Subgroups — C₁₃×#35031 #15721370

Order 3328.

2966 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2622	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2613	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2602	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2600	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2485	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2415	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2414	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2407	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
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	C₁₃×#525	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#120	C₂²	1	2	yes	—
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	—	2	8	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#397	C₂²	1	4	yes	complemented
47	C₁₃×#397	C₂²	1	4	yes	complemented
48	C₁₃×#394	C₂²	1	4	yes	—
49	C₁₃×#394	C₂²	1	4	yes	—
50	C₁₃×#394	C₂²	1	4	yes	complemented
51	C₁₃×#394	C₂²	1	4	yes	complemented
52	C₁₃×#392	C₂²	1	4	yes	—
53	C₁₃×#392	C₂²	1	4	yes	—
54	C₁₃×#391	C₂²	1	2	yes	complemented
55	C₁₃×#390	C₂²	1	4	yes	complemented
56	C₁₃×#390	C₂²	1	2	yes	complemented
57	C₁₃×#389	C₂²	1	4	yes	complemented
58	C₁₃×#389	C₂²	1	2	yes	complemented
59	C₁₃×#389	C₂²	1	2	yes	complemented
60	C₁₃×#388	C₂²	1	4	yes	complemented
61	C₁₃×#388	C₂²	1	4	yes	complemented
62	C₁₃×#388	C₂²	1	4	yes	complemented
63	C₁₃×#388	C₂²	1	4	yes	complemented
64	C₁₃×#387	C₂²	1	4	yes	complemented
65	C₁₃×#387	C₂²	1	4	yes	complemented
66	C₁₃×#386	C₂²	1	2	yes	—
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	4	yes	complemented
69	C₁₃×#386	C₂²	1	4	yes	complemented
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	4	yes	complemented
73	C₁₃×#385	C₂²	1	4	yes	complemented
74	C₁₃×#381	C₂²	1	2	yes	—
75	C₁₃×#381	C₂²	1	2	yes	complemented
76	C₁₃×#380	C₂²	1	1	yes	characteristic
77	C₁₃×#380	C₂²	1	1	yes	characteristic
78	C₁₃×#380	C₂²	1	2	yes	complemented
79	C₁₃×#380	C₂²	1	2	yes	complemented
80	C₁₃×#380	C₂²	1	2	yes	complemented
81	C₁₃×#379	C₂²	1	2	yes	—
82	C₁₃×#379	C₂²	1	2	yes	—
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
84	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	2	4	no	—
92	C₂²×D₄×C₁₃	—	2	4	no	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	—	2	4	no	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	—	4	4	no	—
103	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#123	—	2	8	no	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	4	4	no	—
121	C₁₃×#121	—	2	4	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#121	—	4	4	no	—
124	C₁₃×#120	—	2	8	no	—
125	C₁₃×#120	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	2	8	no	—
128	C₄×D₄×C₁₃	—	2	8	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	—	2	8	no	—
131	C₄×D₄×C₁₃	—	2	8	no	—
132	C₁₃×#117	—	2	4	no	—
133	C₁₃×#117	—	4	4	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₄²×C₁₃	—	2	4	no	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
172	C₁₃×#95	C₂³	1	4	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	4	yes	—
179	C₁₃×#95	C₂³	1	4	yes	—
180	C₁₃×#95	C₂³	1	4	yes	—
181	#35031	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	—	2	2	no	—
184	C₂⁴×C₁₃	—	2	2	no	—
185	C₂⁴×C₁₃	—	2	2	no	—
186	C₂⁴×C₁₃	—	4	2	no	—
187	C₂⁴×C₁₃	—	4	2	no	—
188	C₂⁴×C₁₃	—	4	2	no	—
189	C₂⁴×C₁₃	—	4	2	no	—
190	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
191	C₂⁴×C₁₃	#41	1	4	yes	complemented
192	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
193	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
196	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₁₃×#41	—	4	16	no	—
198	C₂×Q₈×C₁₃	—	2	2	no	—
199	C₂×Q₈×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	32	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	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	8	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	4	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	4	16	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	4	no	—
240	C₂²×C₄×C₁₃	—	4	16	no	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₁₃	#41	1	4	yes	complemented
248	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	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	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	8	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	4	4	no	—
270	C₁₃×C₄⋊C₄	—	4	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	8	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	8	no	—
284	C₁₃×C₂²⋊C₄	—	4	4	no	—
285	C₁₃×C₂²⋊C₄	—	4	4	no	—
286	C₁₃×C₂²⋊C₄	—	4	4	no	—
287	C₁₃×C₂²⋊C₄	—	4	4	no	—
288	C₁₃×C₂²⋊C₄	—	4	4	no	—
289	C₁₃×C₂²⋊C₄	—	4	4	no	—
290	C₄²×C₁₃	—	2	4	no	—
291	C₄²×C₁₃	—	2	4	no	—
292	C₄²×C₁₃	—	2	4	no	—
293	C₄²×C₁₃	—	4	4	no	—
294	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2855	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2854	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2622	C₂×C₁₃	1	2	yes	complemented
301	#2613	C₂×C₁₃	1	2	yes	complemented
302	#2602	C₂×C₁₃	1	4	yes	complemented
303	#2600	C₂×C₁₃	1	4	yes	complemented
304	#2485	C₂×C₁₃	1	2	yes	complemented
305	#2415	C₂×C₁₃	1	2	yes	complemented
306	#2414	C₂×C₁₃	1	2	yes	complemented
307	#2407	C₂×C₁₃	1	2	yes	complemented
308	#2322	C₂×C₁₃	1	2	yes	complemented
309	#2321	C₂×C₁₃	1	2	yes	complemented
310	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	8	no	—
314	C₂³×C₁₃	—	2	8	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	1	no	—
317	C₂³×C₁₃	—	2	1	no	—
318	C₂³×C₁₃	—	2	1	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	4	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	4	4	no	—
335	C₂³×C₁₃	—	4	4	no	—
336	C₂³×C₁₃	—	4	8	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	4	no	—
339	C₂³×C₁₃	—	4	8	no	—
340	C₂³×C₁₃	—	4	8	no	—
341	C₂³×C₁₃	—	4	8	no	—
342	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
344	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₁₃	C₂×#41	1	4	yes	—
346	C₂³×C₁₃	C₂×#41	1	2	yes	—
347	C₂³×C₁₃	C₂×#41	1	2	yes	—
348	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
349	Q₈×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	2	16	no	—
351	D₄×C₁₃	—	2	16	no	—
352	D₄×C₁₃	—	4	8	no	—
353	D₄×C₁₃	—	4	8	no	—
354	D₄×C₁₃	—	4	8	no	—
355	D₄×C₁₃	—	4	4	no	—
356	D₄×C₁₃	—	8	8	no	—
357	C₂×C₄×C₁₃	—	2	8	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	8	no	—
364	C₂×C₄×C₁₃	—	2	8	no	—
365	C₂×C₄×C₁₃	—	2	8	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	4	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	4	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	2	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	8	no	—
389	C₂×C₄×C₁₃	—	4	8	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
398	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
399	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	C₂³×D₄	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	#525	—	2	8	no	—
404	C₂×#123	C₂²×C₁₃	1	2	yes	—
405	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
406	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
409	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
412	C₂×#120	C₂²×C₁₃	1	2	yes	—
413	C₂×#120	C₂²×C₁₃	1	2	yes	—
414	C₂×C₄×D₄	—	2	8	no	—
415	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
421	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
423	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
425	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
426	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
427	#397	C₂²×C₁₃	1	4	yes	complemented
428	#397	C₂²×C₁₃	1	4	yes	complemented
429	#394	C₂²×C₁₃	1	4	yes	—
430	#394	C₂²×C₁₃	1	4	yes	—
431	#394	C₂²×C₁₃	1	4	yes	complemented
432	#394	C₂²×C₁₃	1	4	yes	complemented
433	#392	C₂²×C₁₃	1	4	yes	—
434	#392	C₂²×C₁₃	1	4	yes	—
435	#391	C₂²×C₁₃	1	2	yes	complemented
436	#390	C₂²×C₁₃	1	4	yes	complemented
437	#390	C₂²×C₁₃	1	2	yes	complemented
438	#389	C₂²×C₁₃	1	4	yes	complemented
439	#389	C₂²×C₁₃	1	2	yes	complemented
440	#389	C₂²×C₁₃	1	2	yes	complemented
441	#388	C₂²×C₁₃	1	4	yes	complemented
442	#388	C₂²×C₁₃	1	4	yes	complemented
443	#388	C₂²×C₁₃	1	4	yes	complemented
444	#388	C₂²×C₁₃	1	4	yes	complemented
445	#387	C₂²×C₁₃	1	4	yes	complemented
446	#387	C₂²×C₁₃	1	4	yes	complemented
447	#386	C₂²×C₁₃	1	2	yes	—
448	#386	C₂²×C₁₃	1	2	yes	—
449	#386	C₂²×C₁₃	1	4	yes	complemented
450	#386	C₂²×C₁₃	1	4	yes	complemented
451	#385	C₂²×C₁₃	1	2	yes	—
452	#385	C₂²×C₁₃	1	2	yes	—
453	#385	C₂²×C₁₃	1	4	yes	complemented
454	#385	C₂²×C₁₃	1	4	yes	complemented
455	#381	C₂²×C₁₃	1	2	yes	—
456	#381	C₂²×C₁₃	1	2	yes	complemented
457	#380	C₂²×C₁₃	1	1	yes	characteristic
458	#380	C₂²×C₁₃	1	1	yes	characteristic
459	#380	C₂²×C₁₃	1	2	yes	complemented
460	#380	C₂²×C₁₃	1	2	yes	complemented
461	#380	C₂²×C₁₃	1	2	yes	complemented
462	#379	C₂²×C₁₃	1	2	yes	—
463	#379	C₂²×C₁₃	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
466	C₂²×C₁₃	—	2	2	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	4	no	—
473	C₂²×C₁₃	—	2	2	no	—
474	C₂²×C₁₃	—	2	2	no	—
475	C₂²×C₁₃	—	2	2	no	—
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	2	4	no	—
478	C₂²×C₁₃	—	2	4	no	—
479	C₂²×C₁₃	—	4	16	no	—
480	C₂²×C₁₃	—	4	16	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	2	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	—	4	4	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	#525	1	4	yes	—
495	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
496	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₁₃	#585	1	2	yes	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	2	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	4	no	—
510	C₄×C₁₃	—	4	4	no	—
511	C₄×C₁₃	#534	1	4	yes	—
512	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
513	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×#41	—	2	4	no	—
515	C₂×#41	—	4	4	no	—
516	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×D₄	—	2	4	no	—
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
522	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
523	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
527	C₂³×C₄	—	2	4	no	—
528	C₂³×C₄	—	4	4	no	—
529	C₂³×C₄	—	4	4	no	—
530	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
531	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	#123	—	2	8	no	—
544	#123	—	2	8	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	4	4	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	4	4	no	—
551	#120	—	2	8	no	—
552	#120	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	—	2	8	no	—
555	C₄×D₄	—	2	8	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	8	no	—
558	C₄×D₄	—	2	8	no	—
559	#117	—	2	4	no	—
560	#117	—	4	4	no	—
561	C₂×C₄⋊C₄	—	2	4	no	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₂²⋊C₄	—	2	4	no	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
594	C₂×C₄²	—	2	4	no	—
595	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
599	#95	C₂³×C₁₃	1	4	yes	—
600	#95	C₂³×C₁₃	1	2	yes	—
601	#95	C₂³×C₁₃	1	2	yes	—
602	#95	C₂³×C₁₃	1	4	yes	—
603	#95	C₂³×C₁₃	1	4	yes	—
604	#95	C₂³×C₁₃	1	4	yes	—
605	#95	C₂³×C₁₃	1	4	yes	—
606	#95	C₂³×C₁₃	1	4	yes	—
607	#95	C₂³×C₁₃	1	4	yes	—
608	C₂×C₁₃	—	2	4	no	—
609	C₂×C₁₃	—	4	2	no	—
610	C₂×C₁₃	—	4	2	no	—
611	C₂×C₁₃	—	4	4	no	—
612	C₂×C₁₃	—	8	2	no	—
613	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
614	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
615	C₂×C₁₃	#3449	1	1	yes	characteristic
616	C₂×C₁₃	#3505	1	2	yes	—
617	C₂×C₁₃	#3506	1	2	yes	—
618	C₂⁴	—	2	2	no	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	4	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	2	no	—
626	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
627	C₂⁴	C₁₃×#41	1	4	yes	complemented
628	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
629	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
632	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
633	#41	—	4	16	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	4	no	—
636	C₂×D₄	—	2	32	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	4	16	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	16	no	—
677	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
679	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
680	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
681	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
682	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
683	C₂²×C₄	C₁₃×#41	1	4	yes	complemented
684	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	2	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	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	8	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	4	4	no	—
706	C₄⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	8	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	8	no	—
720	C₂²⋊C₄	—	4	4	no	—
721	C₂²⋊C₄	—	4	4	no	—
722	C₂²⋊C₄	—	4	4	no	—
723	C₂²⋊C₄	—	4	4	no	—
724	C₂²⋊C₄	—	4	4	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	4	4	no	—
730	C₁₃	#35031	1	1	yes	characteristic, direct product factor, Sylow
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	8	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	4	4	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	8	no	—
762	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
763	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
764	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
765	C₂³	C₂×C₁₃×#41	1	4	yes	—
766	C₂³	C₂×C₁₃×#41	1	2	yes	—
767	C₂³	C₂×C₁₃×#41	1	2	yes	—
768	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
769	Q₈	—	4	4	no	—
770	D₄	—	2	16	no	—
771	D₄	—	2	16	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	4	no	—
776	D₄	—	8	8	no	—
777	C₂×C₄	—	2	8	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	8	no	—
784	C₂×C₄	—	2	8	no	—
785	C₂×C₄	—	2	8	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	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
818	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	16	no	—
833	C₂²	—	4	16	no	—
834	C₂²	—	4	2	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	—	4	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	4	no	—
847	C₂²	C₁₃×#525	1	4	yes	—
848	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
849	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
850	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
851	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
852	C₂²	C₁₃×#585	1	2	yes	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	4	no	—
864	C₄	C₁₃×#534	1	4	yes	—
865	C₂	—	2	4	no	—
866	C₂	—	4	2	no	—
867	C₂	—	4	2	no	—
868	C₂	—	4	4	no	—
869	C₂	—	8	2	no	—
870	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
871	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
872	C₂	C₁₃×#3449	1	1	yes	characteristic
873	C₂	C₁₃×#3505	1	2	yes	—
874	C₂	C₁₃×#3506	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×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
4. C₁₃×#2854	C₂	semidirect
5. C₁₃×#2848	C₂	semidirect
6. C₁₃×#2847	C₂	semidirect
7. C₁₃×#2622	C₂	semidirect
8. C₁₃×#2613	C₂	semidirect
9. C₁₃×#2602	C₂	semidirect
10. C₁₃×#2600	C₂	semidirect
11. C₁₃×#2485	C₂	semidirect
12. C₁₃×#2415	C₂	semidirect
13. C₁₃×#2414	C₂	semidirect
14. C₁₃×#2407	C₂	semidirect
15. C₁₃×#2322	C₂	semidirect
16. C₁₃×#2321	C₂	semidirect
17. C₁₃×#2280	C₂	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#117	C₂²	semidirect
41. C₂×C₁₃×#117	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
47. C₁₃×#397	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
51. C₁₃×#394	C₂²	semidirect
54. C₁₃×#391	C₂²	semidirect
55. C₁₃×#390	C₂²	semidirect
56. C₁₃×#390	C₂²	semidirect
57. C₁₃×#389	C₂²	semidirect
58. C₁₃×#389	C₂²	semidirect
59. C₁₃×#389	C₂²	semidirect
60. C₁₃×#388	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#387	C₂²	semidirect
65. C₁₃×#387	C₂²	semidirect
68. C₁₃×#386	C₂²	semidirect
69. C₁₃×#386	C₂²	semidirect
72. C₁₃×#385	C₂²	semidirect
73. C₁₃×#385	C₂²	semidirect
75. C₁₃×#381	C₂²	semidirect
78. C₁₃×#380	C₂²	semidirect
79. C₁₃×#380	C₂²	semidirect
80. C₁₃×#380	C₂²	semidirect
84. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
103. C₂³×C₄×C₁₃	D₄	semidirect
181. #35031	C₁₃	direct (N × H)
191. C₂⁴×C₁₃	#41	semidirect
247. C₂²×C₄×C₁₃	#41	semidirect
294. C₂×#525	C₂×C₁₃	semidirect
295. C₂²×C₄×D₄	C₂×C₁₃	semidirect
296. #2855	C₂×C₁₃	semidirect
297. #2854	C₂×C₁₃	semidirect
298. #2848	C₂×C₁₃	semidirect
299. #2847	C₂×C₁₃	semidirect
300. #2622	C₂×C₁₃	semidirect
301. #2613	C₂×C₁₃	semidirect
302. #2602	C₂×C₁₃	semidirect
303. #2600	C₂×C₁₃	semidirect
304. #2485	C₂×C₁₃	semidirect
305. #2415	C₂×C₁₃	semidirect
306. #2414	C₂×C₁₃	semidirect
307. #2407	C₂×C₁₃	semidirect
308. #2322	C₂×C₁₃	semidirect
309. #2321	C₂×C₁₃	semidirect
310. #2280	C₂×C₁₃	semidirect
399. C₂²×#41	C₂²×C₁₃	semidirect
405. C₂×#123	C₂²×C₁₃	semidirect
407. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
408. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
410. C₂×#121	C₂²×C₁₃	semidirect
411. C₂×#121	C₂²×C₁₃	semidirect
420. C₂×C₄×D₄	C₂²×C₁₃	semidirect
421. C₂×#117	C₂²×C₁₃	semidirect
422. C₂×#117	C₂²×C₁₃	semidirect
427. #397	C₂²×C₁₃	semidirect
428. #397	C₂²×C₁₃	semidirect
431. #394	C₂²×C₁₃	semidirect
432. #394	C₂²×C₁₃	semidirect
435. #391	C₂²×C₁₃	semidirect
436. #390	C₂²×C₁₃	semidirect
437. #390	C₂²×C₁₃	semidirect
438. #389	C₂²×C₁₃	semidirect
439. #389	C₂²×C₁₃	semidirect
440. #389	C₂²×C₁₃	semidirect
441. #388	C₂²×C₁₃	semidirect
442. #388	C₂²×C₁₃	semidirect
443. #388	C₂²×C₁₃	semidirect
444. #388	C₂²×C₁₃	semidirect
445. #387	C₂²×C₁₃	semidirect
446. #387	C₂²×C₁₃	semidirect
449. #386	C₂²×C₁₃	semidirect
450. #386	C₂²×C₁₃	semidirect
453. #385	C₂²×C₁₃	semidirect
454. #385	C₂²×C₁₃	semidirect
456. #381	C₂²×C₁₃	semidirect
459. #380	C₂²×C₁₃	semidirect
460. #380	C₂²×C₁₃	semidirect
461. #380	C₂²×C₁₃	semidirect
465. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
530. C₂³×C₄	D₄×C₁₃	semidirect
627. C₂⁴	C₁₃×#41	semidirect
683. C₂²×C₄	C₁₃×#41	semidirect
730. C₁₃	#35031	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2855	2
C₁₃×#2854	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2622	2
C₁₃×#2613	2
C₁₃×#2602	2
C₁₃×#2600	2
C₁₃×#2485	2
C₁₃×#2415	2
C₁₃×#2414	2
C₁₃×#2407	2
C₁₃×#2322	2
C₁₃×#2321	2
C₁₃×#2280	2
#35031	13

Subgroups — C13×#35031 #15721370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35031 #15721370