Subgroups — #30593865

Order 15616.

10836 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#585×D₆₁	C₂	1	2	yes	maximal, complemented
2	#21460604	C₂	1	8	yes	maximal, complemented
3	#21460601	C₂	1	8	yes	maximal, complemented
4	#21460597	C₂	1	8	yes	maximal, complemented
5	#21460594	C₂	1	8	yes	maximal, complemented
6	#21460593	C₂	1	1	yes	maximal, characteristic, complemented
7	#21460592	C₂	1	6	yes	maximal, complemented
8	#21460590	C₂	1	2	yes	maximal, complemented
9	#21460588	C₂	1	6	yes	maximal, complemented
10	C₂×#16840559	C₂	1	6	yes	maximal, complemented
11	#575×D₆₁	C₂	1	6	yes	maximal, complemented
12	C₂×#16840527	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3584	C₂	1	1	yes	maximal, characteristic, complemented
14	#16840599	—	2	2	no	—
15	#16840599	C₂²	1	8	yes	complemented
16	#16840598	—	2	8	no	—
17	#16840598	C₂²	1	2	yes	complemented
18	#16840598	C₂²	1	12	yes	complemented
19	#16840597	—	2	6	no	—
20	#16840597	C₂²	1	8	yes	complemented
21	2₋¹⁺⁴×D₆₁	—	2	2	no	—
22	2₋¹⁺⁴×D₆₁	C₂²	1	8	yes	complemented
23	H(5,𝔽₂)×D₆₁	—	2	6	no	—
24	H(5,𝔽₂)×D₆₁	C₂²	1	8	yes	complemented
25	C₂×#41×D₆₁	—	2	8	no	—
26	C₂×#41×D₆₁	C₂²	1	1	yes	characteristic
27	C₂×#41×D₆₁	C₂²	1	12	yes	complemented
28	#16840579	C₂²	1	4	yes	complemented
29	#16840578	C₂²	1	24	yes	complemented
30	#16840577	C₂²	1	8	yes	complemented
31	#16840576	C₂²	1	12	yes	complemented
32	#16840575	C₂²	1	12	yes	complemented
33	#16840574	C₂²	1	8	yes	complemented
34	#16840573	C₂²	1	8	yes	complemented
35	#16840572	C₂²	1	24	yes	complemented
36	#16840571	C₂²	1	24	yes	complemented
37	#16840570	C₂²	1	8	yes	complemented
38	#16840569	C₂²	1	24	yes	complemented
39	#16840568	C₂²	1	24	yes	complemented
40	#16840567	C₂²	1	4	yes	complemented
41	#16840566	C₂²	1	24	yes	complemented
42	#16840565	C₂²	1	8	yes	complemented
43	#16840564	C₂²	1	12	yes	complemented
44	#16840563	C₂²	1	12	yes	complemented
45	#16840562	C₂²	1	6	yes	complemented
46	#16840561	C₂²	1	24	yes	complemented
47	#16840560	C₂²	1	12	yes	complemented
48	#16840559	C₂²	1	12	yes	complemented
49	#16840559	C₂²	1	4	yes	complemented
50	#16840559	C₂²	1	24	yes	complemented
51	#16840559	C₂²	1	24	yes	complemented
52	#16840559	C₂²	1	12	yes	complemented
53	#16840559	C₂²	1	12	yes	complemented
54	#16840558	C₂²	1	24	yes	complemented
55	C₂×#14519809	C₂²	1	12	yes	complemented
56	C₂×#14519806	C₂²	1	12	yes	complemented
57	#137×D₆₁	C₂²	1	24	yes	complemented
58	C₂×#14519804	C₂²	1	12	yes	complemented
59	C₂×#14519801	C₂²	1	12	yes	complemented
60	AGL(1,ℤ/8)×D₆₁	C₂²	1	24	yes	complemented
61	C₂×#14519799	C₂²	1	6	yes	complemented
62	C₂×#14519797	C₂²	1	12	yes	complemented
63	#135×D₆₁	C₂²	1	24	yes	complemented
64	#16840527	C₂²	1	8	yes	complemented
65	#16840527	C₂²	1	8	yes	complemented
66	C₂×#14519785	C₂²	1	3	yes	complemented
67	C₂×#14519784	C₂²	1	1	yes	characteristic, complemented
68	C₂×#14519783	C₂²	1	3	yes	complemented
69	C₂²×#11758189	C₂²	1	3	yes	complemented
70	C₂×M₁₆×D₆₁	C₂²	1	3	yes	complemented
71	C₆₁×#585	C₂²	1	2	yes	complemented
72	C₆₁×#578	C₂²	1	4	yes	complemented
73	C₆₁×#577	C₂²	1	8	yes	complemented
74	C₆₁×#576	C₂²	1	4	yes	complemented
75	C₆₁×#575	C₂²	1	6	yes	complemented
76	C₂×#135×C₆₁	C₂²	1	6	yes	complemented
77	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic, complemented
78	#14519825	—	2	2	no	—
79	#14519825	—	2	8	no	—
80	#14519825	—	2	8	no	—
81	#14519825	C₂³	1	24	yes	complemented
82	#14519824	—	2	8	no	—
83	#14519824	—	2	24	no	—
84	#14519824	—	2	12	no	—
85	#14519824	C₂³	1	24	yes	complemented
86	#14519824	C₂³	1	8	yes	complemented
87	#14519823	—	2	8	no	—
88	#14519823	—	2	24	no	—
89	#14519823	—	2	12	no	—
90	#14519823	C₂³	1	24	yes	complemented
91	#14519823	C₂³	1	8	yes	complemented
92	#14519822	—	2	6	no	—
93	#14519822	—	2	24	no	—
94	#14519822	—	2	24	no	—
95	#14519822	—	2	24	no	—
96	#14519822	C₂³	1	24	yes	complemented
97	C₂×#11758226	—	2	8	no	—
98	C₂×#11758226	D₄	1	1	yes	characteristic
99	C₂×#11758226	C₂³	1	12	yes	—
100	C₂×#11758222	—	2	24	no	—
101	C₂×#11758222	—	2	12	no	—
102	C₂×#11758222	C₂³	1	3	yes	—
103	C₂×#11758222	C₂³	1	12	yes	complemented
104	C₂×#11758224	—	2	12	no	—
105	C₂×#11758224	—	2	24	no	—
106	C₂×#11758224	D₄	1	3	yes	—
107	C₂×#11758224	C₂³	1	12	yes	—
108	#41×D₆₁	—	2	8	no	—
109	#41×D₆₁	—	2	8	no	—
110	#41×D₆₁	—	2	8	no	—
111	#41×D₆₁	—	2	24	no	—
112	#41×D₆₁	—	2	24	no	—
113	#41×D₆₁	—	2	24	no	—
114	#41×D₆₁	—	2	12	no	—
115	#41×D₆₁	—	2	12	no	—
116	#41×D₆₁	—	2	12	no	—
117	#41×D₆₁	—	2	12	no	—
118	#41×D₆₁	D₄	1	8	yes	—
119	#41×D₆₁	C₂³	1	24	yes	—
120	#41×D₆₁	C₂³	1	8	yes	—
121	#41×D₆₁	C₂³	1	8	yes	—
122	#41×D₆₁	C₂³	1	24	yes	complemented
123	#41×D₆₁	C₂³	1	24	yes	complemented
124	C₂×Q₈×D₆₁	—	2	8	no	—
125	C₂×Q₈×D₆₁	D₄	1	1	yes	characteristic
126	C₂×Q₈×D₆₁	C₂³	1	12	yes	complemented
127	C₂×D₄×D₆₁	—	2	12	no	—
128	C₂×D₄×D₆₁	—	2	24	no	—
129	C₂×D₄×D₆₁	D₄	1	3	yes	—
130	C₂×D₄×D₆₁	C₂³	1	12	yes	complemented
131	C₂²×C₄×D₆₁	—	2	12	no	—
132	C₂²×C₄×D₆₁	C₂³	1	3	yes	—
133	#14519810	C₂³	1	24	yes	complemented
134	#14519809	C₂³	1	24	yes	complemented
135	#14519809	C₂³	1	8	yes	complemented
136	#14519809	C₂³	1	24	yes	complemented
137	#14519809	C₂³	1	24	yes	complemented
138	#14519808	C₂³	1	24	yes	complemented
139	#14519807	C₂³	1	24	yes	complemented
140	#14519806	C₂³	1	24	yes	complemented
141	#14519806	C₂³	1	8	yes	complemented
142	#14519806	C₂³	1	24	yes	complemented
143	#14519806	C₂³	1	24	yes	complemented
144	#14519805	C₂³	1	24	yes	complemented
145	#14519804	C₂³	1	24	yes	complemented
146	#14519804	C₂³	1	8	yes	complemented
147	#14519804	C₂³	1	24	yes	complemented
148	#14519804	C₂³	1	24	yes	complemented
149	#14519803	C₂³	1	24	yes	complemented
150	#14519802	C₂³	1	24	yes	complemented
151	#14519801	C₂³	1	24	yes	complemented
152	#14519801	C₂³	1	8	yes	complemented
153	#14519801	C₂³	1	24	yes	complemented
154	#14519801	C₂³	1	24	yes	complemented
155	#14519800	C₂³	1	24	yes	complemented
156	#14519799	C₂³	1	12	yes	complemented
157	#14519799	C₂³	1	4	yes	complemented
158	#14519799	C₂³	1	12	yes	complemented
159	#14519799	C₂³	1	12	yes	complemented
160	#14519798	C₂³	1	48	yes	complemented
161	#14519797	C₂³	1	24	yes	complemented
162	#14519797	C₂³	1	8	yes	complemented
163	#14519797	C₂³	1	24	yes	complemented
164	#14519797	C₂³	1	24	yes	complemented
165	#14519796	C₂³	1	24	yes	complemented
166	C₂×Dic₂₄₄	C₂³	1	6	yes	complemented
167	C₂×#11758202	C₂³	1	12	yes	complemented
168	Q₁₆×D₆₁	C₂³	1	24	yes	complemented
169	C₂×#11758190	C₂³	1	12	yes	complemented
170	C₂×#11758200	C₂³	1	12	yes	complemented
171	C₂×#11758201	C₂³	1	12	yes	complemented
172	SD₁₆×D₆₁	C₂³	1	48	yes	complemented
173	C₂×D₄₈₈	C₂³	1	6	yes	complemented
174	C₂×#11758199	C₂³	1	12	yes	complemented
175	D₈×D₆₁	C₂³	1	24	yes	complemented
176	#14519785	C₂³	1	24	yes	complemented
177	#14519784	C₂³	1	8	yes	complemented
178	#14519783	C₂³	1	12	yes	complemented
179	#14519783	C₂³	1	12	yes	complemented
180	C₂×#11758194	C₂³	1	3	yes	complemented
181	C₂×#11758189	C₂³	1	3	yes	—
182	C₂×#11758189	C₂³	1	1	yes	characteristic
183	C₂×#11758189	C₂³	1	3	yes	complemented
184	C₂×#11758189	C₂³	1	3	yes	complemented
185	C₂×#11758189	C₂³	1	12	yes	complemented
186	C₂×#11758189	C₂³	1	12	yes	complemented
187	M₁₆×D₆₁	C₂³	1	24	yes	complemented
188	C₂²×#92418	C₂³	1	3	yes	complemented
189	C₂×C₈×D₆₁	C₂³	1	6	yes	complemented
190	2₋¹⁺⁴×C₆₁	—	2	2	no	—
191	2₋¹⁺⁴×C₆₁	C₂³	1	8	yes	complemented
192	H(5,𝔽₂)×C₆₁	—	2	6	no	—
193	H(5,𝔽₂)×C₆₁	C₂³	1	8	yes	complemented
194	C₂×#41×C₆₁	—	2	8	no	—
195	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×#41×C₆₁	C₂³	1	12	yes	complemented
197	#137×C₆₁	C₂³	1	24	yes	complemented
198	AGL(1,ℤ/8)×C₆₁	C₂³	1	24	yes	complemented
199	#135×C₆₁	C₂³	1	4	yes	complemented
200	#135×C₆₁	C₂³	1	12	yes	complemented
201	#135×C₆₁	C₂³	1	12	yes	complemented
202	#135×C₆₁	C₂³	1	12	yes	complemented
203	C₂×Q₁₆×C₆₁	C₂³	1	6	yes	complemented
204	C₂×SD₁₆×C₆₁	C₂³	1	12	yes	complemented
205	C₂×D₈×C₆₁	C₂³	1	6	yes	complemented
206	#131×C₆₁	C₂³	1	4	yes	complemented
207	#131×C₆₁	C₂³	1	4	yes	complemented
208	C₂×M₁₆×C₆₁	C₂³	1	3	yes	complemented
209	C₂²×C₈×C₆₁	C₂³	1	3	yes	complemented
210	C₂³×D₆₁	—	2	12	no	—
211	C₂³×D₆₁	C₂×D₄	1	3	yes	—
212	#41×C₆₁	—	2	8	no	—
213	#41×C₆₁	—	2	24	no	—
214	#41×C₆₁	—	2	12	no	—
215	#41×C₆₁	—	2	12	no	—
216	#41×C₆₁	C₂×D₄	1	4	yes	—
217	#41×C₆₁	C₂⁴	1	8	yes	—
218	#41×C₆₁	C₂⁴	1	24	yes	—
219	#41×C₆₁	C₂⁴	1	4	yes	—
220	C₂×Q₈×C₆₁	—	2	8	no	—
221	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
222	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
223	C₂×D₄×C₆₁	—	2	12	no	—
224	C₂×D₄×C₆₁	—	2	24	no	—
225	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
226	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
227	C₂²×C₄×C₆₁	—	2	12	no	—
228	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
229	C₂×C₂²⋊D₆₁	—	2	12	no	—
230	C₂×C₂²⋊D₆₁	—	2	12	no	—
231	C₂×C₂²⋊D₆₁	—	2	48	no	—
232	C₂×C₂²⋊D₆₁	—	2	12	no	—
233	C₂×C₂²⋊D₆₁	C₂×D₄	1	6	yes	—
234	C₂²×Dic₆₁	—	2	12	no	—
235	C₂²×Dic₆₁	C₂×D₄	1	3	yes	—
236	#11758226	—	2	8	no	—
237	#11758226	—	2	24	no	—
238	#11758226	—	2	12	no	—
239	#11758226	—	2	12	no	—
240	#11758226	C₂×D₄	1	8	yes	—
241	#11758226	C₂⁴	1	8	yes	—
242	#11758226	C₂⁴	1	24	yes	—
243	Q₈×D₆₁	—	2	8	no	—
244	Q₈×D₆₁	—	2	12	no	—
245	Q₈×D₆₁	—	2	12	no	—
246	Q₈×D₆₁	—	2	24	no	—
247	Q₈×D₆₁	C₂×D₄	1	8	yes	—
248	Q₈×D₆₁	C₂⁴	1	8	yes	—
249	Q₈×D₆₁	C₂⁴	1	24	yes	—
250	#11758224	—	2	24	no	—
251	#11758224	—	2	48	no	—
252	#11758224	—	2	24	no	—
253	#11758224	—	2	8	no	—
254	#11758224	—	2	24	no	—
255	#11758224	—	2	24	no	—
256	#11758224	—	2	12	no	—
257	#11758224	—	2	12	no	—
258	#11758224	—	2	24	no	—
259	#11758224	C₂×D₄	1	24	yes	—
260	#11758224	C₂⁴	1	8	yes	—
261	#11758224	C₂⁴	1	24	yes	—
262	D₄×D₆₁	—	2	8	no	—
263	D₄×D₆₁	—	2	24	no	—
264	D₄×D₆₁	—	2	24	no	—
265	D₄×D₆₁	—	2	24	no	—
266	D₄×D₆₁	—	2	24	no	—
267	D₄×D₆₁	—	2	48	no	—
268	D₄×D₆₁	—	2	24	no	—
269	D₄×D₆₁	—	2	12	no	—
270	D₄×D₆₁	—	2	12	no	—
271	D₄×D₆₁	C₂×D₄	1	24	yes	—
272	D₄×D₆₁	C₂⁴	1	8	yes	—
273	D₄×D₆₁	C₂⁴	1	24	yes	—
274	#11758222	—	2	12	no	—
275	#11758222	—	2	12	no	—
276	#11758222	—	2	48	no	—
277	#11758222	—	2	24	no	—
278	#11758222	—	2	8	no	—
279	#11758222	—	2	24	no	—
280	#11758222	—	2	24	no	—
281	#11758222	—	2	24	no	—
282	#11758222	—	2	24	no	—
283	#11758222	C₂×D₄	1	12	yes	—
284	#11758222	C₂⁴	1	12	yes	—
285	#11758222	C₂⁴	1	24	yes	—
286	#11758222	C₂⁴	1	8	yes	—
287	C₂×D₂₄₄	—	2	12	no	—
288	C₂×D₂₄₄	—	2	24	no	—
289	C₂×D₂₄₄	C₂×D₄	1	3	yes	—
290	C₂×D₂₄₄	C₂⁴	1	12	yes	—
291	C₂×C₄×D₆₁	—	2	12	no	—
292	C₂×C₄×D₆₁	—	2	12	no	—
293	C₂×C₄×D₆₁	—	2	12	no	—
294	C₂×C₄×D₆₁	—	2	8	no	—
295	C₂×C₄×D₆₁	—	2	24	no	—
296	C₂×C₄×D₆₁	—	2	24	no	—
297	C₂×C₄×D₆₁	—	2	24	no	—
298	C₂×C₄×D₆₁	C₂×D₄	1	12	yes	—
299	C₂×C₄×D₆₁	C₂×D₄	1	3	yes	—
300	C₂×C₄×D₆₁	C₂×D₄	1	3	yes	—
301	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×D₆₁	C₂⁴	1	12	yes	—
303	C₂×C₄×D₆₁	C₂⁴	1	3	yes	—
304	C₂×Dic₁₂₂	—	2	12	no	—
305	C₂×Dic₁₂₂	—	2	24	no	—
306	C₂×Dic₁₂₂	C₂×D₄	1	3	yes	—
307	C₂×Dic₁₂₂	C₂⁴	1	12	yes	—
308	Q₁₆×C₆₁	C₂⁴	1	4	yes	—
309	Q₁₆×C₆₁	C₂⁴	1	12	yes	—
310	SD₁₆×C₆₁	C₂⁴	1	8	yes	—
311	SD₁₆×C₆₁	C₂⁴	1	24	yes	—
312	D₈×C₆₁	C₂⁴	1	4	yes	—
313	D₈×C₆₁	C₂⁴	1	12	yes	—
314	M₁₆×C₆₁	C₂⁴	1	12	yes	—
315	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
317	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
318	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
319	#11758202	C₂⁴	1	24	yes	—
320	#11758202	C₂⁴	1	8	yes	—
321	#11758201	C₂⁴	1	24	yes	—
322	#11758201	C₂⁴	1	8	yes	—
323	#11758200	C₂⁴	1	24	yes	—
324	#11758200	C₂⁴	1	8	yes	—
325	#11758199	C₂⁴	1	24	yes	—
326	#11758199	C₂⁴	1	8	yes	—
327	#11758194	C₂⁴	1	12	yes	—
328	C₂×#92418	C₂⁴	1	3	yes	—
329	C₂×#92418	C₂⁴	1	1	yes	characteristic
330	C₂×#92418	C₂⁴	1	12	yes	—
331	Dic₂₄₄	C₂⁴	1	12	yes	—
332	Dic₂₄₄	C₂⁴	1	4	yes	—
333	D₄₈₈	C₂⁴	1	12	yes	—
334	D₄₈₈	C₂⁴	1	4	yes	—
335	#11758190	C₂⁴	1	8	yes	—
336	#11758190	C₂⁴	1	24	yes	—
337	#11758189	C₂⁴	1	2	yes	—
338	#11758189	C₂⁴	1	6	yes	—
339	#11758189	C₂⁴	1	12	yes	—
340	#11758189	C₂⁴	1	12	yes	—
341	#11758189	C₂⁴	1	2	yes	—
342	#11758189	C₂⁴	1	6	yes	—
343	C₈×D₆₁	C₂⁴	1	24	yes	—
344	C₂³×C₆₁	—	2	12	no	—
345	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
346	C₂²×D₆₁	—	2	12	no	—
347	C₂²×D₆₁	—	2	8	no	—
348	C₂²×D₆₁	—	2	24	no	—
349	C₂²×D₆₁	—	8	3	no	—
350	C₂²×D₆₁	—	8	24	no	—
351	C₂²×D₆₁	C₂²×D₄	1	12	yes	—
352	C₂²×D₆₁	C₂²×D₄	1	1	yes	characteristic
353	C₂²×D₆₁	C₂²×D₄	1	3	yes	—
354	Q₈×C₆₁	—	2	12	no	—
355	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
356	Q₈×C₆₁	C₂⁵	1	8	yes	—
357	D₄×C₆₁	—	2	24	no	—
358	D₄×C₆₁	—	2	8	no	—
359	D₄×C₆₁	—	2	12	no	—
360	D₄×C₆₁	C₂²×D₄	1	12	yes	—
361	D₄×C₆₁	C₂⁵	1	8	yes	—
362	C₂×C₄×C₆₁	—	2	12	no	—
363	C₂×C₄×C₆₁	—	2	24	no	—
364	C₂×C₄×C₆₁	—	2	8	no	—
365	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
366	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
367	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
368	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
369	C₂²⋊D₆₁	—	2	24	no	—
370	C₂²⋊D₆₁	—	2	8	no	—
371	C₂²⋊D₆₁	—	2	8	no	—
372	C₂²⋊D₆₁	—	2	24	no	—
373	C₂²⋊D₆₁	—	2	24	no	—
374	C₂²⋊D₆₁	—	2	8	no	—
375	C₂²⋊D₆₁	C₂²×D₄	1	24	yes	—
376	C₂×Dic₆₁	—	2	12	no	—
377	C₂×Dic₆₁	—	2	24	no	—
378	C₂×Dic₆₁	—	2	8	no	—
379	C₂×Dic₆₁	C₂²×D₄	1	12	yes	—
380	C₂×Dic₆₁	C₂²×D₄	1	3	yes	—
381	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
382	D₂₄₄	—	2	8	no	—
383	D₂₄₄	—	2	24	no	—
384	D₂₄₄	—	2	12	no	—
385	D₂₄₄	C₂²×D₄	1	12	yes	—
386	D₂₄₄	C₂⁵	1	8	yes	—
387	C₄×D₆₁	—	2	8	no	—
388	C₄×D₆₁	—	2	24	no	—
389	C₄×D₆₁	—	2	8	no	—
390	C₄×D₆₁	—	2	24	no	—
391	C₄×D₆₁	—	2	8	no	—
392	C₄×D₆₁	—	2	24	no	—
393	C₄×D₆₁	C₂²×D₄	1	2	yes	—
394	C₄×D₆₁	C₂²×D₄	1	6	yes	—
395	C₄×D₆₁	C₂²×D₄	1	12	yes	—
396	C₄×D₆₁	C₂²×D₄	1	12	yes	—
397	C₄×D₆₁	C₂⁵	1	6	yes	—
398	C₄×D₆₁	C₂⁵	1	2	yes	—
399	Dic₁₂₂	—	2	12	no	—
400	Dic₁₂₂	—	2	24	no	—
401	Dic₁₂₂	—	2	8	no	—
402	Dic₁₂₂	C₂²×D₄	1	12	yes	—
403	Dic₁₂₂	C₂⁵	1	8	yes	—
404	C₈×C₆₁	C₂⁵	1	6	yes	—
405	C₈×C₆₁	C₂⁵	1	1	yes	characteristic
406	C₈×C₆₁	C₂⁵	1	1	yes	characteristic
407	#92418	C₂⁵	1	6	yes	—
408	#92418	C₂⁵	1	2	yes	—
409	#63090	—	61	1	no	maximal, Sylow
410	C₂²×C₆₁	—	2	8	no	—
411	C₂²×C₆₁	—	4	3	no	—
412	C₂²×C₆₁	—	8	12	no	—
413	C₂²×C₆₁	C₂³×D₄	1	6	yes	—
414	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
415	C₂×D₆₁	—	2	8	no	—
416	C₂×D₆₁	—	4	1	no	—
417	C₂×D₆₁	—	4	12	no	—
418	C₂×D₆₁	—	4	3	no	—
419	C₂×D₆₁	—	4	16	no	—
420	C₂×D₆₁	—	8	24	no	—
421	C₂×D₆₁	—	8	12	no	—
422	C₂×D₆₁	C₂³×D₄	1	2	yes	—
423	C₂×D₆₁	C₂³×D₄	1	6	yes	—
424	C₄×C₆₁	—	2	8	no	—
425	C₄×C₆₁	C₂³×D₄	1	6	yes	—
426	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₆₁	C₂⁶	1	1	yes	characteristic
428	Dic₆₁	—	2	8	no	—
429	Dic₆₁	C₂³×D₄	1	6	yes	—
430	Dic₆₁	C₂³×D₄	1	2	yes	—
431	C₂×#585	—	61	2	no	—
432	#3586	—	61	8	no	—
433	#3586	—	61	8	no	—
434	#3585	—	61	8	no	—
435	#3585	—	61	8	no	—
436	#3584	—	61	2	no	—
437	#3584	—	61	6	no	—
438	#3584	—	61	6	no	—
439	#3584	—	61	1	no	—
440	#3584	D₆₁	1	1	yes	characteristic, complemented
441	C₂×#575	—	61	6	no	—
442	C₂×#575	—	61	6	no	—
443	C₂×#568	—	61	1	no	—
444	C₂×C₆₁	—	2	1	no	—
445	C₂×C₆₁	—	2	6	no	—
446	C₂×C₆₁	—	4	8	no	—
447	C₂×C₆₁	C₂⁴×D₄	1	1	yes	characteristic
448	D₆₁	—	2	2	no	—
449	D₆₁	—	2	6	no	—
450	D₆₁	—	4	8	no	—
451	#585	—	61	8	no	—
452	#585	—	61	8	no	—
453	#585	—	61	2	no	—
454	#585	—	61	12	no	—
455	#585	—	122	8	no	—
456	#585	—	122	6	no	—
457	#585	—	122	2	no	—
458	#585	C₂×D₆₁	1	2	yes	complemented
459	C₂×2₋¹⁺⁴	—	61	8	no	—
460	C₂×2₋¹⁺⁴	—	122	2	no	—
461	C₂×H(5,𝔽₂)	—	61	8	no	—
462	C₂×H(5,𝔽₂)	—	122	6	no	—
463	C₂²×#41	—	61	1	no	—
464	C₂²×#41	—	61	12	no	—
465	C₂²×#41	—	122	8	no	—
466	#578	—	61	8	no	—
467	#578	—	61	24	no	—
468	#578	—	61	12	no	—
469	#578	—	61	12	no	—
470	#578	—	61	4	no	—
471	#578	C₂×D₆₁	1	4	yes	complemented
472	#577	—	61	8	no	—
473	#577	—	61	8	no	—
474	#577	—	61	24	no	—
475	#577	—	61	24	no	—
476	#577	—	61	24	no	—
477	#577	—	61	24	no	—
478	#577	—	61	8	no	—
479	#577	C₂×D₆₁	1	8	yes	complemented
480	#576	—	61	8	no	—
481	#576	—	61	24	no	—
482	#576	—	61	12	no	—
483	#576	—	61	12	no	—
484	#576	—	61	4	no	—
485	#576	C₂×D₆₁	1	4	yes	complemented
486	#575	—	61	12	no	—
487	#575	—	61	24	no	—
488	#575	—	61	24	no	—
489	#575	—	61	12	no	—
490	#575	—	61	12	no	—
491	#575	—	61	24	no	—
492	#575	—	61	24	no	—
493	#575	—	61	12	no	—
494	#575	—	61	4	no	—
495	#575	—	61	6	no	—
496	#575	C₂×D₆₁	1	6	yes	complemented
497	C₂×#137	—	61	24	no	—
498	C₂×#137	—	61	12	no	—
499	C₂×#137	—	61	12	no	—
500	C₂×AGL(1,ℤ/8)	—	61	24	no	—
501	C₂×AGL(1,ℤ/8)	—	61	12	no	—
502	C₂×AGL(1,ℤ/8)	—	61	12	no	—
503	C₂×#135	—	61	12	no	—
504	C₂×#135	—	61	24	no	—
505	C₂×#135	—	61	6	no	—
506	C₂×#135	C₂×D₆₁	1	6	yes	complemented
507	#568	—	61	8	no	—
508	#568	—	61	8	no	—
509	C₂×#131	—	61	1	no	—
510	C₂×#131	—	61	3	no	—
511	C₂×#131	—	61	3	no	—
512	C₂×#131	C₂×D₆₁	1	1	yes	characteristic, complemented
513	C₂²×M₁₆	—	61	3	no	—
514	C₂²×M₁₆	—	61	3	no	—
515	C₆₁	#63090	1	1	yes	characteristic, complemented, Sylow
516	2₋¹⁺⁴	—	2	2	no	—
517	2₋¹⁺⁴	—	61	24	no	—
518	2₋¹⁺⁴	—	61	8	no	—
519	2₋¹⁺⁴	—	61	24	no	—
520	2₋¹⁺⁴	—	122	8	no	—
521	2₋¹⁺⁴	—	122	8	no	—
522	2₋¹⁺⁴	—	122	8	no	—
523	2₋¹⁺⁴	—	122	12	no	—
524	2₋¹⁺⁴	—	122	24	no	—
525	2₋¹⁺⁴	—	122	2	no	—
526	2₋¹⁺⁴	C₂²×D₆₁	1	8	yes	complemented
527	H(5,𝔽₂)	—	2	6	no	—
528	H(5,𝔽₂)	—	61	24	no	—
529	H(5,𝔽₂)	—	61	8	no	—
530	H(5,𝔽₂)	—	61	24	no	—
531	H(5,𝔽₂)	—	122	24	no	—
532	H(5,𝔽₂)	—	122	24	no	—
533	H(5,𝔽₂)	—	122	24	no	—
534	H(5,𝔽₂)	—	122	24	no	—
535	H(5,𝔽₂)	—	122	12	no	—
536	H(5,𝔽₂)	—	122	8	no	—
537	H(5,𝔽₂)	—	122	6	no	—
538	H(5,𝔽₂)	C₂²×D₆₁	1	8	yes	complemented
539	C₂×#41	—	2	8	no	—
540	C₂×#41	—	61	8	no	—
541	C₂×#41	—	61	8	no	—
542	C₂×#41	—	61	1	no	—
543	C₂×#41	—	61	3	no	—
544	C₂×#41	—	61	3	no	—
545	C₂×#41	—	61	24	no	—
546	C₂×#41	—	61	8	no	—
547	C₂×#41	—	61	24	no	—
548	C₂×#41	—	61	24	no	—
549	C₂×#41	—	61	12	no	—
550	C₂×#41	—	61	12	no	—
551	C₂×#41	—	61	12	no	—
552	C₂×#41	—	122	12	no	—
553	C₂×#41	—	122	24	no	—
554	C₂×#41	—	122	12	no	—
555	C₂×#41	—	122	12	no	—
556	C₂×#41	—	122	12	no	—
557	C₂×#41	—	122	12	no	—
558	C₂×#41	—	122	12	no	—
559	C₂×#41	—	122	24	no	—
560	C₂×#41	—	122	24	no	—
561	C₂×#41	—	122	8	no	—
562	C₂×#41	—	122	8	no	—
563	C₂×#41	—	122	8	no	—
564	C₂×#41	—	122	24	no	—
565	C₂×#41	—	122	24	no	—
566	C₂×#41	—	122	8	no	—
567	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
568	C₂×#41	C₂²×D₆₁	1	12	yes	complemented
569	C₂²×Q₈	—	61	1	no	—
570	C₂²×Q₈	—	61	12	no	—
571	C₂²×Q₈	—	122	8	no	—
572	C₂²×D₄	—	61	3	no	—
573	C₂²×D₄	—	61	12	no	—
574	C₂²×D₄	—	122	24	no	—
575	C₂²×D₄	—	122	12	no	—
576	C₂³×C₄	—	61	3	no	—
577	C₂³×C₄	—	122	12	no	—
578	#137	—	61	24	no	—
579	#137	—	61	24	no	—
580	#137	—	61	24	no	—
581	#137	—	61	8	no	—
582	#137	—	61	24	no	—
583	#137	—	61	24	no	—
584	#137	—	61	24	no	—
585	#137	—	61	8	no	—
586	#137	—	61	24	no	—
587	#137	—	61	24	no	—
588	#137	—	61	24	no	—
589	#137	C₂²×D₆₁	1	24	yes	complemented
590	AGL(1,ℤ/8)	—	61	24	no	—
591	AGL(1,ℤ/8)	—	61	24	no	—
592	AGL(1,ℤ/8)	—	61	24	no	—
593	AGL(1,ℤ/8)	—	61	8	no	—
594	AGL(1,ℤ/8)	—	61	24	no	—
595	AGL(1,ℤ/8)	—	61	24	no	—
596	AGL(1,ℤ/8)	—	61	24	no	—
597	AGL(1,ℤ/8)	—	61	8	no	—
598	AGL(1,ℤ/8)	—	61	24	no	—
599	AGL(1,ℤ/8)	—	61	24	no	—
600	AGL(1,ℤ/8)	—	61	24	no	—
601	AGL(1,ℤ/8)	C₂²×D₆₁	1	24	yes	complemented
602	#135	—	61	8	no	—
603	#135	—	61	24	no	—
604	#135	—	61	24	no	—
605	#135	—	61	24	no	—
606	#135	—	61	24	no	—
607	#135	—	61	48	no	—
608	#135	—	61	24	no	—
609	#135	—	61	12	no	—
610	#135	—	61	4	no	—
611	#135	—	61	12	no	—
612	#135	—	61	12	no	—
613	#135	C₂²×D₆₁	1	12	yes	complemented
614	#135	C₂²×D₆₁	1	4	yes	complemented
615	#135	C₂²×D₆₁	1	12	yes	complemented
616	#135	C₂²×D₆₁	1	12	yes	complemented
617	C₂×Q₁₆	—	61	12	no	—
618	C₂×Q₁₆	—	61	24	no	—
619	C₂×Q₁₆	—	61	6	no	—
620	C₂×Q₁₆	C₂²×D₆₁	1	6	yes	complemented
621	C₂×SD₁₆	—	61	12	no	—
622	C₂×SD₁₆	—	61	12	no	—
623	C₂×SD₁₆	—	61	48	no	—
624	C₂×SD₁₆	—	61	12	no	—
625	C₂×SD₁₆	C₂²×D₆₁	1	12	yes	complemented
626	C₂×D₈	—	61	12	no	—
627	C₂×D₈	—	61	24	no	—
628	C₂×D₈	—	61	6	no	—
629	C₂×D₈	C₂²×D₆₁	1	6	yes	complemented
630	#131	—	61	8	no	—
631	#131	—	61	24	no	—
632	#131	—	61	12	no	—
633	#131	—	61	12	no	—
634	#131	C₂²×D₆₁	1	4	yes	complemented
635	#131	C₂²×D₆₁	1	4	yes	complemented
636	C₂×M₁₆	—	61	3	no	—
637	C₂×M₁₆	—	61	24	no	—
638	C₂×M₁₆	—	61	3	no	—
639	C₂×M₁₆	—	61	1	no	—
640	C₂×M₁₆	—	61	3	no	—
641	C₂×M₁₆	—	61	3	no	—
642	C₂×M₁₆	—	61	12	no	—
643	C₂×M₁₆	—	61	12	no	—
644	C₂×M₁₆	C₂²×D₆₁	1	3	yes	complemented
645	C₂²×C₈	—	61	3	no	—
646	C₂²×C₈	—	61	6	no	—
647	C₂²×C₈	C₂²×D₆₁	1	3	yes	complemented
648	C₂⁴	—	61	3	no	—
649	C₂⁴	—	122	12	no	—
650	#41	—	2	8	no	—
651	#41	—	2	24	no	—
652	#41	—	2	12	no	—
653	#41	—	2	12	no	—
654	#41	—	61	8	no	—
655	#41	—	61	24	no	—
656	#41	—	61	12	no	—
657	#41	—	61	12	no	—
658	#41	—	61	24	no	—
659	#41	—	61	8	no	—
660	#41	—	61	24	no	—
661	#41	—	61	8	no	—
662	#41	—	61	8	no	—
663	#41	—	61	24	no	—
664	#41	—	122	8	no	—
665	#41	—	122	24	no	—
666	#41	—	122	24	no	—
667	#41	—	122	24	no	—
668	#41	—	122	48	no	—
669	#41	—	122	24	no	—
670	#41	—	122	24	no	—
671	#41	—	122	8	no	—
672	#41	—	122	24	no	—
673	#41	—	122	12	no	—
674	#41	—	122	24	no	—
675	#41	—	122	24	no	—
676	#41	—	122	12	no	—
677	#41	—	122	12	no	—
678	#41	—	122	12	no	—
679	#41	—	122	48	no	—
680	#41	—	122	24	no	—
681	#41	—	122	24	no	—
682	#41	—	122	8	no	—
683	#41	—	122	24	no	—
684	#41	—	122	12	no	—
685	#41	—	122	12	no	—
686	#41	D₄×D₆₁	1	4	yes	—
687	#41	C₂³×D₆₁	1	8	yes	—
688	#41	C₂³×D₆₁	1	24	yes	—
689	#41	C₂³×D₆₁	1	4	yes	—
690	C₂×Q₈	—	2	8	no	—
691	C₂×Q₈	—	61	8	no	—
692	C₂×Q₈	—	61	3	no	—
693	C₂×Q₈	—	61	24	no	—
694	C₂×Q₈	—	61	8	no	—
695	C₂×Q₈	—	61	12	no	—
696	C₂×Q₈	—	122	12	no	—
697	C₂×Q₈	—	122	24	no	—
698	C₂×Q₈	—	122	12	no	—
699	C₂×Q₈	—	122	12	no	—
700	C₂×Q₈	—	122	24	no	—
701	C₂×Q₈	—	122	8	no	—
702	C₂×Q₈	D₄×D₆₁	1	1	yes	characteristic
703	C₂×Q₈	C₂³×D₆₁	1	12	yes	—
704	C₂×D₄	—	2	12	no	—
705	C₂×D₄	—	2	24	no	—
706	C₂×D₄	—	61	6	no	—
707	C₂×D₄	—	61	24	no	—
708	C₂×D₄	—	61	24	no	—
709	C₂×D₄	—	61	8	no	—
710	C₂×D₄	—	61	3	no	—
711	C₂×D₄	—	61	12	no	—
712	C₂×D₄	—	122	24	no	—
713	C₂×D₄	—	122	12	no	—
714	C₂×D₄	—	122	12	no	—
715	C₂×D₄	—	122	12	no	—
716	C₂×D₄	—	122	12	no	—
717	C₂×D₄	—	122	48	no	—
718	C₂×D₄	—	122	24	no	—
719	C₂×D₄	—	122	8	no	—
720	C₂×D₄	—	122	24	no	—
721	C₂×D₄	—	122	24	no	—
722	C₂×D₄	—	122	24	no	—
723	C₂×D₄	—	122	48	no	—
724	C₂×D₄	—	122	12	no	—
725	C₂×D₄	—	122	12	no	—
726	C₂×D₄	—	122	24	no	—
727	C₂×D₄	D₄×D₆₁	1	3	yes	—
728	C₂×D₄	C₂³×D₆₁	1	12	yes	—
729	C₂²×C₄	—	2	12	no	—
730	C₂²×C₄	—	61	3	no	—
731	C₂²×C₄	—	61	12	no	—
732	C₂²×C₄	—	61	3	no	—
733	C₂²×C₄	—	61	3	no	—
734	C₂²×C₄	—	61	3	no	—
735	C₂²×C₄	—	61	1	no	—
736	C₂²×C₄	—	61	12	no	—
737	C₂²×C₄	—	122	8	no	—
738	C₂²×C₄	—	122	24	no	—
739	C₂²×C₄	—	122	12	no	—
740	C₂²×C₄	—	122	24	no	—
741	C₂²×C₄	—	122	24	no	—
742	C₂²×C₄	—	122	12	no	—
743	C₂²×C₄	—	122	12	no	—
744	C₂²×C₄	—	122	12	no	—
745	C₂²×C₄	C₂³×D₆₁	1	3	yes	—
746	Q₁₆	—	61	24	no	—
747	Q₁₆	—	61	8	no	—
748	Q₁₆	—	61	12	no	—
749	Q₁₆	—	61	4	no	—
750	Q₁₆	C₂³×D₆₁	1	12	yes	—
751	Q₁₆	C₂³×D₆₁	1	4	yes	—
752	SD₁₆	—	61	24	no	—
753	SD₁₆	—	61	8	no	—
754	SD₁₆	—	61	24	no	—
755	SD₁₆	—	61	8	no	—
756	SD₁₆	—	61	24	no	—
757	SD₁₆	—	61	8	no	—
758	SD₁₆	C₂³×D₆₁	1	24	yes	—
759	SD₁₆	C₂³×D₆₁	1	8	yes	—
760	D₈	—	61	24	no	—
761	D₈	—	61	8	no	—
762	D₈	—	61	12	no	—
763	D₈	—	61	4	no	—
764	D₈	C₂³×D₆₁	1	12	yes	—
765	D₈	C₂³×D₆₁	1	4	yes	—
766	M₁₆	—	61	12	no	—
767	M₁₆	—	61	12	no	—
768	M₁₆	—	61	2	no	—
769	M₁₆	—	61	2	no	—
770	M₁₆	—	61	12	no	—
771	M₁₆	—	61	6	no	—
772	M₁₆	—	61	6	no	—
773	M₁₆	C₂³×D₆₁	1	12	yes	—
774	C₂×C₈	—	61	3	no	—
775	C₂×C₈	—	61	1	no	—
776	C₂×C₈	—	61	12	no	—
777	C₂×C₈	—	61	24	no	—
778	C₂×C₈	C₂³×D₆₁	1	3	yes	—
779	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
780	C₂×C₈	C₂³×D₆₁	1	6	yes	—
781	C₂×C₈	C₂³×D₆₁	1	6	yes	—
782	C₂³	—	2	12	no	—
783	C₂³	—	61	1	no	—
784	C₂³	—	61	12	no	—
785	C₂³	—	61	3	no	—
786	C₂³	—	122	24	no	—
787	C₂³	—	122	8	no	—
788	C₂³	—	122	12	no	—
789	C₂³	—	488	3	no	—
790	C₂³	—	488	24	no	—
791	C₂³	C₂×D₄×D₆₁	1	3	yes	—
792	Q₈	—	2	12	no	—
793	Q₈	—	61	12	no	—
794	Q₈	—	61	8	no	—
795	Q₈	—	122	8	no	—
796	Q₈	—	122	24	no	—
797	Q₈	—	122	12	no	—
798	Q₈	C₂×D₄×D₆₁	1	4	yes	—
799	Q₈	C₂⁴×D₆₁	1	8	yes	—
800	D₄	—	2	24	no	—
801	D₄	—	2	8	no	—
802	D₄	—	2	12	no	—
803	D₄	—	61	24	no	—
804	D₄	—	61	12	no	—
805	D₄	—	61	8	no	—
806	D₄	—	122	8	no	—
807	D₄	—	122	24	no	—
808	D₄	—	122	8	no	—
809	D₄	—	122	24	no	—
810	D₄	—	122	8	no	—
811	D₄	—	122	24	no	—
812	D₄	—	122	24	no	—
813	D₄	—	122	8	no	—
814	D₄	—	122	12	no	—
815	D₄	C₂×D₄×D₆₁	1	12	yes	—
816	D₄	C₂⁴×D₆₁	1	8	yes	—
817	C₂×C₄	—	2	12	no	—
818	C₂×C₄	—	2	24	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	61	1	no	—
821	C₂×C₄	—	61	12	no	—
822	C₂×C₄	—	61	3	no	—
823	C₂×C₄	—	61	12	no	—
824	C₂×C₄	—	61	12	no	—
825	C₂×C₄	—	61	2	no	—
826	C₂×C₄	—	61	6	no	—
827	C₂×C₄	—	61	6	no	—
828	C₂×C₄	—	61	2	no	—
829	C₂×C₄	—	122	8	no	—
830	C₂×C₄	—	122	24	no	—
831	C₂×C₄	—	122	8	no	—
832	C₂×C₄	—	122	24	no	—
833	C₂×C₄	—	122	8	no	—
834	C₂×C₄	—	122	24	no	—
835	C₂×C₄	—	122	12	no	—
836	C₂×C₄	—	122	24	no	—
837	C₂×C₄	—	122	8	no	—
838	C₂×C₄	C₂×D₄×D₆₁	1	3	yes	—
839	C₂×C₄	C₂×D₄×D₆₁	1	6	yes	—
840	C₂×C₄	C₂⁴×D₆₁	1	6	yes	—
841	C₂×C₄	C₂⁴×D₆₁	1	1	yes	characteristic
842	C₈	—	61	6	no	—
843	C₈	—	61	2	no	—
844	C₈	C₂⁴×D₆₁	1	6	yes	—
845	C₈	C₂⁴×D₆₁	1	1	yes	characteristic
846	C₈	C₂⁴×D₆₁	1	1	yes	characteristic
847	C₂²	—	2	8	no	—
848	C₂²	—	4	3	no	—
849	C₂²	—	8	12	no	—
850	C₂²	—	61	2	no	—
851	C₂²	—	61	6	no	—
852	C₂²	—	122	8	no	—
853	C₂²	—	488	12	no	—
854	C₂²	—	488	24	no	—
855	C₂²	—	244	3	no	—
856	C₂²	—	244	1	no	—
857	C₂²	—	244	12	no	—
858	C₂²	—	244	16	no	—
859	C₂²	C₂²×D₄×D₆₁	1	6	yes	—
860	C₂²	C₂²×D₄×D₆₁	1	1	yes	characteristic
861	C₄	—	2	8	no	—
862	C₄	—	61	2	no	—
863	C₄	—	61	6	no	—
864	C₄	—	122	8	no	—
865	C₄	C₂²×D₄×D₆₁	1	6	yes	—
866	C₄	C₂²×D₄×D₆₁	1	1	yes	characteristic
867	C₄	C₂⁵×D₆₁	1	1	yes	characteristic
868	C₂	—	2	1	no	—
869	C₂	—	2	6	no	—
870	C₂	—	4	8	no	—
871	C₂	—	122	6	no	—
872	C₂	—	122	2	no	—
873	C₂	—	244	8	no	—
874	C₂	C₂³×D₄×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₆₁
commutator, cosocle	C₄×C₆₁	C₂⁶
Frattini	C₄	C₂⁵×D₆₁
Fitting	C₆₁×#3584	C₂
socle	C₂×C₆₁	C₂⁴×D₄
hypercenter	#3584	D₆₁
hypocenter	C₆₁	#63090
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #585×D₆₁	C₂	semidirect
2. #21460604	C₂	semidirect
3. #21460601	C₂	semidirect
4. #21460597	C₂	semidirect
5. #21460594	C₂	semidirect
6. #21460593	C₂	semidirect
7. #21460592	C₂	semidirect
8. #21460590	C₂	semidirect
9. #21460588	C₂	semidirect
10. C₂×#16840559	C₂	semidirect
11. #575×D₆₁	C₂	semidirect
12. C₂×#16840527	C₂	semidirect
13. C₆₁×#3584	C₂	semidirect
15. #16840599	C₂²	semidirect
17. #16840598	C₂²	semidirect
18. #16840598	C₂²	semidirect
20. #16840597	C₂²	semidirect
22. 2₋¹⁺⁴×D₆₁	C₂²	semidirect
24. H(5,𝔽₂)×D₆₁	C₂²	semidirect
27. C₂×#41×D₆₁	C₂²	semidirect
28. #16840579	C₂²	semidirect
29. #16840578	C₂²	semidirect
30. #16840577	C₂²	semidirect
31. #16840576	C₂²	semidirect
32. #16840575	C₂²	semidirect
33. #16840574	C₂²	semidirect
34. #16840573	C₂²	semidirect
35. #16840572	C₂²	semidirect
36. #16840571	C₂²	semidirect
37. #16840570	C₂²	semidirect
38. #16840569	C₂²	semidirect
39. #16840568	C₂²	semidirect
40. #16840567	C₂²	semidirect
41. #16840566	C₂²	semidirect
42. #16840565	C₂²	semidirect
43. #16840564	C₂²	semidirect
44. #16840563	C₂²	semidirect
45. #16840562	C₂²	semidirect
46. #16840561	C₂²	semidirect
47. #16840560	C₂²	semidirect
48. #16840559	C₂²	semidirect
49. #16840559	C₂²	semidirect
50. #16840559	C₂²	semidirect
51. #16840559	C₂²	semidirect
52. #16840559	C₂²	semidirect
53. #16840559	C₂²	semidirect
54. #16840558	C₂²	semidirect
55. C₂×#14519809	C₂²	semidirect
56. C₂×#14519806	C₂²	semidirect
57. #137×D₆₁	C₂²	semidirect
58. C₂×#14519804	C₂²	semidirect
59. C₂×#14519801	C₂²	semidirect
60. AGL(1,ℤ/8)×D₆₁	C₂²	semidirect
61. C₂×#14519799	C₂²	semidirect
62. C₂×#14519797	C₂²	semidirect
63. #135×D₆₁	C₂²	semidirect
64. #16840527	C₂²	semidirect
65. #16840527	C₂²	semidirect
66. C₂×#14519785	C₂²	semidirect
67. C₂×#14519784	C₂²	semidirect
68. C₂×#14519783	C₂²	semidirect
69. C₂²×#11758189	C₂²	semidirect
70. C₂×M₁₆×D₆₁	C₂²	semidirect
71. C₆₁×#585	C₂²	semidirect
72. C₆₁×#578	C₂²	semidirect
73. C₆₁×#577	C₂²	semidirect
74. C₆₁×#576	C₂²	semidirect
75. C₆₁×#575	C₂²	semidirect
76. C₂×#135×C₆₁	C₂²	semidirect
77. C₂×#131×C₆₁	C₂²	semidirect
81. #14519825	C₂³	semidirect
85. #14519824	C₂³	semidirect
86. #14519824	C₂³	semidirect
90. #14519823	C₂³	semidirect
91. #14519823	C₂³	semidirect
96. #14519822	C₂³	semidirect
103. C₂×#11758222	C₂³	semidirect
122. #41×D₆₁	C₂³	semidirect
123. #41×D₆₁	C₂³	semidirect
126. C₂×Q₈×D₆₁	C₂³	semidirect
130. C₂×D₄×D₆₁	C₂³	semidirect
133. #14519810	C₂³	semidirect
134. #14519809	C₂³	semidirect
135. #14519809	C₂³	semidirect
136. #14519809	C₂³	semidirect
137. #14519809	C₂³	semidirect
138. #14519808	C₂³	semidirect
139. #14519807	C₂³	semidirect
140. #14519806	C₂³	semidirect
141. #14519806	C₂³	semidirect
142. #14519806	C₂³	semidirect
143. #14519806	C₂³	semidirect
144. #14519805	C₂³	semidirect
145. #14519804	C₂³	semidirect
146. #14519804	C₂³	semidirect
147. #14519804	C₂³	semidirect
148. #14519804	C₂³	semidirect
149. #14519803	C₂³	semidirect
150. #14519802	C₂³	semidirect
151. #14519801	C₂³	semidirect
152. #14519801	C₂³	semidirect
153. #14519801	C₂³	semidirect
154. #14519801	C₂³	semidirect
155. #14519800	C₂³	semidirect
156. #14519799	C₂³	semidirect
157. #14519799	C₂³	semidirect
158. #14519799	C₂³	semidirect
159. #14519799	C₂³	semidirect
160. #14519798	C₂³	semidirect
161. #14519797	C₂³	semidirect
162. #14519797	C₂³	semidirect
163. #14519797	C₂³	semidirect
164. #14519797	C₂³	semidirect
165. #14519796	C₂³	semidirect
166. C₂×Dic₂₄₄	C₂³	semidirect
167. C₂×#11758202	C₂³	semidirect
168. Q₁₆×D₆₁	C₂³	semidirect
169. C₂×#11758190	C₂³	semidirect
170. C₂×#11758200	C₂³	semidirect
171. C₂×#11758201	C₂³	semidirect
172. SD₁₆×D₆₁	C₂³	semidirect
173. C₂×D₄₈₈	C₂³	semidirect
174. C₂×#11758199	C₂³	semidirect
175. D₈×D₆₁	C₂³	semidirect
176. #14519785	C₂³	semidirect
177. #14519784	C₂³	semidirect
178. #14519783	C₂³	semidirect
179. #14519783	C₂³	semidirect
180. C₂×#11758194	C₂³	semidirect
183. C₂×#11758189	C₂³	semidirect
184. C₂×#11758189	C₂³	semidirect
185. C₂×#11758189	C₂³	semidirect
186. C₂×#11758189	C₂³	semidirect
187. M₁₆×D₆₁	C₂³	semidirect
188. C₂²×#92418	C₂³	semidirect
189. C₂×C₈×D₆₁	C₂³	semidirect
191. 2₋¹⁺⁴×C₆₁	C₂³	semidirect
193. H(5,𝔽₂)×C₆₁	C₂³	semidirect
196. C₂×#41×C₆₁	C₂³	semidirect
197. #137×C₆₁	C₂³	semidirect
198. AGL(1,ℤ/8)×C₆₁	C₂³	semidirect
199. #135×C₆₁	C₂³	semidirect
200. #135×C₆₁	C₂³	semidirect
201. #135×C₆₁	C₂³	semidirect
202. #135×C₆₁	C₂³	semidirect
203. C₂×Q₁₆×C₆₁	C₂³	semidirect
204. C₂×SD₁₆×C₆₁	C₂³	semidirect
205. C₂×D₈×C₆₁	C₂³	semidirect
206. #131×C₆₁	C₂³	semidirect
207. #131×C₆₁	C₂³	semidirect
208. C₂×M₁₆×C₆₁	C₂³	semidirect
209. C₂²×C₈×C₆₁	C₂³	semidirect
440. #3584	D₆₁	semidirect
458. #585	C₂×D₆₁	semidirect
471. #578	C₂×D₆₁	semidirect
479. #577	C₂×D₆₁	semidirect
485. #576	C₂×D₆₁	semidirect
496. #575	C₂×D₆₁	semidirect
506. C₂×#135	C₂×D₆₁	semidirect
512. C₂×#131	C₂×D₆₁	semidirect
515. C₆₁	#63090	semidirect
526. 2₋¹⁺⁴	C₂²×D₆₁	semidirect
538. H(5,𝔽₂)	C₂²×D₆₁	semidirect
568. C₂×#41	C₂²×D₆₁	semidirect
589. #137	C₂²×D₆₁	semidirect
601. AGL(1,ℤ/8)	C₂²×D₆₁	semidirect
613. #135	C₂²×D₆₁	semidirect
614. #135	C₂²×D₆₁	semidirect
615. #135	C₂²×D₆₁	semidirect
616. #135	C₂²×D₆₁	semidirect
620. C₂×Q₁₆	C₂²×D₆₁	semidirect
625. C₂×SD₁₆	C₂²×D₆₁	semidirect
629. C₂×D₈	C₂²×D₆₁	semidirect
634. #131	C₂²×D₆₁	semidirect
635. #131	C₂²×D₆₁	semidirect
644. C₂×M₁₆	C₂²×D₆₁	semidirect
647. C₂²×C₈	C₂²×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
#585×D₆₁	2
#21460604	2
#21460601	2
#21460597	2
#21460594	2
#21460593	2
#21460592	2
#21460590	2
#21460588	2
C₂×#16840559	2
#575×D₆₁	2
C₂×#16840527	2
C₆₁×#3584	2
#63090	61