Subgroups — C₂×C₁₃×#2443 #15720988

Order 3328.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2443	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	—	2	8	no	—
25	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
26	C₂×C₁₃×#121	—	2	8	no	—
27	C₂×C₁₃×#121	C₂²	1	8	yes	—
28	C₂×C₄×D₄×C₁₃	—	2	8	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#399	C₂²	1	8	yes	complemented
53	C₁₃×#398	C₂²	1	8	yes	complemented
54	C₁₃×#397	C₂²	1	8	yes	complemented
55	C₁₃×#394	C₂²	1	8	yes	complemented
56	C₁₃×#388	C₂²	1	8	yes	complemented
57	C₁₃×#387	C₂²	1	8	yes	complemented
58	C₁₃×#386	C₂²	1	8	yes	complemented
59	C₁₃×#386	C₂²	1	8	yes	complemented
60	C₁₃×#386	C₂²	1	8	yes	complemented
61	C₁₃×#385	C₂²	1	8	yes	complemented
62	C₁₃×#385	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
71	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
72	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
73	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	—	2	4	no	—
75	C₂²×D₄×C₁₃	—	2	4	no	—
76	C₂²×D₄×C₁₃	—	2	4	no	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	—	2	4	no	—
79	C₂²×D₄×C₁₃	—	2	4	no	—
80	C₂²×D₄×C₁₃	—	2	4	no	—
81	C₂²×D₄×C₁₃	—	4	2	no	—
82	C₂²×D₄×C₁₃	D₄	1	8	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	—	2	4	no	—
89	C₂³×C₄×C₁₃	—	2	4	no	—
90	C₂³×C₄×C₁₃	—	2	4	no	—
91	C₂³×C₄×C₁₃	—	2	4	no	—
92	C₂³×C₄×C₁₃	—	2	4	no	—
93	C₂³×C₄×C₁₃	—	2	4	no	—
94	C₂³×C₄×C₁₃	—	2	4	no	—
95	C₂³×C₄×C₁₃	—	4	2	no	—
96	C₂³×C₄×C₁₃	—	4	2	no	—
97	C₂³×C₄×C₁₃	—	4	2	no	—
98	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#123	—	2	32	no	—
115	C₁₃×#121	—	2	32	no	—
116	C₄×D₄×C₁₃	—	2	32	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
122	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
124	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃	—	2	4	no	—
157	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₂×#2443	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	2	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
171	C₂⁴×C₁₃	—	2	2	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	2	2	no	—
175	C₂⁴×C₁₃	—	2	2	no	—
176	C₂⁴×C₁₃	—	2	2	no	—
177	C₂⁴×C₁₃	—	2	2	no	—
178	C₂⁴×C₁₃	—	2	2	no	—
179	C₂⁴×C₁₃	—	2	2	no	—
180	C₂⁴×C₁₃	—	2	2	no	—
181	C₂⁴×C₁₃	—	2	2	no	—
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	—	2	2	no	—
184	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
185	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
186	C₂⁴×C₁₃	#41	1	4	yes	—
187	C₂⁴×C₁₃	#41	1	4	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
190	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
191	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×D₄×C₁₃	—	2	32	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	8	no	—
196	C₂×D₄×C₁₃	—	2	8	no	—
197	C₂×D₄×C₁₃	—	2	8	no	—
198	C₂×D₄×C₁₃	—	2	8	no	—
199	C₂×D₄×C₁₃	—	2	8	no	—
200	C₂×D₄×C₁₃	—	4	4	no	—
201	C₂×D₄×C₁₃	—	4	16	no	—
202	C₂×D₄×C₁₃	—	4	16	no	—
203	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
204	C₂²×C₄×C₁₃	—	2	32	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	8	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	8	no	—
217	C₂²×C₄×C₁₃	—	2	8	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	8	no	—
228	C₂²×C₄×C₁₃	—	2	8	no	—
229	C₂²×C₄×C₁₃	—	2	8	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	8	no	—
243	C₂²×C₄×C₁₃	—	2	8	no	—
244	C₂²×C₄×C₁₃	—	2	8	no	—
245	C₂²×C₄×C₁₃	—	4	4	no	—
246	C₂²×C₄×C₁₃	—	4	4	no	—
247	C₂²×C₄×C₁₃	—	4	4	no	—
248	C₂²×C₄×C₁₃	—	4	16	no	—
249	C₂²×C₄×C₁₃	—	4	16	no	—
250	C₂²×C₄×C₁₃	—	4	16	no	—
251	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
255	C₂²×C₄×C₁₃	#41	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	—	2	8	no	—
269	C₁₃×C₄⋊C₄	—	2	8	no	—
270	C₁₃×C₄⋊C₄	—	2	8	no	—
271	C₁₃×C₄⋊C₄	—	2	8	no	—
272	C₁₃×C₄⋊C₄	—	2	8	no	—
273	C₁₃×C₄⋊C₄	—	2	8	no	—
274	C₁₃×C₄⋊C₄	—	4	4	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
276	C₁₃×C₂²⋊C₄	—	2	8	no	—
277	C₁₃×C₂²⋊C₄	—	2	8	no	—
278	C₁₃×C₂²⋊C₄	—	2	8	no	—
279	C₁₃×C₂²⋊C₄	—	2	8	no	—
280	C₁₃×C₂²⋊C₄	—	2	8	no	—
281	C₁₃×C₂²⋊C₄	—	2	8	no	—
282	C₁₃×C₂²⋊C₄	—	2	8	no	—
283	C₁₃×C₂²⋊C₄	—	2	8	no	—
284	C₁₃×C₂²⋊C₄	—	2	8	no	—
285	C₁₃×C₂²⋊C₄	—	2	8	no	—
286	C₁₃×C₂²⋊C₄	—	4	4	no	—
287	C₄²×C₁₃	—	2	8	no	—
288	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
290	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#2443	C₂×C₁₃	1	16	yes	direct product factor
293	C₂×#399	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#394	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂³×C₁₃	—	2	8	no	—
305	C₂³×C₁₃	—	2	8	no	—
306	C₂³×C₁₃	—	2	8	no	—
307	C₂³×C₁₃	—	2	8	no	—
308	C₂³×C₁₃	—	2	8	no	—
309	C₂³×C₁₃	—	2	8	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	8	no	—
315	C₂³×C₁₃	—	2	8	no	—
316	C₂³×C₁₃	—	2	8	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	4	4	no	—
331	C₂³×C₁₃	—	4	4	no	—
332	C₂³×C₁₃	—	4	4	no	—
333	C₂³×C₁₃	—	4	4	no	—
334	C₂³×C₁₃	—	4	4	no	—
335	C₂³×C₁₃	—	4	4	no	—
336	C₂³×C₁₃	—	4	4	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	4	no	—
339	C₂³×C₁₃	—	4	4	no	—
340	C₂³×C₁₃	—	4	4	no	—
341	C₂³×C₁₃	#123	1	16	yes	complemented
342	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
343	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
344	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₁₃	C₂×#41	1	4	yes	—
347	C₂³×C₁₃	C₂×#41	1	4	yes	—
348	C₂³×C₁₃	C₂×#41	1	2	yes	—
349	C₂³×C₁₃	C₂×#41	1	2	yes	—
350	C₂³×C₁₃	C₂×#41	1	2	yes	—
351	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
352	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
353	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
354	D₄×C₁₃	—	2	32	no	—
355	D₄×C₁₃	—	4	16	no	—
356	D₄×C₁₃	—	4	16	no	—
357	C₂×C₄×C₁₃	—	2	32	no	—
358	C₂×C₄×C₁₃	—	2	8	no	—
359	C₂×C₄×C₁₃	—	2	8	no	—
360	C₂×C₄×C₁₃	—	2	8	no	—
361	C₂×C₄×C₁₃	—	2	8	no	—
362	C₂×C₄×C₁₃	—	2	8	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	4	16	no	—
395	C₂×C₄×C₁₃	—	4	16	no	—
396	C₂×C₄×C₁₃	—	4	16	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	4	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
408	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
409	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#123	—	2	8	no	—
417	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
418	C₂×#121	—	2	8	no	—
419	C₂×#121	C₂²×C₁₃	1	8	yes	—
420	C₂×C₄×D₄	—	2	8	no	—
421	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
422	C₂²×C₄⋊C₄	—	2	8	no	—
423	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
432	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
444	#399	C₂²×C₁₃	1	8	yes	complemented
445	#398	C₂²×C₁₃	1	8	yes	complemented
446	#397	C₂²×C₁₃	1	8	yes	complemented
447	#394	C₂²×C₁₃	1	8	yes	complemented
448	#388	C₂²×C₁₃	1	8	yes	complemented
449	#387	C₂²×C₁₃	1	8	yes	complemented
450	#386	C₂²×C₁₃	1	8	yes	complemented
451	#386	C₂²×C₁₃	1	8	yes	complemented
452	#386	C₂²×C₁₃	1	8	yes	complemented
453	#385	C₂²×C₁₃	1	8	yes	complemented
454	#385	C₂²×C₁₃	1	8	yes	complemented
455	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
463	C₂²×C₁₃	—	2	4	no	—
464	C₂²×C₁₃	—	2	4	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	2	4	no	—
467	C₂²×C₁₃	—	2	4	no	—
468	C₂²×C₁₃	—	2	32	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	4	no	—
471	C₂²×C₁₃	—	2	4	no	—
472	C₂²×C₁₃	—	2	4	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	16	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	8	8	no	—
486	C₂²×C₁₃	C₂×#123	1	4	yes	—
487	C₂²×C₁₃	C₂×#123	1	8	yes	complemented
488	C₂²×C₁₃	#525	1	4	yes	—
489	C₂²×C₁₃	#539	1	4	yes	—
490	C₂²×C₁₃	D₄²	1	4	yes	—
491	C₂²×C₁₃	#547	1	4	yes	—
492	C₂²×C₁₃	#548	1	4	yes	—
493	C₂²×C₁₃	#553	1	4	yes	—
494	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
495	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
496	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₄×C₁₃	—	2	4	no	—
502	C₄×C₁₃	—	2	4	no	—
503	C₄×C₁₃	—	2	4	no	—
504	C₄×C₁₃	—	2	4	no	—
505	C₄×C₁₃	—	2	4	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
514	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
515	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×D₄	—	2	4	no	—
517	C₂²×D₄	—	2	4	no	—
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	4	2	no	—
524	C₂²×D₄	D₄×C₁₃	1	8	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
527	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
528	C₂³×C₄	—	2	4	no	—
529	C₂³×C₄	—	2	4	no	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	2	4	no	—
533	C₂³×C₄	—	2	4	no	—
534	C₂³×C₄	—	2	4	no	—
535	C₂³×C₄	—	2	4	no	—
536	C₂³×C₄	—	2	4	no	—
537	C₂³×C₄	—	4	2	no	—
538	C₂³×C₄	—	4	2	no	—
539	C₂³×C₄	—	4	2	no	—
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
548	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
549	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
550	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
551	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
556	#123	—	2	32	no	—
557	#121	—	2	32	no	—
558	C₄×D₄	—	2	32	no	—
559	C₂×C₄⋊C₄	—	2	4	no	—
560	C₂×C₄⋊C₄	—	2	4	no	—
561	C₂×C₄⋊C₄	—	2	4	no	—
562	C₂×C₄⋊C₄	—	2	4	no	—
563	C₂×C₄⋊C₄	—	2	4	no	—
564	C₂×C₄⋊C₄	—	2	4	no	—
565	C₂×C₄⋊C₄	—	2	32	no	—
566	C₂×C₄⋊C₄	—	4	2	no	—
567	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
576	C₂×C₂²⋊C₄	—	2	4	no	—
577	C₂×C₂²⋊C₄	—	2	4	no	—
578	C₂×C₂²⋊C₄	—	2	4	no	—
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₂²⋊C₄	—	2	4	no	—
582	C₂×C₂²⋊C₄	—	2	4	no	—
583	C₂×C₂²⋊C₄	—	2	4	no	—
584	C₂×C₂²⋊C₄	—	2	4	no	—
585	C₂×C₂²⋊C₄	—	2	4	no	—
586	C₂×C₂²⋊C₄	—	4	2	no	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
598	C₂×C₄²	—	2	4	no	—
599	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
600	#95	C₂³×C₁₃	1	4	yes	—
601	#95	C₂³×C₁₃	1	4	yes	—
602	#95	C₂³×C₁₃	1	4	yes	—
603	#95	C₂³×C₁₃	1	4	yes	—
604	#95	C₂³×C₁₃	1	4	yes	—
605	#95	C₂³×C₁₃	1	4	yes	—
606	#95	C₂³×C₁₃	1	4	yes	—
607	#95	C₂³×C₁₃	1	4	yes	—
608	C₂×C₁₃	—	2	8	no	—
609	C₂×C₁₃	—	4	4	no	—
610	C₂×C₁₃	—	8	2	no	—
611	C₂×C₁₃	#2443	1	8	yes	direct product factor
612	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
613	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
614	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
615	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
616	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
617	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
618	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	2	2	no	—
624	C₂⁴	—	2	2	no	—
625	C₂⁴	—	2	2	no	—
626	C₂⁴	—	2	2	no	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	2	2	no	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
637	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
638	C₂⁴	C₁₃×#41	1	4	yes	—
639	C₂⁴	C₁₃×#41	1	4	yes	—
640	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
641	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
642	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
643	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₂×D₄	—	2	32	no	—
645	C₂×D₄	—	2	8	no	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	8	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	16	no	—
654	C₂×D₄	—	4	16	no	—
655	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
656	C₂²×C₄	—	2	32	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	8	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	8	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	8	no	—
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	8	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	8	no	—
695	C₂²×C₄	—	2	8	no	—
696	C₂²×C₄	—	2	8	no	—
697	C₂²×C₄	—	4	4	no	—
698	C₂²×C₄	—	4	4	no	—
699	C₂²×C₄	—	4	4	no	—
700	C₂²×C₄	—	4	16	no	—
701	C₂²×C₄	—	4	16	no	—
702	C₂²×C₄	—	4	16	no	—
703	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
704	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
705	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
706	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
707	C₂²×C₄	C₁₃×#41	1	4	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
720	C₄⋊C₄	—	2	8	no	—
721	C₄⋊C₄	—	2	8	no	—
722	C₄⋊C₄	—	2	8	no	—
723	C₄⋊C₄	—	2	8	no	—
724	C₄⋊C₄	—	2	8	no	—
725	C₄⋊C₄	—	2	8	no	—
726	C₄⋊C₄	—	4	4	no	—
727	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	2	8	no	—
732	C₂²⋊C₄	—	2	8	no	—
733	C₂²⋊C₄	—	2	8	no	—
734	C₂²⋊C₄	—	2	8	no	—
735	C₂²⋊C₄	—	2	8	no	—
736	C₂²⋊C₄	—	2	8	no	—
737	C₂²⋊C₄	—	2	8	no	—
738	C₂²⋊C₄	—	4	4	no	—
739	C₄²	—	2	8	no	—
740	C₁₃	C₂×#2443	1	1	yes	characteristic, direct product factor, Sylow
741	C₂³	—	2	8	no	—
742	C₂³	—	2	8	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	8	no	—
745	C₂³	—	2	8	no	—
746	C₂³	—	2	8	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	8	no	—
752	C₂³	—	2	8	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	C₁₃×#123	1	16	yes	complemented
779	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
780	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
781	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
782	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
783	C₂³	C₂×C₁₃×#41	1	4	yes	—
784	C₂³	C₂×C₁₃×#41	1	4	yes	—
785	C₂³	C₂×C₁₃×#41	1	2	yes	—
786	C₂³	C₂×C₁₃×#41	1	2	yes	—
787	C₂³	C₂×C₁₃×#41	1	2	yes	—
788	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
789	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
790	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
791	D₄	—	2	32	no	—
792	D₄	—	4	16	no	—
793	D₄	—	4	16	no	—
794	C₂×C₄	—	2	32	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	16	no	—
832	C₂×C₄	—	4	16	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
844	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
845	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	32	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	16	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	8	8	no	—
869	C₂²	C₂×C₁₃×#123	1	4	yes	—
870	C₂²	C₂×C₁₃×#123	1	8	yes	complemented
871	C₂²	C₁₃×#525	1	4	yes	—
872	C₂²	C₁₃×#539	1	4	yes	—
873	C₂²	D₄²×C₁₃	1	4	yes	—
874	C₂²	C₁₃×#547	1	4	yes	—
875	C₂²	C₁₃×#548	1	4	yes	—
876	C₂²	C₁₃×#553	1	4	yes	—
877	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
878	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
879	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
880	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
881	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
882	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
883	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₂	—	2	8	no	—
897	C₂	—	4	4	no	—
898	C₂	—	8	2	no	—
899	C₂	C₁₃×#2443	1	8	yes	direct product factor
900	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
901	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
902	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
903	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
904	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
905	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
906	C₂	C₂×C₁₃×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#123	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2443	C₂	direct (N × H)
6. C₂×C₁₃×#399	C₂	semidirect
7. C₂×C₁₃×#398	C₂	semidirect
8. C₂×C₁₃×#397	C₂	semidirect
9. C₂×C₁₃×#394	C₂	semidirect
10. C₂×C₁₃×#388	C₂	semidirect
11. C₂×C₁₃×#387	C₂	semidirect
12. C₂×C₁₃×#386	C₂	semidirect
13. C₂×C₁₃×#386	C₂	semidirect
14. C₂×C₁₃×#386	C₂	semidirect
15. C₂×C₁₃×#385	C₂	semidirect
16. C₂×C₁₃×#385	C₂	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
52. C₁₃×#399	C₂²	semidirect
53. C₁₃×#398	C₂²	semidirect
54. C₁₃×#397	C₂²	semidirect
55. C₁₃×#394	C₂²	semidirect
56. C₁₃×#388	C₂²	semidirect
57. C₁₃×#387	C₂²	semidirect
58. C₁₃×#386	C₂²	semidirect
59. C₁₃×#386	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
61. C₁₃×#385	C₂²	semidirect
62. C₁₃×#385	C₂²	semidirect
125. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
166. C₂×#2443	C₁₃	direct (N × H)
275. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
288. C₂²×#123	C₂×C₁₃	semidirect
290. C₂²×C₄×D₄	C₂×C₁₃	semidirect
291. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
292. #2443	C₂×C₁₃	direct (N × H)
293. C₂×#399	C₂×C₁₃	semidirect
294. C₂×#398	C₂×C₁₃	semidirect
295. C₂×#397	C₂×C₁₃	semidirect
296. C₂×#394	C₂×C₁₃	semidirect
297. C₂×#388	C₂×C₁₃	semidirect
298. C₂×#387	C₂×C₁₃	semidirect
299. C₂×#386	C₂×C₁₃	semidirect
300. C₂×#386	C₂×C₁₃	semidirect
301. C₂×#386	C₂×C₁₃	semidirect
302. C₂×#385	C₂×C₁₃	semidirect
303. C₂×#385	C₂×C₁₃	semidirect
341. C₂³×C₁₃	#123	semidirect
417. C₂×#123	C₂²×C₁₃	semidirect
421. C₂×C₄×D₄	C₂²×C₁₃	semidirect
431. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
444. #399	C₂²×C₁₃	semidirect
445. #398	C₂²×C₁₃	semidirect
446. #397	C₂²×C₁₃	semidirect
447. #394	C₂²×C₁₃	semidirect
448. #388	C₂²×C₁₃	semidirect
449. #387	C₂²×C₁₃	semidirect
450. #386	C₂²×C₁₃	semidirect
451. #386	C₂²×C₁₃	semidirect
452. #386	C₂²×C₁₃	semidirect
453. #385	C₂²×C₁₃	semidirect
454. #385	C₂²×C₁₃	semidirect
487. C₂²×C₁₃	C₂×#123	semidirect
567. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
611. C₂×C₁₃	#2443	direct (N × H)
727. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
740. C₁₃	C₂×#2443	direct (N × H)
778. C₂³	C₁₃×#123	semidirect
870. C₂²	C₂×C₁₃×#123	semidirect
899. C₂	C₁₃×#2443	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×C₁₃×#123	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2443	2
C₂×C₁₃×#399	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×#2443	13

Subgroups — C2×C13×#2443 #15720988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2443 #15720988