Subgroups — C₁₃×#60819 #15747158

Order 3328.

2058 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3224	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₁₃×#559	—	2	2	no	—
31	C₁₃×#556	—	2	2	no	—
32	C₁₃×#551	—	2	4	no	—
33	C₁₃×#548	—	2	2	no	—
34	C₁₃×#546	—	2	4	no	—
35	C₁₃×#546	—	2	2	no	—
36	C₁₃×#542	C₂²	1	4	yes	complemented
37	C₁₃×#536	C₂²	1	1	yes	characteristic
38	C₁₃×#536	C₂²	1	1	yes	characteristic
39	C₁₃×#536	C₂²	1	2	yes	complemented
40	C₁₃×#535	C₂²	1	1	yes	characteristic
41	C₁₃×#535	C₂²	1	1	yes	characteristic
42	C₁₃×#535	C₂²	1	2	yes	complemented
43	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#532	C₂²	1	1	yes	characteristic
45	C₁₃×#532	C₂²	1	2	yes	complemented
46	C₁₃×#529	C₂²	1	4	yes	complemented
47	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
50	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
53	C₁₃×#497	C₂²	1	2	yes	complemented
54	C₁₃×#496	C₂²	1	2	yes	complemented
55	C₁₃×#495	C₂²	1	4	yes	complemented
56	C₁₃×#495	C₂²	1	4	yes	complemented
57	C₁₃×#495	C₂²	1	2	yes	complemented
58	C₁₃×#495	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	4	yes	complemented
60	C₁₃×#488	C₂²	1	2	yes	complemented
61	C₁₃×#488	C₂²	1	2	yes	complemented
62	C₁₃×#488	C₂²	1	4	yes	complemented
63	C₁₃×#487	C₂²	1	2	yes	complemented
64	C₁₃×#486	C₂²	1	2	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#463	C₂²	1	4	yes	complemented
69	C₁₃×#462	C₂²	1	4	yes	complemented
70	C₁₃×#461	C₂²	1	4	yes	complemented
71	C₁₃×#460	C₂²	1	4	yes	complemented
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#452	C₂²	1	4	yes	complemented
74	C₁₃×#452	C₂²	1	4	yes	complemented
75	C₁₃×#451	C₂²	1	4	yes	complemented
76	C₁₃×#450	C₂²	1	4	yes	complemented
77	C₁₃×#449	C₂²	1	4	yes	—
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#448	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	—
81	C₁₃×#433	C₂²	1	4	yes	complemented
82	C₁₃×#431	C₂²	1	4	yes	complemented
83	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#418	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	1	yes	characteristic
90	C₁₃×#416	C₂²	1	1	yes	characteristic
91	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#408	C₂²	1	1	yes	characteristic
94	C₁₃×#408	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×2₋¹⁺⁴	—	4	2	no	—
98	C₁₃×2₋¹⁺⁴	—	4	2	no	—
99	C₁₃×H(5,𝔽₂)	—	4	2	no	—
100	C₁₃×H(5,𝔽₂)	—	4	2	no	—
101	C₂×C₁₃×#41	—	2	1	no	—
102	C₂×C₁₃×#41	—	2	2	no	—
103	C₂×C₁₃×#41	—	2	1	no	—
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×#41	C₂³	1	2	yes	—
107	C₂×C₁₃×#41	C₂³	1	2	yes	—
108	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	—	2	1	no	—
110	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	—	2	2	no	—
114	C₂²×D₄×C₁₃	—	2	1	no	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₁₃×#137	—	4	2	no	—
119	C₁₃×#137	—	4	2	no	—
120	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
121	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
122	C₂×C₁₃×Q₁₆	—	4	2	no	—
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	—	4	2	no	—
127	C₂×C₁₃×SD₁₆	—	4	2	no	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×D₈	—	4	2	no	—
135	C₂×C₁₃×D₈	C₂³	1	2	yes	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₂×C₁₃×D₈	C₂³	1	2	yes	—
138	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	—	2	1	no	—
143	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×#127	—	2	1	no	—
147	C₁₃×#127	C₂³	1	2	yes	—
148	C₁₃×#127	C₂³	1	1	yes	characteristic
149	C₁₃×#126	—	2	4	no	—
150	C₁₃×#126	—	2	4	no	—
151	C₁₃×#125	C₂³	1	2	yes	—
152	C₁₃×#124	—	2	1	no	—
153	C₁₃×#124	—	2	1	no	—
154	C₁₃×#124	—	2	4	no	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	—	2	4	no	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	C₂³	1	2	yes	—
159	C₁₃×#124	C₂³	1	2	yes	—
160	C₁₃×#124	C₂³	1	2	yes	—
161	C₁₃×#124	C₂³	1	1	yes	characteristic
162	C₁₃×#124	C₂³	1	1	yes	characteristic
163	C₁₃×#124	C₂³	1	2	yes	—
164	C₁₃×#124	C₂³	1	2	yes	—
165	C₁₃×#124	C₂³	1	2	yes	—
166	C₁₃×#123	—	2	2	no	—
167	C₁₃×#123	—	2	4	no	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	—	2	4	no	—
170	C₁₃×#123	—	2	4	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	4	no	—
174	C₁₃×C₂²⋊Q₈	—	2	4	no	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	4	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	4	no	—
180	C₁₃×#121	C₂³	1	4	yes	—
181	C₁₃×#120	—	2	2	no	—
182	C₁₃×#120	—	2	2	no	—
183	C₁₃×#120	—	2	4	no	—
184	C₄×Q₈×C₁₃	—	2	2	no	—
185	C₄×Q₈×C₁₃	—	2	2	no	—
186	C₄×Q₈×C₁₃	D₄	1	2	yes	—
187	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
188	C₄×D₄×C₁₃	—	2	4	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	4	no	—
192	C₄×D₄×C₁₃	D₄	1	4	yes	—
193	C₄×D₄×C₁₃	D₄	1	2	yes	—
194	C₄×D₄×C₁₃	C₂³	1	4	yes	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	4	no	—
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	2	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	2	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₁₃×#97	C₂³	1	2	yes	—
224	C₄×C₈×C₁₃	C₂³	1	2	yes	—
225	C₄×C₈×C₁₃	C₂³	1	2	yes	—
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	#60819	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂⁴×C₁₃	—	2	1	no	—
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₂⁴×C₁₃	—	2	1	no	—
231	C₁₃×#41	—	2	2	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	4	2	no	—
238	C₁₃×#41	—	4	2	no	—
239	C₁₃×#41	—	4	2	no	—
240	C₁₃×#41	—	4	2	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₂×Q₈×C₁₃	—	2	1	no	—
245	C₂×Q₈×C₁₃	—	2	2	no	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	2	no	—
251	C₂×Q₈×C₁₃	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	4	2	no	—
253	C₂×Q₈×C₁₃	—	4	2	no	—
254	C₂×Q₈×C₁₃	—	4	4	no	—
255	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	1	no	—
264	C₂×D₄×C₁₃	—	2	4	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	2	4	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	4	2	no	—
275	C₂×D₄×C₁₃	—	4	2	no	—
276	C₂×D₄×C₁₃	—	4	8	no	—
277	C₂×D₄×C₁₃	—	4	4	no	—
278	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	4	no	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₁₃×Q₁₆	—	4	4	no	—
297	C₁₃×Q₁₆	—	4	2	no	—
298	C₁₃×Q₁₆	—	4	2	no	—
299	C₁₃×SD₁₆	—	4	4	no	—
300	C₁₃×SD₁₆	—	4	4	no	—
301	C₁₃×SD₁₆	—	4	2	no	—
302	C₁₃×SD₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	—	4	2	no	—
304	C₁₃×SD₁₆	—	4	2	no	—
305	C₁₃×D₈	—	4	4	no	—
306	C₁₃×D₈	—	4	2	no	—
307	C₁₃×D₈	—	4	2	no	—
308	C₁₃×M₁₆	—	2	2	no	—
309	C₁₃×M₁₆	—	2	2	no	—
310	C₂×C₈×C₁₃	—	2	2	no	—
311	C₂×C₈×C₁₃	—	2	2	no	—
312	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	4	no	—
318	C₁₃×C₄⋊C₄	—	2	4	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	4	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₁₃×C₂²⋊C₄	—	2	1	no	—
328	C₁₃×C₂²⋊C₄	—	2	1	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	4	no	—
337	C₁₃×C₂²⋊C₄	—	2	4	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
342	C₄²×C₁₃	—	2	4	no	—
343	C₄²×C₁₃	—	2	1	no	—
344	C₄²×C₁₃	—	2	1	no	—
345	C₄²×C₁₃	C₂×D₄	1	4	yes	—
346	C₄²×C₁₃	C₂×D₄	1	2	yes	—
347	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3225	C₂×C₁₃	1	4	yes	complemented
353	#3224	C₂×C₁₃	1	4	yes	complemented
354	#3212	C₂×C₁₃	1	4	yes	complemented
355	#3211	C₂×C₁₃	1	4	yes	complemented
356	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3043	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3042	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3041	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3010	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3009	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3008	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	2	no	—
375	C₂³×C₁₃	—	4	2	no	—
376	C₂³×C₁₃	—	8	2	no	—
377	C₂³×C₁₃	—	8	2	no	—
378	C₂³×C₁₃	—	8	4	no	—
379	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
380	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	Q₈×C₁₃	—	2	2	no	—
382	Q₈×C₁₃	—	2	2	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	2	1	no	—
385	Q₈×C₁₃	—	2	1	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	2	1	no	—
389	Q₈×C₁₃	—	2	1	no	—
390	Q₈×C₁₃	—	4	4	no	—
391	Q₈×C₁₃	—	4	2	no	—
392	Q₈×C₁₃	—	4	2	no	—
393	Q₈×C₁₃	—	8	2	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	2	2	no	—
398	D₄×C₁₃	—	2	1	no	—
399	D₄×C₁₃	—	2	1	no	—
400	D₄×C₁₃	—	2	2	no	—
401	D₄×C₁₃	—	2	2	no	—
402	D₄×C₁₃	—	2	1	no	—
403	D₄×C₁₃	—	2	1	no	—
404	D₄×C₁₃	—	4	4	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	4	no	—
407	D₄×C₁₃	—	4	2	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	4	2	no	—
410	D₄×C₁₃	—	4	2	no	—
411	D₄×C₁₃	—	8	4	no	—
412	D₄×C₁₃	—	8	2	no	—
413	D₄×C₁₃	—	8	4	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	4	no	—
426	C₂×C₄×C₁₃	—	4	4	no	—
427	C₂×C₄×C₁₃	—	4	2	no	—
428	C₂×C₄×C₁₃	—	4	2	no	—
429	C₂×C₄×C₁₃	—	4	2	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	8	4	no	—
432	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
439	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
440	C₈×C₁₃	—	2	2	no	—
441	C₈×C₁₃	—	2	2	no	—
442	C₈×C₁₃	—	2	2	no	—
443	C₈×C₁₃	—	2	2	no	—
444	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
454	#559	—	2	2	no	—
455	#556	—	2	2	no	—
456	#551	—	2	4	no	—
457	#548	—	2	2	no	—
458	#546	—	2	4	no	—
459	#546	—	2	2	no	—
460	#542	C₂²×C₁₃	1	4	yes	complemented
461	#536	C₂²×C₁₃	1	1	yes	characteristic
462	#536	C₂²×C₁₃	1	1	yes	characteristic
463	#536	C₂²×C₁₃	1	2	yes	complemented
464	#535	C₂²×C₁₃	1	1	yes	characteristic
465	#535	C₂²×C₁₃	1	1	yes	characteristic
466	#535	C₂²×C₁₃	1	2	yes	complemented
467	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#532	C₂²×C₁₃	1	1	yes	characteristic
469	#532	C₂²×C₁₃	1	2	yes	complemented
470	#529	C₂²×C₁₃	1	4	yes	complemented
471	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
474	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
477	#497	C₂²×C₁₃	1	2	yes	complemented
478	#496	C₂²×C₁₃	1	2	yes	complemented
479	#495	C₂²×C₁₃	1	4	yes	complemented
480	#495	C₂²×C₁₃	1	4	yes	complemented
481	#495	C₂²×C₁₃	1	2	yes	complemented
482	#495	C₂²×C₁₃	1	2	yes	complemented
483	#489	C₂²×C₁₃	1	4	yes	complemented
484	#488	C₂²×C₁₃	1	2	yes	complemented
485	#488	C₂²×C₁₃	1	2	yes	complemented
486	#488	C₂²×C₁₃	1	4	yes	complemented
487	#487	C₂²×C₁₃	1	2	yes	complemented
488	#486	C₂²×C₁₃	1	2	yes	complemented
489	#464	C₂²×C₁₃	1	4	yes	complemented
490	#464	C₂²×C₁₃	1	4	yes	complemented
491	#463	C₂²×C₁₃	1	4	yes	complemented
492	#463	C₂²×C₁₃	1	4	yes	complemented
493	#462	C₂²×C₁₃	1	4	yes	complemented
494	#461	C₂²×C₁₃	1	4	yes	complemented
495	#460	C₂²×C₁₃	1	4	yes	complemented
496	#459	C₂²×C₁₃	1	4	yes	complemented
497	#452	C₂²×C₁₃	1	4	yes	complemented
498	#452	C₂²×C₁₃	1	4	yes	complemented
499	#451	C₂²×C₁₃	1	4	yes	complemented
500	#450	C₂²×C₁₃	1	4	yes	complemented
501	#449	C₂²×C₁₃	1	4	yes	—
502	#449	C₂²×C₁₃	1	4	yes	complemented
503	#448	C₂²×C₁₃	1	4	yes	complemented
504	#447	C₂²×C₁₃	1	4	yes	—
505	#433	C₂²×C₁₃	1	4	yes	complemented
506	#431	C₂²×C₁₃	1	4	yes	complemented
507	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#418	C₂²×C₁₃	1	1	yes	characteristic
512	#418	C₂²×C₁₃	1	1	yes	characteristic
513	#416	C₂²×C₁₃	1	1	yes	characteristic
514	#416	C₂²×C₁₃	1	1	yes	characteristic
515	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#408	C₂²×C₁₃	1	1	yes	characteristic
518	#408	C₂²×C₁₃	1	1	yes	characteristic
519	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	2	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	4	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	1	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	16	2	no	—
533	C₂²×C₁₃	—	16	2	no	—
534	C₂²×C₁₃	—	16	4	no	—
535	C₂²×C₁₃	#535	1	2	yes	—
536	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	4	no	—
539	C₄×C₁₃	—	2	2	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	1	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	#535	1	2	yes	—
548	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	2₋¹⁺⁴	—	4	2	no	—
551	2₋¹⁺⁴	—	4	2	no	—
552	H(5,𝔽₂)	—	4	2	no	—
553	H(5,𝔽₂)	—	4	2	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×#41	C₂³×C₁₃	1	2	yes	—
560	C₂×#41	C₂³×C₁₃	1	2	yes	—
561	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
566	C₂²×D₄	—	2	2	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
571	#137	—	4	2	no	—
572	#137	—	4	2	no	—
573	AGL(1,ℤ/8)	—	4	2	no	—
574	AGL(1,ℤ/8)	—	4	2	no	—
575	C₂×Q₁₆	—	4	2	no	—
576	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
577	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
578	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
579	C₂×SD₁₆	—	4	2	no	—
580	C₂×SD₁₆	—	4	2	no	—
581	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
585	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×D₈	—	4	2	no	—
588	C₂×D₈	C₂³×C₁₃	1	4	yes	—
589	C₂×D₈	C₂³×C₁₃	1	2	yes	—
590	C₂×D₈	C₂³×C₁₃	1	2	yes	—
591	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	#127	—	2	1	no	—
600	#127	C₂³×C₁₃	1	1	yes	characteristic
601	#127	C₂³×C₁₃	1	2	yes	—
602	#126	—	2	4	no	—
603	#126	—	2	4	no	—
604	#125	C₂³×C₁₃	1	2	yes	—
605	#124	—	2	1	no	—
606	#124	—	2	1	no	—
607	#124	—	2	4	no	—
608	#124	—	2	2	no	—
609	#124	—	2	4	no	—
610	#124	—	2	2	no	—
611	#124	C₂³×C₁₃	1	2	yes	—
612	#124	C₂³×C₁₃	1	2	yes	—
613	#124	C₂³×C₁₃	1	1	yes	characteristic
614	#124	C₂³×C₁₃	1	2	yes	—
615	#124	C₂³×C₁₃	1	2	yes	—
616	#124	C₂³×C₁₃	1	2	yes	—
617	#124	C₂³×C₁₃	1	2	yes	—
618	#124	C₂³×C₁₃	1	1	yes	characteristic
619	#123	—	2	2	no	—
620	#123	—	2	4	no	—
621	#123	—	2	2	no	—
622	#123	—	2	4	no	—
623	#123	—	2	4	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	C₂²⋊Q₈	—	2	4	no	—
628	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
629	#121	—	2	2	no	—
630	#121	—	2	4	no	—
631	#121	—	2	2	no	—
632	#121	—	2	4	no	—
633	#121	C₂³×C₁₃	1	4	yes	—
634	#120	—	2	2	no	—
635	#120	—	2	2	no	—
636	#120	—	2	4	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	—	2	2	no	—
639	C₄×Q₈	D₄×C₁₃	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
641	C₄×D₄	—	2	4	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	D₄×C₁₃	1	4	yes	—
646	C₄×D₄	D₄×C₁₃	1	2	yes	—
647	C₄×D₄	C₂³×C₁₃	1	4	yes	—
648	#117	—	2	2	no	—
649	#117	—	2	4	no	—
650	#117	C₂³×C₁₃	1	1	yes	characteristic
651	#117	C₂³×C₁₃	1	1	yes	characteristic
652	#117	C₂³×C₁₃	1	1	yes	characteristic
653	#117	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	—	2	2	no	—
655	C₂×C₂²⋊C₄	—	2	4	no	—
656	C₂×C₂²⋊C₄	—	2	2	no	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
661	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
662	#103	C₂³×C₁₃	1	2	yes	—
663	#103	C₂³×C₁₃	1	2	yes	—
664	#103	C₂³×C₁₃	1	2	yes	—
665	#103	C₂³×C₁₃	1	2	yes	—
666	#103	C₂³×C₁₃	1	4	yes	—
667	#103	C₂³×C₁₃	1	4	yes	—
668	#102	C₂³×C₁₃	1	2	yes	—
669	#102	C₂³×C₁₃	1	2	yes	—
670	#102	C₂³×C₁₃	1	2	yes	—
671	#102	C₂³×C₁₃	1	2	yes	—
672	#102	C₂³×C₁₃	1	4	yes	—
673	#102	C₂³×C₁₃	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
676	#97	C₂³×C₁₃	1	2	yes	—
677	C₄×C₈	C₂³×C₁₃	1	2	yes	—
678	C₄×C₈	C₂³×C₁₃	1	2	yes	—
679	C₄×C₈	C₂³×C₁₃	1	2	yes	—
680	C₂×C₁₃	—	2	2	no	—
681	C₂×C₁₃	—	4	2	no	—
682	C₂×C₁₃	—	8	1	no	—
683	C₂×C₁₃	—	8	2	no	—
684	C₂×C₁₃	—	8	2	no	—
685	C₂×C₁₃	—	8	1	no	—
686	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
687	C₂×C₁₃	#3584	1	2	yes	—
688	C₂⁴	—	2	1	no	—
689	C₂⁴	—	2	2	no	—
690	C₂⁴	—	2	1	no	—
691	#41	—	2	2	no	—
692	#41	—	2	2	no	—
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	—	4	2	no	—
701	#41	—	4	8	no	—
702	#41	—	4	4	no	—
703	#41	—	4	4	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	—	4	4	no	—
715	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
717	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	8	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	Q₁₆	—	4	4	no	—
757	Q₁₆	—	4	2	no	—
758	Q₁₆	—	4	2	no	—
759	SD₁₆	—	4	4	no	—
760	SD₁₆	—	4	4	no	—
761	SD₁₆	—	4	2	no	—
762	SD₁₆	—	4	2	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	D₈	—	4	4	no	—
766	D₈	—	4	2	no	—
767	D₈	—	4	2	no	—
768	M₁₆	—	2	2	no	—
769	M₁₆	—	2	2	no	—
770	C₂×C₈	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
773	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
774	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
775	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
802	C₄²	—	2	4	no	—
803	C₄²	—	2	1	no	—
804	C₄²	—	2	1	no	—
805	C₄²	C₂×D₄×C₁₃	1	4	yes	—
806	C₄²	C₂×D₄×C₁₃	1	2	yes	—
807	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₁₃	1	2	yes	—
810	C₁₃	#60819	1	1	yes	characteristic, direct product factor, Sylow
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	—	8	4	no	—
821	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
822	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	1	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	1	no	—
831	Q₈	—	2	1	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	2	no	—
834	Q₈	—	4	2	no	—
835	Q₈	—	8	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	1	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	4	2	no	—
852	D₄	—	4	2	no	—
853	D₄	—	8	4	no	—
854	D₄	—	8	2	no	—
855	D₄	—	8	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	8	4	no	—
874	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
875	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
880	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
881	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
882	C₈	—	2	2	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	16	2	no	—
898	C₂²	—	16	2	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₁₃×#535	1	2	yes	—
901	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	C₁₃×#535	1	2	yes	—
913	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
914	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
922	C₂	C₁₃×#3584	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3500	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3224	C₂	semidirect
5. C₁₃×#3212	C₂	semidirect
6. C₁₃×#3211	C₂	semidirect
7. C₁₃×#3153	C₂	semidirect
8. C₂×C₁₃×#495	C₂	semidirect
9. C₁₃×#3140	C₂	semidirect
10. C₁₃×#3131	C₂	semidirect
11. C₁₃×#3044	C₂	semidirect
12. C₁₃×#3043	C₂	semidirect
13. C₁₃×#3042	C₂	semidirect
14. C₁₃×#3041	C₂	semidirect
15. C₁₃×#3011	C₂	semidirect
16. C₁₃×#3010	C₂	semidirect
17. C₁₃×#3009	C₂	semidirect
18. C₁₃×#3008	C₂	semidirect
19. C₁₃×#2922	C₂	semidirect
23. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
36. C₁₃×#542	C₂²	semidirect
39. C₁₃×#536	C₂²	semidirect
42. C₁₃×#535	C₂²	semidirect
43. C₁₃×#533	C₂²	semidirect
45. C₁₃×#532	C₂²	semidirect
46. C₁₃×#529	C₂²	semidirect
48. C₂×C₁₃×#124	C₂²	semidirect
49. C₂×C₁₃×#124	C₂²	semidirect
50. C₁₃×#519	C₂²	semidirect
51. C₁₃×#518	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
54. C₁₃×#496	C₂²	semidirect
55. C₁₃×#495	C₂²	semidirect
56. C₁₃×#495	C₂²	semidirect
57. C₁₃×#495	C₂²	semidirect
58. C₁₃×#495	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#488	C₂²	semidirect
61. C₁₃×#488	C₂²	semidirect
62. C₁₃×#488	C₂²	semidirect
63. C₁₃×#487	C₂²	semidirect
64. C₁₃×#486	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#463	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#452	C₂²	semidirect
74. C₁₃×#452	C₂²	semidirect
75. C₁₃×#451	C₂²	semidirect
76. C₁₃×#450	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
81. C₁₃×#433	C₂²	semidirect
82. C₁₃×#431	C₂²	semidirect
83. C₁₃×#424	C₂²	semidirect
84. C₁₃×#424	C₂²	semidirect
85. C₁₃×#419	C₂²	semidirect
86. C₁₃×#419	C₂²	semidirect
91. C₁₃×#416	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
95. C₄×C₁₃×M₁₆	C₂²	semidirect
96. C₂×C₄×C₈×C₁₃	C₂²	semidirect
227. #60819	C₁₃	direct (N × H)
350. #3510	C₂×C₁₃	semidirect
351. #3500	C₂×C₁₃	semidirect
352. #3225	C₂×C₁₃	semidirect
353. #3224	C₂×C₁₃	semidirect
354. #3212	C₂×C₁₃	semidirect
355. #3211	C₂×C₁₃	semidirect
356. #3153	C₂×C₁₃	semidirect
357. C₂×#495	C₂×C₁₃	semidirect
358. #3140	C₂×C₁₃	semidirect
359. #3131	C₂×C₁₃	semidirect
360. #3044	C₂×C₁₃	semidirect
361. #3043	C₂×C₁₃	semidirect
362. #3042	C₂×C₁₃	semidirect
363. #3041	C₂×C₁₃	semidirect
364. #3011	C₂×C₁₃	semidirect
365. #3010	C₂×C₁₃	semidirect
366. #3009	C₂×C₁₃	semidirect
367. #3008	C₂×C₁₃	semidirect
368. #2922	C₂×C₁₃	semidirect
447. C₂×#137	C₂²×C₁₃	semidirect
449. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
450. C₂²×Q₁₆	C₂²×C₁₃	semidirect
452. C₂²×SD₁₆	C₂²×C₁₃	semidirect
460. #542	C₂²×C₁₃	semidirect
463. #536	C₂²×C₁₃	semidirect
466. #535	C₂²×C₁₃	semidirect
467. #533	C₂²×C₁₃	semidirect
469. #532	C₂²×C₁₃	semidirect
470. #529	C₂²×C₁₃	semidirect
472. C₂×#124	C₂²×C₁₃	semidirect
473. C₂×#124	C₂²×C₁₃	semidirect
474. #519	C₂²×C₁₃	semidirect
475. #518	C₂²×C₁₃	semidirect
477. #497	C₂²×C₁₃	semidirect
478. #496	C₂²×C₁₃	semidirect
479. #495	C₂²×C₁₃	semidirect
480. #495	C₂²×C₁₃	semidirect
481. #495	C₂²×C₁₃	semidirect
482. #495	C₂²×C₁₃	semidirect
483. #489	C₂²×C₁₃	semidirect
484. #488	C₂²×C₁₃	semidirect
485. #488	C₂²×C₁₃	semidirect
486. #488	C₂²×C₁₃	semidirect
487. #487	C₂²×C₁₃	semidirect
488. #486	C₂²×C₁₃	semidirect
489. #464	C₂²×C₁₃	semidirect
490. #464	C₂²×C₁₃	semidirect
491. #463	C₂²×C₁₃	semidirect
492. #463	C₂²×C₁₃	semidirect
493. #462	C₂²×C₁₃	semidirect
494. #461	C₂²×C₁₃	semidirect
495. #460	C₂²×C₁₃	semidirect
496. #459	C₂²×C₁₃	semidirect
497. #452	C₂²×C₁₃	semidirect
498. #452	C₂²×C₁₃	semidirect
499. #451	C₂²×C₁₃	semidirect
500. #450	C₂²×C₁₃	semidirect
502. #449	C₂²×C₁₃	semidirect
503. #448	C₂²×C₁₃	semidirect
505. #433	C₂²×C₁₃	semidirect
506. #431	C₂²×C₁₃	semidirect
507. #424	C₂²×C₁₃	semidirect
508. #424	C₂²×C₁₃	semidirect
509. #419	C₂²×C₁₃	semidirect
510. #419	C₂²×C₁₃	semidirect
515. #416	C₂²×C₁₃	semidirect
516. #416	C₂²×C₁₃	semidirect
519. C₄×M₁₆	C₂²×C₁₃	semidirect
520. C₂×C₄×C₈	C₂²×C₁₃	semidirect
810. C₁₃	#60819	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×#3510	2
C₁₃×#3500	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3212	2
C₁₃×#3211	2
C₁₃×#3153	2
C₂×C₁₃×#495	2
C₁₃×#3140	2
C₁₃×#3131	2
C₁₃×#3044	2
C₁₃×#3043	2
C₁₃×#3042	2
C₁₃×#3041	2
C₁₃×#3011	2
C₁₃×#3010	2
C₁₃×#3009	2
C₁₃×#3008	2
C₁₃×#2922	2
#60819	13

Subgroups — C13×#60819 #15747158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60819 #15747158