Subgroups — C₁₃×#61418 #15747757

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3398	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3154	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₁₃×#559	C₂²	1	4	yes	—
30	C₁₃×#557	C₂²	1	4	yes	complemented
31	C₁₃×#556	C₂²	1	4	yes	—
32	C₁₃×#556	C₂²	1	4	yes	complemented
33	C₁₃×#552	—	2	4	no	—
34	C₁₃×#551	—	2	4	no	—
35	C₁₃×#542	—	2	2	no	—
36	C₁₃×#541	—	2	2	no	—
37	C₁₃×#536	C₂²	1	1	yes	characteristic
38	C₁₃×#536	C₂²	1	1	yes	characteristic
39	C₁₃×#536	C₂²	1	1	yes	characteristic
40	C₁₃×#535	C₂²	1	1	yes	characteristic
41	C₁₃×#533	—	2	2	no	—
42	C₁₃×#533	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
46	C₁₃×#519	C₂²	1	1	yes	characteristic
47	C₁₃×#519	C₂²	1	1	yes	characteristic
48	C₁₃×#519	C₂²	1	1	yes	characteristic
49	C₁₃×#518	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	2	yes	—
53	C₁₃×#497	C₂²	1	4	yes	—
54	C₁₃×#497	C₂²	1	4	yes	—
55	C₁₃×#497	C₂²	1	2	yes	complemented
56	C₁₃×#497	C₂²	1	2	yes	complemented
57	C₁₃×#496	C₂²	1	2	yes	—
58	C₁₃×#495	C₂²	1	2	yes	—
59	C₁₃×#495	C₂²	1	2	yes	complemented
60	C₁₃×#494	C₂²	1	2	yes	complemented
61	C₁₃×#492	C₂²	1	2	yes	—
62	C₁₃×#464	C₂²	1	4	yes	—
63	C₁₃×#464	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#463	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	4	yes	complemented
69	C₁₃×#462	C₂²	1	4	yes	complemented
70	C₁₃×#462	C₂²	1	4	yes	complemented
71	C₁₃×#461	C₂²	1	4	yes	—
72	C₁₃×#461	C₂²	1	4	yes	complemented
73	C₁₃×#460	C₂²	1	4	yes	—
74	C₁₃×#446	C₂²	1	4	yes	complemented
75	C₁₃×#446	C₂²	1	4	yes	complemented
76	C₁₃×#442	C₂²	1	2	yes	complemented
77	C₁₃×#441	C₂²	1	2	yes	complemented
78	C₁₃×#441	C₂²	1	4	yes	complemented
79	C₁₃×#440	C₂²	1	4	yes	—
80	C₁₃×#440	C₂²	1	2	yes	complemented
81	C₁₃×#440	C₂²	1	2	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
84	C₁₃×#427	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	1	yes	characteristic
86	C₁₃×#424	C₂²	1	1	yes	characteristic
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#419	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	1	yes	characteristic
90	C₁₃×#419	C₂²	1	1	yes	characteristic
91	C₁₃×#418	C₂²	1	1	yes	characteristic
92	C₁₃×#416	C₂²	1	1	yes	characteristic
93	C₁₃×#416	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	1	yes	characteristic
95	C₁₃×#405	C₂²	1	1	yes	characteristic
96	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#137	—	4	2	no	—
104	C₁₃×#137	—	4	2	no	—
105	C₁₃×#137	—	4	2	no	—
106	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
107	C₁₃×#135	—	2	4	no	—
108	C₂×C₁₃×Q₁₆	—	2	4	no	—
109	C₂×C₁₃×Q₁₆	—	4	2	no	—
110	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	—	2	4	no	—
118	C₂×C₁₃×SD₁₆	—	4	2	no	—
119	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×C₄⋊Q₈	—	2	1	no	—
135	C₁₃×C₄⋊Q₈	—	2	1	no	—
136	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×#127	C₂³	1	2	yes	—
142	C₁₃×#126	—	2	4	no	—
143	C₁₃×#126	—	2	4	no	—
144	C₁₃×#126	—	2	4	no	—
145	C₁₃×#126	—	2	4	no	—
146	C₁₃×#125	—	2	4	no	—
147	C₁₃×#125	—	2	4	no	—
148	C₁₃×#125	—	2	4	no	—
149	C₁₃×#125	D₄	1	2	yes	—
150	C₁₃×#124	—	2	4	no	—
151	C₁₃×#124	—	2	1	no	—
152	C₁₃×#124	—	2	1	no	—
153	C₁₃×#124	C₂³	1	2	yes	—
154	C₁₃×#124	C₂³	1	4	yes	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#124	C₂³	1	2	yes	—
158	C₁₃×#123	—	2	4	no	—
159	C₁₃×#123	—	2	4	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	4	no	—
164	C₁₃×C₂²⋊Q₈	—	2	4	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#120	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	4	no	—
172	C₄×Q₈×C₁₃	—	2	2	no	—
173	C₄×Q₈×C₁₃	—	2	2	no	—
174	C₄×Q₈×C₁₃	—	2	2	no	—
175	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	4	no	—
185	C₄×D₄×C₁₃	C₂³	1	4	yes	—
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₁₃×#117	—	2	4	no	—
189	C₁₃×#117	—	2	4	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	1	yes	characteristic
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²×C₁₃	—	2	1	no	—
203	C₂×C₄²×C₁₃	—	2	1	no	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₁₃×#107	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#97	C₂³	1	2	yes	—
219	C₁₃×#97	C₂³	1	2	yes	—
220	C₁₃×#97	C₂³	1	2	yes	—
221	C₁₃×#97	C₂³	1	2	yes	—
222	C₄×C₈×C₁₃	C₂³	1	2	yes	—
223	C₄×C₈×C₁₃	C₂³	1	2	yes	—
224	#61418	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂⁴×C₁₃	—	2	1	no	—
226	C₁₃×#41	—	2	2	no	—
227	C₁₃×#41	—	2	2	no	—
228	C₁₃×#41	—	2	2	no	—
229	C₁₃×#41	—	2	2	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×Q₁₆	—	2	4	no	—
265	C₁₃×Q₁₆	—	2	4	no	—
266	C₁₃×Q₁₆	—	2	2	no	—
267	C₁₃×Q₁₆	—	4	4	no	—
268	C₁₃×Q₁₆	—	4	2	no	—
269	C₁₃×Q₁₆	—	4	2	no	—
270	C₁₃×Q₁₆	—	4	2	no	—
271	C₁₃×SD₁₆	—	2	4	no	—
272	C₁₃×SD₁₆	—	2	4	no	—
273	C₁₃×SD₁₆	—	2	2	no	—
274	C₁₃×SD₁₆	—	2	2	no	—
275	C₁₃×SD₁₆	—	4	4	no	—
276	C₁₃×SD₁₆	—	4	2	no	—
277	C₁₃×SD₁₆	—	4	2	no	—
278	C₁₃×SD₁₆	—	4	2	no	—
279	C₁₃×SD₁₆	—	4	2	no	—
280	C₁₃×D₈	—	2	2	no	—
281	C₁₃×D₈	—	4	2	no	—
282	C₁₃×M₁₆	—	2	2	no	—
283	C₁₃×M₁₆	—	2	2	no	—
284	C₂×C₈×C₁₃	—	2	2	no	—
285	C₂×C₈×C₁₃	#41	1	4	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
289	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	1	no	—
323	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂⁴	1	2	yes	—
331	C₄²×C₁₃	C₂⁴	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	2	yes	—
333	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#3402	C₂×C₁₃	1	4	yes	complemented
336	#3401	C₂×C₁₃	1	4	yes	complemented
337	#3400	C₂×C₁₃	1	4	yes	complemented
338	#3398	C₂×C₁₃	1	4	yes	complemented
339	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3154	C₂×C₁₃	1	1	yes	characteristic
341	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3043	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3042	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#2949	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	—	4	2	no	—
356	C₂³×C₁₃	—	8	2	no	—
357	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	1	no	—
360	Q₈×C₁₃	—	2	1	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	4	4	no	—
369	Q₈×C₁₃	—	4	2	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	D₄×C₁₃	—	2	1	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	1	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	4	2	no	—
381	D₄×C₁₃	—	8	4	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	2	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	8	2	no	—
397	C₂×C₄×C₁₃	—	8	4	no	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
404	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₁₃	—	2	2	no	—
407	C₈×C₁₃	—	2	2	no	—
408	C₈×C₁₃	—	2	2	no	—
409	C₈×C₁₃	C₂×#41	1	2	yes	—
410	C₈×C₁₃	C₂×#41	1	2	yes	—
411	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
420	#559	C₂²×C₁₃	1	4	yes	—
421	#557	C₂²×C₁₃	1	4	yes	complemented
422	#556	C₂²×C₁₃	1	4	yes	—
423	#556	C₂²×C₁₃	1	4	yes	complemented
424	#552	—	2	4	no	—
425	#551	—	2	4	no	—
426	#542	—	2	2	no	—
427	#541	—	2	2	no	—
428	#536	C₂²×C₁₃	1	1	yes	characteristic
429	#536	C₂²×C₁₃	1	1	yes	characteristic
430	#536	C₂²×C₁₃	1	1	yes	characteristic
431	#535	C₂²×C₁₃	1	1	yes	characteristic
432	#533	—	2	2	no	—
433	#533	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	#529	—	2	2	no	—
436	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
437	#519	C₂²×C₁₃	1	1	yes	characteristic
438	#519	C₂²×C₁₃	1	1	yes	characteristic
439	#519	C₂²×C₁₃	1	1	yes	characteristic
440	#518	C₂²×C₁₃	1	1	yes	characteristic
441	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
442	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
443	#497	C₂²×C₁₃	1	2	yes	—
444	#497	C₂²×C₁₃	1	4	yes	—
445	#497	C₂²×C₁₃	1	4	yes	—
446	#497	C₂²×C₁₃	1	2	yes	complemented
447	#497	C₂²×C₁₃	1	2	yes	complemented
448	#496	C₂²×C₁₃	1	2	yes	—
449	#495	C₂²×C₁₃	1	2	yes	—
450	#495	C₂²×C₁₃	1	2	yes	complemented
451	#494	C₂²×C₁₃	1	2	yes	complemented
452	#492	C₂²×C₁₃	1	2	yes	—
453	#464	C₂²×C₁₃	1	4	yes	—
454	#464	C₂²×C₁₃	1	4	yes	—
455	#464	C₂²×C₁₃	1	4	yes	complemented
456	#464	C₂²×C₁₃	1	4	yes	complemented
457	#463	C₂²×C₁₃	1	4	yes	—
458	#463	C₂²×C₁₃	1	4	yes	—
459	#462	C₂²×C₁₃	1	4	yes	complemented
460	#462	C₂²×C₁₃	1	4	yes	complemented
461	#462	C₂²×C₁₃	1	4	yes	complemented
462	#461	C₂²×C₁₃	1	4	yes	—
463	#461	C₂²×C₁₃	1	4	yes	complemented
464	#460	C₂²×C₁₃	1	4	yes	—
465	#446	C₂²×C₁₃	1	4	yes	complemented
466	#446	C₂²×C₁₃	1	4	yes	complemented
467	#442	C₂²×C₁₃	1	2	yes	complemented
468	#441	C₂²×C₁₃	1	2	yes	complemented
469	#441	C₂²×C₁₃	1	4	yes	complemented
470	#440	C₂²×C₁₃	1	4	yes	—
471	#440	C₂²×C₁₃	1	2	yes	complemented
472	#440	C₂²×C₁₃	1	2	yes	complemented
473	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
474	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
475	#427	C₂²×C₁₃	1	1	yes	characteristic
476	#424	C₂²×C₁₃	1	1	yes	characteristic
477	#424	C₂²×C₁₃	1	1	yes	characteristic
478	#423	C₂²×C₁₃	1	1	yes	characteristic
479	#419	C₂²×C₁₃	1	1	yes	characteristic
480	#419	C₂²×C₁₃	1	1	yes	characteristic
481	#419	C₂²×C₁₃	1	1	yes	characteristic
482	#418	C₂²×C₁₃	1	1	yes	characteristic
483	#416	C₂²×C₁₃	1	1	yes	characteristic
484	#416	C₂²×C₁₃	1	1	yes	characteristic
485	#405	C₂²×C₁₃	1	1	yes	characteristic
486	#405	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	16	2	no	—
496	C₂²×C₁₃	#550	1	2	yes	—
497	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	2	no	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	4	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	1	no	—
505	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	#550	1	2	yes	—
510	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
511	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
518	#137	—	4	2	no	—
519	#137	—	4	2	no	—
520	#137	—	4	2	no	—
521	AGL(1,ℤ/8)	—	4	2	no	—
522	#135	—	2	4	no	—
523	C₂×Q₁₆	—	2	4	no	—
524	C₂×Q₁₆	—	4	2	no	—
525	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
526	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
527	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
530	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	—	2	4	no	—
533	C₂×SD₁₆	—	4	2	no	—
534	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
542	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×D₈	C₂³×C₁₃	1	2	yes	—
545	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	#127	C₂³×C₁₃	1	2	yes	—
557	#126	—	2	4	no	—
558	#126	—	2	4	no	—
559	#126	—	2	4	no	—
560	#126	—	2	4	no	—
561	#125	—	2	4	no	—
562	#125	—	2	4	no	—
563	#125	—	2	4	no	—
564	#125	D₄×C₁₃	1	2	yes	—
565	#124	—	2	4	no	—
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	C₂³×C₁₃	1	4	yes	—
569	#124	C₂³×C₁₃	1	2	yes	—
570	#124	C₂³×C₁₃	1	2	yes	—
571	#124	C₂³×C₁₃	1	2	yes	—
572	#124	C₂³×C₁₃	1	2	yes	—
573	#123	—	2	4	no	—
574	#123	—	2	4	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
584	#121	—	2	2	no	—
585	#120	—	2	2	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	C₂³×C₁₃	1	2	yes	—
601	C₄×D₄	C₂³×C₁₃	1	2	yes	—
602	C₄×D₄	C₂³×C₁₃	1	4	yes	—
603	#117	—	2	4	no	—
604	#117	—	2	4	no	—
605	#117	—	2	2	no	—
606	#117	—	2	2	no	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	#117	C₂³×C₁₃	1	1	yes	characteristic
611	#117	C₂³×C₁₃	1	1	yes	characteristic
612	#117	C₂³×C₁₃	1	1	yes	characteristic
613	#117	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₂²⋊C₄	—	2	2	no	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	—	2	1	no	—
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	#107	C₂³×C₁₃	1	2	yes	—
621	#106	C₂³×C₁₃	1	2	yes	—
622	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
623	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
624	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
625	#103	C₂³×C₁₃	1	2	yes	—
626	#103	C₂³×C₁₃	1	2	yes	—
627	#103	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#103	C₂³×C₁₃	1	4	yes	—
630	#102	C₂³×C₁₃	1	2	yes	—
631	#102	C₂³×C₁₃	1	2	yes	—
632	#102	C₂³×C₁₃	1	4	yes	—
633	#97	C₂³×C₁₃	1	2	yes	—
634	#97	C₂³×C₁₃	1	2	yes	—
635	#97	C₂³×C₁₃	1	2	yes	—
636	#97	C₂³×C₁₃	1	2	yes	—
637	C₄×C₈	C₂³×C₁₃	1	2	yes	—
638	C₄×C₈	C₂³×C₁₃	1	2	yes	—
639	C₂×C₁₃	—	2	2	no	—
640	C₂×C₁₃	—	8	1	no	—
641	C₂×C₁₃	—	8	1	no	—
642	C₂×C₁₃	—	8	2	no	—
643	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
644	C₂×C₁₃	#3586	1	2	yes	—
645	C₂⁴	—	2	1	no	—
646	#41	—	2	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	2	no	—
649	#41	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
660	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
663	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	Q₁₆	—	2	4	no	—
685	Q₁₆	—	2	4	no	—
686	Q₁₆	—	2	2	no	—
687	Q₁₆	—	4	4	no	—
688	Q₁₆	—	4	2	no	—
689	Q₁₆	—	4	2	no	—
690	Q₁₆	—	4	2	no	—
691	SD₁₆	—	2	4	no	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	2	2	no	—
694	SD₁₆	—	2	2	no	—
695	SD₁₆	—	4	4	no	—
696	SD₁₆	—	4	2	no	—
697	SD₁₆	—	4	2	no	—
698	SD₁₆	—	4	2	no	—
699	SD₁₆	—	4	2	no	—
700	D₈	—	2	2	no	—
701	D₈	—	4	2	no	—
702	M₁₆	—	2	2	no	—
703	M₁₆	—	2	2	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	C₁₃×#41	1	4	yes	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
723	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₁₃	1	2	yes	—
751	C₄²	C₂⁴×C₁₃	1	2	yes	—
752	C₄²	C₂⁴×C₁₃	1	2	yes	—
753	C₁₃	#61418	1	1	yes	characteristic, direct product factor, Sylow
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	8	2	no	—
759	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	1	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	1	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	1	no	—
770	Q₈	—	4	4	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	2	no	—
774	D₄	—	2	1	no	—
775	D₄	—	2	1	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	1	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	2	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
801	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
806	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
807	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	2	no	—
811	C₈	C₂×C₁₃×#41	1	2	yes	—
812	C₈	C₂×C₁₃×#41	1	2	yes	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	16	2	no	—
821	C₂²	C₁₃×#550	1	2	yes	—
822	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	C₁₃×#550	1	2	yes	—
835	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
836	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂	—	2	2	no	—
838	C₂	—	8	2	no	—
839	C₂	—	8	1	no	—
840	C₂	—	8	1	no	—
841	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
842	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3154	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3400	C₂	semidirect
6. C₁₃×#3398	C₂	semidirect
7. C₁₃×#3156	C₂	semidirect
9. C₂×C₁₃×#497	C₂	semidirect
10. C₁₃×#3044	C₂	semidirect
11. C₁₃×#3044	C₂	semidirect
12. C₁₃×#3043	C₂	semidirect
13. C₁₃×#3042	C₂	semidirect
14. C₁₃×#3040	C₂	semidirect
15. C₁₃×#3039	C₂	semidirect
16. C₁₃×#2961	C₂	semidirect
17. C₁₃×#2950	C₂	semidirect
18. C₁₃×#2949	C₂	semidirect
19. C₁₃×#2943	C₂	semidirect
30. C₁₃×#557	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
55. C₁₃×#497	C₂²	semidirect
56. C₁₃×#497	C₂²	semidirect
59. C₁₃×#495	C₂²	semidirect
60. C₁₃×#494	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#462	C₂²	semidirect
72. C₁₃×#461	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#442	C₂²	semidirect
77. C₁₃×#441	C₂²	semidirect
78. C₁₃×#441	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₁₃×#440	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
224. #61418	C₁₃	direct (N × H)
333. #3510	C₂×C₁₃	semidirect
334. #3509	C₂×C₁₃	semidirect
335. #3402	C₂×C₁₃	semidirect
336. #3401	C₂×C₁₃	semidirect
337. #3400	C₂×C₁₃	semidirect
338. #3398	C₂×C₁₃	semidirect
339. #3156	C₂×C₁₃	semidirect
341. C₂×#497	C₂×C₁₃	semidirect
342. #3044	C₂×C₁₃	semidirect
343. #3044	C₂×C₁₃	semidirect
344. #3043	C₂×C₁₃	semidirect
345. #3042	C₂×C₁₃	semidirect
346. #3040	C₂×C₁₃	semidirect
347. #3039	C₂×C₁₃	semidirect
348. #2961	C₂×C₁₃	semidirect
349. #2950	C₂×C₁₃	semidirect
350. #2949	C₂×C₁₃	semidirect
351. #2943	C₂×C₁₃	semidirect
421. #557	C₂²×C₁₃	semidirect
423. #556	C₂²×C₁₃	semidirect
446. #497	C₂²×C₁₃	semidirect
447. #497	C₂²×C₁₃	semidirect
450. #495	C₂²×C₁₃	semidirect
451. #494	C₂²×C₁₃	semidirect
455. #464	C₂²×C₁₃	semidirect
456. #464	C₂²×C₁₃	semidirect
459. #462	C₂²×C₁₃	semidirect
460. #462	C₂²×C₁₃	semidirect
461. #462	C₂²×C₁₃	semidirect
463. #461	C₂²×C₁₃	semidirect
465. #446	C₂²×C₁₃	semidirect
466. #446	C₂²×C₁₃	semidirect
467. #442	C₂²×C₁₃	semidirect
468. #441	C₂²×C₁₃	semidirect
469. #441	C₂²×C₁₃	semidirect
471. #440	C₂²×C₁₃	semidirect
472. #440	C₂²×C₁₃	semidirect
473. C₄×Q₁₆	C₂²×C₁₃	semidirect
753. C₁₃	#61418	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×#3510	2
C₁₃×#3509	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3156	2
C₁₃×#3154	2
C₂×C₁₃×#497	2
C₁₃×#3044	2
C₁₃×#3043	2
C₁₃×#3042	2
C₁₃×#3040	2
C₁₃×#3039	2
C₁₃×#2961	2
C₁₃×#2950	2
C₁₃×#2949	2
C₁₃×#2943	2
#61418	13

Subgroups — C13×#61418 #15747757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61418 #15747757