Subgroups — C₁₃×#36816 #15723155

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2797	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2759	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2746	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2737	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2716	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2712	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2685	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2684	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2653	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2607	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2597	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2474	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2404	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2332	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#401	C₂²	1	2	yes	complemented
32	C₁₃×#400	C₂²	1	2	yes	complemented
33	C₁₃×#399	C₂²	1	2	yes	—
34	C₁₃×#398	C₂²	1	2	yes	complemented
35	C₁₃×#397	C₂²	1	2	yes	—
36	C₁₃×#397	C₂²	1	2	yes	—
37	C₁₃×#397	C₂²	1	2	yes	—
38	C₁₃×#397	C₂²	1	2	yes	complemented
39	C₁₃×#397	C₂²	1	2	yes	complemented
40	C₁₃×#397	C₂²	1	2	yes	complemented
41	C₁₃×#396	C₂²	1	2	yes	—
42	C₁₃×#395	C₂²	1	2	yes	complemented
43	C₁₃×#394	C₂²	1	2	yes	—
44	C₁₃×#394	C₂²	1	2	yes	—
45	C₁₃×#394	C₂²	1	2	yes	—
46	C₁₃×#394	C₂²	1	2	yes	—
47	C₁₃×#394	C₂²	1	2	yes	—
48	C₁₃×#394	C₂²	1	2	yes	—
49	C₁₃×#393	C₂²	1	2	yes	—
50	C₁₃×#393	C₂²	1	2	yes	—
51	C₁₃×#393	C₂²	1	2	yes	—
52	C₁₃×#393	C₂²	1	2	yes	—
53	C₁₃×#393	C₂²	1	2	yes	complemented
54	C₁₃×#392	C₂²	1	2	yes	—
55	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#391	C₂²	1	2	yes	complemented
57	C₁₃×#391	C₂²	1	2	yes	complemented
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#391	C₂²	1	2	yes	complemented
60	C₁₃×#390	C₂²	1	2	yes	—
61	C₁₃×#390	C₂²	1	2	yes	—
62	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	complemented
75	C₁₃×#388	C₂²	1	2	yes	complemented
76	C₁₃×#387	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#387	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#387	C₂²	1	2	yes	complemented
82	C₁₃×#387	C₂²	1	2	yes	complemented
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	1	yes	characteristic
89	C₁₃×#386	C₂²	1	1	yes	characteristic
90	C₁₃×#386	C₂²	1	2	yes	complemented
91	C₁₃×#385	C₂²	1	2	yes	complemented
92	C₁₃×#385	C₂²	1	2	yes	complemented
93	C₁₃×#385	C₂²	1	2	yes	complemented
94	C₁₃×#385	C₂²	1	2	yes	complemented
95	C₁₃×#383	C₂²	1	2	yes	complemented
96	C₁₃×#381	C₂²	1	2	yes	—
97	C₁₃×#381	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#379	C₂²	1	2	yes	—
100	C₁₃×#379	C₂²	1	2	yes	—
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×#41	—	2	4	no	—
109	C₂×C₁₃×#41	—	4	2	no	—
110	C₂×C₁₃×#41	—	4	2	no	—
111	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	—	4	2	no	—
125	C₁₃×#126	—	4	4	no	—
126	C₁₃×#124	—	4	4	no	—
127	C₁₃×#124	—	4	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×#120	—	4	2	no	—
130	C₁₃×#120	—	4	2	no	—
131	C₁₃×#117	—	4	2	no	—
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	1	yes	characteristic
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	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	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	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₁₃	—	4	2	no	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
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	#36816	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	—	2	2	no	—
209	C₂⁴×C₁₃	—	4	2	no	—
210	C₂⁴×C₁₃	—	4	1	no	—
211	C₂⁴×C₁₃	—	4	1	no	—
212	C₂⁴×C₁₃	—	4	2	no	—
213	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×#41	—	4	16	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	4	1	no	—
222	C₂×Q₈×C₁₃	—	4	1	no	—
223	C₂×Q₈×C₁₃	—	4	2	no	—
224	C₂×Q₈×C₁₃	—	4	1	no	—
225	C₂×Q₈×C₁₃	—	4	2	no	—
226	C₂×Q₈×C₁₃	—	4	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	4	1	no	—
235	C₂×D₄×C₁₃	—	4	1	no	—
236	C₂×D₄×C₁₃	—	4	1	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	2	no	—
241	C₂×D₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	—	4	2	no	—
250	C₂²×C₄×C₁₃	—	4	1	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
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	1	yes	characteristic
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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	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	4	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	1	no	—
303	C₁₃×C₂²⋊C₄	—	4	2	no	—
304	C₁₃×C₂²⋊C₄	—	4	1	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	2	no	—
308	C₁₃×C₂²⋊C₄	—	4	2	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₄²×C₁₃	—	2	4	no	—
311	C₄²×C₁₃	—	4	1	no	—
312	C₄²×C₁₃	—	4	1	no	—
313	C₄²×C₁₃	—	4	2	no	—
314	C₄²×C₁₃	—	4	1	no	—
315	C₄²×C₁₃	—	4	1	no	—
316	C₄²×C₁₃	—	4	1	no	—
317	C₄²×C₁₃	—	4	2	no	—
318	C₄²×C₁₃	—	4	1	no	—
319	#2852	C₂×C₁₃	1	2	yes	complemented
320	#2797	C₂×C₁₃	1	2	yes	complemented
321	#2759	C₂×C₁₃	1	2	yes	complemented
322	#2746	C₂×C₁₃	1	2	yes	complemented
323	#2737	C₂×C₁₃	1	2	yes	complemented
324	#2716	C₂×C₁₃	1	2	yes	complemented
325	#2712	C₂×C₁₃	1	2	yes	complemented
326	#2685	C₂×C₁₃	1	2	yes	complemented
327	#2684	C₂×C₁₃	1	2	yes	complemented
328	#2653	C₂×C₁₃	1	2	yes	complemented
329	#2607	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#2597	C₂×C₁₃	1	2	yes	complemented
331	#2561	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2474	C₂×C₁₃	1	2	yes	complemented
333	#2432	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#2404	C₂×C₁₃	1	1	yes	characteristic
335	#2332	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	1	no	—
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	1	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	4	4	no	—
359	C₂³×C₁₃	—	8	2	no	—
360	C₂³×C₁₃	—	8	2	no	—
361	C₂³×C₁₃	—	8	4	no	—
362	C₂³×C₁₃	—	8	4	no	—
363	C₂³×C₁₃	C₂×#41	1	2	yes	—
364	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
365	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
366	Q₈×C₁₃	—	4	4	no	—
367	Q₈×C₁₃	—	8	2	no	—
368	Q₈×C₁₃	—	8	4	no	—
369	D₄×C₁₃	—	4	4	no	—
370	D₄×C₁₃	—	4	4	no	—
371	D₄×C₁₃	—	4	4	no	—
372	D₄×C₁₃	—	8	4	no	—
373	D₄×C₁₃	—	8	4	no	—
374	C₂×C₄×C₁₃	—	2	8	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	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	1	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	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
424	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂×#126	C₂²×C₁₃	1	2	yes	—
427	C₂×#124	C₂²×C₁₃	1	2	yes	—
428	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
434	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#401	C₂²×C₁₃	1	2	yes	complemented
436	#400	C₂²×C₁₃	1	2	yes	complemented
437	#399	C₂²×C₁₃	1	2	yes	—
438	#398	C₂²×C₁₃	1	2	yes	complemented
439	#397	C₂²×C₁₃	1	2	yes	—
440	#397	C₂²×C₁₃	1	2	yes	—
441	#397	C₂²×C₁₃	1	2	yes	—
442	#397	C₂²×C₁₃	1	2	yes	complemented
443	#397	C₂²×C₁₃	1	2	yes	complemented
444	#397	C₂²×C₁₃	1	2	yes	complemented
445	#396	C₂²×C₁₃	1	2	yes	—
446	#395	C₂²×C₁₃	1	2	yes	complemented
447	#394	C₂²×C₁₃	1	2	yes	—
448	#394	C₂²×C₁₃	1	2	yes	—
449	#394	C₂²×C₁₃	1	2	yes	—
450	#394	C₂²×C₁₃	1	2	yes	—
451	#394	C₂²×C₁₃	1	2	yes	—
452	#394	C₂²×C₁₃	1	2	yes	—
453	#393	C₂²×C₁₃	1	2	yes	—
454	#393	C₂²×C₁₃	1	2	yes	—
455	#393	C₂²×C₁₃	1	2	yes	—
456	#393	C₂²×C₁₃	1	2	yes	—
457	#393	C₂²×C₁₃	1	2	yes	complemented
458	#392	C₂²×C₁₃	1	2	yes	—
459	#391	C₂²×C₁₃	1	2	yes	complemented
460	#391	C₂²×C₁₃	1	2	yes	complemented
461	#391	C₂²×C₁₃	1	2	yes	complemented
462	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#391	C₂²×C₁₃	1	2	yes	complemented
464	#390	C₂²×C₁₃	1	2	yes	—
465	#390	C₂²×C₁₃	1	2	yes	—
466	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#388	C₂²×C₁₃	1	2	yes	—
468	#388	C₂²×C₁₃	1	2	yes	—
469	#388	C₂²×C₁₃	1	2	yes	—
470	#388	C₂²×C₁₃	1	2	yes	—
471	#388	C₂²×C₁₃	1	2	yes	—
472	#388	C₂²×C₁₃	1	2	yes	—
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#388	C₂²×C₁₃	1	2	yes	—
476	#388	C₂²×C₁₃	1	2	yes	—
477	#388	C₂²×C₁₃	1	2	yes	—
478	#388	C₂²×C₁₃	1	2	yes	complemented
479	#388	C₂²×C₁₃	1	2	yes	complemented
480	#387	C₂²×C₁₃	1	2	yes	complemented
481	#387	C₂²×C₁₃	1	2	yes	complemented
482	#387	C₂²×C₁₃	1	2	yes	complemented
483	#387	C₂²×C₁₃	1	2	yes	complemented
484	#387	C₂²×C₁₃	1	2	yes	complemented
485	#387	C₂²×C₁₃	1	2	yes	complemented
486	#387	C₂²×C₁₃	1	2	yes	complemented
487	#386	C₂²×C₁₃	1	2	yes	—
488	#386	C₂²×C₁₃	1	2	yes	—
489	#386	C₂²×C₁₃	1	2	yes	—
490	#386	C₂²×C₁₃	1	2	yes	—
491	#386	C₂²×C₁₃	1	1	yes	characteristic
492	#386	C₂²×C₁₃	1	1	yes	characteristic
493	#386	C₂²×C₁₃	1	2	yes	—
494	#386	C₂²×C₁₃	1	2	yes	complemented
495	#385	C₂²×C₁₃	1	2	yes	complemented
496	#385	C₂²×C₁₃	1	2	yes	complemented
497	#385	C₂²×C₁₃	1	2	yes	complemented
498	#385	C₂²×C₁₃	1	2	yes	complemented
499	#383	C₂²×C₁₃	1	2	yes	complemented
500	#381	C₂²×C₁₃	1	2	yes	—
501	#381	C₂²×C₁₃	1	1	yes	characteristic
502	#380	C₂²×C₁₃	1	2	yes	—
503	#379	C₂²×C₁₃	1	2	yes	—
504	#379	C₂²×C₁₃	1	2	yes	—
505	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
506	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
507	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
509	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	2	4	no	—
516	C₂²×C₁₃	—	4	1	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	2	no	—
521	C₂²×C₁₃	—	4	1	no	—
522	C₂²×C₁₃	—	4	2	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	8	8	no	—
534	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
535	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×C₁₃	#585	1	2	yes	—
538	C₂²×C₁₃	#585	1	2	yes	—
539	C₄×C₁₃	—	2	2	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	2	no	—
548	C₄×C₁₃	—	4	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×#41	—	2	4	no	—
556	C₂×#41	—	4	2	no	—
557	C₂×#41	—	4	2	no	—
558	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
561	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
565	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
570	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	—	4	2	no	—
572	#126	—	4	4	no	—
573	#124	—	4	4	no	—
574	#124	—	4	2	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	#120	—	4	2	no	—
577	#120	—	4	2	no	—
578	#117	—	4	2	no	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄²	—	4	2	no	—
620	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	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	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	2	yes	—
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	C₂×C₁₃	—	4	2	no	—
655	C₂×C₁₃	—	4	2	no	—
656	C₂×C₁₃	—	8	1	no	—
657	C₂×C₁₃	—	8	2	no	—
658	C₂×C₁₃	#3455	1	1	yes	characteristic
659	C₂×C₁₃	#3490	1	1	yes	characteristic
660	C₂×C₁₃	#3510	1	1	yes	characteristic
661	C₂×C₁₃	#3540	1	2	yes	—
662	C₂×C₁₃	#3560	1	2	yes	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	1	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
669	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
672	#41	—	4	16	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	4	1	no	—
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×Q₈	—	4	1	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	4	1	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	C₁₃×#41	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	4	1	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	1	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	4	1	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	1	no	—
773	C₄²	—	4	2	no	—
774	C₁₃	#36816	1	1	yes	characteristic, direct product factor, Sylow
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	8	2	no	—
797	C₂³	—	8	2	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	4	no	—
800	C₂³	C₂×C₁₃×#41	1	2	yes	—
801	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
802	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
803	Q₈	—	4	4	no	—
804	Q₈	—	8	2	no	—
805	Q₈	—	8	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	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	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
859	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
860	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
885	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₁₃×#585	1	2	yes	—
888	C₂²	C₁₃×#585	1	2	yes	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₂	—	4	2	no	—
905	C₂	—	4	2	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	1	no	—
908	C₂	C₁₃×#3455	1	1	yes	characteristic
909	C₂	C₁₃×#3490	1	1	yes	characteristic
910	C₂	C₁₃×#3510	1	1	yes	characteristic
911	C₂	C₁₃×#3540	1	2	yes	—
912	C₂	C₁₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₁₃×#2404	C₂
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. C₁₃×#2852	C₂	semidirect
2. C₁₃×#2797	C₂	semidirect
3. C₁₃×#2759	C₂	semidirect
4. C₁₃×#2746	C₂	semidirect
5. C₁₃×#2737	C₂	semidirect
6. C₁₃×#2716	C₂	semidirect
7. C₁₃×#2712	C₂	semidirect
8. C₁₃×#2685	C₂	semidirect
9. C₁₃×#2684	C₂	semidirect
10. C₁₃×#2653	C₂	semidirect
11. C₁₃×#2607	C₂	semidirect
12. C₁₃×#2597	C₂	semidirect
13. C₁₃×#2561	C₂	semidirect
14. C₁₃×#2474	C₂	semidirect
15. C₁₃×#2432	C₂	semidirect
17. C₁₃×#2332	C₂	semidirect
18. C₁₃×#2312	C₂	semidirect
19. C₁₃×#2297	C₂	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
28. C₂×C₁₃×#117	C₂²	semidirect
30. C₂²×C₄²×C₁₃	C₂²	semidirect
31. C₁₃×#401	C₂²	semidirect
32. C₁₃×#400	C₂²	semidirect
34. C₁₃×#398	C₂²	semidirect
38. C₁₃×#397	C₂²	semidirect
39. C₁₃×#397	C₂²	semidirect
40. C₁₃×#397	C₂²	semidirect
42. C₁₃×#395	C₂²	semidirect
53. C₁₃×#393	C₂²	semidirect
55. C₁₃×#391	C₂²	semidirect
56. C₁₃×#391	C₂²	semidirect
57. C₁₃×#391	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
59. C₁₃×#391	C₂²	semidirect
62. C₁₃×#390	C₂²	semidirect
74. C₁₃×#388	C₂²	semidirect
75. C₁₃×#388	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
79. C₁₃×#387	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
81. C₁₃×#387	C₂²	semidirect
82. C₁₃×#387	C₂²	semidirect
90. C₁₃×#386	C₂²	semidirect
91. C₁₃×#385	C₂²	semidirect
92. C₁₃×#385	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#385	C₂²	semidirect
95. C₁₃×#383	C₂²	semidirect
101. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
105. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
106. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
207. #36816	C₁₃	direct (N × H)
319. #2852	C₂×C₁₃	semidirect
320. #2797	C₂×C₁₃	semidirect
321. #2759	C₂×C₁₃	semidirect
322. #2746	C₂×C₁₃	semidirect
323. #2737	C₂×C₁₃	semidirect
324. #2716	C₂×C₁₃	semidirect
325. #2712	C₂×C₁₃	semidirect
326. #2685	C₂×C₁₃	semidirect
327. #2684	C₂×C₁₃	semidirect
328. #2653	C₂×C₁₃	semidirect
329. #2607	C₂×C₁₃	semidirect
330. #2597	C₂×C₁₃	semidirect
331. #2561	C₂×C₁₃	semidirect
332. #2474	C₂×C₁₃	semidirect
333. #2432	C₂×C₁₃	semidirect
335. #2332	C₂×C₁₃	semidirect
336. #2312	C₂×C₁₃	semidirect
337. #2297	C₂×C₁₃	semidirect
425. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
428. C₂×#124	C₂²×C₁₃	semidirect
432. C₂×#117	C₂²×C₁₃	semidirect
434. C₂²×C₄²	C₂²×C₁₃	semidirect
435. #401	C₂²×C₁₃	semidirect
436. #400	C₂²×C₁₃	semidirect
438. #398	C₂²×C₁₃	semidirect
442. #397	C₂²×C₁₃	semidirect
443. #397	C₂²×C₁₃	semidirect
444. #397	C₂²×C₁₃	semidirect
446. #395	C₂²×C₁₃	semidirect
457. #393	C₂²×C₁₃	semidirect
459. #391	C₂²×C₁₃	semidirect
460. #391	C₂²×C₁₃	semidirect
461. #391	C₂²×C₁₃	semidirect
462. #391	C₂²×C₁₃	semidirect
463. #391	C₂²×C₁₃	semidirect
466. #390	C₂²×C₁₃	semidirect
478. #388	C₂²×C₁₃	semidirect
479. #388	C₂²×C₁₃	semidirect
480. #387	C₂²×C₁₃	semidirect
481. #387	C₂²×C₁₃	semidirect
482. #387	C₂²×C₁₃	semidirect
483. #387	C₂²×C₁₃	semidirect
484. #387	C₂²×C₁₃	semidirect
485. #387	C₂²×C₁₃	semidirect
486. #387	C₂²×C₁₃	semidirect
494. #386	C₂²×C₁₃	semidirect
495. #385	C₂²×C₁₃	semidirect
496. #385	C₂²×C₁₃	semidirect
497. #385	C₂²×C₁₃	semidirect
498. #385	C₂²×C₁₃	semidirect
499. #383	C₂²×C₁₃	semidirect
505. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
509. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
510. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
774. C₁₃	#36816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2852	2
C₁₃×#2797	2
C₁₃×#2759	2
C₁₃×#2746	2
C₁₃×#2737	2
C₁₃×#2716	2
C₁₃×#2712	2
C₁₃×#2685	2
C₁₃×#2684	2
C₁₃×#2653	2
C₁₃×#2607	2
C₁₃×#2597	2
C₁₃×#2561	2
C₁₃×#2474	2
C₁₃×#2432	2
C₁₃×#2404	2
C₁₃×#2332	2
C₁₃×#2312	2
C₁₃×#2297	2
#36816	13

Subgroups — C13×#36816 #15723155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36816 #15723155