Subgroups — C₂×#21454736 #30544334

Order 15616.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840529	C₂	1	2	yes	maximal, complemented
2	#21454736	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16839884	C₂	1	4	yes	maximal, complemented
4	C₂×#16839879	C₂	1	4	yes	maximal, complemented
5	C₂²×#14519713	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16839779	C₂	1	2	yes	maximal, complemented
7	C₂×#16839717	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#135×C₆₁	C₂	1	1	yes	maximal, characteristic
9	#16840529	—	2	8	no	—
10	#16840529	C₂²	1	16	yes	complemented
11	C₂×#14519784	—	2	4	no	—
12	C₂×#14519784	C₂²	1	8	yes	complemented
13	C₂²×#11758194	—	2	4	no	—
14	C₂²×#11758194	C₂²	1	2	yes	—
15	C₂²×#11758194	C₂²	1	1	yes	characteristic
16	C₂×#14519736	C₂²	1	1	yes	characteristic
17	#16839884	C₂²	1	32	yes	complemented
18	#16839879	C₂²	1	32	yes	complemented
19	C₂×#14519713	C₂²	1	2	yes	complemented
20	C₂×#14519713	C₂²	1	2	yes	complemented
21	C₂×#14519713	C₂²	1	8	yes	complemented
22	#16839779	C₂²	1	16	yes	complemented
23	C₂×#14519704	C₂²	1	8	yes	complemented
24	#16839717	C₂²	1	8	yes	complemented
25	C₂×#14519687	C₂²	1	2	yes	complemented
26	C₂×C₈×Dic₆₁	C₂²	1	2	yes	complemented
27	C₂²×#41×C₆₁	C₂²	1	2	yes	—
28	C₂×#135×C₆₁	C₄	1	2	yes	complemented
29	C₂×#135×C₆₁	C₄	1	2	yes	complemented
30	C₂×#135×C₆₁	C₄	1	8	yes	complemented
31	C₂×#135×C₆₁	C₂²	1	2	yes	—
32	C₂×#135×C₆₁	C₂²	1	2	yes	—
33	C₂×#135×C₆₁	C₂²	1	8	yes	—
34	C₂²×Q₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
35	C₂²×SD₁₆×C₆₁	C₄	1	2	yes	complemented
36	C₂²×D₈×C₆₁	C₄	1	1	yes	characteristic, complemented
37	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	#14519784	—	2	32	no	—
39	#14519784	—	2	16	no	—
40	#14519784	C₂³	1	32	yes	complemented
41	C₂×#11758194	—	2	2	no	—
42	C₂×#11758194	—	2	4	no	—
43	C₂×#11758194	—	2	32	no	—
44	C₂×#11758194	—	2	8	no	—
45	C₂×#11758194	D₄	1	2	yes	—
46	C₂×#11758194	D₄	1	2	yes	—
47	C₂×#11758194	D₄	1	4	yes	—
48	C₂×#11758194	C₂³	1	4	yes	—
49	C₂×#11758194	C₂³	1	8	yes	—
50	C₂×#11758194	C₂³	1	4	yes	—
51	C₂²×#92418	—	2	2	no	—
52	C₂²×#92418	—	2	8	no	—
53	C₂²×#92418	C₂³	1	2	yes	—
54	#14519736	—	2	2	no	—
55	#14519736	C₂³	1	4	yes	—
56	C₂×C₄⋊Dic₆₁	—	2	1	no	—
57	C₂×C₂²⋊Dic₆₁	—	2	1	no	—
58	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
59	#14519713	C₂³	1	8	yes	complemented
60	#14519713	C₂³	1	8	yes	complemented
61	#14519704	C₂³	1	32	yes	complemented
62	#14519687	C₂³	1	8	yes	complemented
63	C₈×Dic₆₁	C₂³	1	8	yes	complemented
64	C₂×#41×C₆₁	—	2	2	no	—
65	C₂×#41×C₆₁	—	2	4	no	—
66	C₂×#41×C₆₁	—	2	2	no	—
67	C₂×#41×C₆₁	—	2	4	no	—
68	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
69	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
70	C₂×#41×C₆₁	C₂³	1	4	yes	—
71	C₂×#41×C₆₁	C₂³	1	8	yes	—
72	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
73	C₂²×D₄×C₆₁	—	2	2	no	—
74	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
75	C₂³×C₄×C₆₁	—	2	2	no	—
76	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
77	#135×C₆₁	C₂×C₄	1	8	yes	—
78	#135×C₆₁	C₂×C₄	1	8	yes	—
79	#135×C₆₁	C₂×C₄	1	16	yes	complemented
80	#135×C₆₁	C₂×C₄	1	16	yes	complemented
81	#135×C₆₁	C₂³	1	8	yes	—
82	#135×C₆₁	C₂³	1	8	yes	—
83	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
84	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
85	C₂×Q₁₆×C₆₁	C₂×C₄	1	8	yes	complemented
86	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
87	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
88	C₂×SD₁₆×C₆₁	C₂×C₄	1	16	yes	complemented
89	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
90	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
91	C₂×D₈×C₆₁	C₂×C₄	1	8	yes	complemented
92	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
97	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
100	C₂⁴×C₆₁	—	2	2	no	—
101	C₂⁴×C₆₁	#41	1	1	yes	characteristic
102	#41×C₆₁	—	2	8	no	—
103	#41×C₆₁	—	2	8	no	—
104	#41×C₆₁	—	2	8	no	—
105	#41×C₆₁	—	2	8	no	—
106	#41×C₆₁	—	2	4	no	—
107	#41×C₆₁	—	2	4	no	—
108	#41×C₆₁	—	2	8	no	—
109	#41×C₆₁	C₂²×C₄	1	8	yes	—
110	#41×C₆₁	C₂²×C₄	1	16	yes	—
111	#41×C₆₁	C₂⁴	1	8	yes	—
112	C₂×Q₈×C₆₁	—	2	2	no	—
113	C₂×Q₈×C₆₁	—	2	4	no	—
114	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
115	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	—
116	C₂×D₄×C₆₁	—	2	4	no	—
117	C₂×D₄×C₆₁	—	2	8	no	—
118	C₂×D₄×C₆₁	—	2	4	no	—
119	C₂×D₄×C₆₁	—	2	8	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
123	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	4	no	—
126	C₂²×C₄×C₆₁	—	2	8	no	—
127	C₂²×C₄×C₆₁	—	2	4	no	—
128	C₂²×C₄×C₆₁	—	2	8	no	—
129	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	#41	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
139	C₂²×Dic₆₁	—	2	2	no	—
140	Q₁₆×C₆₁	C₂²×C₄	1	8	yes	—
141	Q₁₆×C₆₁	C₂²×C₄	1	8	yes	—
142	SD₁₆×C₆₁	C₂²×C₄	1	16	yes	—
143	SD₁₆×C₆₁	C₂²×C₄	1	16	yes	—
144	D₈×C₆₁	C₂²×C₄	1	8	yes	—
145	D₈×C₆₁	C₂²×C₄	1	8	yes	—
146	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
149	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
152	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
155	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
156	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
157	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
158	C₂²⋊Dic₆₁	—	2	4	no	—
159	C₄⋊Dic₆₁	—	2	4	no	—
160	C₄×Dic₆₁	—	2	2	no	—
161	C₄×Dic₆₁	C₂⁴	1	4	yes	—
162	#11758194	—	2	8	no	—
163	#11758194	—	2	4	no	—
164	#11758194	—	2	32	no	—
165	#11758194	C₂×D₄	1	8	yes	—
166	#11758194	C₂×D₄	1	8	yes	—
167	#11758194	C₂⁴	1	8	yes	—
168	C₂×#92418	—	2	4	no	—
169	C₂×#92418	—	2	8	no	—
170	C₂×#92418	—	2	32	no	—
171	C₂×#92418	C₂×D₄	1	4	yes	—
172	C₂×#92418	C₂×D₄	1	4	yes	—
173	C₂×#92418	C₂⁴	1	4	yes	—
174	C₂³×C₆₁	—	2	4	no	—
175	C₂³×C₆₁	—	2	8	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	8	4	no	—
178	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
179	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
180	C₂³×C₆₁	C₄×D₄	1	2	yes	—
181	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
182	C₂³×C₆₁	C₂×#41	1	2	yes	—
183	Q₈×C₆₁	—	2	4	no	—
184	Q₈×C₆₁	—	2	8	no	—
185	Q₈×C₆₁	C₂³×C₄	1	8	yes	—
186	D₄×C₆₁	—	2	8	no	—
187	D₄×C₆₁	—	2	16	no	—
188	D₄×C₆₁	—	2	8	no	—
189	D₄×C₆₁	—	2	4	no	—
190	D₄×C₆₁	—	2	8	no	—
191	D₄×C₆₁	C₂³×C₄	1	8	yes	—
192	C₂×C₄×C₆₁	—	2	8	no	—
193	C₂×C₄×C₆₁	—	2	4	no	—
194	C₂×C₄×C₆₁	—	2	8	no	—
195	C₂×C₄×C₆₁	—	2	16	no	—
196	C₂×C₄×C₆₁	—	2	8	no	—
197	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
214	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
215	C₂×Dic₆₁	—	2	4	no	—
216	C₂×Dic₆₁	—	4	4	no	—
217	C₈×C₆₁	C₂³×C₄	1	2	yes	—
218	C₈×C₆₁	C₂³×C₄	1	2	yes	—
219	C₈×C₆₁	C₂³×C₄	1	2	yes	—
220	C₈×C₆₁	C₂³×C₄	1	2	yes	—
221	#92418	—	2	8	no	—
222	#92418	C₂²×D₄	1	8	yes	—
223	C₂×#2957	—	61	1	no	maximal, Sylow
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	2	2	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	8	no	—
228	C₂²×C₆₁	—	4	2	no	—
229	C₂²×C₆₁	—	4	2	no	—
230	C₂²×C₆₁	—	4	8	no	—
231	C₂²×C₆₁	—	8	8	no	—
232	C₂²×C₆₁	C₂×C₄×D₄	1	2	yes	—
233	C₂²×C₆₁	C₂×C₄×D₄	1	2	yes	—
234	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
237	C₄×C₆₁	—	2	8	no	—
238	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
239	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
241	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
243	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
244	Dic₆₁	—	4	4	no	—
245	C₂²×#135	D₆₁	1	1	yes	characteristic
246	C₂×#568	—	61	2	no	—
247	#2957	—	61	16	no	—
248	C₂×#444	—	61	4	no	—
249	C₂×#443	—	61	4	no	—
250	C₂²×#108	—	61	1	no	—
251	C₂×#421	—	61	2	no	—
252	C₂×#405	—	61	1	no	—
253	C₂×C₆₁	—	2	1	no	—
254	C₂×C₆₁	—	2	2	no	—
255	C₂×C₆₁	—	2	1	no	—
256	C₂×C₆₁	—	2	2	no	—
257	C₂×C₆₁	—	4	8	no	—
258	C₂×C₆₁	#2957	1	2	yes	complemented
259	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
260	C₂²×#41	C₂×D₆₁	1	2	yes	—
261	C₂×#135	Dic₆₁	1	2	yes	complemented
262	C₂×#135	Dic₆₁	1	2	yes	complemented
263	C₂×#135	Dic₆₁	1	8	yes	complemented
264	C₂×#135	C₂×D₆₁	1	2	yes	—
265	C₂×#135	C₂×D₆₁	1	2	yes	—
266	C₂×#135	C₂×D₆₁	1	8	yes	—
267	C₂²×Q₁₆	Dic₆₁	1	1	yes	characteristic, complemented
268	C₂²×SD₁₆	Dic₆₁	1	2	yes	complemented
269	C₂²×D₈	Dic₆₁	1	1	yes	characteristic, complemented
270	#568	—	61	16	no	—
271	#568	—	122	8	no	—
272	C₂×#131	—	61	8	no	—
273	C₂×#131	—	122	4	no	—
274	C₂²×M₁₆	—	61	1	no	—
275	C₂²×M₁₆	—	61	2	no	—
276	C₂²×M₁₆	—	122	4	no	—
277	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
278	C₂×#117	—	61	1	no	—
279	#444	—	61	32	no	—
280	#443	—	61	32	no	—
281	C₂×#108	—	61	2	no	—
282	C₂×#108	—	61	2	no	—
283	C₂×#108	—	61	8	no	—
284	#421	—	61	16	no	—
285	C₂×#104	—	61	8	no	—
286	#405	—	61	8	no	—
287	C₂×#97	—	61	2	no	—
288	C₂×C₄×C₈	—	61	2	no	—
289	C₆₁	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	C₂×Dic₆₁	1	4	yes	—
295	C₂×#41	C₂×Dic₆₁	1	8	yes	—
296	C₂×#41	C₂²×D₆₁	1	4	yes	—
297	C₂×#41	C₂²×D₆₁	1	8	yes	—
298	C₂²×Q₈	C₂×Dic₆₁	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	C₂×Dic₆₁	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
303	#135	C₂×Dic₆₁	1	8	yes	—
304	#135	C₂×Dic₆₁	1	8	yes	—
305	#135	C₂×Dic₆₁	1	16	yes	complemented
306	#135	C₂×Dic₆₁	1	16	yes	complemented
307	#135	C₂²×D₆₁	1	8	yes	—
308	#135	C₂²×D₆₁	1	8	yes	—
309	C₂×Q₁₆	C₂×Dic₆₁	1	2	yes	—
310	C₂×Q₁₆	C₂×Dic₆₁	1	2	yes	—
311	C₂×Q₁₆	C₂×Dic₆₁	1	8	yes	complemented
312	C₂×SD₁₆	C₂×Dic₆₁	1	4	yes	—
313	C₂×SD₁₆	C₂×Dic₆₁	1	4	yes	—
314	C₂×SD₁₆	C₂×Dic₆₁	1	16	yes	complemented
315	C₂×D₈	C₂×Dic₆₁	1	2	yes	—
316	C₂×D₈	C₂×Dic₆₁	1	2	yes	—
317	C₂×D₈	C₂×Dic₆₁	1	8	yes	complemented
318	#131	—	61	32	no	—
319	#131	—	122	16	no	—
320	#131	—	122	32	no	—
321	C₂×M₁₆	—	61	2	no	—
322	C₂×M₁₆	—	61	2	no	—
323	C₂×M₁₆	—	61	4	no	—
324	C₂×M₁₆	—	61	4	no	—
325	C₂×M₁₆	—	61	4	no	—
326	C₂×M₁₆	—	61	8	no	—
327	C₂×M₁₆	—	122	8	no	—
328	C₂×M₁₆	—	122	32	no	—
329	C₂×M₁₆	—	122	2	no	—
330	C₂×M₁₆	—	122	4	no	—
331	C₂²×C₈	—	61	2	no	—
332	C₂²×C₈	—	122	8	no	—
333	C₂²×C₈	—	122	2	no	—
334	C₂²×C₈	C₂×Dic₆₁	1	1	yes	characteristic
335	C₂²×C₈	C₂×Dic₆₁	1	1	yes	characteristic
336	C₂²×C₈	C₂×Dic₆₁	1	1	yes	characteristic
337	C₂²×C₈	C₂×Dic₆₁	1	1	yes	characteristic
338	C₂²×C₈	C₂×Dic₆₁	1	4	yes	—
339	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₆₁	1	4	yes	—
342	#117	—	61	4	no	—
343	#117	—	122	2	no	—
344	C₂×C₄⋊C₄	—	122	1	no	—
345	C₂×C₂²⋊C₄	—	122	1	no	—
346	C₂×C₄²	—	61	2	no	—
347	#108	—	61	8	no	—
348	#108	—	61	8	no	—
349	#104	—	61	32	no	—
350	#97	—	61	8	no	—
351	C₄×C₈	—	61	8	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	#11758224	1	1	yes	characteristic
354	#41	—	2	4	no	—
355	#41	—	2	8	no	—
356	#41	—	2	4	no	—
357	#41	—	2	8	no	—
358	#41	—	2	8	no	—
359	#41	—	2	8	no	—
360	#41	—	2	8	no	—
361	#41	C₂²×Dic₆₁	1	8	yes	—
362	#41	C₂²×Dic₆₁	1	16	yes	—
363	#41	C₂³×D₆₁	1	8	yes	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	C₂²×Dic₆₁	1	4	yes	—
367	C₂×Q₈	C₂²×Dic₆₁	1	8	yes	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	C₂²×Dic₆₁	1	4	yes	—
375	C₂×D₄	C₂²×Dic₆₁	1	8	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	122	2	no	—
382	C₂²×C₄	D₄×D₆₁	1	2	yes	—
383	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
384	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
385	C₂²×C₄	#11758224	1	1	yes	characteristic
386	C₂²×C₄	#11758224	1	2	yes	—
387	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₆₁	1	2	yes	—
390	C₂²×C₄	C₂³×D₆₁	1	2	yes	—
391	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
392	Q₁₆	C₂²×Dic₆₁	1	8	yes	—
393	Q₁₆	C₂²×Dic₆₁	1	8	yes	—
394	SD₁₆	C₂²×Dic₆₁	1	16	yes	—
395	SD₁₆	C₂²×Dic₆₁	1	16	yes	—
396	D₈	C₂²×Dic₆₁	1	8	yes	—
397	D₈	C₂²×Dic₆₁	1	8	yes	—
398	M₁₆	—	61	8	no	—
399	M₁₆	—	61	8	no	—
400	M₁₆	—	61	8	no	—
401	M₁₆	—	122	32	no	—
402	M₁₆	—	122	8	no	—
403	M₁₆	—	122	4	no	—
404	C₂×C₈	—	61	4	no	—
405	C₂×C₈	—	61	4	no	—
406	C₂×C₈	—	61	4	no	—
407	C₂×C₈	—	122	32	no	—
408	C₂×C₈	—	122	8	no	—
409	C₂×C₈	—	122	4	no	—
410	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
411	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
412	C₂×C₈	C₂²×Dic₆₁	1	4	yes	—
413	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
414	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
415	C₂×C₈	C₂²×Dic₆₁	1	4	yes	—
416	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
417	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
418	C₂×C₈	C₂²×Dic₆₁	1	4	yes	—
419	C₂×C₈	C₂²×Dic₆₁	1	4	yes	—
420	C₂×C₈	C₂³×D₆₁	1	2	yes	—
421	C₂×C₈	C₂³×D₆₁	1	2	yes	—
422	C₄⋊C₄	—	122	4	no	—
423	C₂²⋊C₄	—	122	4	no	—
424	C₄²	—	61	4	no	—
425	C₄²	—	122	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	D₄×Dic₆₁	1	1	yes	characteristic
431	C₂³	D₄×Dic₆₁	1	1	yes	characteristic
432	C₂³	D₄×Dic₆₁	1	2	yes	—
433	C₂³	C₂×#11758224	1	1	yes	characteristic
434	C₂³	C₂×#11758224	1	2	yes	—
435	Q₈	—	2	4	no	—
436	Q₈	—	2	8	no	—
437	Q₈	C₂³×Dic₆₁	1	8	yes	—
438	D₄	—	2	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	C₂³×Dic₆₁	1	8	yes	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	16	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	122	4	no	—
450	C₂×C₄	—	244	4	no	—
451	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
452	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
453	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
454	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
456	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
457	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
458	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
459	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₆₁	1	2	yes	—
461	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₆₁	1	2	yes	—
464	C₂×C₄	C₂×D₄×D₆₁	1	2	yes	—
465	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
467	C₂×C₄	C₂×#11758224	1	2	yes	—
468	C₂×C₄	C₂⁴×D₆₁	1	1	yes	characteristic
469	C₈	—	61	8	no	—
470	C₈	—	122	8	no	—
471	C₈	C₂³×Dic₆₁	1	2	yes	—
472	C₈	C₂³×Dic₆₁	1	2	yes	—
473	C₈	C₂³×Dic₆₁	1	2	yes	—
474	C₈	C₂³×Dic₆₁	1	2	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	8	8	no	—
483	C₂²	C₂×D₄×Dic₆₁	1	2	yes	—
484	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
485	C₂²	C₂×D₄×Dic₆₁	1	2	yes	—
486	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
487	C₂²	C₂²×#11758224	1	1	yes	characteristic
488	C₄	—	2	8	no	—
489	C₄	—	244	4	no	—
490	C₄	C₂×D₄×Dic₆₁	1	2	yes	—
491	C₄	C₂×D₄×Dic₆₁	1	1	yes	characteristic
492	C₄	C₂×D₄×Dic₆₁	1	1	yes	characteristic
493	C₄	C₂×D₄×Dic₆₁	1	2	yes	—
494	C₄	C₂⁴×Dic₆₁	1	1	yes	characteristic
495	C₄	C₂²×D₄×D₆₁	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	8	no	—
501	C₂	#21454736	1	2	yes	direct product factor
502	C₂	C₂²×D₄×Dic₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₄×C₆₁	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₁
Fitting, prime radical	C₂²×#135×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
cosocle	C₂×C₄×C₆₁	C₂⁵
hypercenter	C₂²×#135	D₆₁
hypocenter	C₆₁	C₂×#2957
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#16840529	C₂	semidirect
2. #21454736	C₂	direct (N × H)
3. C₂×#16839884	C₂	semidirect
4. C₂×#16839879	C₂	semidirect
5. C₂²×#14519713	C₂	semidirect
6. C₂×#16839779	C₂	semidirect
7. C₂×#16839717	C₂	semidirect
10. #16840529	C₂²	semidirect
12. C₂×#14519784	C₂²	semidirect
17. #16839884	C₂²	semidirect
18. #16839879	C₂²	semidirect
19. C₂×#14519713	C₂²	semidirect
20. C₂×#14519713	C₂²	semidirect
21. C₂×#14519713	C₂²	semidirect
22. #16839779	C₂²	semidirect
23. C₂×#14519704	C₂²	semidirect
24. #16839717	C₂²	semidirect
25. C₂×#14519687	C₂²	semidirect
26. C₂×C₈×Dic₆₁	C₂²	semidirect
28. C₂×#135×C₆₁	C₄	semidirect
29. C₂×#135×C₆₁	C₄	semidirect
30. C₂×#135×C₆₁	C₄	semidirect
34. C₂²×Q₁₆×C₆₁	C₄	semidirect
35. C₂²×SD₁₆×C₆₁	C₄	semidirect
36. C₂²×D₈×C₆₁	C₄	semidirect
40. #14519784	C₂³	semidirect
59. #14519713	C₂³	semidirect
60. #14519713	C₂³	semidirect
61. #14519704	C₂³	semidirect
62. #14519687	C₂³	semidirect
63. C₈×Dic₆₁	C₂³	semidirect
79. #135×C₆₁	C₂×C₄	semidirect
80. #135×C₆₁	C₂×C₄	semidirect
85. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
88. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
91. C₂×D₈×C₆₁	C₂×C₄	semidirect
258. C₂×C₆₁	#2957	semidirect
261. C₂×#135	Dic₆₁	semidirect
262. C₂×#135	Dic₆₁	semidirect
263. C₂×#135	Dic₆₁	semidirect
267. C₂²×Q₁₆	Dic₆₁	semidirect
268. C₂²×SD₁₆	Dic₆₁	semidirect
269. C₂²×D₈	Dic₆₁	semidirect
289. C₆₁	C₂×#2957	semidirect
305. #135	C₂×Dic₆₁	semidirect
306. #135	C₂×Dic₆₁	semidirect
311. C₂×Q₁₆	C₂×Dic₆₁	semidirect
314. C₂×SD₁₆	C₂×Dic₆₁	semidirect
317. C₂×D₈	C₂×Dic₆₁	semidirect
501. C₂	#21454736	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16840529	2
#21454736	2
C₂×#16839884	2
C₂×#16839879	2
C₂²×#14519713	2
C₂×#16839779	2
C₂×#16839717	2
C₂²×#135×C₆₁	2
C₂×#2957	61

Subgroups — C2×#21454736 #30544334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21454736 #30544334