Subgroups — C₁₃×#34310 #15720649

Order 3328.

3764 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2358	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	D₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2321	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#390	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
20	D₄²×C₁₃	C₄	1	16	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₁₃×#120	C₂²	1	4	yes	—
25	C₁₃×#518	—	2	16	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
44	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#390	C₂²	1	2	yes	—
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	2	yes	complemented
49	C₁₃×#390	C₂²	1	4	yes	complemented
50	C₁₃×#390	C₂²	1	4	yes	complemented
51	C₁₃×#390	C₂²	1	2	yes	complemented
52	C₁₃×#390	C₂²	1	2	yes	complemented
53	C₁₃×#390	C₂²	1	2	yes	complemented
54	C₁₃×#390	C₂²	1	2	yes	complemented
55	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#389	C₂²	1	2	yes	complemented
58	C₁₃×#388	C₂²	1	2	yes	complemented
59	C₁₃×#388	C₂²	1	2	yes	complemented
60	C₁₃×#388	C₂²	1	4	yes	complemented
61	C₁₃×#388	C₂²	1	4	yes	complemented
62	C₁₃×#388	C₂²	1	4	yes	complemented
63	C₁₃×#386	C₂²	1	4	yes	complemented
64	C₁₃×#386	C₂²	1	4	yes	complemented
65	C₁₃×#386	C₂²	1	4	yes	complemented
66	C₁₃×#386	C₂²	1	4	yes	complemented
67	C₁₃×#386	C₂²	1	4	yes	complemented
68	C₁₃×#385	C₂²	1	4	yes	complemented
69	C₁₃×#385	C₂²	1	4	yes	complemented
70	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#380	C₂²	1	2	yes	complemented
72	C₁₃×#380	C₂²	1	2	yes	complemented
73	C₁₃×#379	C₂²	1	4	yes	complemented
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
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	2	yes	complemented
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₂⁵×C₁₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃	—	2	8	no	—
87	C₂²×D₄×C₁₃	—	2	8	no	—
88	C₂²×D₄×C₁₃	—	4	4	no	—
89	C₂²×D₄×C₁₃	—	4	4	no	—
90	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
91	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×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	4	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₁₃×#127	C₂×C₄	1	8	yes	complemented
107	C₁₃×#121	C₂×C₄	1	16	yes	complemented
108	C₁₃×#121	C₂×C₄	1	16	yes	complemented
109	C₁₃×#120	C₂×C₄	1	32	yes	complemented
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	16	no	—
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₄×D₄×C₁₃	—	2	16	no	—
115	C₄×D₄×C₁₃	—	2	8	no	—
116	C₄×D₄×C₁₃	—	4	4	no	—
117	C₄×D₄×C₁₃	—	4	4	no	—
118	C₄×D₄×C₁₃	—	4	4	no	—
119	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
120	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
121	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
122	C₁₃×#117	—	2	8	no	—
123	C₁₃×#117	—	2	8	no	—
124	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	—	4	4	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	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	2	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	#34310	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	8	no	—
181	C₂⁴×C₁₃	—	2	8	no	—
182	C₂⁴×C₁₃	—	4	4	no	—
183	C₂⁴×C₁₃	—	4	4	no	—
184	C₂⁴×C₁₃	—	4	4	no	—
185	C₂⁴×C₁₃	—	4	4	no	—
186	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
187	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
189	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	8	no	—
192	C₂×D₄×C₁₃	—	2	64	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
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	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	4	32	no	—
200	C₂×D₄×C₁₃	—	4	2	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	2	no	—
204	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
205	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
206	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
207	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
208	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
209	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
210	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
211	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
212	C₂×D₄×C₁₃	#41	1	4	yes	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	4	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	8	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	8	no	—
222	C₂²×C₄×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	4	no	—
226	C₂²×C₄×C₁₃	—	4	4	no	—
227	C₂²×C₄×C₁₃	—	4	4	no	—
228	C₂²×C₄×C₁₃	—	4	4	no	—
229	C₂²×C₄×C₁₃	—	4	4	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
232	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	4	4	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
258	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
260	C₁₃×C₂²⋊C₄	—	2	8	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	8	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	8	no	—
266	C₁₃×C₂²⋊C₄	—	2	8	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	8	no	—
269	C₁₃×C₂²⋊C₄	—	4	4	no	—
270	C₁₃×C₂²⋊C₄	—	4	4	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	4	no	—
273	C₁₃×C₂²⋊C₄	—	4	4	no	—
274	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
275	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
276	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
278	C₄²×C₁₃	—	2	8	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	2	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	4	2	no	—
286	C₄²×C₁₃	—	4	2	no	—
287	C₄²×C₁₃	—	4	1	no	—
288	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
289	C₄²×C₁₃	C₂×D₄	1	4	yes	complemented
290	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
291	C₂×#518	C₂×C₁₃	1	2	yes	complemented
292	#2366	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2363	C₂×C₁₃	1	2	yes	complemented
294	#2361	C₂×C₁₃	1	2	yes	complemented
295	#2358	C₂×C₁₃	1	4	yes	complemented
296	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
297	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
298	D₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
299	D₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
300	#2324	C₂×C₁₃	1	2	yes	complemented
301	#2321	C₂×C₁₃	1	4	yes	complemented
302	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₄×#121	C₂×C₁₃	1	2	yes	complemented
304	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#390	C₂×C₁₃	1	2	yes	complemented
306	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
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	4	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	4	no	—
317	C₂³×C₁₃	—	2	4	no	—
318	C₂³×C₁₃	—	2	4	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	4	no	—
323	C₂³×C₁₃	—	2	32	no	—
324	C₂³×C₁₃	—	4	16	no	—
325	C₂³×C₁₃	—	4	16	no	—
326	C₂³×C₁₃	—	8	8	no	—
327	C₂³×C₁₃	—	8	8	no	—
328	C₂³×C₁₃	—	8	8	no	—
329	C₂³×C₁₃	—	8	8	no	—
330	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
331	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
332	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
333	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
334	C₂³×C₁₃	C₂×#41	1	4	yes	—
335	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
336	D₄×C₁₃	—	2	32	no	—
337	D₄×C₁₃	—	2	16	no	—
338	D₄×C₁₃	—	2	8	no	—
339	D₄×C₁₃	—	2	16	no	—
340	D₄×C₁₃	—	4	16	no	—
341	D₄×C₁₃	—	4	8	no	—
342	D₄×C₁₃	C₄×D₄	1	16	yes	complemented
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	16	no	—
358	C₂×C₄×C₁₃	—	2	16	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	4	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	2	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	4	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	4	8	no	—
375	C₂×C₄×C₁₃	—	4	8	no	—
376	C₂×C₄×C₁₃	—	8	8	no	—
377	C₂×C₄×C₁₃	—	8	8	no	—
378	C₂×C₄×C₁₃	—	8	8	no	—
379	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
382	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
389	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
392	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
393	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
394	D₄²	C₄×C₁₃	1	16	yes	complemented
395	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#121	C₂²×C₁₃	1	2	yes	—
397	C₂×#121	C₂²×C₁₃	1	2	yes	—
398	C₂×#120	C₂²×C₁₃	1	4	yes	—
399	#518	—	2	16	no	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
406	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
407	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
408	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
409	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
410	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
411	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
412	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
413	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
414	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
416	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
417	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
418	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
419	#390	C₂²×C₁₃	1	1	yes	characteristic
420	#390	C₂²×C₁₃	1	2	yes	—
421	#390	C₂²×C₁₃	1	1	yes	characteristic
422	#390	C₂²×C₁₃	1	2	yes	complemented
423	#390	C₂²×C₁₃	1	2	yes	complemented
424	#390	C₂²×C₁₃	1	2	yes	complemented
425	#390	C₂²×C₁₃	1	4	yes	complemented
426	#390	C₂²×C₁₃	1	2	yes	complemented
427	#390	C₂²×C₁₃	1	4	yes	complemented
428	#390	C₂²×C₁₃	1	2	yes	complemented
429	#389	C₂²×C₁₃	1	2	yes	complemented
430	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#388	C₂²×C₁₃	1	2	yes	complemented
433	#388	C₂²×C₁₃	1	4	yes	complemented
434	#388	C₂²×C₁₃	1	4	yes	complemented
435	#388	C₂²×C₁₃	1	4	yes	complemented
436	#388	C₂²×C₁₃	1	2	yes	complemented
437	#386	C₂²×C₁₃	1	4	yes	complemented
438	#386	C₂²×C₁₃	1	4	yes	complemented
439	#386	C₂²×C₁₃	1	4	yes	complemented
440	#386	C₂²×C₁₃	1	4	yes	complemented
441	#386	C₂²×C₁₃	1	4	yes	complemented
442	#385	C₂²×C₁₃	1	4	yes	complemented
443	#385	C₂²×C₁₃	1	4	yes	complemented
444	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#380	C₂²×C₁₃	1	2	yes	complemented
446	#380	C₂²×C₁₃	1	2	yes	complemented
447	#379	C₂²×C₁₃	1	4	yes	complemented
448	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
451	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
454	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
455	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
456	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
457	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
458	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	4	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	4	no	—
464	C₂²×C₁₃	—	2	4	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	2	8	no	—
467	C₂²×C₁₃	—	2	4	no	—
468	C₂²×C₁₃	—	2	8	no	—
469	C₂²×C₁₃	—	2	8	no	—
470	C₂²×C₁₃	—	2	4	no	—
471	C₂²×C₁₃	—	4	4	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	4	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	4	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	4	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	8	32	no	—
480	C₂²×C₁₃	C₂×C₄×D₄	1	8	yes	—
481	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
482	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
483	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²×C₁₃	#585	1	1	yes	characteristic
488	C₄×C₁₃	—	2	4	no	—
489	C₄×C₁₃	—	2	4	no	—
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	2	4	no	—
493	C₄×C₁₃	—	2	2	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	4	no	—
498	C₄×C₁₃	—	4	1	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
501	C₄×C₁₃	#518	1	4	yes	complemented
502	C₂⁵	C₂³×C₁₃	1	4	yes	—
503	C₂²×D₄	—	2	8	no	—
504	C₂²×D₄	—	2	8	no	—
505	C₂²×D₄	—	4	4	no	—
506	C₂²×D₄	—	4	4	no	—
507	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
508	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
509	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
511	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
512	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
513	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
514	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
515	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
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	4	yes	—
521	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
522	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
523	#127	C₂×C₄×C₁₃	1	8	yes	complemented
524	#121	C₂×C₄×C₁₃	1	16	yes	complemented
525	#121	C₂×C₄×C₁₃	1	16	yes	complemented
526	#120	C₂×C₄×C₁₃	1	32	yes	complemented
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	16	no	—
530	C₄×D₄	—	2	8	no	—
531	C₄×D₄	—	2	16	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	4	4	no	—
534	C₄×D₄	—	4	4	no	—
535	C₄×D₄	—	4	4	no	—
536	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
537	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
538	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
539	#117	—	2	8	no	—
540	#117	—	2	8	no	—
541	C₂×C₄⋊C₄	—	4	4	no	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	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	1	yes	characteristic
554	C₂×C₂²⋊C₄	—	2	16	no	—
555	C₂×C₂²⋊C₄	—	2	16	no	—
556	C₂×C₂²⋊C₄	—	4	8	no	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	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	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	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	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄²	—	4	4	no	—
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	4	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	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	4	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	4	yes	—
595	#95	C₂³×C₁₃	1	2	yes	—
596	C₂×C₁₃	—	2	8	no	—
597	C₂×C₁₃	—	4	8	no	—
598	C₂×C₁₃	—	4	4	no	—
599	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
600	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
601	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂×C₁₃	#3496	1	1	yes	characteristic
603	C₂×C₁₃	#3498	1	1	yes	characteristic
604	C₂×C₁₃	#3514	1	1	yes	characteristic
605	C₂×C₁₃	#3519	1	1	yes	characteristic
606	C₂⁴	—	2	8	no	—
607	C₂⁴	—	2	8	no	—
608	C₂⁴	—	4	4	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	4	4	no	—
612	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	—
613	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
614	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
615	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	64	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	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	4	32	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
631	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
632	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
633	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
634	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
635	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
636	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
637	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
638	C₂×D₄	C₁₃×#41	1	4	yes	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	8	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	8	no	—
647	C₂²×C₄	—	2	8	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	4	no	—
654	C₂²×C₄	—	4	4	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
658	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	complemented
660	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	4	4	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
684	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	complemented
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	8	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
701	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
702	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
703	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	complemented
704	C₄²	—	2	8	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	1	no	—
714	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
715	C₄²	C₂×D₄×C₁₃	1	4	yes	complemented
716	C₁₃	#34310	1	1	yes	characteristic, direct product factor, Sylow
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	32	no	—
734	C₂³	—	4	16	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	8	8	no	—
737	C₂³	—	8	8	no	—
738	C₂³	—	8	8	no	—
739	C₂³	—	8	8	no	—
740	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
741	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
742	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
743	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
744	C₂³	C₂×C₁₃×#41	1	4	yes	—
745	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
746	D₄	—	2	32	no	—
747	D₄	—	2	16	no	—
748	D₄	—	2	8	no	—
749	D₄	—	2	16	no	—
750	D₄	—	4	16	no	—
751	D₄	—	4	8	no	—
752	D₄	C₄×D₄×C₁₃	1	16	yes	complemented
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	8	8	no	—
787	C₂×C₄	—	8	8	no	—
788	C₂×C₄	—	8	8	no	—
789	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
790	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
791	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
792	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
793	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
798	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
799	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
800	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
801	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
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	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	8	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	2	8	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	32	no	—
823	C₂²	C₂×C₄×D₄×C₁₃	1	8	yes	—
824	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
825	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
826	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
827	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
828	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
829	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂²	C₁₃×#585	1	1	yes	characteristic
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	4	no	—
842	C₄	—	4	1	no	—
843	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
844	C₄	C₁₃×#518	1	4	yes	complemented
845	C₂	—	2	8	no	—
846	C₂	—	4	4	no	—
847	C₂	—	4	8	no	—
848	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
849	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
850	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
851	C₂	C₁₃×#3496	1	1	yes	characteristic
852	C₂	C₁₃×#3498	1	1	yes	characteristic
853	C₂	C₁₃×#3514	1	1	yes	characteristic
854	C₂	C₁₃×#3519	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×D₄²×C₁₃	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×#518	C₂	semidirect
3. C₁₃×#2366	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2361	C₂	semidirect
6. C₁₃×#2358	C₂	semidirect
7. C₁₃×#2354	C₂	semidirect
8. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
9. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
10. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
11. C₁₃×#2324	C₂	semidirect
12. C₁₃×#2321	C₂	semidirect
13. C₄×C₁₃×#127	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₁₃×#2293	C₂	semidirect
16. C₂×C₁₃×#390	C₂	semidirect
17. C₄²×D₄×C₁₃	C₂	semidirect
20. D₄²×C₁₃	C₄	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₁₃×#117	C₂²	semidirect
39. C₂×C₁₃×#117	C₂²	semidirect
40. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
41. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
43. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂²×C₄²×C₁₃	C₂²	semidirect
48. C₁₃×#390	C₂²	semidirect
49. C₁₃×#390	C₂²	semidirect
50. C₁₃×#390	C₂²	semidirect
51. C₁₃×#390	C₂²	semidirect
52. C₁₃×#390	C₂²	semidirect
53. C₁₃×#390	C₂²	semidirect
54. C₁₃×#390	C₂²	semidirect
55. C₁₃×#389	C₂²	semidirect
56. C₁₃×#389	C₂²	semidirect
57. C₁₃×#389	C₂²	semidirect
58. C₁₃×#388	C₂²	semidirect
59. C₁₃×#388	C₂²	semidirect
60. C₁₃×#388	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#386	C₂²	semidirect
64. C₁₃×#386	C₂²	semidirect
65. C₁₃×#386	C₂²	semidirect
66. C₁₃×#386	C₂²	semidirect
67. C₁₃×#386	C₂²	semidirect
68. C₁₃×#385	C₂²	semidirect
69. C₁₃×#385	C₂²	semidirect
70. C₁₃×#384	C₂²	semidirect
71. C₁₃×#380	C₂²	semidirect
72. C₁₃×#380	C₂²	semidirect
73. C₁₃×#379	C₂²	semidirect
74. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
75. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
76. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
77. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
78. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
79. C₄×C₁₃×C₂²⋊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. C₄³×C₁₃	C₂²	semidirect
90. C₂²×D₄×C₁₃	C₂×C₄	semidirect
91. C₂²×D₄×C₁₃	C₂×C₄	semidirect
106. C₁₃×#127	C₂×C₄	semidirect
107. C₁₃×#121	C₂×C₄	semidirect
108. C₁₃×#121	C₂×C₄	semidirect
109. C₁₃×#120	C₂×C₄	semidirect
119. C₄×D₄×C₁₃	C₂×C₄	semidirect
120. C₄×D₄×C₁₃	C₂×C₄	semidirect
121. C₄×D₄×C₁₃	D₄	semidirect
179. #34310	C₁₃	direct (N × H)
233. C₂²×C₄×C₁₃	C₂×D₄	semidirect
259. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
277. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
289. C₄²×C₁₃	C₂×D₄	semidirect
291. C₂×#518	C₂×C₁₃	semidirect
292. #2366	C₂×C₁₃	semidirect
293. #2363	C₂×C₁₃	semidirect
294. #2361	C₂×C₁₃	semidirect
295. #2358	C₂×C₁₃	semidirect
296. #2354	C₂×C₁₃	semidirect
297. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
298. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
299. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
300. #2324	C₂×C₁₃	semidirect
301. #2321	C₂×C₁₃	semidirect
302. C₄×#127	C₂×C₁₃	semidirect
303. C₄×#121	C₂×C₁₃	semidirect
304. #2293	C₂×C₁₃	semidirect
305. C₂×#390	C₂×C₁₃	semidirect
306. C₄²×D₄	C₂×C₁₃	semidirect
342. D₄×C₁₃	C₄×D₄	semidirect
394. D₄²	C₄×C₁₃	semidirect
405. C₂×C₄×D₄	C₂²×C₁₃	semidirect
406. C₂×C₄×D₄	C₂²×C₁₃	semidirect
407. C₂×C₄×D₄	C₂²×C₁₃	semidirect
408. C₂×C₄×D₄	C₂²×C₁₃	semidirect
409. C₂×C₄×D₄	C₂²×C₁₃	semidirect
410. C₂×C₄×D₄	C₂²×C₁₃	semidirect
411. C₂×C₄×D₄	C₂²×C₁₃	semidirect
412. C₂×#117	C₂²×C₁₃	semidirect
413. C₂×#117	C₂²×C₁₃	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
415. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
416. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
417. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
418. C₂²×C₄²	C₂²×C₁₃	semidirect
422. #390	C₂²×C₁₃	semidirect
423. #390	C₂²×C₁₃	semidirect
424. #390	C₂²×C₁₃	semidirect
425. #390	C₂²×C₁₃	semidirect
426. #390	C₂²×C₁₃	semidirect
427. #390	C₂²×C₁₃	semidirect
428. #390	C₂²×C₁₃	semidirect
429. #389	C₂²×C₁₃	semidirect
430. #389	C₂²×C₁₃	semidirect
431. #389	C₂²×C₁₃	semidirect
432. #388	C₂²×C₁₃	semidirect
433. #388	C₂²×C₁₃	semidirect
434. #388	C₂²×C₁₃	semidirect
435. #388	C₂²×C₁₃	semidirect
436. #388	C₂²×C₁₃	semidirect
437. #386	C₂²×C₁₃	semidirect
438. #386	C₂²×C₁₃	semidirect
439. #386	C₂²×C₁₃	semidirect
440. #386	C₂²×C₁₃	semidirect
441. #386	C₂²×C₁₃	semidirect
442. #385	C₂²×C₁₃	semidirect
443. #385	C₂²×C₁₃	semidirect
444. #384	C₂²×C₁₃	semidirect
445. #380	C₂²×C₁₃	semidirect
446. #380	C₂²×C₁₃	semidirect
447. #379	C₂²×C₁₃	semidirect
448. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
449. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
450. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
451. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
452. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
453. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
454. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
456. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
457. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
458. C₄³	C₂²×C₁₃	semidirect
501. C₄×C₁₃	#518	semidirect
507. C₂²×D₄	C₂×C₄×C₁₃	semidirect
508. C₂²×D₄	C₂×C₄×C₁₃	semidirect
523. #127	C₂×C₄×C₁₃	semidirect
524. #121	C₂×C₄×C₁₃	semidirect
525. #121	C₂×C₄×C₁₃	semidirect
526. #120	C₂×C₄×C₁₃	semidirect
536. C₄×D₄	C₂×C₄×C₁₃	semidirect
537. C₄×D₄	C₂×C₄×C₁₃	semidirect
538. C₄×D₄	D₄×C₁₃	semidirect
659. C₂²×C₄	C₂×D₄×C₁₃	semidirect
685. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
703. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
715. C₄²	C₂×D₄×C₁₃	semidirect
716. C₁₃	#34310	direct (N × H)
752. D₄	C₄×D₄×C₁₃	semidirect
844. C₄	C₁₃×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₃	2
C₂×C₁₃×#518	2
C₁₃×#2366	2
C₁₃×#2363	2
C₁₃×#2361	2
C₁₃×#2358	2
C₁₃×#2354	2
D₄×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2324	2
C₁₃×#2321	2
C₄×C₁₃×#127	2
C₄×C₁₃×#121	2
C₁₃×#2293	2
C₂×C₁₃×#390	2
C₄²×D₄×C₁₃	2
#34310	13

Subgroups — C13×#34310 #15720649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34310 #15720649