Subgroups — #29645794

Order 15616.

688 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	#21454786	C₂	1	1	yes	maximal, characteristic
2	#21454463	C₂	1	1	yes	maximal, characteristic
3	#21444122	C₂	1	1	yes	maximal, characteristic, complemented
4	#21444119	C₂	1	1	yes	maximal, characteristic, complemented
5	#21444119	C₂	1	1	yes	maximal, characteristic, complemented
6	#21444116	C₂	1	1	yes	maximal, characteristic, complemented
7	#21444114	C₂	1	1	yes	maximal, characteristic, complemented
8	#21444114	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444112	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444111	C₂	1	1	yes	maximal, characteristic, complemented
11	#21444109	C₂	1	1	yes	maximal, characteristic, complemented
12	#21444108	C₂	1	1	yes	maximal, characteristic, complemented
13	#21444106	C₂	1	1	yes	maximal, characteristic, complemented
14	#21444106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2965	C₂	1	1	yes	maximal, characteristic
16	#16839893	C₄	1	2	yes	—
17	#16839840	C₄	1	2	yes	—
18	#16839834	C₄	1	2	yes	—
19	#16839834	C₄	1	2	yes	—
20	#16839823	C₄	1	2	yes	—
21	#16839823	C₄	1	2	yes	—
22	#16839815	C₂²	1	1	yes	characteristic
23	#16839815	C₂²	1	1	yes	characteristic
24	#16839815	C₂²	1	1	yes	characteristic
25	#16839815	C₂²	1	1	yes	characteristic
26	#16839815	C₂²	1	1	yes	characteristic
27	#16839815	C₂²	1	1	yes	characteristic
28	#16839815	C₂²	1	1	yes	characteristic
29	#16839789	C₄	1	2	yes	—
30	#16839729	C₄	1	2	yes	—
31	C₄×#11758194	C₂²	1	1	yes	characteristic
32	C₄×#11758194	C₂²	1	1	yes	characteristic
33	C₄×#11758194	C₂²	1	1	yes	characteristic
34	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
35	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
36	#16839484	C₂²	1	1	yes	characteristic
37	#16839484	C₂²	1	1	yes	characteristic
38	#16839484	C₂²	1	1	yes	characteristic
39	#16839484	C₂²	1	1	yes	characteristic
40	#16839484	C₂²	1	1	yes	characteristic
41	#16839484	C₂²	1	1	yes	characteristic
42	#16839484	C₂²	1	1	yes	characteristic
43	#16839484	C₂²	1	1	yes	characteristic
44	#16839484	C₂²	1	1	yes	characteristic
45	#16839484	C₂²	1	1	yes	characteristic
46	#16839483	C₂²	1	1	yes	characteristic
47	#16839483	C₂²	1	1	yes	characteristic
48	#16839483	C₂²	1	1	yes	characteristic
49	#16839483	C₂²	1	1	yes	characteristic
50	C₈×#92418	C₂²	1	1	yes	characteristic
51	C₈×#92418	C₂²	1	1	yes	characteristic
52	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
53	C₆₁×#446	C₄	1	2	yes	—
54	C₆₁×#436	C₄	1	2	yes	—
55	C₆₁×#435	C₄	1	2	yes	—
56	C₆₁×#435	C₄	1	2	yes	—
57	C₆₁×#431	C₂²	1	1	yes	characteristic
58	C₆₁×#431	C₂²	1	1	yes	characteristic
59	C₆₁×#431	C₂²	1	1	yes	characteristic
60	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#11758194	C₂×C₄	1	2	yes	—
64	C₂×#11758194	C₂×C₄	1	2	yes	—
65	C₂×#11758194	C₂×C₄	1	2	yes	—
66	C₂²×#92418	C₂×C₄	1	2	yes	—
67	C₂²×#92418	C₂×C₄	1	2	yes	—
68	C₄⋊#92418	C₂×C₄	1	2	yes	—
69	C₄⋊#92418	C₂×C₄	1	2	yes	—
70	C₄⋊#92418	C₂×C₄	1	2	yes	—
71	C₄⋊#92418	C₂×C₄	1	2	yes	—
72	C₄⋊#92418	C₂×C₄	1	2	yes	—
73	C₄⋊#92418	C₂×C₄	1	2	yes	—
74	C₄⋊#92418	C₂×C₄	1	2	yes	—
75	C₂²⋊#92418	C₂×C₄	1	2	yes	—
76	C₂²⋊#92418	C₂×C₄	1	2	yes	—
77	C₂²⋊#92418	C₂×C₄	1	2	yes	—
78	C₂²⋊#92418	C₂×C₄	1	2	yes	—
79	C₂²⋊#92418	C₂×C₄	1	2	yes	—
80	C₂²⋊#92418	C₂×C₄	1	2	yes	—
81	C₂²⋊#92418	C₂×C₄	1	2	yes	—
82	#14519688	C₂×C₄	1	2	yes	—
83	#14519688	C₂×C₄	1	2	yes	—
84	#14519688	C₂×C₄	1	2	yes	—
85	C₄×#92418	C₂×C₄	1	2	yes	—
86	C₄×#92418	C₂×C₄	1	2	yes	—
87	C₄×#92418	C₂³	1	1	yes	characteristic
88	C₄×#92418	C₂³	1	1	yes	characteristic
89	C₄×#92418	C₂³	1	1	yes	characteristic
90	C₄×#92418	C₂³	1	1	yes	characteristic
91	C₄×#92418	C₂³	1	1	yes	characteristic
92	C₄×#92418	C₂³	1	1	yes	characteristic
93	C₄×#92418	C₂³	1	1	yes	characteristic
94	C₄×#92418	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
97	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
98	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
107	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
108	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
109	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
114	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
115	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
116	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
118	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
119	#97×C₆₁	C₂×C₄	1	2	yes	—
120	#97×C₆₁	C₂×C₄	1	2	yes	—
121	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
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	#41×C₆₁	—	4	2	no	—
127	C₂×Q₈×C₆₁	C₄²	1	1	yes	characteristic
128	C₂×D₄×C₆₁	C₄²	1	1	yes	characteristic
129	C₂×D₄×C₆₁	C₄²	1	1	yes	characteristic
130	C₂×D₄×C₆₁	C₄²	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
140	M₁₆×C₆₁	—	4	2	no	—
141	M₁₆×C₆₁	—	4	2	no	—
142	C₂×C₈×C₆₁	—	4	2	no	—
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	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
148	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
149	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
150	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
151	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
152	C₄⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
153	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
154	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
155	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
156	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
157	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
158	C₂²⋊C₄×C₆₁	C₄²	1	1	yes	characteristic
159	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
169	#11758194	—	4	2	no	—
170	#11758194	—	4	2	no	—
171	#11758194	—	4	2	no	—
172	C₂×#92418	—	4	2	no	—
173	C₂×#92418	—	4	2	no	—
174	C₂×#92418	C₂²×C₄	1	2	yes	—
175	C₂×#92418	C₂²×C₄	1	2	yes	—
176	C₂×#92418	C₂²×C₄	1	2	yes	—
177	C₂×#92418	C₂²×C₄	1	2	yes	—
178	C₂×#92418	C₂²×C₄	1	2	yes	—
179	C₂×#92418	C₂²×C₄	1	2	yes	—
180	C₂×#92418	C₂²×C₄	1	2	yes	—
181	C₂×#92418	C₂²×C₄	1	2	yes	—
182	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
183	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
184	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
185	Q₈×C₆₁	—	4	1	no	—
186	D₄×C₆₁	—	4	1	no	—
187	D₄×C₆₁	—	4	1	no	—
188	D₄×C₆₁	—	4	1	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
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	#92418	—	2	2	no	—
215	#92418	—	2	2	no	—
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	#17342	—	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	—	2	1	no	—
227	C₂²×C₆₁	—	2	1	no	—
228	C₂²×C₆₁	—	2	1	no	—
229	C₂²×C₆₁	—	2	1	no	—
230	C₂²×C₆₁	—	2	1	no	—
231	C₂²×C₆₁	—	2	1	no	—
232	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
233	C₄×C₆₁	—	2	1	no	—
234	C₄×C₆₁	—	2	1	no	—
235	C₄×C₆₁	—	2	1	no	—
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	2	1	no	—
238	C₄×C₆₁	—	2	1	no	—
239	C₄×C₆₁	—	2	1	no	—
240	C₄×C₆₁	—	2	1	no	—
241	C₄×C₆₁	—	2	1	no	—
242	C₄×C₆₁	#568	1	2	yes	—
243	C₄×C₆₁	#568	1	2	yes	—
244	C₄×C₆₁	#568	1	2	yes	—
245	#2965	—	61	1	no	—
246	#2965	D₆₁	1	1	yes	characteristic
247	#2922	—	61	1	no	—
248	#1455	—	61	1	no	—
249	#1454	—	61	1	no	—
250	#1454	—	61	1	no	—
251	#1453	—	61	1	no	—
252	#1453	—	61	1	no	—
253	#1453	—	61	1	no	—
254	#1452	—	61	1	no	—
255	#1452	—	61	1	no	—
256	#1451	—	61	1	no	—
257	#1451	—	61	1	no	—
258	#1451	—	61	1	no	—
259	#1451	—	61	1	no	—
260	C₂×C₆₁	—	4	1	no	—
261	C₂×C₆₁	—	4	1	no	—
262	C₂×C₆₁	—	4	1	no	—
263	C₂×C₆₁	#2873	1	1	yes	characteristic
264	C₂×C₆₁	#2875	1	1	yes	characteristic
265	C₂×C₆₁	#2875	1	1	yes	characteristic
266	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
267	#446	—	61	2	no	—
268	#446	Dic₆₁	1	2	yes	—
269	#436	—	61	2	no	—
270	#436	Dic₆₁	1	2	yes	—
271	#435	—	61	2	no	—
272	#435	—	61	2	no	—
273	#435	Dic₆₁	1	2	yes	—
274	#435	Dic₆₁	1	2	yes	—
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	C₂×D₆₁	1	1	yes	characteristic
285	#431	C₂×D₆₁	1	1	yes	characteristic
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	—	61	1	no	—
292	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
293	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
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	—	61	1	no	—
306	#322	—	61	1	no	—
307	#322	—	61	1	no	—
308	#322	—	61	1	no	—
309	#322	—	61	1	no	—
310	#322	—	61	1	no	—
311	C₈²	—	61	1	no	—
312	C₈²	—	61	1	no	—
313	C₆₁	#17342	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	C₄×D₆₁	1	1	yes	characteristic
315	C₂×M₁₆	—	61	2	no	—
316	C₂×M₁₆	—	61	2	no	—
317	C₂×M₁₆	—	61	2	no	—
318	C₂×M₁₆	C₂×Dic₆₁	1	2	yes	—
319	C₂×M₁₆	C₂×Dic₆₁	1	2	yes	—
320	C₂²×C₈	—	61	2	no	—
321	C₂²×C₈	—	61	2	no	—
322	C₂²×C₈	C₂×Dic₆₁	1	2	yes	—
323	C₄×Q₈	C₄×D₆₁	1	1	yes	characteristic
324	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
325	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
326	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
327	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
328	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
329	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
330	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
331	#117	C₄×D₆₁	1	1	yes	characteristic
332	#117	C₄×D₆₁	1	1	yes	characteristic
333	#117	C₄×D₆₁	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
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	C₂×Dic₆₁	1	2	yes	—
345	C₄⋊C₈	C₂×Dic₆₁	1	2	yes	—
346	C₄⋊C₈	C₂×Dic₆₁	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	C₂×Dic₆₁	1	2	yes	—
355	C₂²⋊C₈	C₂×Dic₆₁	1	2	yes	—
356	C₂²⋊C₈	C₂×Dic₆₁	1	2	yes	—
357	#97	—	61	2	no	—
358	#97	—	61	2	no	—
359	#97	—	61	2	no	—
360	#97	C₂×Dic₆₁	1	2	yes	—
361	#97	C₂×Dic₆₁	1	2	yes	—
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	—	61	1	no	—
371	C₄×C₈	—	61	1	no	—
372	C₄×C₈	C₂×Dic₆₁	1	2	yes	—
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	—	4	2	no	—
378	C₂×Q₈	C₄×Dic₆₁	1	1	yes	characteristic
379	C₂×D₄	C₄×Dic₆₁	1	1	yes	characteristic
380	C₂×D₄	C₄×Dic₆₁	1	1	yes	characteristic
381	C₂×D₄	C₄×Dic₆₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
391	M₁₆	—	4	2	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	244	2	no	—
394	M₁₆	—	244	2	no	—
395	M₁₆	—	244	2	no	—
396	C₂×C₈	—	4	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	—	61	2	no	—
402	C₂×C₈	—	61	2	no	—
403	C₂×C₈	—	61	2	no	—
404	C₂×C₈	—	61	2	no	—
405	C₂×C₈	—	244	2	no	—
406	C₂×C₈	—	244	2	no	—
407	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
408	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
409	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
410	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
411	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
412	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
413	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
414	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
415	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
416	C₄⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
417	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
418	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
419	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
420	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
421	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
422	C₂²⋊C₄	C₄×Dic₆₁	1	1	yes	characteristic
423	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
425	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
428	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
429	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
430	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
431	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
432	C₄²	C₂³×D₆₁	1	1	yes	characteristic
433	C₂³	C₂×C₄×Dic₆₁	1	1	yes	characteristic
434	C₂³	C₂×C₄×Dic₆₁	1	1	yes	characteristic
435	C₂³	C₂×C₄×Dic₆₁	1	1	yes	characteristic
436	Q₈	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄×Dic₆₁	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	C₂³×Dic₆₁	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	—	122	2	no	—
472	C₈	—	122	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄×Dic₆₁	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	#16840527	1	2	yes	—
493	C₄	#16840528	1	2	yes	—
494	C₄	#16840529	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	#21454237	1	1	yes	characteristic
499	C₂	#21454245	1	1	yes	characteristic
500	C₂	#21454247	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₄²
Fitting	C₆₁×#2965	C₂
prime radical	C₂×#41×C₆₁	C₂×C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	#2965	D₆₁
hypocenter	C₆₁	#17342
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
3. #21444122	C₂	semidirect
4. #21444119	C₂	semidirect
5. #21444119	C₂	semidirect
6. #21444116	C₂	semidirect
7. #21444114	C₂	semidirect
8. #21444114	C₂	semidirect
9. #21444112	C₂	semidirect
10. #21444111	C₂	semidirect
11. #21444109	C₂	semidirect
12. #21444108	C₂	semidirect
13. #21444106	C₂	semidirect
14. #21444106	C₂	semidirect
313. C₆₁	#17342	semidirect

Maximal subgroups

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

subgroup	index
#21454786	2
#21454463	2
#21444122	2
#21444119	2
#21444116	2
#21444114	2
#21444112	2
#21444111	2
#21444109	2
#21444108	2
#21444106	2
C₆₁×#2965	2
#17342	61