Subgroups — C₁₃×#34278 #15720617

Order 3328.

2314 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#539	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2371	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2370	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2325	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#539	C₄	1	16	yes	complemented
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#125	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	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×#387	C₂²	1	2	yes	—
56	C₁₃×#387	C₂²	1	2	yes	—
57	C₁₃×#387	C₂²	1	2	yes	—
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	2	yes	—
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#386	C₂²	1	2	yes	—
71	C₁₃×#386	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	2	yes	—
73	C₁₃×#385	C₂²	1	2	yes	—
74	C₁₃×#385	C₂²	1	2	yes	—
75	C₁₃×#385	C₂²	1	2	yes	—
76	C₁₃×#385	C₂²	1	2	yes	—
77	C₁₃×#381	C₂²	1	2	yes	—
78	C₁₃×#380	C₂²	1	1	yes	characteristic
79	C₁₃×#380	C₂²	1	1	yes	characteristic
80	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
83	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
84	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
85	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
86	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	2	yes	—
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#95	C₂²	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#126	C₂×C₄	1	16	yes	complemented
122	C₁₃×#125	C₂×C₄	1	16	yes	complemented
123	C₁₃×#123	C₂×C₄	1	16	yes	complemented
124	C₁₃×#123	C₂×C₄	1	16	yes	complemented
125	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
126	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
127	C₁₃×#121	C₂×C₄	1	8	yes	—
128	C₄×Q₈×C₁₃	—	4	2	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	—	2	8	no	—
131	C₄×D₄×C₁₃	—	4	2	no	—
132	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
133	C₁₃×#117	—	4	4	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
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	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	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊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×C₄²×C₁₃	—	2	4	no	—
170	C₂×C₄²×C₁₃	—	4	2	no	—
171	C₂×C₄²×C₁₃	—	4	2	no	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	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	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	#34278	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₁₃	—	4	1	no	—
217	C₂×Q₈×C₁₃	—	4	1	no	—
218	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	4	no	—
221	C₂×D₄×C₁₃	—	4	1	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
224	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
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	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	4	1	no	—
234	C₂²×C₄×C₁₃	—	4	1	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	1	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	1	no	—
241	C₂²×C₄×C₁₃	—	4	1	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	1	no	—
244	C₂²×C₄×C₁₃	—	4	1	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
253	C₂²×C₄×C₁₃	#41	1	4	yes	—
254	C₂²×C₄×C₁₃	#41	1	4	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	1	no	—
280	C₁₃×C₄⋊C₄	—	4	1	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	1	no	—
283	C₁₃×C₄⋊C₄	—	4	1	no	—
284	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
285	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
286	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
287	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
288	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
289	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
290	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
291	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
301	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
302	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
303	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
304	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
305	C₄²×C₁₃	—	2	4	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	4	no	—
308	C₄²×C₁₃	—	2	4	no	—
309	C₄²×C₁₃	—	2	4	no	—
310	C₄²×C₁₃	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	4	1	no	—
313	C₄²×C₁₃	—	4	2	no	—
314	C₄²×C₁₃	—	4	1	no	—
315	C₄²×C₁₃	—	4	2	no	—
316	C₄²×C₁₃	—	4	2	no	—
317	C₄²×C₁₃	—	4	2	no	—
318	C₄²×C₁₃	—	4	2	no	—
319	C₄²×C₁₃	—	4	2	no	—
320	C₄²×C₁₃	—	4	2	no	—
321	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
322	C₂×#539	C₂×C₁₃	1	1	yes	characteristic
323	#2374	C₂×C₁₃	1	2	yes	complemented
324	#2373	C₂×C₁₃	1	2	yes	complemented
325	#2373	C₂×C₁₃	1	2	yes	complemented
326	#2371	C₂×C₁₃	1	2	yes	complemented
327	#2370	C₂×C₁₃	1	2	yes	complemented
328	#2368	C₂×C₁₃	1	2	yes	complemented
329	#2362	C₂×C₁₃	1	2	yes	complemented
330	#2359	C₂×C₁₃	1	2	yes	complemented
331	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2325	C₂×C₁₃	1	1	yes	characteristic
333	#2322	C₂×C₁₃	1	2	yes	complemented
334	#2313	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₄×#123	C₂×C₁₃	1	2	yes	complemented
337	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
338	#2290	C₂×C₁₃	1	2	yes	complemented
339	#2275	C₂×C₁₃	1	2	yes	complemented
340	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	1	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
352	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
353	C₂³×C₁₃	C₂×#41	1	2	yes	—
354	C₂³×C₁₃	C₂×#41	1	2	yes	—
355	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
356	Q₈×C₁₃	—	4	4	no	—
357	D₄×C₁₃	—	2	16	no	—
358	D₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	2	8	no	—
360	C₂×C₄×C₁₃	—	2	8	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	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	1	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	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	1	no	—
376	C₂×C₄×C₁₃	—	2	2	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	1	no	—
383	C₂×C₄×C₁₃	—	2	1	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	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	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	8	4	no	—
407	C₂×C₄×C₁₃	—	8	4	no	—
408	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
410	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
412	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
416	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
418	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
420	#539	C₄×C₁₃	1	16	yes	complemented
421	C₂×#126	C₂²×C₁₃	1	2	yes	—
422	C₂×#125	C₂²×C₁₃	1	2	yes	—
423	C₂×#123	C₂²×C₁₃	1	2	yes	—
424	C₂×#123	C₂²×C₁₃	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
427	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
433	C₂×#117	C₂²×C₁₃	1	2	yes	—
434	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
439	#391	C₂²×C₁₃	1	2	yes	—
440	#391	C₂²×C₁₃	1	1	yes	characteristic
441	#390	C₂²×C₁₃	1	1	yes	characteristic
442	#389	C₂²×C₁₃	1	2	yes	—
443	#389	C₂²×C₁₃	1	2	yes	—
444	#389	C₂²×C₁₃	1	2	yes	—
445	#389	C₂²×C₁₃	1	1	yes	characteristic
446	#389	C₂²×C₁₃	1	1	yes	characteristic
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	—
453	#388	C₂²×C₁₃	1	2	yes	—
454	#388	C₂²×C₁₃	1	2	yes	—
455	#387	C₂²×C₁₃	1	2	yes	—
456	#387	C₂²×C₁₃	1	2	yes	—
457	#387	C₂²×C₁₃	1	2	yes	—
458	#387	C₂²×C₁₃	1	2	yes	—
459	#387	C₂²×C₁₃	1	2	yes	—
460	#387	C₂²×C₁₃	1	2	yes	—
461	#387	C₂²×C₁₃	1	2	yes	—
462	#387	C₂²×C₁₃	1	2	yes	—
463	#387	C₂²×C₁₃	1	2	yes	—
464	#387	C₂²×C₁₃	1	2	yes	—
465	#387	C₂²×C₁₃	1	2	yes	—
466	#387	C₂²×C₁₃	1	2	yes	—
467	#387	C₂²×C₁₃	1	2	yes	—
468	#387	C₂²×C₁₃	1	2	yes	—
469	#386	C₂²×C₁₃	1	2	yes	—
470	#386	C₂²×C₁₃	1	2	yes	—
471	#386	C₂²×C₁₃	1	2	yes	—
472	#385	C₂²×C₁₃	1	2	yes	—
473	#385	C₂²×C₁₃	1	2	yes	—
474	#385	C₂²×C₁₃	1	2	yes	—
475	#385	C₂²×C₁₃	1	2	yes	—
476	#385	C₂²×C₁₃	1	2	yes	—
477	#381	C₂²×C₁₃	1	2	yes	—
478	#380	C₂²×C₁₃	1	1	yes	characteristic
479	#380	C₂²×C₁₃	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
493	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
503	#376	C₂²×C₁₃	1	2	yes	—
504	#376	C₂²×C₁₃	1	2	yes	—
505	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
506	C₂×#95	C₂²×C₁₃	1	2	yes	—
507	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	2	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	4	no	—
515	C₂²×C₁₃	—	2	4	no	—
516	C₂²×C₁₃	—	2	4	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	2	no	—
521	C₂²×C₁₃	C₄×#41	1	4	yes	—
522	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
523	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
524	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
525	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂²×C₁₃	#585	1	1	yes	characteristic
528	C₂²×C₁₃	#585	1	1	yes	characteristic
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	4	no	—
531	C₄×C₁₃	—	2	4	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	4	no	—
535	C₄×C₁₃	—	2	4	no	—
536	C₄×C₁₃	—	2	4	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	2	no	—
539	C₄×C₁₃	—	2	2	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
548	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
557	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
559	#126	C₂×C₄×C₁₃	1	16	yes	complemented
560	#125	C₂×C₄×C₁₃	1	16	yes	complemented
561	#123	C₂×C₄×C₁₃	1	16	yes	complemented
562	#123	C₂×C₄×C₁₃	1	16	yes	complemented
563	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
564	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
565	#121	C₂×C₄×C₁₃	1	8	yes	—
566	C₄×Q₈	—	4	2	no	—
567	C₄×D₄	—	2	8	no	—
568	C₄×D₄	—	2	8	no	—
569	C₄×D₄	—	4	2	no	—
570	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
571	#117	—	4	4	no	—
572	C₂×C₄⋊C₄	—	2	4	no	—
573	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊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	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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×C₄²	—	2	4	no	—
608	C₂×C₄²	—	4	2	no	—
609	C₂×C₄²	—	4	2	no	—
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	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	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	#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	C₂×C₁₃	—	2	4	no	—
652	C₂×C₁₃	—	4	4	no	—
653	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
654	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
656	C₂×C₁₃	#3491	1	1	yes	characteristic
657	C₂×C₁₃	#3492	1	1	yes	characteristic
658	C₂×C₁₃	#3505	1	1	yes	characteristic
659	C₂×C₁₃	#3507	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
661	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₂×Q₈	—	4	1	no	—
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	4	1	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
670	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
696	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
697	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
698	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
699	C₂²×C₄	C₁₃×#41	1	4	yes	—
700	C₂²×C₄	C₁₃×#41	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
731	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
732	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
733	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
734	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
735	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
736	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
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	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
747	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
748	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
749	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
750	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	2	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
768	C₁₃	#34278	1	1	yes	characteristic, direct product factor, Sylow
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
780	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
781	C₂³	C₂×C₁₃×#41	1	2	yes	—
782	C₂³	C₂×C₁₃×#41	1	2	yes	—
783	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
784	Q₈	—	4	4	no	—
785	D₄	—	2	16	no	—
786	D₄	—	4	4	no	—
787	C₂×C₄	—	2	8	no	—
788	C₂×C₄	—	2	8	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	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	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
837	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
838	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
839	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
840	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
841	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
843	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
844	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
845	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
846	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
847	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	C₄×C₁₃×#41	1	4	yes	—
862	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
863	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
864	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
865	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
867	C₂²	C₁₃×#585	1	1	yes	characteristic
868	C₂²	C₁₃×#585	1	1	yes	characteristic
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	4	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₂	—	2	4	no	—
887	C₂	—	4	4	no	—
888	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
889	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
891	C₂	C₁₃×#3491	1	1	yes	characteristic
892	C₂	C₁₃×#3492	1	1	yes	characteristic
893	C₂	C₁₃×#3505	1	1	yes	characteristic
894	C₂	C₁₃×#3507	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	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×#2374	C₂	semidirect
3. C₁₃×#2373	C₂	semidirect
4. C₁₃×#2373	C₂	semidirect
5. C₁₃×#2371	C₂	semidirect
6. C₁₃×#2370	C₂	semidirect
7. C₁₃×#2368	C₂	semidirect
8. C₁₃×#2362	C₂	semidirect
9. C₁₃×#2359	C₂	semidirect
10. C₁₃×#2329	C₂	semidirect
12. C₁₃×#2322	C₂	semidirect
13. C₁₃×#2313	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₁₃×#123	C₂	semidirect
17. C₁₃×#2290	C₂	semidirect
18. C₁₃×#2275	C₂	semidirect
19. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
20. C₁₃×#539	C₄	semidirect
121. C₁₃×#126	C₂×C₄	semidirect
122. C₁₃×#125	C₂×C₄	semidirect
123. C₁₃×#123	C₂×C₄	semidirect
124. C₁₃×#123	C₂×C₄	semidirect
125. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
126. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₄×D₄×C₁₃	C₂×C₄	semidirect
135. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
213. #34278	C₁₃	direct (N × H)
323. #2374	C₂×C₁₃	semidirect
324. #2373	C₂×C₁₃	semidirect
325. #2373	C₂×C₁₃	semidirect
326. #2371	C₂×C₁₃	semidirect
327. #2370	C₂×C₁₃	semidirect
328. #2368	C₂×C₁₃	semidirect
329. #2362	C₂×C₁₃	semidirect
330. #2359	C₂×C₁₃	semidirect
331. #2329	C₂×C₁₃	semidirect
333. #2322	C₂×C₁₃	semidirect
334. #2313	C₂×C₁₃	semidirect
335. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
336. C₄×#123	C₂×C₁₃	semidirect
338. #2290	C₂×C₁₃	semidirect
339. #2275	C₂×C₁₃	semidirect
340. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
420. #539	C₄×C₁₃	semidirect
559. #126	C₂×C₄×C₁₃	semidirect
560. #125	C₂×C₄×C₁₃	semidirect
561. #123	C₂×C₄×C₁₃	semidirect
562. #123	C₂×C₄×C₁₃	semidirect
563. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
564. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
570. C₄×D₄	C₂×C₄×C₁₃	semidirect
573. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
768. C₁₃	#34278	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×#539	2
C₁₃×#2374	2
C₁₃×#2373	2
C₁₃×#2371	2
C₁₃×#2370	2
C₁₃×#2368	2
C₁₃×#2362	2
C₁₃×#2359	2
C₁₃×#2329	2
C₁₃×#2325	2
C₁₃×#2322	2
C₁₃×#2313	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2290	2
C₁₃×#2275	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34278	13

Subgroups — C13×#34278 #15720617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34278 #15720617