Subgroups — C₁₃×#34502 #15720841

Order 3328.

2156 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#551	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2375	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2321	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2319	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2312	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₁₃×#551	C₄	1	16	yes	complemented
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#391	C₂²	1	2	yes	complemented
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	2	yes	—
40	C₁₃×#389	C₂²	1	2	yes	complemented
41	C₁₃×#389	C₂²	1	2	yes	complemented
42	C₁₃×#389	C₂²	1	2	yes	complemented
43	C₁₃×#389	C₂²	1	2	yes	complemented
44	C₁₃×#389	C₂²	1	2	yes	complemented
45	C₁₃×#388	C₂²	1	2	yes	—
46	C₁₃×#388	C₂²	1	2	yes	—
47	C₁₃×#388	C₂²	1	2	yes	—
48	C₁₃×#388	C₂²	1	2	yes	—
49	C₁₃×#388	C₂²	1	2	yes	—
50	C₁₃×#388	C₂²	1	2	yes	—
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
55	C₁₃×#388	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	complemented
63	C₁₃×#388	C₂²	1	2	yes	complemented
64	C₁₃×#388	C₂²	1	2	yes	complemented
65	C₁₃×#387	C₂²	1	2	yes	complemented
66	C₁₃×#387	C₂²	1	2	yes	complemented
67	C₁₃×#387	C₂²	1	2	yes	complemented
68	C₁₃×#387	C₂²	1	2	yes	complemented
69	C₁₃×#387	C₂²	1	2	yes	complemented
70	C₁₃×#387	C₂²	1	2	yes	complemented
71	C₁₃×#387	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	2	yes	complemented
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	1	yes	characteristic
75	C₁₃×#386	C₂²	1	1	yes	characteristic
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#385	C₂²	1	1	yes	characteristic
78	C₁₃×#385	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#382	C₂²	1	2	yes	complemented
83	C₁₃×#381	C₂²	1	2	yes	—
84	C₁₃×#381	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#380	C₂²	1	2	yes	—
86	C₁₃×#380	C₂²	1	2	yes	—
87	C₁₃×#380	C₂²	1	2	yes	—
88	C₁₃×#380	C₂²	1	2	yes	complemented
89	C₁₃×#379	C₂²	1	1	yes	characteristic
90	C₁₃×#379	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₁₃×#376	C₂²	1	2	yes	complemented
106	C₁₃×#376	C₂²	1	2	yes	complemented
107	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#126	C₂×C₄	1	16	yes	complemented
120	C₁₃×#124	C₂×C₄	1	8	yes	—
121	C₁₃×#123	C₂×C₄	1	8	yes	—
122	C₁₃×#123	C₂×C₄	1	16	yes	complemented
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
124	C₁₃×#120	C₂×C₄	1	8	yes	—
125	C₄×Q₈×C₁₃	—	4	2	no	—
126	C₄×D₄×C₁₃	—	4	2	no	—
127	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
128	C₁₃×#117	—	4	4	no	—
129	C₁₃×#117	C₂×C₄	1	16	yes	complemented
130	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
148	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	#34502	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	—	4	1	no	—
211	C₂⁴×C₁₃	—	4	2	no	—
212	C₂⁴×C₁₃	—	4	2	no	—
213	C₂⁴×C₁₃	—	4	1	no	—
214	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂×Q₈×C₁₃	—	4	1	no	—
219	C₂×Q₈×C₁₃	—	4	1	no	—
220	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₁₃	—	4	1	no	—
222	C₂×D₄×C₁₃	—	4	2	no	—
223	C₂×D₄×C₁₃	—	4	2	no	—
224	C₂×D₄×C₁₃	—	4	1	no	—
225	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
226	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	1	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	1	no	—
236	C₂²×C₄×C₁₃	—	4	1	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
242	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
243	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	—	4	2	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	2	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	1	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	1	no	—
272	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
273	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
274	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
275	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	4	2	no	—
284	C₁₃×C₂²⋊C₄	—	4	2	no	—
285	C₁₃×C₂²⋊C₄	—	4	2	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	—	4	1	no	—
288	C₁₃×C₂²⋊C₄	—	4	1	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₁₃×C₂²⋊C₄	—	4	1	no	—
292	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
293	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
294	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
295	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
296	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
297	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
298	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
299	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	4	2	no	—
303	C₄²×C₁₃	—	4	2	no	—
304	C₄²×C₁₃	—	4	2	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	C₄²×C₁₃	—	4	2	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	C₄²×C₁₃	—	4	2	no	—
310	C₄²×C₁₃	—	4	1	no	—
311	C₄²×C₁₃	—	4	2	no	—
312	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
313	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
314	C₂×#551	C₂×C₁₃	1	1	yes	characteristic
315	#2378	C₂×C₁₃	1	2	yes	complemented
316	#2376	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2375	C₂×C₁₃	1	1	yes	characteristic
318	#2374	C₂×C₁₃	1	2	yes	complemented
319	#2373	C₂×C₁₃	1	2	yes	complemented
320	#2372	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2352	C₂×C₁₃	1	2	yes	complemented
322	#2346	C₂×C₁₃	1	2	yes	complemented
323	#2342	C₂×C₁₃	1	2	yes	complemented
324	#2335	C₂×C₁₃	1	2	yes	complemented
325	#2334	C₂×C₁₃	1	2	yes	complemented
326	#2323	C₂×C₁₃	1	2	yes	complemented
327	#2322	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2321	C₂×C₁₃	1	1	yes	characteristic
329	#2319	C₂×C₁₃	1	2	yes	complemented
330	#2312	C₂×C₁₃	1	2	yes	complemented
331	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2298	C₂×C₁₃	1	2	yes	complemented
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	1	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	4	8	no	—
348	C₂³×C₁₃	—	4	4	no	—
349	C₂³×C₁₃	—	8	2	no	—
350	C₂³×C₁₃	—	8	2	no	—
351	C₂³×C₁₃	—	8	4	no	—
352	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
353	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
354	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
355	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
356	Q₈×C₁₃	—	4	4	no	—
357	D₄×C₁₃	—	4	8	no	—
358	D₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	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	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	1	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	1	no	—
377	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	4	8	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	8	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	2	no	—
401	C₂×C₄×C₁₃	—	8	2	no	—
402	C₂×C₄×C₁₃	—	8	2	no	—
403	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
408	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
410	#551	C₄×C₁₃	1	16	yes	complemented
411	C₂×#126	C₂²×C₁₃	1	2	yes	—
412	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#123	C₂²×C₁₃	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
416	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
420	C₂×#117	C₂²×C₁₃	1	2	yes	—
421	C₂×#117	C₂²×C₁₃	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
425	#391	C₂²×C₁₃	1	2	yes	complemented
426	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#390	C₂²×C₁₃	1	2	yes	—
428	#390	C₂²×C₁₃	1	2	yes	—
429	#390	C₂²×C₁₃	1	1	yes	characteristic
430	#389	C₂²×C₁₃	1	2	yes	complemented
431	#389	C₂²×C₁₃	1	2	yes	complemented
432	#389	C₂²×C₁₃	1	2	yes	complemented
433	#389	C₂²×C₁₃	1	2	yes	complemented
434	#389	C₂²×C₁₃	1	2	yes	complemented
435	#388	C₂²×C₁₃	1	2	yes	—
436	#388	C₂²×C₁₃	1	2	yes	—
437	#388	C₂²×C₁₃	1	2	yes	—
438	#388	C₂²×C₁₃	1	2	yes	—
439	#388	C₂²×C₁₃	1	2	yes	—
440	#388	C₂²×C₁₃	1	2	yes	—
441	#388	C₂²×C₁₃	1	2	yes	—
442	#388	C₂²×C₁₃	1	2	yes	—
443	#388	C₂²×C₁₃	1	2	yes	—
444	#388	C₂²×C₁₃	1	2	yes	—
445	#388	C₂²×C₁₃	1	2	yes	—
446	#388	C₂²×C₁₃	1	2	yes	—
447	#388	C₂²×C₁₃	1	2	yes	—
448	#388	C₂²×C₁₃	1	2	yes	—
449	#388	C₂²×C₁₃	1	2	yes	—
450	#388	C₂²×C₁₃	1	2	yes	—
451	#388	C₂²×C₁₃	1	2	yes	—
452	#388	C₂²×C₁₃	1	2	yes	complemented
453	#388	C₂²×C₁₃	1	2	yes	complemented
454	#388	C₂²×C₁₃	1	2	yes	complemented
455	#387	C₂²×C₁₃	1	2	yes	complemented
456	#387	C₂²×C₁₃	1	2	yes	complemented
457	#387	C₂²×C₁₃	1	2	yes	complemented
458	#387	C₂²×C₁₃	1	2	yes	complemented
459	#387	C₂²×C₁₃	1	2	yes	complemented
460	#387	C₂²×C₁₃	1	2	yes	complemented
461	#387	C₂²×C₁₃	1	2	yes	complemented
462	#387	C₂²×C₁₃	1	2	yes	complemented
463	#386	C₂²×C₁₃	1	2	yes	—
464	#386	C₂²×C₁₃	1	1	yes	characteristic
465	#386	C₂²×C₁₃	1	1	yes	characteristic
466	#386	C₂²×C₁₃	1	2	yes	—
467	#385	C₂²×C₁₃	1	1	yes	characteristic
468	#385	C₂²×C₁₃	1	2	yes	—
469	#385	C₂²×C₁₃	1	2	yes	—
470	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	#382	C₂²×C₁₃	1	2	yes	complemented
472	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#381	C₂²×C₁₃	1	2	yes	—
474	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#380	C₂²×C₁₃	1	2	yes	—
476	#380	C₂²×C₁₃	1	2	yes	—
477	#380	C₂²×C₁₃	1	2	yes	—
478	#380	C₂²×C₁₃	1	2	yes	complemented
479	#379	C₂²×C₁₃	1	1	yes	characteristic
480	#379	C₂²×C₁₃	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
482	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
483	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
484	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
485	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
486	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
494	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
495	#376	C₂²×C₁₃	1	2	yes	complemented
496	#376	C₂²×C₁₃	1	2	yes	complemented
497	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	C₂²×C₁₃	—	2	4	no	—
499	C₂²×C₁₃	—	2	4	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	2	4	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	4	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	8	8	no	—
516	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
517	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₁₃	#585	1	2	yes	—
519	C₂²×C₁₃	#585	1	2	yes	—
520	C₂²×C₁₃	#585	1	1	yes	characteristic
521	C₄×C₁₃	—	2	4	no	—
522	C₄×C₁₃	—	2	4	no	—
523	C₄×C₁₃	—	2	4	no	—
524	C₄×C₁₃	—	2	4	no	—
525	C₄×C₁₃	—	2	4	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
546	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
548	#126	C₂×C₄×C₁₃	1	16	yes	complemented
549	#124	C₂×C₄×C₁₃	1	8	yes	—
550	#123	C₂×C₄×C₁₃	1	8	yes	—
551	#123	C₂×C₄×C₁₃	1	16	yes	complemented
552	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
553	#120	C₂×C₄×C₁₃	1	8	yes	—
554	C₄×Q₈	—	4	2	no	—
555	C₄×D₄	—	4	2	no	—
556	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
557	#117	—	4	4	no	—
558	#117	C₂×C₄×C₁₃	1	16	yes	complemented
559	C₂×C₄⋊C₄	—	4	2	no	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₂²⋊C₄	—	4	2	no	—
577	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	2	yes	—
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	#95	C₂³×C₁₃	1	2	yes	—
627	#95	C₂³×C₁₃	1	2	yes	—
628	#95	C₂³×C₁₃	1	2	yes	—
629	#95	C₂³×C₁₃	1	2	yes	—
630	#95	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	C₂×C₁₃	—	4	2	no	—
639	C₂×C₁₃	—	4	4	no	—
640	C₂×C₁₃	—	4	2	no	—
641	C₂×C₁₃	#3428	1	2	yes	—
642	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₁₃	#3545	1	1	yes	characteristic
644	C₂×C₁₃	#3551	1	1	yes	characteristic
645	C₂×C₁₃	#3566	1	2	yes	—
646	C₂⁴	—	4	1	no	—
647	C₂⁴	—	4	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
651	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
652	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂×Q₈	—	4	1	no	—
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
657	C₂×D₄	—	4	1	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	1	no	—
661	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
662	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
678	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
679	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
709	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
710	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
711	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
729	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
733	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
734	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
735	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	2	no	—
746	C₄²	—	4	2	no	—
747	C₄²	—	4	1	no	—
748	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
749	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
750	C₁₃	#34502	1	1	yes	characteristic, direct product factor, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	—	8	4	no	—
770	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
771	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
772	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
773	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
774	Q₈	—	4	4	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	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	—	4	8	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
822	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
823	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
824	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
825	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
826	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
827	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	8	8	no	—
846	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
847	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
848	C₂²	C₁₃×#585	1	2	yes	—
849	C₂²	C₁₃×#585	1	2	yes	—
850	C₂²	C₁₃×#585	1	1	yes	characteristic
851	C₄	—	2	2	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	4	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₂	—	4	4	no	—
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	C₁₃×#3428	1	2	yes	—
871	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
872	C₂	C₁₃×#3545	1	1	yes	characteristic
873	C₂	C₁₃×#3551	1	1	yes	characteristic
874	C₂	C₁₃×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#120	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2378	C₂	semidirect
3. C₁₃×#2376	C₂	semidirect
5. C₁₃×#2374	C₂	semidirect
6. C₁₃×#2373	C₂	semidirect
7. C₁₃×#2372	C₂	semidirect
8. C₁₃×#2352	C₂	semidirect
9. C₁₃×#2346	C₂	semidirect
10. C₁₃×#2342	C₂	semidirect
11. C₁₃×#2335	C₂	semidirect
12. C₁₃×#2334	C₂	semidirect
13. C₁₃×#2323	C₂	semidirect
14. C₁₃×#2322	C₂	semidirect
16. C₁₃×#2319	C₂	semidirect
17. C₁₃×#2312	C₂	semidirect
18. C₄×C₁₃×#124	C₂	semidirect
19. C₁₃×#2298	C₂	semidirect
20. C₁₃×#551	C₄	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
35. C₁₃×#391	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
40. C₁₃×#389	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
44. C₁₃×#389	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#387	C₂²	semidirect
66. C₁₃×#387	C₂²	semidirect
67. C₁₃×#387	C₂²	semidirect
68. C₁₃×#387	C₂²	semidirect
69. C₁₃×#387	C₂²	semidirect
70. C₁₃×#387	C₂²	semidirect
71. C₁₃×#387	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
80. C₁₃×#385	C₂²	semidirect
81. C₁₃×#382	C₂²	semidirect
82. C₁₃×#382	C₂²	semidirect
84. C₁₃×#381	C₂²	semidirect
88. C₁₃×#380	C₂²	semidirect
91. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
92. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
93. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
94. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
95. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
102. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
103. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
104. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
105. C₁₃×#376	C₂²	semidirect
106. C₁₃×#376	C₂²	semidirect
107. C₄³×C₁₃	C₂²	semidirect
119. C₁₃×#126	C₂×C₄	semidirect
122. C₁₃×#123	C₂×C₄	semidirect
123. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
127. C₄×D₄×C₁₃	C₂×C₄	semidirect
129. C₁₃×#117	C₂×C₄	semidirect
148. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
209. #34502	C₁₃	direct (N × H)
315. #2378	C₂×C₁₃	semidirect
316. #2376	C₂×C₁₃	semidirect
318. #2374	C₂×C₁₃	semidirect
319. #2373	C₂×C₁₃	semidirect
320. #2372	C₂×C₁₃	semidirect
321. #2352	C₂×C₁₃	semidirect
322. #2346	C₂×C₁₃	semidirect
323. #2342	C₂×C₁₃	semidirect
324. #2335	C₂×C₁₃	semidirect
325. #2334	C₂×C₁₃	semidirect
326. #2323	C₂×C₁₃	semidirect
327. #2322	C₂×C₁₃	semidirect
329. #2319	C₂×C₁₃	semidirect
330. #2312	C₂×C₁₃	semidirect
331. C₄×#124	C₂×C₁₃	semidirect
332. #2298	C₂×C₁₃	semidirect
410. #551	C₄×C₁₃	semidirect
417. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
422. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
425. #391	C₂²×C₁₃	semidirect
426. #391	C₂²×C₁₃	semidirect
430. #389	C₂²×C₁₃	semidirect
431. #389	C₂²×C₁₃	semidirect
432. #389	C₂²×C₁₃	semidirect
433. #389	C₂²×C₁₃	semidirect
434. #389	C₂²×C₁₃	semidirect
452. #388	C₂²×C₁₃	semidirect
453. #388	C₂²×C₁₃	semidirect
454. #388	C₂²×C₁₃	semidirect
455. #387	C₂²×C₁₃	semidirect
456. #387	C₂²×C₁₃	semidirect
457. #387	C₂²×C₁₃	semidirect
458. #387	C₂²×C₁₃	semidirect
459. #387	C₂²×C₁₃	semidirect
460. #387	C₂²×C₁₃	semidirect
461. #387	C₂²×C₁₃	semidirect
462. #387	C₂²×C₁₃	semidirect
470. #385	C₂²×C₁₃	semidirect
471. #382	C₂²×C₁₃	semidirect
472. #382	C₂²×C₁₃	semidirect
474. #381	C₂²×C₁₃	semidirect
478. #380	C₂²×C₁₃	semidirect
481. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
482. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
483. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
484. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
485. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
492. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
493. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
494. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
495. #376	C₂²×C₁₃	semidirect
496. #376	C₂²×C₁₃	semidirect
497. C₄³	C₂²×C₁₃	semidirect
548. #126	C₂×C₄×C₁₃	semidirect
551. #123	C₂×C₄×C₁₃	semidirect
552. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
556. C₄×D₄	C₂×C₄×C₁₃	semidirect
558. #117	C₂×C₄×C₁₃	semidirect
577. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
750. C₁₃	#34502	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×C₁₃×#551	2
C₁₃×#2378	2
C₁₃×#2376	2
C₁₃×#2375	2
C₁₃×#2374	2
C₁₃×#2373	2
C₁₃×#2372	2
C₁₃×#2352	2
C₁₃×#2346	2
C₁₃×#2342	2
C₁₃×#2335	2
C₁₃×#2334	2
C₁₃×#2323	2
C₁₃×#2322	2
C₁₃×#2321	2
C₁₃×#2319	2
C₁₃×#2312	2
C₄×C₁₃×#124	2
C₁₃×#2298	2
#34502	13

Subgroups — C13×#34502 #15720841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34502 #15720841