Subgroups — #30612058

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462741	C₂	1	2	yes	maximal
2	#21461385	C₂	1	2	yes	maximal, complemented
3	#21461383	C₂	1	2	yes	maximal, complemented
4	#21461380	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461379	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461374	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461373	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461371	C₂	1	2	yes	maximal, complemented
9	#21461367	C₂	1	1	yes	maximal, characteristic, complemented
10	D₆₁⋊#334	C₂	1	1	yes	maximal, characteristic, complemented
11	#21454241	C₂	1	1	yes	maximal, characteristic
12	#16840814	—	2	2	no	—
13	#16840795	—	2	2	no	—
14	#16840794	—	2	2	no	—
15	#16840792	—	2	2	no	—
16	#16840784	C₂²	1	2	yes	—
17	#16840783	C₂²	1	2	yes	—
18	#16840781	C₂²	1	2	yes	—
19	#16840766	C₂²	1	2	yes	—
20	#16840765	C₂²	1	2	yes	—
21	D₆₁⋊(C₄⋊C₈)	C₂²	1	2	yes	—
22	#16840626	C₂²	1	2	yes	—
23	#16840626	C₂²	1	2	yes	—
24	#16840625	C₂²	1	2	yes	—
25	#16840624	C₂²	1	2	yes	—
26	#16840624	C₂²	1	2	yes	—
27	#16840623	C₂²	1	1	yes	characteristic
28	#16840623	C₂²	1	1	yes	characteristic
29	#16840623	C₂²	1	1	yes	characteristic
30	#16840623	C₂²	1	1	yes	characteristic
31	#16840623	C₂²	1	2	yes	—
32	C₂×#14519785	C₄	1	1	yes	characteristic
33	C₂×#14519783	C₄	1	1	yes	characteristic
34	#16840230	C₂²	1	1	yes	characteristic
35	#16839719	C₄	1	1	yes	characteristic
36	#16839719	C₄	1	1	yes	characteristic
37	#16839718	C₄	1	1	yes	characteristic
38	#16839716	C₄	1	1	yes	characteristic
39	#16839716	C₄	1	1	yes	characteristic
40	#16839714	C₂²	1	1	yes	characteristic
41	#16839714	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#405	C₄	1	1	yes	characteristic
47	C₂×#11758213	—	2	2	no	—
48	C₂×#11758217	—	2	2	no	—
49	C₂×D₆₁⋊C₈	—	2	2	no	—
50	#14519844	—	2	2	no	—
51	#14519844	—	2	2	no	—
52	C₄⋊#92420	—	2	2	no	—
53	C₄⋊#92420	C₂³	1	2	yes	—
54	C₄⋊#92420	C₂³	1	2	yes	—
55	C₄⋊#92420	C₂³	1	2	yes	—
56	C₄⋊#92420	C₂³	1	2	yes	—
57	#14519834	—	2	2	no	—
58	#14519834	—	2	2	no	—
59	C₂²⋊#92420	—	2	2	no	—
60	#14519832	—	2	2	no	—
61	#14519832	—	2	2	no	—
62	C₄×#92420	—	2	2	no	—
63	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
64	#14519785	—	2	4	no	—
65	#14519783	—	2	4	no	—
66	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
67	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
68	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
69	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
70	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
71	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
76	#14519742	D₄	1	1	yes	characteristic
77	#14519742	Q₈	1	1	yes	characteristic
78	#14519739	D₄	1	1	yes	characteristic
79	#14519739	Q₈	1	1	yes	characteristic
80	#14519737	D₄	1	1	yes	characteristic
81	#14519737	D₄	1	1	yes	characteristic
82	#14519737	Q₈	1	1	yes	characteristic
83	#14519737	Q₈	1	1	yes	characteristic
84	#14519734	C₂×C₄	1	1	yes	characteristic
85	#14519734	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
87	C₄²×D₆₁	C₂³	1	1	yes	characteristic
88	C₄²×D₆₁	C₂³	1	1	yes	characteristic
89	#14519688	C₂×C₄	1	1	yes	characteristic
90	#14519688	C₂×C₄	1	1	yes	characteristic
91	#14519687	C₂×C₄	1	1	yes	characteristic
92	#14519687	C₂×C₄	1	1	yes	characteristic
93	C₄×#92418	C₂×C₄	1	1	yes	characteristic
94	C₄×#92418	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
98	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
99	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
100	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
103	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
104	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
105	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₆₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
113	#11758222	—	2	2	no	—
114	#11758222	—	2	2	no	—
115	C₂×D₂₄₄	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
122	C₂×Dic₁₂₂	C₄⋊C₄	1	1	yes	characteristic
123	#11758217	—	8	2	no	—
124	C₂×#92420	—	2	2	no	—
125	C₂×#92420	—	2	2	no	—
126	C₂×#92420	—	2	2	no	—
127	C₂×#92420	—	2	2	no	—
128	#11758213	—	8	2	no	—
129	D₆₁⋊C₈	—	8	2	no	—
130	M₁₆×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
140	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
142	#11758198	C₄⋊C₄	1	1	yes	characteristic
143	#11758198	C₄⋊C₄	1	1	yes	characteristic
144	#11758198	C₄⋊C₄	1	1	yes	characteristic
145	#11758198	C₄⋊C₄	1	1	yes	characteristic
146	#11758196	C₄⋊C₄	1	1	yes	characteristic
147	#11758196	C₄⋊C₄	1	1	yes	characteristic
148	#11758196	C₄⋊C₄	1	1	yes	characteristic
149	#11758196	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
158	#11758194	—	2	2	no	—
159	C₂×#92418	—	2	2	no	—
160	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
161	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
162	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
163	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
164	#11758189	—	2	2	no	—
165	#11758189	—	2	2	no	—
166	#11758189	—	2	2	no	—
167	#11758189	M₁₆	1	4	yes	complemented
168	C₈×D₆₁	—	2	2	no	—
169	C₈×D₆₁	—	2	2	no	—
170	C₈×D₆₁	—	2	2	no	—
171	C₈×D₆₁	M₁₆	1	4	yes	complemented
172	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
183	C₂²⋊D₆₁	—	2	2	no	—
184	C₂²⋊D₆₁	—	2	2	no	—
185	C₂×Dic₆₁	—	2	2	no	—
186	C₂×Dic₆₁	—	4	1	no	—
187	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×Dic₆₁	C₂²×Q₈	1	1	yes	characteristic
193	D₂₄₄	—	2	2	no	—
194	C₄×D₆₁	—	2	1	no	—
195	C₄×D₆₁	—	2	1	no	—
196	C₄×D₆₁	—	2	2	no	—
197	C₄×D₆₁	—	2	2	no	—
198	C₄×D₆₁	—	4	1	no	—
199	C₄×D₆₁	—	4	1	no	—
200	C₄×D₆₁	C₂×M₁₆	1	2	yes	—
201	C₄×D₆₁	C₂×M₁₆	1	2	yes	—
202	Dic₁₂₂	—	2	2	no	—
203	#92420	—	4	2	no	—
204	#92420	—	4	2	no	—
205	#92420	—	4	2	no	—
206	#92420	—	4	2	no	—
207	C₈×C₆₁	—	2	1	no	—
208	C₈×C₆₁	—	2	1	no	—
209	C₈×C₆₁	C₂×M₁₆	1	2	yes	—
210	C₈×C₆₁	C₂×M₁₆	1	2	yes	—
211	#92418	—	2	1	no	—
212	#92418	—	2	1	no	—
213	#92418	C₂×M₁₆	1	2	yes	—
214	#92418	C₂×M₁₆	1	2	yes	—
215	#17798	—	61	1	no	maximal, Sylow
216	C₂²×C₆₁	—	2	1	no	—
217	C₂²×C₆₁	—	2	1	no	—
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₆₁	—	2	1	no	—
221	C₂×D₆₁	—	2	1	no	—
222	C₂×D₆₁	—	2	1	no	—
223	C₂×D₆₁	—	2	1	no	—
224	C₂×D₆₁	—	2	1	no	—
225	C₂×D₆₁	#423	1	2	yes	—
226	C₄×C₆₁	—	2	1	no	—
227	C₄×C₆₁	—	2	1	no	—
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	1	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
232	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
233	Dic₆₁	—	2	1	no	—
234	Dic₆₁	—	2	1	no	—
235	Dic₆₁	—	2	1	no	—
236	Dic₆₁	—	2	1	no	—
237	Dic₆₁	#423	1	2	yes	—
238	Dic₆₁	#577	1	2	yes	—
239	#2989	—	61	2	no	—
240	C₄×#131	—	61	1	no	—
241	#1569	—	61	2	no	—
242	#1569	—	61	2	no	—
243	#1568	—	61	1	no	—
244	#1568	—	61	1	no	—
245	#1566	—	61	1	no	—
246	#1566	—	61	1	no	—
247	#1565	—	61	2	no	—
248	#1564	—	61	1	no	—
249	C₂×#334	—	61	1	no	—
250	C₂×C₆₁	—	4	1	no	—
251	C₂×C₆₁	C₂×#423	1	1	yes	characteristic
252	C₂×C₆₁	#2912	1	1	yes	characteristic
253	C₂×C₆₁	#2916	1	1	yes	characteristic
254	D₆₁	—	2	2	no	—
255	D₆₁	—	4	1	no	—
256	C₂×#131	—	61	1	no	—
257	C₂×#131	—	61	1	no	—
258	C₄×#41	—	61	1	no	—
259	#446	—	122	2	no	—
260	#436	—	122	2	no	—
261	#435	—	122	2	no	—
262	#435	—	122	2	no	—
263	#432	—	61	2	no	—
264	#432	—	61	2	no	—
265	#431	—	61	2	no	—
266	#423	—	61	2	no	—
267	#423	—	61	2	no	—
268	C₂×C₄⋊C₈	—	61	2	no	—
269	#405	—	61	1	no	—
270	#405	—	61	1	no	—
271	#405	—	61	1	no	—
272	#405	—	61	1	no	—
273	#405	—	61	1	no	—
274	#405	#6923	1	1	yes	characteristic
275	C₄×M₁₆	—	61	1	no	—
276	C₄×M₁₆	—	61	1	no	—
277	C₄×M₁₆	—	61	1	no	—
278	C₂×C₄×C₈	—	61	1	no	—
279	C₂×C₄×C₈	—	61	1	no	—
280	C₂×C₄×C₈	—	61	1	no	—
281	#335	—	61	2	no	—
282	#335	—	61	2	no	—
283	#335	—	61	2	no	—
284	#334	—	61	1	no	—
285	#334	—	61	1	no	—
286	#334	—	61	2	no	—
287	#334	—	61	1	no	—
288	#334	—	61	1	no	—
289	#334	—	61	2	no	—
290	#334	—	61	2	no	—
291	C₆₁	#17798	1	1	yes	characteristic, complemented, Sylow
292	C₂×#41	—	61	1	no	—
293	#131	—	122	4	no	—
294	#131	—	122	4	no	—
295	C₂×M₁₆	—	61	1	no	—
296	C₂×M₁₆	—	61	1	no	—
297	C₂×M₁₆	—	61	1	no	—
298	C₂×M₁₆	—	61	1	no	—
299	C₂×M₁₆	—	61	1	no	—
300	C₂×M₁₆	—	122	2	no	—
301	C₂×M₁₆	—	122	2	no	—
302	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
303	C₂²×C₈	—	61	1	no	—
304	C₂²×C₈	—	61	1	no	—
305	C₂²×C₈	—	61	1	no	—
306	C₂²×C₈	—	61	1	no	—
307	C₂²×C₈	—	61	1	no	—
308	C₂²×C₈	—	122	2	no	—
309	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
310	C₄×Q₈	—	61	1	no	—
311	C₄×Q₈	—	61	1	no	—
312	C₄×D₄	—	61	1	no	—
313	C₄×D₄	—	61	1	no	—
314	C₄×D₄	—	61	1	no	—
315	C₄×D₄	—	61	1	no	—
316	C₄×D₄	—	61	1	no	—
317	C₄×D₄	—	61	1	no	—
318	#117	—	61	1	no	—
319	#117	—	61	1	no	—
320	#117	C₂×#6923	1	1	yes	characteristic
321	C₂×C₄²	—	61	1	no	—
322	C₂×C₄²	—	61	1	no	—
323	C₂×C₄²	—	61	1	no	—
324	C₄⋊C₈	—	61	2	no	—
325	C₄⋊C₈	—	61	2	no	—
326	C₄⋊C₈	—	61	2	no	—
327	C₄⋊C₈	—	61	2	no	—
328	C₄⋊C₈	—	122	2	no	—
329	C₄⋊C₈	—	122	2	no	—
330	C₄⋊C₈	—	122	2	no	—
331	C₂²⋊C₈	—	122	2	no	—
332	C₂²⋊C₈	—	122	2	no	—
333	C₂²⋊C₈	—	122	2	no	—
334	#97	—	61	1	no	—
335	#97	—	61	1	no	—
336	#97	—	61	1	no	—
337	#97	—	61	1	no	—
338	#97	—	122	2	no	—
339	#97	—	122	2	no	—
340	#97	C₂×#6923	1	1	yes	characteristic
341	#97	C₂×#6923	1	1	yes	characteristic
342	C₄×C₈	—	61	1	no	—
343	C₄×C₈	—	61	1	no	—
344	C₄×C₈	—	61	1	no	—
345	C₄×C₈	—	61	1	no	—
346	C₄×C₈	—	61	1	no	—
347	C₄×C₈	—	61	1	no	—
348	C₄×C₈	—	61	1	no	—
349	C₄×C₈	—	61	1	no	—
350	C₄×C₈	—	122	2	no	—
351	C₄×C₈	C₂×#6923	1	1	yes	characteristic
352	C₄×C₈	C₂×#6923	1	1	yes	characteristic
353	#41	—	122	2	no	—
354	#41	—	122	2	no	—
355	C₂×Q₈	—	61	1	no	—
356	C₂×D₄	—	61	1	no	—
357	C₂×D₄	—	61	1	no	—
358	C₂×D₄	—	61	1	no	—
359	C₂²×C₄	—	61	1	no	—
360	C₂²×C₄	—	61	1	no	—
361	C₂²×C₄	—	61	1	no	—
362	C₂²×C₄	—	61	1	no	—
363	C₂²×C₄	—	61	1	no	—
364	C₂²×C₄	—	61	1	no	—
365	C₂²×C₄	—	61	1	no	—
366	C₂²×C₄	—	61	1	no	—
367	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	61	4	no	—
370	M₁₆	—	122	2	no	—
371	M₁₆	—	122	2	no	—
372	M₁₆	—	122	2	no	—
373	M₁₆	—	122	2	no	—
374	M₁₆	—	488	2	no	—
375	M₁₆	—	488	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	61	1	no	—
378	C₂×C₈	—	61	1	no	—
379	C₂×C₈	—	61	4	no	—
380	C₂×C₈	—	61	1	no	—
381	C₂×C₈	—	61	1	no	—
382	C₂×C₈	—	122	2	no	—
383	C₂×C₈	—	122	2	no	—
384	C₂×C₈	—	122	2	no	—
385	C₂×C₈	—	122	2	no	—
386	C₂×C₈	—	122	2	no	—
387	C₂×C₈	—	122	2	no	—
388	C₂×C₈	—	122	2	no	—
389	C₂×C₈	—	122	2	no	—
390	C₂×C₈	—	488	2	no	—
391	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
392	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
393	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
394	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
395	C₄⋊C₄	—	61	1	no	—
396	C₄⋊C₄	—	61	1	no	—
397	C₄⋊C₄	—	61	1	no	—
398	C₄⋊C₄	—	61	1	no	—
399	C₄⋊C₄	C₄⋊#6923	1	1	yes	characteristic
400	C₄⋊C₄	C₄⋊#6923	1	1	yes	characteristic
401	C₂²⋊C₄	—	61	1	no	—
402	C₂²⋊C₄	—	61	1	no	—
403	C₂²⋊C₄	—	61	1	no	—
404	C₂²⋊C₄	—	61	1	no	—
405	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
406	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
407	C₄²	—	61	1	no	—
408	C₄²	—	61	1	no	—
409	C₄²	—	61	1	no	—
410	C₄²	—	61	1	no	—
411	C₄²	—	61	1	no	—
412	C₄²	—	61	1	no	—
413	C₄²	—	61	1	no	—
414	C₄²	—	61	1	no	—
415	C₄²	C₂²×#6923	1	1	yes	characteristic
416	C₄²	C₂²×#6923	1	1	yes	characteristic
417	C₂³	—	61	1	no	—
418	C₂³	—	61	1	no	—
419	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
420	Q₈	—	122	2	no	—
421	D₄	—	122	2	no	—
422	D₄	—	122	2	no	—
423	D₄	—	122	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	61	1	no	—
427	C₂×C₄	—	61	1	no	—
428	C₂×C₄	—	61	2	no	—
429	C₂×C₄	—	61	2	no	—
430	C₂×C₄	—	61	1	no	—
431	C₂×C₄	—	61	1	no	—
432	C₂×C₄	—	61	1	no	—
433	C₂×C₄	—	61	1	no	—
434	C₂×C₄	—	122	2	no	—
435	C₂×C₄	—	122	2	no	—
436	C₂×C₄	—	122	2	no	—
437	C₂×C₄	—	122	1	no	—
438	C₂×C₄	—	122	1	no	—
439	C₂×C₄	—	244	1	no	—
440	C₂×C₄	—	244	1	no	—
441	C₂×C₄	—	244	1	no	—
442	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
447	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	61	2	no	—
451	C₈	—	61	2	no	—
452	C₈	—	122	1	no	—
453	C₈	—	122	1	no	—
454	C₈	—	244	2	no	—
455	C₈	—	244	2	no	—
456	C₈	—	244	2	no	—
457	C₈	—	244	2	no	—
458	C₈	D₆₁⋊M₁₆	1	2	yes	—
459	C₈	D₆₁⋊M₁₆	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	61	2	no	—
464	C₂²	—	122	1	no	—
465	C₂²	—	122	1	no	—
466	C₂²	—	122	1	no	—
467	C₂²	—	122	1	no	—
468	C₂²	—	122	1	no	—
469	C₂²	C₂²×C₄⋊#6923	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	61	2	no	—
476	C₄	—	61	2	no	—
477	C₄	—	122	1	no	—
478	C₄	—	122	1	no	—
479	C₄	—	122	1	no	—
480	C₄	—	122	1	no	—
481	C₄	C₂×D₆₁⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₆₁⋊M₁₆	1	1	yes	characteristic
483	C₂	—	4	1	no	—
484	C₂	—	122	2	no	—
485	C₂	—	244	1	no	—
486	C₂	D₆₁⋊#423	1	1	yes	characteristic
487	C₂	#21462473	1	1	yes	characteristic
488	C₂	#21462480	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#405	C₄
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂×#11758222	C₂×C₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	#405	#6923
hypocenter	C₆₁	#17798
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #21461385	C₂	semidirect
3. #21461383	C₂	semidirect
4. #21461380	C₂	semidirect
5. #21461379	C₂	semidirect
6. #21461374	C₂	semidirect
7. #21461373	C₂	semidirect
8. #21461371	C₂	semidirect
9. #21461367	C₂	semidirect
10. D₆₁⋊#334	C₂	semidirect
167. #11758189	M₁₆	semidirect
171. C₈×D₆₁	M₁₆	semidirect
291. C₆₁	#17798	semidirect

Maximal subgroups

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

subgroup	index
#21462741	2
#21461385	2
#21461383	2
#21461380	2
#21461379	2
#21461374	2
#21461373	2
#21461371	2
#21461367	2
D₆₁⋊#334	2
#21454241	2
#17798	61