Subgroups — C₂×C₁₃×#2335 #15720417

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2335	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
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
20	C₂×C₁₃×#123	C₄	1	16	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	8	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	8	yes	—
45	C₁₃×#389	C₂²	1	8	yes	complemented
46	C₁₃×#388	C₂²	1	8	yes	complemented
47	C₁₃×#388	C₂²	1	8	yes	complemented
48	C₁₃×#388	C₂²	1	8	yes	complemented
49	C₁₃×#388	C₂²	1	8	yes	complemented
50	C₁₃×#387	C₂²	1	8	yes	complemented
51	C₁₃×#387	C₂²	1	8	yes	complemented
52	C₁₃×#386	C₂²	1	8	yes	—
53	C₁₃×#385	C₂²	1	8	yes	complemented
54	C₁₃×#380	C₂²	1	8	yes	complemented
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	—	4	2	no	—
71	C₂²×D₄×C₁₃	—	4	2	no	—
72	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	—	2	4	no	—
75	C₂³×C₄×C₁₃	—	4	2	no	—
76	C₂³×C₄×C₁₃	—	4	2	no	—
77	C₂³×C₄×C₁₃	—	4	2	no	—
78	C₂³×C₄×C₁₃	—	4	2	no	—
79	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
95	C₁₃×#123	C₂×C₄	1	64	yes	complemented
96	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
101	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
102	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	—	2	4	no	—
131	C₂×C₄²×C₁₃	—	4	2	no	—
132	C₂×C₄²×C₁₃	—	4	2	no	—
133	C₂×C₄²×C₁₃	—	4	2	no	—
134	C₂×C₄²×C₁₃	—	4	2	no	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₂×#2335	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	2	no	—
152	C₂⁴×C₁₃	—	2	2	no	—
153	C₂⁴×C₁₃	—	2	2	no	—
154	C₂⁴×C₁₃	—	2	2	no	—
155	C₂⁴×C₁₃	—	2	2	no	—
156	C₂⁴×C₁₃	—	2	2	no	—
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	—	2	2	no	—
159	C₂⁴×C₁₃	—	2	2	no	—
160	C₂⁴×C₁₃	—	2	2	no	—
161	C₂⁴×C₁₃	—	2	2	no	—
162	C₂⁴×C₁₃	—	2	2	no	—
163	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
164	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₁₃	—	4	16	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	—	4	4	no	—
171	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	8	no	—
205	C₂²×C₄×C₁₃	—	4	16	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	4	no	—
210	C₂²×C₄×C₁₃	—	4	16	no	—
211	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
217	C₂²×C₄×C₁₃	#41	1	4	yes	—
218	C₂²×C₄×C₁₃	#41	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	—	2	8	no	—
233	C₁₃×C₄⋊C₄	—	4	4	no	—
234	C₁₃×C₄⋊C₄	—	4	4	no	—
235	C₁₃×C₄⋊C₄	—	4	4	no	—
236	C₁₃×C₄⋊C₄	—	4	4	no	—
237	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
238	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
239	C₁₃×C₂²⋊C₄	—	2	8	no	—
240	C₁₃×C₂²⋊C₄	—	2	8	no	—
241	C₁₃×C₂²⋊C₄	—	2	8	no	—
242	C₁₃×C₂²⋊C₄	—	4	4	no	—
243	C₁₃×C₂²⋊C₄	—	4	4	no	—
244	C₁₃×C₂²⋊C₄	—	4	4	no	—
245	C₁₃×C₂²⋊C₄	—	4	4	no	—
246	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
247	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
248	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
249	C₄²×C₁₃	—	2	8	no	—
250	C₄²×C₁₃	—	4	4	no	—
251	C₄²×C₁₃	—	4	4	no	—
252	C₄²×C₁₃	—	4	4	no	—
253	C₄²×C₁₃	—	4	4	no	—
254	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic
255	#2335	C₂×C₁₃	1	16	yes	direct product factor
256	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
257	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
265	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
270	C₂³×C₁₃	—	2	8	no	—
271	C₂³×C₁₃	—	2	8	no	—
272	C₂³×C₁₃	—	2	8	no	—
273	C₂³×C₁₃	—	2	8	no	—
274	C₂³×C₁₃	—	2	8	no	—
275	C₂³×C₁₃	—	2	8	no	—
276	C₂³×C₁₃	—	2	2	no	—
277	C₂³×C₁₃	—	2	2	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	4	4	no	—
289	C₂³×C₁₃	—	4	4	no	—
290	C₂³×C₁₃	—	4	4	no	—
291	C₂³×C₁₃	—	4	4	no	—
292	C₂³×C₁₃	—	4	4	no	—
293	C₂³×C₁₃	—	4	4	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
297	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
298	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
299	C₂³×C₁₃	C₂×#41	1	2	yes	—
300	C₂³×C₁₃	C₂×#41	1	2	yes	—
301	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
302	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
303	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
304	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
305	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
306	D₄×C₁₃	—	4	16	no	—
307	C₂×C₄×C₁₃	—	2	8	no	—
308	C₂×C₄×C₁₃	—	2	8	no	—
309	C₂×C₄×C₁₃	—	2	8	no	—
310	C₂×C₄×C₁₃	—	2	8	no	—
311	C₂×C₄×C₁₃	—	2	8	no	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	8	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	4	16	no	—
347	C₂×C₄×C₁₃	—	4	16	no	—
348	C₂×C₄×C₁₃	—	4	4	no	—
349	C₂×C₄×C₁₃	—	4	4	no	—
350	C₂×C₄×C₁₃	—	4	4	no	—
351	C₂×C₄×C₁₃	—	4	4	no	—
352	C₂×C₄×C₁₃	—	4	4	no	—
353	C₂×C₄×C₁₃	—	4	4	no	—
354	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
355	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
356	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
357	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
358	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
359	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
361	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#123	C₄×C₁₃	1	16	yes	complemented
365	C₂×#123	C₂²×C₁₃	1	8	yes	—
366	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
388	#390	C₂²×C₁₃	1	8	yes	—
389	#389	C₂²×C₁₃	1	8	yes	complemented
390	#388	C₂²×C₁₃	1	8	yes	complemented
391	#388	C₂²×C₁₃	1	8	yes	complemented
392	#388	C₂²×C₁₃	1	8	yes	complemented
393	#388	C₂²×C₁₃	1	8	yes	complemented
394	#387	C₂²×C₁₃	1	8	yes	complemented
395	#387	C₂²×C₁₃	1	8	yes	complemented
396	#386	C₂²×C₁₃	1	8	yes	—
397	#385	C₂²×C₁₃	1	8	yes	complemented
398	#380	C₂²×C₁₃	1	8	yes	complemented
399	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
400	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
401	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
402	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×C₁₃	—	2	4	no	—
413	C₂²×C₁₃	—	2	4	no	—
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	4	no	—
417	C₂²×C₁₃	—	2	4	no	—
418	C₂²×C₁₃	—	4	16	no	—
419	C₂²×C₁₃	—	4	16	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	C₄×#41	1	4	yes	—
429	C₂²×C₁₃	#518	1	4	yes	—
430	C₂²×C₁₃	#520	1	4	yes	—
431	C₂²×C₁₃	#538	1	4	yes	—
432	C₂²×C₁₃	#539	1	4	yes	—
433	C₂²×C₁₃	#540	1	4	yes	—
434	C₂²×C₁₃	#542	1	4	yes	—
435	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
436	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
442	C₄×C₁₃	—	2	4	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	2	4	no	—
446	C₄×C₁₃	—	2	4	no	—
447	C₄×C₁₃	—	2	4	no	—
448	C₄×C₁₃	—	2	4	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
456	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×D₄	—	4	2	no	—
458	C₂²×D₄	—	4	2	no	—
459	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
460	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
461	C₂³×C₄	—	2	4	no	—
462	C₂³×C₄	—	4	2	no	—
463	C₂³×C₄	—	4	2	no	—
464	C₂³×C₄	—	4	2	no	—
465	C₂³×C₄	—	4	2	no	—
466	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
467	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
481	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
482	#123	C₂×C₄×C₁₃	1	64	yes	complemented
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	—	4	2	no	—
485	C₂×C₄⋊C₄	—	4	2	no	—
486	C₂×C₄⋊C₄	—	4	2	no	—
487	C₂×C₄⋊C₄	—	4	2	no	—
488	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
489	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	4	2	no	—
501	C₂×C₂²⋊C₄	—	4	2	no	—
502	C₂×C₂²⋊C₄	—	4	2	no	—
503	C₂×C₂²⋊C₄	—	4	2	no	—
504	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
505	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
506	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
517	C₂×C₄²	—	2	4	no	—
518	C₂×C₄²	—	4	2	no	—
519	C₂×C₄²	—	4	2	no	—
520	C₂×C₄²	—	4	2	no	—
521	C₂×C₄²	—	4	2	no	—
522	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
523	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
527	#95	C₂³×C₁₃	1	4	yes	—
528	#95	C₂³×C₁₃	1	4	yes	—
529	#95	C₂³×C₁₃	1	4	yes	—
530	#95	C₂³×C₁₃	1	4	yes	—
531	#95	C₂³×C₁₃	1	4	yes	—
532	#95	C₂³×C₁₃	1	4	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	#95	C₂³×C₁₃	1	4	yes	—
535	#95	C₂³×C₁₃	1	4	yes	—
536	#95	C₂³×C₁₃	1	4	yes	—
537	C₂×C₁₃	—	4	4	no	—
538	C₂×C₁₃	—	4	4	no	—
539	C₂×C₁₃	#2335	1	8	yes	direct product factor
540	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
541	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
542	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
543	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
544	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
545	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
546	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
560	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
561	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
562	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
563	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
564	C₂×D₄	—	4	16	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	4	16	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	16	no	—
607	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
608	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
609	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
610	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
611	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
612	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
613	C₂²×C₄	C₁₃×#41	1	4	yes	—
614	C₂²×C₄	C₁₃×#41	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₄⋊C₄	—	4	4	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
634	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
644	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
645	C₄²	—	2	8	no	—
646	C₄²	—	4	4	no	—
647	C₄²	—	4	4	no	—
648	C₄²	—	4	4	no	—
649	C₄²	—	4	4	no	—
650	C₁₃	C₂×#2335	1	1	yes	characteristic, direct product factor, Sylow
651	C₂³	—	2	8	no	—
652	C₂³	—	2	8	no	—
653	C₂³	—	2	8	no	—
654	C₂³	—	2	8	no	—
655	C₂³	—	2	8	no	—
656	C₂³	—	2	8	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
678	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
679	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
680	C₂³	C₂×C₁₃×#41	1	2	yes	—
681	C₂³	C₂×C₁₃×#41	1	2	yes	—
682	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
683	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
684	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
685	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
686	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
687	D₄	—	4	16	no	—
688	C₂×C₄	—	2	8	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	16	no	—
728	C₂×C₄	—	4	16	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
736	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
737	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
738	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
739	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
740	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
741	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	16	no	—
749	C₂²	—	4	16	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₄×C₁₃×#41	1	4	yes	—
759	C₂²	C₁₃×#518	1	4	yes	—
760	C₂²	C₁₃×#520	1	4	yes	—
761	C₂²	C₁₃×#538	1	4	yes	—
762	C₂²	C₁₃×#539	1	4	yes	—
763	C₂²	C₁₃×#540	1	4	yes	—
764	C₂²	C₁₃×#542	1	4	yes	—
765	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
766	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
767	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
768	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
769	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
770	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
772	C₄	—	2	4	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	4	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	4	no	—
778	C₄	—	2	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₂	—	4	4	no	—
786	C₂	—	4	4	no	—
787	C₂	C₁₃×#2335	1	8	yes	direct product factor
788	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
789	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
790	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
791	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
792	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
793	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
794	C₂	C₂×C₁₃×#542	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2335	C₂	direct (N × H)
4. C₂×C₁₃×#389	C₂	semidirect
5. C₂×C₁₃×#388	C₂	semidirect
6. C₂×C₁₃×#388	C₂	semidirect
7. C₂×C₁₃×#388	C₂	semidirect
8. C₂×C₁₃×#388	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₁₃×#387	C₂	semidirect
12. C₂×C₁₃×#385	C₂	semidirect
13. C₂×C₁₃×#380	C₂	semidirect
14. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
16. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
20. C₂×C₁₃×#123	C₄	semidirect
45. C₁₃×#389	C₂²	semidirect
46. C₁₃×#388	C₂²	semidirect
47. C₁₃×#388	C₂²	semidirect
48. C₁₃×#388	C₂²	semidirect
49. C₁₃×#388	C₂²	semidirect
50. C₁₃×#387	C₂²	semidirect
51. C₁₃×#387	C₂²	semidirect
53. C₁₃×#385	C₂²	semidirect
54. C₁₃×#380	C₂²	semidirect
55. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
56. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
57. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
79. C₂³×C₄×C₁₃	C₂×C₄	semidirect
95. C₁₃×#123	C₂×C₄	semidirect
101. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
102. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
119. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
150. C₂×#2335	C₁₃	direct (N × H)
216. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
237. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
238. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
248. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
255. #2335	C₂×C₁₃	direct (N × H)
257. C₂×#389	C₂×C₁₃	semidirect
258. C₂×#388	C₂×C₁₃	semidirect
259. C₂×#388	C₂×C₁₃	semidirect
260. C₂×#388	C₂×C₁₃	semidirect
261. C₂×#388	C₂×C₁₃	semidirect
262. C₂×#387	C₂×C₁₃	semidirect
263. C₂×#387	C₂×C₁₃	semidirect
265. C₂×#385	C₂×C₁₃	semidirect
266. C₂×#380	C₂×C₁₃	semidirect
267. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
268. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
269. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
364. C₂×#123	C₄×C₁₃	semidirect
389. #389	C₂²×C₁₃	semidirect
390. #388	C₂²×C₁₃	semidirect
391. #388	C₂²×C₁₃	semidirect
392. #388	C₂²×C₁₃	semidirect
393. #388	C₂²×C₁₃	semidirect
394. #387	C₂²×C₁₃	semidirect
395. #387	C₂²×C₁₃	semidirect
397. #385	C₂²×C₁₃	semidirect
398. #380	C₂²×C₁₃	semidirect
399. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
400. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
401. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
466. C₂³×C₄	C₂×C₄×C₁₃	semidirect
482. #123	C₂×C₄×C₁₃	semidirect
488. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
489. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
506. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
539. C₂×C₁₃	#2335	direct (N × H)
612. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
633. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
634. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
644. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
650. C₁₃	C₂×#2335	direct (N × H)
787. C₂	C₁₃×#2335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#123	2
C₁₃×#2335	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2335	13

Subgroups — C2×C13×#2335 #15720417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2335 #15720417