Subgroups — C₁₃₁×#34570 #45720454

Order 33536.

2094 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2653×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#2652×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2649×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2648×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2646×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2643×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2639×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2626×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2622×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2617×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#2401×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2398×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2395×C₁₃₁	C₂	1	2	yes	maximal, complemented
14	#2392×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#120×C₁₃₁	C₂	1	2	yes	maximal, complemented
18	#2290×C₁₃₁	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×#120×C₁₃₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#117×C₁₃₁	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
34	#401×C₁₃₁	C₂²	1	2	yes	complemented
35	#400×C₁₃₁	C₂²	1	2	yes	complemented
36	#400×C₁₃₁	C₂²	1	2	yes	complemented
37	#400×C₁₃₁	C₂²	1	2	yes	complemented
38	#400×C₁₃₁	C₂²	1	2	yes	complemented
39	#400×C₁₃₁	C₂²	1	2	yes	complemented
40	#400×C₁₃₁	C₂²	1	2	yes	complemented
41	#399×C₁₃₁	C₂²	1	2	yes	—
42	#398×C₁₃₁	C₂²	1	2	yes	complemented
43	#398×C₁₃₁	C₂²	1	2	yes	complemented
44	#397×C₁₃₁	C₂²	1	2	yes	—
45	#397×C₁₃₁	C₂²	1	2	yes	—
46	#397×C₁₃₁	C₂²	1	2	yes	—
47	#397×C₁₃₁	C₂²	1	2	yes	—
48	#397×C₁₃₁	C₂²	1	2	yes	—
49	#397×C₁₃₁	C₂²	1	2	yes	complemented
50	#397×C₁₃₁	C₂²	1	2	yes	complemented
51	#397×C₁₃₁	C₂²	1	2	yes	complemented
52	#397×C₁₃₁	C₂²	1	2	yes	complemented
53	#396×C₁₃₁	C₂²	1	2	yes	—
54	#396×C₁₃₁	C₂²	1	2	yes	—
55	#396×C₁₃₁	C₂²	1	2	yes	complemented
56	#394×C₁₃₁	C₂²	1	2	yes	—
57	#394×C₁₃₁	C₂²	1	2	yes	—
58	#394×C₁₃₁	C₂²	1	2	yes	—
59	#394×C₁₃₁	C₂²	1	2	yes	—
60	#394×C₁₃₁	C₂²	1	2	yes	—
61	#394×C₁₃₁	C₂²	1	2	yes	—
62	#394×C₁₃₁	C₂²	1	2	yes	complemented
63	#393×C₁₃₁	C₂²	1	2	yes	—
64	#393×C₁₃₁	C₂²	1	2	yes	complemented
65	#392×C₁₃₁	C₂²	1	2	yes	—
66	#391×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
67	#390×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
68	#389×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
69	#389×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
70	#388×C₁₃₁	C₂²	1	2	yes	complemented
71	#388×C₁₃₁	C₂²	1	2	yes	complemented
72	#388×C₁₃₁	C₂²	1	2	yes	complemented
73	#387×C₁₃₁	C₂²	1	2	yes	complemented
74	#387×C₁₃₁	C₂²	1	2	yes	complemented
75	#387×C₁₃₁	C₂²	1	2	yes	complemented
76	#386×C₁₃₁	C₂²	1	2	yes	—
77	#386×C₁₃₁	C₂²	1	2	yes	—
78	#386×C₁₃₁	C₂²	1	2	yes	—
79	#386×C₁₃₁	C₂²	1	2	yes	—
80	#386×C₁₃₁	C₂²	1	2	yes	—
81	#386×C₁₃₁	C₂²	1	2	yes	—
82	#385×C₁₃₁	C₂²	1	2	yes	—
83	#385×C₁₃₁	C₂²	1	2	yes	—
84	#385×C₁₃₁	C₂²	1	2	yes	—
85	#385×C₁₃₁	C₂²	1	2	yes	—
86	#385×C₁₃₁	C₂²	1	2	yes	—
87	#385×C₁₃₁	C₂²	1	2	yes	—
88	#380×C₁₃₁	C₂²	1	1	yes	characteristic
89	#380×C₁₃₁	C₂²	1	1	yes	characteristic
90	#379×C₁₃₁	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
104	#376×C₁₃₁	C₂²	1	2	yes	complemented
105	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₁	—	2	4	no	—
114	C₂³×C₄×C₁₃₁	—	4	2	no	—
115	C₂³×C₄×C₁₃₁	—	4	2	no	—
116	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
125	C₂²⋊Q₈×C₁₃₁	—	2	4	no	—
126	#121×C₁₃₁	—	2	4	no	—
127	#120×C₁₃₁	—	2	8	no	—
128	C₄×Q₈×C₁₃₁	—	4	2	no	—
129	C₄×D₄×C₁₃₁	—	2	8	no	—
130	C₄×D₄×C₁₃₁	—	4	4	no	—
131	C₄×D₄×C₁₃₁	—	4	4	no	—
132	C₄×D₄×C₁₃₁	—	4	2	no	—
133	#117×C₁₃₁	—	4	4	no	—
134	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
152	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃₁	—	4	2	no	—
176	C₂×C₄²×C₁₃₁	—	4	2	no	—
177	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
186	#95×C₁₃₁	C₂³	1	2	yes	—
187	#95×C₁₃₁	C₂³	1	2	yes	—
188	#95×C₁₃₁	C₂³	1	2	yes	—
189	#95×C₁₃₁	C₂³	1	2	yes	—
190	#95×C₁₃₁	C₂³	1	2	yes	—
191	#95×C₁₃₁	C₂³	1	2	yes	—
192	#95×C₁₃₁	C₂³	1	2	yes	—
193	#95×C₁₃₁	C₂³	1	2	yes	—
194	#95×C₁₃₁	C₂³	1	2	yes	—
195	#95×C₁₃₁	C₂³	1	2	yes	—
196	#95×C₁₃₁	C₂³	1	2	yes	—
197	#95×C₁₃₁	C₂³	1	2	yes	—
198	#95×C₁₃₁	C₂³	1	2	yes	—
199	#95×C₁₃₁	C₂³	1	2	yes	—
200	#95×C₁₃₁	C₂³	1	2	yes	—
201	#95×C₁₃₁	C₂³	1	2	yes	—
202	#95×C₁₃₁	C₂³	1	2	yes	—
203	#95×C₁₃₁	C₂³	1	2	yes	—
204	#95×C₁₃₁	C₂³	1	2	yes	—
205	#95×C₁₃₁	C₂³	1	2	yes	—
206	#95×C₁₃₁	C₂³	1	2	yes	—
207	#95×C₁₃₁	C₂³	1	2	yes	—
208	#95×C₁₃₁	C₂³	1	2	yes	—
209	#95×C₁₃₁	C₂³	1	2	yes	—
210	C₂⁴×C₁₃₁	—	2	2	no	—
211	C₂⁴×C₁₃₁	—	2	2	no	—
212	C₂⁴×C₁₃₁	—	4	1	no	—
213	C₂⁴×C₁₃₁	—	4	1	no	—
214	C₂⁴×C₁₃₁	—	4	1	no	—
215	C₂⁴×C₁₃₁	—	4	1	no	—
216	C₂⁴×C₁₃₁	#41	1	4	yes	—
217	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
218	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
220	C₂×Q₈×C₁₃₁	—	2	2	no	—
221	C₂×Q₈×C₁₃₁	—	4	1	no	—
222	C₂×Q₈×C₁₃₁	—	4	1	no	—
223	C₂×D₄×C₁₃₁	—	2	4	no	—
224	C₂×D₄×C₁₃₁	—	2	4	no	—
225	C₂×D₄×C₁₃₁	—	2	4	no	—
226	C₂×D₄×C₁₃₁	—	2	4	no	—
227	C₂×D₄×C₁₃₁	—	2	4	no	—
228	C₂×D₄×C₁₃₁	—	2	2	no	—
229	C₂×D₄×C₁₃₁	—	4	1	no	—
230	C₂×D₄×C₁₃₁	—	4	2	no	—
231	C₂×D₄×C₁₃₁	—	4	2	no	—
232	C₂×D₄×C₁₃₁	—	4	1	no	—
233	C₂×D₄×C₁₃₁	—	4	2	no	—
234	C₂×D₄×C₁₃₁	—	4	2	no	—
235	C₂²×C₄×C₁₃₁	—	2	2	no	—
236	C₂²×C₄×C₁₃₁	—	2	2	no	—
237	C₂²×C₄×C₁₃₁	—	2	2	no	—
238	C₂²×C₄×C₁₃₁	—	2	2	no	—
239	C₂²×C₄×C₁₃₁	—	2	2	no	—
240	C₂²×C₄×C₁₃₁	—	2	2	no	—
241	C₂²×C₄×C₁₃₁	—	2	4	no	—
242	C₂²×C₄×C₁₃₁	—	2	4	no	—
243	C₂²×C₄×C₁₃₁	—	2	4	no	—
244	C₂²×C₄×C₁₃₁	—	2	4	no	—
245	C₂²×C₄×C₁₃₁	—	2	4	no	—
246	C₂²×C₄×C₁₃₁	—	2	4	no	—
247	C₂²×C₄×C₁₃₁	—	2	4	no	—
248	C₂²×C₄×C₁₃₁	—	4	1	no	—
249	C₂²×C₄×C₁₃₁	—	4	1	no	—
250	C₂²×C₄×C₁₃₁	—	4	1	no	—
251	C₂²×C₄×C₁₃₁	—	4	1	no	—
252	C₂²×C₄×C₁₃₁	—	4	2	no	—
253	C₂²×C₄×C₁₃₁	—	4	2	no	—
254	C₂²×C₄×C₁₃₁	—	4	1	no	—
255	C₂²×C₄×C₁₃₁	—	4	1	no	—
256	C₂²×C₄×C₁₃₁	—	4	1	no	—
257	C₂²×C₄×C₁₃₁	—	4	1	no	—
258	C₂²×C₄×C₁₃₁	—	4	1	no	—
259	C₂²×C₄×C₁₃₁	—	4	1	no	—
260	C₂²×C₄×C₁₃₁	—	4	16	no	—
261	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
262	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
263	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₁₃₁	—	2	4	no	—
280	C₄⋊C₄×C₁₃₁	—	2	2	no	—
281	C₄⋊C₄×C₁₃₁	—	2	2	no	—
282	C₄⋊C₄×C₁₃₁	—	2	4	no	—
283	C₄⋊C₄×C₁₃₁	—	4	1	no	—
284	C₄⋊C₄×C₁₃₁	—	4	1	no	—
285	C₄⋊C₄×C₁₃₁	—	4	2	no	—
286	C₄⋊C₄×C₁₃₁	—	4	2	no	—
287	C₄⋊C₄×C₁₃₁	—	4	2	no	—
288	C₄⋊C₄×C₁₃₁	—	4	2	no	—
289	C₄⋊C₄×C₁₃₁	—	4	2	no	—
290	C₄⋊C₄×C₁₃₁	—	4	1	no	—
291	C₄⋊C₄×C₁₃₁	—	4	2	no	—
292	C₄⋊C₄×C₁₃₁	—	4	2	no	—
293	C₄⋊C₄×C₁₃₁	—	4	1	no	—
294	C₄⋊C₄×C₁₃₁	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
302	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
303	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
307	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
308	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
311	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
316	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
318	C₄²×C₁₃₁	—	2	4	no	—
319	C₄²×C₁₃₁	—	2	4	no	—
320	C₄²×C₁₃₁	—	2	2	no	—
321	C₄²×C₁₃₁	—	2	2	no	—
322	C₄²×C₁₃₁	—	2	4	no	—
323	C₄²×C₁₃₁	—	2	4	no	—
324	C₄²×C₁₃₁	—	4	1	no	—
325	C₄²×C₁₃₁	—	4	1	no	—
326	C₄²×C₁₃₁	—	4	2	no	—
327	C₂³×C₁₃₁	—	2	1	no	—
328	C₂³×C₁₃₁	—	2	1	no	—
329	C₂³×C₁₃₁	—	2	1	no	—
330	C₂³×C₁₃₁	—	2	1	no	—
331	C₂³×C₁₃₁	—	2	8	no	—
332	C₂³×C₁₃₁	—	2	2	no	—
333	C₂³×C₁₃₁	—	2	2	no	—
334	C₂³×C₁₃₁	—	2	2	no	—
335	C₂³×C₁₃₁	—	2	2	no	—
336	C₂³×C₁₃₁	—	2	2	no	—
337	C₂³×C₁₃₁	—	2	2	no	—
338	C₂³×C₁₃₁	—	2	2	no	—
339	C₂³×C₁₃₁	—	2	2	no	—
340	C₂³×C₁₃₁	—	2	2	no	—
341	C₂³×C₁₃₁	—	2	2	no	—
342	C₂³×C₁₃₁	—	2	2	no	—
343	C₂³×C₁₃₁	—	2	2	no	—
344	C₂³×C₁₃₁	—	2	2	no	—
345	C₂³×C₁₃₁	—	4	4	no	—
346	C₂³×C₁₃₁	—	4	4	no	—
347	C₂³×C₁₃₁	—	4	4	no	—
348	C₂³×C₁₃₁	—	4	4	no	—
349	C₂³×C₁₃₁	—	4	4	no	—
350	C₂³×C₁₃₁	—	4	4	no	—
351	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
352	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
353	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
354	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
355	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
356	Q₈×C₁₃₁	—	4	4	no	—
357	D₄×C₁₃₁	—	4	4	no	—
358	D₄×C₁₃₁	—	4	8	no	—
359	D₄×C₁₃₁	—	4	8	no	—
360	D₄×C₁₃₁	—	4	8	no	—
361	C₂×C₄×C₁₃₁	—	2	1	no	—
362	C₂×C₄×C₁₃₁	—	2	1	no	—
363	C₂×C₄×C₁₃₁	—	2	1	no	—
364	C₂×C₄×C₁₃₁	—	2	1	no	—
365	C₂×C₄×C₁₃₁	—	2	1	no	—
366	C₂×C₄×C₁₃₁	—	2	1	no	—
367	C₂×C₄×C₁₃₁	—	2	8	no	—
368	C₂×C₄×C₁₃₁	—	2	2	no	—
369	C₂×C₄×C₁₃₁	—	2	2	no	—
370	C₂×C₄×C₁₃₁	—	2	1	no	—
371	C₂×C₄×C₁₃₁	—	2	2	no	—
372	C₂×C₄×C₁₃₁	—	2	1	no	—
373	C₂×C₄×C₁₃₁	—	2	2	no	—
374	C₂×C₄×C₁₃₁	—	2	2	no	—
375	C₂×C₄×C₁₃₁	—	2	2	no	—
376	C₂×C₄×C₁₃₁	—	2	2	no	—
377	C₂×C₄×C₁₃₁	—	2	2	no	—
378	C₂×C₄×C₁₃₁	—	2	2	no	—
379	C₂×C₄×C₁₃₁	—	2	2	no	—
380	C₂×C₄×C₁₃₁	—	2	2	no	—
381	C₂×C₄×C₁₃₁	—	2	2	no	—
382	C₂×C₄×C₁₃₁	—	2	1	no	—
383	C₂×C₄×C₁₃₁	—	2	2	no	—
384	C₂×C₄×C₁₃₁	—	2	2	no	—
385	C₂×C₄×C₁₃₁	—	2	1	no	—
386	C₂×C₄×C₁₃₁	—	2	2	no	—
387	C₂×C₄×C₁₃₁	—	2	2	no	—
388	C₂×C₄×C₁₃₁	—	2	2	no	—
389	C₂×C₄×C₁₃₁	—	2	2	no	—
390	C₂×C₄×C₁₃₁	—	2	2	no	—
391	C₂×C₄×C₁₃₁	—	2	2	no	—
392	C₂×C₄×C₁₃₁	—	2	2	no	—
393	C₂×C₄×C₁₃₁	—	2	2	no	—
394	C₂×C₄×C₁₃₁	—	2	2	no	—
395	C₂×C₄×C₁₃₁	—	2	1	no	—
396	C₂×C₄×C₁₃₁	—	2	2	no	—
397	C₂×C₄×C₁₃₁	—	2	2	no	—
398	C₂×C₄×C₁₃₁	—	2	2	no	—
399	C₂×C₄×C₁₃₁	—	2	2	no	—
400	C₂×C₄×C₁₃₁	—	2	2	no	—
401	C₂×C₄×C₁₃₁	—	2	2	no	—
402	C₂×C₄×C₁₃₁	—	2	1	no	—
403	C₂×C₄×C₁₃₁	—	2	2	no	—
404	C₂×C₄×C₁₃₁	—	4	4	no	—
405	C₂×C₄×C₁₃₁	—	4	8	no	—
406	C₂×C₄×C₁₃₁	—	4	4	no	—
407	C₂×C₄×C₁₃₁	—	4	4	no	—
408	C₂×C₄×C₁₃₁	—	4	4	no	—
409	C₂×C₄×C₁₃₁	—	4	4	no	—
410	C₂×C₄×C₁₃₁	—	4	8	no	—
411	C₂×C₄×C₁₃₁	—	4	8	no	—
412	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
413	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
415	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
416	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
418	C₂²×C₁₃₁	—	2	2	no	—
419	C₂²×C₁₃₁	—	2	2	no	—
420	C₂²×C₁₃₁	—	2	2	no	—
421	C₂²×C₁₃₁	—	2	2	no	—
422	C₂²×C₁₃₁	—	2	2	no	—
423	C₂²×C₁₃₁	—	2	2	no	—
424	C₂²×C₁₃₁	—	2	4	no	—
425	C₂²×C₁₃₁	—	2	4	no	—
426	C₂²×C₁₃₁	—	2	4	no	—
427	C₂²×C₁₃₁	—	4	16	no	—
428	C₂²×C₁₃₁	—	4	2	no	—
429	C₂²×C₁₃₁	—	4	2	no	—
430	C₂²×C₁₃₁	—	4	2	no	—
431	C₂²×C₁₃₁	—	4	2	no	—
432	C₂²×C₁₃₁	—	4	2	no	—
433	C₂²×C₁₃₁	—	4	2	no	—
434	C₂²×C₁₃₁	—	4	2	no	—
435	C₂²×C₁₃₁	—	4	2	no	—
436	C₂²×C₁₃₁	—	4	2	no	—
437	C₂²×C₁₃₁	—	4	2	no	—
438	C₂²×C₁₃₁	—	4	2	no	—
439	C₂²×C₁₃₁	#529	1	4	yes	—
440	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
441	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
443	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²×C₁₃₁	#585	1	1	yes	characteristic
446	C₂²×C₁₃₁	#585	1	1	yes	characteristic
447	C₄×C₁₃₁	—	2	2	no	—
448	C₄×C₁₃₁	—	2	2	no	—
449	C₄×C₁₃₁	—	2	2	no	—
450	C₄×C₁₃₁	—	4	2	no	—
451	C₄×C₁₃₁	—	4	2	no	—
452	C₄×C₁₃₁	—	4	2	no	—
453	C₄×C₁₃₁	—	4	2	no	—
454	C₄×C₁₃₁	—	4	1	no	—
455	C₄×C₁₃₁	—	4	2	no	—
456	C₄×C₁₃₁	—	4	1	no	—
457	C₄×C₁₃₁	—	4	2	no	—
458	C₄×C₁₃₁	—	4	2	no	—
459	C₄×C₁₃₁	—	4	2	no	—
460	C₄×C₁₃₁	—	4	2	no	—
461	C₄×C₁₃₁	—	4	2	no	—
462	C₄×C₁₃₁	#538	1	4	yes	—
463	C₂×C₁₃₁	—	2	4	no	—
464	C₂×C₁₃₁	—	4	4	no	—
465	C₂×C₁₃₁	—	8	2	no	—
466	C₂×C₁₃₁	C₂×#529	1	1	yes	characteristic
467	C₂×C₁₃₁	C₂×#538	1	1	yes	characteristic
468	C₂×C₁₃₁	#3455	1	1	yes	characteristic
469	C₂×C₁₃₁	#3459	1	1	yes	characteristic
470	C₂×C₁₃₁	#3459	1	1	yes	characteristic
471	C₂×C₁₃₁	#3459	1	1	yes	characteristic
472	C₂×C₁₃₁	#3460	1	1	yes	characteristic
473	#34570	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₁₃₁	#34570	1	1	yes	characteristic, direct product factor, Sylow
475	#2653	C₂×C₁₃₁	1	2	yes	complemented
476	#2652	C₂×C₁₃₁	1	2	yes	complemented
477	#2649	C₂×C₁₃₁	1	2	yes	complemented
478	#2648	C₂×C₁₃₁	1	2	yes	complemented
479	#2646	C₂×C₁₃₁	1	1	yes	characteristic, complemented
480	#2643	C₂×C₁₃₁	1	2	yes	complemented
481	#2639	C₂×C₁₃₁	1	1	yes	characteristic, complemented
482	#2626	C₂×C₁₃₁	1	1	yes	characteristic, complemented
483	#2622	C₂×C₁₃₁	1	2	yes	complemented
484	#2617	C₂×C₁₃₁	1	1	yes	characteristic
485	#2401	C₂×C₁₃₁	1	2	yes	complemented
486	#2398	C₂×C₁₃₁	1	2	yes	complemented
487	#2395	C₂×C₁₃₁	1	2	yes	complemented
488	#2392	C₂×C₁₃₁	1	2	yes	complemented
489	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
490	C₄×#121	C₂×C₁₃₁	1	1	yes	characteristic, complemented
491	C₄×#120	C₂×C₁₃₁	1	2	yes	complemented
492	#2290	C₂×C₁₃₁	1	2	yes	complemented
493	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
494	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
495	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
496	C₂×#121	C₂²×C₁₃₁	1	1	yes	characteristic
497	C₂×#120	C₂²×C₁₃₁	1	2	yes	—
498	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
500	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
502	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
503	C₂×#117	C₂²×C₁₃₁	1	2	yes	complemented
504	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
505	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
506	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
507	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
508	#401	C₂²×C₁₃₁	1	2	yes	complemented
509	#400	C₂²×C₁₃₁	1	2	yes	complemented
510	#400	C₂²×C₁₃₁	1	2	yes	complemented
511	#400	C₂²×C₁₃₁	1	2	yes	complemented
512	#400	C₂²×C₁₃₁	1	2	yes	complemented
513	#400	C₂²×C₁₃₁	1	2	yes	complemented
514	#400	C₂²×C₁₃₁	1	2	yes	complemented
515	#399	C₂²×C₁₃₁	1	2	yes	—
516	#398	C₂²×C₁₃₁	1	2	yes	complemented
517	#398	C₂²×C₁₃₁	1	2	yes	complemented
518	#397	C₂²×C₁₃₁	1	2	yes	—
519	#397	C₂²×C₁₃₁	1	2	yes	—
520	#397	C₂²×C₁₃₁	1	2	yes	—
521	#397	C₂²×C₁₃₁	1	2	yes	—
522	#397	C₂²×C₁₃₁	1	2	yes	—
523	#397	C₂²×C₁₃₁	1	2	yes	complemented
524	#397	C₂²×C₁₃₁	1	2	yes	complemented
525	#397	C₂²×C₁₃₁	1	2	yes	complemented
526	#397	C₂²×C₁₃₁	1	2	yes	complemented
527	#396	C₂²×C₁₃₁	1	2	yes	—
528	#396	C₂²×C₁₃₁	1	2	yes	—
529	#396	C₂²×C₁₃₁	1	2	yes	complemented
530	#394	C₂²×C₁₃₁	1	2	yes	—
531	#394	C₂²×C₁₃₁	1	2	yes	—
532	#394	C₂²×C₁₃₁	1	2	yes	—
533	#394	C₂²×C₁₃₁	1	2	yes	—
534	#394	C₂²×C₁₃₁	1	2	yes	—
535	#394	C₂²×C₁₃₁	1	2	yes	—
536	#394	C₂²×C₁₃₁	1	2	yes	complemented
537	#393	C₂²×C₁₃₁	1	2	yes	—
538	#393	C₂²×C₁₃₁	1	2	yes	complemented
539	#392	C₂²×C₁₃₁	1	2	yes	—
540	#391	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
541	#390	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
542	#389	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
543	#389	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
544	#388	C₂²×C₁₃₁	1	2	yes	complemented
545	#388	C₂²×C₁₃₁	1	2	yes	complemented
546	#388	C₂²×C₁₃₁	1	2	yes	complemented
547	#387	C₂²×C₁₃₁	1	2	yes	complemented
548	#387	C₂²×C₁₃₁	1	2	yes	complemented
549	#387	C₂²×C₁₃₁	1	2	yes	complemented
550	#386	C₂²×C₁₃₁	1	2	yes	—
551	#386	C₂²×C₁₃₁	1	2	yes	—
552	#386	C₂²×C₁₃₁	1	2	yes	—
553	#386	C₂²×C₁₃₁	1	2	yes	—
554	#386	C₂²×C₁₃₁	1	2	yes	—
555	#386	C₂²×C₁₃₁	1	2	yes	—
556	#385	C₂²×C₁₃₁	1	2	yes	—
557	#385	C₂²×C₁₃₁	1	2	yes	—
558	#385	C₂²×C₁₃₁	1	2	yes	—
559	#385	C₂²×C₁₃₁	1	2	yes	—
560	#385	C₂²×C₁₃₁	1	2	yes	—
561	#385	C₂²×C₁₃₁	1	2	yes	—
562	#380	C₂²×C₁₃₁	1	1	yes	characteristic
563	#380	C₂²×C₁₃₁	1	1	yes	characteristic
564	#379	C₂²×C₁₃₁	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
566	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
567	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
568	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
569	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
577	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
578	#376	C₂²×C₁₃₁	1	2	yes	complemented
579	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
580	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
581	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
584	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
585	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
587	C₂³×C₄	—	2	4	no	—
588	C₂³×C₄	—	4	2	no	—
589	C₂³×C₄	—	4	2	no	—
590	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
591	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
592	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
598	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
599	C₂²⋊Q₈	—	2	4	no	—
600	#121	—	2	4	no	—
601	#120	—	2	8	no	—
602	C₄×Q₈	—	4	2	no	—
603	C₄×D₄	—	2	8	no	—
604	C₄×D₄	—	4	4	no	—
605	C₄×D₄	—	4	4	no	—
606	C₄×D₄	—	4	2	no	—
607	#117	—	4	4	no	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	—	2	4	no	—
625	C₂×C₂²⋊C₄	—	2	4	no	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
649	C₂×C₄²	—	4	2	no	—
650	C₂×C₄²	—	4	2	no	—
651	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
652	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
658	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
660	#95	C₂³×C₁₃₁	1	2	yes	—
661	#95	C₂³×C₁₃₁	1	2	yes	—
662	#95	C₂³×C₁₃₁	1	2	yes	—
663	#95	C₂³×C₁₃₁	1	2	yes	—
664	#95	C₂³×C₁₃₁	1	2	yes	—
665	#95	C₂³×C₁₃₁	1	2	yes	—
666	#95	C₂³×C₁₃₁	1	2	yes	—
667	#95	C₂³×C₁₃₁	1	2	yes	—
668	#95	C₂³×C₁₃₁	1	2	yes	—
669	#95	C₂³×C₁₃₁	1	2	yes	—
670	#95	C₂³×C₁₃₁	1	2	yes	—
671	#95	C₂³×C₁₃₁	1	2	yes	—
672	#95	C₂³×C₁₃₁	1	2	yes	—
673	#95	C₂³×C₁₃₁	1	2	yes	—
674	#95	C₂³×C₁₃₁	1	2	yes	—
675	#95	C₂³×C₁₃₁	1	2	yes	—
676	#95	C₂³×C₁₃₁	1	2	yes	—
677	#95	C₂³×C₁₃₁	1	2	yes	—
678	#95	C₂³×C₁₃₁	1	2	yes	—
679	#95	C₂³×C₁₃₁	1	2	yes	—
680	#95	C₂³×C₁₃₁	1	2	yes	—
681	#95	C₂³×C₁₃₁	1	2	yes	—
682	#95	C₂³×C₁₃₁	1	2	yes	—
683	#95	C₂³×C₁₃₁	1	2	yes	—
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	4	1	no	—
687	C₂⁴	—	4	1	no	—
688	C₂⁴	—	4	1	no	—
689	C₂⁴	—	4	1	no	—
690	C₂⁴	#41×C₁₃₁	1	4	yes	—
691	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
692	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
693	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×Q₈	—	4	1	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	16	no	—
735	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
736	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	4	no	—
798	C₄²	—	4	1	no	—
799	C₄²	—	4	1	no	—
800	C₄²	—	4	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	8	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	—	4	4	no	—
823	C₂³	—	4	4	no	—
824	C₂³	—	4	4	no	—
825	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
826	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
827	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
828	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
829	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
830	Q₈	—	4	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	8	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	8	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
887	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
888	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
889	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
890	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
891	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	4	16	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	#529×C₁₃₁	1	4	yes	—
914	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
915	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
916	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
917	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
918	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
919	C₂²	#585×C₁₃₁	1	1	yes	characteristic
920	C₂²	#585×C₁₃₁	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	#538×C₁₃₁	1	4	yes	—
937	C₂	—	2	4	no	—
938	C₂	—	4	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×#529×C₁₃₁	1	1	yes	characteristic
941	C₂	C₂×#538×C₁₃₁	1	1	yes	characteristic
942	C₂	#3455×C₁₃₁	1	1	yes	characteristic
943	C₂	#3459×C₁₃₁	1	1	yes	characteristic
944	C₂	#3459×C₁₃₁	1	1	yes	characteristic
945	C₂	#3459×C₁₃₁	1	1	yes	characteristic
946	C₂	#3460×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
socle	C₂³×C₁₃₁	C₂⁵
prime radical	#2617×C₁₃₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2653×C₁₃₁	C₂	semidirect
2. #2652×C₁₃₁	C₂	semidirect
3. #2649×C₁₃₁	C₂	semidirect
4. #2648×C₁₃₁	C₂	semidirect
5. #2646×C₁₃₁	C₂	semidirect
6. #2643×C₁₃₁	C₂	semidirect
7. #2639×C₁₃₁	C₂	semidirect
8. #2626×C₁₃₁	C₂	semidirect
9. #2622×C₁₃₁	C₂	semidirect
11. #2401×C₁₃₁	C₂	semidirect
12. #2398×C₁₃₁	C₂	semidirect
13. #2395×C₁₃₁	C₂	semidirect
14. #2392×C₁₃₁	C₂	semidirect
15. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
16. C₄×#121×C₁₃₁	C₂	semidirect
17. C₄×#120×C₁₃₁	C₂	semidirect
18. #2290×C₁₃₁	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
24. C₂×C₄×Q₈×C₁₃₁	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
29. C₂×#117×C₁₃₁	C₂²	semidirect
34. #401×C₁₃₁	C₂²	semidirect
35. #400×C₁₃₁	C₂²	semidirect
36. #400×C₁₃₁	C₂²	semidirect
37. #400×C₁₃₁	C₂²	semidirect
38. #400×C₁₃₁	C₂²	semidirect
39. #400×C₁₃₁	C₂²	semidirect
40. #400×C₁₃₁	C₂²	semidirect
42. #398×C₁₃₁	C₂²	semidirect
43. #398×C₁₃₁	C₂²	semidirect
49. #397×C₁₃₁	C₂²	semidirect
50. #397×C₁₃₁	C₂²	semidirect
51. #397×C₁₃₁	C₂²	semidirect
52. #397×C₁₃₁	C₂²	semidirect
55. #396×C₁₃₁	C₂²	semidirect
62. #394×C₁₃₁	C₂²	semidirect
64. #393×C₁₃₁	C₂²	semidirect
66. #391×C₁₃₁	C₂²	semidirect
67. #390×C₁₃₁	C₂²	semidirect
68. #389×C₁₃₁	C₂²	semidirect
69. #389×C₁₃₁	C₂²	semidirect
70. #388×C₁₃₁	C₂²	semidirect
71. #388×C₁₃₁	C₂²	semidirect
72. #388×C₁₃₁	C₂²	semidirect
73. #387×C₁₃₁	C₂²	semidirect
74. #387×C₁₃₁	C₂²	semidirect
75. #387×C₁₃₁	C₂²	semidirect
91. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
92. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
93. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
94. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
104. #376×C₁₃₁	C₂²	semidirect
473. #34570	C₁₃₁	direct (N × H)
474. C₁₃₁	#34570	direct (N × H)
475. #2653	C₂×C₁₃₁	semidirect
476. #2652	C₂×C₁₃₁	semidirect
477. #2649	C₂×C₁₃₁	semidirect
478. #2648	C₂×C₁₃₁	semidirect
479. #2646	C₂×C₁₃₁	semidirect
480. #2643	C₂×C₁₃₁	semidirect
481. #2639	C₂×C₁₃₁	semidirect
482. #2626	C₂×C₁₃₁	semidirect
483. #2622	C₂×C₁₃₁	semidirect
485. #2401	C₂×C₁₃₁	semidirect
486. #2398	C₂×C₁₃₁	semidirect
487. #2395	C₂×C₁₃₁	semidirect
488. #2392	C₂×C₁₃₁	semidirect
489. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
490. C₄×#121	C₂×C₁₃₁	semidirect
491. C₄×#120	C₂×C₁₃₁	semidirect
492. #2290	C₂×C₁₃₁	semidirect
493. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
498. C₂×C₄×Q₈	C₂²×C₁₃₁	semidirect
502. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
503. C₂×#117	C₂²×C₁₃₁	semidirect
508. #401	C₂²×C₁₃₁	semidirect
509. #400	C₂²×C₁₃₁	semidirect
510. #400	C₂²×C₁₃₁	semidirect
511. #400	C₂²×C₁₃₁	semidirect
512. #400	C₂²×C₁₃₁	semidirect
513. #400	C₂²×C₁₃₁	semidirect
514. #400	C₂²×C₁₃₁	semidirect
516. #398	C₂²×C₁₃₁	semidirect
517. #398	C₂²×C₁₃₁	semidirect
523. #397	C₂²×C₁₃₁	semidirect
524. #397	C₂²×C₁₃₁	semidirect
525. #397	C₂²×C₁₃₁	semidirect
526. #397	C₂²×C₁₃₁	semidirect
529. #396	C₂²×C₁₃₁	semidirect
536. #394	C₂²×C₁₃₁	semidirect
538. #393	C₂²×C₁₃₁	semidirect
540. #391	C₂²×C₁₃₁	semidirect
541. #390	C₂²×C₁₃₁	semidirect
542. #389	C₂²×C₁₃₁	semidirect
543. #389	C₂²×C₁₃₁	semidirect
544. #388	C₂²×C₁₃₁	semidirect
545. #388	C₂²×C₁₃₁	semidirect
546. #388	C₂²×C₁₃₁	semidirect
547. #387	C₂²×C₁₃₁	semidirect
548. #387	C₂²×C₁₃₁	semidirect
549. #387	C₂²×C₁₃₁	semidirect
565. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
566. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
567. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
568. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
576. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
577. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
578. #376	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2653×C₁₃₁	2
#2652×C₁₃₁	2
#2649×C₁₃₁	2
#2648×C₁₃₁	2
#2646×C₁₃₁	2
#2643×C₁₃₁	2
#2639×C₁₃₁	2
#2626×C₁₃₁	2
#2622×C₁₃₁	2
#2617×C₁₃₁	2
#2401×C₁₃₁	2
#2398×C₁₃₁	2
#2395×C₁₃₁	2
#2392×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#121×C₁₃₁	2
C₄×#120×C₁₃₁	2
#2290×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
#34570	131

Subgroups — C131×#34570 #45720454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34570 #45720454