Subgroups — C₂×C₁₃×#3257 #15747247

Order 3328.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3257	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#542	—	2	4	no	—
24	C₁₃×#542	C₂²	1	8	yes	complemented
25	C₁₃×#540	—	2	4	no	—
26	C₁₃×#540	C₂²	1	8	yes	complemented
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#126	—	2	1	no	—
30	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#124	—	2	1	no	—
32	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#123	—	2	1	no	—
34	C₂×C₁₃×#123	—	2	1	no	—
35	C₂×C₁₃×#123	—	2	1	no	—
36	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	—	2	1	no	—
39	C₂×C₁₃×#121	—	2	1	no	—
40	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₁₃×#479	C₂²	1	8	yes	complemented
49	C₁₃×#478	C₂²	1	8	yes	complemented
50	C₁₃×#476	C₂²	1	8	yes	complemented
51	C₁₃×#474	C₂²	1	8	yes	complemented
52	C₁₃×#469	C₂²	1	8	yes	complemented
53	C₁₃×#468	C₂²	1	8	yes	complemented
54	C₁₃×#466	C₂²	1	8	yes	complemented
55	C₁₃×#465	C₂²	1	8	yes	complemented
56	C₁₃×#463	C₂²	1	8	yes	complemented
57	C₁₃×#463	C₂²	1	8	yes	complemented
58	C₁₃×#460	C₂²	1	8	yes	complemented
59	C₁₃×#459	C₂²	1	8	yes	complemented
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
64	C₁₃×#424	C₂²	1	8	yes	complemented
65	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
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×#102	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂³×C₄×C₁₃	—	2	1	no	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×SD₁₆	—	4	2	no	—
92	C₂×C₁₃×SD₁₆	—	4	2	no	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×D₈	—	4	2	no	—
96	C₂×C₁₃×D₈	—	4	2	no	—
97	C₂×C₁₃×D₈	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	4	yes	—
99	C₂×C₁₃×M₁₆	—	4	2	no	—
100	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
101	C₂²×C₈×C₁₃	—	4	2	no	—
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×#127	—	2	2	no	—
110	C₁₃×#127	C₂³	1	4	yes	—
111	C₁₃×#126	—	2	8	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#124	—	2	8	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×#123	—	2	8	no	—
119	C₁₃×#123	—	2	8	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	8	no	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	—	2	8	no	—
127	C₁₃×#121	—	2	8	no	—
128	C₁₃×#121	C₂³	1	4	yes	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
133	C₄×D₄×C₁₃	—	2	2	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	C₂³	1	4	yes	—
137	C₄×D₄×C₁₃	C₂³	1	4	yes	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₁₃×#117	D₄	1	4	yes	—
140	C₁₃×#117	C₂³	1	4	yes	—
141	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
162	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₁₃×#107	C₂³	1	4	yes	—
167	C₁₃×#107	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#102	C₂³	1	4	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	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	C₂×#3257	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	—	2	1	no	—
184	C₂⁴×C₁₃	—	2	1	no	—
185	C₂⁴×C₁₃	—	2	1	no	—
186	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	8	2	no	—
192	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	2	no	—
203	C₂×D₄×C₁₃	—	2	2	no	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	8	2	no	—
208	C₂×D₄×C₁₃	—	8	2	no	—
209	C₂×D₄×C₁₃	—	8	2	no	—
210	C₂×D₄×C₁₃	—	8	2	no	—
211	C₂×D₄×C₁₃	—	8	2	no	—
212	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	8	2	no	—
226	C₂²×C₄×C₁₃	—	8	2	no	—
227	C₂²×C₄×C₁₃	—	8	2	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×SD₁₆	—	4	4	no	—
237	C₁₃×SD₁₆	—	4	4	no	—
238	C₁₃×D₈	—	4	4	no	—
239	C₁₃×D₈	—	4	4	no	—
240	C₁₃×M₁₆	—	4	4	no	—
241	C₂×C₈×C₁₃	—	2	2	no	—
242	C₂×C₈×C₁₃	—	2	2	no	—
243	C₂×C₈×C₁₃	—	2	2	no	—
244	C₂×C₈×C₁₃	—	2	2	no	—
245	C₂×C₈×C₁₃	—	4	4	no	—
246	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
276	C₄²×C₁₃	—	2	4	no	—
277	C₄²×C₁₃	C₂×D₄	1	2	yes	—
278	C₄²×C₁₃	C₂×D₄	1	2	yes	—
279	C₄²×C₁₃	C₂⁴	1	2	yes	—
280	C₄²×C₁₃	C₂⁴	1	2	yes	—
281	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#3257	C₂×C₁₃	1	16	yes	direct product factor
284	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	4	2	no	—
304	C₂³×C₁₃	—	4	2	no	—
305	C₂³×C₁₃	—	4	2	no	—
306	C₂³×C₁₃	—	4	2	no	—
307	C₂³×C₁₃	—	4	2	no	—
308	C₂³×C₁₃	—	4	2	no	—
309	C₂³×C₁₃	—	4	2	no	—
310	C₂³×C₁₃	—	4	2	no	—
311	C₂³×C₁₃	—	4	2	no	—
312	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
313	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	4	2	no	—
317	Q₈×C₁₃	—	8	4	no	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	4	2	no	—
325	D₄×C₁₃	—	4	2	no	—
326	D₄×C₁₃	—	4	2	no	—
327	D₄×C₁₃	—	8	4	no	—
328	D₄×C₁₃	—	8	4	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	D₄×C₁₃	—	8	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	4	2	no	—
346	C₂×C₄×C₁₃	—	4	2	no	—
347	C₂×C₄×C₁₃	—	4	2	no	—
348	C₂×C₄×C₁₃	—	4	2	no	—
349	C₂×C₄×C₁₃	—	4	2	no	—
350	C₂×C₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
361	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
362	C₈×C₁₃	—	2	2	no	—
363	C₈×C₁₃	—	2	2	no	—
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	—	2	2	no	—
366	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
371	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
372	#542	—	2	4	no	—
373	#542	C₂²×C₁₃	1	8	yes	complemented
374	#540	—	2	4	no	—
375	#540	C₂²×C₁₃	1	8	yes	complemented
376	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#126	—	2	1	no	—
379	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#124	—	2	1	no	—
381	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#123	—	2	1	no	—
383	C₂×#123	—	2	1	no	—
384	C₂×#123	—	2	1	no	—
385	C₂×C₂²⋊Q₈	—	2	1	no	—
386	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#121	—	2	1	no	—
388	C₂×#121	—	2	1	no	—
389	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
397	#479	C₂²×C₁₃	1	8	yes	complemented
398	#478	C₂²×C₁₃	1	8	yes	complemented
399	#476	C₂²×C₁₃	1	8	yes	complemented
400	#474	C₂²×C₁₃	1	8	yes	complemented
401	#469	C₂²×C₁₃	1	8	yes	complemented
402	#468	C₂²×C₁₃	1	8	yes	complemented
403	#466	C₂²×C₁₃	1	8	yes	complemented
404	#465	C₂²×C₁₃	1	8	yes	complemented
405	#463	C₂²×C₁₃	1	8	yes	complemented
406	#463	C₂²×C₁₃	1	8	yes	complemented
407	#460	C₂²×C₁₃	1	8	yes	complemented
408	#459	C₂²×C₁₃	1	8	yes	complemented
409	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
413	#424	C₂²×C₁₃	1	8	yes	complemented
414	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	2	2	no	—
428	C₂²×C₁₃	—	2	2	no	—
429	C₂²×C₁₃	—	4	4	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	2	no	—
439	C₂²×C₁₃	—	8	4	no	—
440	C₂²×C₁₃	—	8	4	no	—
441	C₂²×C₁₃	—	8	4	no	—
442	C₂²×C₁₃	#537	1	2	yes	—
443	C₂²×C₁₃	#576	1	2	yes	—
444	C₂²×C₁₃	#577	1	2	yes	—
445	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	#537	1	2	yes	—
457	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂²×Q₈	—	2	1	no	—
460	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×SD₁₆	—	4	2	no	—
474	C₂×SD₁₆	—	4	2	no	—
475	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
476	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
477	C₂×D₈	—	4	2	no	—
478	C₂×D₈	—	4	2	no	—
479	C₂×D₈	C₂³×C₁₃	1	4	yes	—
480	C₂×D₈	C₂³×C₁₃	1	4	yes	—
481	C₂×M₁₆	—	4	2	no	—
482	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
483	C₂²×C₈	—	4	2	no	—
484	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
491	#127	—	2	2	no	—
492	#127	C₂³×C₁₃	1	4	yes	—
493	#126	—	2	8	no	—
494	#125	—	2	2	no	—
495	#125	C₂³×C₁₃	1	4	yes	—
496	#124	—	2	8	no	—
497	#124	—	2	2	no	—
498	#124	C₂³×C₁₃	1	4	yes	—
499	#123	—	2	8	no	—
500	#123	—	2	8	no	—
501	#123	—	2	8	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	8	no	—
504	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	8	no	—
509	#121	—	2	8	no	—
510	#121	C₂³×C₁₃	1	4	yes	—
511	#121	C₂³×C₁₃	1	4	yes	—
512	#121	C₂³×C₁₃	1	4	yes	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	C₂³×C₁₃	1	4	yes	—
519	C₄×D₄	C₂³×C₁₃	1	4	yes	—
520	C₄×D₄	C₂³×C₁₃	1	4	yes	—
521	#117	D₄×C₁₃	1	4	yes	—
522	#117	C₂³×C₁₃	1	4	yes	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
548	#107	C₂³×C₁₃	1	4	yes	—
549	#107	C₂³×C₁₃	1	4	yes	—
550	#106	C₂³×C₁₃	1	4	yes	—
551	#106	C₂³×C₁₃	1	4	yes	—
552	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
553	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
554	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
555	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
556	#103	C₂³×C₁₃	1	4	yes	—
557	#103	C₂³×C₁₃	1	4	yes	—
558	#102	C₂³×C₁₃	1	4	yes	—
559	#102	C₂³×C₁₃	1	4	yes	—
560	#102	C₂³×C₁₃	1	4	yes	—
561	#102	C₂³×C₁₃	1	4	yes	—
562	#102	C₂³×C₁₃	1	4	yes	—
563	#102	C₂³×C₁₃	1	4	yes	—
564	C₂×C₁₃	—	4	2	no	—
565	C₂×C₁₃	—	8	2	no	—
566	C₂×C₁₃	—	8	2	no	—
567	C₂×C₁₃	—	8	2	no	—
568	C₂×C₁₃	#3257	1	4	yes	direct product factor
569	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
570	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
571	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
572	C₂⁴	—	2	1	no	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	8	2	no	—
581	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	8	2	no	—
597	C₂×D₄	—	8	2	no	—
598	C₂×D₄	—	8	2	no	—
599	C₂×D₄	—	8	2	no	—
600	C₂×D₄	—	8	2	no	—
601	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	8	2	no	—
615	C₂²×C₄	—	8	2	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	SD₁₆	—	4	4	no	—
626	SD₁₆	—	4	4	no	—
627	D₈	—	4	4	no	—
628	D₈	—	4	4	no	—
629	M₁₆	—	4	4	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	4	4	no	—
635	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
637	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
664	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
665	C₄²	—	2	4	no	—
666	C₄²	C₂×D₄×C₁₃	1	2	yes	—
667	C₄²	C₂×D₄×C₁₃	1	2	yes	—
668	C₄²	C₂⁴×C₁₃	1	2	yes	—
669	C₄²	C₂⁴×C₁₃	1	2	yes	—
670	C₁₃	C₂×#3257	1	1	yes	characteristic, direct product factor, Sylow
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
687	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
733	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
734	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
735	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	8	4	no	—
754	C₂²	—	8	4	no	—
755	C₂²	—	8	4	no	—
756	C₂²	C₁₃×#537	1	2	yes	—
757	C₂²	C₁₃×#576	1	2	yes	—
758	C₂²	C₁₃×#577	1	2	yes	—
759	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	C₁₃×#537	1	2	yes	—
771	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
773	C₂	—	4	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	—	8	2	no	—
777	C₂	C₁₃×#3257	1	4	yes	direct product factor
778	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
779	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
780	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#542	C₂	semidirect
2. C₂×C₁₃×#540	C₂	semidirect
3. C₁₃×#3257	C₂	direct (N × H)
4. C₂×C₁₃×#479	C₂	semidirect
5. C₂×C₁₃×#478	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₁₃×#474	C₂	semidirect
8. C₂×C₁₃×#469	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₁₃×#466	C₂	semidirect
11. C₂×C₁₃×#465	C₂	semidirect
12. C₂×C₁₃×#460	C₂	semidirect
13. C₂×C₁₃×#463	C₂	semidirect
14. C₂×C₁₃×#463	C₂	semidirect
15. C₂×C₁₃×#459	C₂	semidirect
16. C₂×C₁₃×#424	C₂	semidirect
24. C₁₃×#542	C₂²	semidirect
26. C₁₃×#540	C₂²	semidirect
48. C₁₃×#479	C₂²	semidirect
49. C₁₃×#478	C₂²	semidirect
50. C₁₃×#476	C₂²	semidirect
51. C₁₃×#474	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
53. C₁₃×#468	C₂²	semidirect
54. C₁₃×#466	C₂²	semidirect
55. C₁₃×#465	C₂²	semidirect
56. C₁₃×#463	C₂²	semidirect
57. C₁₃×#463	C₂²	semidirect
58. C₁₃×#460	C₂²	semidirect
59. C₁₃×#459	C₂²	semidirect
64. C₁₃×#424	C₂²	semidirect
182. C₂×#3257	C₁₃	direct (N × H)
281. C₂×#542	C₂×C₁₃	semidirect
282. C₂×#540	C₂×C₁₃	semidirect
283. #3257	C₂×C₁₃	direct (N × H)
284. C₂×#479	C₂×C₁₃	semidirect
285. C₂×#478	C₂×C₁₃	semidirect
286. C₂×#476	C₂×C₁₃	semidirect
287. C₂×#474	C₂×C₁₃	semidirect
288. C₂×#469	C₂×C₁₃	semidirect
289. C₂×#468	C₂×C₁₃	semidirect
290. C₂×#466	C₂×C₁₃	semidirect
291. C₂×#465	C₂×C₁₃	semidirect
292. C₂×#460	C₂×C₁₃	semidirect
293. C₂×#463	C₂×C₁₃	semidirect
294. C₂×#463	C₂×C₁₃	semidirect
295. C₂×#459	C₂×C₁₃	semidirect
296. C₂×#424	C₂×C₁₃	semidirect
373. #542	C₂²×C₁₃	semidirect
375. #540	C₂²×C₁₃	semidirect
397. #479	C₂²×C₁₃	semidirect
398. #478	C₂²×C₁₃	semidirect
399. #476	C₂²×C₁₃	semidirect
400. #474	C₂²×C₁₃	semidirect
401. #469	C₂²×C₁₃	semidirect
402. #468	C₂²×C₁₃	semidirect
403. #466	C₂²×C₁₃	semidirect
404. #465	C₂²×C₁₃	semidirect
405. #463	C₂²×C₁₃	semidirect
406. #463	C₂²×C₁₃	semidirect
407. #460	C₂²×C₁₃	semidirect
408. #459	C₂²×C₁₃	semidirect
413. #424	C₂²×C₁₃	semidirect
568. C₂×C₁₃	#3257	direct (N × H)
670. C₁₃	C₂×#3257	direct (N × H)
777. C₂	C₁₃×#3257	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×#542	2
C₂×C₁₃×#540	2
C₁₃×#3257	2
C₂×C₁₃×#479	2
C₂×C₁₃×#478	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₁₃×#469	2
C₂×C₁₃×#468	2
C₂×C₁₃×#466	2
C₂×C₁₃×#465	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#424	2
C₂×#3257	13

Subgroups — C2×C13×#3257 #15747247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3257 #15747247