Subgroups — C₁₃×#60695 #15747034

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3179	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3176	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3175	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3171	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3169	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₁₃×#544	C₂²	1	2	yes	—
24	C₁₃×#542	—	2	2	no	—
25	C₁₃×#542	C₂²	1	4	yes	complemented
26	C₁₃×#540	—	2	2	no	—
27	C₁₃×#540	C₂²	1	4	yes	complemented
28	C₁₃×#538	—	2	4	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#535	C₂²	1	2	yes	—
32	C₁₃×#532	—	2	2	no	—
33	C₁₃×#532	C₂²	1	4	yes	complemented
34	C₁₃×#529	—	2	2	no	—
35	C₁₃×#529	C₂²	1	4	yes	complemented
36	C₁₃×#525	—	2	4	no	—
37	C₄×C₁₃×#41	C₂²	1	2	yes	—
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#501	C₂²	1	4	yes	complemented
41	C₁₃×#500	C₂²	1	2	yes	complemented
42	C₁₃×#499	C₂²	1	2	yes	complemented
43	C₁₃×#496	C₂²	1	4	yes	—
44	C₁₃×#495	C₂²	1	2	yes	—
45	C₁₃×#493	C₂²	1	2	yes	—
46	C₁₃×#490	C₂²	1	4	yes	complemented
47	C₁₃×#489	C₂²	1	4	yes	complemented
48	C₁₃×#488	C₂²	1	4	yes	complemented
49	C₁₃×#486	C₂²	1	4	yes	complemented
50	C₁₃×#469	C₂²	1	4	yes	—
51	C₁₃×#469	C₂²	1	4	yes	complemented
52	C₁₃×#468	C₂²	1	4	yes	complemented
53	C₁₃×#468	C₂²	1	4	yes	complemented
54	C₁₃×#467	C₂²	1	2	yes	complemented
55	C₁₃×#466	C₂²	1	2	yes	—
56	C₁₃×#466	C₂²	1	2	yes	—
57	C₁₃×#466	C₂²	1	2	yes	complemented
58	C₁₃×#466	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#442	C₂²	1	4	yes	complemented
61	C₁₃×#440	C₂²	1	4	yes	complemented
62	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
65	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
67	C₄×C₁₃×D₈	C₂²	1	2	yes	—
68	C₄×C₁₃×D₈	C₂²	1	2	yes	—
69	C₄×C₁₃×D₈	C₂²	1	2	yes	—
70	C₄×C₁₃×D₈	C₂²	1	2	yes	—
71	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
73	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#428	C₂²	1	2	yes	—
75	C₁₃×#427	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
77	C₁₃×#418	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₂×C₁₃×#102	C₂²	1	2	yes	—
81	C₁₃×#405	C₂²	1	1	yes	characteristic
82	C₁₃×#405	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	complemented
84	C₁₃×#405	C₂²	1	2	yes	complemented
85	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
86	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
89	C₂×C₁₃×#41	—	2	4	no	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	—	2	2	no	—
94	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
95	C₁₃×#135	—	2	4	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	—	2	4	no	—
100	C₂×C₁₃×D₈	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	2	yes	—
102	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×D₈	C₂³	1	4	yes	—
104	C₁₃×#131	—	2	4	no	—
105	C₁₃×#131	—	2	4	no	—
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×#127	—	2	2	no	—
117	C₁₃×#127	C₂³	1	4	yes	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	C₂³	1	4	yes	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	—	2	4	no	—
124	C₁₃×#124	—	2	4	no	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#123	—	2	4	no	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	C₂³	1	4	yes	—
142	C₁₃×#121	C₂³	1	4	yes	—
143	C₁₃×#121	C₂³	1	4	yes	—
144	C₁₃×#120	—	2	4	no	—
145	C₁₃×#120	—	2	4	no	—
146	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	2	no	—
152	C₄×D₄×C₁₃	—	2	4	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	4	no	—
156	C₄×D₄×C₁₃	D₄	1	2	yes	—
157	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
158	C₄×D₄×C₁₃	D₄	1	2	yes	—
159	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₁₃	C₂³	1	4	yes	—
161	C₄×D₄×C₁₃	C₂³	1	4	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	4	no	—
166	C₁₃×#117	C₂³	1	2	yes	—
167	C₁₃×#117	C₂³	1	1	yes	characteristic
168	C₁₃×#117	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₂×C₄²×C₁₃	—	2	2	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₁₃×#107	C₂³	1	2	yes	—
175	C₁₃×#107	C₂³	1	2	yes	—
176	C₁₃×#107	C₂³	1	1	yes	characteristic
177	C₁₃×#107	C₂³	1	1	yes	characteristic
178	C₁₃×#107	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	2	yes	—
187	C₁₃×#102	C₂³	1	2	yes	—
188	C₁₃×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	4	yes	—
191	C₁₃×#97	C₂³	1	2	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₁₃×#97	C₂³	1	2	yes	—
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₁₃	C₂³	1	2	yes	—
199	C₄×C₈×C₁₃	C₂³	1	2	yes	—
200	C₄×C₈×C₁₃	C₂³	1	2	yes	—
201	#60695	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₃	—	2	2	no	—
203	C₁₃×#41	—	2	2	no	—
204	C₁₃×#41	—	2	2	no	—
205	C₁₃×#41	—	2	4	no	—
206	C₁₃×#41	—	2	4	no	—
207	C₁₃×#41	—	8	8	no	—
208	C₂×Q₈×C₁₃	—	2	4	no	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	4	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	8	4	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×Q₁₆	—	2	2	no	—
238	C₁₃×SD₁₆	—	2	4	no	—
239	C₁₃×SD₁₆	—	2	8	no	—
240	C₁₃×D₈	—	2	4	no	—
241	C₁₃×D₈	—	2	4	no	—
242	C₁₃×D₈	—	2	2	no	—
243	C₁₃×D₈	—	2	8	no	—
244	C₁₃×M₁₆	—	2	2	no	—
245	C₁₃×M₁₆	—	2	4	no	—
246	C₁₃×M₁₆	—	2	4	no	—
247	C₁₃×M₁₆	#41	1	4	yes	complemented
248	C₂×C₈×C₁₃	—	2	2	no	—
249	C₂×C₈×C₁₃	—	2	4	no	—
250	C₂×C₈×C₁₃	—	2	4	no	—
251	C₂×C₈×C₁₃	#41	1	4	yes	complemented
252	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
268	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₂×D₄	1	2	yes	—
284	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
285	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₁₃	C₂×D₄	1	2	yes	—
291	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₁₃	C₂×D₄	1	2	yes	—
293	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₄²×C₁₃	C₂⁴	1	2	yes	—
295	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
296	#3460	C₂×C₁₃	1	2	yes	complemented
297	#3179	C₂×C₁₃	1	4	yes	complemented
298	#3176	C₂×C₁₃	1	2	yes	complemented
299	#3175	C₂×C₁₃	1	2	yes	complemented
300	#3171	C₂×C₁₃	1	4	yes	complemented
301	#3169	C₂×C₁₃	1	2	yes	complemented
302	#3168	C₂×C₁₃	1	2	yes	complemented
303	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#3136	C₂×C₁₃	1	2	yes	complemented
306	#3062	C₂×C₁₃	1	2	yes	complemented
307	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
310	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	4	no	—
316	C₂³×C₁₃	—	8	2	no	—
317	C₂³×C₁₃	—	8	2	no	—
318	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	2	no	—
323	Q₈×C₁₃	—	8	4	no	—
324	D₄×C₁₃	—	2	4	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	2	4	no	—
327	D₄×C₁₃	—	2	2	no	—
328	D₄×C₁₃	—	2	4	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	4	4	no	—
331	D₄×C₁₃	—	4	4	no	—
332	D₄×C₁₃	—	8	4	no	—
333	D₄×C₁₃	—	8	4	no	—
334	D₄×C₁₃	—	8	4	no	—
335	D₄×C₁₃	—	8	4	no	—
336	D₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	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	4	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	2	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	4	4	no	—
350	C₂×C₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	2	no	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₁₃	—	2	1	no	—
365	C₈×C₁₃	—	2	1	no	—
366	C₈×C₁₃	—	2	2	no	—
367	C₈×C₁₃	C₂×#41	1	2	yes	—
368	C₈×C₁₃	C₂×#41	1	4	yes	—
369	C₈×C₁₃	C₂×#41	1	2	yes	—
370	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
371	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
375	#544	C₂²×C₁₃	1	2	yes	—
376	#542	—	2	2	no	—
377	#542	C₂²×C₁₃	1	4	yes	complemented
378	#540	—	2	2	no	—
379	#540	C₂²×C₁₃	1	4	yes	complemented
380	#538	—	2	4	no	—
381	#537	C₂²×C₁₃	1	2	yes	—
382	#535	C₂²×C₁₃	1	2	yes	—
383	#535	C₂²×C₁₃	1	2	yes	—
384	#532	—	2	2	no	—
385	#532	C₂²×C₁₃	1	4	yes	complemented
386	#529	—	2	2	no	—
387	#529	C₂²×C₁₃	1	4	yes	complemented
388	#525	—	2	4	no	—
389	C₄×#41	C₂²×C₁₃	1	2	yes	—
390	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
392	#501	C₂²×C₁₃	1	4	yes	complemented
393	#500	C₂²×C₁₃	1	2	yes	complemented
394	#499	C₂²×C₁₃	1	2	yes	complemented
395	#496	C₂²×C₁₃	1	4	yes	—
396	#495	C₂²×C₁₃	1	2	yes	—
397	#493	C₂²×C₁₃	1	2	yes	—
398	#490	C₂²×C₁₃	1	4	yes	complemented
399	#489	C₂²×C₁₃	1	4	yes	complemented
400	#488	C₂²×C₁₃	1	4	yes	complemented
401	#486	C₂²×C₁₃	1	4	yes	complemented
402	#469	C₂²×C₁₃	1	4	yes	—
403	#469	C₂²×C₁₃	1	4	yes	complemented
404	#468	C₂²×C₁₃	1	4	yes	complemented
405	#468	C₂²×C₁₃	1	4	yes	complemented
406	#467	C₂²×C₁₃	1	2	yes	complemented
407	#466	C₂²×C₁₃	1	2	yes	—
408	#466	C₂²×C₁₃	1	2	yes	—
409	#466	C₂²×C₁₃	1	2	yes	complemented
410	#466	C₂²×C₁₃	1	4	yes	complemented
411	#465	C₂²×C₁₃	1	4	yes	complemented
412	#442	C₂²×C₁₃	1	4	yes	complemented
413	#440	C₂²×C₁₃	1	4	yes	complemented
414	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
417	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
418	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
419	C₄×D₈	C₂²×C₁₃	1	2	yes	—
420	C₄×D₈	C₂²×C₁₃	1	2	yes	—
421	C₄×D₈	C₂²×C₁₃	1	2	yes	—
422	C₄×D₈	C₂²×C₁₃	1	2	yes	—
423	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
425	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#428	C₂²×C₁₃	1	2	yes	—
427	#427	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
429	#418	C₂²×C₁₃	1	2	yes	—
430	#417	C₂²×C₁₃	1	2	yes	—
431	#416	C₂²×C₁₃	1	2	yes	—
432	C₂×#102	C₂²×C₁₃	1	2	yes	—
433	#405	C₂²×C₁₃	1	1	yes	characteristic
434	#405	C₂²×C₁₃	1	1	yes	characteristic
435	#405	C₂²×C₁₃	1	2	yes	complemented
436	#405	C₂²×C₁₃	1	2	yes	complemented
437	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
438	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
439	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	2	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	4	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	4	no	—
450	C₂²×C₁₃	—	4	4	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	8	8	no	—
453	C₂²×C₁₃	#532	1	2	yes	—
454	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₁₃	—	2	1	no	—
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	2	2	no	—
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	4	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	#532	1	2	yes	—
466	C₄×C₁₃	#576	1	2	yes	—
467	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
468	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
469	C₂×#41	—	2	4	no	—
470	C₂×#41	C₂³×C₁₃	1	2	yes	—
471	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
473	C₂³×C₄	—	2	2	no	—
474	AGL(1,ℤ/8)	—	2	8	no	—
475	#135	—	2	4	no	—
476	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
478	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
479	C₂×D₈	—	2	4	no	—
480	C₂×D₈	C₂³×C₁₃	1	2	yes	—
481	C₂×D₈	C₂³×C₁₃	1	2	yes	—
482	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×D₈	C₂³×C₁₃	1	4	yes	—
484	#131	—	2	4	no	—
485	#131	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
489	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
492	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
493	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
496	#127	—	2	2	no	—
497	#127	C₂³×C₁₃	1	4	yes	—
498	#126	—	2	4	no	—
499	#126	—	2	4	no	—
500	#125	—	2	2	no	—
501	#125	C₂³×C₁₃	1	4	yes	—
502	#124	—	2	2	no	—
503	#124	—	2	4	no	—
504	#124	—	2	4	no	—
505	#124	C₂³×C₁₃	1	4	yes	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
514	#121	—	2	4	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	4	no	—
520	#121	—	2	4	no	—
521	#121	C₂³×C₁₃	1	4	yes	—
522	#121	C₂³×C₁₃	1	4	yes	—
523	#121	C₂³×C₁₃	1	4	yes	—
524	#120	—	2	4	no	—
525	#120	—	2	4	no	—
526	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
527	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
528	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
529	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	D₄×C₁₃	1	2	yes	—
537	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
538	C₄×D₄	D₄×C₁₃	1	2	yes	—
539	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
540	C₄×D₄	C₂³×C₁₃	1	4	yes	—
541	C₄×D₄	C₂³×C₁₃	1	4	yes	—
542	C₄×D₄	C₂³×C₁₃	1	2	yes	—
543	C₄×D₄	C₂³×C₁₃	1	2	yes	—
544	#117	—	2	2	no	—
545	#117	—	2	4	no	—
546	#117	C₂³×C₁₃	1	2	yes	—
547	#117	C₂³×C₁₃	1	1	yes	characteristic
548	#117	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₂²⋊C₄	—	2	2	no	—
551	C₂×C₄²	—	2	2	no	—
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
554	#107	C₂³×C₁₃	1	2	yes	—
555	#107	C₂³×C₁₃	1	2	yes	—
556	#107	C₂³×C₁₃	1	1	yes	characteristic
557	#107	C₂³×C₁₃	1	1	yes	characteristic
558	#107	C₂³×C₁₃	1	4	yes	—
559	#106	C₂³×C₁₃	1	2	yes	—
560	#106	C₂³×C₁₃	1	4	yes	—
561	#103	C₂³×C₁₃	1	2	yes	—
562	#103	C₂³×C₁₃	1	2	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#102	C₂³×C₁₃	1	4	yes	—
565	#102	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	2	yes	—
567	#102	C₂³×C₁₃	1	2	yes	—
568	#102	C₂³×C₁₃	1	4	yes	—
569	#102	C₂³×C₁₃	1	4	yes	—
570	#102	C₂³×C₁₃	1	4	yes	—
571	#97	C₂³×C₁₃	1	2	yes	—
572	#97	C₂³×C₁₃	1	2	yes	—
573	#97	C₂³×C₁₃	1	2	yes	—
574	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₄×C₈	C₂³×C₁₃	1	2	yes	—
579	C₄×C₈	C₂³×C₁₃	1	2	yes	—
580	C₄×C₈	C₂³×C₁₃	1	2	yes	—
581	C₂×C₁₃	—	2	2	no	—
582	C₂×C₁₃	—	4	2	no	—
583	C₂×C₁₃	—	8	2	no	—
584	C₂×C₁₃	—	8	4	no	—
585	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
586	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
587	C₂×C₁₃	#3584	1	1	yes	characteristic
588	C₂⁴	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	4	no	—
592	#41	—	2	4	no	—
593	#41	—	8	8	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
607	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	8	4	no	—
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	Q₁₆	—	2	2	no	—
624	SD₁₆	—	2	4	no	—
625	SD₁₆	—	2	8	no	—
626	D₈	—	2	4	no	—
627	D₈	—	2	4	no	—
628	D₈	—	2	2	no	—
629	D₈	—	2	8	no	—
630	M₁₆	—	2	2	no	—
631	M₁₆	—	2	4	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	C₁₃×#41	1	4	yes	complemented
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	4	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	C₁₃×#41	1	4	yes	complemented
638	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
641	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
642	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
643	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₁₃	1	2	yes	—
678	C₄²	C₂×D₄×C₁₃	1	2	yes	—
679	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₄²	C₂⁴×C₁₃	1	2	yes	—
682	C₁₃	#60695	1	1	yes	characteristic, direct product factor, Sylow
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	2	no	—
688	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
689	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	8	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
732	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
733	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂×C₁₃×#41	1	2	yes	—
738	C₈	C₂×C₁₃×#41	1	4	yes	—
739	C₈	C₂×C₁₃×#41	1	2	yes	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	8	8	no	—
752	C₂²	C₁₃×#532	1	2	yes	—
753	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₁₃×#532	1	2	yes	—
765	C₄	C₁₃×#576	1	2	yes	—
766	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
767	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	2	no	—
770	C₂	—	8	4	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
773	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
774	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3460	C₂	semidirect
2. C₁₃×#3179	C₂	semidirect
3. C₁₃×#3176	C₂	semidirect
4. C₁₃×#3175	C₂	semidirect
5. C₁₃×#3171	C₂	semidirect
6. C₁₃×#3169	C₂	semidirect
7. C₁₃×#3168	C₂	semidirect
8. C₁₃×#3164	C₂	semidirect
9. C₁₃×#3155	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3062	C₂	semidirect
12. C₁₃×#3061	C₂	semidirect
13. C₁₃×#3058	C₂	semidirect
14. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₄×C₁₃×#135	C₂	semidirect
16. C₂×C₄×C₁₃×D₈	C₂	semidirect
17. C₄×C₁₃×#131	C₂	semidirect
25. C₁₃×#542	C₂²	semidirect
27. C₁₃×#540	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
35. C₁₃×#529	C₂²	semidirect
40. C₁₃×#501	C₂²	semidirect
41. C₁₃×#500	C₂²	semidirect
42. C₁₃×#499	C₂²	semidirect
46. C₁₃×#490	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#488	C₂²	semidirect
49. C₁₃×#486	C₂²	semidirect
51. C₁₃×#469	C₂²	semidirect
52. C₁₃×#468	C₂²	semidirect
53. C₁₃×#468	C₂²	semidirect
54. C₁₃×#467	C₂²	semidirect
57. C₁₃×#466	C₂²	semidirect
58. C₁₃×#466	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#442	C₂²	semidirect
61. C₁₃×#440	C₂²	semidirect
62. C₄×C₁₃×Q₁₆	C₂²	semidirect
63. C₄×C₁₃×Q₁₆	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
65. C₄×C₁₃×SD₁₆	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
71. C₄×C₁₃×D₈	C₂²	semidirect
72. C₄×C₁₃×D₈	C₂²	semidirect
73. C₄×C₁₃×D₈	C₂²	semidirect
83. C₁₃×#405	C₂²	semidirect
84. C₁₃×#405	C₂²	semidirect
86. C₄×C₁₃×M₁₆	C₂²	semidirect
88. C₂×C₄×C₈×C₁₃	C₂²	semidirect
201. #60695	C₁₃	direct (N × H)
247. C₁₃×M₁₆	#41	semidirect
251. C₂×C₈×C₁₃	#41	semidirect
296. #3460	C₂×C₁₃	semidirect
297. #3179	C₂×C₁₃	semidirect
298. #3176	C₂×C₁₃	semidirect
299. #3175	C₂×C₁₃	semidirect
300. #3171	C₂×C₁₃	semidirect
301. #3169	C₂×C₁₃	semidirect
302. #3168	C₂×C₁₃	semidirect
303. #3164	C₂×C₁₃	semidirect
304. #3155	C₂×C₁₃	semidirect
305. #3136	C₂×C₁₃	semidirect
306. #3062	C₂×C₁₃	semidirect
307. #3061	C₂×C₁₃	semidirect
308. #3058	C₂×C₁₃	semidirect
309. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
310. C₄×#135	C₂×C₁₃	semidirect
311. C₂×C₄×D₈	C₂×C₁₃	semidirect
312. C₄×#131	C₂×C₁₃	semidirect
377. #542	C₂²×C₁₃	semidirect
379. #540	C₂²×C₁₃	semidirect
385. #532	C₂²×C₁₃	semidirect
387. #529	C₂²×C₁₃	semidirect
392. #501	C₂²×C₁₃	semidirect
393. #500	C₂²×C₁₃	semidirect
394. #499	C₂²×C₁₃	semidirect
398. #490	C₂²×C₁₃	semidirect
399. #489	C₂²×C₁₃	semidirect
400. #488	C₂²×C₁₃	semidirect
401. #486	C₂²×C₁₃	semidirect
403. #469	C₂²×C₁₃	semidirect
404. #468	C₂²×C₁₃	semidirect
405. #468	C₂²×C₁₃	semidirect
406. #467	C₂²×C₁₃	semidirect
409. #466	C₂²×C₁₃	semidirect
410. #466	C₂²×C₁₃	semidirect
411. #465	C₂²×C₁₃	semidirect
412. #442	C₂²×C₁₃	semidirect
413. #440	C₂²×C₁₃	semidirect
414. C₄×Q₁₆	C₂²×C₁₃	semidirect
415. C₄×Q₁₆	C₂²×C₁₃	semidirect
416. C₄×SD₁₆	C₂²×C₁₃	semidirect
417. C₄×SD₁₆	C₂²×C₁₃	semidirect
418. C₄×SD₁₆	C₂²×C₁₃	semidirect
423. C₄×D₈	C₂²×C₁₃	semidirect
424. C₄×D₈	C₂²×C₁₃	semidirect
425. C₄×D₈	C₂²×C₁₃	semidirect
435. #405	C₂²×C₁₃	semidirect
436. #405	C₂²×C₁₃	semidirect
438. C₄×M₁₆	C₂²×C₁₃	semidirect
440. C₂×C₄×C₈	C₂²×C₁₃	semidirect
633. M₁₆	C₁₃×#41	semidirect
637. C₂×C₈	C₁₃×#41	semidirect
682. C₁₃	#60695	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3460	2
C₁₃×#3179	2
C₁₃×#3176	2
C₁₃×#3175	2
C₁₃×#3171	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3164	2
C₁₃×#3155	2
C₁₃×#3136	2
C₁₃×#3062	2
C₁₃×#3061	2
C₁₃×#3058	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×D₈	2
C₄×C₁₃×#131	2
#60695	13

Subgroups — C13×#60695 #15747034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60695 #15747034