Subgroups — C₁₃×#34988 #15721327

Order 3328.

4082 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2622	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2480	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2472	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2424	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2418	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
16	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#538	—	2	8	no	—
20	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#120	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	C₂²	1	2	yes	—
30	C₂×C₁₃×#120	C₂²	1	2	yes	—
31	C₂×C₁₃×#120	C₂²	1	4	yes	—
32	C₂×C₁₃×#120	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
35	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
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	4	yes	—
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#399	C₂²	1	2	yes	complemented
43	C₁₃×#397	C₂²	1	2	yes	complemented
44	C₁₃×#397	C₂²	1	4	yes	complemented
45	C₁₃×#397	C₂²	1	4	yes	complemented
46	C₁₃×#396	C₂²	1	4	yes	complemented
47	C₁₃×#394	C₂²	1	4	yes	complemented
48	C₁₃×#394	C₂²	1	4	yes	complemented
49	C₁₃×#394	C₂²	1	4	yes	complemented
50	C₁₃×#393	C₂²	1	2	yes	complemented
51	C₁₃×#392	C₂²	1	2	yes	complemented
52	C₁₃×#390	C₂²	1	4	yes	complemented
53	C₁₃×#388	C₂²	1	4	yes	complemented
54	C₁₃×#388	C₂²	1	4	yes	complemented
55	C₁₃×#388	C₂²	1	4	yes	complemented
56	C₁₃×#388	C₂²	1	4	yes	complemented
57	C₁₃×#386	C₂²	1	4	yes	complemented
58	C₁₃×#386	C₂²	1	2	yes	complemented
59	C₁₃×#386	C₂²	1	4	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	4	yes	complemented
64	C₁₃×#385	C₂²	1	2	yes	complemented
65	C₁₃×#385	C₂²	1	4	yes	complemented
66	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#380	C₂²	1	2	yes	complemented
69	C₁₃×#380	C₂²	1	2	yes	complemented
70	C₁₃×#379	C₂²	1	2	yes	—
71	C₁₃×#379	C₂²	1	2	yes	—
72	C₁₃×#379	C₂²	1	2	yes	—
73	C₁₃×#379	C₂²	1	4	yes	—
74	C₁₃×#379	C₂²	1	4	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
77	C₂⁵×C₁₃	—	2	4	no	—
78	C₂⁵×C₁₃	—	2	4	no	—
79	C₂⁵×C₁₃	—	2	4	no	—
80	C₂⁵×C₁₃	—	4	4	no	—
81	C₂⁵×C₁₃	—	4	4	no	—
82	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
83	C₂⁵×C₁₃	C₂³	1	4	yes	—
84	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
93	C₂³×C₄×C₁₃	—	2	4	no	—
94	C₂³×C₄×C₁₃	—	2	4	no	—
95	C₂³×C₄×C₁₃	—	4	4	no	—
96	C₂³×C₄×C₁₃	—	4	4	no	—
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	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
105	C₁₃×#126	—	2	8	no	—
106	C₁₃×#124	—	2	8	no	—
107	C₁₃×#123	—	2	8	no	—
108	C₁₃×C₂²⋊Q₈	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	—	4	4	no	—
110	C₁₃×#121	—	2	4	no	—
111	C₁₃×#121	—	2	8	no	—
112	C₁₃×#121	—	4	4	no	—
113	C₁₃×#120	—	2	8	no	—
114	C₁₃×#120	—	2	8	no	—
115	C₁₃×#120	—	2	8	no	—
116	C₁₃×#120	—	4	8	no	—
117	C₁₃×#120	—	4	8	no	—
118	C₄×D₄×C₁₃	—	2	8	no	—
119	C₄×D₄×C₁₃	—	4	8	no	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
128	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
158	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
159	C₁₃×#95	C₂³	1	4	yes	complemented
160	C₁₃×#95	C₂³	1	4	yes	complemented
161	C₁₃×#95	C₂³	1	4	yes	complemented
162	C₁₃×#95	C₂³	1	4	yes	complemented
163	C₁₃×#95	C₂³	1	2	yes	complemented
164	C₁₃×#95	C₂³	1	2	yes	complemented
165	C₁₃×#95	C₂³	1	4	yes	complemented
166	#34988	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	2	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	4	no	—
170	C₂⁴×C₁₃	—	2	4	no	—
171	C₂⁴×C₁₃	—	2	32	no	—
172	C₂⁴×C₁₃	—	2	8	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	2	8	no	—
175	C₂⁴×C₁₃	—	2	8	no	—
176	C₂⁴×C₁₃	—	2	2	no	—
177	C₂⁴×C₁₃	—	2	2	no	—
178	C₂⁴×C₁₃	—	2	2	no	—
179	C₂⁴×C₁₃	—	2	8	no	—
180	C₂⁴×C₁₃	—	2	8	no	—
181	C₂⁴×C₁₃	—	4	2	no	—
182	C₂⁴×C₁₃	—	4	2	no	—
183	C₂⁴×C₁₃	—	4	2	no	—
184	C₂⁴×C₁₃	—	4	2	no	—
185	C₂⁴×C₁₃	—	4	4	no	—
186	C₂⁴×C₁₃	—	4	4	no	—
187	C₂⁴×C₁₃	—	4	16	no	—
188	C₂⁴×C₁₃	—	4	16	no	—
189	C₂⁴×C₁₃	—	4	32	no	—
190	C₂⁴×C₁₃	—	4	32	no	—
191	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
192	C₂⁴×C₁₃	#41	1	4	yes	—
193	C₂⁴×C₁₃	#41	1	4	yes	—
194	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
195	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
196	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	4	2	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	8	no	—
205	C₂×D₄×C₁₃	—	2	8	no	—
206	C₂×D₄×C₁₃	—	2	8	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	8	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	4	no	—
214	C₂×D₄×C₁₃	—	4	4	no	—
215	C₂×D₄×C₁₃	—	4	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	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	4	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	2	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	4	no	—
233	C₂²×C₄×C₁₃	—	4	16	no	—
234	C₂²×C₄×C₁₃	—	4	16	no	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	4	4	no	—
252	C₁₃×C₄⋊C₄	—	4	2	no	—
253	C₁₃×C₄⋊C₄	—	4	2	no	—
254	C₁₃×C₄⋊C₄	—	4	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	8	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	8	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	8	no	—
263	C₁₃×C₂²⋊C₄	—	2	8	no	—
264	C₁₃×C₂²⋊C₄	—	2	8	no	—
265	C₁₃×C₂²⋊C₄	—	2	8	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	4	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	C₁₃×C₂²⋊C₄	—	4	4	no	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	—	4	4	no	—
280	C₂×#538	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#2846	C₂×C₁₃	1	2	yes	complemented
285	#2626	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#2622	C₂×C₁₃	1	2	yes	complemented
287	#2617	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#2480	C₂×C₁₃	1	4	yes	complemented
289	#2472	C₂×C₁₃	1	4	yes	complemented
290	#2424	C₂×C₁₃	1	4	yes	complemented
291	#2418	C₂×C₁₃	1	4	yes	complemented
292	#2321	C₂×C₁₃	1	2	yes	complemented
293	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₄×#120	C₂×C₁₃	1	2	yes	complemented
295	C₂³×C₁₃	—	2	8	no	—
296	C₂³×C₁₃	—	2	8	no	—
297	C₂³×C₁₃	—	2	16	no	—
298	C₂³×C₁₃	—	2	8	no	—
299	C₂³×C₁₃	—	2	16	no	—
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	32	no	—
307	C₂³×C₁₃	—	2	8	no	—
308	C₂³×C₁₃	—	2	8	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	4	no	—
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	4	no	—
316	C₂³×C₁₃	—	2	4	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	4	no	—
321	C₂³×C₁₃	—	2	4	no	—
322	C₂³×C₁₃	—	4	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	4	8	no	—
325	C₂³×C₁₃	—	4	16	no	—
326	C₂³×C₁₃	—	4	16	no	—
327	C₂³×C₁₃	—	4	16	no	—
328	C₂³×C₁₃	—	4	16	no	—
329	C₂³×C₁₃	—	4	128	no	—
330	C₂³×C₁₃	—	4	8	no	—
331	C₂³×C₁₃	—	4	8	no	—
332	C₂³×C₁₃	—	4	16	no	—
333	C₂³×C₁₃	—	4	4	no	—
334	C₂³×C₁₃	—	4	4	no	—
335	C₂³×C₁₃	—	4	8	no	—
336	C₂³×C₁₃	—	4	16	no	—
337	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
338	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₁₃	C₂×#41	1	4	yes	—
340	C₂³×C₁₃	C₂×#41	1	2	yes	—
341	C₂³×C₁₃	C₂×#41	1	2	yes	—
342	C₂³×C₁₃	C₂×#41	1	4	yes	—
343	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
344	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
345	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
346	Q₈×C₁₃	—	8	2	no	—
347	D₄×C₁₃	—	4	8	no	—
348	D₄×C₁₃	—	4	16	no	—
349	D₄×C₁₃	—	8	2	no	—
350	D₄×C₁₃	—	8	4	no	—
351	D₄×C₁₃	—	8	4	no	—
352	D₄×C₁₃	—	8	8	no	—
353	C₂×C₄×C₁₃	—	2	4	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	4	no	—
364	C₂×C₄×C₁₃	—	2	4	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	4	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	2	4	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	4	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	4	16	no	—
377	C₂×C₄×C₁₃	—	4	8	no	—
378	C₂×C₄×C₁₃	—	4	8	no	—
379	C₂×C₄×C₁₃	—	4	4	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	8	4	no	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
386	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
388	#538	—	2	8	no	—
389	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
390	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
391	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
392	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
394	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
395	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
397	C₂×#120	C₂²×C₁₃	1	2	yes	—
398	C₂×#120	C₂²×C₁₃	1	2	yes	—
399	C₂×#120	C₂²×C₁₃	1	2	yes	—
400	C₂×#120	C₂²×C₁₃	1	4	yes	—
401	C₂×#120	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	C₂²×C₂²⋊C₄	—	2	8	no	—
405	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
409	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
410	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	#399	C₂²×C₁₃	1	2	yes	complemented
412	#397	C₂²×C₁₃	1	2	yes	complemented
413	#397	C₂²×C₁₃	1	4	yes	complemented
414	#397	C₂²×C₁₃	1	4	yes	complemented
415	#396	C₂²×C₁₃	1	4	yes	complemented
416	#394	C₂²×C₁₃	1	4	yes	complemented
417	#394	C₂²×C₁₃	1	4	yes	complemented
418	#394	C₂²×C₁₃	1	4	yes	complemented
419	#393	C₂²×C₁₃	1	2	yes	complemented
420	#392	C₂²×C₁₃	1	2	yes	complemented
421	#390	C₂²×C₁₃	1	4	yes	complemented
422	#388	C₂²×C₁₃	1	4	yes	complemented
423	#388	C₂²×C₁₃	1	4	yes	complemented
424	#388	C₂²×C₁₃	1	4	yes	complemented
425	#388	C₂²×C₁₃	1	4	yes	complemented
426	#386	C₂²×C₁₃	1	4	yes	complemented
427	#386	C₂²×C₁₃	1	2	yes	complemented
428	#386	C₂²×C₁₃	1	4	yes	complemented
429	#386	C₂²×C₁₃	1	2	yes	complemented
430	#386	C₂²×C₁₃	1	4	yes	complemented
431	#385	C₂²×C₁₃	1	2	yes	complemented
432	#385	C₂²×C₁₃	1	4	yes	complemented
433	#385	C₂²×C₁₃	1	2	yes	complemented
434	#385	C₂²×C₁₃	1	4	yes	complemented
435	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#380	C₂²×C₁₃	1	2	yes	complemented
438	#380	C₂²×C₁₃	1	2	yes	complemented
439	#379	C₂²×C₁₃	1	2	yes	—
440	#379	C₂²×C₁₃	1	2	yes	—
441	#379	C₂²×C₁₃	1	2	yes	—
442	#379	C₂²×C₁₃	1	4	yes	—
443	#379	C₂²×C₁₃	1	4	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
445	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
446	C₂²×C₁₃	—	2	32	no	—
447	C₂²×C₁₃	—	2	4	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	4	no	—
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	2	4	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	—	2	4	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	8	no	—
462	C₂²×C₁₃	—	4	16	no	—
463	C₂²×C₁₃	—	4	16	no	—
464	C₂²×C₁₃	—	4	64	no	—
465	C₂²×C₁₃	—	4	4	no	—
466	C₂²×C₁₃	—	4	4	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	4	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	4	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	4	no	—
475	C₂²×C₁₃	#525	1	4	yes	—
476	C₂²×C₁₃	#538	1	8	yes	complemented
477	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
478	C₂²×C₁₃	C₂²×#41	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	C₂×H(5,𝔽₂)	1	2	yes	—
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	4	no	—
487	C₄×C₁₃	—	4	2	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	—	2	4	no	—
493	C₂⁵	—	2	4	no	—
494	C₂⁵	—	2	4	no	—
495	C₂⁵	—	4	4	no	—
496	C₂⁵	—	4	4	no	—
497	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
498	C₂⁵	C₂³×C₁₃	1	4	yes	—
499	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
500	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
504	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
505	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
506	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
507	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
508	C₂³×C₄	—	2	4	no	—
509	C₂³×C₄	—	2	4	no	—
510	C₂³×C₄	—	4	4	no	—
511	C₂³×C₄	—	4	4	no	—
512	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
513	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
520	#126	—	2	8	no	—
521	#124	—	2	8	no	—
522	#123	—	2	8	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	4	4	no	—
525	#121	—	2	4	no	—
526	#121	—	2	8	no	—
527	#121	—	4	4	no	—
528	#120	—	2	8	no	—
529	#120	—	2	8	no	—
530	#120	—	2	8	no	—
531	#120	—	4	8	no	—
532	#120	—	4	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	4	8	no	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₂²⋊C₄	—	2	4	no	—
546	C₂×C₂²⋊C₄	—	2	16	no	—
547	C₂×C₂²⋊C₄	—	2	16	no	—
548	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	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	2	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	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
573	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
574	#95	C₂³×C₁₃	1	4	yes	complemented
575	#95	C₂³×C₁₃	1	4	yes	complemented
576	#95	C₂³×C₁₃	1	4	yes	complemented
577	#95	C₂³×C₁₃	1	4	yes	complemented
578	#95	C₂³×C₁₃	1	2	yes	complemented
579	#95	C₂³×C₁₃	1	2	yes	complemented
580	#95	C₂³×C₁₃	1	4	yes	complemented
581	C₂×C₁₃	—	2	4	no	—
582	C₂×C₁₃	—	2	8	no	—
583	C₂×C₁₃	—	4	4	no	—
584	C₂×C₁₃	—	4	4	no	—
585	C₂×C₁₃	—	8	2	no	—
586	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
587	C₂×C₁₃	C₂×#538	1	2	yes	—
588	C₂×C₁₃	#3484	1	1	yes	characteristic
589	C₂×C₁₃	#3484	1	1	yes	characteristic
590	C₂×C₁₃	#3490	1	2	yes	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	4	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	32	no	—
596	C₂⁴	—	2	8	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	8	no	—
599	C₂⁴	—	2	8	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	8	no	—
604	C₂⁴	—	2	8	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	—	4	2	no	—
608	C₂⁴	—	4	2	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	4	16	no	—
612	C₂⁴	—	4	16	no	—
613	C₂⁴	—	4	32	no	—
614	C₂⁴	—	4	32	no	—
615	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
616	C₂⁴	C₁₃×#41	1	4	yes	—
617	C₂⁴	C₁₃×#41	1	4	yes	—
618	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
619	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
620	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
621	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
622	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	4	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	8	no	—
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	8	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	—	4	2	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	4	no	—
657	C₂²×C₄	—	4	16	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
660	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	4	4	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	4	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	8	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
701	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
702	C₄²	—	2	4	no	—
703	C₄²	—	4	4	no	—
704	C₁₃	#34988	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	8	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	16	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	16	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	2	no	—
716	C₂³	—	2	32	no	—
717	C₂³	—	2	8	no	—
718	C₂³	—	2	8	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	4	no	—
734	C₂³	—	4	8	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	16	no	—
737	C₂³	—	4	16	no	—
738	C₂³	—	4	16	no	—
739	C₂³	—	4	128	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	16	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	4	16	no	—
747	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
748	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
749	C₂³	C₂×C₁₃×#41	1	4	yes	—
750	C₂³	C₂×C₁₃×#41	1	2	yes	—
751	C₂³	C₂×C₁₃×#41	1	2	yes	—
752	C₂³	C₂×C₁₃×#41	1	4	yes	—
753	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
754	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
755	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
756	Q₈	—	8	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	16	no	—
759	D₄	—	8	2	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	8	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	16	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
795	C₂²	—	2	32	no	—
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	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	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	—	4	16	no	—
812	C₂²	—	4	16	no	—
813	C₂²	—	4	64	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	C₁₃×#525	1	4	yes	—
825	C₂²	C₁₃×#538	1	8	yes	complemented
826	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
827	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
828	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
829	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
830	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
831	C₄	—	2	4	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₂	—	2	4	no	—
842	C₂	—	2	8	no	—
843	C₂	—	4	4	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
847	C₂	C₂×C₁₃×#538	1	2	yes	—
848	C₂	C₁₃×#3484	1	1	yes	characteristic
849	C₂	C₁₃×#3484	1	1	yes	characteristic
850	C₂	C₁₃×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#538	C₂	semidirect
2. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2846	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2622	C₂	semidirect
8. C₁₃×#2617	C₂	semidirect
9. C₁₃×#2480	C₂	semidirect
10. C₁₃×#2472	C₂	semidirect
11. C₁₃×#2424	C₂	semidirect
12. C₁₃×#2418	C₂	semidirect
13. C₁₃×#2321	C₂	semidirect
14. C₁₃×#2312	C₂	semidirect
15. C₄×C₁₃×#120	C₂	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#124	C₂²	semidirect
22. C₂×C₁₃×#123	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
42. C₁₃×#399	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
44. C₁₃×#397	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#394	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#393	C₂²	semidirect
51. C₁₃×#392	C₂²	semidirect
52. C₁₃×#390	C₂²	semidirect
53. C₁₃×#388	C₂²	semidirect
54. C₁₃×#388	C₂²	semidirect
55. C₁₃×#388	C₂²	semidirect
56. C₁₃×#388	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×#380	C₂²	semidirect
67. C₁₃×#380	C₂²	semidirect
68. C₁₃×#380	C₂²	semidirect
69. C₁₃×#380	C₂²	semidirect
75. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
76. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
86. C₂²×Q₈×C₁₃	C₂³	semidirect
92. C₂²×D₄×C₁₃	C₂³	semidirect
104. C₂³×C₄×C₁₃	C₂³	semidirect
120. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
121. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
122. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
123. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
124. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
125. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
126. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
127. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
133. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
153. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
154. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
155. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
156. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
157. C₂×C₄²×C₁₃	C₂³	semidirect
158. C₂×C₄²×C₁₃	C₂³	semidirect
159. C₁₃×#95	C₂³	semidirect
160. C₁₃×#95	C₂³	semidirect
161. C₁₃×#95	C₂³	semidirect
162. C₁₃×#95	C₂³	semidirect
163. C₁₃×#95	C₂³	semidirect
164. C₁₃×#95	C₂³	semidirect
165. C₁₃×#95	C₂³	semidirect
166. #34988	C₁₃	direct (N × H)
280. C₂×#538	C₂×C₁₃	semidirect
281. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
282. #2848	C₂×C₁₃	semidirect
283. #2847	C₂×C₁₃	semidirect
284. #2846	C₂×C₁₃	semidirect
285. #2626	C₂×C₁₃	semidirect
286. #2622	C₂×C₁₃	semidirect
287. #2617	C₂×C₁₃	semidirect
288. #2480	C₂×C₁₃	semidirect
289. #2472	C₂×C₁₃	semidirect
290. #2424	C₂×C₁₃	semidirect
291. #2418	C₂×C₁₃	semidirect
292. #2321	C₂×C₁₃	semidirect
293. #2312	C₂×C₁₃	semidirect
294. C₄×#120	C₂×C₁₃	semidirect
389. C₂×#126	C₂²×C₁₃	semidirect
390. C₂×#124	C₂²×C₁₃	semidirect
391. C₂×#123	C₂²×C₁₃	semidirect
392. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
393. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
394. C₂×#121	C₂²×C₁₃	semidirect
395. C₂×#121	C₂²×C₁₃	semidirect
396. C₂×#121	C₂²×C₁₃	semidirect
402. C₂×C₄×D₄	C₂²×C₁₃	semidirect
403. C₂×C₄×D₄	C₂²×C₁₃	semidirect
411. #399	C₂²×C₁₃	semidirect
412. #397	C₂²×C₁₃	semidirect
413. #397	C₂²×C₁₃	semidirect
414. #397	C₂²×C₁₃	semidirect
415. #396	C₂²×C₁₃	semidirect
416. #394	C₂²×C₁₃	semidirect
417. #394	C₂²×C₁₃	semidirect
418. #394	C₂²×C₁₃	semidirect
419. #393	C₂²×C₁₃	semidirect
420. #392	C₂²×C₁₃	semidirect
421. #390	C₂²×C₁₃	semidirect
422. #388	C₂²×C₁₃	semidirect
423. #388	C₂²×C₁₃	semidirect
424. #388	C₂²×C₁₃	semidirect
425. #388	C₂²×C₁₃	semidirect
426. #386	C₂²×C₁₃	semidirect
427. #386	C₂²×C₁₃	semidirect
428. #386	C₂²×C₁₃	semidirect
429. #386	C₂²×C₁₃	semidirect
430. #386	C₂²×C₁₃	semidirect
431. #385	C₂²×C₁₃	semidirect
432. #385	C₂²×C₁₃	semidirect
433. #385	C₂²×C₁₃	semidirect
434. #385	C₂²×C₁₃	semidirect
435. #380	C₂²×C₁₃	semidirect
436. #380	C₂²×C₁₃	semidirect
437. #380	C₂²×C₁₃	semidirect
438. #380	C₂²×C₁₃	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
445. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
476. C₂²×C₁₃	#538	semidirect
501. C₂²×Q₈	C₂³×C₁₃	semidirect
507. C₂²×D₄	C₂³×C₁₃	semidirect
519. C₂³×C₄	C₂³×C₁₃	semidirect
535. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
536. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
537. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
538. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
539. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
540. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
541. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
542. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
548. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
568. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
569. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
570. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
571. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
572. C₂×C₄²	C₂³×C₁₃	semidirect
573. C₂×C₄²	C₂³×C₁₃	semidirect
574. #95	C₂³×C₁₃	semidirect
575. #95	C₂³×C₁₃	semidirect
576. #95	C₂³×C₁₃	semidirect
577. #95	C₂³×C₁₃	semidirect
578. #95	C₂³×C₁₃	semidirect
579. #95	C₂³×C₁₃	semidirect
580. #95	C₂³×C₁₃	semidirect
704. C₁₃	#34988	direct (N × H)
825. C₂²	C₁₃×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#538	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2846	2
C₁₃×#2626	2
C₁₃×#2622	2
C₁₃×#2617	2
C₁₃×#2480	2
C₁₃×#2472	2
C₁₃×#2424	2
C₁₃×#2418	2
C₁₃×#2321	2
C₁₃×#2312	2
C₄×C₁₃×#120	2
#34988	13

Subgroups — C13×#34988 #15721327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34988 #15721327