Subgroups — C₂×C₁₃×#2438 #15721070

Order 3328.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2438	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
23	C₂×C₁₃×#117	—	2	8	no	—
24	C₂×C₁₃×#117	C₂²	1	8	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#400	C₂²	1	8	yes	complemented
43	C₁₃×#398	C₂²	1	8	yes	complemented
44	C₁₃×#398	C₂²	1	8	yes	complemented
45	C₁₃×#395	C₂²	1	8	yes	complemented
46	C₁₃×#391	C₂²	1	8	yes	complemented
47	C₁₃×#389	C₂²	1	8	yes	complemented
48	C₁₃×#387	C₂²	1	8	yes	complemented
49	C₁₃×#387	C₂²	1	8	yes	complemented
50	C₁₃×#385	C₂²	1	8	yes	—
51	C₁₃×#385	C₂²	1	8	yes	—
52	C₁₃×#381	C₂²	1	8	yes	—
53	C₁₃×#380	C₂²	1	8	yes	—
54	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#95	C₂²	1	8	yes	—
59	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	—	2	4	no	—
71	C₂²×Q₈×C₁₃	—	2	4	no	—
72	C₂²×Q₈×C₁₃	—	4	2	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	—	2	4	no	—
75	C₂³×C₄×C₁₃	—	2	4	no	—
76	C₂³×C₄×C₁₃	—	2	4	no	—
77	C₂³×C₄×C₁₃	—	2	4	no	—
78	C₂³×C₄×C₁₃	—	2	4	no	—
79	C₂³×C₄×C₁₃	—	2	4	no	—
80	C₂³×C₄×C₁₃	—	4	2	no	—
81	C₂³×C₄×C₁₃	—	4	2	no	—
82	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₂²⋊Q₈	—	2	32	no	—
101	C₁₃×#117	—	2	32	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	—	2	4	no	—
133	C₂×C₄²×C₁₃	—	2	4	no	—
134	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₂×#2438	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	2	no	—
152	C₂⁴×C₁₃	—	2	2	no	—
153	C₂⁴×C₁₃	—	2	2	no	—
154	C₂⁴×C₁₃	—	2	2	no	—
155	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
156	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
157	C₂⁴×C₁₃	#41	1	4	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
159	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×Q₈×C₁₃	—	2	8	no	—
161	C₂×Q₈×C₁₃	—	2	8	no	—
162	C₂×Q₈×C₁₃	—	4	4	no	—
163	C₂×Q₈×C₁₃	—	4	16	no	—
164	C₂²×C₄×C₁₃	—	2	32	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	8	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	8	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	8	no	—
206	C₂²×C₄×C₁₃	—	2	8	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	16	no	—
210	C₂²×C₄×C₁₃	—	4	16	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	complemented
216	C₂²×C₄×C₁₃	#41	1	4	yes	—
217	C₂²×C₄×C₁₃	#41	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	—	2	8	no	—
233	C₁₃×C₄⋊C₄	—	2	8	no	—
234	C₁₃×C₄⋊C₄	—	2	8	no	—
235	C₁₃×C₄⋊C₄	—	2	8	no	—
236	C₁₃×C₄⋊C₄	—	2	8	no	—
237	C₁₃×C₄⋊C₄	—	2	8	no	—
238	C₁₃×C₄⋊C₄	—	2	8	no	—
239	C₁₃×C₄⋊C₄	—	2	8	no	—
240	C₁₃×C₄⋊C₄	—	4	4	no	—
241	C₁₃×C₄⋊C₄	—	4	4	no	—
242	C₁₃×C₄⋊C₄	—	4	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	8	no	—
244	C₁₃×C₂²⋊C₄	—	2	8	no	—
245	C₁₃×C₂²⋊C₄	—	2	8	no	—
246	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
247	C₄²×C₁₃	—	2	8	no	—
248	C₄²×C₁₃	—	2	8	no	—
249	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
250	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
251	#2438	C₂×C₁₃	1	16	yes	direct product factor
252	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂×#395	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#385	C₂×C₁₃	1	1	yes	characteristic
261	C₂×#385	C₂×C₁₃	1	1	yes	characteristic
262	C₂×#381	C₂×C₁₃	1	1	yes	characteristic
263	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
264	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic
265	C₂³×C₁₃	—	2	8	no	—
266	C₂³×C₁₃	—	2	8	no	—
267	C₂³×C₁₃	—	2	8	no	—
268	C₂³×C₁₃	—	2	8	no	—
269	C₂³×C₁₃	—	2	8	no	—
270	C₂³×C₁₃	—	2	8	no	—
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	—
276	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
277	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
278	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
279	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
280	C₂³×C₁₃	C₂×#41	1	4	yes	—
281	C₂³×C₁₃	C₂×#41	1	2	yes	—
282	C₂³×C₁₃	C₂×#41	1	2	yes	—
283	C₂³×C₁₃	C₂×#41	1	2	yes	—
284	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
285	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
286	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
287	Q₈×C₁₃	—	4	16	no	—
288	C₂×C₄×C₁₃	—	2	8	no	—
289	C₂×C₄×C₁₃	—	2	8	no	—
290	C₂×C₄×C₁₃	—	2	32	no	—
291	C₂×C₄×C₁₃	—	2	8	no	—
292	C₂×C₄×C₁₃	—	2	8	no	—
293	C₂×C₄×C₁₃	—	2	8	no	—
294	C₂×C₄×C₁₃	—	2	8	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	4	16	no	—
332	C₂×C₄×C₁₃	—	4	16	no	—
333	C₂×C₄×C₁₃	—	4	4	no	—
334	C₂×C₄×C₁₃	—	4	4	no	—
335	C₂×C₄×C₁₃	—	4	4	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	4	4	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
344	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
345	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
346	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
347	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
350	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	—	2	8	no	—
352	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
353	C₂×#117	—	2	8	no	—
354	C₂×#117	C₂²×C₁₃	1	8	yes	—
355	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
365	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
372	#400	C₂²×C₁₃	1	8	yes	complemented
373	#398	C₂²×C₁₃	1	8	yes	complemented
374	#398	C₂²×C₁₃	1	8	yes	complemented
375	#395	C₂²×C₁₃	1	8	yes	complemented
376	#391	C₂²×C₁₃	1	8	yes	complemented
377	#389	C₂²×C₁₃	1	8	yes	complemented
378	#387	C₂²×C₁₃	1	8	yes	complemented
379	#387	C₂²×C₁₃	1	8	yes	complemented
380	#385	C₂²×C₁₃	1	8	yes	—
381	#385	C₂²×C₁₃	1	8	yes	—
382	#381	C₂²×C₁₃	1	8	yes	—
383	#380	C₂²×C₁₃	1	8	yes	—
384	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#95	C₂²×C₁₃	1	8	yes	—
395	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	32	no	—
402	C₂²×C₁₃	—	2	4	no	—
403	C₂²×C₁₃	—	2	4	no	—
404	C₂²×C₁₃	—	2	4	no	—
405	C₂²×C₁₃	—	2	4	no	—
406	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
407	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
408	C₂²×C₁₃	#533	1	4	yes	—
409	C₂²×C₁₃	#544	1	4	yes	—
410	C₂²×C₁₃	#546	1	4	yes	—
411	C₂²×C₁₃	#547	1	4	yes	—
412	C₂²×C₁₃	#551	1	4	yes	—
413	C₂²×C₁₃	#552	1	4	yes	—
414	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
415	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
416	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
418	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
419	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	2	4	no	—
423	C₄×C₁₃	—	2	4	no	—
424	C₄×C₁₃	—	2	4	no	—
425	C₄×C₁₃	—	2	4	no	—
426	C₄×C₁₃	—	2	4	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	2	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	2	no	—
431	C₄×C₁₃	—	4	2	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×Q₈	—	2	4	no	—
437	C₂²×Q₈	—	2	4	no	—
438	C₂²×Q₈	—	4	2	no	—
439	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
440	C₂³×C₄	—	2	4	no	—
441	C₂³×C₄	—	2	4	no	—
442	C₂³×C₄	—	2	4	no	—
443	C₂³×C₄	—	2	4	no	—
444	C₂³×C₄	—	2	4	no	—
445	C₂³×C₄	—	2	4	no	—
446	C₂³×C₄	—	4	2	no	—
447	C₂³×C₄	—	4	2	no	—
448	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
449	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
458	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
464	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²⋊Q₈	—	2	32	no	—
467	#117	—	2	32	no	—
468	C₂×C₄⋊C₄	—	2	4	no	—
469	C₂×C₄⋊C₄	—	2	4	no	—
470	C₂×C₄⋊C₄	—	2	4	no	—
471	C₂×C₄⋊C₄	—	2	4	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	4	2	no	—
477	C₂×C₄⋊C₄	—	4	2	no	—
478	C₂×C₄⋊C₄	—	4	2	no	—
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	4	no	—
493	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
498	C₂×C₄²	—	2	4	no	—
499	C₂×C₄²	—	2	4	no	—
500	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
501	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
502	#95	C₂³×C₁₃	1	4	yes	—
503	#95	C₂³×C₁₃	1	4	yes	—
504	#95	C₂³×C₁₃	1	4	yes	—
505	#95	C₂³×C₁₃	1	4	yes	—
506	#95	C₂³×C₁₃	1	4	yes	—
507	#95	C₂³×C₁₃	1	4	yes	—
508	#95	C₂³×C₁₃	1	4	yes	—
509	#95	C₂³×C₁₃	1	4	yes	—
510	#95	C₂³×C₁₃	1	4	yes	—
511	#95	C₂³×C₁₃	1	4	yes	—
512	#95	C₂³×C₁₃	1	4	yes	—
513	#95	C₂³×C₁₃	1	4	yes	—
514	#95	C₂³×C₁₃	1	4	yes	—
515	#95	C₂³×C₁₃	1	4	yes	—
516	C₂×C₁₃	—	2	8	no	—
517	C₂×C₁₃	#2438	1	8	yes	direct product factor
518	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
519	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
520	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
521	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
522	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
523	C₂×C₁₃	C₂×#551	1	1	yes	characteristic
524	C₂×C₁₃	C₂×#552	1	1	yes	characteristic
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
530	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
531	C₂⁴	C₁₃×#41	1	4	yes	—
532	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
533	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
534	C₂×Q₈	—	2	8	no	—
535	C₂×Q₈	—	2	8	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	—	4	16	no	—
538	C₂²×C₄	—	2	32	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	8	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	4	4	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	16	no	—
584	C₂²×C₄	—	4	16	no	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
587	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
588	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
589	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
590	C₂²×C₄	C₁₃×#41	1	4	yes	—
591	C₂²×C₄	C₁₃×#41	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	2	8	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	4	4	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	8	no	—
623	C₁₃	C₂×#2438	1	1	yes	characteristic, direct product factor, Sylow
624	C₂³	—	2	8	no	—
625	C₂³	—	2	8	no	—
626	C₂³	—	2	8	no	—
627	C₂³	—	2	8	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	8	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	—
635	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
636	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
637	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
638	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
639	C₂³	C₂×C₁₃×#41	1	4	yes	—
640	C₂³	C₂×C₁₃×#41	1	2	yes	—
641	C₂³	C₂×C₁₃×#41	1	2	yes	—
642	C₂³	C₂×C₁₃×#41	1	2	yes	—
643	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
644	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
645	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
646	Q₈	—	4	16	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	32	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	16	no	—
691	C₂×C₄	—	4	16	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
702	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
703	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
704	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
705	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	32	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
714	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
715	C₂²	C₁₃×#533	1	4	yes	—
716	C₂²	C₁₃×#544	1	4	yes	—
717	C₂²	C₁₃×#546	1	4	yes	—
718	C₂²	C₁₃×#547	1	4	yes	—
719	C₂²	C₁₃×#551	1	4	yes	—
720	C₂²	C₁₃×#552	1	4	yes	—
721	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
722	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
723	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
724	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
725	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
726	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
728	C₄	—	2	4	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₂	—	2	8	no	—
743	C₂	C₁₃×#2438	1	8	yes	direct product factor
744	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
745	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
746	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
747	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
748	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
749	C₂	C₂×C₁₃×#551	1	1	yes	characteristic
750	C₂	C₂×C₁₃×#552	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2438	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#398	C₂	semidirect
7. C₂×C₁₃×#395	C₂	semidirect
8. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#389	C₂	semidirect
10. C₂×C₁₃×#387	C₂	semidirect
11. C₂×C₁₃×#387	C₂	semidirect
42. C₁₃×#400	C₂²	semidirect
43. C₁₃×#398	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#395	C₂²	semidirect
46. C₁₃×#391	C₂²	semidirect
47. C₁₃×#389	C₂²	semidirect
48. C₁₃×#387	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
82. C₂³×C₄×C₁₃	Q₈	semidirect
150. C₂×#2438	C₁₃	direct (N × H)
215. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
251. #2438	C₂×C₁₃	direct (N × H)
252. C₂×#400	C₂×C₁₃	semidirect
253. C₂×#398	C₂×C₁₃	semidirect
254. C₂×#398	C₂×C₁₃	semidirect
255. C₂×#395	C₂×C₁₃	semidirect
256. C₂×#391	C₂×C₁₃	semidirect
257. C₂×#389	C₂×C₁₃	semidirect
258. C₂×#387	C₂×C₁₃	semidirect
259. C₂×#387	C₂×C₁₃	semidirect
372. #400	C₂²×C₁₃	semidirect
373. #398	C₂²×C₁₃	semidirect
374. #398	C₂²×C₁₃	semidirect
375. #395	C₂²×C₁₃	semidirect
376. #391	C₂²×C₁₃	semidirect
377. #389	C₂²×C₁₃	semidirect
378. #387	C₂²×C₁₃	semidirect
379. #387	C₂²×C₁₃	semidirect
448. C₂³×C₄	Q₈×C₁₃	semidirect
517. C₂×C₁₃	#2438	direct (N × H)
589. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
623. C₁₃	C₂×#2438	direct (N × H)
743. C₂	C₁₃×#2438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#117	2
C₁₃×#2438	2
C₂×C₁₃×#400	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#385	2
C₂×C₁₃×#381	2
C₂×C₁₃×#380	2
C₂²×C₁₃×#95	2
C₂×#2438	13

Subgroups — C2×C13×#2438 #15721070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2438 #15721070