Subgroups — C₂×C₆₁×#3039 #29563846

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 438 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	2	yes	maximal
2	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#3039	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#462	C₂	1	4	yes	maximal, complemented
6	C₂×C₆₁×#461	C₂	1	4	yes	maximal, complemented
7	C₂×C₆₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#419	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
11	C₂×#137×C₆₁	—	2	16	no	—
12	C₂×#137×C₆₁	C₂²	1	16	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	4	yes	—
14	C₂²×SD₁₆×C₆₁	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
17	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₆₁	—	2	4	no	—
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	8	yes	complemented
21	C₄×#41×C₆₁	—	2	4	no	—
22	C₄×#41×C₆₁	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₁	—	2	2	no	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
26	C₂×#117×C₆₁	—	2	1	no	—
27	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₁	—	2	2	no	—
29	C₂²×C₄²×C₆₁	—	2	1	no	—
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#462	C₂²	1	32	yes	complemented
32	C₆₁×#461	C₂²	1	32	yes	complemented
33	C₆₁×#423	C₂²	1	8	yes	complemented
34	C₂×C₄⋊C₈×C₆₁	C₂²	1	4	yes	—
35	C₆₁×#419	C₂²	1	16	yes	complemented
36	C₂×#103×C₆₁	C₂²	1	8	yes	—
37	C₂×#41×C₆₁	—	2	2	no	—
38	C₂×#41×C₆₁	—	2	4	no	—
39	C₂×#41×C₆₁	D₄	1	8	yes	—
40	C₂×#41×C₆₁	C₂³	1	4	yes	—
41	C₂²×Q₈×C₆₁	—	2	4	no	—
42	C₂²×Q₈×C₆₁	—	2	2	no	—
43	C₂²×Q₈×C₆₁	—	2	8	no	—
44	C₂²×Q₈×C₆₁	—	2	8	no	—
45	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	—	2	1	no	—
49	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	—	2	1	no	—
51	C₂³×C₄×C₆₁	—	2	2	no	—
52	C₂³×C₄×C₆₁	—	2	2	no	—
53	C₂³×C₄×C₆₁	D₄	1	2	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	#137×C₆₁	—	2	64	no	—
56	C₂×Q₁₆×C₆₁	—	2	16	no	—
57	C₂×Q₁₆×C₆₁	C₂³	1	16	yes	—
58	C₂×SD₁₆×C₆₁	—	2	16	no	—
59	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
60	C₂×M₁₆×C₆₁	—	2	8	no	—
61	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
62	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
63	C₄⋊Q₈×C₆₁	—	2	8	no	—
64	C₄⋊Q₈×C₆₁	—	2	8	no	—
65	C₄⋊Q₈×C₆₁	—	2	8	no	—
66	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
67	C₄×Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
69	C₄×D₄×C₆₁	—	2	16	no	—
70	C₄×D₄×C₆₁	—	2	4	no	—
71	C₄×D₄×C₆₁	C₂³	1	8	yes	—
72	#117×C₆₁	—	2	2	no	—
73	#117×C₆₁	—	2	8	no	—
74	#117×C₆₁	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	16	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	—	2	1	no	—
83	C₂×C₄²×C₆₁	—	2	2	no	—
84	C₂×C₄²×C₆₁	—	2	8	no	—
85	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₆₁	D₄	1	4	yes	—
88	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
89	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
90	C₄⋊C₈×C₆₁	C₂³	1	16	yes	—
91	#103×C₆₁	C₂³	1	32	yes	—
92	C₂⁴×C₆₁	—	2	1	no	—
93	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
94	#41×C₆₁	—	2	16	no	—
95	#41×C₆₁	—	2	8	no	—
96	#41×C₆₁	C₂×D₄	1	16	yes	—
97	C₂×Q₈×C₆₁	—	2	1	no	—
98	C₂×Q₈×C₆₁	—	2	8	no	—
99	C₂×Q₈×C₆₁	—	2	4	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	8	no	—
102	C₂×Q₈×C₆₁	—	2	16	no	—
103	C₂×Q₈×C₆₁	—	2	8	no	—
104	C₂×Q₈×C₆₁	—	2	16	no	—
105	C₂×Q₈×C₆₁	—	4	8	no	—
106	C₂×Q₈×C₆₁	—	4	16	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
109	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
110	C₂×D₄×C₆₁	—	2	8	no	—
111	C₂×D₄×C₆₁	—	2	4	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	8	no	—
118	C₂²×C₄×C₆₁	—	2	8	no	—
119	C₂²×C₄×C₆₁	—	2	4	no	—
120	C₂²×C₄×C₆₁	—	2	8	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	4	no	—
123	C₂²×C₄×C₆₁	—	2	8	no	—
124	C₂²×C₄×C₆₁	—	4	8	no	—
125	C₂²×C₄×C₆₁	—	4	8	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	#41	1	4	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₆₁	—	2	32	no	—
136	SD₁₆×C₆₁	—	2	32	no	—
137	M₁₆×C₆₁	—	2	16	no	—
138	C₂×C₈×C₆₁	—	2	8	no	—
139	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
140	C₄⋊C₄×C₆₁	—	2	16	no	—
141	C₄⋊C₄×C₆₁	—	2	16	no	—
142	C₄⋊C₄×C₆₁	—	2	8	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
145	C₂²⋊C₄×C₆₁	—	2	4	no	—
146	C₂²⋊C₄×C₆₁	—	2	8	no	—
147	C₄²×C₆₁	—	2	4	no	—
148	C₄²×C₆₁	—	2	8	no	—
149	C₄²×C₆₁	C₂×D₄	1	4	yes	—
150	C₄²×C₆₁	C₂×D₄	1	4	yes	—
151	C₄²×C₆₁	C₂×D₄	1	4	yes	—
152	C₄²×C₆₁	C₂⁴	1	4	yes	—
153	C₂³×C₆₁	—	2	4	no	—
154	C₂³×C₆₁	—	2	4	no	—
155	C₂³×C₆₁	—	2	2	no	—
156	C₂³×C₆₁	—	4	4	no	—
157	C₂³×C₆₁	#121	1	4	yes	—
158	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
159	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₆₁	—	2	4	no	—
161	Q₈×C₆₁	—	2	2	no	—
162	Q₈×C₆₁	—	2	8	no	—
163	Q₈×C₆₁	—	2	8	no	—
164	Q₈×C₆₁	—	4	16	no	—
165	Q₈×C₆₁	—	4	8	no	—
166	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
167	D₄×C₆₁	—	2	16	no	—
168	D₄×C₆₁	—	2	4	no	—
169	D₄×C₆₁	—	2	2	no	—
170	D₄×C₆₁	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	4	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	16	no	—
175	C₂×C₄×C₆₁	—	2	16	no	—
176	C₂×C₄×C₆₁	—	2	4	no	—
177	C₂×C₄×C₆₁	—	2	8	no	—
178	C₂×C₄×C₆₁	—	4	16	no	—
179	C₂×C₄×C₆₁	—	4	8	no	—
180	C₂×C₄×C₆₁	—	4	4	no	—
181	C₂×C₄×C₆₁	—	4	16	no	—
182	C₂×C₄×C₆₁	#121	1	4	yes	—
183	C₂×C₄×C₆₁	#121	1	8	yes	—
184	C₂×C₄×C₆₁	#137	1	8	yes	complemented
185	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
192	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
193	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
194	C₈×C₆₁	—	2	8	no	—
195	C₂×#3039	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂²×C₆₁	—	2	8	no	—
197	C₂²×C₆₁	—	2	4	no	—
198	C₂²×C₆₁	—	2	4	no	—
199	C₂²×C₆₁	—	4	8	no	—
200	C₂²×C₆₁	—	4	4	no	—
201	C₂²×C₆₁	C₂×#121	1	4	yes	—
202	C₂²×C₆₁	C₂×#121	1	2	yes	—
203	C₂²×C₆₁	C₂×#137	1	4	yes	—
204	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
205	C₄×C₆₁	—	2	4	no	—
206	C₄×C₆₁	—	2	4	no	—
207	C₄×C₆₁	—	4	8	no	—
208	C₄×C₆₁	—	4	4	no	—
209	C₄×C₆₁	C₂×#121	1	4	yes	—
210	C₄×C₆₁	C₂×#121	1	2	yes	—
211	C₄×C₆₁	C₂×#137	1	8	yes	complemented
212	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
214	C₂²×#137	C₂×C₆₁	1	2	yes	—
215	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
216	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic
217	#3039	C₂×C₆₁	1	16	yes	direct product factor
218	C₂×#462	C₂×C₆₁	1	4	yes	complemented
219	C₂×#461	C₂×C₆₁	1	4	yes	complemented
220	C₂×#423	C₂×C₆₁	1	1	yes	characteristic, complemented
221	C₂×#419	C₂×C₆₁	1	2	yes	complemented
222	C₂×C₆₁	—	2	4	no	—
223	C₂×C₆₁	—	4	4	no	—
224	C₂×C₆₁	#3039	1	4	yes	direct product factor
225	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
226	C₂×C₆₁	C₂²×#137	1	2	yes	—
227	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
228	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
229	C₂×#137	—	2	16	no	—
230	C₂×#137	C₂²×C₆₁	1	16	yes	—
231	C₂²×Q₁₆	C₂²×C₆₁	1	4	yes	—
232	C₂²×SD₁₆	C₂²×C₆₁	1	4	yes	—
233	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	—	2	4	no	—
236	C₂×C₄⋊Q₈	—	2	1	no	—
237	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₆₁	1	8	yes	complemented
239	C₄×#41	—	2	4	no	—
240	C₄×#41	C₂²×C₆₁	1	8	yes	—
241	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
242	C₂×C₄×D₄	—	2	2	no	—
243	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
244	C₂×#117	—	2	1	no	—
245	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	—	2	2	no	—
247	C₂²×C₄²	—	2	1	no	—
248	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
249	#462	C₂²×C₆₁	1	32	yes	complemented
250	#461	C₂²×C₆₁	1	32	yes	complemented
251	#423	C₂²×C₆₁	1	8	yes	complemented
252	C₂×C₄⋊C₈	C₂²×C₆₁	1	4	yes	—
253	#419	C₂²×C₆₁	1	16	yes	complemented
254	C₂×#103	C₂²×C₆₁	1	8	yes	—
255	C₆₁	C₂×#3039	1	1	yes	characteristic, direct product factor, Sylow
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	D₄×C₆₁	1	8	yes	—
259	C₂×#41	C₂³×C₆₁	1	4	yes	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	4	no	—
262	C₂²×Q₈	—	2	8	no	—
263	C₂²×Q₈	—	2	8	no	—
264	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
265	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
266	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	D₄×C₆₁	1	2	yes	—
273	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
274	#137	—	2	64	no	—
275	C₂×Q₁₆	—	2	16	no	—
276	C₂×Q₁₆	C₂³×C₆₁	1	16	yes	—
277	C₂×SD₁₆	—	2	16	no	—
278	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
279	C₂×M₁₆	—	2	8	no	—
280	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
281	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
282	C₄⋊Q₈	—	2	8	no	—
283	C₄⋊Q₈	—	2	8	no	—
284	C₄⋊Q₈	—	2	8	no	—
285	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
286	C₄×Q₈	—	2	4	no	—
287	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
288	C₄×D₄	—	2	16	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	C₂³×C₆₁	1	8	yes	—
291	#117	—	2	2	no	—
292	#117	—	2	8	no	—
293	#117	C₂³×C₆₁	1	4	yes	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	16	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	8	no	—
304	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₆₁	1	4	yes	—
306	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
308	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
309	C₄⋊C₈	C₂³×C₆₁	1	16	yes	—
310	#103	C₂³×C₆₁	1	32	yes	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
313	#41	—	2	16	no	—
314	#41	—	2	8	no	—
315	#41	C₂×D₄×C₆₁	1	16	yes	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	8	no	—
321	C₂×Q₈	—	2	16	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	2	16	no	—
324	C₂×Q₈	—	4	8	no	—
325	C₂×Q₈	—	4	16	no	—
326	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
327	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
328	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
334	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	—	4	8	no	—
345	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
347	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
350	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
351	C₂²×C₄	#41×C₆₁	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
354	Q₁₆	—	2	32	no	—
355	SD₁₆	—	2	32	no	—
356	M₁₆	—	2	16	no	—
357	C₂×C₈	—	2	8	no	—
358	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
359	C₄⋊C₄	—	2	16	no	—
360	C₄⋊C₄	—	2	16	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	8	no	—
368	C₄²	C₂×D₄×C₆₁	1	4	yes	—
369	C₄²	C₂×D₄×C₆₁	1	4	yes	—
370	C₄²	C₂×D₄×C₆₁	1	4	yes	—
371	C₄²	C₂⁴×C₆₁	1	4	yes	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	#121×C₆₁	1	4	yes	—
377	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
378	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	4	no	—
381	Q₈	—	2	8	no	—
382	Q₈	—	2	8	no	—
383	Q₈	—	4	16	no	—
384	Q₈	—	4	8	no	—
385	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
386	D₄	—	2	16	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	4	no	—
389	D₄	C₂²×D₄×C₆₁	1	4	yes	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	16	no	—
401	C₂×C₄	#121×C₆₁	1	4	yes	—
402	C₂×C₄	#121×C₆₁	1	8	yes	—
403	C₂×C₄	#137×C₆₁	1	8	yes	complemented
404	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
411	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
412	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
413	C₈	—	2	8	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	4	4	no	—
419	C₂²	C₂×#121×C₆₁	1	4	yes	—
420	C₂²	C₂×#121×C₆₁	1	2	yes	—
421	C₂²	C₂×#137×C₆₁	1	4	yes	—
422	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	C₂×#121×C₆₁	1	4	yes	—
428	C₄	C₂×#121×C₆₁	1	2	yes	—
429	C₄	C₂×#137×C₆₁	1	8	yes	complemented
430	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
431	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
432	C₂	—	2	4	no	—
433	C₂	—	4	4	no	—
434	C₂	C₆₁×#3039	1	4	yes	direct product factor
435	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
436	C₂	C₂²×#137×C₆₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈×C₆₁	C₂	semidirect
4. C₆₁×#3039	C₂	direct (N × H)
5. C₂×C₆₁×#462	C₂	semidirect
6. C₂×C₆₁×#461	C₂	semidirect
7. C₂×C₆₁×#423	C₂	semidirect
8. C₂×C₆₁×#419	C₂	semidirect
20. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
31. C₆₁×#462	C₂²	semidirect
32. C₆₁×#461	C₂²	semidirect
33. C₆₁×#423	C₂²	semidirect
35. C₆₁×#419	C₂²	semidirect
184. C₂×C₄×C₆₁	#137	semidirect
195. C₂×#3039	C₆₁	direct (N × H)
211. C₄×C₆₁	C₂×#137	semidirect
215. C₂²×C₄⋊Q₈	C₂×C₆₁	semidirect
217. #3039	C₂×C₆₁	direct (N × H)
218. C₂×#462	C₂×C₆₁	semidirect
219. C₂×#461	C₂×C₆₁	semidirect
220. C₂×#423	C₂×C₆₁	semidirect
221. C₂×#419	C₂×C₆₁	semidirect
224. C₂×C₆₁	#3039	direct (N × H)
238. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
249. #462	C₂²×C₆₁	semidirect
250. #461	C₂²×C₆₁	semidirect
251. #423	C₂²×C₆₁	semidirect
253. #419	C₂²×C₆₁	semidirect
255. C₆₁	C₂×#3039	direct (N × H)
403. C₂×C₄	#137×C₆₁	semidirect
429. C₄	C₂×#137×C₆₁	semidirect
434. C₂	C₆₁×#3039	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
C₂²×C₄⋊Q₈×C₆₁	2
C₂×C₄×#41×C₆₁	2
C₆₁×#3039	2
C₂×C₆₁×#462	2
C₂×C₆₁×#461	2
C₂×C₆₁×#423	2
C₂×C₆₁×#419	2
C₂×#3039	61

Subgroups — C2×C61×#3039 #29563846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3039 #29563846