Subgroups — C₁₃×#61419 #15747758

Order 3328.

2028 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3399	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	complemented
24	C₁₃×#559	C₂²	1	4	yes	complemented
25	C₁₃×#559	C₂²	1	2	yes	complemented
26	C₁₃×#556	C₂²	1	2	yes	complemented
27	C₁₃×#555	—	2	1	no	—
28	C₁₃×#553	—	2	2	no	—
29	C₁₃×#550	C₂²	1	2	yes	complemented
30	C₁₃×#550	C₂²	1	2	yes	complemented
31	C₁₃×#550	C₂²	1	2	yes	complemented
32	C₁₃×#547	—	2	1	no	—
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	—	2	2	no	—
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#538	—	2	2	no	—
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	—	2	1	no	—
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#525	—	2	2	no	—
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#518	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#496	C₂²	1	4	yes	complemented
50	C₁₃×#496	C₂²	1	4	yes	complemented
51	C₁₃×#496	C₂²	1	4	yes	complemented
52	C₁₃×#495	C₂²	1	4	yes	complemented
53	C₁₃×#493	C₂²	1	2	yes	complemented
54	C₁₃×#493	C₂²	1	4	yes	complemented
55	C₁₃×#492	C₂²	1	2	yes	complemented
56	C₁₃×#464	C₂²	1	2	yes	complemented
57	C₁₃×#464	C₂²	1	4	yes	complemented
58	C₁₃×#463	C₂²	1	2	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#463	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#460	C₂²	1	4	yes	complemented
66	C₁₃×#459	C₂²	1	2	yes	—
67	C₁₃×#459	C₂²	1	2	yes	—
68	C₁₃×#459	C₂²	1	4	yes	—
69	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#459	C₂²	1	4	yes	complemented
71	C₁₃×#459	C₂²	1	4	yes	complemented
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#446	C₂²	1	2	yes	complemented
74	C₁₃×#446	C₂²	1	4	yes	complemented
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
76	C₁₃×#442	C₂²	1	2	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	complemented
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₁₃×#440	C₂²	1	2	yes	complemented
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#102	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	2	no	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	—	2	1	no	—
103	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
104	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
105	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
106	C₁₃×#135	—	4	4	no	—
107	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×D₈	—	4	4	no	—
114	C₂×C₁₃×D₈	C₂³	1	2	yes	—
115	C₂×C₁₃×D₈	C₂³	1	4	yes	—
116	C₂×C₁₃×D₈	C₂³	1	4	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	2	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
123	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×#127	—	2	1	no	—
127	C₁₃×#127	—	2	1	no	—
128	C₁₃×#127	C₂³	1	2	yes	—
129	C₁₃×#127	C₂³	1	2	yes	—
130	C₁₃×#127	C₂³	1	4	yes	—
131	C₁₃×#127	C₂³	1	1	yes	characteristic
132	C₁₃×#127	C₂³	1	4	yes	—
133	C₁₃×#126	—	2	4	no	—
134	C₁₃×#125	D₄	1	2	yes	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	C₂³	1	4	yes	—
139	C₁₃×#124	C₂³	1	4	yes	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	—	2	4	no	—
160	C₁₃×#120	—	2	4	no	—
161	C₁₃×#120	—	2	4	no	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	4	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	4	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	4	yes	—
182	C₄×D₄×C₁₃	C₂³	1	4	yes	—
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	C₂³	1	1	yes	characteristic
190	C₁₃×#117	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₄²×C₁₃	—	2	1	no	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	2	yes	—
198	C₁₃×#106	C₂³	1	2	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	2	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×#102	C₂³	1	2	yes	—
212	C₁₃×#102	C₂³	1	2	yes	—
213	C₁₃×#102	C₂³	1	2	yes	—
214	C₁₃×#97	C₂³	1	2	yes	—
215	C₁₃×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	C₄×C₈×C₁₃	C₂³	1	4	yes	—
218	#61419	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂⁴×C₁₃	—	2	2	no	—
220	C₂⁴×C₁₃	—	2	1	no	—
221	C₁₃×#41	—	2	4	no	—
222	C₁₃×#41	—	2	2	no	—
223	C₁₃×#41	—	2	2	no	—
224	C₁₃×#41	—	2	4	no	—
225	C₁₃×#41	—	8	4	no	—
226	C₁₃×#41	—	8	4	no	—
227	C₁₃×#41	—	8	4	no	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	8	2	no	—
251	C₂×D₄×C₁₃	—	8	2	no	—
252	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	8	2	no	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₁₃×Q₁₆	—	4	2	no	—
271	C₁₃×SD₁₆	—	2	8	no	—
272	C₁₃×SD₁₆	—	2	4	no	—
273	C₁₃×SD₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	4	2	no	—
275	C₁₃×SD₁₆	—	4	4	no	—
276	C₁₃×D₈	—	2	8	no	—
277	C₁₃×D₈	—	2	4	no	—
278	C₁₃×D₈	—	4	4	no	—
279	C₁₃×D₈	—	4	4	no	—
280	C₁₃×D₈	—	4	2	no	—
281	C₁₃×D₈	—	4	4	no	—
282	C₁₃×M₁₆	—	2	2	no	—
283	C₁₃×M₁₆	#41	1	4	yes	complemented
284	C₂×C₈×C₁₃	—	2	4	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	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	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₄	—	2	1	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	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	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₄²×C₁₃	C₂⁴	1	4	yes	—
327	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
328	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3403	C₂×C₁₃	1	4	yes	complemented
331	#3399	C₂×C₁₃	1	2	yes	complemented
332	#3399	C₂×C₁₃	1	4	yes	complemented
333	#3397	C₂×C₁₃	1	2	yes	complemented
334	#3394	C₂×C₁₃	1	2	yes	complemented
335	#3391	C₂×C₁₃	1	2	yes	complemented
336	#3155	C₂×C₁₃	1	2	yes	complemented
337	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3045	C₂×C₁₃	1	2	yes	complemented
339	#3041	C₂×C₁₃	1	2	yes	complemented
340	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2946	C₂×C₁₃	1	2	yes	complemented
344	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	4	no	—
348	C₂³×C₁₃	—	2	1	no	—
349	C₂³×C₁₃	—	4	2	no	—
350	C₂³×C₁₃	—	4	4	no	—
351	C₂³×C₁₃	—	8	1	no	—
352	C₂³×C₁₃	—	8	1	no	—
353	C₂³×C₁₃	—	8	2	no	—
354	C₂³×C₁₃	—	8	2	no	—
355	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	Q₈×C₁₃	—	2	4	no	—
357	Q₈×C₁₃	—	2	1	no	—
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	1	no	—
361	Q₈×C₁₃	—	4	2	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	2	1	no	—
364	D₄×C₁₃	—	2	2	no	—
365	D₄×C₁₃	—	2	4	no	—
366	D₄×C₁₃	—	2	2	no	—
367	D₄×C₁₃	—	2	4	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	4	4	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	8	1	no	—
378	D₄×C₁₃	—	8	4	no	—
379	D₄×C₁₃	—	8	2	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	8	4	no	—
382	D₄×C₁₃	—	8	4	no	—
383	D₄×C₁₃	—	8	4	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	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	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	—	8	4	no	—
399	C₂×C₄×C₁₃	—	8	4	no	—
400	C₂×C₄×C₁₃	—	8	1	no	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
409	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
411	C₈×C₁₃	—	2	2	no	—
412	C₈×C₁₃	—	2	2	no	—
413	C₈×C₁₃	—	2	2	no	—
414	C₈×C₁₃	C₂×#41	1	4	yes	—
415	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
416	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
418	C₂×#135	C₂²×C₁₃	1	2	yes	—
419	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
420	#559	C₂²×C₁₃	1	2	yes	complemented
421	#559	C₂²×C₁₃	1	4	yes	complemented
422	#559	C₂²×C₁₃	1	2	yes	complemented
423	#556	C₂²×C₁₃	1	2	yes	complemented
424	#555	—	2	1	no	—
425	#553	—	2	2	no	—
426	#550	C₂²×C₁₃	1	2	yes	complemented
427	#550	C₂²×C₁₃	1	2	yes	complemented
428	#550	C₂²×C₁₃	1	2	yes	complemented
429	#547	—	2	1	no	—
430	#546	—	2	2	no	—
431	#546	—	2	2	no	—
432	#540	—	2	2	no	—
433	#538	—	2	2	no	—
434	#535	C₂²×C₁₃	1	2	yes	—
435	#535	C₂²×C₁₃	1	2	yes	—
436	#533	C₂²×C₁₃	1	1	yes	characteristic
437	#532	—	2	1	no	—
438	#532	—	2	1	no	—
439	#532	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
441	#525	—	2	2	no	—
442	#520	C₂²×C₁₃	1	2	yes	—
443	#518	C₂²×C₁₃	1	2	yes	—
444	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
446	#496	C₂²×C₁₃	1	4	yes	complemented
447	#496	C₂²×C₁₃	1	4	yes	complemented
448	#496	C₂²×C₁₃	1	4	yes	complemented
449	#495	C₂²×C₁₃	1	4	yes	complemented
450	#493	C₂²×C₁₃	1	2	yes	complemented
451	#493	C₂²×C₁₃	1	4	yes	complemented
452	#492	C₂²×C₁₃	1	2	yes	complemented
453	#464	C₂²×C₁₃	1	4	yes	complemented
454	#464	C₂²×C₁₃	1	2	yes	complemented
455	#463	C₂²×C₁₃	1	4	yes	complemented
456	#463	C₂²×C₁₃	1	4	yes	complemented
457	#463	C₂²×C₁₃	1	2	yes	complemented
458	#463	C₂²×C₁₃	1	4	yes	complemented
459	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	#460	C₂²×C₁₃	1	4	yes	complemented
462	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#459	C₂²×C₁₃	1	2	yes	—
464	#459	C₂²×C₁₃	1	2	yes	—
465	#459	C₂²×C₁₃	1	4	yes	—
466	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#459	C₂²×C₁₃	1	4	yes	complemented
468	#459	C₂²×C₁₃	1	4	yes	complemented
469	#459	C₂²×C₁₃	1	4	yes	complemented
470	#446	C₂²×C₁₃	1	2	yes	complemented
471	#446	C₂²×C₁₃	1	4	yes	complemented
472	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
473	#442	C₂²×C₁₃	1	2	yes	complemented
474	#442	C₂²×C₁₃	1	4	yes	complemented
475	#440	C₂²×C₁₃	1	4	yes	complemented
476	#440	C₂²×C₁₃	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
478	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
479	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
480	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
481	#428	C₂²×C₁₃	1	1	yes	characteristic
482	#424	C₂²×C₁₃	1	2	yes	—
483	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
484	#418	C₂²×C₁₃	1	1	yes	characteristic
485	#417	C₂²×C₁₃	1	1	yes	characteristic
486	#416	C₂²×C₁₃	1	2	yes	—
487	C₂×#102	C₂²×C₁₃	1	2	yes	—
488	#405	C₂²×C₁₃	1	2	yes	—
489	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	4	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	4	no	—
504	C₂²×C₁₃	—	8	4	no	—
505	C₂²×C₁₃	—	16	4	no	—
506	C₂²×C₁₃	#550	1	2	yes	—
507	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	4	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	4	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	#550	1	2	yes	—
519	C₄×C₁₃	#576	1	2	yes	—
520	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
521	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	2	no	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×#41	C₂³×C₁₃	1	2	yes	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
531	C₂³×C₄	—	2	1	no	—
532	AGL(1,ℤ/8)	—	2	8	no	—
533	AGL(1,ℤ/8)	—	2	4	no	—
534	AGL(1,ℤ/8)	—	4	4	no	—
535	#135	—	4	4	no	—
536	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
542	C₂×D₈	—	4	4	no	—
543	C₂×D₈	C₂³×C₁₃	1	2	yes	—
544	C₂×D₈	C₂³×C₁₃	1	4	yes	—
545	C₂×D₈	C₂³×C₁₃	1	4	yes	—
546	C₂×D₈	C₂³×C₁₃	1	4	yes	—
547	C₂×D₈	C₂³×C₁₃	1	2	yes	—
548	C₂×D₈	C₂³×C₁₃	1	4	yes	—
549	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
553	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	#127	—	2	1	no	—
556	#127	—	2	1	no	—
557	#127	C₂³×C₁₃	1	2	yes	—
558	#127	C₂³×C₁₃	1	2	yes	—
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#127	C₂³×C₁₃	1	4	yes	—
561	#127	C₂³×C₁₃	1	4	yes	—
562	#126	—	2	4	no	—
563	#125	D₄×C₁₃	1	2	yes	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	4	no	—
567	#124	C₂³×C₁₃	1	2	yes	—
568	#124	C₂³×C₁₃	1	4	yes	—
569	#124	C₂³×C₁₃	1	4	yes	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
576	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	4	no	—
587	#121	—	2	4	no	—
588	#121	—	2	4	no	—
589	#120	—	2	4	no	—
590	#120	—	2	4	no	—
591	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	2	yes	—
610	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₃	1	4	yes	—
613	C₄×D₄	C₂³×C₁₃	1	4	yes	—
614	C₄×D₄	C₂³×C₁₃	1	4	yes	—
615	#117	—	2	2	no	—
616	#117	—	2	2	no	—
617	#117	—	2	1	no	—
618	#117	C₂³×C₁₃	1	1	yes	characteristic
619	#117	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	4	no	—
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	#107	C₂³×C₁₃	1	2	yes	—
627	#106	C₂³×C₁₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
629	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
630	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
631	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
632	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
633	#103	C₂³×C₁₃	1	2	yes	—
634	#103	C₂³×C₁₃	1	2	yes	—
635	#103	C₂³×C₁₃	1	2	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	4	yes	—
638	#102	C₂³×C₁₃	1	2	yes	—
639	#102	C₂³×C₁₃	1	2	yes	—
640	#102	C₂³×C₁₃	1	2	yes	—
641	#102	C₂³×C₁₃	1	2	yes	—
642	#102	C₂³×C₁₃	1	2	yes	—
643	#97	C₂³×C₁₃	1	2	yes	—
644	#97	C₂³×C₁₃	1	4	yes	—
645	C₄×C₈	C₂³×C₁₃	1	2	yes	—
646	C₄×C₈	C₂³×C₁₃	1	4	yes	—
647	C₂×C₁₃	—	2	2	no	—
648	C₂×C₁₃	—	8	1	no	—
649	C₂×C₁₃	—	8	2	no	—
650	C₂×C₁₃	—	8	2	no	—
651	C₂×C₁₃	—	8	4	no	—
652	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
653	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
654	C₂×C₁₃	#3585	1	1	yes	characteristic
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	1	no	—
657	#41	—	2	2	no	—
658	#41	—	2	4	no	—
659	#41	—	2	2	no	—
660	#41	—	2	4	no	—
661	#41	—	8	4	no	—
662	#41	—	8	4	no	—
663	#41	—	8	4	no	—
664	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
665	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	8	2	no	—
687	C₂×D₄	—	8	2	no	—
688	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
691	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	8	2	no	—
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	Q₁₆	—	4	2	no	—
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	4	no	—
709	SD₁₆	—	4	2	no	—
710	SD₁₆	—	4	2	no	—
711	SD₁₆	—	4	4	no	—
712	D₈	—	2	8	no	—
713	D₈	—	2	4	no	—
714	D₈	—	4	4	no	—
715	D₈	—	4	4	no	—
716	D₈	—	4	2	no	—
717	D₈	—	4	4	no	—
718	M₁₆	—	2	2	no	—
719	M₁₆	C₁₃×#41	1	4	yes	complemented
720	C₂×C₈	—	2	4	no	—
721	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
722	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
723	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
724	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	4	no	—
759	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₁₃	1	4	yes	—
763	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₁₃	#61419	1	1	yes	characteristic, direct product factor, Sylow
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	2	no	—
774	C₂³	—	8	2	no	—
775	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	1	no	—
781	Q₈	—	4	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	2	no	—
798	D₄	—	8	2	no	—
799	D₄	—	8	1	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	—	8	1	no	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
829	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
830	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	C₂×C₁₃×#41	1	4	yes	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	8	4	no	—
850	C₂²	—	16	4	no	—
851	C₂²	C₁₃×#550	1	2	yes	—
852	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	C₁₃×#550	1	2	yes	—
864	C₄	C₁₃×#576	1	2	yes	—
865	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
866	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	4	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	2	no	—
872	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
873	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
874	C₂	C₁₃×#3585	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3399	C₂	semidirect
5. C₁₃×#3399	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3394	C₂	semidirect
8. C₁₃×#3391	C₂	semidirect
9. C₁₃×#3155	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3041	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#459	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2946	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#559	C₂²	semidirect
25. C₁₃×#559	C₂²	semidirect
26. C₁₃×#556	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. C₁₃×#550	C₂²	semidirect
49. C₁₃×#496	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#495	C₂²	semidirect
53. C₁₃×#493	C₂²	semidirect
54. C₁₃×#493	C₂²	semidirect
55. C₁₃×#492	C₂²	semidirect
56. C₁₃×#464	C₂²	semidirect
57. C₁₃×#464	C₂²	semidirect
58. C₁₃×#463	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#462	C₂²	semidirect
63. C₁₃×#461	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#460	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₈×Q₈×C₁₃	C₂²	semidirect
76. C₁₃×#442	C₂²	semidirect
77. C₁₃×#442	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₁₃×#440	C₂²	semidirect
80. C₄×C₁₃×SD₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×D₈	C₂²	semidirect
83. C₄×C₁₃×D₈	C₂²	semidirect
218. #61419	C₁₃	direct (N × H)
283. C₁₃×M₁₆	#41	semidirect
328. #3508	C₂×C₁₃	semidirect
329. #3506	C₂×C₁₃	semidirect
330. #3403	C₂×C₁₃	semidirect
331. #3399	C₂×C₁₃	semidirect
332. #3399	C₂×C₁₃	semidirect
333. #3397	C₂×C₁₃	semidirect
334. #3394	C₂×C₁₃	semidirect
335. #3391	C₂×C₁₃	semidirect
336. #3155	C₂×C₁₃	semidirect
337. #3151	C₂×C₁₃	semidirect
338. #3045	C₂×C₁₃	semidirect
339. #3041	C₂×C₁₃	semidirect
340. #3035	C₂×C₁₃	semidirect
341. C₂×#459	C₂×C₁₃	semidirect
342. #2962	C₂×C₁₃	semidirect
343. #2946	C₂×C₁₃	semidirect
344. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
420. #559	C₂²×C₁₃	semidirect
421. #559	C₂²×C₁₃	semidirect
422. #559	C₂²×C₁₃	semidirect
423. #556	C₂²×C₁₃	semidirect
426. #550	C₂²×C₁₃	semidirect
427. #550	C₂²×C₁₃	semidirect
428. #550	C₂²×C₁₃	semidirect
446. #496	C₂²×C₁₃	semidirect
447. #496	C₂²×C₁₃	semidirect
448. #496	C₂²×C₁₃	semidirect
449. #495	C₂²×C₁₃	semidirect
450. #493	C₂²×C₁₃	semidirect
451. #493	C₂²×C₁₃	semidirect
452. #492	C₂²×C₁₃	semidirect
453. #464	C₂²×C₁₃	semidirect
454. #464	C₂²×C₁₃	semidirect
455. #463	C₂²×C₁₃	semidirect
456. #463	C₂²×C₁₃	semidirect
457. #463	C₂²×C₁₃	semidirect
458. #463	C₂²×C₁₃	semidirect
459. #462	C₂²×C₁₃	semidirect
460. #461	C₂²×C₁₃	semidirect
461. #460	C₂²×C₁₃	semidirect
462. #460	C₂²×C₁₃	semidirect
466. #459	C₂²×C₁₃	semidirect
467. #459	C₂²×C₁₃	semidirect
468. #459	C₂²×C₁₃	semidirect
469. #459	C₂²×C₁₃	semidirect
470. #446	C₂²×C₁₃	semidirect
471. #446	C₂²×C₁₃	semidirect
472. C₈×Q₈	C₂²×C₁₃	semidirect
473. #442	C₂²×C₁₃	semidirect
474. #442	C₂²×C₁₃	semidirect
475. #440	C₂²×C₁₃	semidirect
476. #440	C₂²×C₁₃	semidirect
477. C₄×SD₁₆	C₂²×C₁₃	semidirect
478. C₄×SD₁₆	C₂²×C₁₃	semidirect
479. C₄×D₈	C₂²×C₁₃	semidirect
480. C₄×D₈	C₂²×C₁₃	semidirect
719. M₁₆	C₁₃×#41	semidirect
764. C₁₃	#61419	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×#3508	2
C₁₃×#3506	2
C₁₃×#3403	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3394	2
C₁₃×#3391	2
C₁₃×#3155	2
C₁₃×#3151	2
C₁₃×#3045	2
C₁₃×#3041	2
C₁₃×#3035	2
C₂×C₁₃×#459	2
C₁₃×#2962	2
C₁₃×#2946	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61419	13

Subgroups — C13×#61419 #15747758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61419 #15747758