Subgroups — C₁₃×#34264 #15720603

Order 3328.

3658 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2364	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2359	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2358	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2273	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#534	C₄	1	16	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₁₃×#120	C₂²	1	2	yes	—
25	C₂×C₁₃×#120	C₂²	1	2	yes	—
26	C₁₃×#518	—	2	8	no	—
27	C₂×C₄×D₄×C₁₃	—	2	8	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
45	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#390	C₂²	1	4	yes	complemented
47	C₁₃×#389	C₂²	1	4	yes	complemented
48	C₁₃×#388	C₂²	1	4	yes	complemented
49	C₁₃×#388	C₂²	1	4	yes	complemented
50	C₁₃×#388	C₂²	1	4	yes	complemented
51	C₁₃×#388	C₂²	1	4	yes	complemented
52	C₁₃×#387	C₂²	1	4	yes	complemented
53	C₁₃×#387	C₂²	1	4	yes	complemented
54	C₁₃×#386	C₂²	1	2	yes	—
55	C₁₃×#386	C₂²	1	2	yes	—
56	C₁₃×#386	C₂²	1	4	yes	—
57	C₁₃×#386	C₂²	1	4	yes	complemented
58	C₁₃×#386	C₂²	1	4	yes	complemented
59	C₁₃×#386	C₂²	1	2	yes	complemented
60	C₁₃×#386	C₂²	1	2	yes	complemented
61	C₁₃×#386	C₂²	1	4	yes	complemented
62	C₁₃×#385	C₂²	1	2	yes	complemented
63	C₁₃×#385	C₂²	1	2	yes	complemented
64	C₁₃×#385	C₂²	1	4	yes	complemented
65	C₁₃×#385	C₂²	1	4	yes	complemented
66	C₁₃×#385	C₂²	1	4	yes	complemented
67	C₁₃×#381	C₂²	1	2	yes	complemented
68	C₁₃×#379	C₂²	1	2	yes	complemented
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
77	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
78	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
80	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	—	2	4	no	—
82	C₂²×D₄×C₁₃	—	2	4	no	—
83	C₂²×D₄×C₁₃	—	2	4	no	—
84	C₂²×D₄×C₁₃	—	2	4	no	—
85	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
86	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃	—	2	4	no	—
93	C₂³×C₄×C₁₃	—	2	4	no	—
94	C₂³×C₄×C₁₃	—	4	4	no	—
95	C₂³×C₄×C₁₃	—	4	4	no	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#123	C₂×C₄	1	16	yes	complemented
112	C₁₃×#123	C₂×C₄	1	16	yes	complemented
113	C₁₃×#121	C₂×C₄	1	32	yes	complemented
114	C₁₃×#120	C₂×C₄	1	16	yes	complemented
115	C₁₃×#120	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₁₃	—	2	8	no	—
117	C₄×D₄×C₁₃	—	2	8	no	—
118	C₄×D₄×C₁₃	—	2	16	no	—
119	C₄×D₄×C₁₃	—	2	16	no	—
120	C₄×D₄×C₁₃	—	2	8	no	—
121	C₄×D₄×C₁₃	—	2	8	no	—
122	C₄×D₄×C₁₃	—	4	8	no	—
123	C₁₃×#117	—	2	8	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
138	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	—	2	4	no	—
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	C₁₃×#95	C₂³	1	4	yes	—
170	#34264	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂⁴×C₁₃	—	2	2	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	2	2	no	—
175	C₂⁴×C₁₃	—	4	2	no	—
176	C₂⁴×C₁₃	—	4	2	no	—
177	C₂⁴×C₁₃	—	4	2	no	—
178	C₂⁴×C₁₃	—	4	2	no	—
179	C₂⁴×C₁₃	—	4	2	no	—
180	C₂⁴×C₁₃	—	4	2	no	—
181	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
182	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
183	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	complemented
184	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
185	C₂⁴×C₁₃	#41	1	4	yes	—
186	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×D₄×C₁₃	—	2	32	no	—
192	C₂×D₄×C₁₃	—	2	32	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
204	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
205	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
206	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	complemented
207	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	complemented
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	8	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	4	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	4	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	4	16	no	—
241	C₂²×C₄×C₁₃	—	4	16	no	—
242	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	complemented
244	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
245	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₁₃×C₄⋊C₄	—	2	8	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	8	no	—
261	C₁₃×C₄⋊C₄	—	4	4	no	—
262	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	8	no	—
270	C₁₃×C₂²⋊C₄	—	2	8	no	—
271	C₁₃×C₂²⋊C₄	—	4	4	no	—
272	C₁₃×C₂²⋊C₄	—	4	4	no	—
273	C₁₃×C₂²⋊C₄	—	4	4	no	—
274	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
275	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
276	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
277	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
280	C₄²×C₁₃	—	2	8	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	4	4	no	—
284	C₄²×C₁₃	—	4	4	no	—
285	C₂×#534	C₂×C₁₃	1	1	yes	characteristic
286	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#2364	C₂×C₁₃	1	4	yes	complemented
289	#2361	C₂×C₁₃	1	4	yes	complemented
290	#2359	C₂×C₁₃	1	4	yes	complemented
291	#2358	C₂×C₁₃	1	4	yes	complemented
292	#2322	C₂×C₁₃	1	2	yes	complemented
293	#2321	C₂×C₁₃	1	2	yes	complemented
294	#2308	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₄×#123	C₂×C₁₃	1	2	yes	complemented
296	C₄×#120	C₂×C₁₃	1	2	yes	complemented
297	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2273	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	8	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	4	no	—
312	C₂³×C₁₃	—	2	4	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	8	no	—
316	C₂³×C₁₃	—	4	4	no	—
317	C₂³×C₁₃	—	4	8	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	4	no	—
320	C₂³×C₁₃	—	4	8	no	—
321	C₂³×C₁₃	—	4	8	no	—
322	C₂³×C₁₃	—	4	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	4	8	no	—
325	C₂³×C₁₃	—	8	2	no	—
326	C₂³×C₁₃	—	8	2	no	—
327	C₂³×C₁₃	—	8	4	no	—
328	C₂³×C₁₃	C₄×D₄	1	16	yes	complemented
329	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
330	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
331	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
332	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
333	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
334	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
336	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
337	C₂³×C₁₃	C₂×#41	1	2	yes	—
338	C₂³×C₁₃	C₂×#41	1	2	yes	—
339	C₂³×C₁₃	C₂×#41	1	2	yes	—
340	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
341	D₄×C₁₃	—	2	16	no	—
342	D₄×C₁₃	—	2	16	no	—
343	D₄×C₁₃	—	2	16	no	—
344	D₄×C₁₃	—	2	16	no	—
345	D₄×C₁₃	—	4	16	no	—
346	C₂×C₄×C₁₃	—	2	8	no	—
347	C₂×C₄×C₁₃	—	2	8	no	—
348	C₂×C₄×C₁₃	—	2	8	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	4	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	4	16	no	—
373	C₂×C₄×C₁₃	—	4	8	no	—
374	C₂×C₄×C₁₃	—	4	8	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	—	8	2	no	—
379	C₂×C₄×C₁₃	—	8	2	no	—
380	C₂×C₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
382	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
383	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
387	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
389	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	#534	C₄×C₁₃	1	16	yes	complemented
392	C₂×#123	C₂²×C₁₃	1	2	yes	—
393	C₂×#123	C₂²×C₁₃	1	2	yes	—
394	C₂×#121	C₂²×C₁₃	1	4	yes	—
395	C₂×#120	C₂²×C₁₃	1	2	yes	—
396	C₂×#120	C₂²×C₁₃	1	2	yes	—
397	#518	—	2	8	no	—
398	C₂×C₄×D₄	—	2	8	no	—
399	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
403	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
405	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
406	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
407	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
409	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
416	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#390	C₂²×C₁₃	1	4	yes	complemented
418	#389	C₂²×C₁₃	1	4	yes	complemented
419	#388	C₂²×C₁₃	1	4	yes	complemented
420	#388	C₂²×C₁₃	1	4	yes	complemented
421	#388	C₂²×C₁₃	1	4	yes	complemented
422	#388	C₂²×C₁₃	1	4	yes	complemented
423	#387	C₂²×C₁₃	1	4	yes	complemented
424	#387	C₂²×C₁₃	1	4	yes	complemented
425	#386	C₂²×C₁₃	1	4	yes	—
426	#386	C₂²×C₁₃	1	2	yes	—
427	#386	C₂²×C₁₃	1	2	yes	—
428	#386	C₂²×C₁₃	1	2	yes	complemented
429	#386	C₂²×C₁₃	1	2	yes	complemented
430	#386	C₂²×C₁₃	1	4	yes	complemented
431	#386	C₂²×C₁₃	1	4	yes	complemented
432	#386	C₂²×C₁₃	1	4	yes	complemented
433	#385	C₂²×C₁₃	1	2	yes	complemented
434	#385	C₂²×C₁₃	1	4	yes	complemented
435	#385	C₂²×C₁₃	1	4	yes	complemented
436	#385	C₂²×C₁₃	1	4	yes	complemented
437	#385	C₂²×C₁₃	1	2	yes	complemented
438	#381	C₂²×C₁₃	1	2	yes	complemented
439	#379	C₂²×C₁₃	1	2	yes	complemented
440	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
441	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
442	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
443	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
445	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
446	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
447	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
448	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
449	C₂²×C₁₃	—	2	4	no	—
450	C₂²×C₁₃	—	2	4	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	2	2	no	—
454	C₂²×C₁₃	—	2	2	no	—
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	4	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	8	no	—
464	C₂²×C₁₃	—	2	8	no	—
465	C₂²×C₁₃	—	4	16	no	—
466	C₂²×C₁₃	—	4	16	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	4	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	—	8	8	no	—
474	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
475	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
476	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
477	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
478	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
479	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
481	C₂²×C₁₃	#585	1	2	yes	—
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	2	4	no	—
484	C₄×C₁₃	—	2	8	no	—
485	C₄×C₁₃	—	2	4	no	—
486	C₄×C₁₃	—	2	4	no	—
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	4	no	—
492	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
493	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
494	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
500	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
501	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
505	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	2	4	no	—
508	C₂³×C₄	—	4	4	no	—
509	C₂³×C₄	—	4	4	no	—
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
512	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
514	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
521	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	#123	C₂×C₄×C₁₃	1	16	yes	complemented
526	#123	C₂×C₄×C₁₃	1	16	yes	complemented
527	#121	C₂×C₄×C₁₃	1	32	yes	complemented
528	#120	C₂×C₄×C₁₃	1	16	yes	complemented
529	#120	C₂×C₄×C₁₃	1	16	yes	complemented
530	C₄×D₄	—	2	8	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	16	no	—
533	C₄×D₄	—	2	16	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	4	8	no	—
537	#117	—	2	8	no	—
538	C₂×C₄⋊C₄	—	2	4	no	—
539	C₂×C₄⋊C₄	—	4	4	no	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
546	C₂×C₂²⋊C₄	—	2	4	no	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₂²⋊C₄	—	2	4	no	—
549	C₂×C₂²⋊C₄	—	2	8	no	—
550	C₂×C₂²⋊C₄	—	4	4	no	—
551	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
552	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄²	—	2	4	no	—
571	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
575	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
576	#95	C₂³×C₁₃	1	4	yes	—
577	#95	C₂³×C₁₃	1	4	yes	—
578	#95	C₂³×C₁₃	1	4	yes	—
579	#95	C₂³×C₁₃	1	4	yes	—
580	#95	C₂³×C₁₃	1	4	yes	—
581	#95	C₂³×C₁₃	1	4	yes	—
582	#95	C₂³×C₁₃	1	4	yes	—
583	#95	C₂³×C₁₃	1	4	yes	—
584	C₂×C₁₃	—	2	4	no	—
585	C₂×C₁₃	—	2	4	no	—
586	C₂×C₁₃	—	2	4	no	—
587	C₂×C₁₃	—	4	4	no	—
588	C₂×C₁₃	—	4	4	no	—
589	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
590	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
591	C₂×C₁₃	#3484	1	1	yes	characteristic
592	C₂×C₁₃	#3485	1	1	yes	characteristic
593	C₂×C₁₃	#3505	1	2	yes	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	4	2	no	—
599	C₂⁴	—	4	2	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	4	2	no	—
604	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
605	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
606	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	complemented
607	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
608	C₂⁴	C₁₃×#41	1	4	yes	—
609	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
610	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
611	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
612	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂×D₄	—	2	32	no	—
615	C₂×D₄	—	2	32	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
627	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
628	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
629	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	complemented
630	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	complemented
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	8	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	4	no	—
660	C₂²×C₄	—	4	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	16	no	—
664	C₂²×C₄	—	4	16	no	—
665	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
666	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	complemented
667	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
668	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
669	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	—	2	8	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	4	4	no	—
685	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	8	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
698	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
699	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
700	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
701	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
702	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
703	C₄²	—	2	8	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	4	4	no	—
707	C₄²	—	4	4	no	—
708	C₁₃	#34264	1	1	yes	characteristic, direct product factor, Sylow
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	8	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	8	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	8	no	—
730	C₂³	—	4	8	no	—
731	C₂³	—	4	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	8	2	no	—
735	C₂³	—	8	2	no	—
736	C₂³	—	8	4	no	—
737	C₂³	C₄×D₄×C₁₃	1	16	yes	complemented
738	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
739	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
740	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
741	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
742	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
744	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
745	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
746	C₂³	C₂×C₁₃×#41	1	2	yes	—
747	C₂³	C₂×C₁₃×#41	1	2	yes	—
748	C₂³	C₂×C₁₃×#41	1	2	yes	—
749	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
750	D₄	—	2	16	no	—
751	D₄	—	2	16	no	—
752	D₄	—	2	16	no	—
753	D₄	—	2	16	no	—
754	D₄	—	4	16	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	8	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	16	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	4	no	—
790	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
791	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
792	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
795	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	8	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	4	16	no	—
813	C₂²	—	4	16	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	8	8	no	—
821	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
822	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
823	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
824	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
825	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
826	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
827	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
828	C₂²	C₁₃×#585	1	2	yes	—
829	C₄	—	2	4	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	8	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₂	—	2	4	no	—
840	C₂	—	2	4	no	—
841	C₂	—	2	4	no	—
842	C₂	—	4	4	no	—
843	C₂	—	4	4	no	—
844	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
845	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
846	C₂	C₁₃×#3484	1	1	yes	characteristic
847	C₂	C₁₃×#3485	1	1	yes	characteristic
848	C₂	C₁₃×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#534	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. C₂×C₁₃×#518	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2364	C₂	semidirect
5. C₁₃×#2361	C₂	semidirect
6. C₁₃×#2359	C₂	semidirect
7. C₁₃×#2358	C₂	semidirect
8. C₁₃×#2322	C₂	semidirect
9. C₁₃×#2321	C₂	semidirect
10. C₁₃×#2308	C₂	semidirect
11. C₄×C₁₃×#123	C₂	semidirect
12. C₄×C₁₃×#120	C₂	semidirect
13. C₂×C₁₃×#386	C₂	semidirect
14. C₂×C₁₃×#385	C₂	semidirect
15. C₁₃×#2273	C₂	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₁₃×#534	C₄	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₁₃×#117	C₂²	semidirect
36. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
42. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
43. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
45. C₂²×C₄²×C₁₃	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#389	C₂²	semidirect
48. C₁₃×#388	C₂²	semidirect
49. C₁₃×#388	C₂²	semidirect
50. C₁₃×#388	C₂²	semidirect
51. C₁₃×#388	C₂²	semidirect
52. C₁₃×#387	C₂²	semidirect
53. C₁₃×#387	C₂²	semidirect
57. C₁₃×#386	C₂²	semidirect
58. C₁₃×#386	C₂²	semidirect
59. C₁₃×#386	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
61. C₁₃×#386	C₂²	semidirect
62. C₁₃×#385	C₂²	semidirect
63. C₁₃×#385	C₂²	semidirect
64. C₁₃×#385	C₂²	semidirect
65. C₁₃×#385	C₂²	semidirect
66. C₁₃×#385	C₂²	semidirect
67. C₁₃×#381	C₂²	semidirect
68. C₁₃×#379	C₂²	semidirect
69. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
70. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
71. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
72. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
73. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
74. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
75. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
76. C₂×C₁₃×#95	C₂²	semidirect
77. C₂×C₁₃×#95	C₂²	semidirect
85. C₂²×D₄×C₁₃	C₂×C₄	semidirect
86. C₂²×D₄×C₁₃	C₂×C₄	semidirect
111. C₁₃×#123	C₂×C₄	semidirect
112. C₁₃×#123	C₂×C₄	semidirect
113. C₁₃×#121	C₂×C₄	semidirect
114. C₁₃×#120	C₂×C₄	semidirect
115. C₁₃×#120	C₂×C₄	semidirect
137. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
138. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
170. #34264	C₁₃	direct (N × H)
183. C₂⁴×C₁₃	C₂²×C₄	semidirect
206. C₂×D₄×C₁₃	C₂²×C₄	semidirect
207. C₂×D₄×C₁₃	C₂²×C₄	semidirect
243. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
244. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
262. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
275. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
276. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
277. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
286. C₂×#518	C₂×C₁₃	semidirect
287. C₂²×C₄×D₄	C₂×C₁₃	semidirect
288. #2364	C₂×C₁₃	semidirect
289. #2361	C₂×C₁₃	semidirect
290. #2359	C₂×C₁₃	semidirect
291. #2358	C₂×C₁₃	semidirect
292. #2322	C₂×C₁₃	semidirect
293. #2321	C₂×C₁₃	semidirect
294. #2308	C₂×C₁₃	semidirect
295. C₄×#123	C₂×C₁₃	semidirect
296. C₄×#120	C₂×C₁₃	semidirect
297. C₂×#386	C₂×C₁₃	semidirect
298. C₂×#385	C₂×C₁₃	semidirect
299. #2273	C₂×C₁₃	semidirect
328. C₂³×C₁₃	C₄×D₄	semidirect
390. C₂⁴×C₄	C₂²×C₁₃	semidirect
391. #534	C₄×C₁₃	semidirect
402. C₂×C₄×D₄	C₂²×C₁₃	semidirect
403. C₂×C₄×D₄	C₂²×C₁₃	semidirect
404. C₂×C₄×D₄	C₂²×C₁₃	semidirect
405. C₂×C₄×D₄	C₂²×C₁₃	semidirect
406. C₂×#117	C₂²×C₁₃	semidirect
407. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
408. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
413. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
414. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
415. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
416. C₂²×C₄²	C₂²×C₁₃	semidirect
417. #390	C₂²×C₁₃	semidirect
418. #389	C₂²×C₁₃	semidirect
419. #388	C₂²×C₁₃	semidirect
420. #388	C₂²×C₁₃	semidirect
421. #388	C₂²×C₁₃	semidirect
422. #388	C₂²×C₁₃	semidirect
423. #387	C₂²×C₁₃	semidirect
424. #387	C₂²×C₁₃	semidirect
428. #386	C₂²×C₁₃	semidirect
429. #386	C₂²×C₁₃	semidirect
430. #386	C₂²×C₁₃	semidirect
431. #386	C₂²×C₁₃	semidirect
432. #386	C₂²×C₁₃	semidirect
433. #385	C₂²×C₁₃	semidirect
434. #385	C₂²×C₁₃	semidirect
435. #385	C₂²×C₁₃	semidirect
436. #385	C₂²×C₁₃	semidirect
437. #385	C₂²×C₁₃	semidirect
438. #381	C₂²×C₁₃	semidirect
439. #379	C₂²×C₁₃	semidirect
440. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
441. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
442. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
443. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
445. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
446. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
447. C₂×#95	C₂²×C₁₃	semidirect
448. C₂×#95	C₂²×C₁₃	semidirect
499. C₂²×D₄	C₂×C₄×C₁₃	semidirect
500. C₂²×D₄	C₂×C₄×C₁₃	semidirect
525. #123	C₂×C₄×C₁₃	semidirect
526. #123	C₂×C₄×C₁₃	semidirect
527. #121	C₂×C₄×C₁₃	semidirect
528. #120	C₂×C₄×C₁₃	semidirect
529. #120	C₂×C₄×C₁₃	semidirect
551. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
552. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
606. C₂⁴	C₂²×C₄×C₁₃	semidirect
629. C₂×D₄	C₂²×C₄×C₁₃	semidirect
630. C₂×D₄	C₂²×C₄×C₁₃	semidirect
666. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
667. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
685. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
698. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
699. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
700. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
708. C₁₃	#34264	direct (N × H)
737. C₂³	C₄×D₄×C₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#534	2
C₂×C₁₃×#518	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2364	2
C₁₃×#2361	2
C₁₃×#2359	2
C₁₃×#2358	2
C₁₃×#2322	2
C₁₃×#2321	2
C₁₃×#2308	2
C₄×C₁₃×#123	2
C₄×C₁₃×#120	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₁₃×#2273	2
#34264	13

Subgroups — C13×#34264 #15720603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34264 #15720603