	—
157	C₂²×C₄×C₆₁	—	2	2	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	8	2	no	—
161	C₂²×C₄×C₆₁	—	8	4	no	—
162	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
166	Q₁₆×C₆₁	—	2	8	no	—
167	SD₁₆×C₆₁	—	2	8	no	—
168	M₁₆×C₆₁	—	2	2	no	—
169	M₁₆×C₆₁	—	2	2	no	—
170	M₁₆×C₆₁	—	2	2	no	—
171	M₁₆×C₆₁	C₂²×C₄	1	4	yes	complemented
172	C₂×C₈×C₆₁	—	2	2	no	—
173	C₂×C₈×C₆₁	—	2	2	no	—
174	C₄⋊C₄×C₆₁	—	2	4	no	—
175	C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₄⋊C₄×C₆₁	—	2	2	no	—
177	C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₄⋊C₄×C₆₁	—	2	2	no	—
179	C₄⋊C₄×C₆₁	—	4	1	no	—
180	C₄⋊C₄×C₆₁	—	4	1	no	—
181	C₄⋊C₄×C₆₁	—	8	2	no	—
182	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
184	C₂²⋊C₄×C₆₁	—	2	4	no	—
185	C₂²⋊C₄×C₆₁	—	2	4	no	—
186	C₂²⋊C₄×C₆₁	—	2	8	no	—
187	C₂²⋊C₄×C₆₁	—	2	2	no	—
188	C₂²⋊C₄×C₆₁	—	2	2	no	—
189	C₂²⋊C₄×C₆₁	—	2	2	no	—
190	C₂²⋊C₄×C₆₁	—	2	4	no	—
191	C₂²⋊C₄×C₆₁	—	8	2	no	—
192	C₄²×C₆₁	—	2	4	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	—	2	2	no	—
195	C₄²×C₆₁	—	2	2	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	—	2	2	no	—
198	C₄²×C₆₁	—	4	2	no	—
199	C₄²×C₆₁	C₂²×C₄	1	2	yes	complemented
200	C₄²×C₆₁	C₂×D₄	1	2	yes	—
201	C₄²×C₆₁	C₂×D₄	1	2	yes	—
202	C₂³×C₆₁	—	2	8	no	—
203	C₂³×C₆₁	—	2	2	no	—
204	C₂³×C₆₁	—	2	2	no	—
205	C₂³×C₆₁	—	2	2	no	—
206	C₂³×C₆₁	—	4	2	no	—
207	C₂³×C₆₁	—	4	2	no	—
208	C₂³×C₆₁	—	8	2	no	—
209	C₂³×C₆₁	—	8	2	no	—
210	C₂³×C₆₁	C₄×D₄	1	4	yes	—
211	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₆₁	—	2	2	no	—
213	Q₈×C₆₁	—	2	4	no	—
214	Q₈×C₆₁	—	4	2	no	—
215	Q₈×C₆₁	C₄×D₄	1	4	yes	—
216	D₄×C₆₁	—	2	16	no	—
217	D₄×C₆₁	—	2	4	no	—
218	D₄×C₆₁	—	2	4	no	—
219	D₄×C₆₁	—	2	4	no	—
220	D₄×C₆₁	—	2	2	no	—
221	D₄×C₆₁	—	2	4	no	—
222	D₄×C₆₁	C₄×D₄	1	4	yes	—
223	C₂×C₄×C₆₁	—	2	8	no	—
224	C₂×C₄×C₆₁	—	2	2	no	—
225	C₂×C₄×C₆₁	—	2	4	no	—
226	C₂×C₄×C₆₁	—	2	4	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	4	1	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	4	no	—
235	C₂×C₄×C₆₁	—	4	4	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	4	2	no	—
241	C₂×C₄×C₆₁	—	4	1	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	8	2	no	—
247	C₂×C₄×C₆₁	—	8	2	no	—
248	C₂×C₄×C₆₁	—	8	2	no	—
249	C₂×C₄×C₆₁	—	8	4	no	—
250	C₂×C₄×C₆₁	—	8	2	no	—
251	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
252	C₂×C₄×C₆₁	#120	1	2	yes	—
253	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
257	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
258	C₈×C₆₁	—	2	4	no	—
259	C₈×C₆₁	—	4	2	no	—
260	#21474	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₆₁	—	2	1	no	—
262	C₂²×C₆₁	—	2	1	no	—
263	C₂²×C₆₁	—	2	4	no	—
264	C₂²×C₆₁	—	2	4	no	—
265	C₂²×C₆₁	—	4	4	no	—
266	C₂²×C₆₁	—	4	2	no	—
267	C₂²×C₆₁	—	4	2	no	—
268	C₂²×C₆₁	—	4	2	no	—
269	C₂²×C₆₁	—	4	2	no	—
270	C₂²×C₆₁	—	8	2	no	—
271	C₂²×C₆₁	—	8	8	no	—
272	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
274	C₂²×C₆₁	#525	1	1	yes	characteristic
275	C₄×C₆₁	—	2	1	no	—
276	C₄×C₆₁	—	2	1	no	—
277	C₄×C₆₁	—	2	2	no	—
278	C₄×C₆₁	—	2	4	no	—
279	C₄×C₆₁	—	4	2	no	—
280	C₄×C₆₁	—	4	2	no	—
281	C₄×C₆₁	—	4	2	no	—
282	C₄×C₆₁	—	4	2	no	—
283	C₄×C₆₁	—	4	2	no	—
284	C₄×C₆₁	—	8	1	no	—
285	C₄×C₆₁	—	8	1	no	—
286	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
287	C₄×C₆₁	#525	1	2	yes	—
288	C₄×H(5,𝔽₂)	C₂×C₆₁	1	1	yes	characteristic
289	C₂×#455	C₂×C₆₁	1	1	yes	characteristic
290	C₄×#137	C₂×C₆₁	1	2	yes	complemented
291	#2326	C₂×C₆₁	1	1	yes	characteristic, complemented
292	#1885	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#1882	C₂×C₆₁	1	2	yes	complemented
294	#1859	C₂×C₆₁	1	2	yes	complemented
295	#1856	C₂×C₆₁	1	1	yes	characteristic, complemented
296	#1792	C₂×C₆₁	1	1	yes	characteristic
297	#1759	C₂×C₆₁	1	2	yes	complemented
298	C₄×#100	C₂×C₆₁	1	1	yes	characteristic, complemented
299	C₂×C₆₁	—	2	1	no	—
300	C₂×C₆₁	—	2	1	no	—
301	C₂×C₆₁	—	4	4	no	—
302	C₂×C₆₁	—	4	4	no	—
303	C₂×C₆₁	C₄×#120	1	1	yes	characteristic
304	C₂×C₆₁	#3019	1	1	yes	characteristic
305	C₂×C₆₁	#3022	1	1	yes	characteristic
306	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
307	C₂×#137	C₂²×C₆₁	1	2	yes	—
308	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
309	#520	—	2	2	no	—
310	#520	C₂²×C₆₁	1	2	yes	—
311	#518	—	2	2	no	—
312	#518	—	2	2	no	—
313	#518	C₂²×C₆₁	1	1	yes	characteristic
314	C₄×#41	—	2	2	no	—
315	C₄×#41	C₂²×C₆₁	1	2	yes	—
316	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
317	C₂×C₄×D₄	—	2	2	no	—
318	C₂×C₄×D₄	—	2	2	no	—
319	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
320	#455	C₄×C₆₁	1	8	yes	complemented
321	#441	—	2	2	no	—
322	#440	—	2	2	no	—
323	C₄×Q₁₆	—	2	2	no	—
324	C₄×SD₁₆	—	2	2	no	—
325	#428	C₂²×C₆₁	1	2	yes	complemented
326	C₂×#104	C₂²×C₆₁	1	2	yes	—
327	C₂×#104	C₂²×C₆₁	1	2	yes	—
328	#419	C₂²×C₆₁	1	2	yes	complemented
329	#417	C₂²×C₆₁	1	2	yes	—
330	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
332	C₄×M₁₆	C₂²×C₆₁	1	2	yes	complemented
333	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
334	#390	C₂²×C₆₁	1	1	yes	characteristic
335	#388	—	2	2	no	—
336	#385	—	2	2	no	—
337	#384	C₂²×C₆₁	1	1	yes	characteristic, complemented
338	#376	C₂²×C₆₁	1	1	yes	characteristic, complemented
339	#343	C₂²×C₆₁	1	2	yes	complemented
340	#339	C₂²×C₆₁	1	2	yes	complemented
341	#339	C₂²×C₆₁	1	2	yes	complemented
342	C₆₁	#21474	1	1	yes	characteristic, direct product factor, Sylow
343	H(5,𝔽₂)	—	2	4	no	—
344	H(5,𝔽₂)	—	2	2	no	—
345	H(5,𝔽₂)	C₂×C₄×C₆₁	1	4	yes	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	C₂³×C₆₁	1	2	yes	—
348	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
352	C₂³×C₄	—	2	2	no	—
353	C₂³×C₄	D₄×C₆₁	1	2	yes	—
354	#137	—	2	4	no	—
355	#137	C₂×C₄×C₆₁	1	8	yes	complemented
356	C₂×Q₁₆	—	2	2	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
359	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
360	#124	—	2	2	no	—
361	#124	C₂×C₄×C₆₁	1	4	yes	complemented
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	D₄×C₆₁	1	2	yes	—
366	C₄×Q₈	D₄×C₆₁	1	2	yes	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	4	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	D₄×C₆₁	1	2	yes	—
380	C₄×D₄	D₄×C₆₁	1	2	yes	—
381	#117	—	2	4	no	—
382	#117	—	2	2	no	—
383	#117	—	2	2	no	—
384	#117	C₂³×C₆₁	1	2	yes	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	4	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	—	2	2	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
403	#107	—	2	2	no	—
404	#106	—	2	2	no	—
405	#104	—	2	4	no	—
406	#104	C₂×C₄×C₆₁	1	8	yes	complemented
407	#103	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#102	—	2	2	no	—
411	#100	—	2	2	no	—
412	#100	C₂×C₄×C₆₁	1	4	yes	complemented
413	#97	—	2	2	no	—
414	C₄×C₈	—	2	2	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
420	#41	—	2	8	no	—
421	#41	—	2	8	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	C₂²×C₄×C₆₁	1	4	yes	—
425	#41	#41×C₆₁	1	4	yes	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	complemented
430	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
440	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
441	C₂×D₄	#41×C₆₁	1	2	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	8	2	no	—
456	C₂²×C₄	—	8	4	no	—
457	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
461	Q₁₆	—	2	8	no	—
462	SD₁₆	—	2	8	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	C₂²×C₄×C₆₁	1	4	yes	complemented
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	8	2	no	—
477	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
478	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	8	2	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	4	2	no	—
494	C₄²	C₂²×C₄×C₆₁	1	2	yes	complemented
495	C₄²	C₂×D₄×C₆₁	1	2	yes	—
496	C₄²	C₂×D₄×C₆₁	1	2	yes	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	2	no	—
505	C₂³	C₄×D₄×C₆₁	1	4	yes	—
506	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
507	Q₈	—	2	2	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	4	2	no	—
510	Q₈	C₄×D₄×C₆₁	1	4	yes	—
511	D₄	—	2	16	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	4	no	—
517	D₄	C₄×D₄×C₆₁	1	4	yes	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	4	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
547	C₂×C₄	#120×C₆₁	1	2	yes	—
548	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
549	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
551	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
552	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
553	C₈	—	2	4	no	—
554	C₈	—	4	2	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	8	no	—
566	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
567	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
568	C₂²	C₆₁×#525	1	1	yes	characteristic
569	C₄	—	2	4	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
581	C₄	C₆₁×#525	1	2	yes	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	4	4	no	—
585	C₂	—	4	4	no	—
586	C₂	C₄×#120×C₆₁	1	1	yes	characteristic
587	C₂	C₆₁×#3019	1	1	yes	characteristic
588	C₂	C₆₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×H(5,𝔽₂)×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×#137×C₆₁	C₂	semidirect
4. C₆₁×#2326	C₂	semidirect
5. C₆₁×#1885	C₂	semidirect
6. C₆₁×#1882	C₂	semidirect
7. C₆₁×#1859	C₂	semidirect
8. C₆₁×#1856	C₂	semidirect
10. C₆₁×#1759	C₂	semidirect
11. C₄×#100×C₆₁	C₂	semidirect
22. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
26. C₆₁×#455	C₄	semidirect
31. C₆₁×#428	C₂²	semidirect
34. C₆₁×#419	C₂²	semidirect
38. C₄×M₁₆×C₆₁	C₂²	semidirect
39. C₆₁×#391	C₂²	semidirect
43. C₆₁×#384	C₂²	semidirect
44. C₆₁×#376	C₂²	semidirect
45. C₆₁×#343	C₂²	semidirect
46. C₆₁×#339	C₂²	semidirect
47. C₆₁×#339	C₂²	semidirect
60. #137×C₆₁	C₂×C₄	semidirect
66. #124×C₆₁	C₂×C₄	semidirect
111. #104×C₆₁	C₂×C₄	semidirect
117. #100×C₆₁	C₂×C₄	semidirect
134. C₂×Q₈×C₆₁	C₂²×C₄	semidirect
171. M₁₆×C₆₁	C₂²×C₄	semidirect
199. C₄²×C₆₁	C₂²×C₄	semidirect
260. #21474	C₆₁	direct (N × H)
290. C₄×#137	C₂×C₆₁	semidirect
291. #2326	C₂×C₆₁	semidirect
292. #1885	C₂×C₆₁	semidirect
293. #1882	C₂×C₆₁	semidirect
294. #1859	C₂×C₆₁	semidirect
295. #1856	C₂×C₆₁	semidirect
297. #1759	C₂×C₆₁	semidirect
298. C₄×#100	C₂×C₆₁	semidirect
316. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
320. #455	C₄×C₆₁	semidirect
325. #428	C₂²×C₆₁	semidirect
328. #419	C₂²×C₆₁	semidirect
332. C₄×M₁₆	C₂²×C₆₁	semidirect
333. #391	C₂²×C₆₁	semidirect
337. #384	C₂²×C₆₁	semidirect
338. #376	C₂²×C₆₁	semidirect
339. #343	C₂²×C₆₁	semidirect
340. #339	C₂²×C₆₁	semidirect
341. #339	C₂²×C₆₁	semidirect
342. C₆₁	#21474	direct (N × H)
355. #137	C₂×C₄×C₆₁	semidirect
361. #124	C₂×C₄×C₆₁	semidirect
406. #104	C₂×C₄×C₆₁	semidirect
412. #100	C₂×C₄×C₆₁	semidirect
429. C₂×Q₈	C₂²×C₄×C₆₁	semidirect
466. M₁₆	C₂²×C₄×C₆₁	semidirect
494. C₄²	C₂²×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×H(5,𝔽₂)×C₆₁	2
C₂×C₆₁×#455	2
C₄×#137×C₆₁	2
C₆₁×#2326	2
C₆₁×#1885	2
C₆₁×#1882	2
C₆₁×#1859	2
C₆₁×#1856	2
C₆₁×#1792	2
C₆₁×#1759	2
C₄×#100×C₆₁	2
#21474	61

Subgroups — C61×#21474 #29524907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21474 #29524907