Subgroups — #30624179

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462186	C₂	1	2	yes	maximal, complemented
2	#21462185	C₂	1	2	yes	maximal, complemented
3	#21462183	C₂	1	1	yes	maximal, characteristic, complemented
4	#21462180	C₂	1	1	yes	maximal, characteristic, complemented
5	#21462179	C₂	1	1	yes	maximal, characteristic, complemented
6	#21462176	C₂	1	1	yes	maximal, characteristic, complemented
7	#21462152	C₂	1	1	yes	maximal, characteristic, complemented
8	D₆₁⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	#21462050	C₂	1	2	yes	maximal
10	#21462029	C₂	1	2	yes	maximal, complemented
11	C₄×#14519785	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519852	C₂²	1	2	yes	—
13	C₂×D₆₁⋊C₁₆	C₂²	1	2	yes	—
14	#16840683	C₂²	1	2	yes	—
15	#16840683	C₂²	1	2	yes	—
16	C₄⋊#11758187	C₂²	1	1	yes	characteristic
17	C₄⋊#11758187	C₂²	1	1	yes	characteristic
18	C₄⋊#11758187	C₂²	1	1	yes	characteristic
19	C₄⋊#11758187	C₂²	1	1	yes	characteristic
20	#16840657	C₂²	1	2	yes	—
21	#16840657	C₂²	1	2	yes	—
22	C₂²⋊#11758187	C₂²	1	2	yes	—
23	C₂²⋊#11758187	C₂²	1	2	yes	—
24	#16840651	C₂²	1	2	yes	—
25	#16840650	C₂²	1	2	yes	—
26	#16840648	C₂²	1	2	yes	—
27	C₄×#11758187	C₂²	1	2	yes	—
28	C₂×#14519785	C₄	1	1	yes	characteristic
29	C₂×#14519785	C₂²	1	1	yes	characteristic
30	C₄×#11758222	C₄	1	1	yes	characteristic
31	#16839720	C₄	1	1	yes	characteristic
32	#16839720	C₂²	1	1	yes	characteristic
33	#16839719	C₄	1	1	yes	characteristic
34	#16839719	C₄	1	1	yes	characteristic
35	#16839719	C₂²	1	1	yes	characteristic
36	#16839719	C₂²	1	1	yes	characteristic
37	C₄×#11758189	C₄	1	1	yes	characteristic
38	C₄×#11758189	C₄	1	1	yes	characteristic
39	C₂×C₄×#92418	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×M₁₆×C₆₁	C₄	1	1	yes	characteristic
43	#14519852	—	2	4	no	—
44	D₆₁⋊C₁₆	—	2	4	no	—
45	C₂×#11758187	C₂³	1	2	yes	—
46	C₂×#11758187	C₂³	1	2	yes	—
47	C₂×#11758187	C₂³	1	2	yes	—
48	C₂×#11758187	C₂³	1	2	yes	—
49	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
50	#14519785	—	2	4	no	—
51	#14519785	—	2	2	no	—
52	#14519785	—	2	2	no	—
53	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
54	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
55	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
56	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
57	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
58	C₂²×#92418	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
63	C₄×Dic₁₂₂	C₈	1	1	yes	characteristic
64	C₄×Dic₁₂₂	C₈	1	1	yes	characteristic
65	C₄×D₂₄₄	C₈	1	1	yes	characteristic
66	C₄×D₂₄₄	C₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
70	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
71	#14519736	C₂×C₄	1	1	yes	characteristic
72	#14519734	C₂×C₄	1	1	yes	characteristic
73	#14519734	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
76	#14519687	C₂×C₄	1	1	yes	characteristic
77	#14519687	C₂×C₄	1	1	yes	characteristic
78	#14519687	C₂×C₄	1	1	yes	characteristic
79	#14519687	C₂×C₄	1	1	yes	characteristic
80	C₄×#92418	C₂×C₄	1	1	yes	characteristic
81	C₄×#92418	C₂×C₄	1	1	yes	characteristic
82	C₄×#92418	C₂³	1	1	yes	characteristic
83	C₄×#92418	C₂³	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
87	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
91	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
92	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
100	#11758222	—	2	2	no	—
101	#11758222	—	2	2	no	—
102	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
110	M₁₆×C₆₁	—	2	2	no	—
111	M₁₆×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
121	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
122	#11758198	C₂×C₈	1	1	yes	characteristic
123	#11758198	C₂×C₈	1	1	yes	characteristic
124	#11758198	C₂×C₈	1	1	yes	characteristic
125	#11758198	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
128	#11758196	C₂×C₈	1	1	yes	characteristic
129	#11758196	C₂×C₈	1	1	yes	characteristic
130	#11758196	C₂×C₈	1	1	yes	characteristic
131	#11758196	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×#92418	—	2	2	no	—
139	C₂×#92418	—	2	1	no	—
140	C₂×#92418	—	2	1	no	—
141	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
142	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
143	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
144	C₂×#92418	C₂⁴	1	1	yes	characteristic
145	#11758189	—	2	2	no	—
146	#11758189	—	2	2	no	—
147	#11758189	—	2	2	no	—
148	#11758189	M₁₆	1	4	yes	—
149	C₈×D₆₁	—	2	2	no	—
150	C₈×D₆₁	—	2	2	no	—
151	C₈×D₆₁	—	2	1	no	—
152	C₈×D₆₁	—	2	1	no	—
153	C₈×D₆₁	#41	1	2	yes	—
154	C₈×D₆₁	#41	1	2	yes	—
155	#11758187	—	2	2	no	—
156	#11758187	—	2	2	no	—
157	#11758187	—	2	2	no	—
158	#11758187	—	2	2	no	—
159	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₆₁	—	2	2	no	—
173	C₂²⋊D₆₁	—	2	2	no	—
174	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
180	D₂₄₄	—	2	2	no	—
181	C₄×D₆₁	—	2	1	no	—
182	C₄×D₆₁	—	2	1	no	—
183	C₄×D₆₁	—	2	2	no	—
184	C₄×D₆₁	—	2	2	no	—
185	C₄×D₆₁	—	4	1	no	—
186	C₄×D₆₁	—	4	1	no	—
187	C₄×D₆₁	#117	1	2	yes	—
188	C₄×D₆₁	C₂×M₁₆	1	2	yes	—
189	Dic₁₂₂	—	2	2	no	—
190	C₈×C₆₁	—	2	1	no	—
191	C₈×C₆₁	—	2	1	no	—
192	C₈×C₆₁	#117	1	2	yes	—
193	C₈×C₆₁	C₂×M₁₆	1	2	yes	—
194	#92418	—	2	1	no	—
195	#92418	—	2	1	no	—
196	#92418	C₂×M₁₆	1	2	yes	—
197	#92418	C₂×#41	1	1	yes	characteristic
198	#92418	C₂×#41	1	1	yes	characteristic
199	#33423	—	61	1	no	maximal, Sylow
200	C₂²×C₆₁	—	2	1	no	—
201	C₂²×C₆₁	—	2	1	no	—
202	C₂²×C₆₁	—	2	1	no	—
203	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
204	C₂×D₆₁	—	2	1	no	—
205	C₂×D₆₁	—	2	1	no	—
206	C₂×D₆₁	—	2	1	no	—
207	C₂×D₆₁	—	2	1	no	—
208	C₂×D₆₁	—	2	1	no	—
209	C₂×D₆₁	#431	1	2	yes	—
210	C₄×C₆₁	—	2	1	no	—
211	C₄×C₆₁	—	2	1	no	—
212	C₄×C₆₁	—	2	1	no	—
213	C₄×C₆₁	—	2	1	no	—
214	C₄×C₆₁	#504	1	2	yes	—
215	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
216	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
217	Dic₆₁	—	2	1	no	—
218	Dic₆₁	—	2	1	no	—
219	Dic₆₁	—	2	1	no	—
220	Dic₆₁	—	2	1	no	—
221	Dic₆₁	—	2	1	no	—
222	Dic₆₁	#431	1	2	yes	—
223	C₄×#131	—	61	1	no	—
224	#2164	—	61	2	no	—
225	#2164	—	61	2	no	—
226	#2163	—	61	1	no	—
227	#2163	—	61	1	no	—
228	#2162	—	61	1	no	—
229	#2162	—	61	1	no	—
230	#2150	—	61	1	no	—
231	C₂×C₄⋊C₁₆	—	61	1	no	—
232	#2113	—	61	2	no	—
233	#2108	—	61	2	no	—
234	C₂×C₆₁	—	4	1	no	—
235	C₂×C₆₁	C₂×#431	1	1	yes	characteristic
236	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
237	C₂×C₆₁	#3407	1	1	yes	characteristic
238	D₆₁	—	2	2	no	—
239	D₆₁	—	4	1	no	—
240	C₂×#131	—	61	1	no	—
241	C₂×#131	—	61	1	no	—
242	C₄×#41	—	61	1	no	—
243	C₂×M₃₂	—	61	2	no	—
244	C₂²×C₁₆	—	61	2	no	—
245	#405	—	61	1	no	—
246	#405	—	61	1	no	—
247	#405	—	61	1	no	—
248	#405	—	61	1	no	—
249	#405	—	61	1	no	—
250	#405	—	61	1	no	—
251	C₄×M₁₆	—	61	1	no	—
252	C₄×M₁₆	—	61	1	no	—
253	C₄×M₁₆	#6923	1	1	yes	characteristic
254	C₂×C₄×C₈	—	61	1	no	—
255	C₂×C₄×C₈	—	61	1	no	—
256	C₂×C₄×C₈	—	61	1	no	—
257	C₄⋊C₁₆	—	61	1	no	—
258	C₄⋊C₁₆	—	61	1	no	—
259	C₄⋊C₁₆	—	61	2	no	—
260	C₄⋊C₁₆	—	61	1	no	—
261	C₄⋊C₁₆	—	61	1	no	—
262	C₄⋊C₁₆	—	61	2	no	—
263	C₂²⋊C₁₆	—	61	2	no	—
264	C₂²⋊C₁₆	—	61	2	no	—
265	C₂²⋊C₁₆	—	61	2	no	—
266	C₂²⋊C₁₆	—	61	2	no	—
267	#346	—	61	2	no	—
268	#346	—	61	2	no	—
269	C₄×C₁₆	—	61	2	no	—
270	C₄×C₁₆	—	61	2	no	—
271	C₆₁	#33423	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	61	1	no	—
273	#131	—	122	2	no	—
274	#131	—	122	2	no	—
275	#131	—	122	4	no	—
276	C₂×M₁₆	—	61	1	no	—
277	C₂×M₁₆	—	61	1	no	—
278	C₂×M₁₆	—	61	1	no	—
279	C₂×M₁₆	—	61	1	no	—
280	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
281	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
282	C₂²×C₈	—	61	1	no	—
283	C₂²×C₈	—	61	1	no	—
284	C₂²×C₈	—	61	1	no	—
285	C₂²×C₈	—	61	1	no	—
286	C₂²×C₈	—	61	1	no	—
287	C₂²×C₈	—	61	1	no	—
288	C₄×Q₈	—	61	1	no	—
289	C₄×Q₈	—	61	1	no	—
290	C₄×D₄	—	61	1	no	—
291	C₄×D₄	—	61	1	no	—
292	C₄×D₄	—	61	1	no	—
293	C₄×D₄	—	61	1	no	—
294	C₄×D₄	—	61	1	no	—
295	C₄×D₄	—	61	1	no	—
296	#117	—	61	1	no	—
297	#117	—	61	1	no	—
298	#117	—	61	1	no	—
299	C₂×C₄²	—	61	1	no	—
300	C₂×C₄²	—	61	1	no	—
301	C₂×C₄²	C₂×#6923	1	1	yes	characteristic
302	M₃₂	—	122	4	no	—
303	C₂×C₁₆	—	61	2	no	—
304	C₂×C₁₆	—	61	2	no	—
305	C₂×C₁₆	—	61	2	no	—
306	C₂×C₁₆	—	61	2	no	—
307	C₂×C₁₆	—	122	4	no	—
308	#97	—	61	1	no	—
309	#97	—	61	1	no	—
310	#97	—	61	1	no	—
311	#97	—	61	1	no	—
312	#97	C₂×#6923	1	1	yes	characteristic
313	#97	C₂×#6923	1	1	yes	characteristic
314	C₄×C₈	—	61	1	no	—
315	C₄×C₈	—	61	1	no	—
316	C₄×C₈	—	61	1	no	—
317	C₄×C₈	—	61	1	no	—
318	C₄×C₈	—	61	1	no	—
319	C₄×C₈	—	61	1	no	—
320	C₄×C₈	—	61	1	no	—
321	C₄×C₈	—	61	1	no	—
322	C₄×C₈	C₂×#6923	1	1	yes	characteristic
323	C₄×C₈	C₂×#6923	1	1	yes	characteristic
324	#41	—	122	2	no	—
325	#41	—	122	2	no	—
326	C₂×Q₈	—	61	1	no	—
327	C₂×D₄	—	61	1	no	—
328	C₂×D₄	—	61	1	no	—
329	C₂×D₄	—	61	1	no	—
330	C₂²×C₄	—	61	1	no	—
331	C₂²×C₄	—	61	1	no	—
332	C₂²×C₄	—	61	1	no	—
333	C₂²×C₄	—	61	1	no	—
334	C₂²×C₄	—	61	1	no	—
335	C₂²×C₄	—	61	1	no	—
336	C₂²×C₄	D₆₁⋊C₈	1	1	yes	characteristic
337	C₂²×C₄	D₆₁⋊C₈	1	1	yes	characteristic
338	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	61	4	no	—
342	M₁₆	—	122	2	no	—
343	M₁₆	—	122	2	no	—
344	M₁₆	—	122	2	no	—
345	C₂×C₈	—	61	1	no	—
346	C₂×C₈	—	61	1	no	—
347	C₂×C₈	—	61	2	no	—
348	C₂×C₈	—	61	2	no	—
349	C₂×C₈	—	61	1	no	—
350	C₂×C₈	—	61	1	no	—
351	C₂×C₈	—	122	1	no	—
352	C₂×C₈	—	122	1	no	—
353	C₂×C₈	—	122	2	no	—
354	C₂×C₈	—	122	1	no	—
355	C₂×C₈	—	122	1	no	—
356	C₂×C₈	—	122	2	no	—
357	C₂×C₈	—	122	2	no	—
358	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
359	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
360	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
361	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
362	C₄⋊C₄	—	61	1	no	—
363	C₄⋊C₄	—	61	1	no	—
364	C₄⋊C₄	—	61	1	no	—
365	C₄⋊C₄	—	61	1	no	—
366	C₄⋊C₄	—	61	1	no	—
367	C₄⋊C₄	—	61	1	no	—
368	C₂²⋊C₄	—	61	1	no	—
369	C₂²⋊C₄	—	61	1	no	—
370	C₂²⋊C₄	—	61	1	no	—
371	C₂²⋊C₄	—	61	1	no	—
372	C₂²⋊C₄	—	61	1	no	—
373	C₂²⋊C₄	—	61	1	no	—
374	C₄²	—	61	1	no	—
375	C₄²	—	61	1	no	—
376	C₄²	—	61	1	no	—
377	C₄²	—	61	1	no	—
378	C₄²	—	61	1	no	—
379	C₄²	—	61	1	no	—
380	C₄²	D₆₁⋊C₈	1	1	yes	characteristic
381	C₄²	D₆₁⋊C₈	1	1	yes	characteristic
382	C₄²	C₂²×#6923	1	1	yes	characteristic
383	C₄²	C₂²×#6923	1	1	yes	characteristic
384	C₁₆	—	122	2	no	—
385	C₁₆	—	122	2	no	—
386	C₁₆	—	122	2	no	—
387	C₁₆	—	122	2	no	—
388	C₂³	—	61	1	no	—
389	C₂³	—	61	1	no	—
390	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
391	Q₈	—	122	2	no	—
392	D₄	—	122	2	no	—
393	D₄	—	122	2	no	—
394	D₄	—	122	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	61	1	no	—
400	C₂×C₄	—	61	2	no	—
401	C₂×C₄	—	61	2	no	—
402	C₂×C₄	—	61	1	no	—
403	C₂×C₄	—	61	1	no	—
404	C₂×C₄	—	61	1	no	—
405	C₂×C₄	—	61	1	no	—
406	C₂×C₄	—	61	1	no	—
407	C₂×C₄	—	122	2	no	—
408	C₂×C₄	—	122	2	no	—
409	C₂×C₄	—	122	1	no	—
410	C₂×C₄	—	122	1	no	—
411	C₂×C₄	—	244	1	no	—
412	C₂×C₄	—	244	1	no	—
413	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
414	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
415	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
416	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
417	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
418	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	61	1	no	—
422	C₈	—	61	1	no	—
423	C₈	—	61	2	no	—
424	C₈	—	122	1	no	—
425	C₈	—	122	1	no	—
426	C₈	#14519856	1	2	yes	—
427	C₈	D₆₁⋊M₁₆	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	61	2	no	—
432	C₂²	—	122	1	no	—
433	C₂²	—	122	1	no	—
434	C₂²	—	122	1	no	—
435	C₂²	—	122	1	no	—
436	C₂²	—	122	1	no	—
437	C₂²	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	61	2	no	—
443	C₄	—	122	1	no	—
444	C₄	—	122	1	no	—
445	C₄	—	122	1	no	—
446	C₄	—	122	1	no	—
447	C₄	—	122	1	no	—
448	C₄	#16840821	1	2	yes	—
449	C₄	C₂×#14519856	1	1	yes	characteristic
450	C₄	C₂×D₆₁⋊M₁₆	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	122	2	no	—
453	C₂	—	244	1	no	—
454	C₂	D₆₁⋊#431	1	1	yes	characteristic
455	C₂	C₂×#16840821	1	1	yes	characteristic
456	C₂	#21462788	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₄×M₁₆×C₆₁	C₄
prime radical	C₂×#11758222	C₂×C₄
cosocle	C₂×#92418	C₂⁴
hypercenter	C₄×M₁₆	#6923
hypocenter	C₆₁	#33423
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. #21462186	C₂	semidirect
2. #21462185	C₂	semidirect
3. #21462183	C₂	semidirect
4. #21462180	C₂	semidirect
5. #21462179	C₂	semidirect
6. #21462176	C₂	semidirect
7. #21462152	C₂	semidirect
8. D₆₁⋊(C₄⋊C₁₆)	C₂	semidirect
10. #21462029	C₂	semidirect
271. C₆₁	#33423	semidirect

Maximal subgroups

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

subgroup	index
#21462186	2
#21462185	2
#21462183	2
#21462180	2
#21462179	2
#21462176	2
#21462152	2
D₆₁⋊(C₄⋊C₁₆)	2
#21462050	2
#21462029	2
C₄×#14519785	2
#33423	61