Subgroups — C₁₃×#34267 #15720606

Order 3328.

3154 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2364	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₁₃×#537	C₄	1	16	yes	complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	4	yes	—
26	C₁₃×#520	—	2	8	no	—
27	C₄×C₁₃×#41	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#117	C₂²	1	2	yes	—
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	2	yes	—
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	2	yes	—
54	C₁₃×#390	C₂²	1	4	yes	—
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	4	yes	—
60	C₁₃×#388	C₂²	1	4	yes	—
61	C₁₃×#388	C₂²	1	4	yes	—
62	C₁₃×#388	C₂²	1	4	yes	—
63	C₁₃×#388	C₂²	1	4	yes	—
64	C₁₃×#387	C₂²	1	4	yes	—
65	C₁₃×#387	C₂²	1	4	yes	—
66	C₁₃×#386	C₂²	1	2	yes	—
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	4	yes	—
69	C₁₃×#386	C₂²	1	4	yes	—
70	C₁₃×#386	C₂²	1	4	yes	—
71	C₁₃×#385	C₂²	1	4	yes	—
72	C₁₃×#385	C₂²	1	4	yes	—
73	C₁₃×#380	C₂²	1	2	yes	—
74	C₁₃×#380	C₂²	1	2	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
85	C₂×C₁₃×#95	C₂²	1	2	yes	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	2	4	no	—
89	C₂×C₁₃×#41	—	2	4	no	—
90	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
91	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
110	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
111	C₁₃×#121	C₂×C₄	1	16	yes	complemented
112	C₁₃×#121	C₂×C₄	1	16	yes	complemented
113	C₁₃×#121	C₂×C₄	1	32	yes	complemented
114	C₄×Q₈×C₁₃	—	2	4	no	—
115	C₄×Q₈×C₁₃	—	2	4	no	—
116	C₄×Q₈×C₁₃	—	2	8	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	—	2	8	no	—
120	C₄×D₄×C₁₃	—	2	8	no	—
121	C₄×D₄×C₁₃	—	2	16	no	—
122	C₄×D₄×C₁₃	—	2	8	no	—
123	C₄×D₄×C₁₃	—	4	8	no	—
124	C₁₃×#117	—	2	4	no	—
125	C₁₃×#117	—	2	8	no	—
126	C₁₃×#117	—	2	8	no	—
127	C₁₃×#117	D₄	1	8	yes	complemented
128	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	4	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	4	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃	—	2	4	no	—
160	C₂×C₄²×C₁₃	—	2	8	no	—
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	4	yes	—
181	C₁₃×#95	C₂³	1	4	yes	—
182	#34267	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
184	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×#41	—	2	32	no	—
187	C₁₃×#41	—	2	32	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	2	no	—
192	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
193	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	4	no	—
204	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
205	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
206	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
207	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
208	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	8	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	1	no	—
228	C₂²×C₄×C₁₃	—	4	1	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	—	4	4	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
234	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
235	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
236	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₁₃	#41	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	8	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	8	no	—
261	C₁₃×C₄⋊C₄	—	4	4	no	—
262	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
263	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
264	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
266	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
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	8	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	4	2	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	4	no	—
276	C₁₃×C₂²⋊C₄	—	4	4	no	—
277	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
278	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	2	no	—
286	C₄²×C₁₃	—	2	8	no	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	—	4	4	no	—
289	C₄²×C₁₃	—	4	4	no	—
290	C₄²×C₁₃	C₂×D₄	1	8	yes	—
291	C₂×#537	C₂×C₁₃	1	1	yes	characteristic
292	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2364	C₂×C₁₃	1	4	yes	complemented
295	#2363	C₂×C₁₃	1	2	yes	complemented
296	#2362	C₂×C₁₃	1	2	yes	complemented
297	#2361	C₂×C₁₃	1	2	yes	complemented
298	#2361	C₂×C₁₃	1	4	yes	complemented
299	#2360	C₂×C₁₃	1	2	yes	complemented
300	#2324	C₂×C₁₃	1	2	yes	complemented
301	#2323	C₂×C₁₃	1	2	yes	complemented
302	#2311	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
304	C₄×#121	C₂×C₁₃	1	2	yes	complemented
305	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
325	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
326	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
327	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂³×C₁₃	C₂×#41	1	2	yes	—
329	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
330	Q₈×C₁₃	—	2	8	no	—
331	Q₈×C₁₃	—	2	8	no	—
332	D₄×C₁₃	—	2	16	no	—
333	D₄×C₁₃	—	2	16	no	—
334	D₄×C₁₃	—	2	8	no	—
335	D₄×C₁₃	—	2	8	no	—
336	D₄×C₁₃	—	4	16	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	4	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	16	no	—
352	C₂×C₄×C₁₃	—	2	16	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	4	8	no	—
369	C₂×C₄×C₁₃	—	4	8	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	8	8	no	—
374	C₂×C₄×C₁₃	—	8	4	no	—
375	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
376	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
377	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
378	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
379	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	4	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	2	yes	—
386	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
389	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
391	#537	C₄×C₁₃	1	16	yes	complemented
392	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
394	C₂×#121	C₂²×C₁₃	1	2	yes	—
395	C₂×#121	C₂²×C₁₃	1	2	yes	—
396	C₂×#121	C₂²×C₁₃	1	4	yes	—
397	#520	—	2	8	no	—
398	C₄×#41	—	2	8	no	—
399	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
406	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
409	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#117	C₂²×C₁₃	1	2	yes	—
411	C₂×#117	C₂²×C₁₃	1	2	yes	—
412	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
415	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
416	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
419	#391	C₂²×C₁₃	1	2	yes	—
420	#391	C₂²×C₁₃	1	1	yes	characteristic
421	#391	C₂²×C₁₃	1	1	yes	characteristic
422	#390	C₂²×C₁₃	1	2	yes	—
423	#390	C₂²×C₁₃	1	1	yes	characteristic
424	#390	C₂²×C₁₃	1	4	yes	—
425	#390	C₂²×C₁₃	1	1	yes	characteristic
426	#389	C₂²×C₁₃	1	2	yes	—
427	#389	C₂²×C₁₃	1	4	yes	—
428	#389	C₂²×C₁₃	1	2	yes	—
429	#389	C₂²×C₁₃	1	2	yes	—
430	#389	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	4	yes	—
432	#388	C₂²×C₁₃	1	4	yes	—
433	#388	C₂²×C₁₃	1	4	yes	—
434	#388	C₂²×C₁₃	1	4	yes	—
435	#387	C₂²×C₁₃	1	4	yes	—
436	#387	C₂²×C₁₃	1	4	yes	—
437	#386	C₂²×C₁₃	1	4	yes	—
438	#386	C₂²×C₁₃	1	4	yes	—
439	#386	C₂²×C₁₃	1	2	yes	—
440	#386	C₂²×C₁₃	1	4	yes	—
441	#386	C₂²×C₁₃	1	2	yes	—
442	#385	C₂²×C₁₃	1	4	yes	—
443	#385	C₂²×C₁₃	1	4	yes	—
444	#380	C₂²×C₁₃	1	2	yes	—
445	#380	C₂²×C₁₃	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
456	C₂×#95	C₂²×C₁₃	1	2	yes	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	2	no	—
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	2	4	no	—
464	C₂²×C₁₃	—	2	4	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	2	4	no	—
467	C₂²×C₁₃	—	2	4	no	—
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
478	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
479	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
480	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
481	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂²×C₁₃	#585	1	1	yes	characteristic
484	C₂²×C₁₃	#585	1	1	yes	characteristic
485	C₄×C₁₃	—	2	4	no	—
486	C₄×C₁₃	—	2	4	no	—
487	C₄×C₁₃	—	2	8	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	4	no	—
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	2	4	no	—
492	C₄×C₁₃	—	4	1	no	—
493	C₄×C₁₃	—	4	4	no	—
494	C₄×C₁₃	—	4	1	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
498	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	2	4	no	—
501	C₂×#41	—	2	4	no	—
502	C₂×#41	—	2	4	no	—
503	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
504	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
505	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
509	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
519	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
520	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
523	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
524	#121	C₂×C₄×C₁₃	1	16	yes	complemented
525	#121	C₂×C₄×C₁₃	1	16	yes	complemented
526	#121	C₂×C₄×C₁₃	1	32	yes	complemented
527	C₄×Q₈	—	2	4	no	—
528	C₄×Q₈	—	2	4	no	—
529	C₄×Q₈	—	2	8	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	16	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	4	8	no	—
537	#117	—	2	4	no	—
538	#117	—	2	8	no	—
539	#117	—	2	8	no	—
540	#117	D₄×C₁₃	1	8	yes	complemented
541	C₂×C₄⋊C₄	—	2	4	no	—
542	C₂×C₄⋊C₄	—	2	8	no	—
543	C₂×C₄⋊C₄	—	4	4	no	—
544	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	2	yes	—
572	C₂×C₄²	—	2	4	no	—
573	C₂×C₄²	—	2	8	no	—
574	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
583	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
584	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	4	yes	—
586	#95	C₂³×C₁₃	1	4	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	4	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	4	yes	—
591	#95	C₂³×C₁₃	1	4	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	4	yes	—
595	C₂×C₁₃	—	2	4	no	—
596	C₂×C₁₃	—	4	4	no	—
597	C₂×C₁₃	—	4	4	no	—
598	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
599	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
601	C₂×C₁₃	#3488	1	1	yes	characteristic
602	C₂×C₁₃	#3489	1	1	yes	characteristic
603	C₂×C₁₃	#3511	1	1	yes	characteristic
604	C₂×C₁₃	#3512	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
606	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
607	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
608	#41	—	2	32	no	—
609	#41	—	2	32	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
615	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
627	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
628	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
629	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
630	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	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	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	8	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	4	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
656	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
657	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
658	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
660	C₂²×C₄	C₁₃×#41	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₁₃	1	4	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	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	8	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	—	4	4	no	—
684	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
685	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
686	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
687	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
700	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
701	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	8	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	4	4	no	—
711	C₄²	—	4	4	no	—
712	C₄²	C₂×D₄×C₁₃	1	8	yes	—
713	C₁₃	#34267	1	1	yes	characteristic, direct product factor, Sylow
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
731	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
732	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
733	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
734	C₂³	C₂×C₁₃×#41	1	2	yes	—
735	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
736	Q₈	—	2	8	no	—
737	Q₈	—	2	8	no	—
738	D₄	—	2	16	no	—
739	D₄	—	2	16	no	—
740	D₄	—	2	8	no	—
741	D₄	—	2	8	no	—
742	D₄	—	4	16	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	16	no	—
758	C₂×C₄	—	2	16	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	4	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	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	8	no	—
776	C₂×C₄	—	4	8	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	8	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
782	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
783	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
784	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
785	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
786	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
788	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
791	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
792	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
793	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
794	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
816	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
817	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
818	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
819	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
820	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
821	C₂²	C₁₃×#585	1	1	yes	characteristic
822	C₂²	C₁₃×#585	1	1	yes	characteristic
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	8	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	4	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	4	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
836	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
837	C₂	—	2	4	no	—
838	C₂	—	4	4	no	—
839	C₂	—	4	4	no	—
840	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
841	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
843	C₂	C₁₃×#3488	1	1	yes	characteristic
844	C₂	C₁₃×#3489	1	1	yes	characteristic
845	C₂	C₁₃×#3511	1	1	yes	characteristic
846	C₂	C₁₃×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#537	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#520	C₂	semidirect
3. C₂×C₄×C₁₃×#41	C₂	semidirect
4. C₁₃×#2364	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2361	C₂	semidirect
9. C₁₃×#2360	C₂	semidirect
10. C₁₃×#2324	C₂	semidirect
11. C₁₃×#2323	C₂	semidirect
12. C₁₃×#2311	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₁₃×#2297	C₂	semidirect
16. C₂×C₁₃×#389	C₂	semidirect
17. C₁₃×#2274	C₂	semidirect
20. C₁₃×#537	C₄	semidirect
90. C₂×C₁₃×#41	C₂×C₄	semidirect
91. C₂×C₁₃×#41	C₂×C₄	semidirect
109. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
110. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
111. C₁₃×#121	C₂×C₄	semidirect
112. C₁₃×#121	C₂×C₄	semidirect
113. C₁₃×#121	C₂×C₄	semidirect
127. C₁₃×#117	D₄	semidirect
131. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
182. #34267	C₁₃	direct (N × H)
292. C₂×#520	C₂×C₁₃	semidirect
293. C₂×C₄×#41	C₂×C₁₃	semidirect
294. #2364	C₂×C₁₃	semidirect
295. #2363	C₂×C₁₃	semidirect
296. #2362	C₂×C₁₃	semidirect
297. #2361	C₂×C₁₃	semidirect
298. #2361	C₂×C₁₃	semidirect
299. #2360	C₂×C₁₃	semidirect
300. #2324	C₂×C₁₃	semidirect
301. #2323	C₂×C₁₃	semidirect
302. #2311	C₂×C₁₃	semidirect
303. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
304. C₄×#121	C₂×C₁₃	semidirect
305. #2297	C₂×C₁₃	semidirect
306. C₂×#389	C₂×C₁₃	semidirect
307. #2274	C₂×C₁₃	semidirect
375. C₂×C₄×C₁₃	C₄×D₄	semidirect
391. #537	C₄×C₁₃	semidirect
503. C₂×#41	C₂×C₄×C₁₃	semidirect
504. C₂×#41	C₂×C₄×C₁₃	semidirect
522. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
523. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
524. #121	C₂×C₄×C₁₃	semidirect
525. #121	C₂×C₄×C₁₃	semidirect
526. #121	C₂×C₄×C₁₃	semidirect
540. #117	D₄×C₁₃	semidirect
544. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
713. C₁₃	#34267	direct (N × H)
781. C₂×C₄	C₄×D₄×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#537	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2364	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2324	2
C₁₃×#2323	2
C₁₃×#2311	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₂×C₁₃×#389	2
C₁₃×#2274	2
#34267	13

Subgroups — C13×#34267 #15720606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34267 #15720606