Subgroups — C₁₃×#36729 #15723068

Order 3328.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1000 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	1	yes	maximal, characteristic, complemented
2	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2747	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2742	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2741	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2717	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2702	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2692	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2691	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2672	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2481	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2472	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2449	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2418	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#400	C₂²	1	2	yes	complemented
39	C₁₃×#400	C₂²	1	2	yes	complemented
40	C₁₃×#400	C₂²	1	2	yes	complemented
41	C₁₃×#399	C₂²	1	2	yes	—
42	C₁₃×#399	C₂²	1	2	yes	complemented
43	C₁₃×#398	C₂²	1	2	yes	complemented
44	C₁₃×#398	C₂²	1	2	yes	complemented
45	C₁₃×#398	C₂²	1	2	yes	complemented
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	complemented
49	C₁₃×#397	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×#395	C₂²	1	2	yes	complemented
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#394	C₂²	1	2	yes	—
57	C₁₃×#394	C₂²	1	2	yes	—
58	C₁₃×#394	C₂²	1	2	yes	—
59	C₁₃×#394	C₂²	1	2	yes	complemented
60	C₁₃×#393	C₂²	1	2	yes	—
61	C₁₃×#393	C₂²	1	2	yes	complemented
62	C₁₃×#391	C₂²	1	2	yes	complemented
63	C₁₃×#390	C₂²	1	2	yes	—
64	C₁₃×#389	C₂²	1	2	yes	complemented
65	C₁₃×#389	C₂²	1	2	yes	complemented
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	complemented
71	C₁₃×#388	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	2	yes	complemented
73	C₁₃×#387	C₂²	1	2	yes	complemented
74	C₁₃×#387	C₂²	1	2	yes	complemented
75	C₁₃×#387	C₂²	1	2	yes	complemented
76	C₁₃×#387	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	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	complemented
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	complemented
91	C₁₃×#385	C₂²	1	2	yes	complemented
92	C₁₃×#380	C₂²	1	2	yes	—
93	C₁₃×#380	C₂²	1	2	yes	—
94	C₁₃×#380	C₂²	1	2	yes	—
95	C₁₃×#380	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	1	yes	characteristic
97	C₁₃×#380	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	1	yes	characteristic
99	C₁₃×#380	C₂²	1	1	yes	characteristic
100	C₁₃×#380	C₂²	1	1	yes	characteristic
101	C₁₃×#380	C₂²	1	1	yes	characteristic
102	C₁₃×#380	C₂²	1	2	yes	—
103	C₁₃×#379	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	—	2	4	no	—
115	C₂³×C₄×C₁₃	—	4	2	no	—
116	C₂³×C₄×C₁₃	—	4	2	no	—
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×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	1	yes	characteristic
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	C₁₃×#126	—	4	4	no	—
129	C₁₃×#124	—	4	4	no	—
130	C₁₃×#123	—	4	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	4	4	no	—
133	C₁₃×C₂²⋊Q₈	—	4	4	no	—
134	C₁₃×C₂²⋊Q₈	—	4	2	no	—
135	C₁₃×C₂²⋊Q₈	—	4	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	—	4	2	no	—
138	C₁₃×#121	—	4	2	no	—
139	C₁₃×#120	—	4	4	no	—
140	C₄×D₄×C₁₃	—	4	4	no	—
141	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
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	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	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	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	#36729	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂⁴×C₁₃	—	2	2	no	—
216	C₂⁴×C₁₃	—	2	2	no	—
217	C₂⁴×C₁₃	—	2	2	no	—
218	C₂⁴×C₁₃	—	2	2	no	—
219	C₂⁴×C₁₃	—	2	2	no	—
220	C₂⁴×C₁₃	—	4	1	no	—
221	C₂⁴×C₁₃	—	4	1	no	—
222	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
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	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	4	1	no	—
228	C₂×Q₈×C₁₃	—	4	1	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	2	no	—
231	C₂×Q₈×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	1	no	—
241	C₂×D₄×C₁₃	—	4	1	no	—
242	C₂×D₄×C₁₃	—	4	2	no	—
243	C₂×D₄×C₁₃	—	4	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	2	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	4	1	no	—
260	C₂²×C₄×C₁₃	—	4	1	no	—
261	C₂²×C₄×C₁₃	—	4	1	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	—	4	1	no	—
264	C₂²×C₄×C₁₃	—	4	1	no	—
265	C₂²×C₄×C₁₃	—	4	1	no	—
266	C₂²×C₄×C₁₃	—	4	1	no	—
267	C₂²×C₄×C₁₃	—	4	1	no	—
268	C₂²×C₄×C₁₃	—	4	1	no	—
269	C₂²×C₄×C₁₃	—	4	1	no	—
270	C₂²×C₄×C₁₃	—	4	1	no	—
271	C₂²×C₄×C₁₃	—	4	1	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	16	no	—
277	C₂²×C₄×C₁₃	#41	1	4	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	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
304	C₁₃×C₄⋊C₄	—	4	1	no	—
305	C₁₃×C₄⋊C₄	—	4	1	no	—
306	C₁₃×C₄⋊C₄	—	4	1	no	—
307	C₁₃×C₄⋊C₄	—	4	2	no	—
308	C₁₃×C₄⋊C₄	—	4	2	no	—
309	C₁₃×C₄⋊C₄	—	4	2	no	—
310	C₁₃×C₄⋊C₄	—	4	2	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	—	4	2	no	—
313	C₁₃×C₄⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	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	C₁₃×C₂²⋊C₄	—	4	2	no	—
332	C₁₃×C₂²⋊C₄	—	4	2	no	—
333	C₁₃×C₂²⋊C₄	—	4	2	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₁₃×C₂²⋊C₄	—	4	2	no	—
336	C₁₃×C₂²⋊C₄	—	4	2	no	—
337	C₄²×C₁₃	—	4	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₄²×C₁₃	—	4	2	no	—
340	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2847	C₂×C₁₃	1	1	yes	characteristic
342	#2747	C₂×C₁₃	1	2	yes	complemented
343	#2742	C₂×C₁₃	1	2	yes	complemented
344	#2741	C₂×C₁₃	1	2	yes	complemented
345	#2717	C₂×C₁₃	1	2	yes	complemented
346	#2702	C₂×C₁₃	1	2	yes	complemented
347	#2692	C₂×C₁₃	1	2	yes	complemented
348	#2691	C₂×C₁₃	1	2	yes	complemented
349	#2672	C₂×C₁₃	1	2	yes	complemented
350	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2639	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2481	C₂×C₁₃	1	2	yes	complemented
353	#2472	C₂×C₁₃	1	2	yes	complemented
354	#2449	C₂×C₁₃	1	2	yes	complemented
355	#2418	C₂×C₁₃	1	2	yes	complemented
356	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2325	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	8	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	1	no	—
369	C₂³×C₁₃	—	2	1	no	—
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	1	no	—
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	4	4	no	—
384	C₂³×C₁₃	—	4	4	no	—
385	C₂³×C₁₃	—	4	4	no	—
386	C₂³×C₁₃	—	4	4	no	—
387	C₂³×C₁₃	—	4	4	no	—
388	C₂³×C₁₃	—	4	4	no	—
389	C₂³×C₁₃	C₂×#41	1	2	yes	—
390	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
391	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
392	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
393	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
394	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
395	Q₈×C₁₃	—	8	2	no	—
396	Q₈×C₁₃	—	8	4	no	—
397	D₄×C₁₃	—	4	8	no	—
398	D₄×C₁₃	—	8	2	no	—
399	D₄×C₁₃	—	8	4	no	—
400	D₄×C₁₃	—	8	4	no	—
401	C₂×C₄×C₁₃	—	2	8	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	4	4	no	—
444	C₂×C₄×C₁₃	—	4	4	no	—
445	C₂×C₄×C₁₃	—	4	4	no	—
446	C₂×C₄×C₁₃	—	4	4	no	—
447	C₂×C₄×C₁₃	—	4	4	no	—
448	C₂×C₄×C₁₃	—	8	2	no	—
449	C₂×C₄×C₁₃	—	8	2	no	—
450	C₂×C₄×C₁₃	—	8	2	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	4	no	—
453	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
454	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
455	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
456	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
457	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
459	C₂×#124	C₂²×C₁₃	1	2	yes	—
460	C₂×#123	C₂²×C₁₃	1	2	yes	—
461	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
466	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#120	C₂²×C₁₃	1	2	yes	—
470	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
471	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
472	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
475	#400	C₂²×C₁₃	1	2	yes	complemented
476	#400	C₂²×C₁₃	1	2	yes	complemented
477	#400	C₂²×C₁₃	1	2	yes	complemented
478	#399	C₂²×C₁₃	1	2	yes	—
479	#399	C₂²×C₁₃	1	2	yes	complemented
480	#398	C₂²×C₁₃	1	2	yes	complemented
481	#398	C₂²×C₁₃	1	2	yes	complemented
482	#398	C₂²×C₁₃	1	2	yes	complemented
483	#397	C₂²×C₁₃	1	2	yes	—
484	#397	C₂²×C₁₃	1	2	yes	—
485	#397	C₂²×C₁₃	1	2	yes	complemented
486	#397	C₂²×C₁₃	1	2	yes	complemented
487	#396	C₂²×C₁₃	1	2	yes	complemented
488	#396	C₂²×C₁₃	1	2	yes	complemented
489	#395	C₂²×C₁₃	1	2	yes	complemented
490	#395	C₂²×C₁₃	1	2	yes	complemented
491	#395	C₂²×C₁₃	1	2	yes	complemented
492	#394	C₂²×C₁₃	1	2	yes	—
493	#394	C₂²×C₁₃	1	2	yes	—
494	#394	C₂²×C₁₃	1	2	yes	—
495	#394	C₂²×C₁₃	1	2	yes	—
496	#394	C₂²×C₁₃	1	2	yes	complemented
497	#393	C₂²×C₁₃	1	2	yes	—
498	#393	C₂²×C₁₃	1	2	yes	complemented
499	#391	C₂²×C₁₃	1	2	yes	complemented
500	#390	C₂²×C₁₃	1	2	yes	—
501	#389	C₂²×C₁₃	1	2	yes	complemented
502	#389	C₂²×C₁₃	1	2	yes	complemented
503	#388	C₂²×C₁₃	1	2	yes	—
504	#388	C₂²×C₁₃	1	2	yes	—
505	#388	C₂²×C₁₃	1	2	yes	—
506	#388	C₂²×C₁₃	1	2	yes	—
507	#388	C₂²×C₁₃	1	2	yes	complemented
508	#388	C₂²×C₁₃	1	2	yes	complemented
509	#387	C₂²×C₁₃	1	2	yes	complemented
510	#387	C₂²×C₁₃	1	2	yes	complemented
511	#387	C₂²×C₁₃	1	2	yes	complemented
512	#387	C₂²×C₁₃	1	2	yes	complemented
513	#387	C₂²×C₁₃	1	2	yes	complemented
514	#387	C₂²×C₁₃	1	2	yes	complemented
515	#386	C₂²×C₁₃	1	2	yes	—
516	#386	C₂²×C₁₃	1	2	yes	—
517	#386	C₂²×C₁₃	1	2	yes	—
518	#386	C₂²×C₁₃	1	2	yes	—
519	#386	C₂²×C₁₃	1	2	yes	—
520	#386	C₂²×C₁₃	1	2	yes	—
521	#386	C₂²×C₁₃	1	2	yes	—
522	#386	C₂²×C₁₃	1	2	yes	complemented
523	#385	C₂²×C₁₃	1	2	yes	—
524	#385	C₂²×C₁₃	1	2	yes	—
525	#385	C₂²×C₁₃	1	2	yes	—
526	#385	C₂²×C₁₃	1	2	yes	—
527	#385	C₂²×C₁₃	1	2	yes	complemented
528	#385	C₂²×C₁₃	1	2	yes	complemented
529	#380	C₂²×C₁₃	1	1	yes	characteristic
530	#380	C₂²×C₁₃	1	1	yes	characteristic
531	#380	C₂²×C₁₃	1	1	yes	characteristic
532	#380	C₂²×C₁₃	1	1	yes	characteristic
533	#380	C₂²×C₁₃	1	1	yes	characteristic
534	#380	C₂²×C₁₃	1	1	yes	characteristic
535	#380	C₂²×C₁₃	1	2	yes	—
536	#380	C₂²×C₁₃	1	2	yes	—
537	#380	C₂²×C₁₃	1	2	yes	—
538	#380	C₂²×C₁₃	1	2	yes	—
539	#380	C₂²×C₁₃	1	2	yes	—
540	#379	C₂²×C₁₃	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
542	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
543	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	2	2	no	—
546	C₂²×C₁₃	—	2	2	no	—
547	C₂²×C₁₃	—	2	2	no	—
548	C₂²×C₁₃	—	2	2	no	—
549	C₂²×C₁₃	—	2	2	no	—
550	C₂²×C₁₃	—	2	2	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	2	2	no	—
555	C₂²×C₁₃	—	2	2	no	—
556	C₂²×C₁₃	—	4	16	no	—
557	C₂²×C₁₃	—	4	1	no	—
558	C₂²×C₁₃	—	4	1	no	—
559	C₂²×C₁₃	—	4	1	no	—
560	C₂²×C₁₃	—	4	1	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	1	no	—
563	C₂²×C₁₃	—	4	1	no	—
564	C₂²×C₁₃	—	4	1	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	#542	1	4	yes	—
573	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
574	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
579	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
580	C₄×C₁₃	—	2	2	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	2	no	—
583	C₄×C₁₃	—	2	2	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
599	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
600	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
601	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂³×C₄	—	2	4	no	—
603	C₂³×C₄	—	4	2	no	—
604	C₂³×C₄	—	4	2	no	—
605	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
615	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
616	#126	—	4	4	no	—
617	#124	—	4	4	no	—
618	#123	—	4	4	no	—
619	C₂²⋊Q₈	—	2	4	no	—
620	C₂²⋊Q₈	—	4	4	no	—
621	C₂²⋊Q₈	—	4	4	no	—
622	C₂²⋊Q₈	—	4	2	no	—
623	C₂²⋊Q₈	—	4	2	no	—
624	#121	—	2	4	no	—
625	#121	—	4	2	no	—
626	#121	—	4	2	no	—
627	#120	—	4	4	no	—
628	C₄×D₄	—	4	4	no	—
629	C₂×C₄⋊C₄	—	4	2	no	—
630	C₂×C₄⋊C₄	—	4	2	no	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	—	4	2	no	—
653	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄²	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	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	2	yes	—
690	#95	C₂³×C₁₃	1	2	yes	—
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	2	yes	—
700	#95	C₂³×C₁₃	1	2	yes	—
701	#95	C₂³×C₁₃	1	2	yes	—
702	C₂×C₁₃	—	2	4	no	—
703	C₂×C₁₃	—	4	2	no	—
704	C₂×C₁₃	—	4	2	no	—
705	C₂×C₁₃	—	8	2	no	—
706	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
707	C₂×C₁₃	#3490	1	1	yes	characteristic
708	C₂×C₁₃	#3492	1	1	yes	characteristic
709	C₂×C₁₃	#3536	1	1	yes	characteristic
710	C₂×C₁₃	#3536	1	1	yes	characteristic
711	C₂×C₁₃	#3537	1	1	yes	characteristic
712	C₂×C₁₃	#3538	1	1	yes	characteristic
713	C₂⁴	—	2	2	no	—
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	2	no	—
717	C₂⁴	—	2	2	no	—
718	C₂⁴	—	4	1	no	—
719	C₂⁴	—	4	1	no	—
720	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
721	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	4	1	no	—
726	C₂×Q₈	—	4	1	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	16	no	—
775	C₂²×C₄	C₁₃×#41	1	4	yes	—
776	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	1	no	—
802	C₄⋊C₄	—	4	1	no	—
803	C₄⋊C₄	—	4	1	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₁₃	#36729	1	1	yes	characteristic, direct product factor, Sylow
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	4	no	—
869	C₂³	C₂×C₁₃×#41	1	2	yes	—
870	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
871	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
872	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
873	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
874	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
875	Q₈	—	8	2	no	—
876	Q₈	—	8	4	no	—
877	D₄	—	4	8	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	4	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	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	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
934	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
935	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
936	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	16	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	C₁₃×#542	1	4	yes	—
966	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
967	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
969	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
972	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	—	4	2	no	—
991	C₂	—	8	2	no	—
992	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
993	C₂	C₁₃×#3490	1	1	yes	characteristic
994	C₂	C₁₃×#3492	1	1	yes	characteristic
995	C₂	C₁₃×#3536	1	1	yes	characteristic
996	C₂	C₁₃×#3536	1	1	yes	characteristic
997	C₂	C₁₃×#3537	1	1	yes	characteristic
998	C₂	C₁₃×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₁₃×#2847	C₂
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
3. C₁₃×#2747	C₂	semidirect
4. C₁₃×#2742	C₂	semidirect
5. C₁₃×#2741	C₂	semidirect
6. C₁₃×#2717	C₂	semidirect
7. C₁₃×#2702	C₂	semidirect
8. C₁₃×#2692	C₂	semidirect
9. C₁₃×#2691	C₂	semidirect
10. C₁₃×#2672	C₂	semidirect
11. C₁₃×#2659	C₂	semidirect
12. C₁₃×#2639	C₂	semidirect
13. C₁₃×#2481	C₂	semidirect
14. C₁₃×#2472	C₂	semidirect
15. C₁₃×#2449	C₂	semidirect
16. C₁₃×#2418	C₂	semidirect
17. C₁₃×#2329	C₂	semidirect
18. C₁₃×#2325	C₂	semidirect
19. C₂×C₁₃×#380	C₂	semidirect
21. C₂×C₁₃×#126	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×#400	C₂²	semidirect
39. C₁₃×#400	C₂²	semidirect
40. C₁₃×#400	C₂²	semidirect
42. C₁₃×#399	C₂²	semidirect
43. C₁₃×#398	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#398	C₂²	semidirect
48. C₁₃×#397	C₂²	semidirect
49. C₁₃×#397	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#396	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
53. C₁₃×#395	C₂²	semidirect
54. C₁₃×#395	C₂²	semidirect
59. C₁₃×#394	C₂²	semidirect
61. C₁₃×#393	C₂²	semidirect
62. C₁₃×#391	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
70. C₁₃×#388	C₂²	semidirect
71. C₁₃×#388	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
73. C₁₃×#387	C₂²	semidirect
74. C₁₃×#387	C₂²	semidirect
75. C₁₃×#387	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
85. C₁₃×#386	C₂²	semidirect
90. C₁₃×#385	C₂²	semidirect
91. C₁₃×#385	C₂²	semidirect
214. #36729	C₁₃	direct (N × H)
340. #2848	C₂×C₁₃	semidirect
342. #2747	C₂×C₁₃	semidirect
343. #2742	C₂×C₁₃	semidirect
344. #2741	C₂×C₁₃	semidirect
345. #2717	C₂×C₁₃	semidirect
346. #2702	C₂×C₁₃	semidirect
347. #2692	C₂×C₁₃	semidirect
348. #2691	C₂×C₁₃	semidirect
349. #2672	C₂×C₁₃	semidirect
350. #2659	C₂×C₁₃	semidirect
351. #2639	C₂×C₁₃	semidirect
352. #2481	C₂×C₁₃	semidirect
353. #2472	C₂×C₁₃	semidirect
354. #2449	C₂×C₁₃	semidirect
355. #2418	C₂×C₁₃	semidirect
356. #2329	C₂×C₁₃	semidirect
357. #2325	C₂×C₁₃	semidirect
358. C₂×#380	C₂×C₁₃	semidirect
458. C₂×#126	C₂²×C₁₃	semidirect
465. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
475. #400	C₂²×C₁₃	semidirect
476. #400	C₂²×C₁₃	semidirect
477. #400	C₂²×C₁₃	semidirect
479. #399	C₂²×C₁₃	semidirect
480. #398	C₂²×C₁₃	semidirect
481. #398	C₂²×C₁₃	semidirect
482. #398	C₂²×C₁₃	semidirect
485. #397	C₂²×C₁₃	semidirect
486. #397	C₂²×C₁₃	semidirect
487. #396	C₂²×C₁₃	semidirect
488. #396	C₂²×C₁₃	semidirect
489. #395	C₂²×C₁₃	semidirect
490. #395	C₂²×C₁₃	semidirect
491. #395	C₂²×C₁₃	semidirect
496. #394	C₂²×C₁₃	semidirect
498. #393	C₂²×C₁₃	semidirect
499. #391	C₂²×C₁₃	semidirect
501. #389	C₂²×C₁₃	semidirect
502. #389	C₂²×C₁₃	semidirect
507. #388	C₂²×C₁₃	semidirect
508. #388	C₂²×C₁₃	semidirect
509. #387	C₂²×C₁₃	semidirect
510. #387	C₂²×C₁₃	semidirect
511. #387	C₂²×C₁₃	semidirect
512. #387	C₂²×C₁₃	semidirect
513. #387	C₂²×C₁₃	semidirect
514. #387	C₂²×C₁₃	semidirect
522. #386	C₂²×C₁₃	semidirect
527. #385	C₂²×C₁₃	semidirect
528. #385	C₂²×C₁₃	semidirect
838. C₁₃	#36729	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×#2847	2
C₁₃×#2747	2
C₁₃×#2742	2
C₁₃×#2741	2
C₁₃×#2717	2
C₁₃×#2702	2
C₁₃×#2692	2
C₁₃×#2691	2
C₁₃×#2672	2
C₁₃×#2659	2
C₁₃×#2639	2
C₁₃×#2481	2
C₁₃×#2472	2
C₁₃×#2449	2
C₁₃×#2418	2
C₁₃×#2329	2
C₁₃×#2325	2
C₂×C₁₃×#380	2
#36729	13

Subgroups — C13×#36729 #15723068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36729 #15723068