Subgroups — C₁₃×#34893 #15721232

Order 3328.

1900 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2589	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2587	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2580	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2566	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2522	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2465	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2454	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2452	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2296	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
21	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
22	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	2	yes	—
40	C₁₃×#399	C₂²	1	2	yes	—
41	C₁₃×#399	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#396	C₂²	1	2	yes	—
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#395	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	—
52	C₁₃×#393	C₂²	1	2	yes	—
53	C₁₃×#393	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	2	yes	—
55	C₁₃×#391	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
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×#389	C₂²	1	1	yes	characteristic
64	C₁₃×#389	C₂²	1	1	yes	characteristic
65	C₁₃×#389	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	1	yes	characteristic
67	C₁₃×#389	C₂²	1	2	yes	—
68	C₁₃×#389	C₂²	1	1	yes	characteristic
69	C₁₃×#389	C₂²	1	1	yes	characteristic
70	C₁₃×#389	C₂²	1	2	yes	—
71	C₁₃×#389	C₂²	1	2	yes	—
72	C₁₃×#389	C₂²	1	2	yes	—
73	C₁₃×#389	C₂²	1	2	yes	—
74	C₁₃×#389	C₂²	1	1	yes	characteristic
75	C₁₃×#389	C₂²	1	1	yes	characteristic
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	—
78	C₁₃×#388	C₂²	1	2	yes	—
79	C₁₃×#388	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	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×#384	C₂²	1	1	yes	characteristic
93	C₁₃×#382	C₂²	1	1	yes	characteristic
94	C₁₃×#382	C₂²	1	1	yes	characteristic
95	C₁₃×#380	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
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	C₄³×C₁₃	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	—	2	4	no	—
130	C₁₃×#125	—	2	4	no	—
131	C₁₃×#125	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	8	no	—
133	C₄×Q₈×C₁₃	—	2	4	no	—
134	C₄×Q₈×C₁₃	—	2	4	no	—
135	C₄×Q₈×C₁₃	—	2	4	no	—
136	C₄×Q₈×C₁₃	—	4	4	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
140	C₁₃×#117	—	2	8	no	—
141	C₁₃×#117	—	4	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	—	4	4	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	1	yes	characteristic
219	C₁₃×#95	C₂³	1	1	yes	characteristic
220	C₁₃×#95	C₂³	1	1	yes	characteristic
221	C₁₃×#95	C₂³	1	1	yes	characteristic
222	C₁₃×#95	C₂³	1	1	yes	characteristic
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
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	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	#34893	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	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	4	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	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	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	C₂×Q₈	1	4	yes	—
309	C₁₃×C₄⋊C₄	#41	1	4	yes	—
310	C₁₃×C₄⋊C₄	#41	1	4	yes	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	4	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₄²×C₁₃	—	4	2	no	—
340	C₄²×C₁₃	—	4	1	no	—
341	C₄²×C₁₃	—	4	1	no	—
342	C₄²×C₁₃	—	4	1	no	—
343	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
344	C₄²×C₁₃	#41	1	4	yes	—
345	C₄²×C₁₃	#41	1	4	yes	—
346	#2589	C₂×C₁₃	1	2	yes	complemented
347	#2587	C₂×C₁₃	1	2	yes	complemented
348	#2584	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2580	C₂×C₁₃	1	1	yes	characteristic
350	#2566	C₂×C₁₃	1	1	yes	characteristic
351	#2550	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2522	C₂×C₁₃	1	2	yes	complemented
353	#2509	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2507	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#2465	C₂×C₁₃	1	2	yes	complemented
356	#2454	C₂×C₁₃	1	1	yes	characteristic
357	#2452	C₂×C₁₃	1	1	yes	characteristic
358	#2396	C₂×C₁₃	1	2	yes	complemented
359	#2396	C₂×C₁₃	1	2	yes	complemented
360	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
364	#2296	C₂×C₁₃	1	2	yes	complemented
365	#2293	C₂×C₁₃	1	1	yes	characteristic
366	#2293	C₂×C₁₃	1	1	yes	characteristic
367	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
376	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
377	Q₈×C₁₃	—	2	8	no	—
378	Q₈×C₁₃	—	4	8	no	—
379	D₄×C₁₃	—	2	8	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	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	2	no	—
391	C₂×C₄×C₁₃	—	2	2	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	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	16	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	2	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	1	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	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	4	8	no	—
432	C₂×C₄×C₁₃	—	4	8	no	—
433	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
435	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
436	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
437	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
439	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
445	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
446	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
447	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
448	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
453	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#117	C₂²×C₁₃	1	2	yes	—
461	C₂×#117	C₂²×C₁₃	1	2	yes	—
462	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
463	#400	C₂²×C₁₃	1	2	yes	—
464	#400	C₂²×C₁₃	1	2	yes	—
465	#399	C₂²×C₁₃	1	2	yes	—
466	#399	C₂²×C₁₃	1	2	yes	—
467	#398	C₂²×C₁₃	1	2	yes	—
468	#398	C₂²×C₁₃	1	2	yes	—
469	#398	C₂²×C₁₃	1	2	yes	—
470	#398	C₂²×C₁₃	1	2	yes	—
471	#396	C₂²×C₁₃	1	2	yes	—
472	#396	C₂²×C₁₃	1	2	yes	—
473	#396	C₂²×C₁₃	1	2	yes	—
474	#396	C₂²×C₁₃	1	2	yes	—
475	#395	C₂²×C₁₃	1	2	yes	—
476	#395	C₂²×C₁₃	1	2	yes	—
477	#393	C₂²×C₁₃	1	2	yes	—
478	#393	C₂²×C₁₃	1	2	yes	—
479	#391	C₂²×C₁₃	1	2	yes	—
480	#391	C₂²×C₁₃	1	2	yes	—
481	#390	C₂²×C₁₃	1	1	yes	characteristic
482	#390	C₂²×C₁₃	1	1	yes	characteristic
483	#390	C₂²×C₁₃	1	1	yes	characteristic
484	#390	C₂²×C₁₃	1	1	yes	characteristic
485	#389	C₂²×C₁₃	1	1	yes	characteristic
486	#389	C₂²×C₁₃	1	1	yes	characteristic
487	#389	C₂²×C₁₃	1	1	yes	characteristic
488	#389	C₂²×C₁₃	1	1	yes	characteristic
489	#389	C₂²×C₁₃	1	1	yes	characteristic
490	#389	C₂²×C₁₃	1	1	yes	characteristic
491	#389	C₂²×C₁₃	1	2	yes	—
492	#389	C₂²×C₁₃	1	2	yes	—
493	#389	C₂²×C₁₃	1	2	yes	—
494	#389	C₂²×C₁₃	1	1	yes	characteristic
495	#389	C₂²×C₁₃	1	1	yes	characteristic
496	#389	C₂²×C₁₃	1	2	yes	—
497	#389	C₂²×C₁₃	1	2	yes	—
498	#389	C₂²×C₁₃	1	2	yes	—
499	#389	C₂²×C₁₃	1	1	yes	characteristic
500	#389	C₂²×C₁₃	1	1	yes	characteristic
501	#388	C₂²×C₁₃	1	2	yes	—
502	#388	C₂²×C₁₃	1	2	yes	—
503	#388	C₂²×C₁₃	1	2	yes	—
504	#388	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	2	yes	—
508	#387	C₂²×C₁₃	1	2	yes	—
509	#387	C₂²×C₁₃	1	2	yes	—
510	#387	C₂²×C₁₃	1	2	yes	—
511	#385	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	—
513	#385	C₂²×C₁₃	1	2	yes	—
514	#385	C₂²×C₁₃	1	2	yes	—
515	#385	C₂²×C₁₃	1	2	yes	—
516	#385	C₂²×C₁₃	1	2	yes	—
517	#384	C₂²×C₁₃	1	1	yes	characteristic
518	#382	C₂²×C₁₃	1	1	yes	characteristic
519	#382	C₂²×C₁₃	1	1	yes	characteristic
520	#380	C₂²×C₁₃	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
540	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
545	C₄³	C₂²×C₁₃	1	1	yes	characteristic
546	C₄³	C₂²×C₁₃	1	1	yes	characteristic
547	C₄³	C₂²×C₁₃	1	1	yes	characteristic
548	C₂²×C₁₃	—	2	4	no	—
549	C₂²×C₁₃	—	2	4	no	—
550	C₂²×C₁₃	—	2	4	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
556	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
557	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
558	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
559	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
560	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₁₃	#585	1	1	yes	characteristic
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	2	no	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	2	4	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	4	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	—	4	1	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	1	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₄×C₁₃	—	4	1	no	—
580	C₄×C₁₃	—	4	1	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	#533	1	4	yes	—
583	C₄×C₁₃	#554	1	4	yes	—
584	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
588	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
589	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
590	C₄⋊Q₈	—	2	4	no	—
591	#125	—	2	4	no	—
592	#125	—	2	4	no	—
593	C₂²⋊Q₈	—	2	8	no	—
594	C₄×Q₈	—	2	4	no	—
595	C₄×Q₈	—	2	4	no	—
596	C₄×Q₈	—	2	4	no	—
597	C₄×Q₈	—	4	4	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
601	#117	—	2	8	no	—
602	#117	—	4	4	no	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	—	4	4	no	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
668	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
672	#95	C₂³×C₁₃	1	2	yes	—
673	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	1	yes	characteristic
680	#95	C₂³×C₁₃	1	1	yes	characteristic
681	#95	C₂³×C₁₃	1	1	yes	characteristic
682	#95	C₂³×C₁₃	1	1	yes	characteristic
683	#95	C₂³×C₁₃	1	1	yes	characteristic
684	#95	C₂³×C₁₃	1	1	yes	characteristic
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	2	yes	—
690	#95	C₂³×C₁₃	1	2	yes	—
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	C₂×C₁₃	—	4	4	no	—
698	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
699	C₂×C₁₃	#3444	1	1	yes	characteristic
700	C₂×C₁₃	#3460	1	1	yes	characteristic
701	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
702	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
703	C₂×C₁₃	#3480	1	1	yes	characteristic
704	C₂×C₁₃	#3481	1	1	yes	characteristic
705	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
777	C₄⋊C₄	C₁₃×#41	1	4	yes	—
778	C₄⋊C₄	C₁₃×#41	1	4	yes	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	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	C₂×Q₈×C₁₃	1	8	yes	—
790	C₄²	—	2	4	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	4	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	4	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	1	no	—
809	C₄²	—	4	1	no	—
810	C₄²	—	4	1	no	—
811	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
812	C₄²	C₁₃×#41	1	4	yes	—
813	C₄²	C₁₃×#41	1	4	yes	—
814	C₁₃	#34893	1	1	yes	characteristic, direct product factor, Sylow
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
822	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
823	Q₈	—	2	8	no	—
824	Q₈	—	4	8	no	—
825	D₄	—	2	8	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	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	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
880	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
881	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
882	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
883	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
884	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
885	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
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	C₂×C₁₃×#41	1	4	yes	—
891	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
892	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
893	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
894	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
895	C₂²	—	2	4	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
903	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
904	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
905	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
906	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
907	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
908	C₂²	C₁₃×#585	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	4	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	4	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	C₁₃×#533	1	4	yes	—
930	C₄	C₁₃×#554	1	4	yes	—
931	C₂	—	4	4	no	—
932	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
933	C₂	C₁₃×#3444	1	1	yes	characteristic
934	C₂	C₁₃×#3460	1	1	yes	characteristic
935	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
936	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
937	C₂	C₁₃×#3480	1	1	yes	characteristic
938	C₂	C₁₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2589	C₂	semidirect
2. C₁₃×#2587	C₂	semidirect
3. C₁₃×#2584	C₂	semidirect
6. C₁₃×#2550	C₂	semidirect
7. C₁₃×#2522	C₂	semidirect
8. C₁₃×#2509	C₂	semidirect
9. C₁₃×#2507	C₂	semidirect
10. C₁₃×#2465	C₂	semidirect
13. C₁₃×#2396	C₂	semidirect
14. C₁₃×#2396	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₄×C₁₃×#125	C₂	semidirect
17. C₄×C₁₃×#125	C₂	semidirect
18. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
19. C₁₃×#2296	C₂	semidirect
22. C₄²×Q₈×C₁₃	C₂	semidirect
139. C₄×D₄×C₁₃	Q₈	semidirect
236. #34893	C₁₃	direct (N × H)
346. #2589	C₂×C₁₃	semidirect
347. #2587	C₂×C₁₃	semidirect
348. #2584	C₂×C₁₃	semidirect
351. #2550	C₂×C₁₃	semidirect
352. #2522	C₂×C₁₃	semidirect
353. #2509	C₂×C₁₃	semidirect
354. #2507	C₂×C₁₃	semidirect
355. #2465	C₂×C₁₃	semidirect
358. #2396	C₂×C₁₃	semidirect
359. #2396	C₂×C₁₃	semidirect
360. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
361. C₄×#125	C₂×C₁₃	semidirect
362. C₄×#125	C₂×C₁₃	semidirect
363. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
364. #2296	C₂×C₁₃	semidirect
367. C₄²×Q₈	C₂×C₁₃	semidirect
600. C₄×D₄	Q₈×C₁₃	semidirect
814. C₁₃	#34893	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×#2589	2
C₁₃×#2587	2
C₁₃×#2584	2
C₁₃×#2580	2
C₁₃×#2566	2
C₁₃×#2550	2
C₁₃×#2522	2
C₁₃×#2509	2
C₁₃×#2507	2
C₁₃×#2465	2
C₁₃×#2454	2
C₁₃×#2452	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2296	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
C₄²×D₄×C₁₃	2
#34893	13

Subgroups — C13×#34893 #15721232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34893 #15721232