Subgroups — #29645679

Order 15616.

750 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454781	C₂	1	1	yes	maximal, characteristic
2	C₈×#11758222	C₂	1	1	yes	maximal, characteristic
3	#21454458	C₂	1	1	yes	maximal, characteristic
4	#21444120	C₂	1	1	yes	maximal, characteristic, complemented
5	#21444119	C₂	1	1	yes	maximal, characteristic, complemented
6	#21444117	C₂	1	1	yes	maximal, characteristic, complemented
7	#21444116	C₂	1	1	yes	maximal, characteristic, complemented
8	#21444110	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444105	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444102	C₂	1	1	yes	maximal, characteristic, complemented
11	#21444101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#11758189	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#11758189	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11758222	C₂²	1	1	yes	characteristic
17	#16839890	C₄	1	2	yes	—
18	C₈×Dic₁₂₂	C₄	1	2	yes	—
19	#16839838	C₄	1	2	yes	—
20	#16839835	C₄	1	2	yes	—
21	#16839831	C₄	1	2	yes	—
22	C₈×D₂₄₄	C₄	1	2	yes	—
23	C₈×C₂²⋊D₆₁	C₄	1	2	yes	—
24	C₈×C₂²⋊D₆₁	C₄	1	2	yes	—
25	#16839822	C₄	1	2	yes	—
26	#16839820	C₄	1	2	yes	—
27	#16839815	C₂²	1	1	yes	characteristic
28	#16839815	C₂²	1	1	yes	characteristic
29	#16839815	C₂²	1	1	yes	characteristic
30	#16839813	C₂²	1	1	yes	characteristic
31	#16839813	C₂²	1	1	yes	characteristic
32	#16839813	C₂²	1	1	yes	characteristic
33	#16839813	C₂²	1	1	yes	characteristic
34	#16839813	C₂²	1	1	yes	characteristic
35	#16839813	C₂²	1	1	yes	characteristic
36	#16839787	C₄	1	2	yes	—
37	#16839727	C₄	1	2	yes	—
38	C₄×#11758189	C₂²	1	1	yes	characteristic
39	C₄×#11758189	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
44	#16839484	C₂²	1	1	yes	characteristic
45	#16839484	C₂²	1	1	yes	characteristic
46	#16839484	C₂²	1	1	yes	characteristic
47	#16839484	C₂²	1	1	yes	characteristic
48	#16839483	C₂²	1	1	yes	characteristic
49	#16839483	C₂²	1	1	yes	characteristic
50	#16839483	C₂²	1	1	yes	characteristic
51	#16839483	C₂²	1	1	yes	characteristic
52	C₈×#92418	C₂²	1	1	yes	characteristic
53	C₈×#92418	C₂²	1	1	yes	characteristic
54	C₈×#92418	C₂²	1	1	yes	characteristic
55	C₈×#92418	C₂²	1	1	yes	characteristic
56	C₆₁×#431	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#322	C₂²	1	1	yes	characteristic
60	C₆₁×#322	C₂²	1	1	yes	characteristic
61	C₈²×C₆₁	C₂²	1	1	yes	characteristic
62	C₈²×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
64	C₂×#11758189	C₂×C₄	1	2	yes	—
65	C₂×#11758189	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
70	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
72	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
73	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
78	#14519736	C₂×C₄	1	1	yes	characteristic
79	#14519734	C₂×C₄	1	1	yes	characteristic
80	#14519734	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₆₁	C₂³	1	1	yes	characteristic
82	C₄²×D₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊#92418	C₂×C₄	1	2	yes	—
84	C₄⋊#92418	C₂×C₄	1	2	yes	—
85	C₄⋊#92418	C₂×C₄	1	2	yes	—
86	#14519706	C₂×C₄	1	2	yes	—
87	#14519706	C₂×C₄	1	2	yes	—
88	#14519706	C₂×C₄	1	2	yes	—
89	#14519706	C₂×C₄	1	2	yes	—
90	#14519706	C₂×C₄	1	2	yes	—
91	#14519706	C₂×C₄	1	2	yes	—
92	C₂²⋊#92418	C₂×C₄	1	2	yes	—
93	C₂²⋊#92418	C₂×C₄	1	2	yes	—
94	C₂²⋊#92418	C₂×C₄	1	2	yes	—
95	#14519689	C₂×C₄	1	2	yes	—
96	#14519689	C₂×C₄	1	2	yes	—
97	#14519689	C₂×C₄	1	2	yes	—
98	#14519689	C₂×C₄	1	2	yes	—
99	#14519689	C₂×C₄	1	2	yes	—
100	#14519689	C₂×C₄	1	2	yes	—
101	#14519687	C₂×C₄	1	2	yes	—
102	#14519687	C₂×C₄	1	2	yes	—
103	C₄×#92418	C₂³	1	1	yes	characteristic
104	C₄×#92418	C₂³	1	1	yes	characteristic
105	C₄×#92418	C₂³	1	1	yes	characteristic
106	C₄×#92418	C₂³	1	1	yes	characteristic
107	C₄×#92418	C₂³	1	1	yes	characteristic
108	C₄×#92418	C₂³	1	1	yes	characteristic
109	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
110	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
111	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
112	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
113	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
114	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
118	#97×C₆₁	C₂×C₄	1	2	yes	—
119	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
120	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₆₁	C₄²	1	1	yes	characteristic
130	C₂×C₂²⋊D₆₁	C₄²	1	1	yes	characteristic
131	#11758222	—	2	4	no	—
132	C₂×D₂₄₄	C₄²	1	1	yes	characteristic
133	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₁₂₂	C₄²	1	1	yes	characteristic
140	M₁₆×C₆₁	—	2	4	no	—
141	C₂×C₈×C₆₁	—	2	4	no	—
142	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
148	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
152	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
153	C₂²⋊Dic₆₁	C₄²	1	1	yes	characteristic
154	#11758198	C₄²	1	1	yes	characteristic
155	#11758198	C₄²	1	1	yes	characteristic
156	#11758198	C₄²	1	1	yes	characteristic
157	#11758198	C₄²	1	1	yes	characteristic
158	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
159	C₄⋊Dic₆₁	C₄²	1	1	yes	characteristic
160	#11758196	C₄²	1	1	yes	characteristic
161	#11758196	C₄²	1	1	yes	characteristic
162	#11758196	C₄²	1	1	yes	characteristic
163	#11758196	C₄²	1	1	yes	characteristic
164	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
170	C₂×#92418	C₂²×C₄	1	2	yes	—
171	C₂×#92418	C₂²×C₄	1	2	yes	—
172	C₂×#92418	C₂²×C₄	1	2	yes	—
173	C₂×#92418	C₂²×C₄	1	2	yes	—
174	C₂×#92418	C₂²×C₄	1	2	yes	—
175	C₂×#92418	C₂²×C₄	1	2	yes	—
176	#11758189	—	2	4	no	—
177	#11758189	—	2	4	no	—
178	C₈×D₆₁	—	2	4	no	—
179	C₈×D₆₁	—	2	4	no	—
180	C₈×D₆₁	—	2	4	no	—
181	C₈×D₆₁	—	2	4	no	—
182	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
183	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
184	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
194	C₂²⋊D₆₁	—	2	2	no	—
195	C₂²⋊D₆₁	—	2	2	no	—
196	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
200	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
202	D₂₄₄	—	2	2	no	—
203	C₄×D₆₁	—	2	2	no	—
204	C₄×D₆₁	—	2	2	no	—
205	C₄×D₆₁	—	2	2	no	—
206	C₄×D₆₁	—	2	2	no	—
207	C₄×D₆₁	—	2	2	no	—
208	C₄×D₆₁	#131	1	4	yes	—
209	Dic₁₂₂	—	2	2	no	—
210	C₈×C₆₁	—	2	2	no	—
211	C₈×C₆₁	—	2	2	no	—
212	C₈×C₆₁	—	2	2	no	—
213	C₈×C₆₁	—	2	2	no	—
214	C₈×C₆₁	#131	1	4	yes	—
215	C₈×C₆₁	#131	1	4	yes	—
216	#92418	—	2	2	no	—
217	#92418	—	2	2	no	—
218	#92418	—	2	2	no	—
219	#92418	—	2	2	no	—
220	#92418	—	2	2	no	—
221	#92418	—	2	2	no	—
222	#17328	—	61	1	no	maximal, Sylow
223	C₂²×C₆₁	—	2	1	no	—
224	C₂²×C₆₁	—	2	1	no	—
225	C₂²×C₆₁	—	2	1	no	—
226	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
227	C₂×D₆₁	—	2	1	no	—
228	C₂×D₆₁	—	2	1	no	—
229	C₂×D₆₁	—	2	1	no	—
230	C₂×D₆₁	—	2	1	no	—
231	C₂×D₆₁	—	2	1	no	—
232	C₂×D₆₁	#405	1	2	yes	—
233	C₄×C₆₁	—	2	1	no	—
234	C₄×C₆₁	—	2	1	no	—
235	C₄×C₆₁	—	2	1	no	—
236	C₄×C₆₁	C₂×#131	1	2	yes	—
237	C₄×C₆₁	C₂×#131	1	2	yes	—
238	C₄×C₆₁	C₂×#131	1	2	yes	—
239	Dic₆₁	—	2	1	no	—
240	Dic₆₁	—	2	1	no	—
241	Dic₆₁	—	2	1	no	—
242	Dic₆₁	—	2	1	no	—
243	Dic₆₁	—	2	1	no	—
244	Dic₆₁	#405	1	2	yes	—
245	#2965	—	61	1	no	—
246	C₈×#41	—	61	1	no	—
247	#2922	—	61	1	no	—
248	#1454	—	61	1	no	—
249	#1454	—	61	1	no	—
250	#1453	—	61	1	no	—
251	#1453	—	61	1	no	—
252	#1452	—	61	1	no	—
253	#1451	—	61	1	no	—
254	#1450	—	61	1	no	—
255	#1450	—	61	1	no	—
256	C₈×M₁₆	—	61	1	no	—
257	C₈×M₁₆	—	61	1	no	—
258	C₈×M₁₆	D₆₁	1	1	yes	characteristic, complemented
259	C₂×C₈²	—	61	1	no	—
260	C₂×C₆₁	—	4	1	no	—
261	C₂×C₆₁	C₂×#405	1	1	yes	characteristic
262	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
263	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
264	D₆₁	—	2	2	no	—
265	D₆₁	—	4	1	no	—
266	C₄×#41	—	61	1	no	—
267	#446	—	61	2	no	—
268	C₈×Q₈	—	61	2	no	—
269	#436	—	61	2	no	—
270	#435	—	61	2	no	—
271	#435	—	61	2	no	—
272	C₈×D₄	—	61	2	no	—
273	C₈×D₄	—	61	2	no	—
274	C₈×D₄	—	61	2	no	—
275	#433	—	61	2	no	—
276	#433	—	61	2	no	—
277	#431	—	61	1	no	—
278	#431	—	61	1	no	—
279	#431	—	61	1	no	—
280	#431	—	61	1	no	—
281	#431	—	61	1	no	—
282	#431	—	61	1	no	—
283	#431	—	61	1	no	—
284	#431	—	61	1	no	—
285	#431	—	61	1	no	—
286	#431	C₂×D₆₁	1	1	yes	characteristic
287	#424	—	61	2	no	—
288	#408	—	61	2	no	—
289	C₄×M₁₆	—	61	1	no	—
290	C₄×M₁₆	—	61	1	no	—
291	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
292	C₂×C₄×C₈	—	61	1	no	—
293	C₂×C₄×C₈	—	61	1	no	—
294	C₂×C₄×C₈	—	61	1	no	—
295	C₂×C₄×C₈	—	61	1	no	—
296	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
297	#322	—	61	1	no	—
298	#322	—	61	1	no	—
299	#322	—	61	1	no	—
300	#322	—	61	1	no	—
301	#322	—	61	1	no	—
302	#322	—	61	1	no	—
303	#322	—	61	1	no	—
304	#322	—	61	1	no	—
305	#322	C₂×D₆₁	1	1	yes	characteristic
306	#322	C₂×D₆₁	1	1	yes	characteristic
307	C₈²	—	61	1	no	—
308	C₈²	—	61	1	no	—
309	C₈²	—	61	1	no	—
310	C₈²	—	61	1	no	—
311	C₈²	C₂×D₆₁	1	1	yes	characteristic
312	C₈²	C₂×D₆₁	1	1	yes	characteristic
313	C₆₁	#17328	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	61	1	no	—
315	C₂×M₁₆	—	61	2	no	—
316	C₂×M₁₆	—	61	2	no	—
317	C₂×M₁₆	C₄×D₆₁	1	2	yes	—
318	C₂²×C₈	—	61	2	no	—
319	C₂²×C₈	—	61	2	no	—
320	C₂²×C₈	—	61	2	no	—
321	C₂²×C₈	—	61	2	no	—
322	C₂²×C₈	C₄×D₆₁	1	2	yes	—
323	C₄×Q₈	—	61	1	no	—
324	C₄×Q₈	—	61	1	no	—
325	C₄×D₄	—	61	1	no	—
326	C₄×D₄	—	61	1	no	—
327	C₄×D₄	—	61	1	no	—
328	C₄×D₄	—	61	1	no	—
329	C₄×D₄	—	61	1	no	—
330	C₄×D₄	—	61	1	no	—
331	#117	—	61	1	no	—
332	#117	—	61	1	no	—
333	#117	—	61	1	no	—
334	C₂×C₄²	—	61	1	no	—
335	C₂×C₄²	—	61	1	no	—
336	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
337	C₄⋊C₈	—	61	2	no	—
338	C₄⋊C₈	—	61	2	no	—
339	C₄⋊C₈	—	61	2	no	—
340	C₄⋊C₈	—	61	2	no	—
341	C₄⋊C₈	—	61	2	no	—
342	C₄⋊C₈	—	61	2	no	—
343	C₄⋊C₈	—	61	2	no	—
344	C₄⋊C₈	—	61	2	no	—
345	C₄⋊C₈	—	61	2	no	—
346	C₄⋊C₈	C₄×D₆₁	1	2	yes	—
347	C₂²⋊C₈	—	61	2	no	—
348	C₂²⋊C₈	—	61	2	no	—
349	C₂²⋊C₈	—	61	2	no	—
350	C₂²⋊C₈	—	61	2	no	—
351	C₂²⋊C₈	—	61	2	no	—
352	C₂²⋊C₈	—	61	2	no	—
353	C₂²⋊C₈	—	61	2	no	—
354	C₂²⋊C₈	—	61	2	no	—
355	C₂²⋊C₈	—	61	2	no	—
356	C₂²⋊C₈	C₄×D₆₁	1	2	yes	—
357	#97	—	61	2	no	—
358	#97	—	61	2	no	—
359	#97	C₄×D₆₁	1	2	yes	—
360	C₄×C₈	—	61	2	no	—
361	C₄×C₈	—	61	2	no	—
362	C₄×C₈	—	61	2	no	—
363	C₄×C₈	—	61	2	no	—
364	C₄×C₈	—	61	1	no	—
365	C₄×C₈	—	61	1	no	—
366	C₄×C₈	—	61	1	no	—
367	C₄×C₈	—	61	1	no	—
368	C₄×C₈	—	61	1	no	—
369	C₄×C₈	—	61	1	no	—
370	C₄×C₈	C₄×D₆₁	1	2	yes	—
371	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
376	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
377	#41	—	122	4	no	—
378	C₂×Q₈	—	61	1	no	—
379	C₂×D₄	—	61	1	no	—
380	C₂×D₄	—	61	1	no	—
381	C₂×D₄	—	61	1	no	—
382	C₂²×C₄	—	61	1	no	—
383	C₂²×C₄	—	61	1	no	—
384	C₂²×C₄	—	61	1	no	—
385	C₂²×C₄	—	61	1	no	—
386	C₂²×C₄	—	61	1	no	—
387	C₂²×C₄	—	61	1	no	—
388	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
391	M₁₆	—	2	4	no	—
392	M₁₆	—	122	4	no	—
393	M₁₆	—	122	4	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	61	2	no	—
396	C₂×C₈	—	61	2	no	—
397	C₂×C₈	—	61	2	no	—
398	C₂×C₈	—	61	2	no	—
399	C₂×C₈	—	61	2	no	—
400	C₂×C₈	—	61	2	no	—
401	C₂×C₈	—	122	4	no	—
402	C₂×C₈	—	122	4	no	—
403	C₂×C₈	—	122	4	no	—
404	C₂×C₈	—	122	4	no	—
405	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
411	C₄⋊C₄	—	61	1	no	—
412	C₄⋊C₄	—	61	1	no	—
413	C₄⋊C₄	—	61	1	no	—
414	C₄⋊C₄	—	61	1	no	—
415	C₄⋊C₄	—	61	1	no	—
416	C₄⋊C₄	—	61	1	no	—
417	C₂²⋊C₄	—	61	1	no	—
418	C₂²⋊C₄	—	61	1	no	—
419	C₂²⋊C₄	—	61	1	no	—
420	C₂²⋊C₄	—	61	1	no	—
421	C₂²⋊C₄	—	61	1	no	—
422	C₂²⋊C₄	—	61	1	no	—
423	C₄²	—	61	1	no	—
424	C₄²	—	61	1	no	—
425	C₄²	—	61	1	no	—
426	C₄²	—	61	1	no	—
427	C₄²	—	61	1	no	—
428	C₄²	—	61	1	no	—
429	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
432	C₄²	C₂³×D₆₁	1	1	yes	characteristic
433	C₂³	—	61	1	no	—
434	C₂³	—	61	1	no	—
435	C₂³	C₄²×D₆₁	1	1	yes	characteristic
436	Q₈	—	122	2	no	—
437	D₄	—	122	2	no	—
438	D₄	—	122	2	no	—
439	D₄	—	122	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	61	1	no	—
444	C₂×C₄	—	61	4	no	—
445	C₂×C₄	—	61	1	no	—
446	C₂×C₄	—	61	1	no	—
447	C₂×C₄	—	61	1	no	—
448	C₂×C₄	—	61	1	no	—
449	C₂×C₄	—	61	1	no	—
450	C₂×C₄	—	122	2	no	—
451	C₂×C₄	—	122	2	no	—
452	C₂×C₄	—	122	2	no	—
453	C₂×C₄	—	122	2	no	—
454	C₂×C₄	—	122	2	no	—
455	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	122	2	no	—
466	C₈	—	122	2	no	—
467	C₈	—	122	2	no	—
468	C₈	—	122	2	no	—
469	C₈	—	122	2	no	—
470	C₈	—	122	2	no	—
471	C₈	#14519783	1	4	yes	—
472	C₈	#14519785	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	61	2	no	—
477	C₂²	—	122	1	no	—
478	C₂²	—	122	1	no	—
479	C₂²	—	122	1	no	—
480	C₂²	—	122	1	no	—
481	C₂²	—	122	1	no	—
482	C₂²	C₂×C₄²×D₆₁	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	61	2	no	—
487	C₄	—	122	1	no	—
488	C₄	—	122	1	no	—
489	C₄	—	122	1	no	—
490	C₄	—	122	1	no	—
491	C₄	—	122	1	no	—
492	C₄	#131×D₆₁	1	2	yes	—
493	C₄	C₂×#14519783	1	2	yes	—
494	C₄	C₂×#14519785	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	122	2	no	—
497	C₂	—	244	1	no	—
498	C₂	#405×D₆₁	1	1	yes	characteristic
499	C₂	C₄×#14519783	1	1	yes	characteristic
500	C₂	C₄×#14519785	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₄²
Frattini	C₄²	C₂³×D₆₁
Fitting	C₈×M₁₆×C₆₁	C₂
prime radical	C₂×#11758222	C₂×C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₈×M₁₆	D₆₁
hypocenter	C₆₁	#17328
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #21444120	C₂	semidirect
5. #21444119	C₂	semidirect
6. #21444117	C₂	semidirect
7. #21444116	C₂	semidirect
8. #21444110	C₂	semidirect
9. #21444105	C₂	semidirect
10. #21444102	C₂	semidirect
11. #21444101	C₂	semidirect
12. C₈×#11758189	C₂	semidirect
13. C₈×#11758189	C₂	semidirect
14. C₈²×D₆₁	C₂	semidirect
15. C₈×M₁₆×C₆₁	C₂	semidirect
258. C₈×M₁₆	D₆₁	semidirect
313. C₆₁	#17328	semidirect

Maximal subgroups

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

subgroup	index
#21454781	2
C₈×#11758222	2
#21454458	2
#21444120	2
#21444119	2
#21444117	2
#21444116	2
#21444110	2
#21444105	2
#21444102	2
#21444101	2
C₈×#11758189	2
C₈²×D₆₁	2
C₈×M₁₆×C₆₁	2
#17328	61