Subgroups — C₁₃×#36747 #15723086

Order 3328.

2146 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2784	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2780	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2780	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2748	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2748	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2732	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2692	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2692	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2683	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2438	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2438	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2437	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2437	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic
19	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#399	C₂²	1	2	yes	complemented
37	C₁₃×#399	C₂²	1	2	yes	complemented
38	C₁₃×#399	C₂²	1	2	yes	complemented
39	C₁₃×#399	C₂²	1	2	yes	complemented
40	C₁₃×#398	C₂²	1	2	yes	complemented
41	C₁₃×#398	C₂²	1	2	yes	complemented
42	C₁₃×#398	C₂²	1	2	yes	complemented
43	C₁₃×#398	C₂²	1	2	yes	complemented
44	C₁₃×#396	C₂²	1	2	yes	complemented
45	C₁₃×#396	C₂²	1	2	yes	complemented
46	C₁₃×#396	C₂²	1	2	yes	complemented
47	C₁₃×#396	C₂²	1	2	yes	complemented
48	C₁₃×#396	C₂²	1	2	yes	complemented
49	C₁₃×#396	C₂²	1	2	yes	complemented
50	C₁₃×#396	C₂²	1	2	yes	complemented
51	C₁₃×#396	C₂²	1	2	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#395	C₂²	1	2	yes	complemented
54	C₁₃×#393	C₂²	1	2	yes	complemented
55	C₁₃×#393	C₂²	1	2	yes	complemented
56	C₁₃×#393	C₂²	1	2	yes	complemented
57	C₁₃×#393	C₂²	1	2	yes	complemented
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#391	C₂²	1	2	yes	complemented
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#390	C₂²	1	2	yes	—
62	C₁₃×#390	C₂²	1	2	yes	—
63	C₁₃×#390	C₂²	1	1	yes	characteristic
64	C₁₃×#390	C₂²	1	1	yes	characteristic
65	C₁₃×#390	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#389	C₂²	1	2	yes	complemented
68	C₁₃×#387	C₂²	1	2	yes	complemented
69	C₁₃×#387	C₂²	1	2	yes	complemented
70	C₁₃×#387	C₂²	1	2	yes	complemented
71	C₁₃×#387	C₂²	1	2	yes	complemented
72	C₁₃×#386	C₂²	1	1	yes	characteristic
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	1	yes	characteristic
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	1	yes	characteristic
79	C₁₃×#386	C₂²	1	1	yes	characteristic
80	C₁₃×#386	C₂²	1	1	yes	characteristic
81	C₁₃×#386	C₂²	1	1	yes	characteristic
82	C₁₃×#386	C₂²	1	1	yes	characteristic
83	C₁₃×#386	C₂²	1	1	yes	characteristic
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	complemented
89	C₁₃×#385	C₂²	1	2	yes	complemented
90	C₁₃×#385	C₂²	1	2	yes	complemented
91	C₁₃×#385	C₂²	1	2	yes	complemented
92	C₁₃×#385	C₂²	1	2	yes	complemented
93	C₁₃×#385	C₂²	1	2	yes	complemented
94	C₁₃×#385	C₂²	1	2	yes	complemented
95	C₁₃×#385	C₂²	1	2	yes	complemented
96	C₁₃×#381	C₂²	1	2	yes	—
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	complemented
100	C₁₃×#380	C₂²	1	2	yes	complemented
101	C₁₃×#380	C₂²	1	2	yes	complemented
102	C₁₃×#380	C₂²	1	2	yes	complemented
103	C₁₃×#379	C₂²	1	2	yes	—
104	C₁₃×#379	C₂²	1	2	yes	—
105	C₁₃×#379	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	—	4	2	no	—
112	C₂²×D₄×C₁₃	—	4	2	no	—
113	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	—	4	4	no	—
119	C₂³×C₄×C₁₃	—	4	2	no	—
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×C₂²⋊Q₈	—	4	4	no	—
130	C₁₃×C₂²⋊Q₈	—	4	4	no	—
131	C₁₃×C₂²⋊Q₈	—	4	4	no	—
132	C₁₃×C₂²⋊Q₈	—	4	4	no	—
133	C₁₃×C₂²⋊Q₈	—	4	4	no	—
134	C₁₃×C₂²⋊Q₈	—	4	4	no	—
135	C₁₃×#117	—	4	2	no	—
136	C₁₃×#117	—	4	2	no	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
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	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
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×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₂²⋊C₄	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	1	yes	characteristic
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
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	#36747	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂⁴×C₁₃	—	2	2	no	—
213	C₂⁴×C₁₃	—	2	2	no	—
214	C₂⁴×C₁₃	—	2	2	no	—
215	C₂⁴×C₁₃	—	2	2	no	—
216	C₂⁴×C₁₃	—	4	2	no	—
217	C₂⁴×C₁₃	—	4	2	no	—
218	C₂⁴×C₁₃	—	4	2	no	—
219	C₂⁴×C₁₃	—	4	2	no	—
220	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
221	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
222	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₁₃	—	2	4	no	—
228	C₂×Q₈×C₁₃	—	4	2	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	2	no	—
231	C₂×Q₈×C₁₃	—	4	2	no	—
232	C₂×Q₈×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	16	no	—
234	C₂×D₄×C₁₃	—	4	1	no	—
235	C₂×D₄×C₁₃	—	4	1	no	—
236	C₂×D₄×C₁₃	—	4	1	no	—
237	C₂×D₄×C₁₃	—	4	1	no	—
238	C₂×D₄×C₁₃	—	4	1	no	—
239	C₂×D₄×C₁₃	—	4	1	no	—
240	C₂×D₄×C₁₃	—	4	1	no	—
241	C₂×D₄×C₁₃	—	4	1	no	—
242	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
243	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
244	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
245	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	1	no	—
259	C₂²×C₄×C₁₃	—	4	1	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	16	no	—
269	C₂²×C₄×C₁₃	C₂×Q₈	1	4	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	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	—	4	2	no	—
288	C₁₃×C₄⋊C₄	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	4	2	no	—
290	C₁₃×C₄⋊C₄	—	4	1	no	—
291	C₁₃×C₄⋊C₄	—	4	2	no	—
292	C₁₃×C₄⋊C₄	—	4	1	no	—
293	C₁₃×C₄⋊C₄	—	4	2	no	—
294	C₁₃×C₄⋊C₄	—	4	2	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	—	4	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	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	—	4	1	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	1	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	1	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	1	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	4	2	no	—
322	C₁₃×C₂²⋊C₄	—	4	2	no	—
323	C₁₃×C₂²⋊C₄	—	4	2	no	—
324	C₁₃×C₂²⋊C₄	—	4	2	no	—
325	C₁₃×C₂²⋊C₄	—	4	2	no	—
326	C₁₃×C₂²⋊C₄	—	4	2	no	—
327	C₁₃×C₂²⋊C₄	—	4	2	no	—
328	C₁₃×C₂²⋊C₄	—	4	2	no	—
329	C₁₃×C₂²⋊C₄	—	4	2	no	—
330	C₁₃×C₂²⋊C₄	—	4	2	no	—
331	C₄²×C₁₃	—	4	1	no	—
332	C₄²×C₁₃	—	4	2	no	—
333	C₄²×C₁₃	—	4	1	no	—
334	#2848	C₂×C₁₃	1	2	yes	complemented
335	#2804	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2784	C₂×C₁₃	1	2	yes	complemented
337	#2780	C₂×C₁₃	1	2	yes	complemented
338	#2780	C₂×C₁₃	1	2	yes	complemented
339	#2748	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2748	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2732	C₂×C₁₃	1	2	yes	complemented
342	#2692	C₂×C₁₃	1	2	yes	complemented
343	#2692	C₂×C₁₃	1	2	yes	complemented
344	#2683	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#2626	C₂×C₁₃	1	2	yes	complemented
346	#2438	C₂×C₁₃	1	2	yes	complemented
347	#2438	C₂×C₁₃	1	2	yes	complemented
348	#2437	C₂×C₁₃	1	2	yes	complemented
349	#2437	C₂×C₁₃	1	2	yes	complemented
350	#2309	C₂×C₁₃	1	1	yes	characteristic
351	#2308	C₂×C₁₃	1	1	yes	characteristic
352	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	8	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	—	2	1	no	—
367	C₂³×C₁₃	—	2	1	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	8	no	—
373	C₂³×C₁₃	—	4	8	no	—
374	C₂³×C₁₃	—	4	8	no	—
375	C₂³×C₁₃	—	4	4	no	—
376	C₂³×C₁₃	—	4	4	no	—
377	C₂³×C₁₃	—	4	8	no	—
378	C₂³×C₁₃	—	8	2	no	—
379	C₂³×C₁₃	—	8	2	no	—
380	C₂³×C₁₃	—	8	4	no	—
381	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
382	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
383	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
384	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
385	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
386	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
387	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
388	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
389	Q₈×C₁₃	—	8	4	no	—
390	Q₈×C₁₃	—	8	4	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	2	8	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	4	8	no	—
437	C₂×C₄×C₁₃	—	4	8	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	8	4	no	—
440	C₂×C₄×C₁₃	—	8	2	no	—
441	C₂×C₄×C₁₃	—	8	2	no	—
442	C₂×C₄×C₁₃	—	8	4	no	—
443	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
444	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
445	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
446	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
447	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
449	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
450	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
451	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
452	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
453	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
454	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
457	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
459	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
460	#400	C₂²×C₁₃	1	2	yes	complemented
461	#400	C₂²×C₁₃	1	2	yes	complemented
462	#399	C₂²×C₁₃	1	2	yes	complemented
463	#399	C₂²×C₁₃	1	2	yes	complemented
464	#399	C₂²×C₁₃	1	2	yes	complemented
465	#399	C₂²×C₁₃	1	2	yes	complemented
466	#398	C₂²×C₁₃	1	2	yes	complemented
467	#398	C₂²×C₁₃	1	2	yes	complemented
468	#398	C₂²×C₁₃	1	2	yes	complemented
469	#398	C₂²×C₁₃	1	2	yes	complemented
470	#396	C₂²×C₁₃	1	2	yes	complemented
471	#396	C₂²×C₁₃	1	2	yes	complemented
472	#396	C₂²×C₁₃	1	2	yes	complemented
473	#396	C₂²×C₁₃	1	2	yes	complemented
474	#396	C₂²×C₁₃	1	2	yes	complemented
475	#396	C₂²×C₁₃	1	2	yes	complemented
476	#396	C₂²×C₁₃	1	2	yes	complemented
477	#396	C₂²×C₁₃	1	2	yes	complemented
478	#395	C₂²×C₁₃	1	2	yes	complemented
479	#395	C₂²×C₁₃	1	2	yes	complemented
480	#393	C₂²×C₁₃	1	2	yes	complemented
481	#393	C₂²×C₁₃	1	2	yes	complemented
482	#393	C₂²×C₁₃	1	2	yes	complemented
483	#393	C₂²×C₁₃	1	2	yes	complemented
484	#391	C₂²×C₁₃	1	2	yes	complemented
485	#391	C₂²×C₁₃	1	2	yes	complemented
486	#390	C₂²×C₁₃	1	1	yes	characteristic
487	#390	C₂²×C₁₃	1	1	yes	characteristic
488	#390	C₂²×C₁₃	1	2	yes	—
489	#390	C₂²×C₁₃	1	2	yes	—
490	#390	C₂²×C₁₃	1	1	yes	characteristic
491	#390	C₂²×C₁₃	1	1	yes	characteristic
492	#389	C₂²×C₁₃	1	2	yes	complemented
493	#389	C₂²×C₁₃	1	2	yes	complemented
494	#387	C₂²×C₁₃	1	2	yes	complemented
495	#387	C₂²×C₁₃	1	2	yes	complemented
496	#387	C₂²×C₁₃	1	2	yes	complemented
497	#387	C₂²×C₁₃	1	2	yes	complemented
498	#386	C₂²×C₁₃	1	1	yes	characteristic
499	#386	C₂²×C₁₃	1	2	yes	—
500	#386	C₂²×C₁₃	1	2	yes	—
501	#386	C₂²×C₁₃	1	1	yes	characteristic
502	#386	C₂²×C₁₃	1	1	yes	characteristic
503	#386	C₂²×C₁₃	1	1	yes	characteristic
504	#386	C₂²×C₁₃	1	1	yes	characteristic
505	#386	C₂²×C₁₃	1	1	yes	characteristic
506	#386	C₂²×C₁₃	1	2	yes	—
507	#386	C₂²×C₁₃	1	2	yes	—
508	#386	C₂²×C₁₃	1	1	yes	characteristic
509	#386	C₂²×C₁₃	1	1	yes	characteristic
510	#385	C₂²×C₁₃	1	2	yes	—
511	#385	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	—
513	#385	C₂²×C₁₃	1	2	yes	—
514	#385	C₂²×C₁₃	1	2	yes	complemented
515	#385	C₂²×C₁₃	1	2	yes	complemented
516	#385	C₂²×C₁₃	1	2	yes	complemented
517	#385	C₂²×C₁₃	1	2	yes	complemented
518	#385	C₂²×C₁₃	1	2	yes	complemented
519	#385	C₂²×C₁₃	1	2	yes	complemented
520	#385	C₂²×C₁₃	1	2	yes	complemented
521	#385	C₂²×C₁₃	1	2	yes	complemented
522	#381	C₂²×C₁₃	1	2	yes	—
523	#380	C₂²×C₁₃	1	2	yes	—
524	#380	C₂²×C₁₃	1	2	yes	—
525	#380	C₂²×C₁₃	1	2	yes	complemented
526	#380	C₂²×C₁₃	1	2	yes	complemented
527	#380	C₂²×C₁₃	1	2	yes	complemented
528	#380	C₂²×C₁₃	1	2	yes	complemented
529	#379	C₂²×C₁₃	1	2	yes	—
530	#379	C₂²×C₁₃	1	2	yes	—
531	#379	C₂²×C₁₃	1	2	yes	—
532	C₂×#95	C₂²×C₁₃	1	2	yes	—
533	C₂²×C₁₃	—	2	4	no	—
534	C₂²×C₁₃	—	2	2	no	—
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	4	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	2	no	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	4	no	—
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	2	4	no	—
544	C₂²×C₁₃	—	2	4	no	—
545	C₂²×C₁₃	—	4	16	no	—
546	C₂²×C₁₃	—	4	1	no	—
547	C₂²×C₁₃	—	4	1	no	—
548	C₂²×C₁₃	—	4	1	no	—
549	C₂²×C₁₃	—	4	1	no	—
550	C₂²×C₁₃	—	4	1	no	—
551	C₂²×C₁₃	—	4	1	no	—
552	C₂²×C₁₃	—	4	1	no	—
553	C₂²×C₁₃	—	4	1	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	2	no	—
558	C₂²×C₁₃	—	8	8	no	—
559	C₂²×C₁₃	#543	1	4	yes	—
560	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
561	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
564	C₂²×C₁₃	#585	1	2	yes	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	4	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
580	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
581	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₂²×D₄	—	4	2	no	—
584	C₂²×D₄	—	4	2	no	—
585	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
586	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
590	C₂³×C₄	—	4	4	no	—
591	C₂³×C₄	—	4	2	no	—
592	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
593	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
596	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
597	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²⋊Q₈	—	4	4	no	—
602	C₂²⋊Q₈	—	4	4	no	—
603	C₂²⋊Q₈	—	4	4	no	—
604	C₂²⋊Q₈	—	4	4	no	—
605	C₂²⋊Q₈	—	4	4	no	—
606	C₂²⋊Q₈	—	4	4	no	—
607	#117	—	4	2	no	—
608	#117	—	4	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	—	4	4	no	—
631	C₂×C₂²⋊C₄	—	4	2	no	—
632	C₂×C₂²⋊C₄	—	4	2	no	—
633	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	C₂×C₁₃	—	2	4	no	—
684	C₂×C₁₃	—	4	2	no	—
685	C₂×C₁₃	—	4	2	no	—
686	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	—	4	2	no	—
688	C₂×C₁₃	C₂×#543	1	1	yes	characteristic
689	C₂×C₁₃	#3501	1	2	yes	—
690	C₂×C₁₃	#3532	1	1	yes	characteristic
691	C₂×C₁₃	#3533	1	1	yes	characteristic
692	C₂×C₁₃	#3542	1	2	yes	—
693	C₂⁴	—	2	2	no	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	—	2	2	no	—
696	C₂⁴	—	2	2	no	—
697	C₂⁴	—	4	2	no	—
698	C₂⁴	—	4	2	no	—
699	C₂⁴	—	4	2	no	—
700	C₂⁴	—	4	2	no	—
701	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
702	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
703	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×D₄	—	4	16	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	1	no	—
723	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
724	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
725	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
726	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	16	no	—
750	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	4	1	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	4	1	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	1	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	1	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	1	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	1	no	—
815	C₁₃	#36747	1	1	yes	characteristic, direct product factor, Sylow
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	8	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	8	no	—
836	C₂³	—	4	8	no	—
837	C₂³	—	4	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	8	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	2	no	—
843	C₂³	—	8	4	no	—
844	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
845	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
846	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
847	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
848	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
849	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
850	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
851	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
852	Q₈	—	8	4	no	—
853	Q₈	—	8	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	4	4	no	—
857	D₄	—	4	4	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	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	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	8	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	4	no	—
906	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
907	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
908	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	8	8	no	—
935	C₂²	C₁₃×#543	1	4	yes	—
936	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
937	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
938	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
939	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
940	C₂²	C₁₃×#585	1	2	yes	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×C₁₃×#543	1	1	yes	characteristic
961	C₂	C₁₃×#3501	1	2	yes	—
962	C₂	C₁₃×#3532	1	1	yes	characteristic
963	C₂	C₁₃×#3533	1	1	yes	characteristic
964	C₂	C₁₃×#3542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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×#2848	C₂	semidirect
2. C₁₃×#2804	C₂	semidirect
3. C₁₃×#2784	C₂	semidirect
4. C₁₃×#2780	C₂	semidirect
5. C₁₃×#2780	C₂	semidirect
6. C₁₃×#2748	C₂	semidirect
7. C₁₃×#2748	C₂	semidirect
8. C₁₃×#2732	C₂	semidirect
9. C₁₃×#2692	C₂	semidirect
10. C₁₃×#2692	C₂	semidirect
11. C₁₃×#2683	C₂	semidirect
12. C₁₃×#2626	C₂	semidirect
13. C₁₃×#2438	C₂	semidirect
14. C₁₃×#2438	C₂	semidirect
15. C₁₃×#2437	C₂	semidirect
16. C₁₃×#2437	C₂	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#399	C₂²	semidirect
37. C₁₃×#399	C₂²	semidirect
38. C₁₃×#399	C₂²	semidirect
39. C₁₃×#399	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
42. C₁₃×#398	C₂²	semidirect
43. C₁₃×#398	C₂²	semidirect
44. C₁₃×#396	C₂²	semidirect
45. C₁₃×#396	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#396	C₂²	semidirect
48. C₁₃×#396	C₂²	semidirect
49. C₁₃×#396	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#396	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
53. C₁₃×#395	C₂²	semidirect
54. C₁₃×#393	C₂²	semidirect
55. C₁₃×#393	C₂²	semidirect
56. C₁₃×#393	C₂²	semidirect
57. C₁₃×#393	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
59. C₁₃×#391	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
67. C₁₃×#389	C₂²	semidirect
68. C₁₃×#387	C₂²	semidirect
69. C₁₃×#387	C₂²	semidirect
70. C₁₃×#387	C₂²	semidirect
71. C₁₃×#387	C₂²	semidirect
88. C₁₃×#385	C₂²	semidirect
89. C₁₃×#385	C₂²	semidirect
90. C₁₃×#385	C₂²	semidirect
91. C₁₃×#385	C₂²	semidirect
92. C₁₃×#385	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#385	C₂²	semidirect
95. C₁₃×#385	C₂²	semidirect
99. C₁₃×#380	C₂²	semidirect
100. C₁₃×#380	C₂²	semidirect
101. C₁₃×#380	C₂²	semidirect
102. C₁₃×#380	C₂²	semidirect
113. C₂²×D₄×C₁₃	Q₈	semidirect
211. #36747	C₁₃	direct (N × H)
334. #2848	C₂×C₁₃	semidirect
335. #2804	C₂×C₁₃	semidirect
336. #2784	C₂×C₁₃	semidirect
337. #2780	C₂×C₁₃	semidirect
338. #2780	C₂×C₁₃	semidirect
339. #2748	C₂×C₁₃	semidirect
340. #2748	C₂×C₁₃	semidirect
341. #2732	C₂×C₁₃	semidirect
342. #2692	C₂×C₁₃	semidirect
343. #2692	C₂×C₁₃	semidirect
344. #2683	C₂×C₁₃	semidirect
345. #2626	C₂×C₁₃	semidirect
346. #2438	C₂×C₁₃	semidirect
347. #2438	C₂×C₁₃	semidirect
348. #2437	C₂×C₁₃	semidirect
349. #2437	C₂×C₁₃	semidirect
450. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
451. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
452. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
453. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
460. #400	C₂²×C₁₃	semidirect
461. #400	C₂²×C₁₃	semidirect
462. #399	C₂²×C₁₃	semidirect
463. #399	C₂²×C₁₃	semidirect
464. #399	C₂²×C₁₃	semidirect
465. #399	C₂²×C₁₃	semidirect
466. #398	C₂²×C₁₃	semidirect
467. #398	C₂²×C₁₃	semidirect
468. #398	C₂²×C₁₃	semidirect
469. #398	C₂²×C₁₃	semidirect
470. #396	C₂²×C₁₃	semidirect
471. #396	C₂²×C₁₃	semidirect
472. #396	C₂²×C₁₃	semidirect
473. #396	C₂²×C₁₃	semidirect
474. #396	C₂²×C₁₃	semidirect
475. #396	C₂²×C₁₃	semidirect
476. #396	C₂²×C₁₃	semidirect
477. #396	C₂²×C₁₃	semidirect
478. #395	C₂²×C₁₃	semidirect
479. #395	C₂²×C₁₃	semidirect
480. #393	C₂²×C₁₃	semidirect
481. #393	C₂²×C₁₃	semidirect
482. #393	C₂²×C₁₃	semidirect
483. #393	C₂²×C₁₃	semidirect
484. #391	C₂²×C₁₃	semidirect
485. #391	C₂²×C₁₃	semidirect
492. #389	C₂²×C₁₃	semidirect
493. #389	C₂²×C₁₃	semidirect
494. #387	C₂²×C₁₃	semidirect
495. #387	C₂²×C₁₃	semidirect
496. #387	C₂²×C₁₃	semidirect
497. #387	C₂²×C₁₃	semidirect
514. #385	C₂²×C₁₃	semidirect
515. #385	C₂²×C₁₃	semidirect
516. #385	C₂²×C₁₃	semidirect
517. #385	C₂²×C₁₃	semidirect
518. #385	C₂²×C₁₃	semidirect
519. #385	C₂²×C₁₃	semidirect
520. #385	C₂²×C₁₃	semidirect
521. #385	C₂²×C₁₃	semidirect
525. #380	C₂²×C₁₃	semidirect
526. #380	C₂²×C₁₃	semidirect
527. #380	C₂²×C₁₃	semidirect
528. #380	C₂²×C₁₃	semidirect
585. C₂²×D₄	Q₈×C₁₃	semidirect
815. C₁₃	#36747	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×#2848	2
C₁₃×#2804	2
C₁₃×#2784	2
C₁₃×#2780	2
C₁₃×#2748	2
C₁₃×#2732	2
C₁₃×#2692	2
C₁₃×#2683	2
C₁₃×#2626	2
C₁₃×#2438	2
C₁₃×#2437	2
C₁₃×#2309	2
C₁₃×#2308	2
C₂×C₁₃×#386	2
#36747	13

Subgroups — C13×#36747 #15723086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36747 #15723086