Subgroups — C₂×C₄×#137×C₆₁ #29563590

Order 15616.

2810 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#137×C₆₁	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#441	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×Q₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
11	C₂×C₆₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#137×C₆₁	C₄	1	16	yes	direct product factor
16	C₂×#137×C₆₁	C₂²	1	8	yes	—
17	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₄×#41×C₆₁	—	2	4	no	—
22	C₄×#41×C₆₁	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
24	C₂×C₄×Q₈×C₆₁	—	2	4	no	—
25	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
26	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
31	C₂×C₄×D₄×C₆₁	—	2	1	no	—
32	C₂×C₄×D₄×C₆₁	—	2	1	no	—
33	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₁	—	2	1	no	—
36	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
38	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₆₁	—	2	1	no	—
40	C₂²×C₄²×C₆₁	—	2	1	no	—
41	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#441	C₂²	1	16	yes	complemented
43	C₆₁×#440	C₂²	1	16	yes	complemented
44	C₄×Q₁₆×C₆₁	C₂²	1	16	yes	complemented
45	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
46	C₆₁×#428	C₂²	1	8	yes	complemented
47	C₂×#107×C₆₁	C₂²	1	2	yes	—
48	C₂×#106×C₆₁	C₂²	1	2	yes	—
49	C₆₁×#419	C₂²	1	8	yes	complemented
50	C₆₁×#417	C₂²	1	8	yes	—
51	C₂×#103×C₆₁	C₂²	1	2	yes	—
52	C₂×#103×C₆₁	C₂²	1	2	yes	—
53	C₂×#103×C₆₁	C₂²	1	2	yes	—
54	C₂×#102×C₆₁	C₂²	1	2	yes	—
55	C₄×M₁₆×C₆₁	C₂²	1	8	yes	complemented
56	C₂×#97×C₆₁	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
58	C₂×#41×C₆₁	—	2	2	no	—
59	C₂×#41×C₆₁	—	2	4	no	—
60	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
61	C₂×#41×C₆₁	C₂³	1	4	yes	—
62	C₂²×Q₈×C₆₁	—	2	1	no	—
63	C₂²×Q₈×C₆₁	—	2	2	no	—
64	C₂²×Q₈×C₆₁	—	2	4	no	—
65	C₂²×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
67	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
69	C₂²×D₄×C₆₁	—	2	1	no	—
70	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₁	—	2	1	no	—
72	C₂³×C₄×C₆₁	—	2	1	no	—
73	C₂³×C₄×C₆₁	—	2	1	no	—
74	C₂³×C₄×C₆₁	—	2	1	no	—
75	C₂³×C₄×C₆₁	—	2	1	no	—
76	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
79	#137×C₆₁	C₂×C₄	1	64	yes	direct product factor
80	C₂×Q₁₆×C₆₁	C₂×C₄	1	16	yes	complemented
81	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
82	C₂×SD₁₆×C₆₁	C₂×C₄	1	16	yes	complemented
83	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
84	C₂×M₁₆×C₆₁	—	2	4	no	—
85	C₂×M₁₆×C₆₁	C₂×C₄	1	8	yes	complemented
86	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
87	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
88	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
90	C₄×Q₈×C₆₁	—	2	4	no	—
91	C₄×Q₈×C₆₁	—	2	4	no	—
92	C₄×Q₈×C₆₁	—	2	8	no	—
93	C₄×Q₈×C₆₁	—	2	8	no	—
94	C₄×Q₈×C₆₁	—	2	2	no	—
95	C₄×Q₈×C₆₁	—	2	2	no	—
96	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
97	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
98	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
99	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
100	C₄×D₄×C₆₁	—	2	8	no	—
101	C₄×D₄×C₆₁	—	2	8	no	—
102	C₄×D₄×C₆₁	—	2	2	no	—
103	C₄×D₄×C₆₁	—	2	2	no	—
104	C₄×D₄×C₆₁	C₂³	1	4	yes	—
105	C₄×D₄×C₆₁	C₂³	1	4	yes	—
106	#117×C₆₁	—	2	2	no	—
107	#117×C₆₁	—	2	8	no	—
108	#117×C₆₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
111	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
112	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
115	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
123	C₂×C₄²×C₆₁	—	2	1	no	—
124	C₂×C₄²×C₆₁	—	2	1	no	—
125	C₂×C₄²×C₆₁	—	2	2	no	—
126	C₂×C₄²×C₆₁	—	2	8	no	—
127	C₂×C₄²×C₆₁	—	2	1	no	—
128	C₂×C₄²×C₆₁	—	2	2	no	—
129	C₂×C₄²×C₆₁	—	2	8	no	—
130	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₆₁	D₄	1	4	yes	—
132	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
133	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
136	#107×C₆₁	C₂³	1	8	yes	—
137	#106×C₆₁	C₂³	1	8	yes	—
138	#103×C₆₁	C₂³	1	8	yes	—
139	#103×C₆₁	C₂³	1	8	yes	—
140	#103×C₆₁	C₂³	1	8	yes	—
141	#102×C₆₁	C₂³	1	8	yes	—
142	#97×C₆₁	C₂³	1	8	yes	—
143	C₄×C₈×C₆₁	C₂³	1	8	yes	—
144	C₂⁴×C₆₁	—	2	1	no	—
145	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
146	#41×C₆₁	—	2	16	no	—
147	#41×C₆₁	—	2	8	no	—
148	#41×C₆₁	C₂²×C₄	1	16	yes	—
149	C₂×Q₈×C₆₁	—	2	8	no	—
150	C₂×Q₈×C₆₁	—	2	16	no	—
151	C₂×Q₈×C₆₁	—	2	4	no	—
152	C₂×Q₈×C₆₁	—	2	2	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	4	no	—
155	C₂×Q₈×C₆₁	—	2	8	no	—
156	C₂×Q₈×C₆₁	—	2	2	no	—
157	C₂×Q₈×C₆₁	C₂²×C₄	1	8	yes	—
158	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
159	C₂×Q₈×C₆₁	C₂²×C₄	1	16	yes	complemented
160	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
161	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
162	C₂×D₄×C₆₁	—	2	8	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	1	no	—
165	C₂×D₄×C₆₁	—	2	2	no	—
166	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
167	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₆₁	—	2	8	no	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	2	no	—
171	C₂²×C₄×C₆₁	—	2	4	no	—
172	C₂²×C₄×C₆₁	—	2	8	no	—
173	C₂²×C₄×C₆₁	—	2	4	no	—
174	C₂²×C₄×C₆₁	—	2	4	no	—
175	C₂²×C₄×C₆₁	—	2	1	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	—	2	4	no	—
178	C₂²×C₄×C₆₁	—	2	2	no	—
179	C₂²×C₄×C₆₁	—	2	4	no	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	4	2	no	—
182	C₂²×C₄×C₆₁	—	4	4	no	—
183	C₂²×C₄×C₆₁	—	4	4	no	—
184	C₂²×C₄×C₆₁	—	4	4	no	—
185	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₁	#41	1	4	yes	—
195	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
197	Q₁₆×C₆₁	C₂²×C₄	1	32	yes	complemented
198	SD₁₆×C₆₁	C₂²×C₄	1	32	yes	complemented
199	M₁₆×C₆₁	—	2	8	no	—
200	M₁₆×C₆₁	C₂²×C₄	1	16	yes	complemented
201	C₂×C₈×C₆₁	—	2	4	no	—
202	C₂×C₈×C₆₁	C₂²×C₄	1	8	yes	—
203	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
204	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
205	C₄⋊C₄×C₆₁	—	2	8	no	—
206	C₄⋊C₄×C₆₁	—	2	8	no	—
207	C₄⋊C₄×C₆₁	—	2	4	no	—
208	C₄⋊C₄×C₆₁	—	2	2	no	—
209	C₄⋊C₄×C₆₁	—	2	4	no	—
210	C₄⋊C₄×C₆₁	—	2	4	no	—
211	C₄⋊C₄×C₆₁	—	2	1	no	—
212	C₄⋊C₄×C₆₁	—	2	1	no	—
213	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
214	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
215	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²⋊C₄×C₆₁	—	2	4	no	—
217	C₂²⋊C₄×C₆₁	—	2	4	no	—
218	C₂²⋊C₄×C₆₁	—	2	4	no	—
219	C₄²×C₆₁	—	2	4	no	—
220	C₄²×C₆₁	—	2	4	no	—
221	C₄²×C₆₁	—	2	4	no	—
222	C₄²×C₆₁	—	2	8	no	—
223	C₄²×C₆₁	—	2	8	no	—
224	C₄²×C₆₁	C₂×D₄	1	4	yes	—
225	C₄²×C₆₁	C₂×D₄	1	4	yes	—
226	C₄²×C₆₁	C₂×D₄	1	2	yes	—
227	C₄²×C₆₁	C₂×D₄	1	2	yes	—
228	C₄²×C₆₁	C₂⁴	1	2	yes	—
229	C₄²×C₆₁	C₂⁴	1	2	yes	—
230	C₂³×C₆₁	—	2	2	no	—
231	C₂³×C₆₁	—	2	2	no	—
232	C₂³×C₆₁	—	2	4	no	—
233	C₂³×C₆₁	—	2	2	no	—
234	C₂³×C₆₁	—	4	2	no	—
235	C₂³×C₆₁	—	4	2	no	—
236	C₂³×C₆₁	C₄×D₄	1	4	yes	—
237	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
238	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₆₁	—	2	8	no	—
240	Q₈×C₆₁	—	2	16	no	—
241	Q₈×C₆₁	—	2	4	no	—
242	Q₈×C₆₁	—	2	4	no	—
243	Q₈×C₆₁	—	2	2	no	—
244	Q₈×C₆₁	C₂³×C₄	1	8	yes	—
245	Q₈×C₆₁	C₂³×C₄	1	4	yes	—
246	D₄×C₆₁	—	2	16	no	—
247	D₄×C₆₁	—	2	4	no	—
248	D₄×C₆₁	—	2	2	no	—
249	D₄×C₆₁	C₂³×C₄	1	4	yes	—
250	C₂×C₄×C₆₁	—	2	4	no	—
251	C₂×C₄×C₆₁	—	2	8	no	—
252	C₂×C₄×C₆₁	—	2	16	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	2	no	—
255	C₂×C₄×C₆₁	—	2	2	no	—
256	C₂×C₄×C₆₁	—	2	2	no	—
257	C₂×C₄×C₆₁	—	2	4	no	—
258	C₂×C₄×C₆₁	—	2	16	no	—
259	C₂×C₄×C₆₁	—	2	8	no	—
260	C₂×C₄×C₆₁	—	2	2	no	—
261	C₂×C₄×C₆₁	—	2	2	no	—
262	C₂×C₄×C₆₁	—	2	4	no	—
263	C₂×C₄×C₆₁	—	4	4	no	—
264	C₂×C₄×C₆₁	—	4	8	no	—
265	C₂×C₄×C₆₁	—	4	8	no	—
266	C₂×C₄×C₆₁	—	4	2	no	—
267	C₂×C₄×C₆₁	—	4	2	no	—
268	C₂×C₄×C₆₁	—	4	4	no	—
269	C₂×C₄×C₆₁	—	4	8	no	—
270	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
271	C₂×C₄×C₆₁	C₄×D₄	1	8	yes	—
272	C₂×C₄×C₆₁	#137	1	4	yes	direct product factor
273	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
275	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
282	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
283	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
284	C₈×C₆₁	—	2	4	no	—
285	C₈×C₆₁	C₂³×C₄	1	8	yes	—
286	C₂×C₄×#137	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂²×C₆₁	—	2	8	no	—
288	C₂²×C₆₁	—	2	2	no	—
289	C₂²×C₆₁	—	2	2	no	—
290	C₂²×C₆₁	—	2	4	no	—
291	C₂²×C₆₁	—	4	8	no	—
292	C₂²×C₆₁	—	4	2	no	—
293	C₂²×C₆₁	—	4	2	no	—
294	C₂²×C₆₁	C₂×C₄×D₄	1	4	yes	—
295	C₂²×C₆₁	C₂×C₄×D₄	1	2	yes	—
296	C₂²×C₆₁	C₂×#137	1	2	yes	—
297	C₂²×C₆₁	#575	1	2	yes	—
298	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₆₁	—	2	4	no	—
300	C₄×C₆₁	—	2	8	no	—
301	C₄×C₆₁	—	2	2	no	—
302	C₄×C₆₁	—	2	2	no	—
303	C₄×C₆₁	—	2	2	no	—
304	C₄×C₆₁	—	4	2	no	—
305	C₄×C₆₁	—	4	2	no	—
306	C₄×C₆₁	—	4	4	no	—
307	C₄×C₆₁	C₂×C₄×D₄	1	4	yes	—
308	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
309	C₄×C₆₁	C₂×#137	1	4	yes	direct product factor
310	C₄×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
311	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
312	C₂²×#137	C₂×C₆₁	1	1	yes	characteristic
313	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic
314	C₂²×C₄×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
315	C₄×#137	C₂×C₆₁	1	16	yes	direct product factor
316	C₂×#441	C₂×C₆₁	1	2	yes	complemented
317	C₂×#440	C₂×C₆₁	1	2	yes	complemented
318	C₂×C₄×Q₁₆	C₂×C₆₁	1	2	yes	complemented
319	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
320	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
321	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
322	C₂×#419	C₂×C₆₁	1	1	yes	characteristic, complemented
323	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
324	C₂×C₆₁	—	2	4	no	—
325	C₂×C₆₁	—	4	4	no	—
326	C₂×C₆₁	C₄×#137	1	4	yes	direct product factor
327	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
328	C₂×C₆₁	C₂²×#137	1	1	yes	characteristic
329	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
330	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
331	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
332	C₂×#137	C₄×C₆₁	1	16	yes	direct product factor
333	C₂×#137	C₂²×C₆₁	1	8	yes	—
334	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
335	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
336	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
337	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
338	C₄×#41	—	2	4	no	—
339	C₄×#41	C₂²×C₆₁	1	8	yes	—
340	C₂×C₄×Q₈	—	2	1	no	—
341	C₂×C₄×Q₈	—	2	1	no	—
342	C₂×C₄×Q₈	—	2	4	no	—
343	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
344	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
345	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×C₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
348	C₂×C₄×D₄	—	2	1	no	—
349	C₂×C₄×D₄	—	2	1	no	—
350	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×#117	—	2	1	no	—
353	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	—	2	1	no	—
355	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
356	C₂²×C₄²	—	2	1	no	—
357	C₂²×C₄²	—	2	1	no	—
358	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
359	#441	C₂²×C₆₁	1	16	yes	complemented
360	#440	C₂²×C₆₁	1	16	yes	complemented
361	C₄×Q₁₆	C₂²×C₆₁	1	16	yes	complemented
362	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
363	#428	C₂²×C₆₁	1	8	yes	complemented
364	C₂×#107	C₂²×C₆₁	1	2	yes	—
365	C₂×#106	C₂²×C₆₁	1	2	yes	—
366	#419	C₂²×C₆₁	1	8	yes	complemented
367	#417	C₂²×C₆₁	1	8	yes	—
368	C₂×#103	C₂²×C₆₁	1	2	yes	—
369	C₂×#103	C₂²×C₆₁	1	2	yes	—
370	C₂×#103	C₂²×C₆₁	1	2	yes	—
371	C₂×#102	C₂²×C₆₁	1	2	yes	—
372	C₄×M₁₆	C₂²×C₆₁	1	8	yes	complemented
373	C₂×#97	C₂²×C₆₁	1	2	yes	—
374	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
375	C₆₁	C₂×C₄×#137	1	1	yes	characteristic, direct product factor, Sylow
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	4	no	—
378	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
379	C₂×#41	C₂³×C₆₁	1	4	yes	—
380	C₂²×Q₈	—	2	1	no	—
381	C₂²×Q₈	—	2	2	no	—
382	C₂²×Q₈	—	2	4	no	—
383	C₂²×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
384	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
385	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
395	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
397	#137	C₂×C₄×C₆₁	1	64	yes	direct product factor
398	C₂×Q₁₆	C₂×C₄×C₆₁	1	16	yes	complemented
399	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
400	C₂×SD₁₆	C₂×C₄×C₆₁	1	16	yes	complemented
401	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
402	C₂×M₁₆	—	2	4	no	—
403	C₂×M₁₆	C₂×C₄×C₆₁	1	8	yes	complemented
404	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
405	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
406	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
407	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
408	C₄×Q₈	—	2	4	no	—
409	C₄×Q₈	—	2	4	no	—
410	C₄×Q₈	—	2	8	no	—
411	C₄×Q₈	—	2	8	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
415	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
416	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
417	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	—	2	8	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	C₂³×C₆₁	1	4	yes	—
423	C₄×D₄	C₂³×C₆₁	1	4	yes	—
424	#117	—	2	2	no	—
425	#117	—	2	8	no	—
426	#117	C₂³×C₆₁	1	4	yes	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	—	2	8	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	2	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	2	no	—
445	C₂×C₄²	—	2	2	no	—
446	C₂×C₄²	—	2	8	no	—
447	C₂×C₄²	—	2	8	no	—
448	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
449	C₂×C₄²	D₄×C₆₁	1	4	yes	—
450	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
454	#107	C₂³×C₆₁	1	8	yes	—
455	#106	C₂³×C₆₁	1	8	yes	—
456	#103	C₂³×C₆₁	1	8	yes	—
457	#103	C₂³×C₆₁	1	8	yes	—
458	#103	C₂³×C₆₁	1	8	yes	—
459	#102	C₂³×C₆₁	1	8	yes	—
460	#97	C₂³×C₆₁	1	8	yes	—
461	C₄×C₈	C₂³×C₆₁	1	8	yes	—
462	C₂⁴	—	2	1	no	—
463	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
464	#41	—	2	16	no	—
465	#41	—	2	8	no	—
466	#41	C₂²×C₄×C₆₁	1	16	yes	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	16	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	4	no	—
473	C₂×Q₈	—	2	8	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	C₂²×C₄×C₆₁	1	8	yes	—
476	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
477	C₂×Q₈	C₂²×C₄×C₆₁	1	16	yes	complemented
478	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
479	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
485	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	8	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
506	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
509	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
511	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
512	C₂²×C₄	#41×C₆₁	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
515	Q₁₆	C₂²×C₄×C₆₁	1	32	yes	complemented
516	SD₁₆	C₂²×C₄×C₆₁	1	32	yes	complemented
517	M₁₆	—	2	8	no	—
518	M₁₆	C₂²×C₄×C₆₁	1	16	yes	complemented
519	C₂×C₈	—	2	4	no	—
520	C₂×C₈	C₂²×C₄×C₆₁	1	8	yes	—
521	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
522	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
523	C₄⋊C₄	—	2	8	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
532	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
533	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	4	no	—
540	C₄²	—	2	8	no	—
541	C₄²	—	2	8	no	—
542	C₄²	C₂×D₄×C₆₁	1	4	yes	—
543	C₄²	C₂×D₄×C₆₁	1	4	yes	—
544	C₄²	C₂×D₄×C₆₁	1	2	yes	—
545	C₄²	C₂×D₄×C₆₁	1	2	yes	—
546	C₄²	C₂⁴×C₆₁	1	2	yes	—
547	C₄²	C₂⁴×C₆₁	1	2	yes	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	C₄×D₄×C₆₁	1	4	yes	—
555	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
556	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
557	Q₈	—	2	4	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	8	no	—
560	Q₈	—	2	16	no	—
561	Q₈	—	2	4	no	—
562	Q₈	C₂³×C₄×C₆₁	1	8	yes	—
563	Q₈	C₂³×C₄×C₆₁	1	4	yes	—
564	D₄	—	2	16	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	C₂³×C₄×C₆₁	1	4	yes	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	16	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
589	C₂×C₄	C₄×D₄×C₆₁	1	8	yes	—
590	C₂×C₄	#137×C₆₁	1	4	yes	direct product factor
591	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
600	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
601	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
602	C₈	—	2	4	no	—
603	C₈	C₂³×C₄×C₆₁	1	8	yes	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	8	no	—
611	C₂²	C₂×C₄×D₄×C₆₁	1	4	yes	—
612	C₂²	C₂×C₄×D₄×C₆₁	1	2	yes	—
613	C₂²	C₂×#137×C₆₁	1	2	yes	—
614	C₂²	C₆₁×#575	1	2	yes	—
615	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	4	no	—
620	C₄	—	2	8	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	C₂×C₄×D₄×C₆₁	1	4	yes	—
625	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
626	C₄	C₂×#137×C₆₁	1	4	yes	direct product factor
627	C₄	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
628	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
629	C₂	—	2	4	no	—
630	C₂	—	4	4	no	—
631	C₂	C₄×#137×C₆₁	1	4	yes	direct product factor
632	C₂	C₂²×C₄×D₄×C₆₁	1	1	yes	characteristic
633	C₂	C₂²×#137×C₆₁	1	1	yes	characteristic
634	C₂	C₂×C₆₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×Q₈×C₆₁	C₂	semidirect
4. C₄×#137×C₆₁	C₂	direct (N × H)
5. C₂×C₆₁×#441	C₂	semidirect
6. C₂×C₆₁×#440	C₂	semidirect
7. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
8. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
9. C₂×C₆₁×#428	C₂	semidirect
11. C₂×C₆₁×#419	C₂	semidirect
12. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
15. C₂×#137×C₆₁	C₄	direct (N × H)
30. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
42. C₆₁×#441	C₂²	semidirect
43. C₆₁×#440	C₂²	semidirect
44. C₄×Q₁₆×C₆₁	C₂²	semidirect
45. C₄×SD₁₆×C₆₁	C₂²	semidirect
46. C₆₁×#428	C₂²	semidirect
49. C₆₁×#419	C₂²	semidirect
55. C₄×M₁₆×C₆₁	C₂²	semidirect
65. C₂²×Q₈×C₆₁	C₂×C₄	semidirect
79. #137×C₆₁	C₂×C₄	direct (N × H)
80. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
82. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
85. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
159. C₂×Q₈×C₆₁	C₂²×C₄	semidirect
197. Q₁₆×C₆₁	C₂²×C₄	semidirect
198. SD₁₆×C₆₁	C₂²×C₄	semidirect
200. M₁₆×C₆₁	C₂²×C₄	semidirect
272. C₂×C₄×C₆₁	#137	direct (N × H)
286. C₂×C₄×#137	C₆₁	direct (N × H)
309. C₄×C₆₁	C₂×#137	direct (N × H)
314. C₂²×C₄×Q₈	C₂×C₆₁	semidirect
315. C₄×#137	C₂×C₆₁	direct (N × H)
316. C₂×#441	C₂×C₆₁	semidirect
317. C₂×#440	C₂×C₆₁	semidirect
318. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
319. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
320. C₂×#428	C₂×C₆₁	semidirect
322. C₂×#419	C₂×C₆₁	semidirect
323. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
326. C₂×C₆₁	C₄×#137	direct (N × H)
332. C₂×#137	C₄×C₆₁	direct (N × H)
347. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
359. #441	C₂²×C₆₁	semidirect
360. #440	C₂²×C₆₁	semidirect
361. C₄×Q₁₆	C₂²×C₆₁	semidirect
362. C₄×SD₁₆	C₂²×C₆₁	semidirect
363. #428	C₂²×C₆₁	semidirect
366. #419	C₂²×C₆₁	semidirect
372. C₄×M₁₆	C₂²×C₆₁	semidirect
375. C₆₁	C₂×C₄×#137	direct (N × H)
383. C₂²×Q₈	C₂×C₄×C₆₁	semidirect
397. #137	C₂×C₄×C₆₁	direct (N × H)
398. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
400. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
403. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
477. C₂×Q₈	C₂²×C₄×C₆₁	semidirect
515. Q₁₆	C₂²×C₄×C₆₁	semidirect
516. SD₁₆	C₂²×C₄×C₆₁	semidirect
518. M₁₆	C₂²×C₄×C₆₁	semidirect
590. C₂×C₄	#137×C₆₁	direct (N × H)
626. C₄	C₂×#137×C₆₁	direct (N × H)
631. C₂	C₄×#137×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₆₁	2
C₂×C₄×#41×C₆₁	2
C₂²×C₄×Q₈×C₆₁	2
C₄×#137×C₆₁	2
C₂×C₆₁×#441	2
C₂×C₆₁×#440	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₆₁×#428	2
C₂×C₆₁×#417	2
C₂×C₆₁×#419	2
C₂×C₄×M₁₆×C₆₁	2
C₂×C₄×#137	61

Subgroups — C2×C4×#137×C61 #29563590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#137×C₆₁ #29563590