Subgroups — C₂×C₁₃×#2444 #15721007

Order 3328.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2444	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#394	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×#386	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×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	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	—	2	8	no	—
25	C₂×C₁₃×#121	C₂²	1	8	yes	—
26	C₂×C₄×D₄×C₁₃	—	2	8	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
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×C₄⋊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×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
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#400	C₂²	1	8	yes	complemented
45	C₁₃×#397	C₂²	1	8	yes	complemented
46	C₁₃×#397	C₂²	1	8	yes	complemented
47	C₁₃×#394	C₂²	1	8	yes	complemented
48	C₁₃×#388	C₂²	1	8	yes	complemented
49	C₁₃×#387	C₂²	1	8	yes	complemented
50	C₁₃×#386	C₂²	1	8	yes	complemented
51	C₁₃×#386	C₂²	1	8	yes	complemented
52	C₁₃×#386	C₂²	1	8	yes	complemented
53	C₁₃×#386	C₂²	1	8	yes	complemented
54	C₁₃×#385	C₂²	1	8	yes	complemented
55	C₁₃×#381	C₂²	1	8	yes	complemented
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	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	—	2	4	no	—
73	C₂²×D₄×C₁₃	—	2	4	no	—
74	C₂²×D₄×C₁₃	—	2	4	no	—
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	—	2	4	no	—
79	C₂²×D₄×C₁₃	—	4	2	no	—
80	C₂²×D₄×C₁₃	D₄	1	8	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	—	2	4	no	—
89	C₂³×C₄×C₁₃	—	2	4	no	—
90	C₂³×C₄×C₁₃	—	2	4	no	—
91	C₂³×C₄×C₁₃	—	4	2	no	—
92	C₂³×C₄×C₁₃	—	4	2	no	—
93	C₂³×C₄×C₁₃	—	4	2	no	—
94	C₂³×C₄×C₁₃	—	4	2	no	—
95	C₂³×C₄×C₁₃	—	4	2	no	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
112	C₁₃×#121	—	2	32	no	—
113	C₄×D₄×C₁₃	—	2	32	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₄²×C₁₃	—	2	4	no	—
145	C₂×C₄²×C₁₃	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	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₂×#2444	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	—	2	2	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
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	—	2	2	no	—
176	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
177	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
178	C₂⁴×C₁₃	#41	1	4	yes	—
179	C₂⁴×C₁₃	#41	1	4	yes	—
180	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×D₄×C₁₃	—	2	32	no	—
185	C₂×D₄×C₁₃	—	2	8	no	—
186	C₂×D₄×C₁₃	—	2	8	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	8	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	16	no	—
194	C₂×D₄×C₁₃	—	4	16	no	—
195	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
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	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	8	no	—
208	C₂²×C₄×C₁₃	—	2	8	no	—
209	C₂²×C₄×C₁₃	—	2	8	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	8	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	8	no	—
234	C₂²×C₄×C₁₃	—	2	8	no	—
235	C₂²×C₄×C₁₃	—	2	8	no	—
236	C₂²×C₄×C₁₃	—	4	4	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	4	4	no	—
239	C₂²×C₄×C₁₃	—	4	4	no	—
240	C₂²×C₄×C₁₃	—	4	4	no	—
241	C₂²×C₄×C₁₃	—	4	16	no	—
242	C₂²×C₄×C₁₃	—	4	16	no	—
243	C₂²×C₄×C₁₃	—	4	16	no	—
244	C₂²×C₄×C₁₃	—	4	16	no	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃	#41	1	4	yes	—
247	C₂²×C₄×C₁₃	#41	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	2	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	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	—	2	8	no	—
261	C₁₃×C₄⋊C₄	—	2	8	no	—
262	C₁₃×C₄⋊C₄	—	2	8	no	—
263	C₁₃×C₄⋊C₄	—	4	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	8	no	—
265	C₁₃×C₂²⋊C₄	—	2	8	no	—
266	C₁₃×C₂²⋊C₄	—	2	8	no	—
267	C₁₃×C₂²⋊C₄	—	2	8	no	—
268	C₁₃×C₂²⋊C₄	—	2	8	no	—
269	C₁₃×C₂²⋊C₄	—	2	8	no	—
270	C₁₃×C₂²⋊C₄	—	4	4	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	—	4	4	no	—
275	C₄²×C₁₃	—	2	8	no	—
276	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
277	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2444	C₂×C₁₃	1	16	yes	direct product factor
279	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#394	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#386	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂³×C₁₃	—	2	8	no	—
293	C₂³×C₁₃	—	2	8	no	—
294	C₂³×C₁₃	—	2	8	no	—
295	C₂³×C₁₃	—	2	8	no	—
296	C₂³×C₁₃	—	2	8	no	—
297	C₂³×C₁₃	—	2	8	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	8	no	—
303	C₂³×C₁₃	—	2	8	no	—
304	C₂³×C₁₃	—	2	8	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	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	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	4	4	no	—
319	C₂³×C₁₃	—	4	4	no	—
320	C₂³×C₁₃	—	4	4	no	—
321	C₂³×C₁₃	—	4	4	no	—
322	C₂³×C₁₃	—	4	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	4	4	no	—
325	C₂³×C₁₃	—	4	4	no	—
326	C₂³×C₁₃	—	4	4	no	—
327	C₂³×C₁₃	—	4	4	no	—
328	C₂³×C₁₃	—	4	4	no	—
329	C₂³×C₁₃	#123	1	16	yes	—
330	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
331	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
332	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₁₃	C₂×#41	1	4	yes	—
334	C₂³×C₁₃	C₂×#41	1	4	yes	—
335	C₂³×C₁₃	C₂×#41	1	2	yes	—
336	C₂³×C₁₃	C₂×#41	1	2	yes	—
337	C₂³×C₁₃	C₂×#41	1	2	yes	—
338	C₂³×C₁₃	C₂×#41	1	2	yes	—
339	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
340	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
341	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
342	D₄×C₁₃	—	2	32	no	—
343	D₄×C₁₃	—	4	16	no	—
344	D₄×C₁₃	—	4	16	no	—
345	C₂×C₄×C₁₃	—	2	8	no	—
346	C₂×C₄×C₁₃	—	2	8	no	—
347	C₂×C₄×C₁₃	—	2	8	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	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	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	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	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	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	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	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	4	16	no	—
382	C₂×C₄×C₁₃	—	4	16	no	—
383	C₂×C₄×C₁₃	—	4	16	no	—
384	C₂×C₄×C₁₃	—	4	16	no	—
385	C₂×C₄×C₁₃	—	4	4	no	—
386	C₂×C₄×C₁₃	—	4	4	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	4	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
395	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
396	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
397	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
398	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
399	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#121	—	2	8	no	—
405	C₂×#121	C₂²×C₁₃	1	8	yes	—
406	C₂×C₄×D₄	—	2	8	no	—
407	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
408	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₄⋊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
414	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
424	#400	C₂²×C₁₃	1	8	yes	complemented
425	#397	C₂²×C₁₃	1	8	yes	complemented
426	#397	C₂²×C₁₃	1	8	yes	complemented
427	#394	C₂²×C₁₃	1	8	yes	complemented
428	#388	C₂²×C₁₃	1	8	yes	complemented
429	#387	C₂²×C₁₃	1	8	yes	complemented
430	#386	C₂²×C₁₃	1	8	yes	complemented
431	#386	C₂²×C₁₃	1	8	yes	complemented
432	#386	C₂²×C₁₃	1	8	yes	complemented
433	#386	C₂²×C₁₃	1	8	yes	complemented
434	#385	C₂²×C₁₃	1	8	yes	complemented
435	#381	C₂²×C₁₃	1	8	yes	complemented
436	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
449	C₂²×C₁₃	—	2	4	no	—
450	C₂²×C₁₃	—	2	4	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	2	32	no	—
454	C₂²×C₁₃	—	2	4	no	—
455	C₂²×C₁₃	—	2	4	no	—
456	C₂²×C₁₃	—	2	4	no	—
457	C₂²×C₁₃	—	2	4	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	16	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	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	—	8	8	no	—
472	C₂²×C₁₃	C₂×#123	1	8	yes	—
473	C₂²×C₁₃	C₂×#123	1	4	yes	—
474	C₂²×C₁₃	#529	1	4	yes	—
475	C₂²×C₁₃	#538	1	4	yes	—
476	C₂²×C₁₃	#546	1	4	yes	—
477	C₂²×C₁₃	#546	1	4	yes	—
478	C₂²×C₁₃	#553	1	4	yes	—
479	C₂²×C₁₃	#553	1	4	yes	—
480	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
481	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
482	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
483	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
485	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	2	4	no	—
489	C₄×C₁₃	—	2	4	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
500	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
501	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	—	2	4	no	—
503	C₂²×D₄	—	2	4	no	—
504	C₂²×D₄	—	2	4	no	—
505	C₂²×D₄	—	2	4	no	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	4	2	no	—
510	C₂²×D₄	D₄×C₁₃	1	8	yes	—
511	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
512	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
513	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
514	C₂³×C₄	—	2	4	no	—
515	C₂³×C₄	—	2	4	no	—
516	C₂³×C₄	—	2	4	no	—
517	C₂³×C₄	—	2	4	no	—
518	C₂³×C₄	—	2	4	no	—
519	C₂³×C₄	—	2	4	no	—
520	C₂³×C₄	—	2	4	no	—
521	C₂³×C₄	—	4	2	no	—
522	C₂³×C₄	—	4	2	no	—
523	C₂³×C₄	—	4	2	no	—
524	C₂³×C₄	—	4	2	no	—
525	C₂³×C₄	—	4	2	no	—
526	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
536	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
537	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
538	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
542	#121	—	2	32	no	—
543	C₄×D₄	—	2	32	no	—
544	C₂×C₄⋊C₄	—	2	4	no	—
545	C₂×C₄⋊C₄	—	2	4	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	4	2	no	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	4	2	no	—
559	C₂×C₂²⋊C₄	—	4	2	no	—
560	C₂×C₂²⋊C₄	—	4	2	no	—
561	C₂×C₂²⋊C₄	—	4	2	no	—
562	C₂×C₂²⋊C₄	—	4	2	no	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	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	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄²	—	2	4	no	—
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	#95	C₂³×C₁₃	1	4	yes	—
585	#95	C₂³×C₁₃	1	4	yes	—
586	#95	C₂³×C₁₃	1	4	yes	—
587	#95	C₂³×C₁₃	1	4	yes	—
588	C₂×C₁₃	—	2	8	no	—
589	C₂×C₁₃	—	4	4	no	—
590	C₂×C₁₃	—	8	2	no	—
591	C₂×C₁₃	#2444	1	8	yes	direct product factor
592	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
593	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
594	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
595	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
596	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
597	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
598	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
599	C₂⁴	—	2	2	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
617	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
618	C₂⁴	C₁₃×#41	1	4	yes	—
619	C₂⁴	C₁₃×#41	1	4	yes	—
620	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
621	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
622	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
623	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂×D₄	—	2	32	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	2	8	no	—
627	C₂×D₄	—	2	8	no	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	16	no	—
634	C₂×D₄	—	4	16	no	—
635	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	2	8	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	8	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	8	no	—
674	C₂²×C₄	—	2	8	no	—
675	C₂²×C₄	—	2	8	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	—	4	4	no	—
678	C₂²×C₄	—	4	4	no	—
679	C₂²×C₄	—	4	4	no	—
680	C₂²×C₄	—	4	4	no	—
681	C₂²×C₄	—	4	16	no	—
682	C₂²×C₄	—	4	16	no	—
683	C₂²×C₄	—	4	16	no	—
684	C₂²×C₄	—	4	16	no	—
685	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
686	C₂²×C₄	C₁₃×#41	1	4	yes	—
687	C₂²×C₄	C₁₃×#41	1	4	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃	1	2	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	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
700	C₄⋊C₄	—	2	8	no	—
701	C₄⋊C₄	—	2	8	no	—
702	C₄⋊C₄	—	2	8	no	—
703	C₄⋊C₄	—	4	4	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	2	8	no	—
707	C₂²⋊C₄	—	2	8	no	—
708	C₂²⋊C₄	—	2	8	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₄²	—	2	8	no	—
716	C₁₃	C₂×#2444	1	1	yes	characteristic, direct product factor, Sylow
717	C₂³	—	2	8	no	—
718	C₂³	—	2	8	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	8	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	8	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	8	no	—
728	C₂³	—	2	8	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	4	no	—
746	C₂³	—	4	4	no	—
747	C₂³	—	4	4	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	4	no	—
751	C₂³	—	4	4	no	—
752	C₂³	—	4	4	no	—
753	C₂³	—	4	4	no	—
754	C₂³	C₁₃×#123	1	16	yes	—
755	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
756	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
757	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
758	C₂³	C₂×C₁₃×#41	1	4	yes	—
759	C₂³	C₂×C₁₃×#41	1	4	yes	—
760	C₂³	C₂×C₁₃×#41	1	2	yes	—
761	C₂³	C₂×C₁₃×#41	1	2	yes	—
762	C₂³	C₂×C₁₃×#41	1	2	yes	—
763	C₂³	C₂×C₁₃×#41	1	2	yes	—
764	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
765	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
766	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
767	D₄	—	2	32	no	—
768	D₄	—	4	16	no	—
769	D₄	—	4	16	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	8	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	4	16	no	—
807	C₂×C₄	—	4	16	no	—
808	C₂×C₄	—	4	16	no	—
809	C₂×C₄	—	4	16	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
820	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
821	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	32	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	16	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	8	no	—
845	C₂²	C₂×C₁₃×#123	1	8	yes	—
846	C₂²	C₂×C₁₃×#123	1	4	yes	—
847	C₂²	C₁₃×#529	1	4	yes	—
848	C₂²	C₁₃×#538	1	4	yes	—
849	C₂²	C₁₃×#546	1	4	yes	—
850	C₂²	C₁₃×#546	1	4	yes	—
851	C₂²	C₁₃×#553	1	4	yes	—
852	C₂²	C₁₃×#553	1	4	yes	—
853	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
854	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
855	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
856	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
857	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
858	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
859	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
860	C₄	—	2	4	no	—
861	C₄	—	2	4	no	—
862	C₄	—	2	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₂	—	2	8	no	—
873	C₂	—	4	4	no	—
874	C₂	—	8	2	no	—
875	C₂	C₁₃×#2444	1	8	yes	direct product factor
876	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
877	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
878	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
879	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
880	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
881	C₂	C₂×C₁₃×#553	1	1	yes	characteristic
882	C₂	C₂×C₁₃×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
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×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2444	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#397	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#394	C₂	semidirect
8. C₂×C₁₃×#388	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₁₃×#386	C₂	semidirect
11. C₂×C₁₃×#386	C₂	semidirect
12. C₂×C₁₃×#386	C₂	semidirect
13. C₂×C₁₃×#386	C₂	semidirect
14. C₂×C₁₃×#385	C₂	semidirect
15. C₂×C₁₃×#381	C₂	semidirect
16. C₂²×C₁₃×#95	C₂	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₁₃×#400	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#388	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
50. C₁₃×#386	C₂²	semidirect
51. C₁₃×#386	C₂²	semidirect
52. C₁₃×#386	C₂²	semidirect
53. C₁₃×#386	C₂²	semidirect
54. C₁₃×#385	C₂²	semidirect
55. C₁₃×#381	C₂²	semidirect
68. C₂×C₁₃×#95	C₂²	semidirect
158. C₂×#2444	C₁₃	direct (N × H)
277. C₂²×C₄×D₄	C₂×C₁₃	semidirect
278. #2444	C₂×C₁₃	direct (N × H)
279. C₂×#400	C₂×C₁₃	semidirect
280. C₂×#397	C₂×C₁₃	semidirect
281. C₂×#397	C₂×C₁₃	semidirect
282. C₂×#394	C₂×C₁₃	semidirect
283. C₂×#388	C₂×C₁₃	semidirect
284. C₂×#387	C₂×C₁₃	semidirect
285. C₂×#386	C₂×C₁₃	semidirect
286. C₂×#386	C₂×C₁₃	semidirect
287. C₂×#386	C₂×C₁₃	semidirect
288. C₂×#386	C₂×C₁₃	semidirect
289. C₂×#385	C₂×C₁₃	semidirect
290. C₂×#381	C₂×C₁₃	semidirect
291. C₂²×#95	C₂×C₁₃	semidirect
407. C₂×C₄×D₄	C₂²×C₁₃	semidirect
424. #400	C₂²×C₁₃	semidirect
425. #397	C₂²×C₁₃	semidirect
426. #397	C₂²×C₁₃	semidirect
427. #394	C₂²×C₁₃	semidirect
428. #388	C₂²×C₁₃	semidirect
429. #387	C₂²×C₁₃	semidirect
430. #386	C₂²×C₁₃	semidirect
431. #386	C₂²×C₁₃	semidirect
432. #386	C₂²×C₁₃	semidirect
433. #386	C₂²×C₁₃	semidirect
434. #385	C₂²×C₁₃	semidirect
435. #381	C₂²×C₁₃	semidirect
448. C₂×#95	C₂²×C₁₃	semidirect
591. C₂×C₁₃	#2444	direct (N × H)
716. C₁₃	C₂×#2444	direct (N × H)
875. C₂	C₁₃×#2444	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×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2444	2
C₂×C₁₃×#400	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#381	2
C₂²×C₁₃×#95	2
C₂×#2444	13

Subgroups — C2×C13×#2444 #15721007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2444 #15721007