Subgroups — C₁₃×#61085 #15747424

Order 3328.

2750 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3282	C₂	1	4	yes	maximal, complemented
6	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3275	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
19	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
20	C₁₃×#577	—	2	16	no	—
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
31	C₁₃×#550	—	2	1	no	—
32	C₁₃×#550	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₁₃	—	2	1	no	—
34	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
35	C₁₃×#548	—	2	2	no	—
36	C₁₃×#548	C₂²	1	4	yes	complemented
37	C₁₃×#547	—	2	1	no	—
38	C₁₃×#547	C₂²	1	2	yes	—
39	C₁₃×#546	—	2	2	no	—
40	C₁₃×#546	C₂²	1	4	yes	—
41	D₄²×C₁₃	—	2	1	no	—
42	D₄²×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#537	—	2	2	no	—
44	C₁₃×#537	C₂²	1	2	yes	—
45	C₁₃×#537	C₂²	1	2	yes	complemented
46	C₁₃×#534	—	2	2	no	—
47	C₁₃×#532	—	2	2	no	—
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#121	—	2	2	no	—
52	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#495	C₂²	1	2	yes	complemented
55	C₁₃×#495	C₂²	1	2	yes	complemented
56	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#470	C₂²	1	4	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#465	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#459	C₂²	1	2	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#451	C₂²	1	4	yes	complemented
73	C₁₃×#450	C₂²	1	4	yes	complemented
74	C₁₃×#449	C₂²	1	4	yes	complemented
75	C₁₃×#449	C₂²	1	4	yes	complemented
76	C₁₃×#448	C₂²	1	4	yes	complemented
77	C₁₃×#447	C₂²	1	4	yes	complemented
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
79	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
82	C₁₃×#436	C₂²	1	2	yes	complemented
83	C₁₃×#436	C₂²	1	2	yes	complemented
84	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
85	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
86	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#417	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	complemented
90	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
92	C₁₃×#408	C₂²	1	2	yes	complemented
93	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×2₋¹⁺⁴	—	2	8	no	—
95	C₁₃×2₋¹⁺⁴	—	4	4	no	—
96	C₁₃×H(5,𝔽₂)	—	2	8	no	—
97	C₁₃×H(5,𝔽₂)	—	4	4	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	4	no	—
100	C₂×C₁₃×#41	—	2	2	no	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	4	yes	—
104	C₂×C₁₃×#41	C₂³	1	4	yes	—
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂²×Q₈×C₁₃	—	2	2	no	—
107	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	—	2	4	no	—
110	C₂²×D₄×C₁₃	—	2	2	no	—
111	C₂²×D₄×C₁₃	—	2	2	no	—
112	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	—	2	1	no	—
115	C₁₃×#137	—	2	8	no	—
116	C₁₃×#137	—	2	16	no	—
117	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
118	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
119	C₁₃×#135	—	2	16	no	—
120	C₁₃×#135	—	2	8	no	—
121	C₁₃×#135	—	4	4	no	—
122	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	—	2	16	no	—
126	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
127	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	4	yes	—
136	C₂×C₁₃×D₈	C₂³	1	2	yes	—
137	C₂×C₁₃×D₈	C₂³	1	2	yes	—
138	C₁₃×#131	—	2	8	no	—
139	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	—	2	2	no	—
145	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
146	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
148	C₁₃×#127	—	2	2	no	—
149	C₁₃×#127	D₄	1	1	yes	characteristic
150	C₁₃×#127	C₂³	1	1	yes	characteristic
151	C₁₃×#127	C₂³	1	1	yes	characteristic
152	C₁₃×#124	—	2	4	no	—
153	C₁₃×#124	D₄	1	2	yes	—
154	C₁₃×#124	C₂³	1	2	yes	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#123	—	2	4	no	—
157	C₁₃×#123	—	2	4	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	2	no	—
160	C₁₃×C₂²⋊Q₈	—	2	4	no	—
161	C₁₃×C₂²⋊Q₈	—	2	4	no	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₁₃×#121	—	2	4	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	4	no	—
167	C₁₃×#121	—	2	4	no	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	1	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	1	no	—
173	C₁₃×#121	—	2	1	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	4	no	—
176	C₁₃×#121	—	2	4	no	—
177	C₁₃×#121	D₄	1	2	yes	—
178	C₁₃×#121	D₄	1	2	yes	—
179	C₁₃×#121	C₂³	1	4	yes	—
180	C₁₃×#121	C₂³	1	4	yes	—
181	C₁₃×#120	—	2	4	no	—
182	C₁₃×#120	—	2	4	no	—
183	C₄×Q₈×C₁₃	—	2	1	no	—
184	C₄×Q₈×C₁₃	—	2	1	no	—
185	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	4	no	—
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	1	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	1	no	—
196	C₄×D₄×C₁₃	C₂³	1	2	yes	—
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₄×D₄×C₁₃	C₂³	1	2	yes	—
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₂×C₄²×C₁₃	—	2	1	no	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	2	yes	—
213	C₁₃×#103	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
226	#61085	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂⁴×C₁₃	—	2	1	no	—
228	C₂⁴×C₁₃	—	2	4	no	—
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	2	8	no	—
232	C₁₃×#41	—	2	8	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	2	4	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	16	no	—
240	C₁₃×#41	—	4	8	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	2	8	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	—	4	8	no	—
248	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
250	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₁₃	—	2	8	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	1	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	1	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	1	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	4	4	no	—
268	C₂×D₄×C₁₃	—	4	8	no	—
269	C₂×D₄×C₁₃	—	4	16	no	—
270	C₂×D₄×C₁₃	—	8	4	no	—
271	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
273	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
275	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	4	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	8	2	no	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₁₃×Q₁₆	—	2	8	no	—
295	C₁₃×Q₁₆	—	2	4	no	—
296	C₁₃×Q₁₆	—	4	2	no	—
297	C₁₃×SD₁₆	—	2	8	no	—
298	C₁₃×SD₁₆	—	2	8	no	—
299	C₁₃×SD₁₆	—	2	4	no	—
300	C₁₃×SD₁₆	—	2	4	no	—
301	C₁₃×SD₁₆	—	4	2	no	—
302	C₁₃×SD₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
304	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
305	C₁₃×D₈	—	2	8	no	—
306	C₁₃×D₈	—	2	4	no	—
307	C₁₃×D₈	—	4	2	no	—
308	C₁₃×M₁₆	—	2	4	no	—
309	C₁₃×M₁₆	—	2	8	no	—
310	C₂×C₈×C₁₃	—	2	2	no	—
311	C₂×C₈×C₁₃	—	2	8	no	—
312	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
313	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	4	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	1	no	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	4	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	4	no	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×#577	C₂×C₁₃	1	2	yes	complemented
351	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3284	C₂×C₁₃	1	2	yes	complemented
354	#3282	C₂×C₁₃	1	4	yes	complemented
355	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
356	#3276	C₂×C₁₃	1	2	yes	complemented
357	#3275	C₂×C₁₃	1	4	yes	complemented
358	#3274	C₂×C₁₃	1	2	yes	complemented
359	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3060	C₂×C₁₃	1	2	yes	complemented
361	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3013	C₂×C₁₃	1	2	yes	complemented
364	#3012	C₂×C₁₃	1	2	yes	complemented
365	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	4	8	no	—
372	C₂³×C₁₃	—	8	1	no	—
373	C₂³×C₁₃	—	8	1	no	—
374	C₂³×C₁₃	—	8	4	no	—
375	C₂³×C₁₃	—	8	4	no	—
376	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
377	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	Q₈×C₁₃	—	2	4	no	—
379	Q₈×C₁₃	—	2	4	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	2	2	no	—
382	Q₈×C₁₃	—	2	2	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	4	8	no	—
386	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
387	D₄×C₁₃	—	2	8	no	—
388	D₄×C₁₃	—	2	4	no	—
389	D₄×C₁₃	—	2	4	no	—
390	D₄×C₁₃	—	2	4	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	2	2	no	—
394	D₄×C₁₃	—	2	2	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	4	8	no	—
398	D₄×C₁₃	—	4	8	no	—
399	D₄×C₁₃	—	4	8	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	4	4	no	—
402	D₄×C₁₃	—	4	2	no	—
403	D₄×C₁₃	—	4	2	no	—
404	D₄×C₁₃	—	8	1	no	—
405	D₄×C₁₃	—	8	1	no	—
406	D₄×C₁₃	—	8	4	no	—
407	D₄×C₁₃	—	8	4	no	—
408	D₄×C₁₃	C₂²×D₄	1	4	yes	—
409	C₂×C₄×C₁₃	—	2	4	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	8	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	8	2	no	—
426	C₂×C₄×C₁₃	—	8	1	no	—
427	C₂×C₄×C₁₃	—	8	1	no	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
437	C₈×C₁₃	—	2	4	no	—
438	C₈×C₁₃	—	2	1	no	—
439	C₈×C₁₃	—	2	1	no	—
440	C₈×C₁₃	C₂²×D₄	1	2	yes	—
441	C₈×C₁₃	C₂²×D₄	1	2	yes	—
442	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
443	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
444	#577	—	2	16	no	—
445	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
446	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
447	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
448	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
449	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
450	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
451	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
452	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
454	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
455	#550	—	2	1	no	—
456	#550	C₂²×C₁₃	1	2	yes	complemented
457	D₄×Q₈	—	2	1	no	—
458	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
459	#548	—	2	2	no	—
460	#548	C₂²×C₁₃	1	4	yes	complemented
461	#547	—	2	1	no	—
462	#547	C₂²×C₁₃	1	2	yes	—
463	#546	—	2	2	no	—
464	#546	C₂²×C₁₃	1	4	yes	—
465	D₄²	—	2	1	no	—
466	D₄²	C₂²×C₁₃	1	2	yes	—
467	#537	—	2	2	no	—
468	#537	C₂²×C₁₃	1	2	yes	—
469	#537	C₂²×C₁₃	1	2	yes	complemented
470	#534	—	2	2	no	—
471	#532	—	2	2	no	—
472	#532	C₂²×C₁₃	1	1	yes	characteristic
473	#532	C₂²×C₁₃	1	1	yes	characteristic
474	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	C₂×#121	—	2	2	no	—
476	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
478	#495	C₂²×C₁₃	1	2	yes	complemented
479	#495	C₂²×C₁₃	1	2	yes	complemented
480	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#470	C₂²×C₁₃	1	4	yes	complemented
485	#469	C₂²×C₁₃	1	4	yes	complemented
486	#465	C₂²×C₁₃	1	4	yes	complemented
487	#465	C₂²×C₁₃	1	4	yes	complemented
488	#464	C₂²×C₁₃	1	4	yes	complemented
489	#463	C₂²×C₁₃	1	4	yes	complemented
490	#462	C₂²×C₁₃	1	2	yes	complemented
491	#461	C₂²×C₁₃	1	2	yes	complemented
492	#460	C₂²×C₁₃	1	2	yes	complemented
493	#459	C₂²×C₁₃	1	2	yes	complemented
494	#452	C₂²×C₁₃	1	4	yes	complemented
495	#452	C₂²×C₁₃	1	4	yes	complemented
496	#451	C₂²×C₁₃	1	4	yes	complemented
497	#450	C₂²×C₁₃	1	4	yes	complemented
498	#449	C₂²×C₁₃	1	4	yes	complemented
499	#449	C₂²×C₁₃	1	4	yes	complemented
500	#448	C₂²×C₁₃	1	4	yes	complemented
501	#447	C₂²×C₁₃	1	4	yes	complemented
502	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
503	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
504	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
505	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
506	#436	C₂²×C₁₃	1	2	yes	complemented
507	#436	C₂²×C₁₃	1	2	yes	complemented
508	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
509	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
510	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#417	C₂²×C₁₃	1	2	yes	complemented
513	#417	C₂²×C₁₃	1	2	yes	complemented
514	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
516	#408	C₂²×C₁₃	1	2	yes	complemented
517	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	4	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	8	4	no	—
533	C₂²×C₁₃	—	16	8	no	—
534	C₂²×C₁₃	D₄²	1	2	yes	—
535	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₁₃	—	2	1	no	—
537	C₄×C₁₃	—	2	1	no	—
538	C₄×C₁₃	—	2	4	no	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	D₄²	1	2	yes	—
546	C₄×C₁₃	#577	1	2	yes	complemented
547	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	2₋¹⁺⁴	—	2	8	no	—
550	2₋¹⁺⁴	—	4	4	no	—
551	H(5,𝔽₂)	—	2	8	no	—
552	H(5,𝔽₂)	—	4	4	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	4	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	C₂³×C₁₃	1	2	yes	—
557	C₂×#41	C₂³×C₁₃	1	2	yes	—
558	C₂×#41	C₂³×C₁₃	1	4	yes	—
559	C₂×#41	C₂³×C₁₃	1	4	yes	—
560	C₂×#41	C₂³×C₁₃	1	2	yes	—
561	C₂²×Q₈	—	2	2	no	—
562	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
563	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×D₄	—	2	4	no	—
565	C₂²×D₄	—	2	2	no	—
566	C₂²×D₄	—	2	2	no	—
567	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂³×C₄	—	2	1	no	—
570	#137	—	2	8	no	—
571	#137	—	2	16	no	—
572	AGL(1,ℤ/8)	—	2	8	no	—
573	AGL(1,ℤ/8)	—	2	16	no	—
574	#135	—	2	16	no	—
575	#135	—	2	8	no	—
576	#135	—	4	4	no	—
577	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
578	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
579	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
580	C₂×SD₁₆	—	2	16	no	—
581	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
582	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
590	C₂×D₈	C₂³×C₁₃	1	4	yes	—
591	C₂×D₈	C₂³×C₁₃	1	2	yes	—
592	C₂×D₈	C₂³×C₁₃	1	2	yes	—
593	#131	—	2	8	no	—
594	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
596	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
597	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄⋊Q₈	—	2	2	no	—
600	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
603	#127	—	2	2	no	—
604	#127	D₄×C₁₃	1	1	yes	characteristic
605	#127	C₂³×C₁₃	1	1	yes	characteristic
606	#127	C₂³×C₁₃	1	1	yes	characteristic
607	#124	—	2	4	no	—
608	#124	D₄×C₁₃	1	2	yes	—
609	#124	C₂³×C₁₃	1	2	yes	—
610	#124	C₂³×C₁₃	1	2	yes	—
611	#123	—	2	4	no	—
612	#123	—	2	4	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	C₂²⋊Q₈	—	2	4	no	—
617	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
618	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
619	#121	—	2	4	no	—
620	#121	—	2	2	no	—
621	#121	—	2	4	no	—
622	#121	—	2	4	no	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	1	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	2	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	D₄×C₁₃	1	2	yes	—
633	#121	D₄×C₁₃	1	2	yes	—
634	#121	C₂³×C₁₃	1	4	yes	—
635	#121	C₂³×C₁₃	1	4	yes	—
636	#120	—	2	4	no	—
637	#120	—	2	4	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	1	no	—
640	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	C₂³×C₁₃	1	2	yes	—
652	C₄×D₄	C₂³×C₁₃	1	2	yes	—
653	C₄×D₄	C₂³×C₁₃	1	2	yes	—
654	C₄×D₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	4	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	#106	C₂³×C₁₃	1	2	yes	—
664	#106	C₂³×C₁₃	1	2	yes	—
665	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	#103	C₂³×C₁₃	1	2	yes	—
668	#103	C₂³×C₁₃	1	2	yes	—
669	#103	C₂³×C₁₃	1	4	yes	—
670	#103	C₂³×C₁₃	1	4	yes	—
671	#102	C₂³×C₁₃	1	2	yes	—
672	#102	C₂³×C₁₃	1	2	yes	—
673	#102	C₂³×C₁₃	1	4	yes	—
674	#102	C₂³×C₁₃	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
676	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
677	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
679	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₁₃	—	2	2	no	—
682	C₂×C₁₃	—	4	4	no	—
683	C₂×C₁₃	—	4	4	no	—
684	C₂×C₁₃	—	8	2	no	—
685	C₂×C₁₃	—	8	2	no	—
686	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
687	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
688	C₂×C₁₃	#3584	1	1	yes	characteristic
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	4	no	—
691	#41	—	2	4	no	—
692	#41	—	2	4	no	—
693	#41	—	2	8	no	—
694	#41	—	2	8	no	—
695	#41	—	2	4	no	—
696	#41	—	2	4	no	—
697	#41	—	2	4	no	—
698	#41	—	2	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	16	no	—
702	#41	—	4	8	no	—
703	#41	—	4	8	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	8	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
711	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	complemented
712	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
714	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	4	8	no	—
731	C₂×D₄	—	4	16	no	—
732	C₂×D₄	—	8	4	no	—
733	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
735	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
737	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	8	2	no	—
752	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	Q₁₆	—	2	8	no	—
757	Q₁₆	—	2	4	no	—
758	Q₁₆	—	4	2	no	—
759	SD₁₆	—	2	8	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
766	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
767	D₈	—	2	8	no	—
768	D₈	—	2	4	no	—
769	D₈	—	4	2	no	—
770	M₁₆	—	2	4	no	—
771	M₁₆	—	2	8	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	—	2	8	no	—
774	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
775	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
778	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
805	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
812	C₁₃	#61085	1	1	yes	characteristic, direct product factor, Sylow
813	C₂³	—	2	2	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	4	8	no	—
818	C₂³	—	8	1	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	4	no	—
821	C₂³	—	8	4	no	—
822	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
823	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	Q₈	—	2	4	no	—
825	Q₈	—	2	4	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	4	8	no	—
832	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
833	D₄	—	2	8	no	—
834	D₄	—	2	4	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	2	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	8	1	no	—
851	D₄	—	8	1	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	C₂²×D₄×C₁₃	1	4	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	1	no	—
873	C₂×C₄	—	8	1	no	—
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
878	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
882	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
883	C₈	—	2	4	no	—
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	C₂²×D₄×C₁₃	1	2	yes	—
887	C₈	C₂²×D₄×C₁₃	1	2	yes	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	16	8	no	—
904	C₂²	D₄²×C₁₃	1	2	yes	—
905	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	D₄²×C₁₃	1	2	yes	—
916	C₄	C₁₃×#577	1	2	yes	complemented
917	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
918	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
919	C₂	—	2	2	no	—
920	C₂	—	4	4	no	—
921	C₂	—	4	4	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	2	no	—
924	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
925	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
926	C₂	C₁₃×#3584	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. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3496	C₂	semidirect
4. C₁₃×#3284	C₂	semidirect
5. C₁₃×#3282	C₂	semidirect
6. D₄×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3275	C₂	semidirect
9. C₁₃×#3274	C₂	semidirect
10. C₁₃×#3147	C₂	semidirect
11. C₁₃×#3060	C₂	semidirect
12. C₁₃×#3037	C₂	semidirect
13. C₁₃×#3036	C₂	semidirect
14. C₁₃×#3013	C₂	semidirect
15. C₁₃×#3012	C₂	semidirect
16. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
17. C₁₃×#2931	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
29. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₂×C₁₃×#131	C₂²	semidirect
32. C₁₃×#550	C₂²	semidirect
34. D₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
45. C₁₃×#537	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#495	C₂²	semidirect
56. C₁₃×#494	C₂²	semidirect
57. C₁₃×#493	C₂²	semidirect
58. C₁₃×#492	C₂²	semidirect
59. C₁₃×#492	C₂²	semidirect
60. C₁₃×#470	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#465	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#451	C₂²	semidirect
73. C₁₃×#450	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#448	C₂²	semidirect
77. C₁₃×#447	C₂²	semidirect
78. C₄×C₁₃×SD₁₆	C₂²	semidirect
79. C₄×C₁₃×SD₁₆	C₂²	semidirect
80. C₄×C₁₃×SD₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₁₃×#436	C₂²	semidirect
83. C₁₃×#436	C₂²	semidirect
84. C₈×D₄×C₁₃	C₂²	semidirect
85. C₈×D₄×C₁₃	C₂²	semidirect
86. C₂×C₁₃×#106	C₂²	semidirect
87. C₁₃×#423	C₂²	semidirect
88. C₁₃×#417	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₂×C₁₃×#103	C₂²	semidirect
92. C₁₃×#408	C₂²	semidirect
93. C₂×C₄×C₈×C₁₃	C₂²	semidirect
126. C₂×C₁₃×SD₁₆	D₄	semidirect
226. #61085	C₁₃	direct (N × H)
249. C₂×Q₈×C₁₃	C₂×D₄	semidirect
303. C₁₃×SD₁₆	C₂×D₄	semidirect
304. C₁₃×SD₁₆	C₂×D₄	semidirect
312. C₂×C₈×C₁₃	C₂×D₄	semidirect
350. C₂×#577	C₂×C₁₃	semidirect
351. #3497	C₂×C₁₃	semidirect
352. #3496	C₂×C₁₃	semidirect
353. #3284	C₂×C₁₃	semidirect
354. #3282	C₂×C₁₃	semidirect
355. D₄×SD₁₆	C₂×C₁₃	semidirect
356. #3276	C₂×C₁₃	semidirect
357. #3275	C₂×C₁₃	semidirect
358. #3274	C₂×C₁₃	semidirect
359. #3147	C₂×C₁₃	semidirect
360. #3060	C₂×C₁₃	semidirect
361. #3037	C₂×C₁₃	semidirect
362. #3036	C₂×C₁₃	semidirect
363. #3013	C₂×C₁₃	semidirect
364. #3012	C₂×C₁₃	semidirect
365. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
366. #2931	C₂×C₁₃	semidirect
442. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
445. C₂×#137	C₂²×C₁₃	semidirect
446. C₂×#137	C₂²×C₁₃	semidirect
448. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
449. C₂×#135	C₂²×C₁₃	semidirect
450. C₂×#135	C₂²×C₁₃	semidirect
451. C₂×#135	C₂²×C₁₃	semidirect
453. C₂²×SD₁₆	C₂²×C₁₃	semidirect
454. C₂×#131	C₂²×C₁₃	semidirect
456. #550	C₂²×C₁₃	semidirect
458. D₄×Q₈	C₂²×C₁₃	semidirect
460. #548	C₂²×C₁₃	semidirect
469. #537	C₂²×C₁₃	semidirect
474. #532	C₂²×C₁₃	semidirect
476. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
478. #495	C₂²×C₁₃	semidirect
479. #495	C₂²×C₁₃	semidirect
480. #494	C₂²×C₁₃	semidirect
481. #493	C₂²×C₁₃	semidirect
482. #492	C₂²×C₁₃	semidirect
483. #492	C₂²×C₁₃	semidirect
484. #470	C₂²×C₁₃	semidirect
485. #469	C₂²×C₁₃	semidirect
486. #465	C₂²×C₁₃	semidirect
487. #465	C₂²×C₁₃	semidirect
488. #464	C₂²×C₁₃	semidirect
489. #463	C₂²×C₁₃	semidirect
490. #462	C₂²×C₁₃	semidirect
491. #461	C₂²×C₁₃	semidirect
492. #460	C₂²×C₁₃	semidirect
493. #459	C₂²×C₁₃	semidirect
494. #452	C₂²×C₁₃	semidirect
495. #452	C₂²×C₁₃	semidirect
496. #451	C₂²×C₁₃	semidirect
497. #450	C₂²×C₁₃	semidirect
498. #449	C₂²×C₁₃	semidirect
499. #449	C₂²×C₁₃	semidirect
500. #448	C₂²×C₁₃	semidirect
501. #447	C₂²×C₁₃	semidirect
502. C₄×SD₁₆	C₂²×C₁₃	semidirect
503. C₄×SD₁₆	C₂²×C₁₃	semidirect
504. C₄×SD₁₆	C₂²×C₁₃	semidirect
505. C₄×SD₁₆	C₂²×C₁₃	semidirect
506. #436	C₂²×C₁₃	semidirect
507. #436	C₂²×C₁₃	semidirect
508. C₈×D₄	C₂²×C₁₃	semidirect
509. C₈×D₄	C₂²×C₁₃	semidirect
510. C₂×#106	C₂²×C₁₃	semidirect
511. #423	C₂²×C₁₃	semidirect
512. #417	C₂²×C₁₃	semidirect
513. #417	C₂²×C₁₃	semidirect
514. C₂×#103	C₂²×C₁₃	semidirect
516. #408	C₂²×C₁₃	semidirect
517. C₂×C₄×C₈	C₂²×C₁₃	semidirect
546. C₄×C₁₃	#577	semidirect
581. C₂×SD₁₆	D₄×C₁₃	semidirect
711. C₂×Q₈	C₂×D₄×C₁₃	semidirect
765. SD₁₆	C₂×D₄×C₁₃	semidirect
766. SD₁₆	C₂×D₄×C₁₃	semidirect
774. C₂×C₈	C₂×D₄×C₁₃	semidirect
812. C₁₃	#61085	direct (N × H)
916. C₄	C₁₃×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#577	2
C₁₃×#3497	2
C₁₃×#3496	2
C₁₃×#3284	2
C₁₃×#3282	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3276	2
C₁₃×#3275	2
C₁₃×#3274	2
C₁₃×#3147	2
C₁₃×#3060	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#3013	2
C₁₃×#3012	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2931	2
#61085	13

Subgroups — C13×#61085 #15747424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61085 #15747424