Subgroups — C₁₃×#61673 #15748012

Order 3328.

2160 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3321	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3319	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3199	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
20	C₁₃×H(3,𝔽₄)	—	2	1	no	—
21	C₁₃×H(3,𝔽₄)	—	2	1	no	—
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#555	C₂²	1	4	yes	complemented
24	C₁₃×#548	C₂²	1	4	yes	complemented
25	C₁₃×#546	—	2	4	no	—
26	C₁₃×#546	C₂²	1	4	yes	complemented
27	D₄²×C₁₃	—	2	1	no	—
28	D₄²×C₁₃	C₂²	1	4	yes	complemented
29	C₁₃×#536	—	2	1	no	—
30	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#535	—	2	1	no	—
32	C₁₃×#535	—	2	4	no	—
33	C₁₃×#535	C₂²	1	2	yes	—
34	C₁₃×#535	C₂²	1	2	yes	complemented
35	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#532	—	2	1	no	—
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#124	—	2	1	no	—
40	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#496	C₂²	1	4	yes	complemented
43	C₁₃×#489	C₂²	1	4	yes	complemented
44	C₁₃×#485	C₂²	1	4	yes	complemented
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#482	C₂²	1	4	yes	complemented
47	C₁₃×#475	C₂²	1	2	yes	complemented
48	C₁₃×#474	C₂²	1	2	yes	complemented
49	C₁₃×#469	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#466	C₂²	1	4	yes	complemented
52	C₁₃×#465	C₂²	1	4	yes	complemented
53	C₁₃×#463	C₂²	1	4	yes	complemented
54	C₁₃×#463	C₂²	1	4	yes	complemented
55	C₁₃×#460	C₂²	1	2	yes	complemented
56	C₁₃×#459	C₂²	1	2	yes	complemented
57	C₁₃×#450	C₂²	1	4	yes	complemented
58	C₁₃×#449	C₂²	1	4	yes	complemented
59	C₁₃×#449	C₂²	1	4	yes	complemented
60	C₁₃×#449	C₂²	1	4	yes	complemented
61	C₁₃×#448	C₂²	1	4	yes	complemented
62	C₁₃×#448	C₂²	1	4	yes	complemented
63	C₁₃×#447	C₂²	1	4	yes	complemented
64	C₁₃×#447	C₂²	1	4	yes	complemented
65	C₁₃×#447	C₂²	1	4	yes	complemented
66	C₁₃×#442	C₂²	1	4	yes	complemented
67	C₁₃×#440	C₂²	1	4	yes	complemented
68	C₁₃×#435	C₂²	1	4	yes	complemented
69	C₁₃×#435	C₂²	1	4	yes	complemented
70	C₁₃×#432	C₂²	1	2	yes	complemented
71	C₁₃×#419	C₂²	1	2	yes	complemented
72	C₁₃×#418	C₂²	1	2	yes	complemented
73	C₁₃×#416	C₂²	1	2	yes	complemented
74	C₁₃×#416	C₂²	1	2	yes	complemented
75	C₁₃×#408	C₂²	1	2	yes	complemented
76	C₁₃×#408	C₂²	1	2	yes	complemented
77	C₁₃×2₋¹⁺⁴	—	4	2	no	—
78	C₁₃×2₋¹⁺⁴	—	4	2	no	—
79	C₁₃×H(5,𝔽₂)	—	4	2	no	—
80	C₁₃×H(5,𝔽₂)	—	4	2	no	—
81	C₂×C₁₃×#41	—	2	1	no	—
82	C₂×C₁₃×#41	—	2	1	no	—
83	C₂×C₁₃×#41	—	2	2	no	—
84	C₂×C₁₃×#41	—	2	2	no	—
85	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	—	2	1	no	—
91	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	—	2	2	no	—
95	C₂²×D₄×C₁₃	—	2	4	no	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
101	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
102	C₂×C₁₃×SD₁₆	—	4	4	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	—	4	4	no	—
107	C₂×C₁₃×D₈	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
112	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×#127	—	2	1	no	—
118	C₁₃×#127	—	2	2	no	—
119	C₁₃×#127	—	2	2	no	—
120	C₁₃×#127	D₄	1	1	yes	characteristic
121	C₁₃×#127	C₂³	1	2	yes	—
122	C₁₃×#124	—	2	1	no	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	D₄	1	1	yes	characteristic
133	C₁₃×#124	D₄	1	1	yes	characteristic
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	4	no	—
143	C₁₃×#121	—	2	4	no	—
144	C₁₃×#121	D₄	1	4	yes	—
145	C₁₃×#121	C₂³	1	4	yes	—
146	C₁₃×#121	C₂³	1	4	yes	—
147	C₁₃×#121	C₂³	1	4	yes	—
148	C₁₃×#121	C₂³	1	4	yes	—
149	C₁₃×#120	—	2	2	no	—
150	C₁₃×#120	—	2	2	no	—
151	C₁₃×#120	—	2	4	no	—
152	C₁₃×#120	—	2	2	no	—
153	C₁₃×#120	—	2	2	no	—
154	C₁₃×#120	—	2	2	no	—
155	C₁₃×#120	—	2	4	no	—
156	C₁₃×#120	—	2	4	no	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	C₂³	1	4	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	4	yes	—
164	C₁₃×#117	—	2	4	no	—
165	C₁₃×#117	—	2	1	no	—
166	C₁₃×#117	C₂³	1	2	yes	—
167	C₁₃×#117	C₂³	1	2	yes	—
168	C₁₃×#117	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₁₃×#107	C₂³	1	4	yes	—
174	C₁₃×#106	C₂³	1	4	yes	—
175	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₃×#97	C₂³	1	4	yes	—
189	#61673	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂⁴×C₁₃	—	2	2	no	—
191	C₂⁴×C₁₃	—	2	1	no	—
192	C₂⁴×C₁₃	—	2	2	no	—
193	C₂⁴×C₁₃	—	2	2	no	—
194	C₁₃×#41	—	2	2	no	—
195	C₁₃×#41	—	2	2	no	—
196	C₁₃×#41	—	2	4	no	—
197	C₁₃×#41	—	2	4	no	—
198	C₁₃×#41	—	4	1	no	—
199	C₁₃×#41	—	4	1	no	—
200	C₁₃×#41	—	4	1	no	—
201	C₁₃×#41	—	4	1	no	—
202	C₁₃×#41	—	4	2	no	—
203	C₁₃×#41	—	4	2	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	4	no	—
206	C₁₃×#41	—	4	8	no	—
207	C₁₃×#41	—	8	4	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	2	no	—
211	C₂×Q₈×C₁₃	—	2	4	no	—
212	C₂×Q₈×C₁₃	—	4	2	no	—
213	C₂×Q₈×C₁₃	—	4	1	no	—
214	C₂×Q₈×C₁₃	—	4	1	no	—
215	C₂×Q₈×C₁₃	—	4	4	no	—
216	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
219	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	2	4	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	1	no	—
236	C₂×D₄×C₁₃	—	4	1	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	2	no	—
241	C₂×D₄×C₁₃	—	4	4	no	—
242	C₂×D₄×C₁₃	—	4	8	no	—
243	C₂×D₄×C₁₃	—	8	8	no	—
244	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₁₃×SD₁₆	—	2	8	no	—
264	C₁₃×SD₁₆	—	4	4	no	—
265	C₁₃×SD₁₆	—	4	4	no	—
266	C₁₃×D₈	—	2	8	no	—
267	C₁₃×D₈	—	4	4	no	—
268	C₁₃×D₈	—	4	4	no	—
269	C₁₃×M₁₆	—	4	2	no	—
270	C₁₃×M₁₆	—	4	2	no	—
271	C₂×C₈×C₁₃	—	4	2	no	—
272	C₂×C₈×C₁₃	—	4	2	no	—
273	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
294	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	2	no	—
299	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂⁴	1	2	yes	—
302	#3549	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#3321	C₂×C₁₃	1	4	yes	complemented
305	#3319	C₂×C₁₃	1	4	yes	complemented
306	#3265	C₂×C₁₃	1	4	yes	complemented
307	#3264	C₂×C₁₃	1	4	yes	complemented
308	#3213	C₂×C₁₃	1	2	yes	complemented
309	#3200	C₂×C₁₃	1	2	yes	complemented
310	#3199	C₂×C₁₃	1	2	yes	complemented
311	#3115	C₂×C₁₃	1	2	yes	complemented
312	#3010	C₂×C₁₃	1	2	yes	complemented
313	#3008	C₂×C₁₃	1	2	yes	complemented
314	#2980	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂³×C₁₃	—	2	1	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	4	no	—
318	C₂³×C₁₃	—	4	4	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	8	2	no	—
321	C₂³×C₁₃	—	8	2	no	—
322	C₂³×C₁₃	—	8	4	no	—
323	C₂³×C₁₃	—	8	4	no	—
324	C₂³×C₁₃	—	8	2	no	—
325	C₂³×C₁₃	—	8	4	no	—
326	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	Q₈×C₁₃	—	2	1	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	4	1	no	—
333	Q₈×C₁₃	—	4	1	no	—
334	Q₈×C₁₃	—	4	4	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	8	2	no	—
337	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
338	D₄×C₁₃	—	2	4	no	—
339	D₄×C₁₃	—	2	1	no	—
340	D₄×C₁₃	—	2	4	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	4	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	—	4	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	4	no	—
351	D₄×C₁₃	—	4	2	no	—
352	D₄×C₁₃	—	4	4	no	—
353	D₄×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	8	2	no	—
355	D₄×C₁₃	—	8	2	no	—
356	D₄×C₁₃	—	8	2	no	—
357	D₄×C₁₃	—	8	4	no	—
358	D₄×C₁₃	—	8	4	no	—
359	D₄×C₁₃	—	8	4	no	—
360	D₄×C₁₃	—	8	4	no	—
361	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	4	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	4	8	no	—
378	C₂×C₄×C₁₃	—	4	2	no	—
379	C₂×C₄×C₁₃	—	8	2	no	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₁₃	—	2	4	no	—
387	C₈×C₁₃	—	2	4	no	—
388	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
391	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
392	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
393	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
394	H(3,𝔽₄)	—	2	1	no	—
395	H(3,𝔽₄)	—	2	1	no	—
396	#555	—	2	1	no	—
397	#555	C₂²×C₁₃	1	4	yes	complemented
398	#548	C₂²×C₁₃	1	4	yes	complemented
399	#546	—	2	4	no	—
400	#546	C₂²×C₁₃	1	4	yes	complemented
401	D₄²	—	2	1	no	—
402	D₄²	C₂²×C₁₃	1	4	yes	complemented
403	#536	—	2	1	no	—
404	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#535	—	2	1	no	—
406	#535	—	2	4	no	—
407	#535	C₂²×C₁₃	1	2	yes	—
408	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#535	C₂²×C₁₃	1	2	yes	complemented
410	#532	—	2	1	no	—
411	#532	C₂²×C₁₃	1	1	yes	characteristic
412	#532	C₂²×C₁₃	1	2	yes	complemented
413	C₂×#124	—	2	1	no	—
414	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#496	C₂²×C₁₃	1	4	yes	complemented
417	#489	C₂²×C₁₃	1	4	yes	complemented
418	#485	C₂²×C₁₃	1	4	yes	complemented
419	#482	C₂²×C₁₃	1	4	yes	complemented
420	#482	C₂²×C₁₃	1	4	yes	complemented
421	#475	C₂²×C₁₃	1	2	yes	complemented
422	#474	C₂²×C₁₃	1	2	yes	complemented
423	#469	C₂²×C₁₃	1	4	yes	complemented
424	#468	C₂²×C₁₃	1	4	yes	complemented
425	#466	C₂²×C₁₃	1	4	yes	complemented
426	#465	C₂²×C₁₃	1	4	yes	complemented
427	#463	C₂²×C₁₃	1	4	yes	complemented
428	#463	C₂²×C₁₃	1	4	yes	complemented
429	#460	C₂²×C₁₃	1	2	yes	complemented
430	#459	C₂²×C₁₃	1	2	yes	complemented
431	#450	C₂²×C₁₃	1	4	yes	complemented
432	#449	C₂²×C₁₃	1	4	yes	complemented
433	#449	C₂²×C₁₃	1	4	yes	complemented
434	#449	C₂²×C₁₃	1	4	yes	complemented
435	#448	C₂²×C₁₃	1	4	yes	complemented
436	#448	C₂²×C₁₃	1	4	yes	complemented
437	#447	C₂²×C₁₃	1	4	yes	complemented
438	#447	C₂²×C₁₃	1	4	yes	complemented
439	#447	C₂²×C₁₃	1	4	yes	complemented
440	#442	C₂²×C₁₃	1	4	yes	complemented
441	#440	C₂²×C₁₃	1	4	yes	complemented
442	#435	C₂²×C₁₃	1	4	yes	complemented
443	#435	C₂²×C₁₃	1	4	yes	complemented
444	#432	C₂²×C₁₃	1	2	yes	complemented
445	#419	C₂²×C₁₃	1	2	yes	complemented
446	#418	C₂²×C₁₃	1	2	yes	complemented
447	#416	C₂²×C₁₃	1	2	yes	complemented
448	#416	C₂²×C₁₃	1	2	yes	complemented
449	#408	C₂²×C₁₃	1	2	yes	complemented
450	#408	C₂²×C₁₃	1	2	yes	complemented
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	2	4	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	4	no	—
460	C₂²×C₁₃	—	4	4	no	—
461	C₂²×C₁₃	—	4	4	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	4	no	—
464	C₂²×C₁₃	—	16	4	no	—
465	C₂²×C₁₃	—	16	2	no	—
466	C₂²×C₁₃	—	16	4	no	—
467	C₂²×C₁₃	—	16	4	no	—
468	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
469	C₄×C₁₃	—	2	2	no	—
470	C₄×C₁₃	—	2	2	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	2	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	2	no	—
475	C₄×C₁₃	—	4	4	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
479	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	2₋¹⁺⁴	—	4	2	no	—
481	2₋¹⁺⁴	—	4	2	no	—
482	H(5,𝔽₂)	—	4	2	no	—
483	H(5,𝔽₂)	—	4	2	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×#41	C₂³×C₁₃	1	2	yes	—
490	C₂×#41	C₂³×C₁₃	1	2	yes	—
491	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
495	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
500	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	AGL(1,ℤ/8)	—	4	4	no	—
504	AGL(1,ℤ/8)	—	4	4	no	—
505	C₂×SD₁₆	—	4	4	no	—
506	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
509	C₂×D₈	—	4	4	no	—
510	C₂×D₈	C₂³×C₁₃	1	4	yes	—
511	C₂×D₈	C₂³×C₁₃	1	4	yes	—
512	C₂×D₈	C₂³×C₁₃	1	4	yes	—
513	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
514	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
515	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
516	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	#127	—	2	1	no	—
521	#127	—	2	2	no	—
522	#127	—	2	2	no	—
523	#127	D₄×C₁₃	1	1	yes	characteristic
524	#127	C₂³×C₁₃	1	2	yes	—
525	#124	—	2	1	no	—
526	#124	—	2	2	no	—
527	#124	—	2	2	no	—
528	#124	—	2	1	no	—
529	#124	—	2	4	no	—
530	#124	—	2	4	no	—
531	#124	—	2	4	no	—
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	—	2	2	no	—
535	#124	D₄×C₁₃	1	1	yes	characteristic
536	#124	D₄×C₁₃	1	1	yes	characteristic
537	#124	C₂³×C₁₃	1	4	yes	—
538	#123	—	2	2	no	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
542	#121	—	2	4	no	—
543	#121	—	2	4	no	—
544	#121	—	2	2	no	—
545	#121	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	D₄×C₁₃	1	4	yes	—
548	#121	C₂³×C₁₃	1	4	yes	—
549	#121	C₂³×C₁₃	1	4	yes	—
550	#121	C₂³×C₁₃	1	4	yes	—
551	#121	C₂³×C₁₃	1	4	yes	—
552	#120	—	2	2	no	—
553	#120	—	2	2	no	—
554	#120	—	2	4	no	—
555	#120	—	2	2	no	—
556	#120	—	2	2	no	—
557	#120	—	2	2	no	—
558	#120	—	2	4	no	—
559	#120	—	2	4	no	—
560	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	C₂³×C₁₃	1	2	yes	—
565	C₄×D₄	C₂³×C₁₃	1	4	yes	—
566	C₄×D₄	C₂³×C₁₃	1	4	yes	—
567	#117	—	2	4	no	—
568	#117	—	2	1	no	—
569	#117	C₂³×C₁₃	1	1	yes	characteristic
570	#117	C₂³×C₁₃	1	2	yes	—
571	#117	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	#107	C₂³×C₁₃	1	4	yes	—
577	#106	C₂³×C₁₃	1	4	yes	—
578	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
579	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
580	#103	C₂³×C₁₃	1	4	yes	—
581	#103	C₂³×C₁₃	1	4	yes	—
582	#103	C₂³×C₁₃	1	4	yes	—
583	#102	C₂³×C₁₃	1	4	yes	—
584	#102	C₂³×C₁₃	1	4	yes	—
585	#102	C₂³×C₁₃	1	4	yes	—
586	#102	C₂³×C₁₃	1	4	yes	—
587	#102	C₂³×C₁₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
591	#97	C₂³×C₁₃	1	4	yes	—
592	C₂×C₁₃	—	4	1	no	—
593	C₂×C₁₃	—	4	2	no	—
594	C₂×C₁₃	—	4	2	no	—
595	C₂×C₁₃	—	4	2	no	—
596	C₂×C₁₃	—	8	4	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	#3484	1	1	yes	characteristic
599	C₂×C₁₃	#3585	1	2	yes	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	1	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	#41	—	2	2	no	—
605	#41	—	2	2	no	—
606	#41	—	2	4	no	—
607	#41	—	2	4	no	—
608	#41	—	4	1	no	—
609	#41	—	4	1	no	—
610	#41	—	4	1	no	—
611	#41	—	4	1	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	8	no	—
617	#41	—	8	4	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	2	no	—
623	C₂×Q₈	—	4	1	no	—
624	C₂×Q₈	—	4	1	no	—
625	C₂×Q₈	—	4	4	no	—
626	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	1	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	8	8	no	—
654	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
655	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
661	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	SD₁₆	—	2	8	no	—
674	SD₁₆	—	4	4	no	—
675	SD₁₆	—	4	4	no	—
676	D₈	—	2	8	no	—
677	D₈	—	4	4	no	—
678	D₈	—	4	4	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	—	4	2	no	—
681	C₂×C₈	—	4	2	no	—
682	C₂×C₈	—	4	2	no	—
683	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
684	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
704	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₄²	C₂⁴×C₁₃	1	2	yes	—
712	C₁₃	#61673	1	1	yes	characteristic, direct product factor, Sylow
713	C₂³	—	2	1	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	8	2	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	2	no	—
723	C₂³	—	8	4	no	—
724	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
725	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
726	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	Q₈	—	2	1	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	4	no	—
733	Q₈	—	4	2	no	—
734	Q₈	—	8	2	no	—
735	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
736	D₄	—	2	4	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	4	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	4	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	4	no	—
751	D₄	—	4	4	no	—
752	D₄	—	8	2	no	—
753	D₄	—	8	2	no	—
754	D₄	—	8	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	—	8	4	no	—
759	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	8	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	8	2	no	—
778	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
783	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
784	C₈	—	2	4	no	—
785	C₈	—	2	4	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	16	4	no	—
800	C₂²	—	16	2	no	—
801	C₂²	—	16	4	no	—
802	C₂²	—	16	4	no	—
803	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
814	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂	—	4	2	no	—
816	C₂	—	4	1	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	4	no	—
820	C₂	—	8	2	no	—
821	C₂	C₁₃×#3484	1	1	yes	characteristic
822	C₂	C₁₃×#3585	1	2	yes	—

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3549	C₂	semidirect
2. C₁₃×#3500	C₂	semidirect
3. C₁₃×#3321	C₂	semidirect
4. C₁₃×#3319	C₂	semidirect
5. C₁₃×#3265	C₂	semidirect
6. C₁₃×#3264	C₂	semidirect
7. C₁₃×#3213	C₂	semidirect
8. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3199	C₂	semidirect
10. C₁₃×#3115	C₂	semidirect
11. C₁₃×#3010	C₂	semidirect
12. C₁₃×#3008	C₂	semidirect
13. C₁₃×#2980	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#548	C₂²	semidirect
26. C₁₃×#546	C₂²	semidirect
28. D₄²×C₁₃	C₂²	semidirect
30. C₁₃×#536	C₂²	semidirect
34. C₁₃×#535	C₂²	semidirect
35. C₁₃×#535	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
40. C₂×C₁₃×#124	C₂²	semidirect
41. C₄×C₁₃×#41	C₂²	semidirect
42. C₁₃×#496	C₂²	semidirect
43. C₁₃×#489	C₂²	semidirect
44. C₁₃×#485	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
47. C₁₃×#475	C₂²	semidirect
48. C₁₃×#474	C₂²	semidirect
49. C₁₃×#469	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#466	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#463	C₂²	semidirect
55. C₁₃×#460	C₂²	semidirect
56. C₁₃×#459	C₂²	semidirect
57. C₁₃×#450	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
59. C₁₃×#449	C₂²	semidirect
60. C₁₃×#449	C₂²	semidirect
61. C₁₃×#448	C₂²	semidirect
62. C₁₃×#448	C₂²	semidirect
63. C₁₃×#447	C₂²	semidirect
64. C₁₃×#447	C₂²	semidirect
65. C₁₃×#447	C₂²	semidirect
66. C₁₃×#442	C₂²	semidirect
67. C₁₃×#440	C₂²	semidirect
68. C₁₃×#435	C₂²	semidirect
69. C₁₃×#435	C₂²	semidirect
70. C₁₃×#432	C₂²	semidirect
71. C₁₃×#419	C₂²	semidirect
72. C₁₃×#418	C₂²	semidirect
73. C₁₃×#416	C₂²	semidirect
74. C₁₃×#416	C₂²	semidirect
75. C₁₃×#408	C₂²	semidirect
76. C₁₃×#408	C₂²	semidirect
189. #61673	C₁₃	direct (N × H)
302. #3549	C₂×C₁₃	semidirect
303. #3500	C₂×C₁₃	semidirect
304. #3321	C₂×C₁₃	semidirect
305. #3319	C₂×C₁₃	semidirect
306. #3265	C₂×C₁₃	semidirect
307. #3264	C₂×C₁₃	semidirect
308. #3213	C₂×C₁₃	semidirect
309. #3200	C₂×C₁₃	semidirect
310. #3199	C₂×C₁₃	semidirect
311. #3115	C₂×C₁₃	semidirect
312. #3010	C₂×C₁₃	semidirect
313. #3008	C₂×C₁₃	semidirect
314. #2980	C₂×C₁₃	semidirect
388. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
389. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
390. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
391. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
392. C₂²×SD₁₆	C₂²×C₁₃	semidirect
393. C₂²×D₈	C₂²×C₁₃	semidirect
397. #555	C₂²×C₁₃	semidirect
398. #548	C₂²×C₁₃	semidirect
400. #546	C₂²×C₁₃	semidirect
402. D₄²	C₂²×C₁₃	semidirect
404. #536	C₂²×C₁₃	semidirect
408. #535	C₂²×C₁₃	semidirect
409. #535	C₂²×C₁₃	semidirect
412. #532	C₂²×C₁₃	semidirect
414. C₂×#124	C₂²×C₁₃	semidirect
415. C₄×#41	C₂²×C₁₃	semidirect
416. #496	C₂²×C₁₃	semidirect
417. #489	C₂²×C₁₃	semidirect
418. #485	C₂²×C₁₃	semidirect
419. #482	C₂²×C₁₃	semidirect
420. #482	C₂²×C₁₃	semidirect
421. #475	C₂²×C₁₃	semidirect
422. #474	C₂²×C₁₃	semidirect
423. #469	C₂²×C₁₃	semidirect
424. #468	C₂²×C₁₃	semidirect
425. #466	C₂²×C₁₃	semidirect
426. #465	C₂²×C₁₃	semidirect
427. #463	C₂²×C₁₃	semidirect
428. #463	C₂²×C₁₃	semidirect
429. #460	C₂²×C₁₃	semidirect
430. #459	C₂²×C₁₃	semidirect
431. #450	C₂²×C₁₃	semidirect
432. #449	C₂²×C₁₃	semidirect
433. #449	C₂²×C₁₃	semidirect
434. #449	C₂²×C₁₃	semidirect
435. #448	C₂²×C₁₃	semidirect
436. #448	C₂²×C₁₃	semidirect
437. #447	C₂²×C₁₃	semidirect
438. #447	C₂²×C₁₃	semidirect
439. #447	C₂²×C₁₃	semidirect
440. #442	C₂²×C₁₃	semidirect
441. #440	C₂²×C₁₃	semidirect
442. #435	C₂²×C₁₃	semidirect
443. #435	C₂²×C₁₃	semidirect
444. #432	C₂²×C₁₃	semidirect
445. #419	C₂²×C₁₃	semidirect
446. #418	C₂²×C₁₃	semidirect
447. #416	C₂²×C₁₃	semidirect
448. #416	C₂²×C₁₃	semidirect
449. #408	C₂²×C₁₃	semidirect
450. #408	C₂²×C₁₃	semidirect
712. C₁₃	#61673	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×#3549	2
C₁₃×#3500	2
C₁₃×#3321	2
C₁₃×#3319	2
C₁₃×#3265	2
C₁₃×#3264	2
C₁₃×#3213	2
C₁₃×#3200	2
C₁₃×#3199	2
C₁₃×#3115	2
C₁₃×#3010	2
C₁₃×#3008	2
C₁₃×#2980	2
#61673	13

Subgroups — C13×#61673 #15748012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61673 #15748012