Subgroups — C₁₃×#60044 #15746383

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2808	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2732	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2682	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2609	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2601	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2574	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2554	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2553	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2476	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2471	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2430	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2407	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#399	C₂²	1	2	yes	—
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#397	C₂²	1	2	yes	—
40	C₁₃×#396	C₂²	1	2	yes	—
41	C₁₃×#396	C₂²	1	2	yes	—
42	C₁₃×#396	C₂²	1	2	yes	—
43	C₁₃×#395	C₂²	1	2	yes	—
44	C₁₃×#394	C₂²	1	2	yes	—
45	C₁₃×#394	C₂²	1	2	yes	—
46	C₁₃×#394	C₂²	1	2	yes	—
47	C₁₃×#394	C₂²	1	2	yes	—
48	C₁₃×#393	C₂²	1	2	yes	—
49	C₁₃×#392	C₂²	1	2	yes	—
50	C₁₃×#392	C₂²	1	2	yes	—
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#391	C₂²	1	1	yes	characteristic
56	C₁₃×#390	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	2	yes	—
61	C₁₃×#390	C₂²	1	2	yes	—
62	C₁₃×#390	C₂²	1	2	yes	—
63	C₁₃×#389	C₂²	1	1	yes	characteristic
64	C₁₃×#389	C₂²	1	2	yes	—
65	C₁₃×#389	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	1	yes	characteristic
67	C₁₃×#389	C₂²	1	1	yes	characteristic
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#382	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₂×C₁₃×#41	—	2	4	no	—
108	C₂×C₁₃×#41	—	2	4	no	—
109	C₂×C₁₃×#41	—	4	2	no	—
110	C₂×C₁₃×#41	—	4	2	no	—
111	C₂×C₁₃×#41	—	4	2	no	—
112	C₂×C₁₃×#41	—	4	2	no	—
113	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×#126	—	4	4	no	—
129	C₁₃×#123	—	2	8	no	—
130	C₁₃×#123	—	4	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	8	no	—
132	C₁₃×#121	—	2	8	no	—
133	C₁₃×#121	—	4	4	no	—
134	C₄×D₄×C₁₃	—	4	4	no	—
135	C₁₃×#117	—	2	4	no	—
136	C₁₃×#117	—	4	2	no	—
137	C₁₃×#117	—	4	2	no	—
138	C₁₃×#117	—	4	4	no	—
139	C₁₃×#117	—	4	2	no	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	—	4	2	no	—
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	#60044	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×#41	—	4	16	no	—
218	C₁₃×#41	—	4	16	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	4	1	no	—
221	C₂×Q₈×C₁₃	—	4	1	no	—
222	C₂×Q₈×C₁₃	—	4	1	no	—
223	C₂×Q₈×C₁₃	—	4	1	no	—
224	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	2	4	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	4	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	1	no	—
235	C₂×D₄×C₁₃	—	4	1	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	1	no	—
238	C₂×D₄×C₁₃	—	4	1	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	2	no	—
241	C₂×D₄×C₁₃	—	4	2	no	—
242	C₂×D₄×C₁₃	#41	1	4	yes	complemented
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	4	1	no	—
289	C₁₃×C₄⋊C₄	—	4	1	no	—
290	C₁₃×C₄⋊C₄	—	4	2	no	—
291	C₁₃×C₄⋊C₄	—	4	1	no	—
292	C₁₃×C₄⋊C₄	—	4	1	no	—
293	C₁₃×C₄⋊C₄	—	4	1	no	—
294	C₁₃×C₄⋊C₄	—	4	1	no	—
295	C₁₃×C₄⋊C₄	—	4	2	no	—
296	C₁₃×C₄⋊C₄	—	4	2	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	#41	1	4	yes	complemented
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	4	2	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	4	1	no	—
326	C₄²×C₁₃	—	4	1	no	—
327	C₄²×C₁₃	—	4	1	no	—
328	C₄²×C₁₃	—	4	1	no	—
329	C₄²×C₁₃	—	4	2	no	—
330	C₄²×C₁₃	—	4	2	no	—
331	C₄²×C₁₃	—	4	2	no	—
332	#2808	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#2806	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#2732	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#2682	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2609	C₂×C₁₃	1	2	yes	complemented
337	#2601	C₂×C₁₃	1	2	yes	complemented
338	#2574	C₂×C₁₃	1	2	yes	complemented
339	#2554	C₂×C₁₃	1	2	yes	complemented
340	#2553	C₂×C₁₃	1	2	yes	complemented
341	#2476	C₂×C₁₃	1	2	yes	complemented
342	#2471	C₂×C₁₃	1	2	yes	complemented
343	#2430	C₂×C₁₃	1	2	yes	complemented
344	#2407	C₂×C₁₃	1	2	yes	complemented
345	#2368	C₂×C₁₃	1	2	yes	complemented
346	#2363	C₂×C₁₃	1	2	yes	complemented
347	#2359	C₂×C₁₃	1	2	yes	complemented
348	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	C₂×#41	1	4	yes	—
371	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
372	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
373	Q₈×C₁₃	—	4	4	no	—
374	Q₈×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	8	no	—
377	D₄×C₁₃	—	4	8	no	—
378	D₄×C₁₃	—	4	4	no	—
379	D₄×C₁₃	—	4	8	no	—
380	D₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	—	2	8	no	—
382	C₂×C₄×C₁₃	—	2	8	no	—
383	C₂×C₄×C₁₃	—	2	8	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	4	8	no	—
425	C₂×C₄×C₁₃	—	4	8	no	—
426	C₂×C₄×C₁₃	—	4	8	no	—
427	C₂×C₄×C₁₃	—	8	4	no	—
428	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
429	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
430	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
431	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
432	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
433	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
434	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
436	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#126	C₂²×C₁₃	1	2	yes	—
439	C₂×#123	C₂²×C₁₃	1	2	yes	—
440	C₂×#123	C₂²×C₁₃	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
442	C₂×#121	C₂²×C₁₃	1	2	yes	—
443	C₂×#121	C₂²×C₁₃	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
445	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#117	C₂²×C₁₃	1	2	yes	—
449	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
451	#399	C₂²×C₁₃	1	2	yes	—
452	#398	C₂²×C₁₃	1	2	yes	—
453	#398	C₂²×C₁₃	1	2	yes	—
454	#398	C₂²×C₁₃	1	2	yes	—
455	#397	C₂²×C₁₃	1	2	yes	—
456	#396	C₂²×C₁₃	1	2	yes	—
457	#396	C₂²×C₁₃	1	2	yes	—
458	#396	C₂²×C₁₃	1	2	yes	—
459	#395	C₂²×C₁₃	1	2	yes	—
460	#394	C₂²×C₁₃	1	2	yes	—
461	#394	C₂²×C₁₃	1	2	yes	—
462	#394	C₂²×C₁₃	1	2	yes	—
463	#394	C₂²×C₁₃	1	2	yes	—
464	#393	C₂²×C₁₃	1	2	yes	—
465	#392	C₂²×C₁₃	1	2	yes	—
466	#392	C₂²×C₁₃	1	2	yes	—
467	#391	C₂²×C₁₃	1	1	yes	characteristic
468	#391	C₂²×C₁₃	1	1	yes	characteristic
469	#391	C₂²×C₁₃	1	2	yes	—
470	#391	C₂²×C₁₃	1	1	yes	characteristic
471	#391	C₂²×C₁₃	1	1	yes	characteristic
472	#390	C₂²×C₁₃	1	2	yes	—
473	#390	C₂²×C₁₃	1	1	yes	characteristic
474	#390	C₂²×C₁₃	1	2	yes	—
475	#390	C₂²×C₁₃	1	2	yes	—
476	#390	C₂²×C₁₃	1	1	yes	characteristic
477	#390	C₂²×C₁₃	1	1	yes	characteristic
478	#390	C₂²×C₁₃	1	1	yes	characteristic
479	#389	C₂²×C₁₃	1	2	yes	—
480	#389	C₂²×C₁₃	1	1	yes	characteristic
481	#389	C₂²×C₁₃	1	1	yes	characteristic
482	#389	C₂²×C₁₃	1	1	yes	characteristic
483	#389	C₂²×C₁₃	1	1	yes	characteristic
484	#388	C₂²×C₁₃	1	2	yes	—
485	#388	C₂²×C₁₃	1	2	yes	—
486	#388	C₂²×C₁₃	1	2	yes	—
487	#388	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#387	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#386	C₂²×C₁₃	1	2	yes	—
498	#386	C₂²×C₁₃	1	2	yes	—
499	#386	C₂²×C₁₃	1	2	yes	—
500	#386	C₂²×C₁₃	1	2	yes	—
501	#386	C₂²×C₁₃	1	2	yes	—
502	#386	C₂²×C₁₃	1	2	yes	—
503	#386	C₂²×C₁₃	1	2	yes	—
504	#386	C₂²×C₁₃	1	2	yes	—
505	#385	C₂²×C₁₃	1	2	yes	—
506	#385	C₂²×C₁₃	1	2	yes	—
507	#385	C₂²×C₁₃	1	2	yes	—
508	#385	C₂²×C₁₃	1	2	yes	—
509	#385	C₂²×C₁₃	1	2	yes	—
510	#385	C₂²×C₁₃	1	2	yes	—
511	#382	C₂²×C₁₃	1	2	yes	—
512	#380	C₂²×C₁₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
516	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
522	C₂×#95	C₂²×C₁₃	1	2	yes	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	2	4	no	—
525	C₂²×C₁₃	—	2	2	no	—
526	C₂²×C₁₃	—	2	2	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	4	1	no	—
530	C₂²×C₁₃	—	4	1	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	1	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	1	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	2	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	2	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
546	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
547	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₄×C₁₃	—	2	4	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	4	no	—
557	C₄×C₁₃	—	2	2	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	4	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	2	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	—	4	2	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	2	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₂×#41	—	2	4	no	—
568	C₂×#41	—	2	4	no	—
569	C₂×#41	—	4	2	no	—
570	C₂×#41	—	4	2	no	—
571	C₂×#41	—	4	2	no	—
572	C₂×#41	—	4	2	no	—
573	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
576	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
577	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
578	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
579	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
585	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
586	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
587	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
588	#126	—	4	4	no	—
589	#123	—	2	8	no	—
590	#123	—	4	4	no	—
591	C₂²⋊Q₈	—	2	8	no	—
592	#121	—	2	8	no	—
593	#121	—	4	4	no	—
594	C₄×D₄	—	4	4	no	—
595	#117	—	2	4	no	—
596	#117	—	4	2	no	—
597	#117	—	4	2	no	—
598	#117	—	4	4	no	—
599	#117	—	4	2	no	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄²	—	4	2	no	—
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	2	yes	—
661	#95	C₂³×C₁₃	1	2	yes	—
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	C₂×C₁₃	—	4	4	no	—
674	C₂×C₁₃	—	4	2	no	—
675	C₂×C₁₃	—	8	2	no	—
676	C₂×C₁₃	#3481	1	1	yes	characteristic
677	C₂×C₁₃	#3482	1	1	yes	characteristic
678	C₂×C₁₃	#3483	1	1	yes	characteristic
679	C₂×C₁₃	#3490	1	1	yes	characteristic
680	C₂×C₁₃	#3490	1	1	yes	characteristic
681	C₂×C₁₃	#3492	1	1	yes	characteristic
682	C₂×C₁₃	#3548	1	1	yes	characteristic
683	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
684	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
685	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
686	#41	—	4	16	no	—
687	#41	—	4	16	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	4	1	no	—
690	C₂×Q₈	—	4	1	no	—
691	C₂×Q₈	—	4	1	no	—
692	C₂×Q₈	—	4	1	no	—
693	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	C₁₃×#41	1	4	yes	complemented
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	C₁₃×#41	1	4	yes	complemented
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	4	1	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	1	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₁₃	#60044	1	1	yes	characteristic, direct product factor, Sylow
802	C₂³	—	2	2	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	C₂×C₁₃×#41	1	4	yes	—
822	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
823	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
824	Q₈	—	4	4	no	—
825	Q₈	—	4	4	no	—
826	D₄	—	4	4	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	8	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	8	no	—
831	D₄	—	8	4	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
880	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
881	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
882	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
883	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
884	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
885	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
886	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
909	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
910	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
911	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
913	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
914	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₁₃×#3481	1	1	yes	characteristic
935	C₂	C₁₃×#3482	1	1	yes	characteristic
936	C₂	C₁₃×#3483	1	1	yes	characteristic
937	C₂	C₁₃×#3490	1	1	yes	characteristic
938	C₂	C₁₃×#3490	1	1	yes	characteristic
939	C₂	C₁₃×#3492	1	1	yes	characteristic
940	C₂	C₁₃×#3548	1	1	yes	characteristic

	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. C₁₃×#2808	C₂	semidirect
2. C₁₃×#2806	C₂	semidirect
3. C₁₃×#2732	C₂	semidirect
4. C₁₃×#2682	C₂	semidirect
5. C₁₃×#2609	C₂	semidirect
6. C₁₃×#2601	C₂	semidirect
7. C₁₃×#2574	C₂	semidirect
8. C₁₃×#2554	C₂	semidirect
9. C₁₃×#2553	C₂	semidirect
10. C₁₃×#2476	C₂	semidirect
11. C₁₃×#2471	C₂	semidirect
12. C₁₃×#2430	C₂	semidirect
13. C₁₃×#2407	C₂	semidirect
14. C₁₃×#2368	C₂	semidirect
15. C₁₃×#2363	C₂	semidirect
16. C₁₃×#2359	C₂	semidirect
17. C₁₃×#2297	C₂	semidirect
18. C₁₃×#2297	C₂	semidirect
19. C₁₃×#2296	C₂	semidirect
213. #60044	C₁₃	direct (N × H)
224. C₂×Q₈×C₁₃	#41	semidirect
242. C₂×D₄×C₁₃	#41	semidirect
299. C₁₃×C₄⋊C₄	#41	semidirect
332. #2808	C₂×C₁₃	semidirect
333. #2806	C₂×C₁₃	semidirect
334. #2732	C₂×C₁₃	semidirect
335. #2682	C₂×C₁₃	semidirect
336. #2609	C₂×C₁₃	semidirect
337. #2601	C₂×C₁₃	semidirect
338. #2574	C₂×C₁₃	semidirect
339. #2554	C₂×C₁₃	semidirect
340. #2553	C₂×C₁₃	semidirect
341. #2476	C₂×C₁₃	semidirect
342. #2471	C₂×C₁₃	semidirect
343. #2430	C₂×C₁₃	semidirect
344. #2407	C₂×C₁₃	semidirect
345. #2368	C₂×C₁₃	semidirect
346. #2363	C₂×C₁₃	semidirect
347. #2359	C₂×C₁₃	semidirect
348. #2297	C₂×C₁₃	semidirect
349. #2297	C₂×C₁₃	semidirect
350. #2296	C₂×C₁₃	semidirect
693. C₂×Q₈	C₁₃×#41	semidirect
711. C₂×D₄	C₁₃×#41	semidirect
768. C₄⋊C₄	C₁₃×#41	semidirect
801. C₁₃	#60044	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2808	2
C₁₃×#2806	2
C₁₃×#2732	2
C₁₃×#2682	2
C₁₃×#2609	2
C₁₃×#2601	2
C₁₃×#2574	2
C₁₃×#2554	2
C₁₃×#2553	2
C₁₃×#2476	2
C₁₃×#2471	2
C₁₃×#2430	2
C₁₃×#2407	2
C₁₃×#2368	2
C₁₃×#2363	2
C₁₃×#2359	2
C₁₃×#2297	2
C₁₃×#2296	2
#60044	13

Subgroups — C13×#60044 #15746383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60044 #15746383