Subgroups — C₁₃×#34527 #15720866

Order 3328.

2216 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#562	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2379	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#562	C₄	1	16	yes	complemented
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	2	yes	—
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×#389	C₂²	1	2	yes	—
50	C₁₃×#389	C₂²	1	2	yes	—
51	C₁₃×#389	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×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	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×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#382	C₂²	1	1	yes	characteristic
87	C₁₃×#382	C₂²	1	1	yes	characteristic
88	C₁₃×#382	C₂²	1	1	yes	characteristic
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₄³×C₁₃	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₁₃×#125	C₂×C₄	1	8	yes	complemented
121	C₁₃×#124	C₂×C₄	1	8	yes	complemented
122	C₁₃×#124	C₂×C₄	1	8	yes	complemented
123	C₁₃×#123	C₂×C₄	1	16	yes	complemented
124	C₁₃×#123	C₂×C₄	1	16	yes	complemented
125	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
126	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
127	C₁₃×#121	C₂×C₄	1	16	yes	complemented
128	C₁₃×#121	C₂×C₄	1	16	yes	complemented
129	C₄×Q₈×C₁₃	—	4	2	no	—
130	C₄×Q₈×C₁₃	—	4	2	no	—
131	C₄×D₄×C₁₃	—	4	4	no	—
132	C₄×D₄×C₁₃	—	4	2	no	—
133	C₄×D₄×C₁₃	—	4	2	no	—
134	C₄×D₄×C₁₃	—	4	4	no	—
135	C₁₃×#117	—	4	4	no	—
136	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	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	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	#34527	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃	—	4	1	no	—
216	C₂×Q₈×C₁₃	—	4	1	no	—
217	C₂×Q₈×C₁₃	—	4	1	no	—
218	C₂×Q₈×C₁₃	—	4	1	no	—
219	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
220	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
221	C₂×D₄×C₁₃	—	4	2	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	—	4	1	no	—
224	C₂×D₄×C₁₃	—	4	2	no	—
225	C₂×D₄×C₁₃	—	4	2	no	—
226	C₂×D₄×C₁₃	—	4	1	no	—
227	C₂×D₄×C₁₃	—	4	1	no	—
228	C₂×D₄×C₁₃	—	4	2	no	—
229	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
230	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
231	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
232	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
250	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	1	no	—
279	C₁₃×C₄⋊C₄	—	4	1	no	—
280	C₁₃×C₄⋊C₄	—	4	1	no	—
281	C₁₃×C₄⋊C₄	—	4	1	no	—
282	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
283	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
284	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
285	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
286	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
287	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
301	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
302	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
303	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
304	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
305	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	2	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	—	2	2	no	—
310	C₄²×C₁₃	—	4	2	no	—
311	C₄²×C₁₃	—	4	1	no	—
312	C₄²×C₁₃	—	4	1	no	—
313	C₄²×C₁₃	—	4	1	no	—
314	C₄²×C₁₃	—	4	2	no	—
315	C₄²×C₁₃	—	4	2	no	—
316	C₄²×C₁₃	—	4	2	no	—
317	C₄²×C₁₃	—	4	2	no	—
318	C₄²×C₁₃	—	4	2	no	—
319	C₄²×C₁₃	—	4	2	no	—
320	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
321	C₂×#562	C₂×C₁₃	1	1	yes	characteristic
322	#2382	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2379	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#2379	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2374	C₂×C₁₃	1	2	yes	complemented
326	#2364	C₂×C₁₃	1	2	yes	complemented
327	#2362	C₂×C₁₃	1	2	yes	complemented
328	#2361	C₂×C₁₃	1	2	yes	complemented
329	#2360	C₂×C₁₃	1	2	yes	complemented
330	#2359	C₂×C₁₃	1	2	yes	complemented
331	#2335	C₂×C₁₃	1	2	yes	complemented
332	#2333	C₂×C₁₃	1	2	yes	complemented
333	#2332	C₂×C₁₃	1	2	yes	complemented
334	#2329	C₂×C₁₃	1	2	yes	complemented
335	#2324	C₂×C₁₃	1	2	yes	complemented
336	#2322	C₂×C₁₃	1	2	yes	complemented
337	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
353	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
354	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
355	Q₈×C₁₃	—	4	4	no	—
356	Q₈×C₁₃	—	4	4	no	—
357	D₄×C₁₃	—	4	8	no	—
358	D₄×C₁₃	—	4	8	no	—
359	D₄×C₁₃	—	4	4	no	—
360	D₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	4	8	no	—
403	C₂×C₄×C₁₃	—	4	8	no	—
404	C₂×C₄×C₁₃	—	8	4	no	—
405	C₂×C₄×C₁₃	—	8	4	no	—
406	C₂×C₄×C₁₃	—	8	4	no	—
407	C₂×C₄×C₁₃	—	8	4	no	—
408	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
412	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
414	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
415	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
418	#562	C₄×C₁₃	1	16	yes	complemented
419	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#123	C₂²×C₁₃	1	2	yes	—
423	C₂×#123	C₂²×C₁₃	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
426	C₂×#121	C₂²×C₁₃	1	2	yes	—
427	C₂×#121	C₂²×C₁₃	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#117	C₂²×C₁₃	1	2	yes	—
435	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
436	#391	C₂²×C₁₃	1	1	yes	characteristic
437	#391	C₂²×C₁₃	1	2	yes	—
438	#391	C₂²×C₁₃	1	1	yes	characteristic
439	#391	C₂²×C₁₃	1	2	yes	—
440	#390	C₂²×C₁₃	1	1	yes	characteristic
441	#390	C₂²×C₁₃	1	2	yes	—
442	#390	C₂²×C₁₃	1	2	yes	—
443	#390	C₂²×C₁₃	1	1	yes	characteristic
444	#389	C₂²×C₁₃	1	1	yes	characteristic
445	#389	C₂²×C₁₃	1	1	yes	characteristic
446	#389	C₂²×C₁₃	1	2	yes	—
447	#389	C₂²×C₁₃	1	2	yes	—
448	#389	C₂²×C₁₃	1	2	yes	—
449	#389	C₂²×C₁₃	1	2	yes	—
450	#388	C₂²×C₁₃	1	2	yes	—
451	#388	C₂²×C₁₃	1	2	yes	—
452	#388	C₂²×C₁₃	1	2	yes	—
453	#388	C₂²×C₁₃	1	2	yes	—
454	#388	C₂²×C₁₃	1	2	yes	—
455	#388	C₂²×C₁₃	1	2	yes	—
456	#388	C₂²×C₁₃	1	2	yes	—
457	#388	C₂²×C₁₃	1	2	yes	—
458	#388	C₂²×C₁₃	1	2	yes	—
459	#388	C₂²×C₁₃	1	2	yes	—
460	#388	C₂²×C₁₃	1	2	yes	—
461	#388	C₂²×C₁₃	1	2	yes	—
462	#387	C₂²×C₁₃	1	2	yes	—
463	#387	C₂²×C₁₃	1	2	yes	—
464	#387	C₂²×C₁₃	1	2	yes	—
465	#387	C₂²×C₁₃	1	2	yes	—
466	#387	C₂²×C₁₃	1	2	yes	—
467	#387	C₂²×C₁₃	1	2	yes	—
468	#387	C₂²×C₁₃	1	2	yes	—
469	#387	C₂²×C₁₃	1	2	yes	—
470	#387	C₂²×C₁₃	1	2	yes	—
471	#387	C₂²×C₁₃	1	2	yes	—
472	#386	C₂²×C₁₃	1	2	yes	—
473	#386	C₂²×C₁₃	1	2	yes	—
474	#386	C₂²×C₁₃	1	2	yes	—
475	#386	C₂²×C₁₃	1	2	yes	—
476	#386	C₂²×C₁₃	1	2	yes	—
477	#386	C₂²×C₁₃	1	2	yes	—
478	#385	C₂²×C₁₃	1	2	yes	—
479	#385	C₂²×C₁₃	1	2	yes	—
480	#385	C₂²×C₁₃	1	2	yes	—
481	#385	C₂²×C₁₃	1	2	yes	—
482	#385	C₂²×C₁₃	1	2	yes	—
483	#385	C₂²×C₁₃	1	2	yes	—
484	#382	C₂²×C₁₃	1	1	yes	characteristic
485	#382	C₂²×C₁₃	1	1	yes	characteristic
486	#382	C₂²×C₁₃	1	1	yes	characteristic
487	#381	C₂²×C₁₃	1	2	yes	—
488	#380	C₂²×C₁₃	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
493	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
504	C₂×#95	C₂²×C₁₃	1	2	yes	—
505	C₄³	C₂²×C₁₃	1	1	yes	characteristic
506	C₂²×C₁₃	—	2	4	no	—
507	C₂²×C₁₃	—	2	4	no	—
508	C₂²×C₁₃	—	2	4	no	—
509	C₂²×C₁₃	—	2	4	no	—
510	C₂²×C₁₃	—	2	4	no	—
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
521	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
524	C₂²×C₁₃	#585	1	1	yes	characteristic
525	C₂²×C₁₃	#585	1	1	yes	characteristic
526	C₂²×C₁₃	#585	1	1	yes	characteristic
527	C₄×C₁₃	—	2	4	no	—
528	C₄×C₁₃	—	2	4	no	—
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	4	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	2	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
547	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
548	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
552	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
555	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
556	#125	C₂×C₄×C₁₃	1	8	yes	complemented
557	#124	C₂×C₄×C₁₃	1	8	yes	complemented
558	#124	C₂×C₄×C₁₃	1	8	yes	complemented
559	#123	C₂×C₄×C₁₃	1	16	yes	complemented
560	#123	C₂×C₄×C₁₃	1	16	yes	complemented
561	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
562	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
563	#121	C₂×C₄×C₁₃	1	16	yes	complemented
564	#121	C₂×C₄×C₁₃	1	16	yes	complemented
565	C₄×Q₈	—	4	2	no	—
566	C₄×Q₈	—	4	2	no	—
567	C₄×D₄	—	4	4	no	—
568	C₄×D₄	—	4	2	no	—
569	C₄×D₄	—	4	2	no	—
570	C₄×D₄	—	4	4	no	—
571	#117	—	4	4	no	—
572	C₂×C₄⋊C₄	—	4	4	no	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	#95	C₂³×C₁₃	1	2	yes	—
627	#95	C₂³×C₁₃	1	2	yes	—
628	#95	C₂³×C₁₃	1	2	yes	—
629	#95	C₂³×C₁₃	1	2	yes	—
630	#95	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	2	yes	—
648	C₂×C₁₃	—	4	4	no	—
649	C₂×C₁₃	—	4	4	no	—
650	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
653	C₂×C₁₃	#3558	1	1	yes	characteristic
654	C₂×C₁₃	#3559	1	1	yes	characteristic
655	C₂×C₁₃	#3561	1	1	yes	characteristic
656	C₂×C₁₃	#3567	1	1	yes	characteristic
657	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
658	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
659	C₂×Q₈	—	4	1	no	—
660	C₂×Q₈	—	4	1	no	—
661	C₂×Q₈	—	4	1	no	—
662	C₂×Q₈	—	4	1	no	—
663	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
664	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	—	4	1	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	1	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
674	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
675	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
676	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
694	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	1	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
727	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
728	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
729	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
730	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
731	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
745	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
746	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
747	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
748	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
749	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	4	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	1	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
765	C₁₃	#34527	1	1	yes	characteristic, direct product factor, Sylow
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
779	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
780	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
781	Q₈	—	4	4	no	—
782	Q₈	—	4	4	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	4	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂×C₄	—	8	4	no	—
834	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
835	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
836	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
837	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
838	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
839	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
840	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
841	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
842	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
843	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
859	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
860	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
862	C₂²	C₁₃×#585	1	1	yes	characteristic
863	C₂²	C₁₃×#585	1	1	yes	characteristic
864	C₂²	C₁₃×#585	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	1	no	—
882	C₂	—	4	4	no	—
883	C₂	—	4	4	no	—
884	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
887	C₂	C₁₃×#3558	1	1	yes	characteristic
888	C₂	C₁₃×#3559	1	1	yes	characteristic
889	C₂	C₁₃×#3561	1	1	yes	characteristic
890	C₂	C₁₃×#3567	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×#562	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×#2382	C₂	semidirect
3. C₁₃×#2379	C₂	semidirect
4. C₁₃×#2379	C₂	semidirect
5. C₁₃×#2374	C₂	semidirect
6. C₁₃×#2364	C₂	semidirect
7. C₁₃×#2362	C₂	semidirect
8. C₁₃×#2361	C₂	semidirect
9. C₁₃×#2360	C₂	semidirect
10. C₁₃×#2359	C₂	semidirect
11. C₁₃×#2335	C₂	semidirect
12. C₁₃×#2333	C₂	semidirect
13. C₁₃×#2332	C₂	semidirect
14. C₁₃×#2329	C₂	semidirect
15. C₁₃×#2324	C₂	semidirect
16. C₁₃×#2322	C₂	semidirect
17. C₄×C₁₃×#125	C₂	semidirect
18. C₄×C₁₃×#124	C₂	semidirect
19. C₄×C₁₃×#124	C₂	semidirect
20. C₁₃×#562	C₄	semidirect
120. C₁₃×#125	C₂×C₄	semidirect
121. C₁₃×#124	C₂×C₄	semidirect
122. C₁₃×#124	C₂×C₄	semidirect
123. C₁₃×#123	C₂×C₄	semidirect
124. C₁₃×#123	C₂×C₄	semidirect
125. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
126. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
127. C₁₃×#121	C₂×C₄	semidirect
128. C₁₃×#121	C₂×C₄	semidirect
212. #34527	C₁₃	direct (N × H)
322. #2382	C₂×C₁₃	semidirect
323. #2379	C₂×C₁₃	semidirect
324. #2379	C₂×C₁₃	semidirect
325. #2374	C₂×C₁₃	semidirect
326. #2364	C₂×C₁₃	semidirect
327. #2362	C₂×C₁₃	semidirect
328. #2361	C₂×C₁₃	semidirect
329. #2360	C₂×C₁₃	semidirect
330. #2359	C₂×C₁₃	semidirect
331. #2335	C₂×C₁₃	semidirect
332. #2333	C₂×C₁₃	semidirect
333. #2332	C₂×C₁₃	semidirect
334. #2329	C₂×C₁₃	semidirect
335. #2324	C₂×C₁₃	semidirect
336. #2322	C₂×C₁₃	semidirect
337. C₄×#125	C₂×C₁₃	semidirect
338. C₄×#124	C₂×C₁₃	semidirect
339. C₄×#124	C₂×C₁₃	semidirect
418. #562	C₄×C₁₃	semidirect
556. #125	C₂×C₄×C₁₃	semidirect
557. #124	C₂×C₄×C₁₃	semidirect
558. #124	C₂×C₄×C₁₃	semidirect
559. #123	C₂×C₄×C₁₃	semidirect
560. #123	C₂×C₄×C₁₃	semidirect
561. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
562. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
563. #121	C₂×C₄×C₁₃	semidirect
564. #121	C₂×C₄×C₁₃	semidirect
765. C₁₃	#34527	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×#562	2
C₁₃×#2382	2
C₁₃×#2379	2
C₁₃×#2374	2
C₁₃×#2364	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2359	2
C₁₃×#2335	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2329	2
C₁₃×#2324	2
C₁₃×#2322	2
C₄×C₁₃×#125	2
C₄×C₁₃×#124	2
#34527	13

Subgroups — C13×#34527 #15720866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34527 #15720866