Subgroups — C₂×C₆₁×#1896 #29524410

Order 15616.

2514 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₆₁	C₂	1	2	yes	maximal, complemented
4	C₂×C₆₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1896	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₆₁×#339	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₆₁	—	2	1	no	—
9	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
11	C₆₁×#525	—	2	2	no	—
12	C₆₁×#525	—	2	2	no	—
13	C₆₁×#525	C₄	1	4	yes	complemented
14	C₆₁×#525	C₂²	1	4	yes	—
15	C₂×#123×C₆₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₆₁	C₄	1	2	yes	complemented
17	C₂×#121×C₆₁	C₄	1	2	yes	complemented
18	C₂×#120×C₆₁	—	2	1	no	—
19	C₂×C₄×D₄×C₆₁	—	2	2	no	—
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₆₁	—	2	2	no	—
22	C₂²×C₄²×C₆₁	—	2	1	no	—
23	C₂²×C₄²×C₆₁	—	2	8	no	—
24	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₁	C₂²	1	4	yes	complemented
26	C₂×#104×C₆₁	—	2	8	no	—
27	C₂×#104×C₆₁	C₂²	1	8	yes	complemented
28	C₆₁×#407	—	2	2	no	—
29	C₆₁×#407	C₂²	1	4	yes	complemented
30	C₂×C₂²⋊C₈×C₆₁	—	2	2	no	—
31	C₆₁×#339	C₂²	1	8	yes	complemented
32	C₂⁵×C₆₁	D₄	1	1	yes	characteristic
33	C₂×#41×C₆₁	—	2	1	no	—
34	C₂×#41×C₆₁	—	2	1	no	—
35	C₂×#41×C₆₁	—	2	4	no	—
36	C₂×#41×C₆₁	—	2	4	no	—
37	C₂×#41×C₆₁	C₂×C₄	1	2	yes	complemented
38	C₂×#41×C₆₁	C₂³	1	2	yes	—
39	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂²×D₄×C₆₁	—	2	2	no	—
41	C₂²×D₄×C₆₁	—	2	1	no	—
42	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂³×C₄×C₆₁	—	2	16	no	—
44	C₂³×C₄×C₆₁	—	2	8	no	—
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	C₂³×C₄×C₆₁	—	2	4	no	—
47	C₂³×C₄×C₆₁	—	2	4	no	—
48	C₂³×C₄×C₆₁	—	2	4	no	—
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₁	D₄	1	2	yes	—
54	C₂³×C₄×C₆₁	D₄	1	2	yes	—
55	C₂³×C₄×C₆₁	D₄	1	2	yes	—
56	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	2	4	no	—
60	C₂×M₁₆×C₆₁	—	2	4	no	—
61	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
62	C₂²×C₈×C₆₁	—	2	2	no	—
63	#123×C₆₁	—	2	4	no	—
64	#123×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	4	no	—
66	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
67	#121×C₆₁	—	2	4	no	—
68	#121×C₆₁	C₂×C₄	1	8	yes	complemented
69	#120×C₆₁	—	2	4	no	—
70	#120×C₆₁	—	2	4	no	—
71	C₄×D₄×C₆₁	—	2	8	no	—
72	C₄×D₄×C₆₁	—	2	8	no	—
73	#117×C₆₁	—	2	1	no	—
74	#117×C₆₁	—	2	1	no	—
75	#117×C₆₁	C₂×C₄	1	2	yes	complemented
76	#117×C₆₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	complemented
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	—	2	8	no	—
83	C₂×C₄²×C₆₁	—	2	16	no	—
84	C₂×C₄²×C₆₁	—	2	2	no	—
85	C₂×C₄²×C₆₁	—	2	4	no	—
86	C₂×C₄²×C₆₁	—	2	4	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	16	no	—
89	C₂×C₄²×C₆₁	D₄	1	8	yes	complemented
90	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
91	#104×C₆₁	—	2	16	no	—
92	C₂²⋊C₈×C₆₁	—	2	8	no	—
93	C₂⁴×C₆₁	—	2	8	no	—
94	C₂⁴×C₆₁	—	2	2	no	—
95	C₂⁴×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	—	2	1	no	—
97	C₂⁴×C₆₁	C₂²⋊C₄	1	2	yes	—
98	C₂⁴×C₆₁	C₂²⋊C₄	1	2	yes	—
99	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
100	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
101	#41×C₆₁	—	2	8	no	—
102	#41×C₆₁	—	2	4	no	—
103	#41×C₆₁	—	2	4	no	—
104	#41×C₆₁	—	4	2	no	—
105	#41×C₆₁	—	4	4	no	—
106	#41×C₆₁	—	4	2	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	4	no	—
109	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	complemented
110	C₂×D₄×C₆₁	—	2	8	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	4	no	—
115	C₂×D₄×C₆₁	—	4	8	no	—
116	C₂×D₄×C₆₁	—	4	2	no	—
117	C₂×D₄×C₆₁	—	4	2	no	—
118	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	complemented
119	C₂²×C₄×C₆₁	—	2	16	no	—
120	C₂²×C₄×C₆₁	—	2	64	no	—
121	C₂²×C₄×C₆₁	—	2	16	no	—
122	C₂²×C₄×C₆₁	—	2	32	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	8	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	4	no	—
127	C₂²×C₄×C₆₁	—	2	8	no	—
128	C₂²×C₄×C₆₁	—	2	8	no	—
129	C₂²×C₄×C₆₁	—	2	4	no	—
130	C₂²×C₄×C₆₁	—	2	8	no	—
131	C₂²×C₄×C₆₁	—	2	8	no	—
132	C₂²×C₄×C₆₁	—	2	4	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	4	4	no	—
140	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
141	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
142	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
143	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
144	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	#41	1	4	yes	—
154	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₆₁	—	2	4	no	—
156	M₁₆×C₆₁	—	2	4	no	—
157	M₁₆×C₆₁	—	4	4	no	—
158	C₂×C₈×C₆₁	—	2	4	no	—
159	C₂×C₈×C₆₁	—	4	4	no	—
160	C₄⋊C₄×C₆₁	—	2	8	no	—
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	complemented
163	C₂²⋊C₄×C₆₁	—	2	2	no	—
164	C₂²⋊C₄×C₆₁	—	2	8	no	—
165	C₂²⋊C₄×C₆₁	—	2	2	no	—
166	C₂²⋊C₄×C₆₁	—	2	8	no	—
167	C₄²×C₆₁	—	2	16	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	2	8	no	—
170	C₄²×C₆₁	—	2	4	no	—
171	C₄²×C₆₁	—	2	2	no	—
172	C₄²×C₆₁	C₂×D₄	1	8	yes	complemented
173	C₂³×C₆₁	—	2	16	no	—
174	C₂³×C₆₁	—	2	16	no	—
175	C₂³×C₆₁	—	2	2	no	—
176	C₂³×C₆₁	—	2	2	no	—
177	C₂³×C₆₁	—	2	4	no	—
178	C₂³×C₆₁	—	2	4	no	—
179	C₂³×C₆₁	—	2	4	no	—
180	C₂³×C₆₁	—	2	4	no	—
181	C₂³×C₆₁	—	2	8	no	—
182	C₂³×C₆₁	—	2	8	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	4	2	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	#104	1	8	yes	complemented
187	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₆₁	#120	1	2	yes	—
191	C₂³×C₆₁	#123	1	2	yes	—
192	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₆₁	—	2	4	no	—
194	Q₈×C₆₁	—	4	2	no	—
195	D₄×C₆₁	—	2	4	no	—
196	D₄×C₆₁	—	4	2	no	—
197	D₄×C₆₁	—	4	2	no	—
198	D₄×C₆₁	—	4	4	no	—
199	D₄×C₆₁	—	4	16	no	—
200	D₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	2	64	no	—
202	C₂×C₄×C₆₁	—	2	16	no	—
203	C₂×C₄×C₆₁	—	2	32	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	8	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	4	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	8	no	—
210	C₂×C₄×C₆₁	—	2	8	no	—
211	C₂×C₄×C₆₁	—	2	8	no	—
212	C₂×C₄×C₆₁	—	2	8	no	—
213	C₂×C₄×C₆₁	—	2	4	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	—	4	4	no	—
217	C₂×C₄×C₆₁	—	4	4	no	—
218	C₂×C₄×C₆₁	—	4	4	no	—
219	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
220	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
223	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
224	C₂×C₄×C₆₁	#120	1	2	yes	—
225	C₂×C₄×C₆₁	#121	1	4	yes	—
226	C₂×C₄×C₆₁	#121	1	4	yes	—
227	C₂×C₄×C₆₁	#123	1	2	yes	—
228	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
232	C₈×C₆₁	—	4	4	no	—
233	C₂×#1896	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₆₁	—	2	8	no	—
235	C₂²×C₆₁	—	2	8	no	—
236	C₂²×C₆₁	—	2	16	no	—
237	C₂²×C₆₁	—	2	2	no	—
238	C₂²×C₆₁	—	2	2	no	—
239	C₂²×C₆₁	—	2	4	no	—
240	C₂²×C₆₁	—	2	4	no	—
241	C₂²×C₆₁	—	2	16	no	—
242	C₂²×C₆₁	—	2	4	no	—
243	C₂²×C₆₁	—	2	4	no	—
244	C₂²×C₆₁	—	4	4	no	—
245	C₂²×C₆₁	—	4	2	no	—
246	C₂²×C₆₁	—	8	4	no	—
247	C₂²×C₆₁	#386	1	2	yes	—
248	C₂²×C₆₁	#386	1	2	yes	—
249	C₂²×C₆₁	C₂×#104	1	4	yes	—
250	C₂²×C₆₁	C₂×#104	1	8	yes	complemented
251	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
253	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
254	C₄×C₆₁	—	2	16	no	—
255	C₄×C₆₁	—	2	4	no	—
256	C₄×C₆₁	—	4	4	no	—
257	C₄×C₆₁	—	4	2	no	—
258	C₄×C₆₁	#386	1	2	yes	—
259	C₄×C₆₁	#386	1	2	yes	—
260	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
261	C₄×C₆₁	C₂×#121	1	2	yes	—
262	C₂×#525	C₂×C₆₁	1	1	yes	characteristic
263	C₂³×C₄²	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂²×#104	C₂×C₆₁	1	2	yes	complemented
265	C₂×#407	C₂×C₆₁	1	1	yes	characteristic, complemented
266	#1896	C₂×C₆₁	1	8	yes	direct product factor
267	C₂×#339	C₂×C₆₁	1	2	yes	complemented
268	C₂×C₆₁	—	2	1	no	—
269	C₂×C₆₁	—	2	1	no	—
270	C₂×C₆₁	—	2	2	no	—
271	C₂×C₆₁	—	2	8	no	—
272	C₂×C₆₁	—	8	2	no	—
273	C₂×C₆₁	#1896	1	4	yes	direct product factor
274	C₂×C₆₁	C₂×#386	1	1	yes	characteristic
275	C₂×C₆₁	C₂²×#104	1	2	yes	—
276	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
277	C₂⁴×C₄	—	2	1	no	—
278	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
280	#525	—	2	2	no	—
281	#525	—	2	2	no	—
282	#525	C₄×C₆₁	1	4	yes	complemented
283	#525	C₂²×C₆₁	1	4	yes	—
284	C₂×#123	—	2	1	no	—
285	C₂×C₂²⋊Q₈	C₄×C₆₁	1	2	yes	complemented
286	C₂×#121	C₄×C₆₁	1	2	yes	complemented
287	C₂×#120	—	2	1	no	—
288	C₂×C₄×D₄	—	2	2	no	—
289	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
290	C₂²×C₄²	—	2	2	no	—
291	C₂²×C₄²	—	2	1	no	—
292	C₂²×C₄²	—	2	8	no	—
293	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
294	C₂²×C₄²	C₂²×C₆₁	1	4	yes	complemented
295	C₂×#104	—	2	8	no	—
296	C₂×#104	C₂²×C₆₁	1	8	yes	complemented
297	#407	—	2	2	no	—
298	#407	C₂²×C₆₁	1	4	yes	complemented
299	C₂×C₂²⋊C₈	—	2	2	no	—
300	#339	C₂²×C₆₁	1	8	yes	complemented
301	C₆₁	C₂×#1896	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁵	D₄×C₆₁	1	1	yes	characteristic
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	4	no	—
307	C₂×#41	C₂×C₄×C₆₁	1	2	yes	complemented
308	C₂×#41	C₂³×C₆₁	1	2	yes	—
309	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic, complemented
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic, complemented
313	C₂³×C₄	—	2	16	no	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	4	no	—
318	C₂³×C₄	—	2	4	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
321	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
322	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
323	C₂³×C₄	D₄×C₆₁	1	2	yes	—
324	C₂³×C₄	D₄×C₆₁	1	2	yes	—
325	C₂³×C₄	D₄×C₆₁	1	2	yes	—
326	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
327	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
328	C₂×M₁₆	—	2	2	no	—
329	C₂×M₁₆	—	2	4	no	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
332	C₂²×C₈	—	2	2	no	—
333	#123	—	2	4	no	—
334	#123	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
337	#121	—	2	4	no	—
338	#121	C₂×C₄×C₆₁	1	8	yes	complemented
339	#120	—	2	4	no	—
340	#120	—	2	4	no	—
341	C₄×D₄	—	2	8	no	—
342	C₄×D₄	—	2	8	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂×C₄×C₆₁	1	2	yes	complemented
346	#117	C₂³×C₆₁	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	complemented
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₄²	—	2	8	no	—
353	C₂×C₄²	—	2	16	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	4	no	—
357	C₂×C₄²	—	2	4	no	—
358	C₂×C₄²	—	2	16	no	—
359	C₂×C₄²	D₄×C₆₁	1	8	yes	complemented
360	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
361	#104	—	2	16	no	—
362	C₂²⋊C₈	—	2	8	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	1	no	—
367	C₂⁴	C₂²⋊C₄×C₆₁	1	2	yes	—
368	C₂⁴	C₂²⋊C₄×C₆₁	1	2	yes	—
369	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
370	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
371	#41	—	2	8	no	—
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	4	2	no	—
375	#41	—	4	4	no	—
376	#41	—	4	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	complemented
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	complemented
389	C₂²×C₄	—	2	16	no	—
390	C₂²×C₄	—	2	64	no	—
391	C₂²×C₄	—	2	16	no	—
392	C₂²×C₄	—	2	32	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
411	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
412	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
413	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
414	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
415	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
416	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
419	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
423	C₂²×C₄	#41×C₆₁	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
425	M₁₆	—	2	4	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	—	4	4	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	4	4	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	complemented
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₄²	—	2	16	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	8	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	2	no	—
442	C₄²	C₂×D₄×C₆₁	1	8	yes	complemented
443	C₂³	—	2	16	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	#104×C₆₁	1	8	yes	complemented
457	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
458	C₂³	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
459	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
460	C₂³	#120×C₆₁	1	2	yes	—
461	C₂³	#123×C₆₁	1	2	yes	—
462	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	Q₈	—	2	4	no	—
464	Q₈	—	4	2	no	—
465	D₄	—	2	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	16	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	C₂×C₄	—	2	64	no	—
472	C₂×C₄	—	2	16	no	—
473	C₂×C₄	—	2	32	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
492	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
493	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
494	C₂×C₄	#120×C₆₁	1	2	yes	—
495	C₂×C₄	#121×C₆₁	1	4	yes	—
496	C₂×C₄	#121×C₆₁	1	4	yes	—
497	C₂×C₄	#123×C₆₁	1	2	yes	—
498	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
502	C₈	—	4	4	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	16	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	16	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	8	4	no	—
516	C₂²	C₆₁×#386	1	2	yes	—
517	C₂²	C₆₁×#386	1	2	yes	—
518	C₂²	C₂×#104×C₆₁	1	4	yes	—
519	C₂²	C₂×#104×C₆₁	1	8	yes	complemented
520	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
521	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
522	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
523	C₄	—	2	16	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	4	no	—
527	C₄	C₆₁×#386	1	2	yes	—
528	C₄	C₆₁×#386	1	2	yes	—
529	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
530	C₄	C₂×#121×C₆₁	1	2	yes	—
531	C₂	—	2	1	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	8	no	—
534	C₂	—	2	1	no	—
535	C₂	—	8	2	no	—
536	C₂	C₆₁×#1896	1	4	yes	direct product factor
537	C₂	C₂×C₆₁×#386	1	1	yes	characteristic
538	C₂	C₂²×#104×C₆₁	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂×C₂²⋊C₄
prime radical	C₂×C₆₁×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂⁴×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₆₁	C₂	semidirect
3. C₂²×#104×C₆₁	C₂	semidirect
4. C₂×C₆₁×#407	C₂	semidirect
5. C₆₁×#1896	C₂	direct (N × H)
6. C₂×C₆₁×#339	C₂	semidirect
13. C₆₁×#525	C₄	semidirect
16. C₂×C₂²⋊Q₈×C₆₁	C₄	semidirect
17. C₂×#121×C₆₁	C₄	semidirect
25. C₂²×C₄²×C₆₁	C₂²	semidirect
27. C₂×#104×C₆₁	C₂²	semidirect
29. C₆₁×#407	C₂²	semidirect
31. C₆₁×#339	C₂²	semidirect
37. C₂×#41×C₆₁	C₂×C₄	semidirect
39. C₂²×Q₈×C₆₁	C₂×C₄	semidirect
42. C₂²×D₄×C₆₁	C₂×C₄	semidirect
66. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
68. #121×C₆₁	C₂×C₄	semidirect
75. #117×C₆₁	C₂×C₄	semidirect
78. C₂×C₄⋊C₄×C₆₁	C₂×C₄	semidirect
89. C₂×C₄²×C₆₁	D₄	semidirect
109. C₂×Q₈×C₆₁	C₂²×C₄	semidirect
118. C₂×D₄×C₆₁	C₂²×C₄	semidirect
162. C₄⋊C₄×C₆₁	C₂²×C₄	semidirect
172. C₄²×C₆₁	C₂×D₄	semidirect
186. C₂³×C₆₁	#104	semidirect
233. C₂×#1896	C₆₁	direct (N × H)
250. C₂²×C₆₁	C₂×#104	semidirect
263. C₂³×C₄²	C₂×C₆₁	semidirect
264. C₂²×#104	C₂×C₆₁	semidirect
265. C₂×#407	C₂×C₆₁	semidirect
266. #1896	C₂×C₆₁	direct (N × H)
267. C₂×#339	C₂×C₆₁	semidirect
273. C₂×C₆₁	#1896	direct (N × H)
282. #525	C₄×C₆₁	semidirect
285. C₂×C₂²⋊Q₈	C₄×C₆₁	semidirect
286. C₂×#121	C₄×C₆₁	semidirect
294. C₂²×C₄²	C₂²×C₆₁	semidirect
296. C₂×#104	C₂²×C₆₁	semidirect
298. #407	C₂²×C₆₁	semidirect
300. #339	C₂²×C₆₁	semidirect
301. C₆₁	C₂×#1896	direct (N × H)
307. C₂×#41	C₂×C₄×C₆₁	semidirect
309. C₂²×Q₈	C₂×C₄×C₆₁	semidirect
312. C₂²×D₄	C₂×C₄×C₆₁	semidirect
336. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
338. #121	C₂×C₄×C₆₁	semidirect
345. #117	C₂×C₄×C₆₁	semidirect
348. C₂×C₄⋊C₄	C₂×C₄×C₆₁	semidirect
359. C₂×C₄²	D₄×C₆₁	semidirect
379. C₂×Q₈	C₂²×C₄×C₆₁	semidirect
388. C₂×D₄	C₂²×C₄×C₆₁	semidirect
432. C₄⋊C₄	C₂²×C₄×C₆₁	semidirect
442. C₄²	C₂×D₄×C₆₁	semidirect
456. C₂³	#104×C₆₁	semidirect
519. C₂²	C₂×#104×C₆₁	semidirect
536. C₂	C₆₁×#1896	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×C₆₁×#525	2
C₂³×C₄²×C₆₁	2
C₂²×#104×C₆₁	2
C₂×C₆₁×#407	2
C₆₁×#1896	2
C₂×C₆₁×#339	2
C₂×#1896	61

Subgroups — C2×C61×#1896 #29524410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1896 #29524410