Subgroups — C₁₃×#34436 #15720775

Order 3328.

2522 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₁₃×#537	C₄	1	16	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	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×#388	C₂²	1	2	yes	—
56	C₁₃×#388	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×#386	C₂²	1	2	yes	—
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#381	C₂²	1	2	yes	—
86	C₁₃×#381	C₂²	1	2	yes	—
87	C₁₃×#381	C₂²	1	2	yes	—
88	C₁₃×#380	C₂²	1	1	yes	characteristic
89	C₁₃×#380	C₂²	1	1	yes	characteristic
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×C₄⋊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	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
103	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
104	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₂×C₁₃×#95	C₂²	1	2	yes	—
108	C₂×C₁₃×#41	—	4	4	no	—
109	C₂×C₁₃×#41	—	4	4	no	—
110	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
111	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
132	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
133	C₁₃×#121	C₂×C₄	1	16	yes	complemented
134	C₁₃×#121	C₂×C₄	1	16	yes	complemented
135	C₁₃×#121	C₂×C₄	1	8	yes	complemented
136	C₁₃×#121	C₂×C₄	1	8	yes	complemented
137	C₁₃×#121	C₂×C₄	1	16	yes	complemented
138	C₄×D₄×C₁₃	—	4	2	no	—
139	C₄×D₄×C₁₃	—	4	2	no	—
140	C₄×D₄×C₁₃	—	4	4	no	—
141	C₄×D₄×C₁₃	—	4	4	no	—
142	C₄×D₄×C₁₃	—	4	4	no	—
143	C₄×D₄×C₁₃	—	4	4	no	—
144	C₄×D₄×C₁₃	—	4	4	no	—
145	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×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×C₄²×C₁₃	—	4	2	no	—
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	#34436	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
217	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
218	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₁₃×#41	—	4	32	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	4	1	no	—
228	C₂×D₄×C₁₃	—	4	1	no	—
229	C₂×D₄×C₁₃	—	4	2	no	—
230	C₂×D₄×C₁₃	—	4	2	no	—
231	C₂×D₄×C₁₃	—	4	1	no	—
232	C₂×D₄×C₁₃	—	4	1	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
236	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
237	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
238	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
240	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	1	no	—
255	C₂²×C₄×C₁₃	—	4	1	no	—
256	C₂²×C₄×C₁₃	—	4	1	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	2	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	1	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	—	4	1	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	1	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
278	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	4	1	no	—
299	C₁₃×C₄⋊C₄	—	4	1	no	—
300	C₁₃×C₄⋊C₄	—	4	1	no	—
301	C₁₃×C₄⋊C₄	—	4	1	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	C₂²×C₄	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	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	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	4	2	no	—
322	C₁₃×C₂²⋊C₄	—	4	2	no	—
323	C₁₃×C₂²⋊C₄	—	4	2	no	—
324	C₁₃×C₂²⋊C₄	—	4	2	no	—
325	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
326	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
327	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
328	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	4	1	no	—
332	C₄²×C₁₃	—	4	1	no	—
333	C₄²×C₁₃	—	4	2	no	—
334	C₄²×C₁₃	—	4	2	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	—	4	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₂×#537	C₂×C₁₃	1	1	yes	characteristic
340	#2378	C₂×C₁₃	1	2	yes	complemented
341	#2377	C₂×C₁₃	1	2	yes	complemented
342	#2368	C₂×C₁₃	1	2	yes	complemented
343	#2364	C₂×C₁₃	1	2	yes	complemented
344	#2364	C₂×C₁₃	1	2	yes	complemented
345	#2361	C₂×C₁₃	1	2	yes	complemented
346	#2339	C₂×C₁₃	1	2	yes	complemented
347	#2339	C₂×C₁₃	1	2	yes	complemented
348	#2333	C₂×C₁₃	1	2	yes	complemented
349	#2332	C₂×C₁₃	1	2	yes	complemented
350	#2329	C₂×C₁₃	1	2	yes	complemented
351	#2325	C₂×C₁₃	1	2	yes	complemented
352	#2325	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2325	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2313	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	2	no	—
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	C₂³×C₄	1	4	yes	—
375	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
376	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
377	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
378	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
379	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
380	Q₈×C₁₃	—	4	8	no	—
381	D₄×C₁₃	—	2	16	no	—
382	D₄×C₁₃	—	2	16	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	8	no	—
386	D₄×C₁₃	—	4	8	no	—
387	C₂×C₄×C₁₃	—	2	8	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	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	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	4	no	—
430	C₂×C₄×C₁₃	—	4	8	no	—
431	C₂×C₄×C₁₃	—	4	8	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	4	no	—
434	C₂×C₄×C₁₃	—	8	4	no	—
435	C₂×C₄×C₁₃	—	8	4	no	—
436	C₂×C₄×C₁₃	—	8	2	no	—
437	C₂×C₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	8	4	no	—
439	C₂×C₄×C₁₃	—	8	4	no	—
440	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
443	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
444	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
445	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
446	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
447	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
448	C₂²×#41	C₂²×C₁₃	1	2	yes	—
449	#537	C₄×C₁₃	1	16	yes	complemented
450	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
452	C₂×#121	C₂²×C₁₃	1	2	yes	—
453	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#121	C₂²×C₁₃	1	2	yes	—
456	C₂×#121	C₂²×C₁₃	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
460	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
461	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
463	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
467	#391	C₂²×C₁₃	1	2	yes	—
468	#391	C₂²×C₁₃	1	2	yes	—
469	#391	C₂²×C₁₃	1	2	yes	—
470	#391	C₂²×C₁₃	1	2	yes	—
471	#390	C₂²×C₁₃	1	1	yes	characteristic
472	#390	C₂²×C₁₃	1	2	yes	—
473	#390	C₂²×C₁₃	1	1	yes	characteristic
474	#389	C₂²×C₁₃	1	1	yes	characteristic
475	#389	C₂²×C₁₃	1	2	yes	—
476	#389	C₂²×C₁₃	1	1	yes	characteristic
477	#388	C₂²×C₁₃	1	2	yes	—
478	#388	C₂²×C₁₃	1	2	yes	—
479	#388	C₂²×C₁₃	1	2	yes	—
480	#388	C₂²×C₁₃	1	2	yes	—
481	#388	C₂²×C₁₃	1	2	yes	—
482	#388	C₂²×C₁₃	1	2	yes	—
483	#388	C₂²×C₁₃	1	2	yes	—
484	#388	C₂²×C₁₃	1	2	yes	—
485	#387	C₂²×C₁₃	1	2	yes	—
486	#387	C₂²×C₁₃	1	2	yes	—
487	#387	C₂²×C₁₃	1	2	yes	—
488	#387	C₂²×C₁₃	1	2	yes	—
489	#387	C₂²×C₁₃	1	2	yes	—
490	#387	C₂²×C₁₃	1	2	yes	—
491	#387	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#386	C₂²×C₁₃	1	2	yes	—
498	#386	C₂²×C₁₃	1	2	yes	—
499	#386	C₂²×C₁₃	1	2	yes	—
500	#386	C₂²×C₁₃	1	2	yes	—
501	#386	C₂²×C₁₃	1	2	yes	—
502	#386	C₂²×C₁₃	1	2	yes	—
503	#386	C₂²×C₁₃	1	2	yes	—
504	#386	C₂²×C₁₃	1	2	yes	—
505	#386	C₂²×C₁₃	1	2	yes	—
506	#386	C₂²×C₁₃	1	2	yes	—
507	#386	C₂²×C₁₃	1	2	yes	—
508	#386	C₂²×C₁₃	1	2	yes	—
509	#385	C₂²×C₁₃	1	2	yes	—
510	#385	C₂²×C₁₃	1	2	yes	—
511	#385	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	—
513	#381	C₂²×C₁₃	1	2	yes	—
514	#381	C₂²×C₁₃	1	2	yes	—
515	#381	C₂²×C₁₃	1	2	yes	—
516	#380	C₂²×C₁₃	1	1	yes	characteristic
517	#380	C₂²×C₁₃	1	1	yes	characteristic
518	#380	C₂²×C₁₃	1	2	yes	—
519	#380	C₂²×C₁₃	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
531	C₂×#95	C₂²×C₁₃	1	2	yes	—
532	C₂×#95	C₂²×C₁₃	1	2	yes	—
533	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
534	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
535	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	2	no	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	2	4	no	—
544	C₂²×C₁₃	—	2	4	no	—
545	C₂²×C₁₃	—	2	4	no	—
546	C₂²×C₁₃	—	2	4	no	—
547	C₂²×C₁₃	—	2	4	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	4	2	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	—	4	2	no	—
556	C₂²×C₁₃	#518	1	4	yes	—
557	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
558	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	C₂²×C₁₃	#585	1	1	yes	characteristic
563	C₂²×C₁₃	#585	1	1	yes	characteristic
564	C₄×C₁₃	—	2	4	no	—
565	C₄×C₁₃	—	2	4	no	—
566	C₄×C₁₃	—	2	4	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	4	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	4	1	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	1	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₂×#41	—	4	4	no	—
581	C₂×#41	—	4	4	no	—
582	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
583	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
585	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
588	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
595	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
597	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
598	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
603	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
604	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
605	#121	C₂×C₄×C₁₃	1	16	yes	complemented
606	#121	C₂×C₄×C₁₃	1	16	yes	complemented
607	#121	C₂×C₄×C₁₃	1	8	yes	complemented
608	#121	C₂×C₄×C₁₃	1	8	yes	complemented
609	#121	C₂×C₄×C₁₃	1	16	yes	complemented
610	C₄×D₄	—	4	2	no	—
611	C₄×D₄	—	4	2	no	—
612	C₄×D₄	—	4	4	no	—
613	C₄×D₄	—	4	4	no	—
614	C₄×D₄	—	4	4	no	—
615	C₄×D₄	—	4	4	no	—
616	C₄×D₄	—	4	4	no	—
617	C₂×C₄⋊C₄	—	4	2	no	—
618	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄²	—	4	2	no	—
653	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
658	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	#95	C₂³×C₁₃	1	2	yes	—
664	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	#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	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	C₂×C₁₃	—	2	4	no	—
688	C₂×C₁₃	—	4	4	no	—
689	C₂×C₁₃	—	4	4	no	—
690	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
691	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
693	C₂×C₁₃	#3534	1	1	yes	characteristic
694	C₂×C₁₃	#3536	1	1	yes	characteristic
695	C₂×C₁₃	#3559	1	1	yes	characteristic
696	C₂×C₁₃	#3560	1	1	yes	characteristic
697	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
698	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
699	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
700	#41	—	4	32	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
717	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
719	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
720	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
721	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
757	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
758	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
759	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
760	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	1	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
788	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
789	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
790	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
791	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
809	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	1	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	2	no	—
820	C₁₃	#34436	1	1	yes	characteristic, direct product factor, Sylow
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
838	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
839	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
840	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
841	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
842	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
843	Q₈	—	4	8	no	—
844	D₄	—	2	16	no	—
845	D₄	—	2	16	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	8	no	—
850	C₂×C₄	—	2	8	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	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	—	8	4	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
904	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
905	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
907	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
908	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
909	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
910	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	C₁₃×#518	1	4	yes	—
932	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
933	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
934	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
935	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
936	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
937	C₂²	C₁₃×#585	1	1	yes	characteristic
938	C₂²	C₁₃×#585	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	4	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	4	no	—
957	C₂	—	4	4	no	—
958	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
959	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
960	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
961	C₂	C₁₃×#3534	1	1	yes	characteristic
962	C₂	C₁₃×#3536	1	1	yes	characteristic
963	C₂	C₁₃×#3559	1	1	yes	characteristic
964	C₂	C₁₃×#3560	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×#537	C₂
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×#2378	C₂	semidirect
3. C₁₃×#2377	C₂	semidirect
4. C₁₃×#2368	C₂	semidirect
5. C₁₃×#2364	C₂	semidirect
6. C₁₃×#2364	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2339	C₂	semidirect
9. C₁₃×#2339	C₂	semidirect
10. C₁₃×#2333	C₂	semidirect
11. C₁₃×#2332	C₂	semidirect
12. C₁₃×#2329	C₂	semidirect
13. C₁₃×#2325	C₂	semidirect
14. C₁₃×#2325	C₂	semidirect
15. C₁₃×#2325	C₂	semidirect
16. C₁₃×#2313	C₂	semidirect
17. C₄×C₁₃×#121	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₂×C₁₃×#387	C₂	semidirect
21. C₁₃×#537	C₄	semidirect
110. C₂×C₁₃×#41	C₂×C₄	semidirect
131. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
133. C₁₃×#121	C₂×C₄	semidirect
134. C₁₃×#121	C₂×C₄	semidirect
135. C₁₃×#121	C₂×C₄	semidirect
136. C₁₃×#121	C₂×C₄	semidirect
137. C₁₃×#121	C₂×C₄	semidirect
146. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
215. #34436	C₁₃	direct (N × H)
340. #2378	C₂×C₁₃	semidirect
341. #2377	C₂×C₁₃	semidirect
342. #2368	C₂×C₁₃	semidirect
343. #2364	C₂×C₁₃	semidirect
344. #2364	C₂×C₁₃	semidirect
345. #2361	C₂×C₁₃	semidirect
346. #2339	C₂×C₁₃	semidirect
347. #2339	C₂×C₁₃	semidirect
348. #2333	C₂×C₁₃	semidirect
349. #2332	C₂×C₁₃	semidirect
350. #2329	C₂×C₁₃	semidirect
351. #2325	C₂×C₁₃	semidirect
352. #2325	C₂×C₁₃	semidirect
353. #2325	C₂×C₁₃	semidirect
354. #2313	C₂×C₁₃	semidirect
355. C₄×#121	C₂×C₁₃	semidirect
356. C₄×#121	C₂×C₁₃	semidirect
357. C₂×#387	C₂×C₁₃	semidirect
449. #537	C₄×C₁₃	semidirect
582. C₂×#41	C₂×C₄×C₁₃	semidirect
603. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
604. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
605. #121	C₂×C₄×C₁₃	semidirect
606. #121	C₂×C₄×C₁₃	semidirect
607. #121	C₂×C₄×C₁₃	semidirect
608. #121	C₂×C₄×C₁₃	semidirect
609. #121	C₂×C₄×C₁₃	semidirect
618. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
820. C₁₃	#34436	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×#537	2
C₁₃×#2378	2
C₁₃×#2377	2
C₁₃×#2368	2
C₁₃×#2364	2
C₁₃×#2361	2
C₁₃×#2339	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2329	2
C₁₃×#2325	2
C₁₃×#2313	2
C₄×C₁₃×#121	2
C₂×C₁₃×#387	2
#34436	13

Subgroups — C13×#34436 #15720775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34436 #15720775