Subgroups — D₃₁×#546 #16859152

Order 3968.

1900 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521696	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521695	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521694	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521693	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521692	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521691	C₂	1	2	yes	maximal, complemented
9	#14521690	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521689	C₂	1	2	yes	maximal, complemented
11	#14521688	C₂	1	2	yes	maximal, complemented
12	#14521687	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521686	C₂	1	2	yes	maximal, complemented
14	#124×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₃₁	C₂	1	2	yes	maximal, complemented
16	C₂²⋊Q₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	#121×D₃₁	C₂	1	2	yes	maximal, complemented
19	#120×D₃₁	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂²⋊C₄×D₃₁	C₂	1	2	yes	maximal, complemented
23	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₃₁	C₂²	1	2	yes	—
25	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
28	#41×D₃₁	—	2	8	no	—
29	C₂×#92499	C₂²	1	1	yes	characteristic, complemented
30	C₂×Q₈×D₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#92497	C₂²	1	2	yes	complemented
32	C₂×#92497	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×D₃₁	—	2	8	no	—
34	C₂×D₄×D₃₁	C₂²	1	2	yes	—
35	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₃₁	C₂²	1	2	yes	complemented
40	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₃₁	C₂²	1	2	yes	complemented
42	C₂×D₄×D₃₁	C₂²	1	2	yes	complemented
43	C₂×#92495	C₂²	1	1	yes	characteristic, complemented
44	C₂×#92495	C₂²	1	2	yes	complemented
45	C₂²×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄×D₃₁	C₂²	1	2	yes	complemented
48	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄×D₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#123	C₂²	1	2	yes	complemented
52	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#121	C₂²	1	2	yes	complemented
54	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#120	C₂²	1	2	yes	complemented
56	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
59	#11758530	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊Dic₃₁	C₂²	1	2	yes	complemented
61	#11758524	C₂²	1	1	yes	characteristic, complemented
62	#11758523	C₂²	1	1	yes	characteristic, complemented
63	#11758516	C₂²	1	2	yes	complemented
64	#11758516	C₂²	1	2	yes	complemented
65	#11758516	C₂²	1	2	yes	complemented
66	#11758515	C₂²	1	2	yes	complemented
67	#11758515	C₂²	1	1	yes	characteristic, complemented
68	#11758514	C₂²	1	2	yes	complemented
69	#11758514	C₂²	1	2	yes	complemented
70	#11758514	C₂²	1	2	yes	complemented
71	#11758513	C₂²	1	1	yes	characteristic, complemented
72	#11758512	C₂²	1	2	yes	complemented
73	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
75	#11758507	C₂²	1	1	yes	characteristic, complemented
76	#11758507	C₂²	1	2	yes	complemented
77	#11758506	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
81	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	2	yes	complemented
82	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	2	yes	complemented
83	#11758501	C₂²	1	1	yes	characteristic, complemented
84	#11758474	C₂²	1	1	yes	characteristic, complemented
85	#11758473	C₂²	1	2	yes	complemented
86	#11758472	C₂²	1	2	yes	complemented
87	#11758472	C₂²	1	1	yes	characteristic, complemented
88	#11758471	C₂²	1	2	yes	complemented
89	#11758471	C₂²	1	2	yes	complemented
90	#11758470	C₂²	1	1	yes	characteristic, complemented
91	#11758470	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
93	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
95	#11758463	C₂²	1	2	yes	complemented
96	#11758462	C₂²	1	2	yes	complemented
97	#11758462	C₂²	1	2	yes	complemented
98	#11758461	C₂²	1	2	yes	complemented
99	#11758461	C₂²	1	2	yes	complemented
100	#11758461	C₂²	1	2	yes	complemented
101	#11758460	C₂²	1	2	yes	complemented
102	#11758460	C₂²	1	2	yes	complemented
103	#11758459	C₂²	1	2	yes	complemented
104	#11758459	C₂²	1	2	yes	complemented
105	#11758459	C₂²	1	2	yes	complemented
106	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
114	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
115	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
116	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
117	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
118	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
120	#11758455	C₂²	1	2	yes	complemented
121	#11758452	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
124	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₂⁴×C₃₁	C₂³	1	2	yes	—
126	C₂³×D₃₁	—	2	8	no	—
127	C₂³×D₃₁	—	2	8	no	—
128	C₂³×D₃₁	—	4	4	no	—
129	C₂³×D₃₁	C₂³	1	2	yes	—
130	C₂³×D₃₁	C₂³	1	1	yes	characteristic
131	C₂³×D₃₁	C₂³	1	2	yes	—
132	C₂³×D₃₁	C₂³	1	2	yes	—
133	C₂³×D₃₁	C₂³	1	2	yes	—
134	C₂³×D₃₁	C₂³	1	2	yes	—
135	C₂³×D₃₁	C₂³	1	1	yes	characteristic
136	#41×C₃₁	—	2	4	no	—
137	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic, complemented
138	C₂×D₄×C₃₁	—	2	4	no	—
139	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₃₁	C₂³	1	2	yes	complemented
144	C₂×D₄×C₃₁	C₂³	1	2	yes	complemented
145	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₃₁	C₂³	1	2	yes	complemented
147	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic, complemented
148	C₂²×C₄×C₃₁	C₂³	1	2	yes	complemented
149	C₂×C₂²⋊D₃₁	—	2	8	no	—
150	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	complemented
157	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	complemented
158	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	complemented
159	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	complemented
160	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
161	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic, complemented
162	C₂²×Dic₃₁	C₂³	1	2	yes	complemented
163	C₂²×Dic₃₁	C₂³	1	2	yes	complemented
164	#92499	—	2	4	no	—
165	Q₈×D₃₁	—	2	4	no	—
166	#92497	—	2	4	no	—
167	#92497	—	2	8	no	—
168	D₄×D₃₁	—	2	8	no	—
169	D₄×D₃₁	—	2	8	no	—
170	D₄×D₃₁	—	2	4	no	—
171	D₄×D₃₁	—	2	4	no	—
172	D₄×D₃₁	—	2	8	no	—
173	D₄×D₃₁	—	2	4	no	—
174	D₄×D₃₁	—	2	4	no	—
175	D₄×D₃₁	—	4	4	no	—
176	D₄×D₃₁	D₄	1	8	yes	complemented
177	#92495	—	2	8	no	—
178	#92495	—	2	4	no	—
179	C₂×D₁₂₄	—	2	4	no	—
180	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
181	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
182	C₂×D₁₂₄	C₂³	1	2	yes	—
183	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
184	C₂×D₁₂₄	C₂³	1	2	yes	complemented
185	C₂×D₁₂₄	C₂³	1	2	yes	complemented
186	C₂×C₄×D₃₁	—	2	8	no	—
187	C₂×C₄×D₃₁	—	2	4	no	—
188	C₂×C₄×D₃₁	—	2	4	no	—
189	C₂×C₄×D₃₁	—	4	4	no	—
190	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄×D₃₁	C₂³	1	2	yes	—
194	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄×D₃₁	C₂³	1	2	yes	—
196	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic, complemented
200	C₂×C₄×D₃₁	C₂³	1	2	yes	complemented
201	C₂×C₄×D₃₁	C₂³	1	2	yes	complemented
202	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic, complemented
203	C₂×C₄×D₃₁	C₂³	1	2	yes	complemented
204	C₂×C₄×D₃₁	C₂³	1	2	yes	complemented
205	C₂×Dic₆₂	C₂³	1	1	yes	characteristic, complemented
206	C₂×Dic₆₂	C₂³	1	2	yes	complemented
207	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic, complemented
208	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic, complemented
209	C₄⋊C₄×C₃₁	C₂³	1	2	yes	complemented
210	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	complemented
213	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	complemented
214	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	complemented
215	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic, complemented
216	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	complemented
217	C₄²×C₃₁	C₂³	1	1	yes	characteristic, complemented
218	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
219	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
220	C₂²⋊Dic₃₁	C₂³	1	2	yes	complemented
221	C₂²⋊Dic₃₁	C₂³	1	2	yes	complemented
222	C₂²⋊Dic₃₁	C₂³	1	2	yes	complemented
223	C₂²⋊Dic₃₁	C₂³	1	2	yes	complemented
224	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic, complemented
225	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
227	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
228	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
230	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic, complemented
231	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
232	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
233	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
234	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
235	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
236	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
237	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	complemented
238	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic, complemented
239	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic, complemented
240	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic, complemented
241	C₄⋊Dic₃₁	C₂³	1	2	yes	complemented
242	Dic₃₁⋊C₄	C₂³	1	2	yes	complemented
243	Dic₃₁⋊C₄	C₂³	1	2	yes	complemented
244	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic, complemented
245	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic, complemented
246	Dic₃₁⋊C₄	C₂³	1	2	yes	complemented
247	C₄×Dic₃₁	C₂³	1	1	yes	characteristic, complemented
248	C₄×Dic₃₁	C₂³	1	1	yes	characteristic, complemented
249	C₄×Dic₃₁	C₂³	1	1	yes	characteristic, complemented
250	C₂³×C₃₁	—	2	4	no	—
251	C₂³×C₃₁	—	2	4	no	—
252	C₂³×C₃₁	—	4	2	no	—
253	C₂³×C₃₁	C₂⁴	1	2	yes	—
254	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂³×C₃₁	C₂⁴	1	2	yes	—
256	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×D₃₁	—	2	2	no	—
258	C₂²×D₃₁	—	2	4	no	—
259	C₂²×D₃₁	—	2	4	no	—
260	C₂²×D₃₁	—	2	2	no	—
261	C₂²×D₃₁	—	2	4	no	—
262	C₂²×D₃₁	—	2	4	no	—
263	C₂²×D₃₁	—	2	2	no	—
264	C₂²×D₃₁	—	2	4	no	—
265	C₂²×D₃₁	—	2	4	no	—
266	C₂²×D₃₁	—	2	4	no	—
267	C₂²×D₃₁	—	2	2	no	—
268	C₂²×D₃₁	—	2	4	no	—
269	C₂²×D₃₁	—	2	4	no	—
270	C₂²×D₃₁	—	2	4	no	—
271	C₂²×D₃₁	—	2	2	no	—
272	C₂²×D₃₁	—	2	4	no	—
273	C₂²×D₃₁	—	4	2	no	—
274	C₂²×D₃₁	—	4	2	no	—
275	C₂²×D₃₁	—	4	2	no	—
276	C₂²×D₃₁	—	4	32	no	—
277	C₂²×D₃₁	C₂×D₄	1	8	yes	—
278	C₂²×D₃₁	#41	1	4	yes	complemented
279	C₂²×D₃₁	C₂⁴	1	2	yes	—
280	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×D₃₁	C₂⁴	1	2	yes	—
282	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
284	Q₈×C₃₁	—	2	2	no	—
285	D₄×C₃₁	—	2	4	no	—
286	D₄×C₃₁	—	2	4	no	—
287	D₄×C₃₁	—	2	2	no	—
288	D₄×C₃₁	—	2	2	no	—
289	D₄×C₃₁	—	4	2	no	—
290	D₄×C₃₁	C₂×D₄	1	4	yes	complemented
291	C₂×C₄×C₃₁	—	2	4	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	4	2	no	—
295	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²⋊D₃₁	—	2	4	no	—
303	C₂²⋊D₃₁	—	2	4	no	—
304	C₂²⋊D₃₁	—	2	2	no	—
305	C₂²⋊D₃₁	—	2	4	no	—
306	C₂²⋊D₃₁	—	2	4	no	—
307	C₂²⋊D₃₁	—	2	2	no	—
308	C₂²⋊D₃₁	—	2	4	no	—
309	C₂²⋊D₃₁	—	4	2	no	—
310	C₂²⋊D₃₁	—	4	2	no	—
311	C₂²⋊D₃₁	C₂×D₄	1	8	yes	complemented
312	C₂×Dic₃₁	—	2	4	no	—
313	C₂×Dic₃₁	—	2	2	no	—
314	C₂×Dic₃₁	—	2	2	no	—
315	C₂×Dic₃₁	—	4	2	no	—
316	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
318	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
319	C₂×Dic₃₁	C₂⁴	1	2	yes	—
320	C₂×Dic₃₁	C₂⁴	1	2	yes	—
321	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
322	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
323	D₁₂₄	—	2	4	no	—
324	D₁₂₄	—	2	4	no	—
325	D₁₂₄	—	2	2	no	—
326	D₁₂₄	—	2	2	no	—
327	D₁₂₄	—	4	2	no	—
328	D₁₂₄	C₂×D₄	1	4	yes	complemented
329	C₄×D₃₁	—	2	2	no	—
330	C₄×D₃₁	—	2	2	no	—
331	C₄×D₃₁	—	2	4	no	—
332	C₄×D₃₁	—	2	4	no	—
333	C₄×D₃₁	—	2	4	no	—
334	C₄×D₃₁	—	2	2	no	—
335	C₄×D₃₁	—	2	2	no	—
336	C₄×D₃₁	—	2	4	no	—
337	C₄×D₃₁	—	2	2	no	—
338	C₄×D₃₁	—	2	2	no	—
339	C₄×D₃₁	—	2	2	no	—
340	C₄×D₃₁	—	2	2	no	—
341	C₄×D₃₁	—	4	2	no	—
342	C₄×D₃₁	—	4	2	no	—
343	C₄×D₃₁	C₂×D₄	1	4	yes	—
344	Dic₆₂	—	2	2	no	—
345	Dic₆₂	—	2	4	no	—
346	C₂×#546	—	31	1	no	maximal, Sylow
347	C₂²×C₃₁	—	2	1	no	—
348	C₂²×C₃₁	—	2	2	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	1	no	—
351	C₂²×C₃₁	—	2	1	no	—
352	C₂²×C₃₁	—	2	2	no	—
353	C₂²×C₃₁	—	2	1	no	—
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	2	no	—
357	C₂²×C₃₁	—	4	8	no	—
358	C₂²×C₃₁	C₂²×D₄	1	4	yes	—
359	C₂²×C₃₁	C₂×#41	1	2	yes	complemented
360	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
361	C₂×D₃₁	—	2	1	no	—
362	C₂×D₃₁	—	2	2	no	—
363	C₂×D₃₁	—	2	2	no	—
364	C₂×D₃₁	—	2	1	no	—
365	C₂×D₃₁	—	2	8	no	—
366	C₂×D₃₁	—	2	16	no	—
367	C₂×D₃₁	—	2	1	no	—
368	C₂×D₃₁	—	2	2	no	—
369	C₂×D₃₁	—	2	1	no	—
370	C₂×D₃₁	—	2	2	no	—
371	C₂×D₃₁	—	2	1	no	—
372	C₂×D₃₁	—	2	2	no	—
373	C₂×D₃₁	—	4	8	no	—
374	C₂×D₃₁	—	4	8	no	—
375	C₂×D₃₁	—	4	8	no	—
376	C₂×D₃₁	—	4	4	no	—
377	C₂×D₃₁	—	4	8	no	—
378	C₂×D₃₁	C₂²×D₄	1	4	yes	—
379	C₂×D₃₁	C₂²×D₄	1	2	yes	—
380	C₂×D₃₁	C₂×#41	1	2	yes	—
381	C₂×D₃₁	C₂×#41	1	2	yes	complemented
382	C₂×D₃₁	H(5,𝔽₂)	1	2	yes	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	C₂²×D₄	1	2	yes	—
390	Dic₃₁	—	2	2	no	—
391	Dic₃₁	—	2	1	no	—
392	Dic₃₁	—	2	1	no	—
393	Dic₃₁	—	2	1	no	—
394	Dic₃₁	—	2	1	no	—
395	Dic₃₁	—	2	2	no	—
396	Dic₃₁	C₂²×D₄	1	2	yes	—
397	C₂²×#41	—	31	1	no	—
398	C₂³×D₄	—	31	1	no	—
399	#546	—	31	1	no	—
400	#546	—	31	1	no	—
401	#546	—	31	1	no	—
402	#546	—	31	2	no	—
403	#546	—	31	1	no	—
404	#546	—	31	2	no	—
405	#546	—	31	1	no	—
406	#546	—	31	2	no	—
407	#546	—	31	1	no	—
408	#546	—	31	1	no	—
409	#546	—	31	2	no	—
410	#546	D₃₁	1	1	yes	characteristic, direct product factor
411	C₂×#124	—	31	1	no	—
412	C₂×#123	—	31	2	no	—
413	C₂×C₂²⋊Q₈	—	31	1	no	—
414	C₂×#121	—	31	1	no	—
415	C₂×#121	—	31	2	no	—
416	C₂×#120	—	31	2	no	—
417	C₂×C₄×D₄	—	31	1	no	—
418	C₂×C₄×D₄	—	31	1	no	—
419	C₂²×C₂²⋊C₄	—	31	2	no	—
420	C₂×C₃₁	—	2	2	no	—
421	C₂×C₃₁	—	2	4	no	—
422	C₂×C₃₁	—	4	2	no	—
423	C₂×C₃₁	—	4	1	no	—
424	C₂×C₃₁	C₂³×D₄	1	1	yes	characteristic
425	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
426	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	D₃₁	—	2	2	no	—
428	D₃₁	—	2	4	no	—
429	D₃₁	—	4	1	no	—
430	D₃₁	—	4	2	no	—
431	D₃₁	#546	1	4	yes	direct product factor
432	C₂⁵	—	31	2	no	—
433	C₂×#41	—	31	1	no	—
434	C₂×#41	—	31	1	no	—
435	C₂×#41	—	31	2	no	—
436	C₂×#41	—	31	1	no	—
437	C₂×#41	—	31	2	no	—
438	C₂×#41	—	62	8	no	—
439	C₂×#41	C₂×D₃₁	1	1	yes	characteristic, complemented
440	C₂²×Q₈	—	31	1	no	—
441	C₂²×D₄	—	31	1	no	—
442	C₂²×D₄	—	31	2	no	—
443	C₂²×D₄	—	31	1	no	—
444	C₂²×D₄	—	31	2	no	—
445	C₂²×D₄	—	31	1	no	—
446	C₂²×D₄	—	31	2	no	—
447	C₂²×D₄	—	31	1	no	—
448	C₂²×D₄	—	31	1	no	—
449	C₂²×D₄	—	31	2	no	—
450	C₂²×D₄	—	31	2	no	—
451	C₂²×D₄	—	31	1	no	—
452	C₂²×D₄	—	62	8	no	—
453	C₂²×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
454	C₂³×C₄	—	31	1	no	—
455	C₂³×C₄	—	31	2	no	—
456	C₂³×C₄	—	31	1	no	—
457	C₂³×C₄	—	31	2	no	—
458	#124	—	31	1	no	—
459	#124	—	31	1	no	—
460	#124	—	31	2	no	—
461	#124	—	31	2	no	—
462	#124	—	31	1	no	—
463	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
464	#123	—	31	2	no	—
465	#123	—	31	2	no	—
466	#123	—	31	2	no	—
467	#123	—	31	2	no	—
468	#123	—	31	2	no	—
469	#123	—	31	2	no	—
470	#123	—	31	2	no	—
471	#123	C₂×D₃₁	1	2	yes	complemented
472	C₂²⋊Q₈	—	31	1	no	—
473	C₂²⋊Q₈	—	31	1	no	—
474	C₂²⋊Q₈	—	31	2	no	—
475	C₂²⋊Q₈	—	31	1	no	—
476	C₂²⋊Q₈	—	31	2	no	—
477	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
478	#121	—	31	1	no	—
479	#121	—	31	2	no	—
480	#121	—	31	2	no	—
481	#121	—	31	2	no	—
482	#121	—	31	2	no	—
483	#121	—	31	1	no	—
484	#121	—	31	2	no	—
485	#121	—	31	1	no	—
486	#121	—	31	2	no	—
487	#121	—	31	2	no	—
488	#121	—	31	2	no	—
489	#121	—	31	2	no	—
490	#121	C₂×D₃₁	1	1	yes	characteristic, complemented
491	#121	C₂×D₃₁	1	2	yes	complemented
492	#120	—	31	2	no	—
493	#120	—	31	2	no	—
494	#120	—	31	2	no	—
495	#120	—	31	2	no	—
496	#120	—	31	2	no	—
497	#120	—	31	2	no	—
498	#120	—	31	2	no	—
499	#120	C₂×D₃₁	1	2	yes	complemented
500	C₄×D₄	—	31	1	no	—
501	C₄×D₄	—	31	1	no	—
502	C₄×D₄	—	31	1	no	—
503	C₄×D₄	—	31	2	no	—
504	C₄×D₄	—	31	1	no	—
505	C₄×D₄	—	31	1	no	—
506	C₄×D₄	—	31	1	no	—
507	C₄×D₄	—	31	1	no	—
508	C₄×D₄	—	31	1	no	—
509	C₄×D₄	—	31	2	no	—
510	C₄×D₄	—	31	1	no	—
511	C₄×D₄	—	31	1	no	—
512	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
513	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
514	C₂×C₄⋊C₄	—	31	1	no	—
515	C₂×C₄⋊C₄	—	31	1	no	—
516	C₂×C₄⋊C₄	—	31	2	no	—
517	C₂×C₂²⋊C₄	—	31	2	no	—
518	C₂×C₂²⋊C₄	—	31	2	no	—
519	C₂×C₂²⋊C₄	—	31	2	no	—
520	C₂×C₂²⋊C₄	—	31	1	no	—
521	C₂×C₂²⋊C₄	—	31	2	no	—
522	C₂×C₂²⋊C₄	—	31	2	no	—
523	C₂×C₂²⋊C₄	—	31	2	no	—
524	C₂×C₂²⋊C₄	—	31	2	no	—
525	C₂×C₂²⋊C₄	—	31	2	no	—
526	C₂×C₂²⋊C₄	—	31	2	no	—
527	C₂×C₂²⋊C₄	—	31	2	no	—
528	C₂×C₂²⋊C₄	—	31	2	no	—
529	C₂×C₂²⋊C₄	—	31	1	no	—
530	C₂×C₂²⋊C₄	—	31	2	no	—
531	C₂×C₂²⋊C₄	C₂×D₃₁	1	2	yes	complemented
532	C₂×C₄²	—	31	1	no	—
533	C₃₁	C₂×#546	1	1	yes	characteristic, complemented, Sylow
534	C₂⁴	—	31	1	no	—
535	C₂⁴	—	31	2	no	—
536	C₂⁴	—	31	2	no	—
537	C₂⁴	—	31	1	no	—
538	C₂⁴	—	31	2	no	—
539	C₂⁴	—	31	2	no	—
540	C₂⁴	—	31	2	no	—
541	C₂⁴	—	62	8	no	—
542	C₂⁴	—	62	8	no	—
543	C₂⁴	—	124	4	no	—
544	C₂⁴	C₂²×D₃₁	1	2	yes	—
545	#41	—	2	4	no	—
546	#41	—	62	8	no	—
547	#41	—	62	4	no	—
548	#41	—	62	8	no	—
549	#41	—	62	4	no	—
550	#41	—	62	4	no	—
551	C₂×Q₈	—	31	2	no	—
552	C₂×Q₈	—	31	1	no	—
553	C₂×Q₈	—	62	4	no	—
554	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic, complemented
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	31	2	no	—
557	C₂×D₄	—	31	8	no	—
558	C₂×D₄	—	31	1	no	—
559	C₂×D₄	—	31	1	no	—
560	C₂×D₄	—	31	2	no	—
561	C₂×D₄	—	31	2	no	—
562	C₂×D₄	—	31	2	no	—
563	C₂×D₄	—	31	2	no	—
564	C₂×D₄	—	31	2	no	—
565	C₂×D₄	—	31	2	no	—
566	C₂×D₄	—	31	2	no	—
567	C₂×D₄	—	31	1	no	—
568	C₂×D₄	—	31	1	no	—
569	C₂×D₄	—	31	2	no	—
570	C₂×D₄	—	31	1	no	—
571	C₂×D₄	—	31	2	no	—
572	C₂×D₄	—	31	2	no	—
573	C₂×D₄	—	62	4	no	—
574	C₂×D₄	—	62	4	no	—
575	C₂×D₄	—	62	8	no	—
576	C₂×D₄	—	62	4	no	—
577	C₂×D₄	—	62	4	no	—
578	C₂×D₄	—	62	8	no	—
579	C₂×D₄	—	62	8	no	—
580	C₂×D₄	—	62	8	no	—
581	C₂×D₄	—	62	4	no	—
582	C₂×D₄	—	124	4	no	—
583	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
584	C₂×D₄	C₂²×D₃₁	1	2	yes	—
585	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
586	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
587	C₂×D₄	C₂²×D₃₁	1	2	yes	complemented
588	C₂×D₄	C₂²×D₃₁	1	2	yes	complemented
589	C₂²×C₄	—	31	1	no	—
590	C₂²×C₄	—	31	1	no	—
591	C₂²×C₄	—	31	2	no	—
592	C₂²×C₄	—	31	1	no	—
593	C₂²×C₄	—	31	2	no	—
594	C₂²×C₄	—	31	1	no	—
595	C₂²×C₄	—	31	1	no	—
596	C₂²×C₄	—	31	2	no	—
597	C₂²×C₄	—	31	1	no	—
598	C₂²×C₄	—	31	2	no	—
599	C₂²×C₄	—	31	1	no	—
600	C₂²×C₄	—	31	1	no	—
601	C₂²×C₄	—	31	1	no	—
602	C₂²×C₄	—	31	2	no	—
603	C₂²×C₄	—	31	2	no	—
604	C₂²×C₄	—	31	1	no	—
605	C₂²×C₄	—	31	1	no	—
606	C₂²×C₄	—	31	2	no	—
607	C₂²×C₄	—	31	2	no	—
608	C₂²×C₄	—	62	4	no	—
609	C₂²×C₄	—	62	4	no	—
610	C₂²×C₄	—	62	8	no	—
611	C₂²×C₄	—	124	4	no	—
612	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂²×D₃₁	1	2	yes	complemented
614	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic, complemented
615	C₂²×C₄	C₂²×D₃₁	1	2	yes	complemented
616	C₄⋊C₄	—	31	2	no	—
617	C₄⋊C₄	—	31	1	no	—
618	C₄⋊C₄	—	31	1	no	—
619	C₄⋊C₄	—	31	2	no	—
620	C₄⋊C₄	—	31	2	no	—
621	C₄⋊C₄	—	31	1	no	—
622	C₄⋊C₄	—	31	1	no	—
623	C₄⋊C₄	—	31	2	no	—
624	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic, complemented
625	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic, complemented
626	C₄⋊C₄	C₂²×D₃₁	1	2	yes	complemented
627	C₂²⋊C₄	—	31	1	no	—
628	C₂²⋊C₄	—	31	2	no	—
629	C₂²⋊C₄	—	31	2	no	—
630	C₂²⋊C₄	—	31	2	no	—
631	C₂²⋊C₄	—	31	2	no	—
632	C₂²⋊C₄	—	31	1	no	—
633	C₂²⋊C₄	—	31	2	no	—
634	C₂²⋊C₄	—	31	1	no	—
635	C₂²⋊C₄	—	31	1	no	—
636	C₂²⋊C₄	—	31	2	no	—
637	C₂²⋊C₄	—	31	2	no	—
638	C₂²⋊C₄	—	31	2	no	—
639	C₂²⋊C₄	—	31	2	no	—
640	C₂²⋊C₄	—	31	2	no	—
641	C₂²⋊C₄	—	31	2	no	—
642	C₂²⋊C₄	—	31	2	no	—
643	C₂²⋊C₄	—	31	2	no	—
644	C₂²⋊C₄	—	31	1	no	—
645	C₂²⋊C₄	—	31	1	no	—
646	C₂²⋊C₄	—	31	2	no	—
647	C₂²⋊C₄	—	31	2	no	—
648	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
649	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
650	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	complemented
651	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	complemented
652	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	complemented
653	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic, complemented
654	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	complemented
655	C₄²	—	31	1	no	—
656	C₄²	—	31	1	no	—
657	C₄²	—	31	1	no	—
658	C₄²	C₂²×D₃₁	1	1	yes	characteristic, complemented
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	31	1	no	—
663	C₂³	—	31	8	no	—
664	C₂³	—	31	4	no	—
665	C₂³	—	31	1	no	—
666	C₂³	—	31	2	no	—
667	C₂³	—	31	2	no	—
668	C₂³	—	31	1	no	—
669	C₂³	—	62	2	no	—
670	C₂³	—	62	4	no	—
671	C₂³	—	62	4	no	—
672	C₂³	—	62	2	no	—
673	C₂³	—	62	2	no	—
674	C₂³	—	62	4	no	—
675	C₂³	—	62	4	no	—
676	C₂³	—	62	4	no	—
677	C₂³	—	62	2	no	—
678	C₂³	—	62	2	no	—
679	C₂³	—	62	4	no	—
680	C₂³	—	62	4	no	—
681	C₂³	—	62	4	no	—
682	C₂³	—	62	4	no	—
683	C₂³	—	62	4	no	—
684	C₂³	—	62	4	no	—
685	C₂³	—	124	2	no	—
686	C₂³	—	124	2	no	—
687	C₂³	—	124	2	no	—
688	C₂³	—	124	32	no	—
689	C₂³	C₂³×D₃₁	1	2	yes	—
690	C₂³	C₂³×D₃₁	1	1	yes	characteristic
691	C₂³	C₂³×D₃₁	1	2	yes	—
692	C₂³	C₂³×D₃₁	1	1	yes	characteristic
693	Q₈	—	2	2	no	—
694	Q₈	—	62	4	no	—
695	Q₈	—	62	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	31	8	no	—
702	D₄	—	31	4	no	—
703	D₄	—	62	2	no	—
704	D₄	—	62	4	no	—
705	D₄	—	62	4	no	—
706	D₄	—	62	4	no	—
707	D₄	—	62	2	no	—
708	D₄	—	62	4	no	—
709	D₄	—	62	4	no	—
710	D₄	—	62	4	no	—
711	D₄	—	62	4	no	—
712	D₄	—	62	2	no	—
713	D₄	—	62	2	no	—
714	D₄	—	124	2	no	—
715	D₄	—	124	2	no	—
716	D₄	—	124	2	no	—
717	D₄	D₄×D₃₁	1	4	yes	complemented
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	31	1	no	—
723	C₂×C₄	—	31	4	no	—
724	C₂×C₄	—	31	1	no	—
725	C₂×C₄	—	31	1	no	—
726	C₂×C₄	—	31	2	no	—
727	C₂×C₄	—	31	1	no	—
728	C₂×C₄	—	31	2	no	—
729	C₂×C₄	—	31	1	no	—
730	C₂×C₄	—	62	2	no	—
731	C₂×C₄	—	62	2	no	—
732	C₂×C₄	—	62	2	no	—
733	C₂×C₄	—	62	2	no	—
734	C₂×C₄	—	62	4	no	—
735	C₂×C₄	—	62	4	no	—
736	C₂×C₄	—	62	4	no	—
737	C₂×C₄	—	62	2	no	—
738	C₂×C₄	—	62	4	no	—
739	C₂×C₄	—	62	2	no	—
740	C₂×C₄	—	62	2	no	—
741	C₂×C₄	—	62	2	no	—
742	C₂×C₄	—	62	4	no	—
743	C₂×C₄	—	62	2	no	—
744	C₂×C₄	—	62	2	no	—
745	C₂×C₄	—	124	2	no	—
746	C₂×C₄	—	124	2	no	—
747	C₂×C₄	—	124	2	no	—
748	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
750	C₂×C₄	C₂³×D₃₁	1	2	yes	—
751	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
752	C₂×C₄	C₂³×D₃₁	1	2	yes	—
753	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
754	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	4	8	no	—
766	C₂²	—	31	2	no	—
767	C₂²	—	31	2	no	—
768	C₂²	—	31	2	no	—
769	C₂²	—	31	4	no	—
770	C₂²	—	31	2	no	—
771	C₂²	—	62	8	no	—
772	C₂²	—	62	16	no	—
773	C₂²	—	62	1	no	—
774	C₂²	—	62	2	no	—
775	C₂²	—	62	2	no	—
776	C₂²	—	62	1	no	—
777	C₂²	—	62	1	no	—
778	C₂²	—	62	2	no	—
779	C₂²	—	62	1	no	—
780	C₂²	—	62	2	no	—
781	C₂²	—	62	1	no	—
782	C₂²	—	62	2	no	—
783	C₂²	—	124	8	no	—
784	C₂²	—	124	8	no	—
785	C₂²	—	124	8	no	—
786	C₂²	—	124	4	no	—
787	C₂²	—	124	8	no	—
788	C₂²	C₂×D₄×D₃₁	1	4	yes	—
789	C₂²	#41×D₃₁	1	2	yes	complemented
790	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	2	no	—
797	C₄	—	31	2	no	—
798	C₄	—	62	1	no	—
799	C₄	—	62	1	no	—
800	C₄	—	62	2	no	—
801	C₄	—	62	1	no	—
802	C₄	—	62	1	no	—
803	C₄	—	62	2	no	—
804	C₄	C₂×D₄×D₃₁	1	2	yes	—
805	C₂	—	2	2	no	—
806	C₂	—	2	4	no	—
807	C₂	—	4	2	no	—
808	C₂	—	4	1	no	—
809	C₂	—	31	4	no	—
810	C₂	—	62	2	no	—
811	C₂	—	62	4	no	—
812	C₂	—	124	2	no	—
813	C₂	—	124	1	no	—
814	C₂	C₂²×D₄×D₃₁	1	1	yes	characteristic
815	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
816	C₂	H(5,𝔽₂)×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Fitting	C₃₁×#546	C₂
hypercenter	#546	D₃₁
hypocenter	C₃₁	C₂×#546
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₃₁	C₂	semidirect
2. C₂²×D₄×D₃₁	C₂	semidirect
3. #14521696	C₂	semidirect
4. #14521695	C₂	semidirect
5. #14521694	C₂	semidirect
6. #14521693	C₂	semidirect
7. #14521692	C₂	semidirect
8. #14521691	C₂	semidirect
9. #14521690	C₂	semidirect
10. #14521689	C₂	semidirect
11. #14521688	C₂	semidirect
12. #14521687	C₂	semidirect
13. #14521686	C₂	semidirect
14. #124×D₃₁	C₂	semidirect
15. #123×D₃₁	C₂	semidirect
16. C₂²⋊Q₈×D₃₁	C₂	semidirect
17. #121×D₃₁	C₂	semidirect
18. #121×D₃₁	C₂	semidirect
19. #120×D₃₁	C₂	semidirect
20. C₄×D₄×D₃₁	C₂	semidirect
21. C₄×D₄×D₃₁	C₂	semidirect
22. C₂×C₂²⋊C₄×D₃₁	C₂	semidirect
23. C₃₁×#546	C₂	semidirect
25. C₂×#41×C₃₁	C₂²	semidirect
26. C₂²×D₄×C₃₁	C₂²	semidirect
27. C₂²×C₂²⋊D₃₁	C₂²	semidirect
29. C₂×#92499	C₂²	semidirect
30. C₂×Q₈×D₃₁	C₂²	semidirect
31. C₂×#92497	C₂²	semidirect
32. C₂×#92497	C₂²	semidirect
38. C₂×D₄×D₃₁	C₂²	semidirect
39. C₂×D₄×D₃₁	C₂²	semidirect
40. C₂×D₄×D₃₁	C₂²	semidirect
41. C₂×D₄×D₃₁	C₂²	semidirect
42. C₂×D₄×D₃₁	C₂²	semidirect
43. C₂×#92495	C₂²	semidirect
44. C₂×#92495	C₂²	semidirect
45. C₂²×D₁₂₄	C₂²	semidirect
47. C₂²×C₄×D₃₁	C₂²	semidirect
48. C₂²×C₄×D₃₁	C₂²	semidirect
49. C₂²×C₄×D₃₁	C₂²	semidirect
50. C₃₁×#124	C₂²	semidirect
51. C₃₁×#123	C₂²	semidirect
52. C₃₁×C₂²⋊Q₈	C₂²	semidirect
53. C₃₁×#121	C₂²	semidirect
54. C₃₁×#121	C₂²	semidirect
55. C₃₁×#120	C₂²	semidirect
56. C₄×D₄×C₃₁	C₂²	semidirect
57. C₄×D₄×C₃₁	C₂²	semidirect
58. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
59. #11758530	C₂²	semidirect
60. C₂×C₂²⋊Dic₃₁	C₂²	semidirect
61. #11758524	C₂²	semidirect
62. #11758523	C₂²	semidirect
63. #11758516	C₂²	semidirect
64. #11758516	C₂²	semidirect
65. #11758516	C₂²	semidirect
66. #11758515	C₂²	semidirect
67. #11758515	C₂²	semidirect
68. #11758514	C₂²	semidirect
69. #11758514	C₂²	semidirect
70. #11758514	C₂²	semidirect
71. #11758513	C₂²	semidirect
72. #11758512	C₂²	semidirect
73. D₄×Dic₃₁	C₂²	semidirect
74. D₄×Dic₃₁	C₂²	semidirect
75. #11758507	C₂²	semidirect
76. #11758507	C₂²	semidirect
77. #11758506	C₂²	semidirect
78. C₄×C₂²⋊D₃₁	C₂²	semidirect
79. C₄×C₂²⋊D₃₁	C₂²	semidirect
80. C₄×C₂²⋊D₃₁	C₂²	semidirect
81. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
82. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
83. #11758501	C₂²	semidirect
84. #11758474	C₂²	semidirect
85. #11758473	C₂²	semidirect
86. #11758472	C₂²	semidirect
87. #11758472	C₂²	semidirect
88. #11758471	C₂²	semidirect
89. #11758471	C₂²	semidirect
90. #11758470	C₂²	semidirect
91. #11758470	C₂²	semidirect
92. C₄⋊C₄×D₃₁	C₂²	semidirect
93. C₄⋊C₄×D₃₁	C₂²	semidirect
94. C₄⋊C₄×D₃₁	C₂²	semidirect
95. #11758463	C₂²	semidirect
96. #11758462	C₂²	semidirect
97. #11758462	C₂²	semidirect
98. #11758461	C₂²	semidirect
99. #11758461	C₂²	semidirect
100. #11758461	C₂²	semidirect
101. #11758460	C₂²	semidirect
102. #11758460	C₂²	semidirect
103. #11758459	C₂²	semidirect
104. #11758459	C₂²	semidirect
105. #11758459	C₂²	semidirect
106. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
108. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
111. C₂²⋊C₄×D₃₁	C₂²	semidirect
112. C₂²⋊C₄×D₃₁	C₂²	semidirect
113. C₂²⋊C₄×D₃₁	C₂²	semidirect
114. C₂²⋊C₄×D₃₁	C₂²	semidirect
115. C₂²⋊C₄×D₃₁	C₂²	semidirect
116. C₂²⋊C₄×D₃₁	C₂²	semidirect
117. C₂²⋊C₄×D₃₁	C₂²	semidirect
118. C₂²⋊C₄×D₃₁	C₂²	semidirect
119. C₂²⋊C₄×D₃₁	C₂²	semidirect
120. #11758455	C₂²	semidirect
121. #11758452	C₂²	semidirect
122. C₄×D₁₂₄	C₂²	semidirect
123. C₄×D₁₂₄	C₂²	semidirect
124. C₄²×D₃₁	C₂²	semidirect
137. C₂×Q₈×C₃₁	C₂³	semidirect
143. C₂×D₄×C₃₁	C₂³	semidirect
144. C₂×D₄×C₃₁	C₂³	semidirect
146. C₂²×C₄×C₃₁	C₂³	semidirect
147. C₂²×C₄×C₃₁	C₂³	semidirect
148. C₂²×C₄×C₃₁	C₂³	semidirect
156. C₂×C₂²⋊D₃₁	C₂³	semidirect
157. C₂×C₂²⋊D₃₁	C₂³	semidirect
158. C₂×C₂²⋊D₃₁	C₂³	semidirect
159. C₂×C₂²⋊D₃₁	C₂³	semidirect
161. C₂²×Dic₃₁	C₂³	semidirect
162. C₂²×Dic₃₁	C₂³	semidirect
163. C₂²×Dic₃₁	C₂³	semidirect
176. D₄×D₃₁	D₄	semidirect
184. C₂×D₁₂₄	C₂³	semidirect
185. C₂×D₁₂₄	C₂³	semidirect
199. C₂×C₄×D₃₁	C₂³	semidirect
200. C₂×C₄×D₃₁	C₂³	semidirect
201. C₂×C₄×D₃₁	C₂³	semidirect
202. C₂×C₄×D₃₁	C₂³	semidirect
203. C₂×C₄×D₃₁	C₂³	semidirect
204. C₂×C₄×D₃₁	C₂³	semidirect
205. C₂×Dic₆₂	C₂³	semidirect
206. C₂×Dic₆₂	C₂³	semidirect
207. C₄⋊C₄×C₃₁	C₂³	semidirect
208. C₄⋊C₄×C₃₁	C₂³	semidirect
209. C₄⋊C₄×C₃₁	C₂³	semidirect
212. C₂²⋊C₄×C₃₁	C₂³	semidirect
213. C₂²⋊C₄×C₃₁	C₂³	semidirect
214. C₂²⋊C₄×C₃₁	C₂³	semidirect
215. C₂²⋊C₄×C₃₁	C₂³	semidirect
216. C₂²⋊C₄×C₃₁	C₂³	semidirect
217. C₄²×C₃₁	C₂³	semidirect
220. C₂²⋊Dic₃₁	C₂³	semidirect
221. C₂²⋊Dic₃₁	C₂³	semidirect
222. C₂²⋊Dic₃₁	C₂³	semidirect
223. C₂²⋊Dic₃₁	C₂³	semidirect
224. C₂²⋊Dic₃₁	C₂³	semidirect
229. (C₂×D₃₁)⋊C₄	C₂³	semidirect
230. (C₂×D₃₁)⋊C₄	C₂³	semidirect
231. (C₂×D₃₁)⋊C₄	C₂³	semidirect
232. (C₂×D₃₁)⋊C₄	C₂³	semidirect
233. (C₂×D₃₁)⋊C₄	C₂³	semidirect
234. (C₂×D₃₁)⋊C₄	C₂³	semidirect
235. (C₂×D₃₁)⋊C₄	C₂³	semidirect
236. (C₂×D₃₁)⋊C₄	C₂³	semidirect
237. (C₂×D₃₁)⋊C₄	C₂³	semidirect
238. (C₂×D₃₁)⋊C₄	C₂³	semidirect
239. C₄⋊Dic₃₁	C₂³	semidirect
240. C₄⋊Dic₃₁	C₂³	semidirect
241. C₄⋊Dic₃₁	C₂³	semidirect
242. Dic₃₁⋊C₄	C₂³	semidirect
243. Dic₃₁⋊C₄	C₂³	semidirect
244. Dic₃₁⋊C₄	C₂³	semidirect
245. Dic₃₁⋊C₄	C₂³	semidirect
246. Dic₃₁⋊C₄	C₂³	semidirect
247. C₄×Dic₃₁	C₂³	semidirect
248. C₄×Dic₃₁	C₂³	semidirect
249. C₄×Dic₃₁	C₂³	semidirect
278. C₂²×D₃₁	#41	semidirect
290. D₄×C₃₁	C₂×D₄	semidirect
311. C₂²⋊D₃₁	C₂×D₄	semidirect
328. D₁₂₄	C₂×D₄	semidirect
359. C₂²×C₃₁	C₂×#41	semidirect
381. C₂×D₃₁	C₂×#41	semidirect
410. #546	D₃₁	direct (N × H)
431. D₃₁	#546	direct (N × H)
439. C₂×#41	C₂×D₃₁	semidirect
453. C₂²×D₄	C₂×D₃₁	semidirect
463. #124	C₂×D₃₁	semidirect
471. #123	C₂×D₃₁	semidirect
477. C₂²⋊Q₈	C₂×D₃₁	semidirect
490. #121	C₂×D₃₁	semidirect
491. #121	C₂×D₃₁	semidirect
499. #120	C₂×D₃₁	semidirect
512. C₄×D₄	C₂×D₃₁	semidirect
513. C₄×D₄	C₂×D₃₁	semidirect
531. C₂×C₂²⋊C₄	C₂×D₃₁	semidirect
533. C₃₁	C₂×#546	semidirect
554. C₂×Q₈	C₂²×D₃₁	semidirect
587. C₂×D₄	C₂²×D₃₁	semidirect
588. C₂×D₄	C₂²×D₃₁	semidirect
613. C₂²×C₄	C₂²×D₃₁	semidirect
614. C₂²×C₄	C₂²×D₃₁	semidirect
615. C₂²×C₄	C₂²×D₃₁	semidirect
624. C₄⋊C₄	C₂²×D₃₁	semidirect
625. C₄⋊C₄	C₂²×D₃₁	semidirect
626. C₄⋊C₄	C₂²×D₃₁	semidirect
650. C₂²⋊C₄	C₂²×D₃₁	semidirect
651. C₂²⋊C₄	C₂²×D₃₁	semidirect
652. C₂²⋊C₄	C₂²×D₃₁	semidirect
653. C₂²⋊C₄	C₂²×D₃₁	semidirect
654. C₂²⋊C₄	C₂²×D₃₁	semidirect
658. C₄²	C₂²×D₃₁	semidirect
717. D₄	D₄×D₃₁	semidirect
789. C₂²	#41×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₃₁	2
C₂²×D₄×D₃₁	2
#14521696	2
#14521695	2
#14521694	2
#14521693	2
#14521692	2
#14521691	2
#14521690	2
#14521689	2
#14521688	2
#14521687	2
#14521686	2
#124×D₃₁	2
#123×D₃₁	2
C₂²⋊Q₈×D₃₁	2
#121×D₃₁	2
#120×D₃₁	2
C₄×D₄×D₃₁	2
C₂×C₂²⋊C₄×D₃₁	2
C₃₁×#546	2
C₂×#546	31

Subgroups — D31×#546 #16859152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×#546 #16859152