Subgroups — C₂×C₁₃×#2449 #15720990

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 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, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2449	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×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	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
27	C₂×C₄×D₄×C₁₃	—	2	8	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
29	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#399	C₂²	1	8	yes	complemented
53	C₁₃×#398	C₂²	1	8	yes	complemented
54	C₁₃×#396	C₂²	1	8	yes	complemented
55	C₁₃×#395	C₂²	1	8	yes	complemented
56	C₁₃×#389	C₂²	1	8	yes	complemented
57	C₁₃×#387	C₂²	1	8	yes	complemented
58	C₁₃×#386	C₂²	1	8	yes	—
59	C₁₃×#386	C₂²	1	8	yes	—
60	C₁₃×#385	C₂²	1	8	yes	complemented
61	C₁₃×#385	C₂²	1	8	yes	complemented
62	C₁₃×#385	C₂²	1	8	yes	complemented
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	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
71	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
72	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃	—	2	4	no	—
74	C₂²×Q₈×C₁₃	—	2	4	no	—
75	C₂²×Q₈×C₁₃	—	4	2	no	—
76	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	—	2	4	no	—
79	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
80	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	—	2	4	no	—
82	C₂³×C₄×C₁₃	—	2	4	no	—
83	C₂³×C₄×C₁₃	—	2	4	no	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	—	2	4	no	—
89	C₂³×C₄×C₁₃	—	2	4	no	—
90	C₂³×C₄×C₁₃	—	4	2	no	—
91	C₂³×C₄×C₁₃	—	4	2	no	—
92	C₂³×C₄×C₁₃	—	4	2	no	—
93	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
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	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×C₂²⋊Q₈	—	2	32	no	—
111	C₁₃×C₂²⋊Q₈	—	2	32	no	—
112	C₄×D₄×C₁₃	—	2	32	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
122	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
124	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃	—	2	4	no	—
155	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₂×#2449	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	—	2	2	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
171	C₂⁴×C₁₃	—	2	2	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	2	2	no	—
175	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
176	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
177	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
178	C₂⁴×C₁₃	#41	1	4	yes	—
179	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×Q₈×C₁₃	—	2	8	no	—
183	C₂×Q₈×C₁₃	—	2	8	no	—
184	C₂×Q₈×C₁₃	—	4	4	no	—
185	C₂×Q₈×C₁₃	—	4	16	no	—
186	C₂×D₄×C₁₃	—	2	32	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	complemented
190	C₂²×C₄×C₁₃	—	2	32	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	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	8	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	2	no	—
206	C₂²×C₄×C₁₃	—	2	8	no	—
207	C₂²×C₄×C₁₃	—	2	8	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	8	no	—
217	C₂²×C₄×C₁₃	—	2	8	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	8	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	4	no	—
233	C₂²×C₄×C₁₃	—	4	4	no	—
234	C₂²×C₄×C₁₃	—	4	4	no	—
235	C₂²×C₄×C₁₃	—	4	16	no	—
236	C₂²×C₄×C₁₃	—	4	16	no	—
237	C₂²×C₄×C₁₃	—	4	16	no	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
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×Q₈	1	4	yes	—
244	C₂²×C₄×C₁₃	#41	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	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₁₃×C₄⋊C₄	—	2	8	no	—
259	C₁₃×C₄⋊C₄	—	2	8	no	—
260	C₁₃×C₄⋊C₄	—	2	8	no	—
261	C₁₃×C₄⋊C₄	—	2	8	no	—
262	C₁₃×C₄⋊C₄	—	2	8	no	—
263	C₁₃×C₄⋊C₄	—	2	8	no	—
264	C₁₃×C₄⋊C₄	—	2	8	no	—
265	C₁₃×C₄⋊C₄	—	2	8	no	—
266	C₁₃×C₄⋊C₄	—	2	8	no	—
267	C₁₃×C₄⋊C₄	—	2	8	no	—
268	C₁₃×C₄⋊C₄	—	4	4	no	—
269	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
270	C₁₃×C₂²⋊C₄	—	2	8	no	—
271	C₁₃×C₂²⋊C₄	—	2	8	no	—
272	C₁₃×C₂²⋊C₄	—	2	8	no	—
273	C₁₃×C₂²⋊C₄	—	2	8	no	—
274	C₁₃×C₂²⋊C₄	—	2	8	no	—
275	C₁₃×C₂²⋊C₄	—	2	8	no	—
276	C₁₃×C₂²⋊C₄	—	4	4	no	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
278	C₄²×C₁₃	—	2	8	no	—
279	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
282	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2449	C₂×C₁₃	1	16	yes	direct product factor
284	C₂×#399	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#396	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#395	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
291	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
292	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂³×C₁₃	—	2	8	no	—
296	C₂³×C₁₃	—	2	8	no	—
297	C₂³×C₁₃	—	2	8	no	—
298	C₂³×C₁₃	—	2	8	no	—
299	C₂³×C₁₃	—	2	8	no	—
300	C₂³×C₁₃	—	2	8	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	8	no	—
306	C₂³×C₁₃	—	2	8	no	—
307	C₂³×C₁₃	—	2	8	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	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	—	4	4	no	—
316	C₂³×C₁₃	—	4	4	no	—
317	C₂³×C₁₃	—	4	4	no	—
318	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
319	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
320	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
321	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
322	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
323	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
324	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
325	C₂³×C₁₃	C₂×#41	1	4	yes	—
326	C₂³×C₁₃	C₂×#41	1	2	yes	—
327	C₂³×C₁₃	C₂×#41	1	2	yes	—
328	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
329	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
330	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
331	Q₈×C₁₃	—	4	16	no	—
332	D₄×C₁₃	—	2	32	no	—
333	C₂×C₄×C₁₃	—	2	32	no	—
334	C₂×C₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	8	no	—
336	C₂×C₄×C₁₃	—	2	8	no	—
337	C₂×C₄×C₁₃	—	2	8	no	—
338	C₂×C₄×C₁₃	—	2	8	no	—
339	C₂×C₄×C₁₃	—	2	8	no	—
340	C₂×C₄×C₁₃	—	2	8	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	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	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	2	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	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	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	4	16	no	—
374	C₂×C₄×C₁₃	—	4	16	no	—
375	C₂×C₄×C₁₃	—	4	16	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	4	4	no	—
378	C₂×C₄×C₁₃	—	4	4	no	—
379	C₂×C₄×C₁₃	—	4	4	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
387	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
388	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
389	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
394	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	—	2	8	no	—
396	C₂×C₂²⋊Q₈	—	2	8	no	—
397	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
398	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
399	C₂×C₄×D₄	—	2	8	no	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
401	C₂²×C₄⋊C₄	—	2	8	no	—
402	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
424	#399	C₂²×C₁₃	1	8	yes	complemented
425	#398	C₂²×C₁₃	1	8	yes	complemented
426	#396	C₂²×C₁₃	1	8	yes	complemented
427	#395	C₂²×C₁₃	1	8	yes	complemented
428	#389	C₂²×C₁₃	1	8	yes	complemented
429	#387	C₂²×C₁₃	1	8	yes	complemented
430	#386	C₂²×C₁₃	1	8	yes	—
431	#386	C₂²×C₁₃	1	8	yes	—
432	#385	C₂²×C₁₃	1	8	yes	complemented
433	#385	C₂²×C₁₃	1	8	yes	complemented
434	#385	C₂²×C₁₃	1	8	yes	complemented
435	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	2	4	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	2	4	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	32	no	—
450	C₂²×C₁₃	—	2	4	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	16	no	—
458	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
459	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	complemented
460	C₂²×C₁₃	#525	1	4	yes	—
461	C₂²×C₁₃	#539	1	4	yes	—
462	C₂²×C₁₃	D₄²	1	4	yes	—
463	C₂²×C₁₃	#547	1	4	yes	—
464	C₂²×C₁₃	D₄×Q₈	1	4	yes	—
465	C₂²×C₁₃	#554	1	4	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
468	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
469	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
470	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
473	C₄×C₁₃	—	2	4	no	—
474	C₄×C₁₃	—	2	4	no	—
475	C₄×C₁₃	—	2	4	no	—
476	C₄×C₁₃	—	2	4	no	—
477	C₄×C₁₃	—	2	4	no	—
478	C₄×C₁₃	—	2	4	no	—
479	C₄×C₁₃	—	2	4	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	2	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
487	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×Q₈	—	2	4	no	—
489	C₂²×Q₈	—	2	4	no	—
490	C₂²×Q₈	—	4	2	no	—
491	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
492	C₂²×D₄	—	2	4	no	—
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
495	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	—	2	4	no	—
500	C₂³×C₄	—	2	4	no	—
501	C₂³×C₄	—	2	4	no	—
502	C₂³×C₄	—	2	4	no	—
503	C₂³×C₄	—	2	4	no	—
504	C₂³×C₄	—	2	4	no	—
505	C₂³×C₄	—	4	2	no	—
506	C₂³×C₄	—	4	2	no	—
507	C₂³×C₄	—	4	2	no	—
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
516	C₂³×C₄	C₂³×C₁₃	1	4	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	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²⋊Q₈	—	2	32	no	—
526	C₂²⋊Q₈	—	2	32	no	—
527	C₄×D₄	—	2	32	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	—	2	4	no	—
530	C₂×C₄⋊C₄	—	2	4	no	—
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	—	2	4	no	—
533	C₂×C₄⋊C₄	—	2	4	no	—
534	C₂×C₄⋊C₄	—	2	4	no	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	—	2	4	no	—
538	C₂×C₄⋊C₄	—	2	32	no	—
539	C₂×C₄⋊C₄	—	4	2	no	—
540	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	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	4	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	4	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	4	2	no	—
560	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	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	4	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×C₄²	—	2	4	no	—
570	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
571	#95	C₂³×C₁₃	1	4	yes	—
572	#95	C₂³×C₁₃	1	4	yes	—
573	#95	C₂³×C₁₃	1	4	yes	—
574	#95	C₂³×C₁₃	1	4	yes	—
575	#95	C₂³×C₁₃	1	4	yes	—
576	#95	C₂³×C₁₃	1	4	yes	—
577	#95	C₂³×C₁₃	1	4	yes	—
578	#95	C₂³×C₁₃	1	4	yes	—
579	C₂×C₁₃	—	2	8	no	—
580	C₂×C₁₃	—	4	4	no	—
581	C₂×C₁₃	#2449	1	8	yes	direct product factor
582	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
583	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
584	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
585	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
586	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
587	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
588	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	2	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
600	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
601	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
602	C₂⁴	C₁₃×#41	1	4	yes	—
603	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
604	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
605	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂×Q₈	—	2	8	no	—
607	C₂×Q₈	—	2	8	no	—
608	C₂×Q₈	—	4	4	no	—
609	C₂×Q₈	—	4	16	no	—
610	C₂×D₄	—	2	32	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	complemented
614	C₂²×C₄	—	2	32	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	8	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	8	no	—
631	C₂²×C₄	—	2	8	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	8	no	—
653	C₂²×C₄	—	2	8	no	—
654	C₂²×C₄	—	2	8	no	—
655	C₂²×C₄	—	2	8	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	4	no	—
659	C₂²×C₄	—	4	16	no	—
660	C₂²×C₄	—	4	16	no	—
661	C₂²×C₄	—	4	16	no	—
662	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
663	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
665	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
666	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
667	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
668	C₂²×C₄	C₁₃×#41	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	2	8	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	2	8	no	—
688	C₄⋊C₄	—	2	8	no	—
689	C₄⋊C₄	—	2	8	no	—
690	C₄⋊C₄	—	2	8	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
694	C₂²⋊C₄	—	2	8	no	—
695	C₂²⋊C₄	—	2	8	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	C₂×D₄×C₁₃	1	16	yes	—
702	C₄²	—	2	8	no	—
703	C₁₃	C₂×#2449	1	1	yes	characteristic, direct product factor, Sylow
704	C₂³	—	2	8	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	8	no	—
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	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	4	no	—
727	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
728	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
729	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
731	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
732	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
733	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
734	C₂³	C₂×C₁₃×#41	1	4	yes	—
735	C₂³	C₂×C₁₃×#41	1	2	yes	—
736	C₂³	C₂×C₁₃×#41	1	2	yes	—
737	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
738	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
739	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
740	Q₈	—	4	16	no	—
741	D₄	—	2	32	no	—
742	C₂×C₄	—	2	32	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	8	no	—
746	C₂×C₄	—	2	8	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	8	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	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	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	16	no	—
783	C₂×C₄	—	4	16	no	—
784	C₂×C₄	—	4	16	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
792	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
796	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
797	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	32	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	16	no	—
813	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
814	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	complemented
815	C₂²	C₁₃×#525	1	4	yes	—
816	C₂²	C₁₃×#539	1	4	yes	—
817	C₂²	D₄²×C₁₃	1	4	yes	—
818	C₂²	C₁₃×#547	1	4	yes	—
819	C₂²	D₄×Q₈×C₁₃	1	4	yes	—
820	C₂²	C₁₃×#554	1	4	yes	—
821	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
822	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
823	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
824	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
825	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
826	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
827	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₂	—	2	8	no	—
842	C₂	—	4	4	no	—
843	C₂	C₁₃×#2449	1	8	yes	direct product factor
844	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
845	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
846	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
847	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
848	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
849	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2449	C₂	direct (N × H)
6. C₂×C₁₃×#399	C₂	semidirect
7. C₂×C₁₃×#398	C₂	semidirect
8. C₂×C₁₃×#396	C₂	semidirect
9. C₂×C₁₃×#395	C₂	semidirect
10. C₂×C₁₃×#389	C₂	semidirect
11. C₂×C₁₃×#387	C₂	semidirect
14. C₂×C₁₃×#385	C₂	semidirect
15. C₂×C₁₃×#385	C₂	semidirect
16. C₂×C₁₃×#385	C₂	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
52. C₁₃×#399	C₂²	semidirect
53. C₁₃×#398	C₂²	semidirect
54. C₁₃×#396	C₂²	semidirect
55. C₁₃×#395	C₂²	semidirect
56. C₁₃×#389	C₂²	semidirect
57. C₁₃×#387	C₂²	semidirect
60. C₁₃×#385	C₂²	semidirect
61. C₁₃×#385	C₂²	semidirect
62. C₁₃×#385	C₂²	semidirect
79. C₂²×D₄×C₁₃	Q₈	semidirect
125. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
164. C₂×#2449	C₁₃	direct (N × H)
189. C₂×D₄×C₁₃	C₂×Q₈	semidirect
269. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
279. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
280. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
282. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
283. #2449	C₂×C₁₃	direct (N × H)
284. C₂×#399	C₂×C₁₃	semidirect
285. C₂×#398	C₂×C₁₃	semidirect
286. C₂×#396	C₂×C₁₃	semidirect
287. C₂×#395	C₂×C₁₃	semidirect
288. C₂×#389	C₂×C₁₃	semidirect
289. C₂×#387	C₂×C₁₃	semidirect
292. C₂×#385	C₂×C₁₃	semidirect
293. C₂×#385	C₂×C₁₃	semidirect
294. C₂×#385	C₂×C₁₃	semidirect
318. C₂³×C₁₃	C₂²⋊Q₈	semidirect
397. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
398. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
414. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
424. #399	C₂²×C₁₃	semidirect
425. #398	C₂²×C₁₃	semidirect
426. #396	C₂²×C₁₃	semidirect
427. #395	C₂²×C₁₃	semidirect
428. #389	C₂²×C₁₃	semidirect
429. #387	C₂²×C₁₃	semidirect
432. #385	C₂²×C₁₃	semidirect
433. #385	C₂²×C₁₃	semidirect
434. #385	C₂²×C₁₃	semidirect
459. C₂²×C₁₃	C₂×C₂²⋊Q₈	semidirect
494. C₂²×D₄	Q₈×C₁₃	semidirect
540. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
581. C₂×C₁₃	#2449	direct (N × H)
613. C₂×D₄	C₂×Q₈×C₁₃	semidirect
693. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
703. C₁₃	C₂×#2449	direct (N × H)
727. C₂³	C₁₃×C₂²⋊Q₈	semidirect
814. C₂²	C₂×C₁₃×C₂²⋊Q₈	semidirect
843. C₂	C₁₃×#2449	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×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2449	2
C₂×C₁₃×#399	2
C₂×C₁₃×#398	2
C₂×C₁₃×#396	2
C₂×C₁₃×#395	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×#2449	13

Subgroups — C2×C13×#2449 #15720990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2449 #15720990