Subgroups — C₁₃×#35022 #15721361

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 948 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×#2849	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2573	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2572	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2553	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2516	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2515	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2458	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2457	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#120	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#400	C₂²	1	2	yes	complemented
37	C₁₃×#399	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	complemented
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#397	C₂²	1	2	yes	—
41	C₁₃×#397	C₂²	1	2	yes	complemented
42	C₁₃×#396	C₂²	1	2	yes	—
43	C₁₃×#396	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	complemented
47	C₁₃×#393	C₂²	1	2	yes	—
48	C₁₃×#393	C₂²	1	2	yes	complemented
49	C₁₃×#392	C₂²	1	2	yes	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#390	C₂²	1	2	yes	—
52	C₁₃×#390	C₂²	1	2	yes	—
53	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
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	complemented
61	C₁₃×#388	C₂²	1	2	yes	complemented
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×#388	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×#386	C₂²	1	2	yes	—
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#383	C₂²	1	2	yes	complemented
87	C₁₃×#383	C₂²	1	2	yes	complemented
88	C₁₃×#382	C₂²	1	2	yes	complemented
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#381	C₂²	1	2	yes	complemented
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	1	yes	characteristic
94	C₁₃×#380	C₂²	1	2	yes	complemented
95	C₁₃×#379	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	—	2	4	no	—
114	C₂³×C₄×C₁₃	—	4	2	no	—
115	C₂³×C₄×C₁₃	—	4	2	no	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#126	—	4	4	no	—
126	C₁₃×#123	—	4	4	no	—
127	C₁₃×#123	—	4	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#120	—	2	8	no	—
131	C₄×Q₈×C₁₃	—	4	2	no	—
132	C₄×D₄×C₁₃	—	2	8	no	—
133	C₄×D₄×C₁₃	—	4	2	no	—
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	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
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	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	—	4	2	no	—
176	C₂×C₄²×C₁₃	—	4	2	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	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	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	#35022	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂⁴×C₁₃	—	2	2	no	—
212	C₂⁴×C₁₃	—	2	2	no	—
213	C₂⁴×C₁₃	—	4	1	no	—
214	C₂⁴×C₁₃	—	4	1	no	—
215	C₂⁴×C₁₃	—	4	1	no	—
216	C₂⁴×C₁₃	—	4	1	no	—
217	C₂⁴×C₁₃	#41	1	4	yes	—
218	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
220	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	4	1	no	—
223	C₂×Q₈×C₁₃	—	4	1	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	2	4	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	4	1	no	—
231	C₂×D₄×C₁₃	—	4	1	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	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	4	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₃	—	2	4	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	4	1	no	—
248	C₂²×C₄×C₁₃	—	4	1	no	—
249	C₂²×C₄×C₁₃	—	4	1	no	—
250	C₂²×C₄×C₁₃	—	4	1	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	1	no	—
255	C₂²×C₄×C₁₃	—	4	1	no	—
256	C₂²×C₄×C₁₃	—	4	1	no	—
257	C₂²×C₄×C₁₃	—	4	1	no	—
258	C₂²×C₄×C₁₃	—	4	1	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	16	no	—
262	C₂²×C₄×C₁₃	#41	1	4	yes	—
263	C₂²×C₄×C₁₃	#41	1	4	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	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	4	1	no	—
287	C₁₃×C₄⋊C₄	—	4	1	no	—
288	C₁₃×C₄⋊C₄	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	4	2	no	—
290	C₁₃×C₄⋊C₄	—	4	1	no	—
291	C₁₃×C₄⋊C₄	—	4	1	no	—
292	C₁₃×C₄⋊C₄	—	4	2	no	—
293	C₁₃×C₄⋊C₄	—	4	2	no	—
294	C₁₃×C₄⋊C₄	—	4	2	no	—
295	C₁₃×C₄⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₄²×C₁₃	—	2	4	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	4	1	no	—
324	C₄²×C₁₃	—	4	1	no	—
325	C₄²×C₁₃	—	4	2	no	—
326	C₄²×C₁₃	—	4	2	no	—
327	C₄²×C₁₃	—	4	2	no	—
328	#2852	C₂×C₁₃	1	2	yes	complemented
329	#2849	C₂×C₁₃	1	2	yes	complemented
330	#2646	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#2639	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2626	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#2617	C₂×C₁₃	1	1	yes	characteristic
334	#2573	C₂×C₁₃	1	2	yes	complemented
335	#2572	C₂×C₁₃	1	2	yes	complemented
336	#2554	C₂×C₁₃	1	2	yes	complemented
337	#2553	C₂×C₁₃	1	2	yes	complemented
338	#2516	C₂×C₁₃	1	2	yes	complemented
339	#2515	C₂×C₁₃	1	2	yes	complemented
340	#2458	C₂×C₁₃	1	2	yes	complemented
341	#2457	C₂×C₁₃	1	2	yes	complemented
342	#2321	C₂×C₁₃	1	2	yes	complemented
343	#2318	C₂×C₁₃	1	2	yes	complemented
344	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
345	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
346	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
347	C₂³×C₁₃	—	2	1	no	—
348	C₂³×C₁₃	—	2	1	no	—
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	8	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	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	4	4	no	—
366	C₂³×C₁₃	—	4	4	no	—
367	C₂³×C₁₃	—	4	4	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	4	4	no	—
371	C₂³×C₁₃	C₂×#41	1	4	yes	—
372	C₂³×C₁₃	C₂×#41	1	2	yes	—
373	C₂³×C₁₃	C₂×#41	1	2	yes	—
374	C₂³×C₁₃	C₂×#41	1	2	yes	—
375	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
376	Q₈×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	4	8	no	—
379	D₄×C₁₃	—	8	4	no	—
380	D₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	—	2	8	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	4	no	—
426	C₂×C₄×C₁₃	—	4	8	no	—
427	C₂×C₄×C₁₃	—	4	8	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	4	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	8	4	no	—
432	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
433	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
438	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
440	C₂×#123	C₂²×C₁₃	1	2	yes	—
441	C₂×#123	C₂²×C₁₃	1	2	yes	—
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#120	C₂²×C₁₃	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
451	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
452	#400	C₂²×C₁₃	1	2	yes	complemented
453	#400	C₂²×C₁₃	1	2	yes	complemented
454	#400	C₂²×C₁₃	1	2	yes	complemented
455	#399	C₂²×C₁₃	1	2	yes	—
456	#398	C₂²×C₁₃	1	2	yes	complemented
457	#398	C₂²×C₁₃	1	2	yes	complemented
458	#397	C₂²×C₁₃	1	2	yes	—
459	#397	C₂²×C₁₃	1	2	yes	complemented
460	#396	C₂²×C₁₃	1	2	yes	—
461	#396	C₂²×C₁₃	1	2	yes	—
462	#394	C₂²×C₁₃	1	2	yes	—
463	#394	C₂²×C₁₃	1	2	yes	—
464	#394	C₂²×C₁₃	1	2	yes	complemented
465	#393	C₂²×C₁₃	1	2	yes	—
466	#393	C₂²×C₁₃	1	2	yes	complemented
467	#392	C₂²×C₁₃	1	2	yes	—
468	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#390	C₂²×C₁₃	1	2	yes	—
470	#390	C₂²×C₁₃	1	2	yes	—
471	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
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	#388	C₂²×C₁₃	1	2	yes	complemented
481	#388	C₂²×C₁₃	1	2	yes	complemented
482	#388	C₂²×C₁₃	1	2	yes	complemented
483	#388	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	#387	C₂²×C₁₃	1	2	yes	complemented
488	#387	C₂²×C₁₃	1	2	yes	complemented
489	#387	C₂²×C₁₃	1	2	yes	complemented
490	#386	C₂²×C₁₃	1	2	yes	—
491	#386	C₂²×C₁₃	1	2	yes	—
492	#386	C₂²×C₁₃	1	2	yes	—
493	#386	C₂²×C₁₃	1	2	yes	—
494	#386	C₂²×C₁₃	1	2	yes	—
495	#386	C₂²×C₁₃	1	2	yes	—
496	#386	C₂²×C₁₃	1	2	yes	—
497	#386	C₂²×C₁₃	1	2	yes	—
498	#385	C₂²×C₁₃	1	2	yes	—
499	#385	C₂²×C₁₃	1	2	yes	—
500	#385	C₂²×C₁₃	1	2	yes	—
501	#385	C₂²×C₁₃	1	2	yes	—
502	#385	C₂²×C₁₃	1	2	yes	—
503	#385	C₂²×C₁₃	1	2	yes	—
504	#383	C₂²×C₁₃	1	2	yes	complemented
505	#383	C₂²×C₁₃	1	2	yes	complemented
506	#382	C₂²×C₁₃	1	2	yes	complemented
507	#381	C₂²×C₁₃	1	2	yes	—
508	#381	C₂²×C₁₃	1	2	yes	—
509	#381	C₂²×C₁₃	1	2	yes	complemented
510	#380	C₂²×C₁₃	1	1	yes	characteristic
511	#380	C₂²×C₁₃	1	1	yes	characteristic
512	#380	C₂²×C₁₃	1	2	yes	complemented
513	#379	C₂²×C₁₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
523	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
524	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
525	C₂²×C₁₃	—	2	2	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	2	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	2	2	no	—
530	C₂²×C₁₃	—	2	2	no	—
531	C₂²×C₁₃	—	2	4	no	—
532	C₂²×C₁₃	—	2	4	no	—
533	C₂²×C₁₃	—	2	4	no	—
534	C₂²×C₁₃	—	4	16	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	2	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	2	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	2	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	4	2	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	#529	1	4	yes	—
547	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
548	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
549	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
550	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂²×C₁₃	#585	1	1	yes	characteristic
553	C₂²×C₁₃	#585	1	1	yes	characteristic
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	2	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	2	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	—	4	2	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	2	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₄×C₁₃	—	4	2	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
575	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
576	C₂³×C₄	—	2	4	no	—
577	C₂³×C₄	—	4	2	no	—
578	C₂³×C₄	—	4	2	no	—
579	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
581	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
582	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
585	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
588	#126	—	4	4	no	—
589	#123	—	4	4	no	—
590	#123	—	4	4	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	#121	—	2	4	no	—
593	#120	—	2	8	no	—
594	C₄×Q₈	—	4	2	no	—
595	C₄×D₄	—	2	8	no	—
596	C₄×D₄	—	4	2	no	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	—	2	4	no	—
614	C₂×C₂²⋊C₄	—	2	4	no	—
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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	—	4	2	no	—
639	C₂×C₄²	—	4	2	no	—
640	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄²	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	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	2	yes	—
661	#95	C₂³×C₁₃	1	2	yes	—
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	C₂×C₁₃	—	2	4	no	—
674	C₂×C₁₃	—	4	4	no	—
675	C₂×C₁₃	—	8	2	no	—
676	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
677	C₂×C₁₃	#3459	1	1	yes	characteristic
678	C₂×C₁₃	#3460	1	1	yes	characteristic
679	C₂×C₁₃	#3490	1	1	yes	characteristic
680	C₂×C₁₃	#3491	1	1	yes	characteristic
681	C₂×C₁₃	#3505	1	1	yes	characteristic
682	C₂×C₁₃	#3506	1	1	yes	characteristic
683	C₂⁴	—	2	2	no	—
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	4	1	no	—
686	C₂⁴	—	4	1	no	—
687	C₂⁴	—	4	1	no	—
688	C₂⁴	—	4	1	no	—
689	C₂⁴	C₁₃×#41	1	4	yes	—
690	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
691	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
692	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	4	1	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	16	no	—
734	C₂²×C₄	C₁₃×#41	1	4	yes	—
735	C₂²×C₄	C₁₃×#41	1	4	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	4	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₁₃	#35022	1	1	yes	characteristic, direct product factor, Sylow
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	8	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	—	4	4	no	—
823	C₂³	—	4	4	no	—
824	C₂³	—	4	4	no	—
825	C₂³	C₂×C₁₃×#41	1	4	yes	—
826	C₂³	C₂×C₁₃×#41	1	2	yes	—
827	C₂³	C₂×C₁₃×#41	1	2	yes	—
828	C₂³	C₂×C₁₃×#41	1	2	yes	—
829	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
830	Q₈	—	4	4	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	8	no	—
833	D₄	—	8	4	no	—
834	D₄	—	8	4	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	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	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	8	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	8	4	no	—
886	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
887	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
888	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
889	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
890	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
891	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	4	16	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	C₁₃×#529	1	4	yes	—
914	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
915	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
916	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
917	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
918	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
919	C₂²	C₁₃×#585	1	1	yes	characteristic
920	C₂²	C₁₃×#585	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₂	—	2	4	no	—
938	C₂	—	4	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
941	C₂	C₁₃×#3459	1	1	yes	characteristic
942	C₂	C₁₃×#3460	1	1	yes	characteristic
943	C₂	C₁₃×#3490	1	1	yes	characteristic
944	C₂	C₁₃×#3491	1	1	yes	characteristic
945	C₂	C₁₃×#3505	1	1	yes	characteristic
946	C₂	C₁₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₁₃×#2617	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×#2849	C₂	semidirect
3. C₁₃×#2646	C₂	semidirect
4. C₁₃×#2639	C₂	semidirect
5. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2573	C₂	semidirect
8. C₁₃×#2572	C₂	semidirect
9. C₁₃×#2554	C₂	semidirect
10. C₁₃×#2553	C₂	semidirect
11. C₁₃×#2516	C₂	semidirect
12. C₁₃×#2515	C₂	semidirect
13. C₁₃×#2458	C₂	semidirect
14. C₁₃×#2457	C₂	semidirect
15. C₁₃×#2321	C₂	semidirect
16. C₁₃×#2318	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
21. C₂×C₁₃×#126	C₂²	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#400	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
41. C₁₃×#397	C₂²	semidirect
46. C₁₃×#394	C₂²	semidirect
48. C₁₃×#393	C₂²	semidirect
50. C₁₃×#391	C₂²	semidirect
53. C₁₃×#390	C₂²	semidirect
54. C₁₃×#389	C₂²	semidirect
55. C₁₃×#389	C₂²	semidirect
60. C₁₃×#388	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#388	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
86. C₁₃×#383	C₂²	semidirect
87. C₁₃×#383	C₂²	semidirect
88. C₁₃×#382	C₂²	semidirect
91. C₁₃×#381	C₂²	semidirect
94. C₁₃×#380	C₂²	semidirect
96. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
97. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
98. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
104. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
210. #35022	C₁₃	direct (N × H)
328. #2852	C₂×C₁₃	semidirect
329. #2849	C₂×C₁₃	semidirect
330. #2646	C₂×C₁₃	semidirect
331. #2639	C₂×C₁₃	semidirect
332. #2626	C₂×C₁₃	semidirect
334. #2573	C₂×C₁₃	semidirect
335. #2572	C₂×C₁₃	semidirect
336. #2554	C₂×C₁₃	semidirect
337. #2553	C₂×C₁₃	semidirect
338. #2516	C₂×C₁₃	semidirect
339. #2515	C₂×C₁₃	semidirect
340. #2458	C₂×C₁₃	semidirect
341. #2457	C₂×C₁₃	semidirect
342. #2321	C₂×C₁₃	semidirect
343. #2318	C₂×C₁₃	semidirect
344. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
345. C₄×#121	C₂×C₁₃	semidirect
346. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
439. C₂×#126	C₂²×C₁₃	semidirect
445. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
447. C₂×C₄×D₄	C₂²×C₁₃	semidirect
452. #400	C₂²×C₁₃	semidirect
453. #400	C₂²×C₁₃	semidirect
454. #400	C₂²×C₁₃	semidirect
456. #398	C₂²×C₁₃	semidirect
457. #398	C₂²×C₁₃	semidirect
459. #397	C₂²×C₁₃	semidirect
464. #394	C₂²×C₁₃	semidirect
466. #393	C₂²×C₁₃	semidirect
468. #391	C₂²×C₁₃	semidirect
471. #390	C₂²×C₁₃	semidirect
472. #389	C₂²×C₁₃	semidirect
473. #389	C₂²×C₁₃	semidirect
478. #388	C₂²×C₁₃	semidirect
479. #388	C₂²×C₁₃	semidirect
480. #388	C₂²×C₁₃	semidirect
481. #388	C₂²×C₁₃	semidirect
482. #388	C₂²×C₁₃	semidirect
483. #388	C₂²×C₁₃	semidirect
484. #387	C₂²×C₁₃	semidirect
485. #387	C₂²×C₁₃	semidirect
486. #387	C₂²×C₁₃	semidirect
487. #387	C₂²×C₁₃	semidirect
488. #387	C₂²×C₁₃	semidirect
489. #387	C₂²×C₁₃	semidirect
504. #383	C₂²×C₁₃	semidirect
505. #383	C₂²×C₁₃	semidirect
506. #382	C₂²×C₁₃	semidirect
509. #381	C₂²×C₁₃	semidirect
512. #380	C₂²×C₁₃	semidirect
514. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
515. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
516. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
522. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
800. C₁₃	#35022	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×#2849	2
C₁₃×#2646	2
C₁₃×#2639	2
C₁₃×#2626	2
C₁₃×#2617	2
C₁₃×#2573	2
C₁₃×#2572	2
C₁₃×#2554	2
C₁₃×#2553	2
C₁₃×#2516	2
C₁₃×#2515	2
C₁₃×#2458	2
C₁₃×#2457	2
C₁₃×#2321	2
C₁₃×#2318	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35022	13

Subgroups — C13×#35022 #15721361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35022 #15721361