Subgroups — #21460597

Order 7808.

1464 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	#16840599	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840571	C₂	1	3	yes	maximal, complemented
4	#16840570	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840568	C₂	1	3	yes	maximal, complemented
6	#16840567	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840566	C₂	1	3	yes	maximal, complemented
8	#16840565	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840564	C₂	1	3	yes	maximal, complemented
10	#16840561	C₂	1	3	yes	maximal, complemented
11	#16840559	C₂	1	3	yes	maximal, complemented
12	C₂×#14519804	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₆₁	C₂	1	3	yes	maximal, complemented
14	#16840527	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
16	#14519825	—	2	1	no	—
17	#14519825	C₂²	1	3	yes	complemented
18	#14519823	—	2	1	no	—
19	#14519823	—	2	3	no	—
20	#14519823	C₂²	1	3	yes	complemented
21	#14519823	C₂²	1	3	yes	complemented
22	#14519823	C₂²	1	1	yes	characteristic, complemented
23	#14519823	C₂²	1	1	yes	characteristic, complemented
24	#14519822	—	2	3	no	—
25	#14519822	C₂²	1	3	yes	complemented
26	C₂×#11758226	—	2	1	no	—
27	C₂×#11758226	C₂²	1	3	yes	complemented
28	#41×D₆₁	—	2	1	no	—
29	#41×D₆₁	—	2	3	no	—
30	#41×D₆₁	C₂²	1	1	yes	characteristic
31	#41×D₆₁	C₂²	1	3	yes	complemented
32	#41×D₆₁	C₂²	1	3	yes	complemented
33	C₂×D₄×D₆₁	—	2	3	no	—
34	C₂×D₄×D₆₁	C₂²	1	3	yes	complemented
35	#14519809	C₂²	1	3	yes	complemented
36	#14519809	C₂²	1	3	yes	complemented
37	#14519808	C₂²	1	3	yes	complemented
38	#14519806	C₂²	1	1	yes	characteristic, complemented
39	#14519806	C₂²	1	3	yes	complemented
40	#14519805	C₂²	1	3	yes	complemented
41	#14519805	C₂²	1	3	yes	complemented
42	#14519804	C₂²	1	6	yes	complemented
43	#14519804	C₂²	1	3	yes	complemented
44	#14519804	C₂²	1	6	yes	complemented
45	#14519804	C₂²	1	6	yes	complemented
46	#14519804	C₂²	1	3	yes	complemented
47	#14519803	C₂²	1	3	yes	complemented
48	#14519802	C₂²	1	3	yes	complemented
49	#14519802	C₂²	1	3	yes	complemented
50	#14519801	C₂²	1	3	yes	complemented
51	#14519801	C₂²	1	3	yes	complemented
52	#14519800	C₂²	1	6	yes	complemented
53	#14519799	C₂²	1	3	yes	complemented
54	#14519798	C₂²	1	6	yes	complemented
55	#14519797	C₂²	1	3	yes	complemented
56	#14519797	C₂²	1	3	yes	complemented
57	C₂×#11758201	C₂²	1	3	yes	complemented
58	SD₁₆×D₆₁	C₂²	1	6	yes	complemented
59	C₂×D₄₈₈	C₂²	1	3	yes	complemented
60	C₂×#11758199	C₂²	1	3	yes	complemented
61	D₈×D₆₁	C₂²	1	6	yes	complemented
62	#14519785	C₂²	1	3	yes	complemented
63	#14519784	C₂²	1	1	yes	characteristic, complemented
64	#14519783	C₂²	1	3	yes	complemented
65	C₂×#11758189	C₂²	1	3	yes	complemented
66	M₁₆×D₆₁	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic, complemented
69	#137×C₆₁	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₆₁	C₂²	1	3	yes	complemented
71	#135×C₆₁	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₆₁	C₂²	1	3	yes	complemented
73	#131×C₆₁	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₆₁	—	2	3	no	—
75	#41×C₆₁	—	2	1	no	—
76	#41×C₆₁	—	2	3	no	—
77	#41×C₆₁	C₂³	1	3	yes	—
78	#41×C₆₁	C₂³	1	1	yes	characteristic
79	#41×C₆₁	C₂³	1	3	yes	complemented
80	C₂×Q₈×C₆₁	—	2	1	no	—
81	C₂×Q₈×C₆₁	C₂³	1	3	yes	complemented
82	C₂×D₄×C₆₁	—	2	3	no	—
83	C₂×D₄×C₆₁	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₆₁	—	2	6	no	—
85	C₂×C₂²⋊D₆₁	—	2	3	no	—
86	#11758226	—	2	1	no	—
87	#11758226	—	2	1	no	—
88	#11758226	—	2	3	no	—
89	#11758226	—	2	3	no	—
90	#11758226	—	2	3	no	—
91	#11758226	D₄	1	1	yes	characteristic
92	#11758226	C₂³	1	3	yes	—
93	#11758226	C₂³	1	3	yes	—
94	#11758226	C₂³	1	6	yes	complemented
95	Q₈×D₆₁	—	2	3	no	—
96	Q₈×D₆₁	D₄	1	1	yes	characteristic
97	Q₈×D₆₁	C₂³	1	1	yes	characteristic
98	Q₈×D₆₁	C₂³	1	3	yes	complemented
99	#11758224	—	2	3	no	—
100	#11758224	—	2	3	no	—
101	#11758224	—	2	3	no	—
102	#11758224	D₄	1	3	yes	—
103	#11758224	C₂³	1	1	yes	characteristic
104	#11758224	C₂³	1	3	yes	—
105	D₄×D₆₁	—	2	3	no	—
106	D₄×D₆₁	—	2	3	no	—
107	D₄×D₆₁	—	2	3	no	—
108	D₄×D₆₁	—	2	3	no	—
109	D₄×D₆₁	—	2	6	no	—
110	D₄×D₆₁	—	2	6	no	—
111	D₄×D₆₁	—	2	3	no	—
112	D₄×D₆₁	—	2	3	no	—
113	D₄×D₆₁	—	2	3	no	—
114	D₄×D₆₁	D₄	1	3	yes	—
115	D₄×D₆₁	C₂³	1	3	yes	—
116	D₄×D₆₁	C₂³	1	6	yes	—
117	D₄×D₆₁	C₂³	1	3	yes	complemented
118	#11758222	—	2	6	no	—
119	#11758222	—	2	3	no	—
120	#11758222	—	2	3	no	—
121	#11758222	—	2	3	no	—
122	#11758222	—	2	3	no	—
123	#11758222	C₂³	1	3	yes	—
124	#11758222	C₂³	1	3	yes	—
125	#11758222	C₂³	1	3	yes	complemented
126	C₂×D₂₄₄	—	2	3	no	—
127	C₂×D₂₄₄	—	2	3	no	—
128	C₂×D₂₄₄	—	2	3	no	—
129	C₂×D₂₄₄	C₂³	1	3	yes	—
130	C₂×D₂₄₄	C₂³	1	3	yes	complemented
131	C₂×C₄×D₆₁	—	2	3	no	—
132	C₂×C₄×D₆₁	—	2	3	no	—
133	C₂×C₄×D₆₁	—	2	3	no	—
134	C₂×C₄×D₆₁	C₂³	1	3	yes	—
135	Q₁₆×C₆₁	C₂³	1	3	yes	complemented
136	SD₁₆×C₆₁	C₂³	1	3	yes	complemented
137	SD₁₆×C₆₁	C₂³	1	6	yes	complemented
138	SD₁₆×C₆₁	C₂³	1	1	yes	characteristic, complemented
139	D₈×C₆₁	C₂³	1	3	yes	complemented
140	M₁₆×C₆₁	C₂³	1	3	yes	complemented
141	C₂×C₈×C₆₁	C₂³	1	3	yes	complemented
142	#11758202	C₂³	1	3	yes	complemented
143	#11758202	C₂³	1	1	yes	characteristic, complemented
144	#11758201	C₂³	1	6	yes	complemented
145	#11758201	C₂³	1	3	yes	complemented
146	#11758201	C₂³	1	3	yes	complemented
147	#11758200	C₂³	1	3	yes	complemented
148	#11758200	C₂³	1	1	yes	characteristic, complemented
149	#11758199	C₂³	1	3	yes	complemented
150	#11758199	C₂³	1	6	yes	complemented
151	#11758199	C₂³	1	3	yes	complemented
152	#11758194	C₂³	1	3	yes	complemented
153	C₂×#92418	C₂³	1	3	yes	complemented
154	Dic₂₄₄	C₂³	1	1	yes	characteristic, complemented
155	D₄₈₈	C₂³	1	6	yes	complemented
156	D₄₈₈	C₂³	1	3	yes	complemented
157	#11758190	C₂³	1	3	yes	complemented
158	#11758190	C₂³	1	3	yes	complemented
159	#11758189	C₂³	1	3	yes	—
160	#11758189	C₂³	1	1	yes	characteristic
161	#11758189	C₂³	1	3	yes	complemented
162	#11758189	C₂³	1	3	yes	complemented
163	C₈×D₆₁	C₂³	1	6	yes	complemented
164	C₂³×C₆₁	—	2	3	no	—
165	C₂²×D₆₁	—	2	3	no	—
166	C₂²×D₆₁	—	2	3	no	—
167	C₂²×D₆₁	—	2	3	no	—
168	C₂²×D₆₁	—	2	3	no	—
169	C₂²×D₆₁	—	2	6	no	—
170	C₂²×D₆₁	—	8	6	no	—
171	C₂²×D₆₁	C₂×D₄	1	3	yes	—
172	Q₈×C₆₁	—	2	3	no	—
173	Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₆₁	C₂⁴	1	3	yes	—
175	Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
176	D₄×C₆₁	—	2	3	no	—
177	D₄×C₆₁	—	2	3	no	—
178	D₄×C₆₁	—	2	3	no	—
179	D₄×C₆₁	C₂×D₄	1	3	yes	—
180	D₄×C₆₁	C₂⁴	1	1	yes	characteristic
181	D₄×C₆₁	C₂⁴	1	3	yes	—
182	C₂×C₄×C₆₁	—	2	3	no	—
183	C₂×C₄×C₆₁	—	2	3	no	—
184	C₂×C₄×C₆₁	—	2	3	no	—
185	C₂×C₄×C₆₁	C₂⁴	1	3	yes	—
186	C₂²⋊D₆₁	—	2	3	no	—
187	C₂²⋊D₆₁	—	2	3	no	—
188	C₂²⋊D₆₁	—	2	1	no	—
189	C₂²⋊D₆₁	—	2	3	no	—
190	C₂²⋊D₆₁	—	2	3	no	—
191	C₂²⋊D₆₁	—	2	6	no	—
192	C₂²⋊D₆₁	—	2	3	no	—
193	C₂²⋊D₆₁	C₂×D₄	1	6	yes	—
194	C₂×Dic₆₁	—	2	1	no	—
195	C₂×Dic₆₁	—	2	3	no	—
196	C₂×Dic₆₁	C₂×D₄	1	3	yes	—
197	D₂₄₄	—	2	3	no	—
198	D₂₄₄	—	2	3	no	—
199	D₂₄₄	—	2	6	no	—
200	D₂₄₄	—	2	3	no	—
201	D₂₄₄	—	2	3	no	—
202	D₂₄₄	C₂×D₄	1	3	yes	—
203	D₂₄₄	C₂⁴	1	3	yes	—
204	D₂₄₄	C₂⁴	1	3	yes	—
205	C₄×D₆₁	—	2	1	no	—
206	C₄×D₆₁	—	2	3	no	—
207	C₄×D₆₁	—	2	3	no	—
208	C₄×D₆₁	—	2	3	no	—
209	C₄×D₆₁	—	2	3	no	—
210	C₄×D₆₁	—	2	3	no	—
211	C₄×D₆₁	—	2	6	no	—
212	C₄×D₆₁	C₂×D₄	1	3	yes	—
213	C₄×D₆₁	C₂×D₄	1	3	yes	—
214	C₄×D₆₁	C₂⁴	1	3	yes	—
215	C₄×D₆₁	C₂⁴	1	1	yes	characteristic
216	Dic₁₂₂	—	2	1	no	—
217	Dic₁₂₂	—	2	3	no	—
218	Dic₁₂₂	C₂×D₄	1	3	yes	—
219	Dic₁₂₂	C₂⁴	1	1	yes	characteristic
220	Dic₁₂₂	C₂⁴	1	1	yes	characteristic
221	C₈×C₆₁	C₂⁴	1	3	yes	—
222	C₈×C₆₁	C₂⁴	1	1	yes	characteristic
223	#92418	C₂⁴	1	3	yes	—
224	#92418	C₂⁴	1	1	yes	characteristic
225	C₂²×C₆₁	—	2	1	no	—
226	C₂²×C₆₁	—	2	3	no	—
227	C₂²×C₆₁	—	8	3	no	—
228	C₂²×C₆₁	C₂²×D₄	1	3	yes	—
229	C₂×D₆₁	—	2	3	no	—
230	C₂×D₆₁	—	2	3	no	—
231	C₂×D₆₁	—	4	3	no	—
232	C₂×D₆₁	—	4	6	no	—
233	C₂×D₆₁	—	8	3	no	—
234	C₂×D₆₁	—	8	6	no	—
235	C₂×D₆₁	—	8	3	no	—
236	C₂×D₆₁	—	8	3	no	—
237	C₂×D₆₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₆₁	C₂²×D₄	1	3	yes	—
239	C₄×C₆₁	—	2	1	no	—
240	C₄×C₆₁	—	2	3	no	—
241	C₄×C₆₁	C₂²×D₄	1	3	yes	—
242	C₄×C₆₁	C₂⁵	1	1	yes	characteristic
243	Dic₆₁	—	2	1	no	—
244	Dic₆₁	—	2	1	no	—
245	Dic₆₁	C₂²×D₄	1	3	yes	—
246	Dic₆₁	C₂²×D₄	1	1	yes	characteristic
247	#3585	—	61	1	no	maximal, Sylow
248	C₂×C₆₁	—	2	3	no	—
249	C₂×C₆₁	—	4	3	no	—
250	C₂×C₆₁	—	4	1	no	—
251	C₂×C₆₁	C₂³×D₄	1	1	yes	characteristic
252	D₆₁	—	2	1	no	—
253	D₆₁	—	2	3	no	—
254	D₆₁	—	4	3	no	—
255	D₆₁	—	4	3	no	—
256	#585	—	61	1	no	—
257	C₂×H(5,𝔽₂)	—	61	1	no	—
258	#577	—	61	1	no	—
259	#577	—	61	3	no	—
260	#577	—	61	3	no	—
261	#577	D₆₁	1	1	yes	characteristic, complemented
262	#576	—	61	1	no	—
263	#576	—	61	3	no	—
264	#576	—	61	3	no	—
265	#576	—	61	1	no	—
266	#575	—	61	3	no	—
267	#575	—	61	3	no	—
268	C₂×AGL(1,ℤ/8)	—	61	3	no	—
269	C₂×AGL(1,ℤ/8)	—	61	3	no	—
270	#568	—	61	1	no	—
271	C₆₁	#3585	1	1	yes	characteristic, complemented, Sylow
272	2₋¹⁺⁴	—	61	3	no	—
273	2₋¹⁺⁴	—	122	1	no	—
274	2₋¹⁺⁴	C₂×D₆₁	1	1	yes	characteristic, complemented
275	H(5,𝔽₂)	—	61	3	no	—
276	H(5,𝔽₂)	—	61	1	no	—
277	H(5,𝔽₂)	—	61	1	no	—
278	H(5,𝔽₂)	—	61	3	no	—
279	H(5,𝔽₂)	—	61	3	no	—
280	H(5,𝔽₂)	—	122	3	no	—
281	H(5,𝔽₂)	—	122	3	no	—
282	H(5,𝔽₂)	—	122	1	no	—
283	H(5,𝔽₂)	C₂×D₆₁	1	1	yes	characteristic, complemented
284	C₂×#41	—	61	1	no	—
285	C₂×#41	—	61	3	no	—
286	C₂×#41	—	61	3	no	—
287	C₂×#41	—	61	3	no	—
288	C₂×#41	—	122	1	no	—
289	C₂×#41	—	122	1	no	—
290	C₂×#41	—	122	3	no	—
291	C₂²×D₄	—	61	3	no	—
292	C₂²×D₄	—	122	3	no	—
293	#137	—	61	3	no	—
294	#137	—	61	3	no	—
295	#137	—	61	3	no	—
296	#137	—	61	1	no	—
297	#137	—	61	3	no	—
298	#137	C₂×D₆₁	1	3	yes	complemented
299	AGL(1,ℤ/8)	—	61	3	no	—
300	AGL(1,ℤ/8)	—	61	3	no	—
301	AGL(1,ℤ/8)	—	61	3	no	—
302	AGL(1,ℤ/8)	—	61	6	no	—
303	AGL(1,ℤ/8)	—	61	3	no	—
304	AGL(1,ℤ/8)	—	61	6	no	—
305	AGL(1,ℤ/8)	—	61	6	no	—
306	AGL(1,ℤ/8)	—	61	3	no	—
307	AGL(1,ℤ/8)	—	61	3	no	—
308	AGL(1,ℤ/8)	—	61	3	no	—
309	AGL(1,ℤ/8)	—	61	3	no	—
310	AGL(1,ℤ/8)	—	61	3	no	—
311	AGL(1,ℤ/8)	C₂×D₆₁	1	3	yes	complemented
312	#135	—	61	3	no	—
313	#135	—	61	3	no	—
314	#135	—	61	6	no	—
315	#135	—	61	6	no	—
316	#135	—	61	3	no	—
317	#135	C₂×D₆₁	1	3	yes	complemented
318	C₂×SD₁₆	—	61	3	no	—
319	C₂×SD₁₆	—	61	6	no	—
320	C₂×SD₁₆	C₂×D₆₁	1	3	yes	complemented
321	C₂×D₈	—	61	3	no	—
322	C₂×D₈	—	61	6	no	—
323	C₂×D₈	—	61	3	no	—
324	#131	—	61	1	no	—
325	#131	—	61	3	no	—
326	#131	—	61	3	no	—
327	#131	C₂×D₆₁	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	61	3	no	—
329	C₂×M₁₆	—	61	3	no	—
330	C₂⁴	—	122	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	3	no	—
333	#41	—	61	1	no	—
334	#41	—	61	3	no	—
335	#41	—	61	3	no	—
336	#41	—	61	6	no	—
337	#41	—	61	3	no	—
338	#41	—	61	3	no	—
339	#41	—	61	3	no	—
340	#41	—	61	1	no	—
341	#41	—	61	3	no	—
342	#41	—	61	3	no	—
343	#41	—	122	3	no	—
344	#41	—	122	3	no	—
345	#41	—	122	6	no	—
346	#41	—	122	3	no	—
347	#41	—	122	3	no	—
348	#41	—	122	3	no	—
349	#41	—	122	3	no	—
350	#41	—	122	3	no	—
351	#41	—	122	3	no	—
352	#41	—	122	3	no	—
353	#41	—	122	3	no	—
354	#41	—	122	1	no	—
355	#41	—	122	1	no	—
356	#41	C₂²×D₆₁	1	3	yes	—
357	#41	C₂²×D₆₁	1	1	yes	characteristic
358	#41	C₂²×D₆₁	1	3	yes	complemented
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	61	1	no	—
361	C₂×Q₈	—	61	3	no	—
362	C₂×Q₈	—	61	1	no	—
363	C₂×Q₈	—	122	3	no	—
364	C₂×Q₈	C₂²×D₆₁	1	3	yes	complemented
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	61	3	no	—
367	C₂×D₄	—	61	3	no	—
368	C₂×D₄	—	61	6	no	—
369	C₂×D₄	—	61	3	no	—
370	C₂×D₄	—	61	3	no	—
371	C₂×D₄	—	61	3	no	—
372	C₂×D₄	—	122	3	no	—
373	C₂×D₄	—	122	3	no	—
374	C₂×D₄	—	122	3	no	—
375	C₂×D₄	—	122	3	no	—
376	C₂×D₄	—	122	3	no	—
377	C₂×D₄	—	122	3	no	—
378	C₂×D₄	—	122	6	no	—
379	C₂×D₄	—	122	3	no	—
380	C₂×D₄	—	122	6	no	—
381	C₂×D₄	—	122	3	no	—
382	C₂×D₄	—	122	3	no	—
383	C₂×D₄	—	122	6	no	—
384	C₂×D₄	—	122	3	no	—
385	C₂×D₄	—	122	3	no	—
386	C₂×D₄	C₂²×D₆₁	1	3	yes	—
387	C₂²×C₄	—	61	3	no	—
388	C₂²×C₄	—	122	3	no	—
389	C₂²×C₄	—	122	3	no	—
390	C₂²×C₄	—	122	3	no	—
391	Q₁₆	—	61	1	no	—
392	Q₁₆	—	61	3	no	—
393	Q₁₆	—	61	1	no	—
394	Q₁₆	C₂²×D₆₁	1	3	yes	complemented
395	SD₁₆	—	61	6	no	—
396	SD₁₆	—	61	3	no	—
397	SD₁₆	—	61	3	no	—
398	SD₁₆	—	61	3	no	—
399	SD₁₆	—	61	1	no	—
400	SD₁₆	—	61	3	no	—
401	SD₁₆	—	61	3	no	—
402	SD₁₆	C₂²×D₆₁	1	6	yes	complemented
403	SD₁₆	C₂²×D₆₁	1	3	yes	complemented
404	SD₁₆	C₂²×D₆₁	1	1	yes	characteristic, complemented
405	D₈	—	61	6	no	—
406	D₈	—	61	3	no	—
407	D₈	—	61	3	no	—
408	D₈	—	61	6	no	—
409	D₈	—	61	3	no	—
410	D₈	C₂²×D₆₁	1	3	yes	complemented
411	M₁₆	—	61	3	no	—
412	M₁₆	—	61	3	no	—
413	M₁₆	—	61	1	no	—
414	M₁₆	—	61	3	no	—
415	M₁₆	—	61	3	no	—
416	M₁₆	C₂²×D₆₁	1	3	yes	complemented
417	C₂×C₈	—	61	3	no	—
418	C₂×C₈	—	61	6	no	—
419	C₂×C₈	C₂²×D₆₁	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	61	3	no	—
422	C₂³	—	122	3	no	—
423	C₂³	—	122	6	no	—
424	C₂³	—	122	3	no	—
425	C₂³	—	122	3	no	—
426	C₂³	—	122	3	no	—
427	C₂³	—	488	6	no	—
428	Q₈	—	2	3	no	—
429	Q₈	—	61	3	no	—
430	Q₈	—	61	1	no	—
431	Q₈	—	61	1	no	—
432	Q₈	—	122	3	no	—
433	Q₈	—	122	1	no	—
434	Q₈	D₄×D₆₁	1	1	yes	characteristic
435	Q₈	C₂³×D₆₁	1	3	yes	—
436	Q₈	C₂³×D₆₁	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	61	6	no	—
441	D₄	—	61	3	no	—
442	D₄	—	61	3	no	—
443	D₄	—	61	3	no	—
444	D₄	—	122	3	no	—
445	D₄	—	122	3	no	—
446	D₄	—	122	6	no	—
447	D₄	—	122	3	no	—
448	D₄	—	122	6	no	—
449	D₄	—	122	3	no	—
450	D₄	—	122	3	no	—
451	D₄	—	122	1	no	—
452	D₄	—	122	3	no	—
453	D₄	—	122	3	no	—
454	D₄	—	122	3	no	—
455	D₄	—	122	3	no	—
456	D₄	D₄×D₆₁	1	3	yes	—
457	D₄	C₂³×D₆₁	1	1	yes	characteristic
458	D₄	C₂³×D₆₁	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	61	3	no	—
463	C₂×C₄	—	61	3	no	—
464	C₂×C₄	—	61	3	no	—
465	C₂×C₄	—	61	3	no	—
466	C₂×C₄	—	61	1	no	—
467	C₂×C₄	—	122	3	no	—
468	C₂×C₄	—	122	3	no	—
469	C₂×C₄	—	122	6	no	—
470	C₂×C₄	—	122	1	no	—
471	C₂×C₄	—	122	3	no	—
472	C₂×C₄	—	122	1	no	—
473	C₂×C₄	—	122	3	no	—
474	C₂×C₄	—	122	3	no	—
475	C₂×C₄	—	122	3	no	—
476	C₂×C₄	C₂³×D₆₁	1	3	yes	—
477	C₈	—	61	3	no	—
478	C₈	—	61	1	no	—
479	C₈	C₂³×D₆₁	1	3	yes	—
480	C₈	C₂³×D₆₁	1	1	yes	characteristic
481	C₂²	—	2	1	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	61	1	no	—
485	C₂²	—	61	3	no	—
486	C₂²	—	122	3	no	—
487	C₂²	—	122	3	no	—
488	C₂²	—	488	3	no	—
489	C₂²	—	488	3	no	—
490	C₂²	—	488	3	no	—
491	C₂²	—	488	6	no	—
492	C₂²	—	244	3	no	—
493	C₂²	—	244	6	no	—
494	C₂²	C₂×D₄×D₆₁	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	61	1	no	—
498	C₄	—	61	3	no	—
499	C₄	—	122	1	no	—
500	C₄	—	122	1	no	—
501	C₄	C₂×D₄×D₆₁	1	3	yes	—
502	C₄	C₂⁴×D₆₁	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	1	no	—
506	C₂	—	122	3	no	—
507	C₂	—	122	1	no	—
508	C₂	—	244	3	no	—
509	C₂	—	244	3	no	—
510	C₂	C₂²×D₄×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₆₁
commutator	C₄×C₆₁	C₂⁵
Frattini	C₄	C₂⁴×D₆₁
Fitting	C₆₁×#577	C₂
socle	C₂×C₆₁	C₂³×D₄
hypercenter	#577	D₆₁
hypocenter	C₆₁	#3585
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #16840599	C₂	semidirect
2. H(5,𝔽₂)×D₆₁	C₂	semidirect
3. #16840571	C₂	semidirect
4. #16840570	C₂	semidirect
5. #16840568	C₂	semidirect
6. #16840567	C₂	semidirect
7. #16840566	C₂	semidirect
8. #16840565	C₂	semidirect
9. #16840564	C₂	semidirect
10. #16840561	C₂	semidirect
11. #16840559	C₂	semidirect
12. C₂×#14519804	C₂	semidirect
13. AGL(1,ℤ/8)×D₆₁	C₂	semidirect
14. #16840527	C₂	semidirect
15. C₆₁×#577	C₂	semidirect
17. #14519825	C₂²	semidirect
20. #14519823	C₂²	semidirect
21. #14519823	C₂²	semidirect
22. #14519823	C₂²	semidirect
23. #14519823	C₂²	semidirect
25. #14519822	C₂²	semidirect
27. C₂×#11758226	C₂²	semidirect
31. #41×D₆₁	C₂²	semidirect
32. #41×D₆₁	C₂²	semidirect
34. C₂×D₄×D₆₁	C₂²	semidirect
35. #14519809	C₂²	semidirect
36. #14519809	C₂²	semidirect
37. #14519808	C₂²	semidirect
38. #14519806	C₂²	semidirect
39. #14519806	C₂²	semidirect
40. #14519805	C₂²	semidirect
41. #14519805	C₂²	semidirect
42. #14519804	C₂²	semidirect
43. #14519804	C₂²	semidirect
44. #14519804	C₂²	semidirect
45. #14519804	C₂²	semidirect
46. #14519804	C₂²	semidirect
47. #14519803	C₂²	semidirect
48. #14519802	C₂²	semidirect
49. #14519802	C₂²	semidirect
50. #14519801	C₂²	semidirect
51. #14519801	C₂²	semidirect
52. #14519800	C₂²	semidirect
53. #14519799	C₂²	semidirect
54. #14519798	C₂²	semidirect
55. #14519797	C₂²	semidirect
56. #14519797	C₂²	semidirect
57. C₂×#11758201	C₂²	semidirect
58. SD₁₆×D₆₁	C₂²	semidirect
59. C₂×D₄₈₈	C₂²	semidirect
60. C₂×#11758199	C₂²	semidirect
61. D₈×D₆₁	C₂²	semidirect
62. #14519785	C₂²	semidirect
63. #14519784	C₂²	semidirect
64. #14519783	C₂²	semidirect
65. C₂×#11758189	C₂²	semidirect
66. M₁₆×D₆₁	C₂²	semidirect
67. 2₋¹⁺⁴×C₆₁	C₂²	semidirect
68. H(5,𝔽₂)×C₆₁	C₂²	semidirect
69. #137×C₆₁	C₂²	semidirect
70. AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
71. #135×C₆₁	C₂²	semidirect
72. C₂×SD₁₆×C₆₁	C₂²	semidirect
73. #131×C₆₁	C₂²	semidirect
79. #41×C₆₁	C₂³	semidirect
81. C₂×Q₈×C₆₁	C₂³	semidirect
94. #11758226	C₂³	semidirect
98. Q₈×D₆₁	C₂³	semidirect
117. D₄×D₆₁	C₂³	semidirect
125. #11758222	C₂³	semidirect
130. C₂×D₂₄₄	C₂³	semidirect
135. Q₁₆×C₆₁	C₂³	semidirect
136. SD₁₆×C₆₁	C₂³	semidirect
137. SD₁₆×C₆₁	C₂³	semidirect
138. SD₁₆×C₆₁	C₂³	semidirect
139. D₈×C₆₁	C₂³	semidirect
140. M₁₆×C₆₁	C₂³	semidirect
141. C₂×C₈×C₆₁	C₂³	semidirect
142. #11758202	C₂³	semidirect
143. #11758202	C₂³	semidirect
144. #11758201	C₂³	semidirect
145. #11758201	C₂³	semidirect
146. #11758201	C₂³	semidirect
147. #11758200	C₂³	semidirect
148. #11758200	C₂³	semidirect
149. #11758199	C₂³	semidirect
150. #11758199	C₂³	semidirect
151. #11758199	C₂³	semidirect
152. #11758194	C₂³	semidirect
153. C₂×#92418	C₂³	semidirect
154. Dic₂₄₄	C₂³	semidirect
155. D₄₈₈	C₂³	semidirect
156. D₄₈₈	C₂³	semidirect
157. #11758190	C₂³	semidirect
158. #11758190	C₂³	semidirect
161. #11758189	C₂³	semidirect
162. #11758189	C₂³	semidirect
163. C₈×D₆₁	C₂³	semidirect
261. #577	D₆₁	semidirect
271. C₆₁	#3585	semidirect
274. 2₋¹⁺⁴	C₂×D₆₁	semidirect
283. H(5,𝔽₂)	C₂×D₆₁	semidirect
298. #137	C₂×D₆₁	semidirect
311. AGL(1,ℤ/8)	C₂×D₆₁	semidirect
317. #135	C₂×D₆₁	semidirect
320. C₂×SD₁₆	C₂×D₆₁	semidirect
327. #131	C₂×D₆₁	semidirect
358. #41	C₂²×D₆₁	semidirect
364. C₂×Q₈	C₂²×D₆₁	semidirect
394. Q₁₆	C₂²×D₆₁	semidirect
402. SD₁₆	C₂²×D₆₁	semidirect
403. SD₁₆	C₂²×D₆₁	semidirect
404. SD₁₆	C₂²×D₆₁	semidirect
410. D₈	C₂²×D₆₁	semidirect
416. M₁₆	C₂²×D₆₁	semidirect
419. C₂×C₈	C₂²×D₆₁	semidirect