Subgroups — C₁₃×#61403 #15747742

Order 3328.

1932 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	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×#3398	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#559	C₂²	1	2	yes	complemented
25	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	—	2	1	no	—
28	C₁₃×#556	—	2	2	no	—
29	C₁₃×#556	C₂²	1	2	yes	—
30	C₁₃×#556	C₂²	1	2	yes	—
31	C₁₃×#556	C₂²	1	4	yes	—
32	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#556	C₂²	1	2	yes	complemented
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#553	—	2	2	no	—
36	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#548	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	1	no	—
42	C₁₃×#529	—	2	2	no	—
43	C₂×C₁₃×#126	—	2	2	no	—
44	C₂×C₁₃×#124	C₂²	1	2	yes	—
45	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#117	—	2	1	no	—
53	C₁₃×#497	C₂²	1	4	yes	—
54	C₁₃×#497	C₂²	1	4	yes	complemented
55	C₁₃×#496	C₂²	1	4	yes	—
56	C₁₃×#495	C₂²	1	4	yes	—
57	C₁₃×#495	C₂²	1	4	yes	—
58	C₁₃×#494	C₂²	1	2	yes	complemented
59	C₁₃×#492	C₂²	1	2	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	—
61	C₁₃×#464	C₂²	1	4	yes	—
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	—
65	C₁₃×#463	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	4	yes	complemented
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#462	C₂²	1	2	yes	complemented
70	C₁₃×#461	C₂²	1	2	yes	—
71	C₁₃×#461	C₂²	1	2	yes	complemented
72	C₁₃×#461	C₂²	1	2	yes	complemented
73	C₁₃×#460	C₂²	1	4	yes	complemented
74	C₁₃×#459	C₂²	1	2	yes	—
75	C₁₃×#446	C₂²	1	2	yes	complemented
76	C₁₃×#446	C₂²	1	4	yes	complemented
77	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
78	C₁₃×#442	C₂²	1	2	yes	—
79	C₁₃×#441	C₂²	1	4	yes	complemented
80	C₁₃×#440	C₂²	1	2	yes	—
81	C₁₃×#440	C₂²	1	4	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	2	yes	—
86	C₁₃×#428	C₂²	1	1	yes	characteristic
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	—
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#418	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₁₃×#137	—	2	8	no	—
103	C₁₃×#137	—	4	4	no	—
104	C₁₃×#137	—	4	4	no	—
105	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
106	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
107	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×D₈	C₂³	1	2	yes	—
116	C₂×C₁₃×D₈	C₂³	1	4	yes	—
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	—	2	1	no	—
121	C₁₃×C₄⋊Q₈	—	2	1	no	—
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×#127	C₂³	1	1	yes	characteristic
127	C₁₃×#127	C₂³	1	2	yes	—
128	C₁₃×#126	—	2	4	no	—
129	C₁₃×#126	—	2	4	no	—
130	C₁₃×#126	—	2	4	no	—
131	C₁₃×#126	—	2	4	no	—
132	C₁₃×#126	—	2	2	no	—
133	C₁₃×#126	—	2	2	no	—
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#125	—	2	1	no	—
136	C₁₃×#125	—	2	2	no	—
137	C₁₃×#124	—	2	1	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	C₂³	1	2	yes	—
142	C₁₃×#124	C₂³	1	4	yes	—
143	C₁₃×#124	C₂³	1	4	yes	—
144	C₁₃×#124	C₂³	1	2	yes	—
145	C₁₃×#124	C₂³	1	2	yes	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	4	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	D₄	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	1	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	4	no	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	—	2	1	no	—
199	C₁₃×#117	—	2	2	no	—
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
205	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²×C₁₃	—	2	2	no	—
211	C₂×C₄²×C₁₃	—	2	1	no	—
212	C₂×C₄²×C₁₃	—	2	2	no	—
213	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×#107	C₂³	1	2	yes	—
216	C₁₃×#106	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#97	C₂³	1	2	yes	—
230	C₁₃×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₁₃	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	4	yes	—
233	#61403	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	1	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	4	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	4	4	no	—
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₁₃×Q₁₆	—	2	8	no	—
279	C₁₃×Q₁₆	—	4	4	no	—
280	C₁₃×Q₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	—	2	4	no	—
282	C₁₃×SD₁₆	—	2	8	no	—
283	C₁₃×SD₁₆	—	4	4	no	—
284	C₁₃×SD₁₆	—	4	4	no	—
285	C₁₃×SD₁₆	—	4	4	no	—
286	C₁₃×D₈	—	2	4	no	—
287	C₁₃×D₈	—	4	4	no	—
288	C₁₃×M₁₆	—	2	4	no	—
289	C₁₃×M₁₆	—	2	2	no	—
290	C₁₃×M₁₆	#41	1	4	yes	complemented
291	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
293	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	1	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	1	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₄²×C₁₃	—	2	1	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	4	no	—
340	C₄²×C₁₃	—	2	4	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	1	no	—
343	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₁₃	C₂×D₄	1	2	yes	—
345	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₁₃	C₂×D₄	1	2	yes	—
347	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	2	yes	—
349	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₁₃	C₂⁴	1	2	yes	—
351	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3402	C₂×C₁₃	1	4	yes	complemented
354	#3401	C₂×C₁₃	1	4	yes	complemented
355	#3398	C₂×C₁₃	1	2	yes	complemented
356	#3397	C₂×C₁₃	1	2	yes	complemented
357	#3394	C₂×C₁₃	1	2	yes	complemented
358	#3393	C₂×C₁₃	1	2	yes	complemented
359	#3153	C₂×C₁₃	1	2	yes	complemented
360	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3040	C₂×C₁₃	1	2	yes	complemented
362	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3037	C₂×C₁₃	1	2	yes	complemented
364	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
365	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₄×#137	C₂×C₁₃	1	2	yes	complemented
367	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	1	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	4	2	no	—
374	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	1	no	—
378	Q₈×C₁₃	—	2	4	no	—
379	Q₈×C₁₃	—	2	2	no	—
380	Q₈×C₁₃	—	2	4	no	—
381	Q₈×C₁₃	—	2	2	no	—
382	Q₈×C₁₃	—	2	1	no	—
383	Q₈×C₁₃	—	4	2	no	—
384	Q₈×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	2	1	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	2	no	—
390	D₄×C₁₃	—	2	1	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	2	no	—
396	D₄×C₁₃	—	8	2	no	—
397	D₄×C₁₃	—	8	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	4	4	no	—
410	C₂×C₄×C₁₃	—	4	2	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	4	4	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	8	1	no	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
428	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
430	C₈×C₁₃	—	2	4	no	—
431	C₈×C₁₃	—	2	2	no	—
432	C₈×C₁₃	C₂×#41	1	4	yes	—
433	C₂×#137	C₂²×C₁₃	1	2	yes	—
434	C₂×#137	C₂²×C₁₃	1	2	yes	—
435	C₂×#137	C₂²×C₁₃	1	2	yes	—
436	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
438	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#559	C₂²×C₁₃	1	2	yes	complemented
440	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#556	—	2	1	no	—
442	#556	—	2	1	no	—
443	#556	—	2	2	no	—
444	#556	C₂²×C₁₃	1	2	yes	—
445	#556	C₂²×C₁₃	1	2	yes	—
446	#556	C₂²×C₁₃	1	4	yes	—
447	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#556	C₂²×C₁₃	1	2	yes	complemented
449	#553	—	2	1	no	—
450	#553	—	2	2	no	—
451	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#548	—	2	1	no	—
453	#532	C₂²×C₁₃	1	1	yes	characteristic
454	#532	C₂²×C₁₃	1	2	yes	—
455	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	#529	—	2	1	no	—
457	#529	—	2	2	no	—
458	C₂×#126	—	2	2	no	—
459	C₂×#124	C₂²×C₁₃	1	2	yes	—
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₄×#41	—	2	1	no	—
462	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
463	C₄×#41	C₂²×C₁₃	1	2	yes	—
464	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
465	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×#117	—	2	1	no	—
468	#497	C₂²×C₁₃	1	4	yes	—
469	#497	C₂²×C₁₃	1	4	yes	complemented
470	#496	C₂²×C₁₃	1	4	yes	—
471	#495	C₂²×C₁₃	1	4	yes	—
472	#495	C₂²×C₁₃	1	4	yes	—
473	#494	C₂²×C₁₃	1	2	yes	complemented
474	#492	C₂²×C₁₃	1	2	yes	complemented
475	#464	C₂²×C₁₃	1	4	yes	—
476	#464	C₂²×C₁₃	1	4	yes	—
477	#464	C₂²×C₁₃	1	4	yes	complemented
478	#464	C₂²×C₁₃	1	4	yes	complemented
479	#463	C₂²×C₁₃	1	4	yes	—
480	#463	C₂²×C₁₃	1	4	yes	—
481	#463	C₂²×C₁₃	1	4	yes	—
482	#462	C₂²×C₁₃	1	2	yes	complemented
483	#462	C₂²×C₁₃	1	4	yes	complemented
484	#462	C₂²×C₁₃	1	2	yes	complemented
485	#461	C₂²×C₁₃	1	2	yes	—
486	#461	C₂²×C₁₃	1	2	yes	complemented
487	#461	C₂²×C₁₃	1	2	yes	complemented
488	#460	C₂²×C₁₃	1	4	yes	complemented
489	#459	C₂²×C₁₃	1	2	yes	—
490	#446	C₂²×C₁₃	1	2	yes	complemented
491	#446	C₂²×C₁₃	1	4	yes	complemented
492	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
493	#442	C₂²×C₁₃	1	2	yes	—
494	#441	C₂²×C₁₃	1	4	yes	complemented
495	#440	C₂²×C₁₃	1	2	yes	—
496	#440	C₂²×C₁₃	1	4	yes	complemented
497	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
498	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
499	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
500	C₄×D₈	C₂²×C₁₃	1	2	yes	—
501	#428	C₂²×C₁₃	1	1	yes	characteristic
502	#423	C₂²×C₁₃	1	1	yes	characteristic
503	#423	C₂²×C₁₃	1	2	yes	—
504	#419	C₂²×C₁₃	1	2	yes	—
505	#418	C₂²×C₁₃	1	1	yes	characteristic
506	#417	C₂²×C₁₃	1	1	yes	characteristic
507	#417	C₂²×C₁₃	1	2	yes	—
508	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
509	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	1	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	8	4	no	—
522	C₂²×C₁₃	#550	1	2	yes	—
523	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	1	no	—
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	4	no	—
535	C₄×C₁₃	—	4	1	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	#550	1	2	yes	—
538	C₄×C₁₃	#575	1	2	yes	—
539	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
540	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂×#41	—	2	1	no	—
542	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×#41	C₂³×C₁₃	1	2	yes	—
544	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	—	2	1	no	—
548	#137	—	2	8	no	—
549	#137	—	4	4	no	—
550	#137	—	4	4	no	—
551	AGL(1,ℤ/8)	—	2	4	no	—
552	AGL(1,ℤ/8)	—	4	4	no	—
553	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
554	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
555	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
559	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
560	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
561	C₂×D₈	C₂³×C₁₃	1	2	yes	—
562	C₂×D₈	C₂³×C₁₃	1	4	yes	—
563	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
564	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	—	2	1	no	—
568	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
572	#127	C₂³×C₁₃	1	1	yes	characteristic
573	#127	C₂³×C₁₃	1	2	yes	—
574	#126	—	2	4	no	—
575	#126	—	2	4	no	—
576	#126	—	2	4	no	—
577	#126	—	2	4	no	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#125	—	2	1	no	—
582	#125	—	2	2	no	—
583	#124	—	2	1	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#124	C₂³×C₁₃	1	4	yes	—
588	#124	C₂³×C₁₃	1	4	yes	—
589	#124	C₂³×C₁₃	1	2	yes	—
590	#124	C₂³×C₁₃	1	2	yes	—
591	#124	C₂³×C₁₃	1	2	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	2	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
610	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
611	C₄×Q₈	D₄×C₁₃	1	2	yes	—
612	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
613	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
614	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
615	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
618	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	C₂³×C₁₃	1	2	yes	—
634	C₄×D₄	C₂³×C₁₃	1	2	yes	—
635	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₁₃	1	2	yes	—
637	C₄×D₄	C₂³×C₁₃	1	2	yes	—
638	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	4	no	—
642	#117	—	2	1	no	—
643	#117	—	2	2	no	—
644	#117	—	2	1	no	—
645	#117	—	2	2	no	—
646	#117	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	2	no	—
656	C₂×C₄²	—	2	2	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	2	no	—
659	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	#107	C₂³×C₁₃	1	2	yes	—
662	#106	C₂³×C₁₃	1	2	yes	—
663	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
664	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
665	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	#103	C₂³×C₁₃	1	2	yes	—
668	#103	C₂³×C₁₃	1	4	yes	—
669	#103	C₂³×C₁₃	1	4	yes	—
670	#103	C₂³×C₁₃	1	4	yes	—
671	#102	C₂³×C₁₃	1	2	yes	—
672	#102	C₂³×C₁₃	1	4	yes	—
673	#102	C₂³×C₁₃	1	2	yes	—
674	#102	C₂³×C₁₃	1	2	yes	—
675	#97	C₂³×C₁₃	1	2	yes	—
676	#97	C₂³×C₁₃	1	4	yes	—
677	C₄×C₈	C₂³×C₁₃	1	2	yes	—
678	C₄×C₈	C₂³×C₁₃	1	4	yes	—
679	C₂×C₁₃	—	2	2	no	—
680	C₂×C₁₃	—	8	1	no	—
681	C₂×C₁₃	—	8	2	no	—
682	C₂×C₁₃	—	8	2	no	—
683	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
684	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
685	C₂×C₁₃	#3586	1	1	yes	characteristic
686	C₂⁴	—	2	1	no	—
687	#41	—	2	2	no	—
688	#41	—	2	4	no	—
689	#41	—	2	4	no	—
690	#41	—	2	2	no	—
691	#41	—	4	4	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	Q₁₆	—	2	8	no	—
731	Q₁₆	—	4	4	no	—
732	Q₁₆	—	4	4	no	—
733	SD₁₆	—	2	4	no	—
734	SD₁₆	—	2	8	no	—
735	SD₁₆	—	4	4	no	—
736	SD₁₆	—	4	4	no	—
737	SD₁₆	—	4	4	no	—
738	D₈	—	2	4	no	—
739	D₈	—	4	4	no	—
740	M₁₆	—	2	4	no	—
741	M₁₆	—	2	2	no	—
742	M₁₆	C₁₃×#41	1	4	yes	complemented
743	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
744	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
745	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	1	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	1	no	—
795	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₄²	C₂×D₄×C₁₃	1	2	yes	—
797	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₄²	C₂×D₄×C₁₃	1	2	yes	—
799	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₄²	C₂⁴×C₁₃	1	2	yes	—
801	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄²	C₂⁴×C₁₃	1	2	yes	—
803	C₁₃	#61403	1	1	yes	characteristic, direct product factor, Sylow
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
811	Q₈	—	2	2	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	2	4	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	2	1	no	—
819	Q₈	—	4	2	no	—
820	Q₈	—	4	4	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	1	no	—
827	D₄	—	4	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	2	no	—
833	D₄	—	8	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
864	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
865	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
866	C₈	—	2	4	no	—
867	C₈	—	2	2	no	—
868	C₈	C₂×C₁₃×#41	1	4	yes	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	8	4	no	—
881	C₂²	C₁₃×#550	1	2	yes	—
882	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	4	no	—
896	C₄	C₁₃×#550	1	2	yes	—
897	C₄	C₁₃×#575	1	2	yes	—
898	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
899	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
900	C₂	—	2	2	no	—
901	C₂	—	8	2	no	—
902	C₂	—	8	2	no	—
903	C₂	—	8	1	no	—
904	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
905	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
906	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3398	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3394	C₂	semidirect
8. C₁₃×#3393	C₂	semidirect
9. C₁₃×#3153	C₂	semidirect
10. C₁₃×#3152	C₂	semidirect
11. C₁₃×#3040	C₂	semidirect
12. C₁₃×#3039	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#559	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
54. C₁₃×#497	C₂²	semidirect
58. C₁₃×#494	C₂²	semidirect
59. C₁₃×#492	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
71. C₁₃×#461	C₂²	semidirect
72. C₁₃×#461	C₂²	semidirect
73. C₁₃×#460	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#446	C₂²	semidirect
77. C₈×Q₈×C₁₃	C₂²	semidirect
79. C₁₃×#441	C₂²	semidirect
81. C₁₃×#440	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
233. #61403	C₁₃	direct (N × H)
290. C₁₃×M₁₆	#41	semidirect
351. #3480	C₂×C₁₃	semidirect
352. C₂×#556	C₂×C₁₃	semidirect
353. #3402	C₂×C₁₃	semidirect
354. #3401	C₂×C₁₃	semidirect
355. #3398	C₂×C₁₃	semidirect
356. #3397	C₂×C₁₃	semidirect
357. #3394	C₂×C₁₃	semidirect
358. #3393	C₂×C₁₃	semidirect
359. #3153	C₂×C₁₃	semidirect
360. #3152	C₂×C₁₃	semidirect
361. #3040	C₂×C₁₃	semidirect
362. #3039	C₂×C₁₃	semidirect
363. #3037	C₂×C₁₃	semidirect
364. #3036	C₂×C₁₃	semidirect
365. Q₈×M₁₆	C₂×C₁₃	semidirect
366. C₄×#137	C₂×C₁₃	semidirect
367. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
438. #559	C₂²×C₁₃	semidirect
439. #559	C₂²×C₁₃	semidirect
440. #557	C₂²×C₁₃	semidirect
447. #556	C₂²×C₁₃	semidirect
448. #556	C₂²×C₁₃	semidirect
451. #550	C₂²×C₁₃	semidirect
469. #497	C₂²×C₁₃	semidirect
473. #494	C₂²×C₁₃	semidirect
474. #492	C₂²×C₁₃	semidirect
477. #464	C₂²×C₁₃	semidirect
478. #464	C₂²×C₁₃	semidirect
482. #462	C₂²×C₁₃	semidirect
483. #462	C₂²×C₁₃	semidirect
484. #462	C₂²×C₁₃	semidirect
486. #461	C₂²×C₁₃	semidirect
487. #461	C₂²×C₁₃	semidirect
488. #460	C₂²×C₁₃	semidirect
490. #446	C₂²×C₁₃	semidirect
491. #446	C₂²×C₁₃	semidirect
492. C₈×Q₈	C₂²×C₁₃	semidirect
494. #441	C₂²×C₁₃	semidirect
496. #440	C₂²×C₁₃	semidirect
497. C₄×Q₁₆	C₂²×C₁₃	semidirect
499. C₄×SD₁₆	C₂²×C₁₃	semidirect
742. M₁₆	C₁₃×#41	semidirect
803. C₁₃	#61403	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×#3480	2
C₂×C₁₃×#556	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3398	2
C₁₃×#3397	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3153	2
C₁₃×#3152	2
C₁₃×#3040	2
C₁₃×#3039	2
C₁₃×#3037	2
C₁₃×#3036	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61403	13

Subgroups — C13×#61403 #15747742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61403 #15747742