Subgroups — C₁₃×#34957 #15721296

Order 3328.

3206 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2602	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2543	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
16	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#525	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#121	C₂²	1	4	yes	—
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#120	C₂²	1	2	yes	—
31	C₂×C₁₃×#120	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	—	2	8	no	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
47	C₁₃×#400	C₂²	1	2	yes	complemented
48	C₁₃×#399	C₂²	1	2	yes	complemented
49	C₁₃×#398	C₂²	1	2	yes	complemented
50	C₁₃×#397	C₂²	1	2	yes	complemented
51	C₁₃×#397	C₂²	1	4	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#394	C₂²	1	4	yes	—
54	C₁₃×#394	C₂²	1	2	yes	complemented
55	C₁₃×#394	C₂²	1	4	yes	complemented
56	C₁₃×#393	C₂²	1	2	yes	complemented
57	C₁₃×#392	C₂²	1	4	yes	—
58	C₁₃×#392	C₂²	1	2	yes	complemented
59	C₁₃×#390	C₂²	1	4	yes	complemented
60	C₁₃×#389	C₂²	1	4	yes	complemented
61	C₁₃×#388	C₂²	1	4	yes	complemented
62	C₁₃×#388	C₂²	1	4	yes	complemented
63	C₁₃×#388	C₂²	1	4	yes	complemented
64	C₁₃×#387	C₂²	1	4	yes	complemented
65	C₁₃×#386	C₂²	1	2	yes	—
66	C₁₃×#386	C₂²	1	4	yes	—
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	4	yes	complemented
69	C₁₃×#386	C₂²	1	4	yes	complemented
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	4	yes	complemented
73	C₁₃×#381	C₂²	1	2	yes	—
74	C₁₃×#380	C₂²	1	4	yes	complemented
75	C₁₃×#379	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	2	8	no	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	2	4	no	—
100	C₂³×C₄×C₁₃	—	4	4	no	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#123	—	2	8	no	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×#121	—	2	16	no	—
121	C₁₃×#121	—	2	4	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#120	—	2	8	no	—
124	C₁₃×#120	—	2	8	no	—
125	C₄×D₄×C₁₃	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	2	8	no	—
128	C₄×D₄×C₁₃	—	2	8	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	—	2	8	no	—
131	C₄×D₄×C₁₃	—	4	8	no	—
132	C₁₃×#117	—	2	4	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	—	2	4	no	—
165	C₂×C₄²×C₁₃	—	4	4	no	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	4	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	4	yes	—
179	C₁₃×#95	C₂³	1	4	yes	—
180	C₁₃×#95	C₂³	1	4	yes	—
181	#34957	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	—	2	4	no	—
184	C₂⁴×C₁₃	—	2	4	no	—
185	C₂⁴×C₁₃	—	2	4	no	—
186	C₂⁴×C₁₃	—	2	4	no	—
187	C₂⁴×C₁₃	—	4	2	no	—
188	C₂⁴×C₁₃	—	4	2	no	—
189	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
190	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
191	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
193	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₁₃×#41	—	4	16	no	—
196	C₂×Q₈×C₁₃	—	2	2	no	—
197	C₂×Q₈×C₁₃	—	4	2	no	—
198	C₂×D₄×C₁₃	—	2	32	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	8	no	—
208	C₂×D₄×C₁₃	—	2	8	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	4	4	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	#41	1	8	yes	complemented
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	8	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	8	no	—
230	C₂²×C₄×C₁₃	—	2	8	no	—
231	C₂²×C₄×C₁₃	—	2	8	no	—
232	C₂²×C₄×C₁₃	—	4	16	no	—
233	C₂²×C₄×C₁₃	—	4	4	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	16	no	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	8	no	—
265	C₁₃×C₄⋊C₄	—	2	8	no	—
266	C₁₃×C₄⋊C₄	—	4	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	8	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	8	no	—
279	C₁₃×C₂²⋊C₄	—	2	8	no	—
280	C₁₃×C₂²⋊C₄	—	2	8	no	—
281	C₁₃×C₂²⋊C₄	—	2	8	no	—
282	C₁₃×C₂²⋊C₄	—	4	4	no	—
283	C₁₃×C₂²⋊C₄	—	4	4	no	—
284	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	—	2	8	no	—
289	C₄²×C₁₃	—	4	2	no	—
290	C₄²×C₁₃	—	4	2	no	—
291	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2602	C₂×C₁₃	1	4	yes	complemented
294	#2591	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#2583	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2564	C₂×C₁₃	1	2	yes	complemented
297	#2561	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2543	C₂×C₁₃	1	2	yes	complemented
299	#2539	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2412	C₂×C₁₃	1	2	yes	complemented
301	#2410	C₂×C₁₃	1	2	yes	complemented
302	#2395	C₂×C₁₃	1	2	yes	complemented
303	#2388	C₂×C₁₃	1	2	yes	complemented
304	C₄×#123	C₂×C₁₃	1	2	yes	complemented
305	C₄×#121	C₂×C₁₃	1	4	yes	complemented
306	C₄×#120	C₂×C₁₃	1	2	yes	complemented
307	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	8	no	—
313	C₂³×C₁₃	—	2	8	no	—
314	C₂³×C₁₃	—	2	8	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	4	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	4	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	4	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	4	no	—
327	C₂³×C₁₃	—	4	4	no	—
328	C₂³×C₁₃	—	4	16	no	—
329	C₂³×C₁₃	—	4	16	no	—
330	C₂³×C₁₃	—	4	4	no	—
331	C₂³×C₁₃	—	4	4	no	—
332	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₁₃	C₂×#41	1	4	yes	—
336	C₂³×C₁₃	C₂×#41	1	4	yes	—
337	C₂³×C₁₃	C₂×#41	1	4	yes	—
338	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
339	Q₈×C₁₃	—	4	4	no	—
340	D₄×C₁₃	—	2	16	no	—
341	D₄×C₁₃	—	2	16	no	—
342	D₄×C₁₃	—	4	16	no	—
343	D₄×C₁₃	—	4	4	no	—
344	D₄×C₁₃	—	4	8	no	—
345	D₄×C₁₃	—	4	8	no	—
346	D₄×C₁₃	—	4	8	no	—
347	C₂×C₄×C₁₃	—	2	8	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	8	no	—
356	C₂×C₄×C₁₃	—	2	8	no	—
357	C₂×C₄×C₁₃	—	2	8	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	4	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	4	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	2	4	no	—
371	C₂×C₄×C₁₃	—	2	4	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	4	16	no	—
376	C₂×C₄×C₁₃	—	4	8	no	—
377	C₂×C₄×C₁₃	—	4	4	no	—
378	C₂×C₄×C₁₃	—	4	4	no	—
379	C₂×C₄×C₁₃	—	4	8	no	—
380	C₂×C₄×C₁₃	—	4	8	no	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
386	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
387	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
388	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
392	#525	—	2	8	no	—
393	C₂×#123	C₂²×C₁₃	1	2	yes	—
394	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
395	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#121	C₂²×C₁₃	1	4	yes	—
399	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	C₂×#120	C₂²×C₁₃	1	2	yes	—
401	C₂×#120	C₂²×C₁₃	1	2	yes	—
402	C₂×C₄×D₄	—	2	8	no	—
403	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
409	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
410	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
415	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
417	#400	C₂²×C₁₃	1	2	yes	complemented
418	#399	C₂²×C₁₃	1	2	yes	complemented
419	#398	C₂²×C₁₃	1	2	yes	complemented
420	#397	C₂²×C₁₃	1	2	yes	complemented
421	#397	C₂²×C₁₃	1	4	yes	complemented
422	#395	C₂²×C₁₃	1	2	yes	complemented
423	#394	C₂²×C₁₃	1	4	yes	—
424	#394	C₂²×C₁₃	1	2	yes	complemented
425	#394	C₂²×C₁₃	1	4	yes	complemented
426	#393	C₂²×C₁₃	1	2	yes	complemented
427	#392	C₂²×C₁₃	1	4	yes	—
428	#392	C₂²×C₁₃	1	2	yes	complemented
429	#390	C₂²×C₁₃	1	4	yes	complemented
430	#389	C₂²×C₁₃	1	4	yes	complemented
431	#388	C₂²×C₁₃	1	4	yes	complemented
432	#388	C₂²×C₁₃	1	4	yes	complemented
433	#388	C₂²×C₁₃	1	4	yes	complemented
434	#387	C₂²×C₁₃	1	4	yes	complemented
435	#386	C₂²×C₁₃	1	4	yes	—
436	#386	C₂²×C₁₃	1	2	yes	—
437	#386	C₂²×C₁₃	1	2	yes	—
438	#386	C₂²×C₁₃	1	4	yes	complemented
439	#386	C₂²×C₁₃	1	4	yes	complemented
440	#385	C₂²×C₁₃	1	2	yes	—
441	#385	C₂²×C₁₃	1	2	yes	—
442	#385	C₂²×C₁₃	1	4	yes	complemented
443	#381	C₂²×C₁₃	1	2	yes	—
444	#380	C₂²×C₁₃	1	4	yes	complemented
445	#379	C₂²×C₁₃	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
447	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
451	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
452	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
453	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
454	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	8	no	—
460	C₂²×C₁₃	—	2	8	no	—
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	2	no	—
464	C₂²×C₁₃	—	2	2	no	—
465	C₂²×C₁₃	—	2	8	no	—
466	C₂²×C₁₃	—	4	16	no	—
467	C₂²×C₁₃	—	4	16	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	4	no	—
471	C₂²×C₁₃	—	4	4	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	4	no	—
476	C₂²×C₁₃	—	4	4	no	—
477	C₂²×C₁₃	#525	1	4	yes	—
478	C₂²×C₁₃	#532	1	4	yes	—
479	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
480	C₂²×C₁₃	C₂²×#41	1	2	yes	—
481	C₂²×C₁₃	C₂²×#41	1	2	yes	—
482	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
483	C₄×C₁₃	—	2	4	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	2	8	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	4	no	—
494	C₄×C₁₃	#534	1	4	yes	—
495	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
496	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×#41	—	2	4	no	—
498	C₂×#41	—	4	4	no	—
499	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	—	2	4	no	—
501	C₂²×D₄	—	2	8	no	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
505	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
506	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
507	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	—	2	4	no	—
510	C₂³×C₄	—	4	4	no	—
511	C₂³×C₄	—	4	4	no	—
512	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
526	#123	—	2	8	no	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	#121	—	2	16	no	—
531	#121	—	2	4	no	—
532	#121	—	2	4	no	—
533	#120	—	2	8	no	—
534	#120	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	2	8	no	—
539	C₄×D₄	—	2	8	no	—
540	C₄×D₄	—	2	8	no	—
541	C₄×D₄	—	4	8	no	—
542	#117	—	2	4	no	—
543	C₂×C₄⋊C₄	—	2	4	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	8	no	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄²	—	2	4	no	—
575	C₂×C₄²	—	4	4	no	—
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
580	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	4	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	4	yes	—
586	#95	C₂³×C₁₃	1	4	yes	—
587	#95	C₂³×C₁₃	1	4	yes	—
588	#95	C₂³×C₁₃	1	4	yes	—
589	#95	C₂³×C₁₃	1	4	yes	—
590	#95	C₂³×C₁₃	1	4	yes	—
591	C₂×C₁₃	—	2	4	no	—
592	C₂×C₁₃	—	2	4	no	—
593	C₂×C₁₃	—	4	2	no	—
594	C₂×C₁₃	—	4	4	no	—
595	C₂×C₁₃	—	8	2	no	—
596	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
597	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
598	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
599	C₂×C₁₃	#3481	1	4	yes	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	2	4	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
608	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
609	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
611	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
612	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
613	#41	—	4	16	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×D₄	—	2	32	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	2	8	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	C₁₃×#41	1	8	yes	complemented
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	2	8	no	—
650	C₂²×C₄	—	4	16	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	16	no	—
658	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
660	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
661	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
662	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
663	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₂²⋊C₄	—	4	4	no	—
702	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
703	C₄²	—	2	4	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	8	no	—
707	C₄²	—	4	2	no	—
708	C₄²	—	4	2	no	—
709	C₁₃	#34957	1	1	yes	characteristic, direct product factor, Sylow
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	16	no	—
731	C₂³	—	4	16	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	4	no	—
734	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
735	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
736	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
737	C₂³	C₂×C₁₃×#41	1	4	yes	—
738	C₂³	C₂×C₁₃×#41	1	4	yes	—
739	C₂³	C₂×C₁₃×#41	1	4	yes	—
740	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
741	Q₈	—	4	4	no	—
742	D₄	—	2	16	no	—
743	D₄	—	2	16	no	—
744	D₄	—	4	16	no	—
745	D₄	—	4	4	no	—
746	D₄	—	4	8	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	8	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	16	no	—
778	C₂×C₄	—	4	8	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	8	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
787	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
788	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
789	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	8	no	—
795	C₂²	—	2	8	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	8	no	—
801	C₂²	—	4	16	no	—
802	C₂²	—	4	16	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	4	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	C₁₃×#525	1	4	yes	—
813	C₂²	C₁₃×#532	1	4	yes	—
814	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
815	C₂²	C₂²×C₁₃×#41	1	2	yes	—
816	C₂²	C₂²×C₁₃×#41	1	2	yes	—
817	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
818	C₄	—	2	4	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	8	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	4	no	—
829	C₄	C₁₃×#534	1	4	yes	—
830	C₂	—	2	4	no	—
831	C₂	—	2	4	no	—
832	C₂	—	4	2	no	—
833	C₂	—	4	4	no	—
834	C₂	—	8	2	no	—
835	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
836	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
837	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
838	C₂	C₁₃×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2602	C₂	semidirect
4. C₁₃×#2591	C₂	semidirect
5. C₁₃×#2583	C₂	semidirect
6. C₁₃×#2564	C₂	semidirect
7. C₁₃×#2561	C₂	semidirect
8. C₁₃×#2543	C₂	semidirect
9. C₁₃×#2539	C₂	semidirect
10. C₁₃×#2412	C₂	semidirect
11. C₁₃×#2410	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
13. C₁₃×#2388	C₂	semidirect
14. C₄×C₁₃×#123	C₂	semidirect
15. C₄×C₁₃×#121	C₂	semidirect
16. C₄×C₁₃×#120	C₂	semidirect
17. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#117	C₂²	semidirect
46. C₂²×C₄²×C₁₃	C₂²	semidirect
47. C₁₃×#400	C₂²	semidirect
48. C₁₃×#399	C₂²	semidirect
49. C₁₃×#398	C₂²	semidirect
50. C₁₃×#397	C₂²	semidirect
51. C₁₃×#397	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
54. C₁₃×#394	C₂²	semidirect
55. C₁₃×#394	C₂²	semidirect
56. C₁₃×#393	C₂²	semidirect
58. C₁₃×#392	C₂²	semidirect
59. C₁₃×#390	C₂²	semidirect
60. C₁₃×#389	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#387	C₂²	semidirect
68. C₁₃×#386	C₂²	semidirect
69. C₁₃×#386	C₂²	semidirect
72. C₁₃×#385	C₂²	semidirect
74. C₁₃×#380	C₂²	semidirect
76. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
80. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
81. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
82. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
83. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
84. C₂×C₁₃×#95	C₂²	semidirect
102. C₂³×C₄×C₁₃	D₄	semidirect
181. #34957	C₁₃	direct (N × H)
216. C₂×D₄×C₁₃	#41	semidirect
284. C₁₃×C₂²⋊C₄	#41	semidirect
291. C₂×#525	C₂×C₁₃	semidirect
292. C₂²×C₄×D₄	C₂×C₁₃	semidirect
293. #2602	C₂×C₁₃	semidirect
294. #2591	C₂×C₁₃	semidirect
295. #2583	C₂×C₁₃	semidirect
296. #2564	C₂×C₁₃	semidirect
297. #2561	C₂×C₁₃	semidirect
298. #2543	C₂×C₁₃	semidirect
299. #2539	C₂×C₁₃	semidirect
300. #2412	C₂×C₁₃	semidirect
301. #2410	C₂×C₁₃	semidirect
302. #2395	C₂×C₁₃	semidirect
303. #2388	C₂×C₁₃	semidirect
304. C₄×#123	C₂×C₁₃	semidirect
305. C₄×#121	C₂×C₁₃	semidirect
306. C₄×#120	C₂×C₁₃	semidirect
307. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
388. C₂²×#41	C₂²×C₁₃	semidirect
394. C₂×#123	C₂²×C₁₃	semidirect
396. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
399. C₂×#121	C₂²×C₁₃	semidirect
408. C₂×C₄×D₄	C₂²×C₁₃	semidirect
409. C₂×C₄×D₄	C₂²×C₁₃	semidirect
410. C₂×#117	C₂²×C₁₃	semidirect
416. C₂²×C₄²	C₂²×C₁₃	semidirect
417. #400	C₂²×C₁₃	semidirect
418. #399	C₂²×C₁₃	semidirect
419. #398	C₂²×C₁₃	semidirect
420. #397	C₂²×C₁₃	semidirect
421. #397	C₂²×C₁₃	semidirect
422. #395	C₂²×C₁₃	semidirect
424. #394	C₂²×C₁₃	semidirect
425. #394	C₂²×C₁₃	semidirect
426. #393	C₂²×C₁₃	semidirect
428. #392	C₂²×C₁₃	semidirect
429. #390	C₂²×C₁₃	semidirect
430. #389	C₂²×C₁₃	semidirect
431. #388	C₂²×C₁₃	semidirect
432. #388	C₂²×C₁₃	semidirect
433. #388	C₂²×C₁₃	semidirect
434. #387	C₂²×C₁₃	semidirect
438. #386	C₂²×C₁₃	semidirect
439. #386	C₂²×C₁₃	semidirect
442. #385	C₂²×C₁₃	semidirect
444. #380	C₂²×C₁₃	semidirect
446. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
450. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
451. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
452. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
453. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
454. C₂×#95	C₂²×C₁₃	semidirect
512. C₂³×C₄	D₄×C₁₃	semidirect
634. C₂×D₄	C₁₃×#41	semidirect
702. C₂²⋊C₄	C₁₃×#41	semidirect
709. C₁₃	#34957	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2602	2
C₁₃×#2591	2
C₁₃×#2583	2
C₁₃×#2564	2
C₁₃×#2561	2
C₁₃×#2543	2
C₁₃×#2539	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2395	2
C₁₃×#2388	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₄×C₁₃×#120	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34957	13

Subgroups — C13×#34957 #15721296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34957 #15721296