Subgroups — C₂×C₁₃×#3316 #15747469

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3316	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#554	—	2	4	no	—
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#548	—	2	4	no	—
27	C₁₃×#548	C₂²	1	8	yes	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	—	2	1	no	—
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	—	2	1	no	—
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	—	2	1	no	—
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#489	C₂²	1	8	yes	complemented
48	C₁₃×#483	C₂²	1	8	yes	complemented
49	C₁₃×#481	C₂²	1	8	yes	complemented
50	C₁₃×#475	C₂²	1	8	yes	complemented
51	C₁₃×#470	C₂²	1	8	yes	complemented
52	C₁₃×#465	C₂²	1	8	yes	complemented
53	C₁₃×#464	C₂²	1	8	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#451	C₂²	1	8	yes	complemented
56	C₁₃×#441	C₂²	1	8	yes	complemented
57	C₁₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×#417	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	2	2	no	—
78	C₂×C₁₃×#41	—	2	4	no	—
79	C₂×C₁₃×#41	—	4	2	no	—
80	C₂×C₁₃×#41	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃	—	2	1	no	—
82	C₂²×Q₈×C₁₃	—	2	2	no	—
83	C₂²×Q₈×C₁₃	—	2	1	no	—
84	C₂²×Q₈×C₁₃	—	2	4	no	—
85	C₂²×Q₈×C₁₃	—	4	2	no	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	—	2	1	no	—
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×Q₁₆	—	2	4	no	—
101	C₂×C₁₃×Q₁₆	—	4	2	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	—	4	2	no	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	—	4	2	no	—
107	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
108	C₂²×C₈×C₁₃	—	4	2	no	—
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×#125	—	2	8	no	—
117	C₁₃×#124	—	2	8	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	C₂³	1	4	yes	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	8	no	—
124	C₁₃×C₂²⋊Q₈	—	2	8	no	—
125	C₁₃×C₂²⋊Q₈	—	2	8	no	—
126	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₁₃×#121	—	2	8	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	C₂³	1	4	yes	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	—	2	2	no	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₄×D₄×C₁₃	—	2	8	no	—
137	C₄×D₄×C₁₃	—	2	8	no	—
138	C₄×D₄×C₁₃	D₄	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	—	2	1	no	—
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×#106	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₁₃×#97	C₂³	1	4	yes	—
185	C₂×#3316	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂⁴×C₁₃	—	2	1	no	—
187	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₁₃×#41	—	2	8	no	—
190	C₁₃×#41	—	4	4	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	4	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	4	no	—
197	C₂×Q₈×C₁₃	—	2	2	no	—
198	C₂×Q₈×C₁₃	—	2	8	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	4	4	no	—
204	C₂×Q₈×C₁₃	—	4	4	no	—
205	C₂×Q₈×C₁₃	—	4	8	no	—
206	C₂×Q₈×C₁₃	—	8	2	no	—
207	C₂×Q₈×C₁₃	#41	1	4	yes	—
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	4	4	no	—
219	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	—	2	1	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	4	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	4	4	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	8	2	no	—
239	C₂²×C₄×C₁₃	—	8	2	no	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₁₃×Q₁₆	—	2	8	no	—
250	C₁₃×Q₁₆	—	4	4	no	—
251	C₁₃×SD₁₆	—	4	4	no	—
252	C₁₃×M₁₆	—	4	4	no	—
253	C₂×C₈×C₁₃	—	2	2	no	—
254	C₂×C₈×C₁₃	—	2	2	no	—
255	C₂×C₈×C₁₃	—	2	2	no	—
256	C₂×C₈×C₁₃	—	2	2	no	—
257	C₂×C₈×C₁₃	—	4	4	no	—
258	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
286	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	—	2	4	no	—
289	C₄²×C₁₃	C₂×D₄	1	2	yes	—
290	C₄²×C₁₃	C₂⁴	1	2	yes	—
291	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#548	C₂×C₁₃	1	1	yes	characteristic
293	#3316	C₂×C₁₃	1	16	yes	direct product factor
294	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂²×#103	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	2	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	—	4	2	no	—
315	C₂³×C₁₃	—	4	2	no	—
316	C₂³×C₁₃	#137	1	4	yes	—
317	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
318	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₁₃	—	2	4	no	—
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	2	no	—
323	Q₈×C₁₃	—	2	2	no	—
324	Q₈×C₁₃	—	2	2	no	—
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	4	8	no	—
327	Q₈×C₁₃	—	4	2	no	—
328	Q₈×C₁₃	—	4	2	no	—
329	Q₈×C₁₃	—	8	4	no	—
330	Q₈×C₁₃	C₂×#41	1	4	yes	—
331	D₄×C₁₃	—	2	8	no	—
332	D₄×C₁₃	—	2	2	no	—
333	D₄×C₁₃	—	2	2	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	4	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	4	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	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	—	4	8	no	—
356	C₂×C₄×C₁₃	—	4	8	no	—
357	C₂×C₄×C₁₃	—	4	2	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	2	no	—
361	C₂×C₄×C₁₃	—	4	2	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	8	4	no	—
364	C₂×C₄×C₁₃	—	8	4	no	—
365	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
373	C₈×C₁₃	—	2	2	no	—
374	C₈×C₁₃	—	2	2	no	—
375	C₈×C₁₃	—	2	2	no	—
376	C₈×C₁₃	—	2	2	no	—
377	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
378	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
381	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
383	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
384	#554	—	2	4	no	—
385	#554	C₂²×C₁₃	1	8	yes	complemented
386	#548	—	2	4	no	—
387	#548	C₂²×C₁₃	1	8	yes	—
388	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#125	—	2	1	no	—
390	C₂×#124	—	2	1	no	—
391	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊Q₈	—	2	1	no	—
393	C₂×C₂²⋊Q₈	—	2	1	no	—
394	C₂×C₂²⋊Q₈	—	2	1	no	—
395	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#121	—	2	1	no	—
399	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₄×D₄	—	2	1	no	—
403	C₂×C₄×D₄	—	2	1	no	—
404	C₂×C₄×D₄	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	#489	C₂²×C₁₃	1	8	yes	complemented
408	#483	C₂²×C₁₃	1	8	yes	complemented
409	#481	C₂²×C₁₃	1	8	yes	complemented
410	#475	C₂²×C₁₃	1	8	yes	complemented
411	#470	C₂²×C₁₃	1	8	yes	complemented
412	#465	C₂²×C₁₃	1	8	yes	complemented
413	#464	C₂²×C₁₃	1	8	yes	complemented
414	#452	C₂²×C₁₃	1	8	yes	complemented
415	#451	C₂²×C₁₃	1	8	yes	complemented
416	#441	C₂²×C₁₃	1	8	yes	complemented
417	#435	C₂²×C₁₃	1	8	yes	complemented
418	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
422	#417	C₂²×C₁₃	1	8	yes	complemented
423	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
431	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×C₁₃	—	2	2	no	—
438	C₂²×C₁₃	—	2	8	no	—
439	C₂²×C₁₃	—	2	2	no	—
440	C₂²×C₁₃	—	2	2	no	—
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	4	4	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	8	4	no	—
448	C₂²×C₁₃	#546	1	2	yes	—
449	C₂²×C₁₃	C₂×#137	1	4	yes	—
450	C₂²×C₁₃	C₂×#137	1	2	yes	—
451	C₂²×C₁₃	#577	1	2	yes	—
452	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₁₃	—	2	2	no	—
454	C₄×C₁₃	—	2	2	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	2	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	#546	1	2	yes	—
465	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
466	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	4	2	no	—
470	C₂×#41	C₂³×C₁₃	1	4	yes	—
471	C₂²×Q₈	—	2	1	no	—
472	C₂²×Q₈	—	2	2	no	—
473	C₂²×Q₈	—	2	1	no	—
474	C₂²×Q₈	—	2	4	no	—
475	C₂²×Q₈	—	4	2	no	—
476	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
479	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×Q₁₆	—	2	4	no	—
491	C₂×Q₁₆	—	4	2	no	—
492	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
494	C₂×SD₁₆	—	4	2	no	—
495	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
496	C₂×M₁₆	—	4	2	no	—
497	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
498	C₂²×C₈	—	4	2	no	—
499	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
506	#125	—	2	8	no	—
507	#124	—	2	8	no	—
508	#124	—	2	2	no	—
509	#124	C₂³×C₁₃	1	4	yes	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	8	no	—
514	C₂²⋊Q₈	—	2	8	no	—
515	C₂²⋊Q₈	—	2	8	no	—
516	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
517	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
518	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
519	#121	—	2	8	no	—
520	#121	—	2	2	no	—
521	#121	C₂³×C₁₃	1	4	yes	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
525	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	D₄×C₁₃	1	4	yes	—
529	C₄×D₄	C₂³×C₁₃	1	4	yes	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
558	#106	C₂³×C₁₃	1	4	yes	—
559	#106	C₂³×C₁₃	1	4	yes	—
560	#106	C₂³×C₁₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
562	#103	C₂³×C₁₃	1	4	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#103	C₂³×C₁₃	1	4	yes	—
565	#103	C₂³×C₁₃	1	4	yes	—
566	#103	C₂³×C₁₃	1	4	yes	—
567	#103	C₂³×C₁₃	1	4	yes	—
568	#103	C₂³×C₁₃	1	4	yes	—
569	#102	C₂³×C₁₃	1	4	yes	—
570	#102	C₂³×C₁₃	1	4	yes	—
571	#102	C₂³×C₁₃	1	4	yes	—
572	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
573	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
574	#97	C₂³×C₁₃	1	4	yes	—
575	C₂×C₁₃	—	2	4	no	—
576	C₂×C₁₃	—	4	2	no	—
577	C₂×C₁₃	—	8	2	no	—
578	C₂×C₁₃	#3316	1	4	yes	direct product factor
579	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
580	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
581	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
582	C₂⁴	—	2	1	no	—
583	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
585	#41	—	2	8	no	—
586	#41	—	4	4	no	—
587	#41	—	4	8	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	4	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	8	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	4	no	—
601	C₂×Q₈	—	4	8	no	—
602	C₂×Q₈	—	8	2	no	—
603	C₂×Q₈	C₁₃×#41	1	4	yes	—
604	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
605	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
606	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
616	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	4	4	no	—
633	C₂²×C₄	—	4	4	no	—
634	C₂²×C₄	—	8	2	no	—
635	C₂²×C₄	—	8	2	no	—
636	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
641	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
645	Q₁₆	—	2	8	no	—
646	Q₁₆	—	4	4	no	—
647	SD₁₆	—	4	4	no	—
648	M₁₆	—	4	4	no	—
649	C₂×C₈	—	2	2	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	2	2	no	—
653	C₂×C₈	—	4	4	no	—
654	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
656	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
657	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
682	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	C₂×D₄×C₁₃	1	2	yes	—
686	C₄²	C₂⁴×C₁₃	1	2	yes	—
687	C₁₃	C₂×#3316	1	1	yes	characteristic, direct product factor, Sylow
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	C₁₃×#137	1	4	yes	—
698	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
699	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
700	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
701	Q₈	—	2	4	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	8	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	Q₈	C₂×C₁₃×#41	1	4	yes	—
712	D₄	—	2	8	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	4	8	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	4	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
749	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
750	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
752	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
753	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	—	2	2	no	—
758	C₂²	—	2	8	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	4	no	—
769	C₂²	C₁₃×#546	1	2	yes	—
770	C₂²	C₂×C₁₃×#137	1	4	yes	—
771	C₂²	C₂×C₁₃×#137	1	2	yes	—
772	C₂²	C₁₃×#577	1	2	yes	—
773	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	C₁₃×#546	1	2	yes	—
786	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
787	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₁₃×#3316	1	4	yes	direct product factor
792	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
793	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
794	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3316	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#483	C₂	semidirect
7. C₂×C₁₃×#475	C₂	semidirect
8. C₂×C₁₃×#470	C₂	semidirect
9. C₂×C₁₃×#465	C₂	semidirect
10. C₂×C₁₃×#464	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#451	C₂	semidirect
13. C₂×C₁₃×#441	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂²×C₁₃×#103	C₂	semidirect
25. C₁₃×#554	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#483	C₂²	semidirect
49. C₁₃×#481	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
51. C₁₃×#470	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#464	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
55. C₁₃×#451	C₂²	semidirect
56. C₁₃×#441	C₂²	semidirect
57. C₁₃×#435	C₂²	semidirect
62. C₁₃×#417	C₂²	semidirect
70. C₂×C₁₃×#103	C₂²	semidirect
185. C₂×#3316	C₁₃	direct (N × H)
291. C₂×#554	C₂×C₁₃	semidirect
293. #3316	C₂×C₁₃	direct (N × H)
294. C₂×#489	C₂×C₁₃	semidirect
295. C₂×#481	C₂×C₁₃	semidirect
296. C₂×#483	C₂×C₁₃	semidirect
297. C₂×#475	C₂×C₁₃	semidirect
298. C₂×#470	C₂×C₁₃	semidirect
299. C₂×#465	C₂×C₁₃	semidirect
300. C₂×#464	C₂×C₁₃	semidirect
301. C₂×#452	C₂×C₁₃	semidirect
302. C₂×#451	C₂×C₁₃	semidirect
303. C₂×#441	C₂×C₁₃	semidirect
304. C₂×#435	C₂×C₁₃	semidirect
305. C₂×#417	C₂×C₁₃	semidirect
306. C₂²×#103	C₂×C₁₃	semidirect
385. #554	C₂²×C₁₃	semidirect
407. #489	C₂²×C₁₃	semidirect
408. #483	C₂²×C₁₃	semidirect
409. #481	C₂²×C₁₃	semidirect
410. #475	C₂²×C₁₃	semidirect
411. #470	C₂²×C₁₃	semidirect
412. #465	C₂²×C₁₃	semidirect
413. #464	C₂²×C₁₃	semidirect
414. #452	C₂²×C₁₃	semidirect
415. #451	C₂²×C₁₃	semidirect
416. #441	C₂²×C₁₃	semidirect
417. #435	C₂²×C₁₃	semidirect
422. #417	C₂²×C₁₃	semidirect
430. C₂×#103	C₂²×C₁₃	semidirect
578. C₂×C₁₃	#3316	direct (N × H)
687. C₁₃	C₂×#3316	direct (N × H)
791. C₂	C₁₃×#3316	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₂×C₁₃×#548	2
C₁₃×#3316	2
C₂×C₁₃×#489	2
C₂×C₁₃×#481	2
C₂×C₁₃×#483	2
C₂×C₁₃×#475	2
C₂×C₁₃×#470	2
C₂×C₁₃×#465	2
C₂×C₁₃×#464	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₁₃×#441	2
C₂×C₁₃×#435	2
C₂×C₁₃×#417	2
C₂²×C₁₃×#103	2
C₂×#3316	13

Subgroups — C2×C13×#3316 #15747469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3316 #15747469