Subgroups — C₁₃×#60803 #15747142

Order 3328.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3214	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3213	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3207	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3151	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3036	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3006	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
16	C₁₃×#532	—	2	1	no	—
17	C₁₃×#532	—	2	1	no	—
18	C₁₃×#532	—	2	1	no	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	—	2	1	no	—
21	C₁₃×#532	—	2	1	no	—
22	C₁₃×#532	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₁₃×#532	C₂²	1	2	yes	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	complemented
29	C₁₃×#532	C₂²	1	2	yes	complemented
30	C₁₃×#532	C₂²	1	2	yes	complemented
31	C₁₃×#532	C₂²	1	2	yes	complemented
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#124	—	2	1	no	—
37	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#121	—	2	1	no	—
39	C₂×C₁₃×#121	—	2	1	no	—
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₁₃×#121	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	—	2	1	no	—
44	C₂×C₄×D₄×C₁₃	—	2	1	no	—
45	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#496	C₂²	1	8	yes	complemented
48	C₁₃×#493	C₂²	1	4	yes	complemented
49	C₁₃×#492	C₂²	1	4	yes	complemented
50	C₁₃×#489	C₂²	1	8	yes	complemented
51	C₁₃×#487	C₂²	1	4	yes	complemented
52	C₁₃×#486	C₂²	1	4	yes	complemented
53	C₁₃×#463	C₂²	1	16	yes	complemented
54	C₁₃×#461	C₂²	1	8	yes	complemented
55	C₁₃×#459	C₂²	1	8	yes	complemented
56	C₁₃×#449	C₂²	1	16	yes	complemented
57	C₁₃×#448	C₂²	1	8	yes	complemented
58	C₁₃×#447	C₂²	1	8	yes	complemented
59	C₁₃×#432	C₂²	1	2	yes	complemented
60	C₁₃×#432	C₂²	1	2	yes	complemented
61	C₁₃×#431	C₂²	1	2	yes	complemented
62	C₁₃×#431	C₂²	1	2	yes	complemented
63	C₁₃×#423	C₂²	1	2	yes	complemented
64	C₁₃×#417	C₂²	1	8	yes	complemented
65	C₁₃×#407	C₂²	1	2	yes	—
66	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	2	2	no	—
72	C₂×C₁₃×#41	—	2	2	no	—
73	C₂×C₁₃×#41	—	4	8	no	—
74	C₂×C₁₃×#41	—	4	8	no	—
75	C₂×C₁₃×#41	C₂³	1	4	yes	—
76	C₂×C₁₃×#41	C₂³	1	4	yes	—
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	—	2	2	no	—
80	C₂²×D₄×C₁₃	—	2	2	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₃	—	2	1	no	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	—	2	2	no	—
88	C₂³×C₄×C₁₃	—	2	2	no	—
89	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
93	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
94	C₂×C₁₃×D₈	C₂³	1	16	yes	—
95	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×C₄⋊Q₈	—	2	1	no	—
98	C₁₃×C₄⋊Q₈	—	2	1	no	—
99	C₁₃×C₄⋊Q₈	—	2	1	no	—
100	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₃×#127	—	2	1	no	—
105	C₁₃×#127	—	2	1	no	—
106	C₁₃×#127	—	2	1	no	—
107	C₁₃×#127	—	2	1	no	—
108	C₁₃×#127	C₂³	1	2	yes	—
109	C₁₃×#127	C₂³	1	2	yes	—
110	C₁₃×#127	C₂³	1	2	yes	—
111	C₁₃×#127	C₂³	1	2	yes	—
112	C₁₃×#124	—	2	2	no	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#124	C₂³	1	4	yes	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	C₂³	1	4	yes	—
135	C₁₃×#121	C₂³	1	4	yes	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	2	no	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	2	no	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	C₂³	1	4	yes	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	16	yes	—
175	C₁₃×#102	C₂³	1	16	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₄×C₈×C₁₃	C₂³	1	4	yes	—
180	#60803	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂⁴×C₁₃	—	2	2	no	—
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₁₃×#41	—	2	16	no	—
185	C₁₃×#41	—	4	8	no	—
186	C₁₃×#41	—	4	8	no	—
187	C₁₃×#41	—	4	8	no	—
188	C₁₃×#41	—	4	8	no	—
189	C₁₃×#41	—	4	8	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	4	4	no	—
196	C₂×Q₈×C₁₃	—	4	4	no	—
197	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	2	2	no	—
203	C₂×D₄×C₁₃	—	2	2	no	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	4	4	no	—
214	C₂×D₄×C₁₃	—	4	4	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	8	no	—
218	C₂×D₄×C₁₃	—	4	8	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
221	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	8	no	—
232	C₂²×C₄×C₁₃	—	4	8	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×SD₁₆	—	4	16	no	—
252	C₁₃×D₈	—	4	16	no	—
253	C₁₃×M₁₆	—	2	8	no	—
254	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3214	C₂×C₁₃	1	4	yes	complemented
290	#3213	C₂×C₁₃	1	4	yes	complemented
291	#3207	C₂×C₁₃	1	4	yes	complemented
292	#3206	C₂×C₁₃	1	2	yes	complemented
293	#3205	C₂×C₁₃	1	2	yes	complemented
294	#3151	C₂×C₁₃	1	2	yes	complemented
295	#3141	C₂×C₁₃	1	2	yes	complemented
296	#3036	C₂×C₁₃	1	4	yes	complemented
297	#3006	C₂×C₁₃	1	4	yes	complemented
298	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	4	no	—
302	C₂³×C₁₃	—	2	4	no	—
303	C₂³×C₁₃	—	4	1	no	—
304	C₂³×C₁₃	—	4	4	no	—
305	C₂³×C₁₃	—	4	4	no	—
306	C₂³×C₁₃	—	4	4	no	—
307	C₂³×C₁₃	—	4	4	no	—
308	C₂³×C₁₃	—	4	4	no	—
309	C₂³×C₁₃	—	4	4	no	—
310	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₁₃	—	2	8	no	—
314	Q₈×C₁₃	—	4	4	no	—
315	Q₈×C₁₃	—	4	4	no	—
316	Q₈×C₁₃	—	4	4	no	—
317	D₄×C₁₃	—	2	8	no	—
318	D₄×C₁₃	—	2	8	no	—
319	D₄×C₁₃	—	4	4	no	—
320	D₄×C₁₃	—	4	4	no	—
321	D₄×C₁₃	—	4	4	no	—
322	D₄×C₁₃	—	4	4	no	—
323	D₄×C₁₃	—	4	8	no	—
324	D₄×C₁₃	—	4	8	no	—
325	D₄×C₁₃	—	4	8	no	—
326	D₄×C₁₃	—	4	8	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	4	4	no	—
331	D₄×C₁₃	—	4	4	no	—
332	D₄×C₁₃	—	4	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	4	no	—
347	C₂×C₄×C₁₃	—	2	4	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	8	no	—
352	C₂×C₄×C₁₃	—	4	8	no	—
353	C₂×C₄×C₁₃	—	4	4	no	—
354	C₂×C₄×C₁₃	—	4	4	no	—
355	C₂×C₄×C₁₃	—	4	8	no	—
356	C₂×C₄×C₁₃	—	4	8	no	—
357	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
370	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
371	C₈×C₁₃	—	2	8	no	—
372	C₂²×#41	—	2	1	no	—
373	C₂²×#41	C₂²×C₁₃	1	2	yes	—
374	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
375	#532	—	2	1	no	—
376	#532	—	2	1	no	—
377	#532	—	2	1	no	—
378	#532	—	2	1	no	—
379	#532	—	2	1	no	—
380	#532	—	2	1	no	—
381	#532	—	2	1	no	—
382	#532	—	2	1	no	—
383	#532	C₂²×C₁₃	1	2	yes	—
384	#532	C₂²×C₁₃	1	2	yes	—
385	#532	C₂²×C₁₃	1	2	yes	—
386	#532	C₂²×C₁₃	1	2	yes	—
387	#532	C₂²×C₁₃	1	2	yes	complemented
388	#532	C₂²×C₁₃	1	2	yes	complemented
389	#532	C₂²×C₁₃	1	2	yes	complemented
390	#532	C₂²×C₁₃	1	2	yes	complemented
391	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#124	—	2	1	no	—
396	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
397	C₂×#121	—	2	1	no	—
398	C₂×#121	—	2	1	no	—
399	C₂×#121	—	2	1	no	—
400	C₂×#121	C₂²×C₁₃	1	2	yes	—
401	C₂×C₄×D₄	—	2	1	no	—
402	C₂×C₄×D₄	—	2	1	no	—
403	C₂×C₄×D₄	—	2	1	no	—
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
405	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
406	#496	C₂²×C₁₃	1	8	yes	complemented
407	#493	C₂²×C₁₃	1	4	yes	complemented
408	#492	C₂²×C₁₃	1	4	yes	complemented
409	#489	C₂²×C₁₃	1	8	yes	complemented
410	#487	C₂²×C₁₃	1	4	yes	complemented
411	#486	C₂²×C₁₃	1	4	yes	complemented
412	#463	C₂²×C₁₃	1	16	yes	complemented
413	#461	C₂²×C₁₃	1	8	yes	complemented
414	#459	C₂²×C₁₃	1	8	yes	complemented
415	#449	C₂²×C₁₃	1	16	yes	complemented
416	#448	C₂²×C₁₃	1	8	yes	complemented
417	#447	C₂²×C₁₃	1	8	yes	complemented
418	#432	C₂²×C₁₃	1	2	yes	complemented
419	#432	C₂²×C₁₃	1	2	yes	complemented
420	#431	C₂²×C₁₃	1	2	yes	complemented
421	#431	C₂²×C₁₃	1	2	yes	complemented
422	#423	C₂²×C₁₃	1	2	yes	complemented
423	#417	C₂²×C₁₃	1	8	yes	complemented
424	#407	C₂²×C₁₃	1	2	yes	—
425	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
426	C₂²×C₁₃	—	2	1	no	—
427	C₂²×C₁₃	—	2	1	no	—
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	2	1	no	—
431	C₂²×C₁₃	—	2	1	no	—
432	C₂²×C₁₃	—	2	1	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	—	4	4	no	—
435	C₂²×C₁₃	—	4	4	no	—
436	C₂²×C₁₃	—	4	4	no	—
437	C₂²×C₁₃	—	4	4	no	—
438	C₂²×C₁₃	—	4	4	no	—
439	C₂²×C₁₃	—	4	4	no	—
440	C₂²×C₁₃	—	8	8	no	—
441	C₂²×C₁₃	—	8	8	no	—
442	C₂²×C₁₃	#535	1	2	yes	—
443	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
444	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₁₃	—	2	1	no	—
446	C₄×C₁₃	—	2	1	no	—
447	C₄×C₁₃	—	2	1	no	—
448	C₄×C₁₃	—	2	1	no	—
449	C₄×C₁₃	—	2	1	no	—
450	C₄×C₁₃	—	2	1	no	—
451	C₄×C₁₃	—	2	1	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	—	4	4	no	—
454	C₄×C₁₃	#535	1	2	yes	—
455	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
456	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
457	C₄×C₁₃	#575	1	2	yes	—
458	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	4	8	no	—
466	C₂×#41	—	4	8	no	—
467	C₂×#41	C₂³×C₁₃	1	4	yes	—
468	C₂×#41	C₂³×C₁₃	1	4	yes	—
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
478	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
479	C₂³×C₄	—	2	2	no	—
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
482	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
484	AGL(1,ℤ/8)	—	4	16	no	—
485	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
486	C₂×D₈	C₂³×C₁₃	1	16	yes	—
487	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
488	C₄⋊Q₈	—	2	1	no	—
489	C₄⋊Q₈	—	2	1	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
493	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
494	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
496	#127	—	2	1	no	—
497	#127	—	2	1	no	—
498	#127	—	2	1	no	—
499	#127	—	2	1	no	—
500	#127	C₂³×C₁₃	1	2	yes	—
501	#127	C₂³×C₁₃	1	2	yes	—
502	#127	C₂³×C₁₃	1	2	yes	—
503	#127	C₂³×C₁₃	1	2	yes	—
504	#124	—	2	2	no	—
505	#124	—	2	2	no	—
506	#124	—	2	2	no	—
507	#124	—	2	2	no	—
508	#124	—	2	2	no	—
509	#124	—	2	2	no	—
510	#124	C₂³×C₁₃	1	4	yes	—
511	#124	C₂³×C₁₃	1	4	yes	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	C₂³×C₁₃	1	4	yes	—
527	#121	C₂³×C₁₃	1	4	yes	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	C₂³×C₁₃	1	4	yes	—
543	C₄×D₄	C₂³×C₁₃	1	4	yes	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	—	2	2	no	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
557	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
564	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
565	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
566	#103	C₂³×C₁₃	1	16	yes	—
567	#102	C₂³×C₁₃	1	16	yes	—
568	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
570	#97	C₂³×C₁₃	1	4	yes	—
571	C₄×C₈	C₂³×C₁₃	1	4	yes	—
572	C₂×C₁₃	—	2	2	no	—
573	C₂×C₁₃	—	2	2	no	—
574	C₂×C₁₃	—	4	1	no	—
575	C₂×C₁₃	—	8	4	no	—
576	C₂×C₁₃	—	8	4	no	—
577	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
578	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
583	#41	—	2	16	no	—
584	#41	—	4	8	no	—
585	#41	—	4	8	no	—
586	#41	—	4	8	no	—
587	#41	—	4	8	no	—
588	#41	—	4	8	no	—
589	#41	—	4	8	no	—
590	#41	—	4	8	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	4	4	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	8	no	—
617	C₂×D₄	—	4	8	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
620	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	8	no	—
631	C₂²×C₄	—	4	8	no	—
632	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
650	SD₁₆	—	4	16	no	—
651	D₈	—	4	16	no	—
652	M₁₆	—	2	8	no	—
653	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₁₃	#60803	1	1	yes	characteristic, direct product factor, Sylow
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	4	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
701	Q₈	—	2	8	no	—
702	Q₈	—	4	4	no	—
703	Q₈	—	4	4	no	—
704	Q₈	—	4	4	no	—
705	D₄	—	2	8	no	—
706	D₄	—	2	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	4	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	8	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
746	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
757	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
758	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
759	C₈	—	2	8	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	8	8	no	—
775	C₂²	—	8	8	no	—
776	C₂²	C₁₃×#535	1	2	yes	—
777	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
778	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	4	4	no	—
787	C₄	—	4	4	no	—
788	C₄	C₁₃×#535	1	2	yes	—
789	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
790	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
791	C₄	C₁₃×#575	1	2	yes	—
792	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
793	C₂	—	2	2	no	—
794	C₂	—	2	2	no	—
795	C₂	—	4	1	no	—
796	C₂	—	8	4	no	—
797	C₂	—	8	4	no	—
798	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
799	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
800	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3214	C₂	semidirect
4. C₁₃×#3213	C₂	semidirect
5. C₁₃×#3207	C₂	semidirect
6. C₁₃×#3206	C₂	semidirect
7. C₁₃×#3205	C₂	semidirect
8. C₁₃×#3151	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3036	C₂	semidirect
11. C₁₃×#3006	C₂	semidirect
12. C₁₃×#2920	C₂	semidirect
15. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
31. C₁₃×#532	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₁₃×#127	C₂²	semidirect
35. C₂×C₁₃×#127	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃	C₂²	semidirect
47. C₁₃×#496	C₂²	semidirect
48. C₁₃×#493	C₂²	semidirect
49. C₁₃×#492	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#461	C₂²	semidirect
55. C₁₃×#459	C₂²	semidirect
56. C₁₃×#449	C₂²	semidirect
57. C₁₃×#448	C₂²	semidirect
58. C₁₃×#447	C₂²	semidirect
59. C₁₃×#432	C₂²	semidirect
60. C₁₃×#432	C₂²	semidirect
61. C₁₃×#431	C₂²	semidirect
62. C₁₃×#431	C₂²	semidirect
63. C₁₃×#423	C₂²	semidirect
64. C₁₃×#417	C₂²	semidirect
66. C₄×C₁₃×M₁₆	C₂²	semidirect
180. #60803	C₁₃	direct (N × H)
287. C₂×#532	C₂×C₁₃	semidirect
288. C₂×#532	C₂×C₁₃	semidirect
289. #3214	C₂×C₁₃	semidirect
290. #3213	C₂×C₁₃	semidirect
291. #3207	C₂×C₁₃	semidirect
292. #3206	C₂×C₁₃	semidirect
293. #3205	C₂×C₁₃	semidirect
294. #3151	C₂×C₁₃	semidirect
295. #3141	C₂×C₁₃	semidirect
296. #3036	C₂×C₁₃	semidirect
297. #3006	C₂×C₁₃	semidirect
298. #2920	C₂×C₁₃	semidirect
357. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
374. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
387. #532	C₂²×C₁₃	semidirect
388. #532	C₂²×C₁₃	semidirect
389. #532	C₂²×C₁₃	semidirect
390. #532	C₂²×C₁₃	semidirect
391. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
392. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
393. C₂×#127	C₂²×C₁₃	semidirect
394. C₂×#127	C₂²×C₁₃	semidirect
396. C₂×#124	C₂²×C₁₃	semidirect
404. C₂×C₄×D₄	C₂²×C₁₃	semidirect
406. #496	C₂²×C₁₃	semidirect
407. #493	C₂²×C₁₃	semidirect
408. #492	C₂²×C₁₃	semidirect
409. #489	C₂²×C₁₃	semidirect
410. #487	C₂²×C₁₃	semidirect
411. #486	C₂²×C₁₃	semidirect
412. #463	C₂²×C₁₃	semidirect
413. #461	C₂²×C₁₃	semidirect
414. #459	C₂²×C₁₃	semidirect
415. #449	C₂²×C₁₃	semidirect
416. #448	C₂²×C₁₃	semidirect
417. #447	C₂²×C₁₃	semidirect
418. #432	C₂²×C₁₃	semidirect
419. #432	C₂²×C₁₃	semidirect
420. #431	C₂²×C₁₃	semidirect
421. #431	C₂²×C₁₃	semidirect
422. #423	C₂²×C₁₃	semidirect
423. #417	C₂²×C₁₃	semidirect
425. C₄×M₁₆	C₂²×C₁₃	semidirect
686. C₁₃	#60803	direct (N × H)
745. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#532	2
C₁₃×#3214	2
C₁₃×#3213	2
C₁₃×#3207	2
C₁₃×#3206	2
C₁₃×#3205	2
C₁₃×#3151	2
C₁₃×#3141	2
C₁₃×#3036	2
C₁₃×#3006	2
C₁₃×#2920	2
#60803	13

Subgroups — C13×#60803 #15747142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60803 #15747142