Subgroups — C₁₃×#61682 #15748021

Order 3328.

2140 conjugacy classes of subgroups.

The subgroup lattice has 808 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×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3321	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3198	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3010	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
19	C₁₃×H(3,𝔽₄)	—	2	2	no	—
20	C₁₃×#555	—	2	1	no	—
21	C₁₃×#555	C₂²	1	2	yes	—
22	C₁₃×#555	C₂²	1	2	yes	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₁₃	—	2	1	no	—
26	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#548	—	2	2	no	—
28	C₁₃×#548	C₂²	1	4	yes	complemented
29	D₄²×C₁₃	—	2	1	no	—
30	D₄²×C₁₃	C₂²	1	2	yes	—
31	D₄²×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#537	—	2	2	no	—
33	C₁₃×#537	C₂²	1	2	yes	complemented
34	C₁₃×#535	—	2	2	no	—
35	C₁₃×#535	—	2	2	no	—
36	C₁₃×#535	C₂²	1	4	yes	—
37	C₁₃×#532	—	2	2	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#496	C₂²	1	2	yes	—
44	C₁₃×#493	C₂²	1	1	yes	characteristic
45	C₁₃×#492	C₂²	1	1	yes	characteristic
46	C₁₃×#489	C₂²	1	2	yes	complemented
47	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#485	C₂²	1	4	yes	complemented
50	C₁₃×#482	C₂²	1	4	yes	complemented
51	C₁₃×#481	C₂²	1	2	yes	complemented
52	C₁₃×#480	C₂²	1	2	yes	complemented
53	C₁₃×#477	C₂²	1	2	yes	complemented
54	C₁₃×#475	C₂²	1	2	yes	complemented
55	C₁₃×#469	C₂²	1	4	yes	complemented
56	C₁₃×#468	C₂²	1	4	yes	complemented
57	C₁₃×#466	C₂²	1	4	yes	complemented
58	C₁₃×#465	C₂²	1	4	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#461	C₂²	1	2	yes	complemented
61	C₁₃×#460	C₂²	1	2	yes	—
62	C₁₃×#460	C₂²	1	2	yes	—
63	C₁₃×#459	C₂²	1	2	yes	complemented
64	C₁₃×#450	C₂²	1	4	yes	complemented
65	C₁₃×#449	C₂²	1	4	yes	complemented
66	C₁₃×#449	C₂²	1	4	yes	complemented
67	C₁₃×#449	C₂²	1	4	yes	complemented
68	C₁₃×#449	C₂²	1	4	yes	complemented
69	C₁₃×#448	C₂²	1	4	yes	complemented
70	C₁₃×#448	C₂²	1	2	yes	complemented
71	C₁₃×#448	C₂²	1	2	yes	complemented
72	C₁₃×#448	C₂²	1	4	yes	complemented
73	C₁₃×#447	C₂²	1	4	yes	complemented
74	C₁₃×#440	C₂²	1	4	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#419	C₂²	1	4	yes	complemented
83	C₁₃×#416	C₂²	1	4	yes	complemented
84	C₁₃×#408	C₂²	1	4	yes	complemented
85	C₁₃×2₋¹⁺⁴	—	4	8	no	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	—	2	1	no	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂²×Q₈×C₁₃	—	2	2	no	—
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	—	2	2	no	—
97	C₂²×D₄×C₁₃	—	2	2	no	—
98	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
99	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
100	C₂×C₁₃×SD₁₆	—	4	8	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
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	C₂³	1	4	yes	—
107	C₂×C₁₃×D₈	C₂³	1	4	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
109	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×#127	—	2	2	no	—
116	C₁₃×#127	—	2	4	no	—
117	C₁₃×#127	D₄	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	1	yes	characteristic
120	C₁₃×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#124	—	2	4	no	—
122	C₁₃×#124	—	2	4	no	—
123	C₁₃×#124	—	2	4	no	—
124	C₁₃×#124	—	2	4	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#124	D₄	1	2	yes	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×#121	—	2	4	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	1	no	—
140	C₁₃×#121	—	2	1	no	—
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	4	no	—
145	C₁₃×#121	D₄	1	2	yes	—
146	C₁₃×#121	D₄	1	2	yes	—
147	C₁₃×#121	C₂³	1	4	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	2	yes	—
150	C₁₃×#121	C₂³	1	4	yes	—
151	C₁₃×#121	C₂³	1	4	yes	—
152	C₁₃×#120	—	2	4	no	—
153	C₁₃×#120	—	2	4	no	—
154	C₁₃×#120	—	2	4	no	—
155	C₁₃×#120	—	2	4	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	2	no	—
173	C₁₃×#117	C₂³	1	4	yes	—
174	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	—	2	1	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₁₃×#107	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
200	#61682	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	—	2	4	no	—
202	C₁₃×#41	—	2	8	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	4	no	—
206	C₁₃×#41	—	4	16	no	—
207	C₁₃×#41	—	4	8	no	—
208	C₁₃×#41	—	8	2	no	—
209	C₁₃×#41	—	8	2	no	—
210	C₂×Q₈×C₁₃	—	2	4	no	—
211	C₂×Q₈×C₁₃	—	2	1	no	—
212	C₂×Q₈×C₁₃	—	2	4	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	2	8	no	—
216	C₂×Q₈×C₁₃	—	4	4	no	—
217	C₂×Q₈×C₁₃	—	4	8	no	—
218	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
219	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	4	4	no	—
236	C₂×D₄×C₁₃	—	4	4	no	—
237	C₂×D₄×C₁₃	—	8	4	no	—
238	C₂×D₄×C₁₃	—	8	4	no	—
239	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
257	C₁₃×SD₁₆	—	2	4	no	—
258	C₁₃×SD₁₆	—	2	8	no	—
259	C₁₃×SD₁₆	—	2	4	no	—
260	C₁₃×SD₁₆	—	4	4	no	—
261	C₁₃×SD₁₆	—	4	4	no	—
262	C₁₃×D₈	—	4	4	no	—
263	C₁₃×D₈	—	4	4	no	—
264	C₁₃×M₁₆	—	4	4	no	—
265	C₂×C₈×C₁₃	—	4	4	no	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
294	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	4	no	—
298	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
302	#3549	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#3329	C₂×C₁₃	1	2	yes	complemented
305	#3321	C₂×C₁₃	1	4	yes	complemented
306	#3305	C₂×C₁₃	1	2	yes	complemented
307	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
308	#3274	C₂×C₁₃	1	2	yes	complemented
309	#3265	C₂×C₁₃	1	4	yes	complemented
310	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3198	C₂×C₁₃	1	4	yes	complemented
313	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3010	C₂×C₁₃	1	4	yes	complemented
316	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	8	4	no	—
321	C₂³×C₁₃	—	8	4	no	—
322	C₂³×C₁₃	—	8	4	no	—
323	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
324	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	4	no	—
328	Q₈×C₁₃	—	4	2	no	—
329	Q₈×C₁₃	—	4	8	no	—
330	Q₈×C₁₃	—	8	1	no	—
331	Q₈×C₁₃	—	8	1	no	—
332	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
333	D₄×C₁₃	—	2	4	no	—
334	D₄×C₁₃	—	2	2	no	—
335	D₄×C₁₃	—	2	4	no	—
336	D₄×C₁₃	—	2	4	no	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	4	2	no	—
339	D₄×C₁₃	—	4	2	no	—
340	D₄×C₁₃	—	4	4	no	—
341	D₄×C₁₃	—	4	8	no	—
342	D₄×C₁₃	—	4	2	no	—
343	D₄×C₁₃	—	4	4	no	—
344	D₄×C₁₃	—	4	2	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	8	1	no	—
347	D₄×C₁₃	—	8	4	no	—
348	D₄×C₁₃	—	8	1	no	—
349	D₄×C₁₃	—	8	1	no	—
350	D₄×C₁₃	—	8	4	no	—
351	D₄×C₁₃	—	8	4	no	—
352	D₄×C₁₃	—	8	4	no	—
353	D₄×C₁₃	—	8	2	no	—
354	D₄×C₁₃	—	8	2	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	—	4	8	no	—
368	C₂×C₄×C₁₃	—	4	4	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	8	1	no	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	4	no	—
381	C₈×C₁₃	—	2	2	no	—
382	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
383	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
384	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
385	H(3,𝔽₄)	—	2	2	no	—
386	#555	—	2	1	no	—
387	#555	C₂²×C₁₃	1	2	yes	—
388	#555	C₂²×C₁₃	1	2	yes	—
389	#550	—	2	1	no	—
390	#550	C₂²×C₁₃	1	2	yes	complemented
391	D₄×Q₈	—	2	1	no	—
392	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
393	#548	—	2	2	no	—
394	#548	C₂²×C₁₃	1	4	yes	complemented
395	D₄²	—	2	1	no	—
396	D₄²	C₂²×C₁₃	1	2	yes	—
397	D₄²	C₂²×C₁₃	1	2	yes	—
398	#537	—	2	2	no	—
399	#537	C₂²×C₁₃	1	2	yes	complemented
400	#535	—	2	2	no	—
401	#535	—	2	2	no	—
402	#535	C₂²×C₁₃	1	4	yes	—
403	#532	—	2	2	no	—
404	#532	C₂²×C₁₃	1	1	yes	characteristic
405	#532	C₂²×C₁₃	1	1	yes	characteristic
406	#532	C₂²×C₁₃	1	1	yes	characteristic
407	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#496	C₂²×C₁₃	1	2	yes	—
410	#493	C₂²×C₁₃	1	1	yes	characteristic
411	#492	C₂²×C₁₃	1	1	yes	characteristic
412	#489	C₂²×C₁₃	1	2	yes	complemented
413	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#485	C₂²×C₁₃	1	4	yes	complemented
416	#482	C₂²×C₁₃	1	4	yes	complemented
417	#481	C₂²×C₁₃	1	2	yes	complemented
418	#480	C₂²×C₁₃	1	2	yes	complemented
419	#477	C₂²×C₁₃	1	2	yes	complemented
420	#475	C₂²×C₁₃	1	2	yes	complemented
421	#469	C₂²×C₁₃	1	4	yes	complemented
422	#468	C₂²×C₁₃	1	4	yes	complemented
423	#466	C₂²×C₁₃	1	4	yes	complemented
424	#465	C₂²×C₁₃	1	4	yes	complemented
425	#463	C₂²×C₁₃	1	4	yes	complemented
426	#461	C₂²×C₁₃	1	2	yes	complemented
427	#460	C₂²×C₁₃	1	2	yes	—
428	#460	C₂²×C₁₃	1	2	yes	—
429	#459	C₂²×C₁₃	1	2	yes	complemented
430	#450	C₂²×C₁₃	1	4	yes	complemented
431	#449	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	2	yes	complemented
437	#448	C₂²×C₁₃	1	2	yes	complemented
438	#448	C₂²×C₁₃	1	4	yes	complemented
439	#447	C₂²×C₁₃	1	4	yes	complemented
440	#440	C₂²×C₁₃	1	4	yes	complemented
441	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
442	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
443	#436	C₂²×C₁₃	1	2	yes	complemented
444	#435	C₂²×C₁₃	1	4	yes	complemented
445	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
446	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#419	C₂²×C₁₃	1	4	yes	complemented
449	#416	C₂²×C₁₃	1	4	yes	complemented
450	#408	C₂²×C₁₃	1	4	yes	complemented
451	C₂²×C₁₃	—	2	1	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	4	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	4	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	16	8	no	—
467	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	4	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	#577	1	2	yes	—
479	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
480	2₋¹⁺⁴	—	4	8	no	—
481	C₂×#41	—	2	4	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	1	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	C₂³×C₁₃	1	4	yes	—
486	C₂×#41	C₂³×C₁₃	1	2	yes	—
487	C₂×#41	C₂³×C₁₃	1	2	yes	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
494	AGL(1,ℤ/8)	—	4	8	no	—
495	C₂×SD₁₆	—	4	8	no	—
496	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
498	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
499	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
501	C₂×D₈	C₂³×C₁₃	1	4	yes	—
502	C₂×D₈	C₂³×C₁₃	1	4	yes	—
503	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
504	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
510	#127	—	2	2	no	—
511	#127	—	2	4	no	—
512	#127	D₄×C₁₃	1	1	yes	characteristic
513	#127	C₂³×C₁₃	1	1	yes	characteristic
514	#127	C₂³×C₁₃	1	1	yes	characteristic
515	#127	C₂³×C₁₃	1	1	yes	characteristic
516	#124	—	2	4	no	—
517	#124	—	2	4	no	—
518	#124	—	2	4	no	—
519	#124	—	2	4	no	—
520	#124	—	2	1	no	—
521	#124	—	2	1	no	—
522	#124	D₄×C₁₃	1	2	yes	—
523	#124	C₂³×C₁₃	1	2	yes	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
528	#121	—	2	4	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	4	no	—
532	#121	—	2	2	no	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	4	no	—
540	#121	D₄×C₁₃	1	2	yes	—
541	#121	D₄×C₁₃	1	2	yes	—
542	#121	C₂³×C₁₃	1	2	yes	—
543	#121	C₂³×C₁₃	1	2	yes	—
544	#121	C₂³×C₁₃	1	4	yes	—
545	#121	C₂³×C₁₃	1	4	yes	—
546	#121	C₂³×C₁₃	1	4	yes	—
547	#120	—	2	4	no	—
548	#120	—	2	4	no	—
549	#120	—	2	4	no	—
550	#120	—	2	4	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₁₃	1	2	yes	—
563	C₄×D₄	C₂³×C₁₃	1	2	yes	—
564	C₄×D₄	C₂³×C₁₃	1	2	yes	—
565	C₄×D₄	C₂³×C₁₃	1	2	yes	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	C₂³×C₁₃	1	4	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
573	#107	C₂³×C₁₃	1	4	yes	—
574	#106	C₂³×C₁₃	1	2	yes	—
575	#106	C₂³×C₁₃	1	2	yes	—
576	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
577	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
578	#103	C₂³×C₁₃	1	2	yes	—
579	#103	C₂³×C₁₃	1	4	yes	—
580	#103	C₂³×C₁₃	1	2	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	2	yes	—
586	#102	C₂³×C₁₃	1	2	yes	—
587	#102	C₂³×C₁₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
592	#97	C₂³×C₁₃	1	2	yes	—
593	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₁₃	—	4	1	no	—
596	C₂×C₁₃	—	4	4	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	—	8	2	no	—
599	C₂×C₁₃	—	8	2	no	—
600	C₂×C₁₃	#3484	1	1	yes	characteristic
601	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
602	C₂×C₁₃	#3585	1	1	yes	characteristic
603	C₂⁴	—	2	4	no	—
604	#41	—	2	8	no	—
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	16	no	—
609	#41	—	4	8	no	—
610	#41	—	8	2	no	—
611	#41	—	8	2	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	8	no	—
618	C₂×Q₈	—	4	4	no	—
619	C₂×Q₈	—	4	8	no	—
620	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
622	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	8	4	no	—
640	C₂×D₄	—	8	4	no	—
641	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
645	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
659	SD₁₆	—	2	4	no	—
660	SD₁₆	—	2	8	no	—
661	SD₁₆	—	2	4	no	—
662	SD₁₆	—	4	4	no	—
663	SD₁₆	—	4	4	no	—
664	D₈	—	4	4	no	—
665	D₈	—	4	4	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
669	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
670	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
696	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₁₃	#61682	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	8	4	no	—
709	C₂³	—	8	4	no	—
710	C₂³	—	8	4	no	—
711	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
712	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	Q₈	—	2	4	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	4	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	8	no	—
718	Q₈	—	8	1	no	—
719	Q₈	—	8	1	no	—
720	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
721	D₄	—	2	4	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	4	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	1	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	4	no	—
741	D₄	—	8	2	no	—
742	D₄	—	8	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
762	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
766	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
767	C₈	—	2	2	no	—
768	C₈	—	2	4	no	—
769	C₈	—	2	2	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	16	8	no	—
786	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	4	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	C₁₃×#577	1	2	yes	—
798	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
799	C₂	—	4	4	no	—
800	C₂	—	4	1	no	—
801	C₂	—	8	2	no	—
802	C₂	—	8	2	no	—
803	C₂	—	8	2	no	—
804	C₂	C₁₃×#3484	1	1	yes	characteristic
805	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
806	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×#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×#3497	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3321	C₂	semidirect
5. C₁₃×#3305	C₂	semidirect
6. D₄×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3274	C₂	semidirect
8. C₁₃×#3265	C₂	semidirect
9. C₁₃×#3214	C₂	semidirect
10. C₁₃×#3207	C₂	semidirect
11. C₁₃×#3198	C₂	semidirect
12. C₁₃×#3112	C₂	semidirect
13. C₁₃×#3103	C₂	semidirect
14. C₁₃×#3010	C₂	semidirect
15. C₁₃×#2981	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
26. D₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
33. C₁₃×#537	C₂²	semidirect
41. C₁₃×#532	C₂²	semidirect
42. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#487	C₂²	semidirect
48. C₁₃×#486	C₂²	semidirect
49. C₁₃×#485	C₂²	semidirect
50. C₁₃×#482	C₂²	semidirect
51. C₁₃×#481	C₂²	semidirect
52. C₁₃×#480	C₂²	semidirect
53. C₁₃×#477	C₂²	semidirect
54. C₁₃×#475	C₂²	semidirect
55. C₁₃×#469	C₂²	semidirect
56. C₁₃×#468	C₂²	semidirect
57. C₁₃×#466	C₂²	semidirect
58. C₁₃×#465	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#461	C₂²	semidirect
63. C₁₃×#459	C₂²	semidirect
64. C₁₃×#450	C₂²	semidirect
65. C₁₃×#449	C₂²	semidirect
66. C₁₃×#449	C₂²	semidirect
67. C₁₃×#449	C₂²	semidirect
68. C₁₃×#449	C₂²	semidirect
69. C₁₃×#448	C₂²	semidirect
70. C₁₃×#448	C₂²	semidirect
71. C₁₃×#448	C₂²	semidirect
72. C₁₃×#448	C₂²	semidirect
73. C₁₃×#447	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#432	C₂²	semidirect
81. C₁₃×#431	C₂²	semidirect
82. C₁₃×#419	C₂²	semidirect
83. C₁₃×#416	C₂²	semidirect
84. C₁₃×#408	C₂²	semidirect
200. #61682	C₁₃	direct (N × H)
302. #3549	C₂×C₁₃	semidirect
303. #3497	C₂×C₁₃	semidirect
304. #3329	C₂×C₁₃	semidirect
305. #3321	C₂×C₁₃	semidirect
306. #3305	C₂×C₁₃	semidirect
307. D₄×SD₁₆	C₂×C₁₃	semidirect
308. #3274	C₂×C₁₃	semidirect
309. #3265	C₂×C₁₃	semidirect
310. #3214	C₂×C₁₃	semidirect
311. #3207	C₂×C₁₃	semidirect
312. #3198	C₂×C₁₃	semidirect
313. #3112	C₂×C₁₃	semidirect
314. #3103	C₂×C₁₃	semidirect
315. #3010	C₂×C₁₃	semidirect
316. #2981	C₂×C₁₃	semidirect
382. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
383. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
384. C₂²×SD₁₆	C₂²×C₁₃	semidirect
390. #550	C₂²×C₁₃	semidirect
392. D₄×Q₈	C₂²×C₁₃	semidirect
394. #548	C₂²×C₁₃	semidirect
399. #537	C₂²×C₁₃	semidirect
407. #532	C₂²×C₁₃	semidirect
408. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
412. #489	C₂²×C₁₃	semidirect
413. #487	C₂²×C₁₃	semidirect
414. #486	C₂²×C₁₃	semidirect
415. #485	C₂²×C₁₃	semidirect
416. #482	C₂²×C₁₃	semidirect
417. #481	C₂²×C₁₃	semidirect
418. #480	C₂²×C₁₃	semidirect
419. #477	C₂²×C₁₃	semidirect
420. #475	C₂²×C₁₃	semidirect
421. #469	C₂²×C₁₃	semidirect
422. #468	C₂²×C₁₃	semidirect
423. #466	C₂²×C₁₃	semidirect
424. #465	C₂²×C₁₃	semidirect
425. #463	C₂²×C₁₃	semidirect
426. #461	C₂²×C₁₃	semidirect
429. #459	C₂²×C₁₃	semidirect
430. #450	C₂²×C₁₃	semidirect
431. #449	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. #448	C₂²×C₁₃	semidirect
438. #448	C₂²×C₁₃	semidirect
439. #447	C₂²×C₁₃	semidirect
440. #440	C₂²×C₁₃	semidirect
441. C₄×SD₁₆	C₂²×C₁₃	semidirect
442. C₄×SD₁₆	C₂²×C₁₃	semidirect
443. #436	C₂²×C₁₃	semidirect
444. #435	C₂²×C₁₃	semidirect
445. C₈×D₄	C₂²×C₁₃	semidirect
446. #432	C₂²×C₁₃	semidirect
447. #431	C₂²×C₁₃	semidirect
448. #419	C₂²×C₁₃	semidirect
449. #416	C₂²×C₁₃	semidirect
450. #408	C₂²×C₁₃	semidirect
704. C₁₃	#61682	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×#3497	2
C₁₃×#3329	2
C₁₃×#3321	2
C₁₃×#3305	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3274	2
C₁₃×#3265	2
C₁₃×#3214	2
C₁₃×#3207	2
C₁₃×#3198	2
C₁₃×#3112	2
C₁₃×#3103	2
C₁₃×#3010	2
C₁₃×#2981	2
#61682	13

Subgroups — C13×#61682 #15748021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61682 #15748021