Subgroups — C₄×#547×C₁₃₁ #45720043

Order 33536.

3268 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2365×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2362×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2361×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2359×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#2354×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2344×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2339×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₂²⋊Q₈×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	C₄×#123×C₁₃₁	C₂	1	4	yes	maximal, complemented
14	C₄×#121×C₁₃₁	C₂	1	2	yes	maximal, complemented
15	C₄²×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄²×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₁	C₂²	1	2	yes	—
19	#547×C₁₃₁	C₄	1	16	yes	direct product factor
20	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₁₃₁	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₁	C₂²	1	2	yes	—
24	C₄×#41×C₁₃₁	—	2	16	no	—
25	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₃₁	C₂²	1	4	yes	—
37	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃₁	C₂²	1	4	yes	—
42	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
43	#391×C₁₃₁	C₂²	1	2	yes	—
44	#391×C₁₃₁	C₂²	1	2	yes	—
45	#390×C₁₃₁	C₂²	1	2	yes	—
46	#389×C₁₃₁	C₂²	1	2	yes	—
47	#389×C₁₃₁	C₂²	1	2	yes	—
48	#389×C₁₃₁	C₂²	1	2	yes	—
49	#389×C₁₃₁	C₂²	1	2	yes	—
50	#388×C₁₃₁	C₂²	1	4	yes	—
51	#388×C₁₃₁	C₂²	1	4	yes	—
52	#388×C₁₃₁	C₂²	1	4	yes	—
53	#387×C₁₃₁	C₂²	1	4	yes	—
54	#387×C₁₃₁	C₂²	1	4	yes	—
55	#387×C₁₃₁	C₂²	1	4	yes	—
56	#386×C₁₃₁	C₂²	1	4	yes	—
57	#386×C₁₃₁	C₂²	1	4	yes	—
58	#385×C₁₃₁	C₂²	1	4	yes	—
59	#385×C₁₃₁	C₂²	1	4	yes	—
60	#384×C₁₃₁	C₂²	1	1	yes	characteristic
61	#381×C₁₃₁	C₂²	1	4	yes	—
62	#380×C₁₃₁	C₂²	1	2	yes	—
63	#380×C₁₃₁	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
83	C₂×#95×C₁₃₁	C₂²	1	4	yes	—
84	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
85	C₂×#41×C₁₃₁	—	2	8	no	—
86	C₂×#41×C₁₃₁	—	2	8	no	—
87	C₂×#41×C₁₃₁	C₂×C₄	1	16	yes	complemented
88	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
101	#123×C₁₃₁	C₂×C₄	1	32	yes	complemented
102	C₂²⋊Q₈×C₁₃₁	C₂×C₄	1	16	yes	complemented
103	#121×C₁₃₁	C₂×C₄	1	16	yes	complemented
104	C₄×Q₈×C₁₃₁	—	2	8	no	—
105	C₄×Q₈×C₁₃₁	—	2	8	no	—
106	C₄×D₄×C₁₃₁	—	2	8	no	—
107	C₄×D₄×C₁₃₁	—	2	4	no	—
108	C₄×D₄×C₁₃₁	—	2	16	no	—
109	C₄×D₄×C₁₃₁	—	2	4	no	—
110	C₄×D₄×C₁₃₁	—	2	16	no	—
111	C₄×D₄×C₁₃₁	—	2	4	no	—
112	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
113	C₄×D₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
114	C₄×D₄×C₁₃₁	D₄	1	8	yes	complemented
115	#117×C₁₃₁	—	2	8	no	—
116	#117×C₁₃₁	—	2	16	no	—
117	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	16	yes	complemented
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₁	—	2	16	no	—
145	C₂×C₄²×C₁₃₁	—	2	8	no	—
146	C₂×C₄²×C₁₃₁	—	2	8	no	—
147	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
163	#95×C₁₃₁	C₂³	1	2	yes	—
164	#95×C₁₃₁	C₂³	1	2	yes	—
165	#95×C₁₃₁	C₂³	1	4	yes	—
166	#95×C₁₃₁	C₂³	1	4	yes	—
167	#95×C₁₃₁	C₂³	1	4	yes	—
168	#95×C₁₃₁	C₂³	1	4	yes	—
169	#95×C₁₃₁	C₂³	1	4	yes	—
170	#95×C₁₃₁	C₂³	1	4	yes	—
171	#95×C₁₃₁	C₂³	1	2	yes	—
172	#95×C₁₃₁	C₂³	1	2	yes	—
173	#95×C₁₃₁	C₂³	1	2	yes	—
174	#95×C₁₃₁	C₂³	1	2	yes	—
175	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
176	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
177	#41×C₁₃₁	—	2	64	no	—
178	C₂×Q₈×C₁₃₁	—	2	4	no	—
179	C₂×Q₈×C₁₃₁	—	2	4	no	—
180	C₂×Q₈×C₁₃₁	C₂²×C₄	1	8	yes	—
181	C₂×D₄×C₁₃₁	—	2	8	no	—
182	C₂×D₄×C₁₃₁	—	2	8	no	—
183	C₂×D₄×C₁₃₁	—	2	2	no	—
184	C₂×D₄×C₁₃₁	—	2	2	no	—
185	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
186	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
187	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
188	C₂×D₄×C₁₃₁	C₂×D₄	1	4	yes	—
189	C₂×D₄×C₁₃₁	#41	1	4	yes	—
190	C₂²×C₄×C₁₃₁	—	2	8	no	—
191	C₂²×C₄×C₁₃₁	—	2	8	no	—
192	C₂²×C₄×C₁₃₁	—	2	4	no	—
193	C₂²×C₄×C₁₃₁	—	2	4	no	—
194	C₂²×C₄×C₁₃₁	—	2	4	no	—
195	C₂²×C₄×C₁₃₁	—	2	4	no	—
196	C₂²×C₄×C₁₃₁	—	2	4	no	—
197	C₂²×C₄×C₁₃₁	—	2	4	no	—
198	C₂²×C₄×C₁₃₁	—	2	8	no	—
199	C₂²×C₄×C₁₃₁	—	2	4	no	—
200	C₂²×C₄×C₁₃₁	—	2	4	no	—
201	C₂²×C₄×C₁₃₁	—	2	4	no	—
202	C₂²×C₄×C₁₃₁	—	2	4	no	—
203	C₂²×C₄×C₁₃₁	—	2	8	no	—
204	C₂²×C₄×C₁₃₁	—	2	4	no	—
205	C₂²×C₄×C₁₃₁	—	2	4	no	—
206	C₂²×C₄×C₁₃₁	—	2	4	no	—
207	C₂²×C₄×C₁₃₁	—	4	2	no	—
208	C₂²×C₄×C₁₃₁	—	4	2	no	—
209	C₂²×C₄×C₁₃₁	—	4	4	no	—
210	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
211	C₂²×C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
212	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
213	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	—
214	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₁₃₁	—	2	8	no	—
230	C₄⋊C₄×C₁₃₁	—	2	8	no	—
231	C₄⋊C₄×C₁₃₁	—	2	4	no	—
232	C₄⋊C₄×C₁₃₁	—	2	8	no	—
233	C₄⋊C₄×C₁₃₁	—	2	4	no	—
234	C₄⋊C₄×C₁₃₁	—	2	2	no	—
235	C₄⋊C₄×C₁₃₁	—	2	2	no	—
236	C₄⋊C₄×C₁₃₁	—	4	2	no	—
237	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
238	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
239	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
240	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
241	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
242	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
243	C₄⋊C₄×C₁₃₁	#41	1	4	yes	complemented
244	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
251	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
252	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
253	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	8	yes	—
254	C₄²×C₁₃₁	—	2	4	no	—
255	C₄²×C₁₃₁	—	2	8	no	—
256	C₄²×C₁₃₁	—	2	4	no	—
257	C₄²×C₁₃₁	—	2	8	no	—
258	C₄²×C₁₃₁	—	2	4	no	—
259	C₄²×C₁₃₁	—	2	8	no	—
260	C₄²×C₁₃₁	—	2	4	no	—
261	C₄²×C₁₃₁	—	2	4	no	—
262	C₄²×C₁₃₁	—	2	4	no	—
263	C₄²×C₁₃₁	—	2	2	no	—
264	C₄²×C₁₃₁	—	2	2	no	—
265	C₄²×C₁₃₁	—	2	2	no	—
266	C₄²×C₁₃₁	—	4	1	no	—
267	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
268	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
269	C₄²×C₁₃₁	#41	1	4	yes	complemented
270	C₂³×C₁₃₁	—	2	2	no	—
271	C₂³×C₁₃₁	—	2	2	no	—
272	C₂³×C₁₃₁	—	2	2	no	—
273	C₂³×C₁₃₁	—	2	2	no	—
274	C₂³×C₁₃₁	—	2	2	no	—
275	C₂³×C₁₃₁	—	2	2	no	—
276	C₂³×C₁₃₁	—	2	2	no	—
277	C₂³×C₁₃₁	—	2	2	no	—
278	C₂³×C₁₃₁	—	2	2	no	—
279	C₂³×C₁₃₁	—	2	2	no	—
280	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
281	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
282	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
283	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
284	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
285	Q₈×C₁₃₁	—	2	16	no	—
286	D₄×C₁₃₁	—	2	32	no	—
287	D₄×C₁₃₁	—	2	8	no	—
288	D₄×C₁₃₁	C₄×D₄	1	16	yes	complemented
289	C₂×C₄×C₁₃₁	—	2	32	no	—
290	C₂×C₄×C₁₃₁	—	2	2	no	—
291	C₂×C₄×C₁₃₁	—	2	2	no	—
292	C₂×C₄×C₁₃₁	—	2	4	no	—
293	C₂×C₄×C₁₃₁	—	2	2	no	—
294	C₂×C₄×C₁₃₁	—	2	2	no	—
295	C₂×C₄×C₁₃₁	—	2	1	no	—
296	C₂×C₄×C₁₃₁	—	2	1	no	—
297	C₂×C₄×C₁₃₁	—	2	2	no	—
298	C₂×C₄×C₁₃₁	—	2	2	no	—
299	C₂×C₄×C₁₃₁	—	2	4	no	—
300	C₂×C₄×C₁₃₁	—	2	1	no	—
301	C₂×C₄×C₁₃₁	—	2	2	no	—
302	C₂×C₄×C₁₃₁	—	2	1	no	—
303	C₂×C₄×C₁₃₁	—	2	1	no	—
304	C₂×C₄×C₁₃₁	—	2	1	no	—
305	C₂×C₄×C₁₃₁	—	2	2	no	—
306	C₂×C₄×C₁₃₁	—	2	16	no	—
307	C₂×C₄×C₁₃₁	—	2	16	no	—
308	C₂×C₄×C₁₃₁	—	2	16	no	—
309	C₂×C₄×C₁₃₁	—	2	2	no	—
310	C₂×C₄×C₁₃₁	—	2	4	no	—
311	C₂×C₄×C₁₃₁	—	2	2	no	—
312	C₂×C₄×C₁₃₁	—	2	1	no	—
313	C₂×C₄×C₁₃₁	—	2	1	no	—
314	C₂×C₄×C₁₃₁	—	2	2	no	—
315	C₂×C₄×C₁₃₁	—	2	2	no	—
316	C₂×C₄×C₁₃₁	—	2	4	no	—
317	C₂×C₄×C₁₃₁	—	2	1	no	—
318	C₂×C₄×C₁₃₁	—	2	2	no	—
319	C₂×C₄×C₁₃₁	—	2	2	no	—
320	C₂×C₄×C₁₃₁	—	2	4	no	—
321	C₂×C₄×C₁₃₁	—	4	8	no	—
322	C₂×C₄×C₁₃₁	—	4	16	no	—
323	C₂×C₄×C₁₃₁	—	4	8	no	—
324	C₂×C₄×C₁₃₁	—	4	8	no	—
325	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
327	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₁₃₁	C₂³×C₄	1	8	yes	—
329	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
331	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
336	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
337	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
340	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
341	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
342	C₂²×C₁₃₁	—	2	4	no	—
343	C₂²×C₁₃₁	—	2	4	no	—
344	C₂²×C₁₃₁	—	2	4	no	—
345	C₂²×C₁₃₁	—	2	4	no	—
346	C₂²×C₁₃₁	—	2	4	no	—
347	C₂²×C₁₃₁	—	2	4	no	—
348	C₂²×C₁₃₁	—	2	4	no	—
349	C₂²×C₁₃₁	—	2	4	no	—
350	C₂²×C₁₃₁	—	2	4	no	—
351	C₂²×C₁₃₁	—	4	2	no	—
352	C₂²×C₁₃₁	—	4	2	no	—
353	C₂²×C₁₃₁	—	4	2	no	—
354	C₂²×C₁₃₁	—	4	2	no	—
355	C₂²×C₁₃₁	C₂×C₄×D₄	1	8	yes	—
356	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
357	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
360	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
361	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
362	C₂²×C₁₃₁	#585	1	1	yes	characteristic
363	C₄×C₁₃₁	—	2	4	no	—
364	C₄×C₁₃₁	—	2	8	no	—
365	C₄×C₁₃₁	—	2	4	no	—
366	C₄×C₁₃₁	—	2	2	no	—
367	C₄×C₁₃₁	—	2	4	no	—
368	C₄×C₁₃₁	—	2	4	no	—
369	C₄×C₁₃₁	—	2	2	no	—
370	C₄×C₁₃₁	—	2	2	no	—
371	C₄×C₁₃₁	—	4	2	no	—
372	C₄×C₁₃₁	—	4	4	no	—
373	C₄×C₁₃₁	—	4	2	no	—
374	C₄×C₁₃₁	—	4	1	no	—
375	C₄×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
376	C₄×C₁₃₁	C₄×#41	1	4	yes	complemented
377	C₄×C₁₃₁	#547	1	4	yes	direct product factor
378	C₂×C₁₃₁	—	2	8	no	—
379	C₂×C₁₃₁	—	4	4	no	—
380	C₂×C₁₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
381	C₂×C₁₃₁	C₂×C₄×#41	1	1	yes	characteristic
382	C₂×C₁₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂×C₁₃₁	C₂×#547	1	1	yes	characteristic
384	C₂×C₁₃₁	D₄×#41	1	1	yes	characteristic
385	C₂×C₁₃₁	#3475	1	1	yes	characteristic
386	C₂×C₁₃₁	#3482	1	1	yes	characteristic
387	C₄×#547	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₁₃₁	C₄×#547	1	1	yes	characteristic, direct product factor, Sylow
389	C₂×#547	C₂×C₁₃₁	1	1	yes	characteristic
390	C₂×C₄×#41	C₂×C₁₃₁	1	2	yes	complemented
391	#2365	C₂×C₁₃₁	1	1	yes	characteristic, complemented
392	#2362	C₂×C₁₃₁	1	2	yes	complemented
393	#2361	C₂×C₁₃₁	1	2	yes	complemented
394	#2359	C₂×C₁₃₁	1	4	yes	complemented
395	#2354	C₂×C₁₃₁	1	1	yes	characteristic, complemented
396	D₄×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
397	#2344	C₂×C₁₃₁	1	2	yes	complemented
398	#2339	C₂×C₁₃₁	1	2	yes	complemented
399	C₄×C₄⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
400	C₄×C₂²⋊Q₈	C₂×C₁₃₁	1	2	yes	complemented
401	C₄×#123	C₂×C₁₃₁	1	4	yes	complemented
402	C₄×#121	C₂×C₁₃₁	1	2	yes	complemented
403	C₄²×D₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
404	C₄²×D₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
405	C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
406	C₂²×#41	C₂²×C₁₃₁	1	2	yes	—
407	#547	C₄×C₁₃₁	1	16	yes	direct product factor
408	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
409	C₂×#123	C₂²×C₁₃₁	1	4	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
411	C₂×#121	C₂²×C₁₃₁	1	2	yes	—
412	C₄×#41	—	2	16	no	—
413	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
414	C₂×C₄×Q₈	C₂²×C₁₃₁	1	2	yes	—
415	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
418	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
424	C₂×#117	C₂²×C₁₃₁	1	4	yes	—
425	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
428	C₂²×C₄²	C₂²×C₁₃₁	1	4	yes	—
429	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
430	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
431	#391	C₂²×C₁₃₁	1	2	yes	—
432	#391	C₂²×C₁₃₁	1	2	yes	—
433	#390	C₂²×C₁₃₁	1	2	yes	—
434	#389	C₂²×C₁₃₁	1	2	yes	—
435	#389	C₂²×C₁₃₁	1	2	yes	—
436	#389	C₂²×C₁₃₁	1	2	yes	—
437	#389	C₂²×C₁₃₁	1	2	yes	—
438	#388	C₂²×C₁₃₁	1	4	yes	—
439	#388	C₂²×C₁₃₁	1	4	yes	—
440	#388	C₂²×C₁₃₁	1	4	yes	—
441	#387	C₂²×C₁₃₁	1	4	yes	—
442	#387	C₂²×C₁₃₁	1	4	yes	—
443	#387	C₂²×C₁₃₁	1	4	yes	—
444	#386	C₂²×C₁₃₁	1	4	yes	—
445	#386	C₂²×C₁₃₁	1	4	yes	—
446	#385	C₂²×C₁₃₁	1	4	yes	—
447	#385	C₂²×C₁₃₁	1	4	yes	—
448	#384	C₂²×C₁₃₁	1	1	yes	characteristic
449	#381	C₂²×C₁₃₁	1	4	yes	—
450	#380	C₂²×C₁₃₁	1	2	yes	—
451	#380	C₂²×C₁₃₁	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
459	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
471	C₂×#95	C₂²×C₁₃₁	1	4	yes	—
472	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
473	C₂×#41	—	2	8	no	—
474	C₂×#41	—	2	8	no	—
475	C₂×#41	C₂×C₄×C₁₃₁	1	16	yes	complemented
476	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
477	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
479	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
481	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
482	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
484	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
485	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
486	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
487	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
488	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
489	#123	C₂×C₄×C₁₃₁	1	32	yes	complemented
490	C₂²⋊Q₈	C₂×C₄×C₁₃₁	1	16	yes	complemented
491	#121	C₂×C₄×C₁₃₁	1	16	yes	complemented
492	C₄×Q₈	—	2	8	no	—
493	C₄×Q₈	—	2	8	no	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	16	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	16	no	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
501	C₄×D₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
502	C₄×D₄	D₄×C₁₃₁	1	8	yes	complemented
503	#117	—	2	8	no	—
504	#117	—	2	16	no	—
505	C₂×C₄⋊C₄	—	2	8	no	—
506	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	16	yes	complemented
507	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
532	C₂×C₄²	—	2	16	no	—
533	C₂×C₄²	—	2	8	no	—
534	C₂×C₄²	—	2	8	no	—
535	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
537	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
538	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
539	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
540	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
544	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
551	#95	C₂³×C₁₃₁	1	2	yes	—
552	#95	C₂³×C₁₃₁	1	4	yes	—
553	#95	C₂³×C₁₃₁	1	4	yes	—
554	#95	C₂³×C₁₃₁	1	4	yes	—
555	#95	C₂³×C₁₃₁	1	2	yes	—
556	#95	C₂³×C₁₃₁	1	2	yes	—
557	#95	C₂³×C₁₃₁	1	2	yes	—
558	#95	C₂³×C₁₃₁	1	2	yes	—
559	#95	C₂³×C₁₃₁	1	2	yes	—
560	#95	C₂³×C₁₃₁	1	4	yes	—
561	#95	C₂³×C₁₃₁	1	4	yes	—
562	#95	C₂³×C₁₃₁	1	4	yes	—
563	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
564	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
565	#41	—	2	64	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	C₂²×C₄×C₁₃₁	1	8	yes	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	2	8	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
574	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
575	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
576	C₂×D₄	C₂×D₄×C₁₃₁	1	4	yes	—
577	C₂×D₄	#41×C₁₃₁	1	4	yes	—
578	C₂²×C₄	—	2	8	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	8	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
599	C₂²×C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
600	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
601	C₂²×C₄	C₂×D₄×C₁₃₁	1	8	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
617	C₄⋊C₄	—	2	8	no	—
618	C₄⋊C₄	—	2	8	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
626	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
627	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
628	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
629	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
630	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
631	C₄⋊C₄	#41×C₁₃₁	1	4	yes	complemented
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
641	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	8	yes	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	8	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	8	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	8	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	4	1	no	—
655	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
656	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
657	C₄²	#41×C₁₃₁	1	4	yes	complemented
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
669	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
670	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
671	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
672	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
673	Q₈	—	2	16	no	—
674	D₄	—	2	32	no	—
675	D₄	—	2	8	no	—
676	D₄	C₄×D₄×C₁₃₁	1	16	yes	complemented
677	C₂×C₄	—	2	32	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	16	no	—
695	C₂×C₄	—	2	16	no	—
696	C₂×C₄	—	2	16	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	4	8	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
714	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
715	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
716	C₂×C₄	C₂³×C₄×C₁₃₁	1	8	yes	—
717	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
720	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
723	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
724	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
725	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
726	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
727	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
728	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
729	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	C₂×C₄×D₄×C₁₃₁	1	8	yes	—
744	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
745	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
746	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
747	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
748	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
749	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
750	C₂²	#585×C₁₃₁	1	1	yes	characteristic
751	C₄	—	2	4	no	—
752	C₄	—	2	8	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
764	C₄	C₄×#41×C₁₃₁	1	4	yes	complemented
765	C₄	#547×C₁₃₁	1	4	yes	direct product factor
766	C₂	—	2	8	no	—
767	C₂	—	4	4	no	—
768	C₂	C₂²×C₄×D₄×C₁₃₁	1	1	yes	characteristic
769	C₂	C₂×C₄×#41×C₁₃₁	1	1	yes	characteristic
770	C₂	C₄×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
771	C₂	C₂×#547×C₁₃₁	1	1	yes	characteristic
772	C₂	D₄×#41×C₁₃₁	1	1	yes	characteristic
773	C₂	#3475×C₁₃₁	1	1	yes	characteristic
774	C₂	#3482×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
socle	C₂³×C₁₃₁	C₂⁵
prime radical	C₂×#547×C₁₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₁₃₁	C₂	semidirect
3. #2365×C₁₃₁	C₂	semidirect
4. #2362×C₁₃₁	C₂	semidirect
5. #2361×C₁₃₁	C₂	semidirect
6. #2359×C₁₃₁	C₂	semidirect
7. #2354×C₁₃₁	C₂	semidirect
8. D₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
9. #2344×C₁₃₁	C₂	semidirect
10. #2339×C₁₃₁	C₂	semidirect
11. C₄×C₄⋊Q₈×C₁₃₁	C₂	semidirect
12. C₄×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
13. C₄×#123×C₁₃₁	C₂	semidirect
14. C₄×#121×C₁₃₁	C₂	semidirect
15. C₄²×D₄×C₁₃₁	C₂	semidirect
16. C₄²×D₄×C₁₃₁	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
19. #547×C₁₃₁	C₄	direct (N × H)
87. C₂×#41×C₁₃₁	C₂×C₄	semidirect
100. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
101. #123×C₁₃₁	C₂×C₄	semidirect
102. C₂²⋊Q₈×C₁₃₁	C₂×C₄	semidirect
103. #121×C₁₃₁	C₂×C₄	semidirect
112. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
113. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
114. C₄×D₄×C₁₃₁	D₄	semidirect
118. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
243. C₄⋊C₄×C₁₃₁	#41	semidirect
269. C₄²×C₁₃₁	#41	semidirect
288. D₄×C₁₃₁	C₄×D₄	semidirect
376. C₄×C₁₃₁	C₄×#41	semidirect
377. C₄×C₁₃₁	#547	direct (N × H)
387. C₄×#547	C₁₃₁	direct (N × H)
388. C₁₃₁	C₄×#547	direct (N × H)
390. C₂×C₄×#41	C₂×C₁₃₁	semidirect
391. #2365	C₂×C₁₃₁	semidirect
392. #2362	C₂×C₁₃₁	semidirect
393. #2361	C₂×C₁₃₁	semidirect
394. #2359	C₂×C₁₃₁	semidirect
395. #2354	C₂×C₁₃₁	semidirect
396. D₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
397. #2344	C₂×C₁₃₁	semidirect
398. #2339	C₂×C₁₃₁	semidirect
399. C₄×C₄⋊Q₈	C₂×C₁₃₁	semidirect
400. C₄×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
401. C₄×#123	C₂×C₁₃₁	semidirect
402. C₄×#121	C₂×C₁₃₁	semidirect
403. C₄²×D₄	C₂×C₁₃₁	semidirect
404. C₄²×D₄	C₂×C₁₃₁	semidirect
405. C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
407. #547	C₄×C₁₃₁	direct (N × H)
475. C₂×#41	C₂×C₄×C₁₃₁	semidirect
488. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
489. #123	C₂×C₄×C₁₃₁	semidirect
490. C₂²⋊Q₈	C₂×C₄×C₁₃₁	semidirect
491. #121	C₂×C₄×C₁₃₁	semidirect
500. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
501. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
502. C₄×D₄	D₄×C₁₃₁	semidirect
506. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
631. C₄⋊C₄	#41×C₁₃₁	semidirect
657. C₄²	#41×C₁₃₁	semidirect
676. D₄	C₄×D₄×C₁₃₁	semidirect
764. C₄	C₄×#41×C₁₃₁	semidirect
765. C₄	#547×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₁	2
C₂×C₄×#41×C₁₃₁	2
#2365×C₁₃₁	2
#2362×C₁₃₁	2
#2361×C₁₃₁	2
#2359×C₁₃₁	2
#2354×C₁₃₁	2
D₄×C₄⋊C₄×C₁₃₁	2
#2344×C₁₃₁	2
#2339×C₁₃₁	2
C₄×C₄⋊Q₈×C₁₃₁	2
C₄×C₂²⋊Q₈×C₁₃₁	2
C₄×#123×C₁₃₁	2
C₄×#121×C₁₃₁	2
C₄²×D₄×C₁₃₁	2
C₂×C₄×C₄⋊C₄×C₁₃₁	2
C₄×#547	131

Subgroups — C4×#547×C131 #45720043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#547×C₁₃₁ #45720043