Subgroups — C₁₃×#35077 #15721416

Order 3328.

3078 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2630	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2579	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2534	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2485	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2417	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2416	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2407	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
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	C₁₃×#525	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	4	yes	—
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₁₃×#120	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	—	2	8	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
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	2	yes	—
47	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#398	C₂²	1	4	yes	complemented
49	C₁₃×#397	C₂²	1	4	yes	complemented
50	C₁₃×#396	C₂²	1	4	yes	complemented
51	C₁₃×#396	C₂²	1	4	yes	complemented
52	C₁₃×#394	C₂²	1	4	yes	—
53	C₁₃×#394	C₂²	1	4	yes	complemented
54	C₁₃×#394	C₂²	1	4	yes	complemented
55	C₁₃×#392	C₂²	1	4	yes	—
56	C₁₃×#391	C₂²	1	2	yes	complemented
57	C₁₃×#390	C₂²	1	2	yes	complemented
58	C₁₃×#389	C₂²	1	2	yes	complemented
59	C₁₃×#389	C₂²	1	2	yes	complemented
60	C₁₃×#388	C₂²	1	4	yes	complemented
61	C₁₃×#388	C₂²	1	4	yes	complemented
62	C₁₃×#387	C₂²	1	4	yes	complemented
63	C₁₃×#387	C₂²	1	4	yes	complemented
64	C₁₃×#386	C₂²	1	2	yes	—
65	C₁₃×#386	C₂²	1	2	yes	—
66	C₁₃×#386	C₂²	1	4	yes	—
67	C₁₃×#386	C₂²	1	4	yes	complemented
68	C₁₃×#386	C₂²	1	4	yes	complemented
69	C₁₃×#386	C₂²	1	4	yes	complemented
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	4	yes	complemented
73	C₁₃×#385	C₂²	1	4	yes	complemented
74	C₁₃×#381	C₂²	1	2	yes	—
75	C₁₃×#380	C₂²	1	2	yes	—
76	C₁₃×#380	C₂²	1	1	yes	characteristic
77	C₁₃×#380	C₂²	1	1	yes	characteristic
78	C₁₃×#380	C₂²	1	2	yes	complemented
79	C₁₃×#380	C₂²	1	2	yes	complemented
80	C₁₃×#380	C₂²	1	4	yes	complemented
81	C₁₃×#380	C₂²	1	2	yes	complemented
82	C₁₃×#380	C₂²	1	2	yes	complemented
83	C₁₃×#379	C₂²	1	2	yes	—
84	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	2	8	no	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	—	2	4	no	—
100	C₂³×C₄×C₁₃	—	4	4	no	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	C₁₃×#123	—	2	8	no	—
117	C₁₃×#123	—	4	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	4	4	no	—
121	C₁₃×#121	—	2	16	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#121	—	2	4	no	—
124	C₁₃×#121	—	4	4	no	—
125	C₁₃×#120	—	2	8	no	—
126	C₁₃×#120	—	4	4	no	—
127	C₄×D₄×C₁₃	—	2	8	no	—
128	C₄×D₄×C₁₃	—	2	8	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	—	2	8	no	—
131	C₄×D₄×C₁₃	—	2	8	no	—
132	C₄×D₄×C₁₃	—	2	8	no	—
133	C₁₃×#117	—	2	4	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
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	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
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	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₄²×C₁₃	—	2	4	no	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	4	yes	—
179	C₁₃×#95	C₂³	1	4	yes	—
180	C₁₃×#95	C₂³	1	4	yes	—
181	C₁₃×#95	C₂³	1	4	yes	—
182	#35077	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	—	2	2	no	—
184	C₂⁴×C₁₃	—	2	4	no	—
185	C₂⁴×C₁₃	—	2	4	no	—
186	C₂⁴×C₁₃	—	2	2	no	—
187	C₂⁴×C₁₃	—	2	2	no	—
188	C₂⁴×C₁₃	—	2	2	no	—
189	C₂⁴×C₁₃	—	2	2	no	—
190	C₂⁴×C₁₃	—	4	2	no	—
191	C₂⁴×C₁₃	—	4	2	no	—
192	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
193	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
194	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
196	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×#41	—	4	16	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	32	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	8	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	4	no	—
219	C₂×D₄×C₁₃	#41	1	8	yes	complemented
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	8	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	4	16	no	—
236	C₂²×C₄×C₁₃	—	4	2	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	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	4	no	—
243	C₂²×C₄×C₁₃	—	4	4	no	—
244	C₂²×C₄×C₁₃	—	4	4	no	—
245	C₂²×C₄×C₁₃	—	4	16	no	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	4	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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	8	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	4	4	no	—
274	C₁₃×C₄⋊C₄	—	4	4	no	—
275	C₁₃×C₄⋊C₄	—	4	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	8	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	8	no	—
289	C₁₃×C₂²⋊C₄	—	4	4	no	—
290	C₁₃×C₂²⋊C₄	—	4	4	no	—
291	C₁₃×C₂²⋊C₄	—	4	4	no	—
292	C₁₃×C₂²⋊C₄	—	4	4	no	—
293	C₁₃×C₂²⋊C₄	—	4	4	no	—
294	C₄²×C₁₃	—	2	4	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	—	2	4	no	—
297	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2855	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2854	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2630	C₂×C₁₃	1	4	yes	complemented
304	#2579	C₂×C₁₃	1	2	yes	complemented
305	#2534	C₂×C₁₃	1	2	yes	complemented
306	#2485	C₂×C₁₃	1	2	yes	complemented
307	#2417	C₂×C₁₃	1	2	yes	complemented
308	#2416	C₂×C₁₃	1	2	yes	complemented
309	#2412	C₂×C₁₃	1	2	yes	complemented
310	#2410	C₂×C₁₃	1	2	yes	complemented
311	#2407	C₂×C₁₃	1	2	yes	complemented
312	#2325	C₂×C₁₃	1	4	yes	complemented
313	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	1	no	—
318	C₂³×C₁₃	—	2	1	no	—
319	C₂³×C₁₃	—	2	8	no	—
320	C₂³×C₁₃	—	2	8	no	—
321	C₂³×C₁₃	—	2	8	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	1	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	—	2	1	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	4	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	8	no	—
339	C₂³×C₁₃	—	4	8	no	—
340	C₂³×C₁₃	—	4	8	no	—
341	C₂³×C₁₃	—	4	8	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	4	no	—
344	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
347	C₂³×C₁₃	C₂×#41	1	4	yes	—
348	C₂³×C₁₃	C₂×#41	1	4	yes	—
349	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
350	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
351	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
352	Q₈×C₁₃	—	4	4	no	—
353	D₄×C₁₃	—	2	16	no	—
354	D₄×C₁₃	—	2	16	no	—
355	D₄×C₁₃	—	4	8	no	—
356	D₄×C₁₃	—	4	8	no	—
357	D₄×C₁₃	—	4	8	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	8	8	no	—
360	C₂×C₄×C₁₃	—	2	8	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	8	no	—
367	C₂×C₄×C₁₃	—	2	8	no	—
368	C₂×C₄×C₁₃	—	2	8	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	4	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	4	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	4	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	4	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	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	4	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	8	no	—
392	C₂×C₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	—	8	8	no	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
402	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
403	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
407	#525	—	2	8	no	—
408	C₂×#123	C₂²×C₁₃	1	2	yes	—
409	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
410	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
413	C₂×#121	C₂²×C₁₃	1	4	yes	—
414	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
417	C₂×#120	C₂²×C₁₃	1	2	yes	—
418	C₂×#120	C₂²×C₁₃	1	2	yes	—
419	C₂×C₄×D₄	—	2	8	no	—
420	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
423	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
426	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
429	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
432	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
433	#398	C₂²×C₁₃	1	4	yes	complemented
434	#397	C₂²×C₁₃	1	4	yes	complemented
435	#396	C₂²×C₁₃	1	4	yes	complemented
436	#396	C₂²×C₁₃	1	4	yes	complemented
437	#394	C₂²×C₁₃	1	4	yes	—
438	#394	C₂²×C₁₃	1	4	yes	complemented
439	#394	C₂²×C₁₃	1	4	yes	complemented
440	#392	C₂²×C₁₃	1	4	yes	—
441	#391	C₂²×C₁₃	1	2	yes	complemented
442	#390	C₂²×C₁₃	1	2	yes	complemented
443	#389	C₂²×C₁₃	1	2	yes	complemented
444	#389	C₂²×C₁₃	1	2	yes	complemented
445	#388	C₂²×C₁₃	1	4	yes	complemented
446	#388	C₂²×C₁₃	1	4	yes	complemented
447	#387	C₂²×C₁₃	1	4	yes	complemented
448	#387	C₂²×C₁₃	1	4	yes	complemented
449	#386	C₂²×C₁₃	1	2	yes	—
450	#386	C₂²×C₁₃	1	2	yes	—
451	#386	C₂²×C₁₃	1	4	yes	—
452	#386	C₂²×C₁₃	1	4	yes	complemented
453	#386	C₂²×C₁₃	1	4	yes	complemented
454	#386	C₂²×C₁₃	1	4	yes	complemented
455	#385	C₂²×C₁₃	1	2	yes	—
456	#385	C₂²×C₁₃	1	2	yes	—
457	#385	C₂²×C₁₃	1	4	yes	complemented
458	#385	C₂²×C₁₃	1	4	yes	complemented
459	#381	C₂²×C₁₃	1	2	yes	—
460	#380	C₂²×C₁₃	1	2	yes	—
461	#380	C₂²×C₁₃	1	1	yes	characteristic
462	#380	C₂²×C₁₃	1	1	yes	characteristic
463	#380	C₂²×C₁₃	1	4	yes	complemented
464	#380	C₂²×C₁₃	1	2	yes	complemented
465	#380	C₂²×C₁₃	1	2	yes	complemented
466	#380	C₂²×C₁₃	1	2	yes	complemented
467	#380	C₂²×C₁₃	1	2	yes	complemented
468	#379	C₂²×C₁₃	1	2	yes	—
469	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	2	no	—
473	C₂²×C₁₃	—	2	2	no	—
474	C₂²×C₁₃	—	2	4	no	—
475	C₂²×C₁₃	—	2	4	no	—
476	C₂²×C₁₃	—	2	4	no	—
477	C₂²×C₁₃	—	2	4	no	—
478	C₂²×C₁₃	—	2	2	no	—
479	C₂²×C₁₃	—	2	4	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	2	4	no	—
483	C₂²×C₁₃	—	2	4	no	—
484	C₂²×C₁₃	—	4	16	no	—
485	C₂²×C₁₃	—	4	16	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	2	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	2	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	4	no	—
496	C₂²×C₁₃	—	4	4	no	—
497	C₂²×C₁₃	#525	1	4	yes	—
498	C₂²×C₁₃	#537	1	4	yes	—
499	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
500	C₂²×C₁₃	C₂²×#41	1	2	yes	—
501	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
502	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
504	C₄×C₁₃	—	2	4	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	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	C₄×C₁₃	—	4	4	no	—
514	C₄×C₁₃	—	4	4	no	—
515	C₄×C₁₃	#534	1	4	yes	—
516	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
517	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	4	4	no	—
520	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	8	no	—
523	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
524	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
528	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
529	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
530	C₂³×C₄	—	2	4	no	—
531	C₂³×C₄	—	4	4	no	—
532	C₂³×C₄	—	4	4	no	—
533	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
542	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
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	#123	—	2	8	no	—
548	#123	—	4	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	#121	—	2	16	no	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	—	4	4	no	—
556	#120	—	2	8	no	—
557	#120	—	4	4	no	—
558	C₄×D₄	—	2	8	no	—
559	C₄×D₄	—	2	8	no	—
560	C₄×D₄	—	2	8	no	—
561	C₄×D₄	—	2	8	no	—
562	C₄×D₄	—	2	8	no	—
563	C₄×D₄	—	2	8	no	—
564	#117	—	2	4	no	—
565	C₂×C₄⋊C₄	—	2	4	no	—
566	C₂×C₄⋊C₄	—	4	4	no	—
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	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₂²⋊C₄	—	4	4	no	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
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	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×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
600	C₂×C₄²	—	2	4	no	—
601	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	4	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	4	yes	—
608	#95	C₂³×C₁₃	1	4	yes	—
609	#95	C₂³×C₁₃	1	4	yes	—
610	#95	C₂³×C₁₃	1	4	yes	—
611	#95	C₂³×C₁₃	1	4	yes	—
612	#95	C₂³×C₁₃	1	4	yes	—
613	C₂×C₁₃	—	2	4	no	—
614	C₂×C₁₃	—	2	4	no	—
615	C₂×C₁₃	—	4	2	no	—
616	C₂×C₁₃	—	4	4	no	—
617	C₂×C₁₃	—	8	2	no	—
618	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
619	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
620	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
621	C₂×C₁₃	#3519	1	2	yes	—
622	C₂×C₁₃	#3520	1	2	yes	—
623	C₂⁴	—	2	2	no	—
624	C₂⁴	—	2	4	no	—
625	C₂⁴	—	2	4	no	—
626	C₂⁴	—	2	2	no	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	4	2	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
633	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
634	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
636	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
638	#41	—	4	16	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×D₄	—	2	32	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	8	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	C₁₃×#41	1	8	yes	complemented
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	4	16	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	4	no	—
683	C₂²×C₄	—	4	4	no	—
684	C₂²×C₄	—	4	4	no	—
685	C₂²×C₄	—	4	16	no	—
686	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
687	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
688	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
689	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
690	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
691	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	8	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	4	4	no	—
714	C₄⋊C₄	—	4	4	no	—
715	C₄⋊C₄	—	4	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	8	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	4	4	no	—
730	C₂²⋊C₄	—	4	4	no	—
731	C₂²⋊C₄	—	4	4	no	—
732	C₂²⋊C₄	—	4	4	no	—
733	C₂²⋊C₄	—	4	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₁₃	#35077	1	1	yes	characteristic, direct product factor, Sylow
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	8	no	—
744	C₂³	—	2	8	no	—
745	C₂³	—	2	8	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
769	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
770	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂³	C₂×C₁₃×#41	1	4	yes	—
772	C₂³	C₂×C₁₃×#41	1	4	yes	—
773	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
774	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
775	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
776	Q₈	—	4	4	no	—
777	D₄	—	2	16	no	—
778	D₄	—	2	16	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	8	8	no	—
784	C₂×C₄	—	2	8	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	8	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	8	no	—
820	C₂×C₄	—	8	8	no	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
826	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	4	16	no	—
842	C₂²	—	4	16	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	C₁₃×#525	1	4	yes	—
855	C₂²	C₁₃×#537	1	4	yes	—
856	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
857	C₂²	C₂²×C₁₃×#41	1	2	yes	—
858	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
859	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
860	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	4	4	no	—
866	C₄	—	4	4	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	C₁₃×#534	1	4	yes	—
873	C₂	—	2	4	no	—
874	C₂	—	2	4	no	—
875	C₂	—	4	4	no	—
876	C₂	—	4	2	no	—
877	C₂	—	8	2	no	—
878	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
879	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
880	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
881	C₂	C₁₃×#3519	1	2	yes	—
882	C₂	C₁₃×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
4. C₁₃×#2854	C₂	semidirect
5. C₁₃×#2848	C₂	semidirect
6. C₁₃×#2847	C₂	semidirect
7. C₁₃×#2630	C₂	semidirect
8. C₁₃×#2579	C₂	semidirect
9. C₁₃×#2534	C₂	semidirect
10. C₁₃×#2485	C₂	semidirect
11. C₁₃×#2417	C₂	semidirect
12. C₁₃×#2416	C₂	semidirect
13. C₁₃×#2412	C₂	semidirect
14. C₁₃×#2410	C₂	semidirect
15. C₁₃×#2407	C₂	semidirect
16. C₁₃×#2325	C₂	semidirect
17. C₂×C₁₃×#380	C₂	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃	C₂²	semidirect
41. C₂×C₁₃×#117	C₂²	semidirect
43. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₁₃×#398	C₂²	semidirect
49. C₁₃×#397	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#396	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
54. C₁₃×#394	C₂²	semidirect
56. C₁₃×#391	C₂²	semidirect
57. C₁₃×#390	C₂²	semidirect
58. C₁₃×#389	C₂²	semidirect
59. C₁₃×#389	C₂²	semidirect
60. C₁₃×#388	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#387	C₂²	semidirect
63. C₁₃×#387	C₂²	semidirect
67. C₁₃×#386	C₂²	semidirect
68. C₁₃×#386	C₂²	semidirect
69. C₁₃×#386	C₂²	semidirect
72. C₁₃×#385	C₂²	semidirect
73. C₁₃×#385	C₂²	semidirect
78. C₁₃×#380	C₂²	semidirect
79. C₁₃×#380	C₂²	semidirect
80. C₁₃×#380	C₂²	semidirect
81. C₁₃×#380	C₂²	semidirect
82. C₁₃×#380	C₂²	semidirect
84. C₂×C₁₃×#95	C₂²	semidirect
102. C₂³×C₄×C₁₃	D₄	semidirect
182. #35077	C₁₃	direct (N × H)
219. C₂×D₄×C₁₃	#41	semidirect
297. C₂×#525	C₂×C₁₃	semidirect
298. C₂²×C₄×D₄	C₂×C₁₃	semidirect
299. #2855	C₂×C₁₃	semidirect
300. #2854	C₂×C₁₃	semidirect
301. #2848	C₂×C₁₃	semidirect
302. #2847	C₂×C₁₃	semidirect
303. #2630	C₂×C₁₃	semidirect
304. #2579	C₂×C₁₃	semidirect
305. #2534	C₂×C₁₃	semidirect
306. #2485	C₂×C₁₃	semidirect
307. #2417	C₂×C₁₃	semidirect
308. #2416	C₂×C₁₃	semidirect
309. #2412	C₂×C₁₃	semidirect
310. #2410	C₂×C₁₃	semidirect
311. #2407	C₂×C₁₃	semidirect
312. #2325	C₂×C₁₃	semidirect
313. C₂×#380	C₂×C₁₃	semidirect
403. C₂²×#41	C₂²×C₁₃	semidirect
409. C₂×#123	C₂²×C₁₃	semidirect
411. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
412. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
415. C₂×#121	C₂²×C₁₃	semidirect
416. C₂×#121	C₂²×C₁₃	semidirect
425. C₂×C₄×D₄	C₂²×C₁₃	semidirect
426. C₂×#117	C₂²×C₁₃	semidirect
428. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
433. #398	C₂²×C₁₃	semidirect
434. #397	C₂²×C₁₃	semidirect
435. #396	C₂²×C₁₃	semidirect
436. #396	C₂²×C₁₃	semidirect
438. #394	C₂²×C₁₃	semidirect
439. #394	C₂²×C₁₃	semidirect
441. #391	C₂²×C₁₃	semidirect
442. #390	C₂²×C₁₃	semidirect
443. #389	C₂²×C₁₃	semidirect
444. #389	C₂²×C₁₃	semidirect
445. #388	C₂²×C₁₃	semidirect
446. #388	C₂²×C₁₃	semidirect
447. #387	C₂²×C₁₃	semidirect
448. #387	C₂²×C₁₃	semidirect
452. #386	C₂²×C₁₃	semidirect
453. #386	C₂²×C₁₃	semidirect
454. #386	C₂²×C₁₃	semidirect
457. #385	C₂²×C₁₃	semidirect
458. #385	C₂²×C₁₃	semidirect
463. #380	C₂²×C₁₃	semidirect
464. #380	C₂²×C₁₃	semidirect
465. #380	C₂²×C₁₃	semidirect
466. #380	C₂²×C₁₃	semidirect
467. #380	C₂²×C₁₃	semidirect
469. C₂×#95	C₂²×C₁₃	semidirect
533. C₂³×C₄	D₄×C₁₃	semidirect
659. C₂×D₄	C₁₃×#41	semidirect
737. C₁₃	#35077	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×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2855	2
C₁₃×#2854	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2630	2
C₁₃×#2579	2
C₁₃×#2534	2
C₁₃×#2485	2
C₁₃×#2417	2
C₁₃×#2416	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2407	2
C₁₃×#2325	2
C₂×C₁₃×#380	2
#35077	13

Subgroups — C13×#35077 #15721416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35077 #15721416