Subgroups — C₂×C₁₃×#2488 #15721086

Order 3328.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 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	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2488	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	8	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊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×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#400	C₂²	1	8	yes	complemented
43	C₁₃×#400	C₂²	1	8	yes	complemented
44	C₁₃×#397	C₂²	1	8	yes	complemented
45	C₁₃×#393	C₂²	1	8	yes	complemented
46	C₁₃×#391	C₂²	1	8	yes	complemented
47	C₁₃×#388	C₂²	1	8	yes	complemented
48	C₁₃×#388	C₂²	1	8	yes	complemented
49	C₁₃×#386	C₂²	1	8	yes	—
50	C₁₃×#386	C₂²	1	8	yes	—
51	C₁₃×#382	C₂²	1	8	yes	complemented
52	C₁₃×#381	C₂²	1	8	yes	complemented
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
54	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	—	2	4	no	—
72	C₂²×Q₈×C₁₃	—	2	4	no	—
73	C₂²×Q₈×C₁₃	—	4	2	no	—
74	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	—	2	4	no	—
76	C₂²×D₄×C₁₃	—	2	4	no	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	—	2	4	no	—
80	C₂³×C₄×C₁₃	—	2	4	no	—
81	C₂³×C₄×C₁₃	—	2	4	no	—
82	C₂³×C₄×C₁₃	—	2	4	no	—
83	C₂³×C₄×C₁₃	—	2	4	no	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	4	2	no	—
87	C₂³×C₄×C₁₃	—	4	2	no	—
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
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	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	4	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	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×#123	—	2	32	no	—
105	C₁₃×C₂²⋊Q₈	—	2	32	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	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×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃	—	2	4	no	—
135	C₂×C₄²×C₁₃	—	4	2	no	—
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	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	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₂×#2488	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
164	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
165	C₂⁴×C₁₃	#41	1	4	yes	—
166	C₂⁴×C₁₃	#41	1	4	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
168	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
169	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×Q₈×C₁₃	—	2	8	no	—
171	C₂×Q₈×C₁₃	—	2	8	no	—
172	C₂×Q₈×C₁₃	—	4	4	no	—
173	C₂×Q₈×C₁₃	—	4	16	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	8	no	—
176	C₂×D₄×C₁₃	—	2	8	no	—
177	C₂×D₄×C₁₃	—	4	16	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	8	no	—
193	C₂²×C₄×C₁₃	—	2	8	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	8	no	—
200	C₂²×C₄×C₁₃	—	2	8	no	—
201	C₂²×C₄×C₁₃	—	2	8	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
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	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	8	no	—
219	C₂²×C₄×C₁₃	—	2	8	no	—
220	C₂²×C₄×C₁₃	—	4	4	no	—
221	C₂²×C₄×C₁₃	—	4	4	no	—
222	C₂²×C₄×C₁₃	—	4	16	no	—
223	C₂²×C₄×C₁₃	—	4	16	no	—
224	C₂²×C₄×C₁₃	—	4	16	no	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
227	C₂²×C₄×C₁₃	#41	1	4	yes	—
228	C₂²×C₄×C₁₃	#41	1	4	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	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₁₃×C₄⋊C₄	—	2	8	no	—
243	C₁₃×C₄⋊C₄	—	2	8	no	—
244	C₁₃×C₄⋊C₄	—	2	8	no	—
245	C₁₃×C₄⋊C₄	—	2	8	no	—
246	C₁₃×C₄⋊C₄	—	2	8	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	8	no	—
249	C₁₃×C₂²⋊C₄	—	2	8	no	—
250	C₁₃×C₂²⋊C₄	—	2	8	no	—
251	C₁₃×C₂²⋊C₄	—	2	8	no	—
252	C₁₃×C₂²⋊C₄	—	2	8	no	—
253	C₁₃×C₂²⋊C₄	—	4	4	no	—
254	C₁₃×C₂²⋊C₄	—	4	4	no	—
255	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
256	C₄²×C₁₃	—	2	8	no	—
257	C₄²×C₁₃	—	4	4	no	—
258	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic
259	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2488	C₂×C₁₃	1	16	yes	direct product factor
261	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#393	C₂×C₁₃	1	1	yes	characteristic, complemented
265	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
269	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
270	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂³×C₁₃	—	2	8	no	—
275	C₂³×C₁₃	—	2	8	no	—
276	C₂³×C₁₃	—	2	8	no	—
277	C₂³×C₁₃	—	2	8	no	—
278	C₂³×C₁₃	—	2	8	no	—
279	C₂³×C₁₃	—	2	8	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	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	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	—	4	4	no	—
297	C₂³×C₁₃	—	4	4	no	—
298	C₂³×C₁₃	#124	1	16	yes	—
299	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
300	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
301	C₂³×C₁₃	C₂×#41	1	4	yes	—
302	C₂³×C₁₃	C₂×#41	1	4	yes	—
303	C₂³×C₁₃	C₂×#41	1	2	yes	—
304	C₂³×C₁₃	C₂×#41	1	2	yes	—
305	C₂³×C₁₃	C₂×#41	1	2	yes	—
306	C₂³×C₁₃	C₂×#41	1	2	yes	—
307	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
308	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
309	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
310	Q₈×C₁₃	—	4	16	no	—
311	D₄×C₁₃	—	4	16	no	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	8	no	—
314	C₂×C₄×C₁₃	—	2	8	no	—
315	C₂×C₄×C₁₃	—	2	8	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	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	4	16	no	—
352	C₂×C₄×C₁₃	—	4	16	no	—
353	C₂×C₄×C₁₃	—	4	16	no	—
354	C₂×C₄×C₁₃	—	4	4	no	—
355	C₂×C₄×C₁₃	—	4	4	no	—
356	C₂×C₄×C₁₃	—	4	4	no	—
357	C₂×C₄×C₁₃	—	4	4	no	—
358	C₂×C₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	4	4	no	—
362	C₂×C₄×C₁₃	—	4	4	no	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
365	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
366	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
367	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#123	—	2	8	no	—
373	C₂×#123	C₂²×C₁₃	1	8	yes	—
374	C₂×C₂²⋊Q₈	—	2	8	no	—
375	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
376	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×C₄⋊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×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
392	#400	C₂²×C₁₃	1	8	yes	complemented
393	#400	C₂²×C₁₃	1	8	yes	complemented
394	#397	C₂²×C₁₃	1	8	yes	complemented
395	#393	C₂²×C₁₃	1	8	yes	complemented
396	#391	C₂²×C₁₃	1	8	yes	complemented
397	#388	C₂²×C₁₃	1	8	yes	complemented
398	#388	C₂²×C₁₃	1	8	yes	complemented
399	#386	C₂²×C₁₃	1	8	yes	—
400	#386	C₂²×C₁₃	1	8	yes	—
401	#382	C₂²×C₁₃	1	8	yes	complemented
402	#381	C₂²×C₁₃	1	8	yes	complemented
403	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
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	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
419	C₂²×C₁₃	—	2	4	no	—
420	C₂²×C₁₃	—	2	4	no	—
421	C₂²×C₁₃	—	2	4	no	—
422	C₂²×C₁₃	—	2	4	no	—
423	C₂²×C₁₃	—	2	4	no	—
424	C₂²×C₁₃	—	2	4	no	—
425	C₂²×C₁₃	—	2	32	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	8	8	no	—
434	C₂²×C₁₃	C₂×#124	1	8	yes	—
435	C₂²×C₁₃	C₂×#124	1	4	yes	—
436	C₂²×C₁₃	#529	1	4	yes	—
437	C₂²×C₁₃	#539	1	4	yes	—
438	C₂²×C₁₃	#546	1	4	yes	—
439	C₂²×C₁₃	#547	1	4	yes	—
440	C₂²×C₁₃	#551	1	4	yes	—
441	C₂²×C₁₃	#552	1	4	yes	—
442	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
443	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	2	4	no	—
451	C₄×C₁₃	—	2	4	no	—
452	C₄×C₁₃	—	2	4	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
463	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×Q₈	—	2	4	no	—
465	C₂²×Q₈	—	2	4	no	—
466	C₂²×Q₈	—	4	2	no	—
467	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	—	2	4	no	—
470	C₂²×D₄	—	2	4	no	—
471	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
472	C₂³×C₄	—	2	4	no	—
473	C₂³×C₄	—	2	4	no	—
474	C₂³×C₄	—	2	4	no	—
475	C₂³×C₄	—	2	4	no	—
476	C₂³×C₄	—	2	4	no	—
477	C₂³×C₄	—	2	4	no	—
478	C₂³×C₄	—	2	4	no	—
479	C₂³×C₄	—	4	2	no	—
480	C₂³×C₄	—	4	2	no	—
481	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
491	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
492	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
493	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	#123	—	2	32	no	—
498	C₂²⋊Q₈	—	2	32	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₄⋊C₄	—	2	4	no	—
503	C₂×C₄⋊C₄	—	2	4	no	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	4	2	no	—
516	C₂×C₂²⋊C₄	—	4	2	no	—
517	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
527	C₂×C₄²	—	2	4	no	—
528	C₂×C₄²	—	4	2	no	—
529	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
530	C₂×C₄²	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	#95	C₂³×C₁₃	1	4	yes	—
538	#95	C₂³×C₁₃	1	4	yes	—
539	#95	C₂³×C₁₃	1	4	yes	—
540	#95	C₂³×C₁₃	1	4	yes	—
541	#95	C₂³×C₁₃	1	4	yes	—
542	#95	C₂³×C₁₃	1	4	yes	—
543	#95	C₂³×C₁₃	1	4	yes	—
544	#95	C₂³×C₁₃	1	4	yes	—
545	C₂×C₁₃	—	2	8	no	—
546	C₂×C₁₃	—	8	2	no	—
547	C₂×C₁₃	#2488	1	8	yes	direct product factor
548	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
549	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
550	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
551	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
552	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
553	C₂×C₁₃	C₂×#551	1	1	yes	characteristic
554	C₂×C₁₃	C₂×#552	1	1	yes	characteristic
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	2	no	—
563	C₂⁴	—	2	2	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	2	no	—
566	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
567	C₂⁴	C₁₃×#41	1	4	yes	—
568	C₂⁴	C₁₃×#41	1	4	yes	—
569	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
570	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
571	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂×Q₈	—	2	8	no	—
573	C₂×Q₈	—	2	8	no	—
574	C₂×Q₈	—	4	4	no	—
575	C₂×Q₈	—	4	16	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	8	no	—
579	C₂×D₄	—	4	16	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	8	no	—
595	C₂²×C₄	—	2	8	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	2	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	8	no	—
621	C₂²×C₄	—	2	8	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	16	no	—
625	C₂²×C₄	—	4	16	no	—
626	C₂²×C₄	—	4	16	no	—
627	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
629	C₂²×C₄	C₁₃×#41	1	4	yes	—
630	C₂²×C₄	C₁₃×#41	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₄⋊C₄	—	2	8	no	—
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	2	8	no	—
648	C₄⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	8	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	—	4	4	no	—
657	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
658	C₄²	—	2	8	no	—
659	C₄²	—	4	4	no	—
660	C₁₃	C₂×#2488	1	1	yes	characteristic, direct product factor, Sylow
661	C₂³	—	2	8	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	8	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	4	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	4	no	—
685	C₂³	C₁₃×#124	1	16	yes	—
686	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
687	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
688	C₂³	C₂×C₁₃×#41	1	4	yes	—
689	C₂³	C₂×C₁₃×#41	1	4	yes	—
690	C₂³	C₂×C₁₃×#41	1	2	yes	—
691	C₂³	C₂×C₁₃×#41	1	2	yes	—
692	C₂³	C₂×C₁₃×#41	1	2	yes	—
693	C₂³	C₂×C₁₃×#41	1	2	yes	—
694	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
695	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
696	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
697	Q₈	—	4	16	no	—
698	D₄	—	4	16	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	8	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	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	16	no	—
739	C₂×C₄	—	4	16	no	—
740	C₂×C₄	—	4	16	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
752	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
753	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	2	32	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	8	no	—
769	C₂²	C₂×C₁₃×#124	1	8	yes	—
770	C₂²	C₂×C₁₃×#124	1	4	yes	—
771	C₂²	C₁₃×#529	1	4	yes	—
772	C₂²	C₁₃×#539	1	4	yes	—
773	C₂²	C₁₃×#546	1	4	yes	—
774	C₂²	C₁₃×#547	1	4	yes	—
775	C₂²	C₁₃×#551	1	4	yes	—
776	C₂²	C₁₃×#552	1	4	yes	—
777	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
778	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
779	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
780	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
781	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
782	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
784	C₄	—	2	4	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₂	—	2	8	no	—
798	C₂	—	8	2	no	—
799	C₂	C₁₃×#2488	1	8	yes	direct product factor
800	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
801	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
802	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
803	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
804	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
805	C₂	C₂×C₁₃×#551	1	1	yes	characteristic
806	C₂	C₂×C₁₃×#552	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2488	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#400	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#393	C₂	semidirect
8. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₁₃×#388	C₂	semidirect
13. C₂×C₁₃×#382	C₂	semidirect
14. C₂×C₁₃×#381	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
16. C₂²×C₁₃×#95	C₂	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
42. C₁₃×#400	C₂²	semidirect
43. C₁₃×#400	C₂²	semidirect
44. C₁₃×#397	C₂²	semidirect
45. C₁₃×#393	C₂²	semidirect
46. C₁₃×#391	C₂²	semidirect
47. C₁₃×#388	C₂²	semidirect
48. C₁₃×#388	C₂²	semidirect
51. C₁₃×#382	C₂²	semidirect
52. C₁₃×#381	C₂²	semidirect
53. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
68. C₂×C₁₃×#95	C₂²	semidirect
152. C₂×#2488	C₁₃	direct (N × H)
259. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
260. #2488	C₂×C₁₃	direct (N × H)
261. C₂×#400	C₂×C₁₃	semidirect
262. C₂×#400	C₂×C₁₃	semidirect
263. C₂×#397	C₂×C₁₃	semidirect
264. C₂×#393	C₂×C₁₃	semidirect
265. C₂×#391	C₂×C₁₃	semidirect
266. C₂×#388	C₂×C₁₃	semidirect
267. C₂×#388	C₂×C₁₃	semidirect
270. C₂×#382	C₂×C₁₃	semidirect
271. C₂×#381	C₂×C₁₃	semidirect
272. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
273. C₂²×#95	C₂×C₁₃	semidirect
375. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
392. #400	C₂²×C₁₃	semidirect
393. #400	C₂²×C₁₃	semidirect
394. #397	C₂²×C₁₃	semidirect
395. #393	C₂²×C₁₃	semidirect
396. #391	C₂²×C₁₃	semidirect
397. #388	C₂²×C₁₃	semidirect
398. #388	C₂²×C₁₃	semidirect
401. #382	C₂²×C₁₃	semidirect
402. #381	C₂²×C₁₃	semidirect
403. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
418. C₂×#95	C₂²×C₁₃	semidirect
547. C₂×C₁₃	#2488	direct (N × H)
660. C₁₃	C₂×#2488	direct (N × H)
799. C₂	C₁₃×#2488	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
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2488	2
C₂×C₁₃×#400	2
C₂×C₁₃×#397	2
C₂×C₁₃×#393	2
C₂×C₁₃×#391	2
C₂×C₁₃×#388	2
C₂×C₁₃×#386	2
C₂×C₁₃×#382	2
C₂×C₁₃×#381	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂²×C₁₃×#95	2
C₂×#2488	13

Subgroups — C2×C13×#2488 #15721086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2488 #15721086