Subgroups — C₁₃×#34429 #15720768

Order 3328.

2174 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2383	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2376	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2326	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#542	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×#123	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	2	yes	—
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	2	yes	—
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#389	C₂²	1	1	yes	characteristic
63	C₁₃×#388	C₂²	1	1	yes	characteristic
64	C₁₃×#388	C₂²	1	1	yes	characteristic
65	C₁₃×#388	C₂²	1	1	yes	characteristic
66	C₁₃×#388	C₂²	1	1	yes	characteristic
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	—
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	1	yes	characteristic
78	C₁₃×#387	C₂²	1	1	yes	characteristic
79	C₁₃×#387	C₂²	1	1	yes	characteristic
80	C₁₃×#387	C₂²	1	1	yes	characteristic
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#385	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	2	yes	—
97	C₁₃×#384	C₂²	1	1	yes	characteristic
98	C₁₃×#384	C₂²	1	1	yes	characteristic
99	C₁₃×#384	C₂²	1	2	yes	—
100	C₁₃×#383	C₂²	1	2	yes	—
101	C₁₃×#382	C₂²	1	1	yes	characteristic
102	C₁₃×#382	C₂²	1	1	yes	characteristic
103	C₁₃×#380	C₂²	1	2	yes	—
104	C₁₃×#380	C₂²	1	2	yes	—
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₁₃×#376	C₂²	1	1	yes	characteristic
121	C₁₃×#376	C₂²	1	2	yes	—
122	C₂×C₁₃×#95	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
134	C₁₃×#126	C₂×C₄	1	16	yes	complemented
135	C₁₃×#124	C₂×C₄	1	8	yes	complemented
136	C₁₃×#124	C₂×C₄	1	16	yes	complemented
137	C₁₃×#123	C₂×C₄	1	16	yes	complemented
138	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
139	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
140	C₁₃×#121	C₂×C₄	1	8	yes	—
141	C₄×Q₈×C₁₃	—	4	4	no	—
142	C₄×Q₈×C₁₃	—	4	2	no	—
143	C₄×Q₈×C₁₃	—	4	2	no	—
144	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₁₃	—	4	4	no	—
146	C₄×D₄×C₁₃	—	4	2	no	—
147	C₄×D₄×C₁₃	—	4	2	no	—
148	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
149	C₁₃×#117	—	4	4	no	—
150	C₁₃×#117	—	4	2	no	—
151	C₁₃×#117	C₂×C₄	1	8	yes	complemented
152	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₁₃×#95	C₂³	1	1	yes	characteristic
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	1	yes	characteristic
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	1	yes	characteristic
226	C₁₃×#95	C₂³	1	1	yes	characteristic
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	1	yes	characteristic
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	1	yes	characteristic
242	C₁₃×#95	C₂³	1	1	yes	characteristic
243	#34429	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
245	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	4	2	no	—
249	C₂×Q₈×C₁₃	—	4	2	no	—
250	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
251	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	—	4	2	no	—
270	C₂²×C₄×C₁₃	—	4	2	no	—
271	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	1	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	1	no	—
305	C₁₃×C₄⋊C₄	—	4	2	no	—
306	C₁₃×C₄⋊C₄	—	4	2	no	—
307	C₁₃×C₄⋊C₄	—	4	2	no	—
308	C₁₃×C₄⋊C₄	—	4	2	no	—
309	C₁₃×C₄⋊C₄	—	4	2	no	—
310	C₁₃×C₄⋊C₄	—	4	2	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	—	4	2	no	—
313	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
314	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
316	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
317	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
319	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	4	2	no	—
324	C₁₃×C₂²⋊C₄	—	4	1	no	—
325	C₁₃×C₂²⋊C₄	—	4	1	no	—
326	C₁₃×C₂²⋊C₄	—	4	2	no	—
327	C₁₃×C₂²⋊C₄	—	4	2	no	—
328	C₁₃×C₂²⋊C₄	—	4	2	no	—
329	C₁₃×C₂²⋊C₄	—	4	2	no	—
330	C₁₃×C₂²⋊C₄	—	4	2	no	—
331	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
332	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
333	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
335	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
336	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
337	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
338	C₄²×C₁₃	—	2	4	no	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	—	2	4	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	4	1	no	—
347	C₄²×C₁₃	—	4	1	no	—
348	C₄²×C₁₃	—	4	2	no	—
349	C₄²×C₁₃	—	4	2	no	—
350	C₄²×C₁₃	—	4	2	no	—
351	C₄²×C₁₃	—	4	2	no	—
352	C₄²×C₁₃	—	4	2	no	—
353	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
354	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
355	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
356	C₂×#542	C₂×C₁₃	1	1	yes	characteristic
357	#2383	C₂×C₁₃	1	2	yes	complemented
358	#2376	C₂×C₁₃	1	2	yes	complemented
359	#2373	C₂×C₁₃	1	2	yes	complemented
360	#2363	C₂×C₁₃	1	1	yes	characteristic
361	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2361	C₂×C₁₃	1	1	yes	characteristic
363	#2360	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#2359	C₂×C₁₃	1	2	yes	complemented
365	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
367	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#2337	C₂×C₁₃	1	2	yes	complemented
370	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#2329	C₂×C₁₃	1	2	yes	complemented
372	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#2326	C₂×C₁₃	1	2	yes	complemented
374	#2323	C₂×C₁₃	1	2	yes	complemented
375	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
376	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
377	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	1	no	—
381	C₂³×C₁₃	—	2	1	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	1	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	1	no	—
389	C₂³×C₁₃	—	2	1	no	—
390	C₂³×C₁₃	—	2	2	no	—
391	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
392	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
393	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
394	Q₈×C₁₃	—	2	8	no	—
395	Q₈×C₁₃	—	4	8	no	—
396	D₄×C₁₃	—	2	8	no	—
397	D₄×C₁₃	—	4	8	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	8	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	4	8	no	—
450	C₂×C₄×C₁₃	—	8	4	no	—
451	C₂×C₄×C₁₃	—	8	4	no	—
452	C₂×C₄×C₁₃	—	8	4	no	—
453	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
454	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
456	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
459	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
464	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
465	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
466	#542	C₄×C₁₃	1	16	yes	complemented
467	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#126	C₂²×C₁₃	1	2	yes	—
469	C₂×#124	C₂²×C₁₃	1	2	yes	—
470	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×#123	C₂²×C₁₃	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
476	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#117	C₂²×C₁₃	1	2	yes	—
485	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
487	#391	C₂²×C₁₃	1	2	yes	—
488	#391	C₂²×C₁₃	1	2	yes	—
489	#391	C₂²×C₁₃	1	2	yes	—
490	#391	C₂²×C₁₃	1	1	yes	characteristic
491	#391	C₂²×C₁₃	1	1	yes	characteristic
492	#390	C₂²×C₁₃	1	1	yes	characteristic
493	#390	C₂²×C₁₃	1	2	yes	—
494	#390	C₂²×C₁₃	1	1	yes	characteristic
495	#389	C₂²×C₁₃	1	1	yes	characteristic
496	#389	C₂²×C₁₃	1	1	yes	characteristic
497	#389	C₂²×C₁₃	1	2	yes	—
498	#389	C₂²×C₁₃	1	2	yes	—
499	#389	C₂²×C₁₃	1	2	yes	—
500	#389	C₂²×C₁₃	1	2	yes	—
501	#389	C₂²×C₁₃	1	2	yes	—
502	#389	C₂²×C₁₃	1	2	yes	—
503	#389	C₂²×C₁₃	1	1	yes	characteristic
504	#389	C₂²×C₁₃	1	1	yes	characteristic
505	#388	C₂²×C₁₃	1	2	yes	—
506	#388	C₂²×C₁₃	1	2	yes	—
507	#388	C₂²×C₁₃	1	2	yes	—
508	#388	C₂²×C₁₃	1	2	yes	—
509	#388	C₂²×C₁₃	1	1	yes	characteristic
510	#388	C₂²×C₁₃	1	2	yes	—
511	#388	C₂²×C₁₃	1	2	yes	—
512	#388	C₂²×C₁₃	1	2	yes	—
513	#388	C₂²×C₁₃	1	1	yes	characteristic
514	#388	C₂²×C₁₃	1	2	yes	—
515	#388	C₂²×C₁₃	1	2	yes	—
516	#388	C₂²×C₁₃	1	1	yes	characteristic
517	#388	C₂²×C₁₃	1	1	yes	characteristic
518	#388	C₂²×C₁₃	1	2	yes	—
519	#387	C₂²×C₁₃	1	1	yes	characteristic
520	#387	C₂²×C₁₃	1	2	yes	—
521	#387	C₂²×C₁₃	1	1	yes	characteristic
522	#387	C₂²×C₁₃	1	2	yes	—
523	#387	C₂²×C₁₃	1	2	yes	—
524	#387	C₂²×C₁₃	1	2	yes	—
525	#387	C₂²×C₁₃	1	2	yes	—
526	#387	C₂²×C₁₃	1	2	yes	—
527	#387	C₂²×C₁₃	1	1	yes	characteristic
528	#387	C₂²×C₁₃	1	1	yes	characteristic
529	#386	C₂²×C₁₃	1	2	yes	—
530	#386	C₂²×C₁₃	1	2	yes	—
531	#385	C₂²×C₁₃	1	2	yes	—
532	#385	C₂²×C₁₃	1	2	yes	—
533	#385	C₂²×C₁₃	1	2	yes	—
534	#385	C₂²×C₁₃	1	2	yes	—
535	#385	C₂²×C₁₃	1	2	yes	—
536	#385	C₂²×C₁₃	1	2	yes	—
537	#385	C₂²×C₁₃	1	2	yes	—
538	#385	C₂²×C₁₃	1	2	yes	—
539	#384	C₂²×C₁₃	1	1	yes	characteristic
540	#384	C₂²×C₁₃	1	1	yes	characteristic
541	#384	C₂²×C₁₃	1	2	yes	—
542	#383	C₂²×C₁₃	1	2	yes	—
543	#382	C₂²×C₁₃	1	1	yes	characteristic
544	#382	C₂²×C₁₃	1	1	yes	characteristic
545	#380	C₂²×C₁₃	1	2	yes	—
546	#380	C₂²×C₁₃	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
554	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
556	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
557	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
561	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
562	#376	C₂²×C₁₃	1	1	yes	characteristic
563	#376	C₂²×C₁₃	1	2	yes	—
564	C₂×#95	C₂²×C₁₃	1	2	yes	—
565	C₄³	C₂²×C₁₃	1	1	yes	characteristic
566	C₂²×C₁₃	—	2	2	no	—
567	C₂²×C₁₃	—	2	4	no	—
568	C₂²×C₁₃	—	2	4	no	—
569	C₂²×C₁₃	—	2	2	no	—
570	C₂²×C₁₃	—	2	2	no	—
571	C₂²×C₁₃	—	2	4	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	1	no	—
574	C₂²×C₁₃	—	4	1	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	2	no	—
577	C₂²×C₁₃	—	4	1	no	—
578	C₂²×C₁₃	—	4	1	no	—
579	C₂²×C₁₃	—	4	2	no	—
580	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
581	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
584	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
585	C₂²×C₁₃	#585	1	1	yes	characteristic
586	C₂²×C₁₃	#585	1	1	yes	characteristic
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	4	no	—
589	C₄×C₁₃	—	2	2	no	—
590	C₄×C₁₃	—	2	4	no	—
591	C₄×C₁₃	—	2	4	no	—
592	C₄×C₁₃	—	2	2	no	—
593	C₄×C₁₃	—	2	2	no	—
594	C₄×C₁₃	—	2	2	no	—
595	C₄×C₁₃	—	2	2	no	—
596	C₄×C₁₃	—	2	2	no	—
597	C₄×C₁₃	—	4	1	no	—
598	C₄×C₁₃	—	4	1	no	—
599	C₄×C₁₃	—	4	2	no	—
600	C₄×C₁₃	—	4	2	no	—
601	C₄×C₁₃	—	4	1	no	—
602	C₄×C₁₃	—	4	2	no	—
603	C₄×C₁₃	—	4	1	no	—
604	C₄×C₁₃	—	4	2	no	—
605	C₄×C₁₃	—	4	1	no	—
606	C₄×C₁₃	—	4	1	no	—
607	C₄×C₁₃	#520	1	4	yes	—
608	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
610	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
615	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
616	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
617	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
618	#126	C₂×C₄×C₁₃	1	16	yes	complemented
619	#124	C₂×C₄×C₁₃	1	8	yes	complemented
620	#124	C₂×C₄×C₁₃	1	16	yes	complemented
621	#123	C₂×C₄×C₁₃	1	16	yes	complemented
622	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
623	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
624	#121	C₂×C₄×C₁₃	1	8	yes	—
625	C₄×Q₈	—	4	4	no	—
626	C₄×Q₈	—	4	2	no	—
627	C₄×Q₈	—	4	2	no	—
628	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
629	C₄×D₄	—	4	4	no	—
630	C₄×D₄	—	4	2	no	—
631	C₄×D₄	—	4	2	no	—
632	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
633	#117	—	4	4	no	—
634	#117	—	4	2	no	—
635	#117	C₂×C₄×C₁₃	1	8	yes	complemented
636	C₂×C₄⋊C₄	—	4	2	no	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
693	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	1	yes	characteristic
700	#95	C₂³×C₁₃	1	2	yes	—
701	#95	C₂³×C₁₃	1	2	yes	—
702	#95	C₂³×C₁₃	1	2	yes	—
703	#95	C₂³×C₁₃	1	1	yes	characteristic
704	#95	C₂³×C₁₃	1	2	yes	—
705	#95	C₂³×C₁₃	1	2	yes	—
706	#95	C₂³×C₁₃	1	1	yes	characteristic
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	1	yes	characteristic
709	#95	C₂³×C₁₃	1	1	yes	characteristic
710	#95	C₂³×C₁₃	1	1	yes	characteristic
711	#95	C₂³×C₁₃	1	1	yes	characteristic
712	#95	C₂³×C₁₃	1	2	yes	—
713	#95	C₂³×C₁₃	1	1	yes	characteristic
714	#95	C₂³×C₁₃	1	2	yes	—
715	#95	C₂³×C₁₃	1	2	yes	—
716	#95	C₂³×C₁₃	1	2	yes	—
717	#95	C₂³×C₁₃	1	2	yes	—
718	#95	C₂³×C₁₃	1	1	yes	characteristic
719	#95	C₂³×C₁₃	1	1	yes	characteristic
720	#95	C₂³×C₁₃	1	1	yes	characteristic
721	#95	C₂³×C₁₃	1	2	yes	—
722	#95	C₂³×C₁₃	1	2	yes	—
723	#95	C₂³×C₁₃	1	1	yes	characteristic
724	#95	C₂³×C₁₃	1	2	yes	—
725	#95	C₂³×C₁₃	1	2	yes	—
726	#95	C₂³×C₁₃	1	2	yes	—
727	C₂×C₁₃	—	4	2	no	—
728	C₂×C₁₃	—	4	4	no	—
729	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
730	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
732	C₂×C₁₃	#3544	1	1	yes	characteristic
733	C₂×C₁₃	#3546	1	1	yes	characteristic
734	C₂×C₁₃	#3561	1	1	yes	characteristic
735	C₂×C₁₃	#3565	1	1	yes	characteristic
736	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
737	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	4	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
743	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
749	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	4	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	C₂²×C₄×C₁₃	1	4	yes	—
764	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	1	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
806	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
807	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
808	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
809	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
810	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	1	no	—
821	C₂²⋊C₄	—	4	1	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
830	C₄²	—	2	4	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	2	no	—
845	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
846	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
847	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
848	C₁₃	#34429	1	1	yes	characteristic, direct product factor, Sylow
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
862	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
863	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	4	8	no	—
866	D₄	—	2	8	no	—
867	D₄	—	4	8	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	8	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	—	8	4	no	—
923	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
924	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
925	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
926	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
927	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
929	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
930	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
931	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
932	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
933	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
934	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
935	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
951	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
954	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
955	C₂²	C₁₃×#585	1	1	yes	characteristic
956	C₂²	C₁₃×#585	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	1	no	—
977	C₄	C₁₃×#520	1	4	yes	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
981	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
983	C₂	C₁₃×#3544	1	1	yes	characteristic
984	C₂	C₁₃×#3546	1	1	yes	characteristic
985	C₂	C₁₃×#3561	1	1	yes	characteristic
986	C₂	C₁₃×#3565	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×#2383	C₂	semidirect
3. C₁₃×#2376	C₂	semidirect
4. C₁₃×#2373	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
8. C₁₃×#2360	C₂	semidirect
9. C₁₃×#2359	C₂	semidirect
10. C₁₃×#2356	C₂	semidirect
11. C₁₃×#2354	C₂	semidirect
12. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₁₃×#2349	C₂	semidirect
14. C₁₃×#2337	C₂	semidirect
15. C₁₃×#2331	C₂	semidirect
16. C₁₃×#2329	C₂	semidirect
17. C₁₃×#2326	C₂	semidirect
18. C₁₃×#2326	C₂	semidirect
19. C₁₃×#2323	C₂	semidirect
20. C₁₃×#2317	C₂	semidirect
21. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
22. C₄×C₁₃×#124	C₂	semidirect
23. C₁₃×#2298	C₂	semidirect
24. C₁₃×#542	C₄	semidirect
133. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
134. C₁₃×#126	C₂×C₄	semidirect
135. C₁₃×#124	C₂×C₄	semidirect
136. C₁₃×#124	C₂×C₄	semidirect
137. C₁₃×#123	C₂×C₄	semidirect
138. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
144. C₄×Q₈×C₁₃	C₂×C₄	semidirect
148. C₄×D₄×C₁₃	C₂×C₄	semidirect
151. C₁₃×#117	C₂×C₄	semidirect
243. #34429	C₁₃	direct (N × H)
357. #2383	C₂×C₁₃	semidirect
358. #2376	C₂×C₁₃	semidirect
359. #2373	C₂×C₁₃	semidirect
361. #2362	C₂×C₁₃	semidirect
363. #2360	C₂×C₁₃	semidirect
364. #2359	C₂×C₁₃	semidirect
365. #2356	C₂×C₁₃	semidirect
366. #2354	C₂×C₁₃	semidirect
367. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
368. #2349	C₂×C₁₃	semidirect
369. #2337	C₂×C₁₃	semidirect
370. #2331	C₂×C₁₃	semidirect
371. #2329	C₂×C₁₃	semidirect
372. #2326	C₂×C₁₃	semidirect
373. #2326	C₂×C₁₃	semidirect
374. #2323	C₂×C₁₃	semidirect
375. #2317	C₂×C₁₃	semidirect
376. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
377. C₄×#124	C₂×C₁₃	semidirect
378. #2298	C₂×C₁₃	semidirect
466. #542	C₄×C₁₃	semidirect
617. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
618. #126	C₂×C₄×C₁₃	semidirect
619. #124	C₂×C₄×C₁₃	semidirect
620. #124	C₂×C₄×C₁₃	semidirect
621. #123	C₂×C₄×C₁₃	semidirect
622. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
623. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
628. C₄×Q₈	C₂×C₄×C₁₃	semidirect
632. C₄×D₄	C₂×C₄×C₁₃	semidirect
635. #117	C₂×C₄×C₁₃	semidirect
848. C₁₃	#34429	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×#542	2
C₁₃×#2383	2
C₁₃×#2376	2
C₁₃×#2373	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2359	2
C₁₃×#2356	2
C₁₃×#2354	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2349	2
C₁₃×#2337	2
C₁₃×#2331	2
C₁₃×#2329	2
C₁₃×#2326	2
C₁₃×#2323	2
C₁₃×#2317	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₁₃×#2298	2
#34429	13

Subgroups — C13×#34429 #15720768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34429 #15720768