Subgroups — C₁₃×#61679 #15748018

Order 3328.

2224 conjugacy classes of subgroups.

The subgroup lattice has 834 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×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3319	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3303	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3264	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×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3008	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×D₈	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	complemented
22	C₁₃×#555	C₂²	1	2	yes	complemented
23	C₁₃×#547	—	2	1	no	—
24	C₁₃×#547	C₂²	1	2	yes	complemented
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	C₂²	1	4	yes	complemented
27	D₄²×C₁₃	—	2	1	no	—
28	D₄²×C₁₃	—	2	1	no	—
29	D₄²×C₁₃	C₂²	1	2	yes	complemented
30	D₄²×C₁₃	C₂²	1	2	yes	complemented
31	D₄²×C₁₃	C₂²	1	2	yes	complemented
32	C₁₃×#537	C₂²	1	2	yes	complemented
33	C₁₃×#535	—	2	2	no	—
34	C₁₃×#535	—	2	2	no	—
35	C₁₃×#535	C₂²	1	4	yes	complemented
36	C₁₃×#534	—	2	2	no	—
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#121	—	2	2	no	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#496	C₂²	1	2	yes	complemented
44	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
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×#476	C₂²	1	2	yes	complemented
54	C₁₃×#474	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×#459	C₂²	1	2	yes	complemented
62	C₁₃×#459	C₂²	1	2	yes	complemented
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×#447	C₂²	1	2	yes	complemented
70	C₁₃×#447	C₂²	1	2	yes	complemented
71	C₁₃×#447	C₂²	1	4	yes	complemented
72	C₁₃×#447	C₂²	1	4	yes	complemented
73	C₁₃×#447	C₂²	1	4	yes	complemented
74	C₁₃×#442	C₂²	1	4	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
76	C₄×C₁₃×D₈	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×#418	C₂²	1	4	yes	complemented
83	C₁₃×#416	C₂²	1	4	yes	complemented
84	C₁₃×#408	C₂²	1	4	yes	complemented
85	C₁₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	—	2	4	no	—
93	C₂²×D₄×C₁₃	—	2	2	no	—
94	C₂²×D₄×C₁₃	—	2	2	no	—
95	C₂²×D₄×C₁₃	—	2	2	no	—
96	C₂²×D₄×C₁₃	—	2	2	no	—
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
102	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×D₈	—	4	8	no	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
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	4	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	D₄	1	2	yes	—
127	C₁₃×#124	C₂³	1	2	yes	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₁₃×#121	—	2	4	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	1	no	—
140	C₁₃×#121	—	2	1	no	—
141	C₁₃×#121	—	2	2	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	2	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	4	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	C₁₃×#120	—	2	4	no	—
157	C₁₃×#120	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
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	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	C₂³	1	4	yes	—
173	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₁₃×#107	C₂³	1	2	yes	—
179	C₁₃×#107	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	4	yes	—
181	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	2	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	#61679	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	4	no	—
203	C₂⁴×C₁₃	—	2	4	no	—
204	C₁₃×#41	—	2	8	no	—
205	C₁₃×#41	—	4	4	no	—
206	C₁₃×#41	—	4	4	no	—
207	C₁₃×#41	—	4	4	no	—
208	C₁₃×#41	—	4	8	no	—
209	C₁₃×#41	—	8	2	no	—
210	C₁₃×#41	—	8	2	no	—
211	C₂×Q₈×C₁₃	—	2	1	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	2	8	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	4	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	1	no	—
225	C₂×D₄×C₁₃	—	2	1	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	4	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	4	no	—
233	C₂×D₄×C₁₃	—	4	4	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	4	4	no	—
236	C₂×D₄×C₁₃	—	4	8	no	—
237	C₂×D₄×C₁₃	—	4	16	no	—
238	C₂×D₄×C₁₃	—	8	4	no	—
239	C₂×D₄×C₁₃	—	8	4	no	—
240	C₂×D₄×C₁₃	—	8	4	no	—
241	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	8	2	no	—
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
261	C₁₃×SD₁₆	—	4	4	no	—
262	C₁₃×SD₁₆	—	4	4	no	—
263	C₁₃×D₈	—	2	4	no	—
264	C₁₃×D₈	—	2	8	no	—
265	C₁₃×D₈	—	2	4	no	—
266	C₁₃×D₈	—	4	4	no	—
267	C₁₃×D₈	—	4	4	no	—
268	C₁₃×M₁₆	—	4	4	no	—
269	C₂×C₈×C₁₃	—	4	4	no	—
270	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	#3549	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#3325	C₂×C₁₃	1	2	yes	complemented
307	#3319	C₂×C₁₃	1	4	yes	complemented
308	#3303	C₂×C₁₃	1	2	yes	complemented
309	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
310	#3272	C₂×C₁₃	1	2	yes	complemented
311	#3264	C₂×C₁₃	1	4	yes	complemented
312	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3198	C₂×C₁₃	1	4	yes	complemented
315	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3008	C₂×C₁₃	1	4	yes	complemented
318	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂³×C₁₃	—	2	4	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	4	8	no	—
325	C₂³×C₁₃	—	8	1	no	—
326	C₂³×C₁₃	—	8	1	no	—
327	C₂³×C₁₃	—	8	4	no	—
328	C₂³×C₁₃	—	8	4	no	—
329	C₂³×C₁₃	—	8	4	no	—
330	C₂³×C₁₃	—	8	4	no	—
331	C₂³×C₁₃	—	8	4	no	—
332	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
333	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₃	—	2	4	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	8	1	no	—
337	Q₈×C₁₃	—	8	1	no	—
338	D₄×C₁₃	—	2	4	no	—
339	D₄×C₁₃	—	2	4	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	4	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	4	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	—	4	2	no	—
348	D₄×C₁₃	—	4	8	no	—
349	D₄×C₁₃	—	4	2	no	—
350	D₄×C₁₃	—	4	8	no	—
351	D₄×C₁₃	—	4	4	no	—
352	D₄×C₁₃	—	4	2	no	—
353	D₄×C₁₃	—	4	2	no	—
354	D₄×C₁₃	—	8	1	no	—
355	D₄×C₁₃	—	8	4	no	—
356	D₄×C₁₃	—	8	1	no	—
357	D₄×C₁₃	—	8	1	no	—
358	D₄×C₁₃	—	8	4	no	—
359	D₄×C₁₃	—	8	4	no	—
360	D₄×C₁₃	—	8	4	no	—
361	D₄×C₁₃	—	8	2	no	—
362	D₄×C₁₃	—	8	2	no	—
363	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	4	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	8	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	4	no	—
378	C₂×C₄×C₁₃	—	8	2	no	—
379	C₂×C₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	2	4	no	—
389	C₈×C₁₃	—	2	2	no	—
390	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
391	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
392	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
393	H(3,𝔽₄)	—	2	2	no	—
394	#555	—	2	1	no	—
395	#555	C₂²×C₁₃	1	2	yes	complemented
396	#555	C₂²×C₁₃	1	2	yes	complemented
397	#547	—	2	1	no	—
398	#547	C₂²×C₁₃	1	2	yes	complemented
399	#546	—	2	2	no	—
400	#546	C₂²×C₁₃	1	4	yes	complemented
401	D₄²	—	2	1	no	—
402	D₄²	—	2	1	no	—
403	D₄²	C₂²×C₁₃	1	2	yes	complemented
404	D₄²	C₂²×C₁₃	1	2	yes	complemented
405	D₄²	C₂²×C₁₃	1	2	yes	complemented
406	#537	C₂²×C₁₃	1	2	yes	complemented
407	#535	—	2	2	no	—
408	#535	—	2	2	no	—
409	#535	C₂²×C₁₃	1	4	yes	complemented
410	#534	—	2	2	no	—
411	#532	C₂²×C₁₃	1	1	yes	characteristic
412	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂×#121	—	2	2	no	—
416	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#496	C₂²×C₁₃	1	2	yes	complemented
418	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#489	C₂²×C₁₃	1	2	yes	complemented
421	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#485	C₂²×C₁₃	1	4	yes	complemented
424	#482	C₂²×C₁₃	1	4	yes	complemented
425	#481	C₂²×C₁₃	1	2	yes	complemented
426	#480	C₂²×C₁₃	1	2	yes	complemented
427	#476	C₂²×C₁₃	1	2	yes	complemented
428	#474	C₂²×C₁₃	1	2	yes	complemented
429	#469	C₂²×C₁₃	1	4	yes	complemented
430	#468	C₂²×C₁₃	1	4	yes	complemented
431	#466	C₂²×C₁₃	1	4	yes	complemented
432	#465	C₂²×C₁₃	1	4	yes	complemented
433	#463	C₂²×C₁₃	1	4	yes	complemented
434	#461	C₂²×C₁₃	1	2	yes	complemented
435	#459	C₂²×C₁₃	1	2	yes	complemented
436	#459	C₂²×C₁₃	1	2	yes	complemented
437	#459	C₂²×C₁₃	1	2	yes	complemented
438	#450	C₂²×C₁₃	1	4	yes	complemented
439	#449	C₂²×C₁₃	1	4	yes	complemented
440	#449	C₂²×C₁₃	1	4	yes	complemented
441	#449	C₂²×C₁₃	1	4	yes	complemented
442	#449	C₂²×C₁₃	1	4	yes	complemented
443	#447	C₂²×C₁₃	1	2	yes	complemented
444	#447	C₂²×C₁₃	1	2	yes	complemented
445	#447	C₂²×C₁₃	1	4	yes	complemented
446	#447	C₂²×C₁₃	1	4	yes	complemented
447	#447	C₂²×C₁₃	1	4	yes	complemented
448	#442	C₂²×C₁₃	1	4	yes	complemented
449	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
450	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
451	#436	C₂²×C₁₃	1	2	yes	complemented
452	#435	C₂²×C₁₃	1	4	yes	complemented
453	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
454	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#418	C₂²×C₁₃	1	4	yes	complemented
457	#416	C₂²×C₁₃	1	4	yes	complemented
458	#408	C₂²×C₁₃	1	4	yes	complemented
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	4	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	8	4	no	—
478	C₂²×C₁₃	—	16	8	no	—
479	C₂²×C₁₃	—	16	8	no	—
480	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	4	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	#576	1	2	yes	—
491	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
492	H(5,𝔽₂)	—	4	8	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	C₂³×C₁₃	1	4	yes	—
497	C₂×#41	C₂³×C₁₃	1	2	yes	—
498	C₂×#41	C₂³×C₁₃	1	2	yes	—
499	C₂²×D₄	—	2	4	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	2	no	—
504	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
506	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
507	C₂³×C₄	—	2	1	no	—
508	AGL(1,ℤ/8)	—	4	8	no	—
509	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
511	C₂×D₈	—	4	8	no	—
512	C₂×D₈	C₂³×C₁₃	1	2	yes	—
513	C₂×D₈	C₂³×C₁₃	1	4	yes	—
514	C₂×D₈	C₂³×C₁₃	1	2	yes	—
515	C₂×D₈	C₂³×C₁₃	1	4	yes	—
516	C₂×D₈	C₂³×C₁₃	1	4	yes	—
517	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
518	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
519	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	#127	—	2	4	no	—
524	#127	D₄×C₁₃	1	1	yes	characteristic
525	#127	C₂³×C₁₃	1	1	yes	characteristic
526	#127	C₂³×C₁₃	1	1	yes	characteristic
527	#127	C₂³×C₁₃	1	1	yes	characteristic
528	#124	—	2	4	no	—
529	#124	—	2	4	no	—
530	#124	—	2	4	no	—
531	#124	—	2	1	no	—
532	#124	—	2	1	no	—
533	#124	D₄×C₁₃	1	2	yes	—
534	#124	C₂³×C₁₃	1	2	yes	—
535	#123	—	2	4	no	—
536	#123	—	2	4	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
539	#121	—	2	4	no	—
540	#121	—	2	2	no	—
541	#121	—	2	2	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	D₄×C₁₃	1	2	yes	—
553	#121	D₄×C₁₃	1	2	yes	—
554	#121	C₂³×C₁₃	1	2	yes	—
555	#121	C₂³×C₁₃	1	2	yes	—
556	#121	C₂³×C₁₃	1	4	yes	—
557	#121	C₂³×C₁₃	1	4	yes	—
558	#121	C₂³×C₁₃	1	4	yes	—
559	#120	—	2	4	no	—
560	#120	—	2	4	no	—
561	#120	—	2	4	no	—
562	#120	—	2	4	no	—
563	#120	—	2	4	no	—
564	#120	—	2	4	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	C₂³×C₁₃	1	2	yes	—
572	C₄×D₄	C₂³×C₁₃	1	2	yes	—
573	C₄×D₄	C₂³×C₁₃	1	2	yes	—
574	C₄×D₄	C₂³×C₁₃	1	2	yes	—
575	C₄×D₄	C₂³×C₁₃	1	2	yes	—
576	C₄×D₄	C₂³×C₁₃	1	2	yes	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	C₂³×C₁₃	1	4	yes	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	4	no	—
584	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
585	#107	C₂³×C₁₃	1	2	yes	—
586	#107	C₂³×C₁₃	1	2	yes	—
587	#106	C₂³×C₁₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
589	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
590	#103	C₂³×C₁₃	1	4	yes	—
591	#103	C₂³×C₁₃	1	4	yes	—
592	#102	C₂³×C₁₃	1	2	yes	—
593	#102	C₂³×C₁₃	1	4	yes	—
594	#102	C₂³×C₁₃	1	2	yes	—
595	#102	C₂³×C₁₃	1	4	yes	—
596	#102	C₂³×C₁₃	1	4	yes	—
597	#102	C₂³×C₁₃	1	2	yes	—
598	#102	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
602	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
603	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
604	#97	C₂³×C₁₃	1	2	yes	—
605	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₁₃	—	4	1	no	—
608	C₂×C₁₃	—	4	4	no	—
609	C₂×C₁₃	—	4	4	no	—
610	C₂×C₁₃	—	8	2	no	—
611	C₂×C₁₃	—	8	2	no	—
612	C₂×C₁₃	—	8	2	no	—
613	C₂×C₁₃	#3484	1	1	yes	characteristic
614	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
615	C₂×C₁₃	#3585	1	1	yes	characteristic
616	C₂⁴	—	2	1	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	4	no	—
619	#41	—	2	8	no	—
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	8	no	—
624	#41	—	8	2	no	—
625	#41	—	8	2	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	2	4	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	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	8	no	—
652	C₂×D₄	—	4	16	no	—
653	C₂×D₄	—	8	4	no	—
654	C₂×D₄	—	8	4	no	—
655	C₂×D₄	—	8	4	no	—
656	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
660	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
661	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	8	2	no	—
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
676	SD₁₆	—	4	4	no	—
677	SD₁₆	—	4	4	no	—
678	D₈	—	2	4	no	—
679	D₈	—	2	8	no	—
680	D₈	—	2	4	no	—
681	D₈	—	4	4	no	—
682	D₈	—	4	4	no	—
683	M₁₆	—	4	4	no	—
684	C₂×C₈	—	4	4	no	—
685	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
686	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
687	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
713	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₁₃	#61679	1	1	yes	characteristic, direct product factor, Sylow
720	C₂³	—	2	4	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	4	no	—
729	C₂³	—	8	4	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
734	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	8	1	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	2	no	—
763	D₄	—	8	2	no	—
764	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₈	—	2	2	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	4	no	—
810	C₂²	—	16	8	no	—
811	C₂²	—	16	8	no	—
812	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	4	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	C₁₃×#576	1	2	yes	—
823	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
824	C₂	—	4	1	no	—
825	C₂	—	4	4	no	—
826	C₂	—	4	4	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	C₁₃×#3484	1	1	yes	characteristic
831	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
832	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×#3496	C₂	semidirect
3. C₁₃×#3325	C₂	semidirect
4. C₁₃×#3319	C₂	semidirect
5. C₁₃×#3303	C₂	semidirect
6. D₄×C₁₃×D₈	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₁₃×#3264	C₂	semidirect
9. C₁₃×#3214	C₂	semidirect
10. C₁₃×#3207	C₂	semidirect
11. C₁₃×#3198	C₂	semidirect
12. C₁₃×#3109	C₂	semidirect
13. C₁₃×#3100	C₂	semidirect
14. C₁₃×#3008	C₂	semidirect
15. C₁₃×#2981	C₂	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
24. C₁₃×#547	C₂²	semidirect
26. C₁₃×#546	C₂²	semidirect
29. D₄²×C₁₃	C₂²	semidirect
30. D₄²×C₁₃	C₂²	semidirect
31. D₄²×C₁₃	C₂²	semidirect
32. C₁₃×#537	C₂²	semidirect
35. C₁₃×#535	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#493	C₂²	semidirect
45. C₁₃×#492	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×#476	C₂²	semidirect
54. C₁₃×#474	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
61. C₁₃×#459	C₂²	semidirect
62. C₁₃×#459	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×#447	C₂²	semidirect
70. C₁₃×#447	C₂²	semidirect
71. C₁₃×#447	C₂²	semidirect
72. C₁₃×#447	C₂²	semidirect
73. C₁₃×#447	C₂²	semidirect
74. C₁₃×#442	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
76. C₄×C₁₃×D₈	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×#418	C₂²	semidirect
83. C₁₃×#416	C₂²	semidirect
84. C₁₃×#408	C₂²	semidirect
200. #61679	C₁₃	direct (N × H)
304. #3549	C₂×C₁₃	semidirect
305. #3496	C₂×C₁₃	semidirect
306. #3325	C₂×C₁₃	semidirect
307. #3319	C₂×C₁₃	semidirect
308. #3303	C₂×C₁₃	semidirect
309. D₄×D₈	C₂×C₁₃	semidirect
310. #3272	C₂×C₁₃	semidirect
311. #3264	C₂×C₁₃	semidirect
312. #3214	C₂×C₁₃	semidirect
313. #3207	C₂×C₁₃	semidirect
314. #3198	C₂×C₁₃	semidirect
315. #3109	C₂×C₁₃	semidirect
316. #3100	C₂×C₁₃	semidirect
317. #3008	C₂×C₁₃	semidirect
318. #2981	C₂×C₁₃	semidirect
390. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
391. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
392. C₂²×D₈	C₂²×C₁₃	semidirect
395. #555	C₂²×C₁₃	semidirect
396. #555	C₂²×C₁₃	semidirect
398. #547	C₂²×C₁₃	semidirect
400. #546	C₂²×C₁₃	semidirect
403. D₄²	C₂²×C₁₃	semidirect
404. D₄²	C₂²×C₁₃	semidirect
405. D₄²	C₂²×C₁₃	semidirect
406. #537	C₂²×C₁₃	semidirect
409. #535	C₂²×C₁₃	semidirect
412. #532	C₂²×C₁₃	semidirect
413. #532	C₂²×C₁₃	semidirect
414. #532	C₂²×C₁₃	semidirect
416. C₂×C₄×D₄	C₂²×C₁₃	semidirect
417. #496	C₂²×C₁₃	semidirect
418. #493	C₂²×C₁₃	semidirect
419. #492	C₂²×C₁₃	semidirect
420. #489	C₂²×C₁₃	semidirect
421. #487	C₂²×C₁₃	semidirect
422. #486	C₂²×C₁₃	semidirect
423. #485	C₂²×C₁₃	semidirect
424. #482	C₂²×C₁₃	semidirect
425. #481	C₂²×C₁₃	semidirect
426. #480	C₂²×C₁₃	semidirect
427. #476	C₂²×C₁₃	semidirect
428. #474	C₂²×C₁₃	semidirect
429. #469	C₂²×C₁₃	semidirect
430. #468	C₂²×C₁₃	semidirect
431. #466	C₂²×C₁₃	semidirect
432. #465	C₂²×C₁₃	semidirect
433. #463	C₂²×C₁₃	semidirect
434. #461	C₂²×C₁₃	semidirect
435. #459	C₂²×C₁₃	semidirect
436. #459	C₂²×C₁₃	semidirect
437. #459	C₂²×C₁₃	semidirect
438. #450	C₂²×C₁₃	semidirect
439. #449	C₂²×C₁₃	semidirect
440. #449	C₂²×C₁₃	semidirect
441. #449	C₂²×C₁₃	semidirect
442. #449	C₂²×C₁₃	semidirect
443. #447	C₂²×C₁₃	semidirect
444. #447	C₂²×C₁₃	semidirect
445. #447	C₂²×C₁₃	semidirect
446. #447	C₂²×C₁₃	semidirect
447. #447	C₂²×C₁₃	semidirect
448. #442	C₂²×C₁₃	semidirect
449. C₄×D₈	C₂²×C₁₃	semidirect
450. C₄×D₈	C₂²×C₁₃	semidirect
451. #436	C₂²×C₁₃	semidirect
452. #435	C₂²×C₁₃	semidirect
453. C₈×D₄	C₂²×C₁₃	semidirect
454. #432	C₂²×C₁₃	semidirect
455. #431	C₂²×C₁₃	semidirect
456. #418	C₂²×C₁₃	semidirect
457. #416	C₂²×C₁₃	semidirect
458. #408	C₂²×C₁₃	semidirect
719. C₁₃	#61679	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×#3496	2
C₁₃×#3325	2
C₁₃×#3319	2
C₁₃×#3303	2
D₄×C₁₃×D₈	2
C₁₃×#3272	2
C₁₃×#3264	2
C₁₃×#3214	2
C₁₃×#3207	2
C₁₃×#3198	2
C₁₃×#3109	2
C₁₃×#3100	2
C₁₃×#3008	2
C₁₃×#2981	2
#61679	13

Subgroups — C13×#61679 #15748018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61679 #15748018