Subgroups — C₁₃×#61095 #15747434

Order 3328.

2790 conjugacy classes of subgroups.

The subgroup lattice has 942 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×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3287	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2935	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	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	2	yes	—
27	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
29	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
31	C₁₃×#550	—	2	1	no	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	C₁₃×#550	C₂²	1	2	yes	—
34	C₁₃×#550	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₁₃	—	2	1	no	—
36	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#548	—	2	2	no	—
38	C₁₃×#548	C₂²	1	4	yes	complemented
39	D₄²×C₁₃	—	2	2	no	—
40	D₄²×C₁₃	—	2	2	no	—
41	D₄²×C₁₃	C₂²	1	2	yes	—
42	D₄²×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#537	—	2	2	no	—
44	C₁₃×#537	C₂²	1	2	yes	complemented
45	C₁₃×#535	—	2	2	no	—
46	C₁₃×#535	C₂²	1	2	yes	—
47	C₁₃×#532	—	2	1	no	—
48	C₁₃×#532	—	2	2	no	—
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#127	—	2	1	no	—
52	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#496	C₂²	1	4	yes	complemented
56	C₁₃×#493	C₂²	1	2	yes	complemented
57	C₁₃×#492	C₂²	1	2	yes	complemented
58	C₁₃×#469	C₂²	1	4	yes	complemented
59	C₁₃×#468	C₂²	1	4	yes	complemented
60	C₁₃×#466	C₂²	1	4	yes	complemented
61	C₁₃×#465	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	2	yes	complemented
63	C₁₃×#463	C₂²	1	2	yes	complemented
64	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#460	C₂²	1	4	yes	complemented
67	C₁₃×#460	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#450	C₂²	1	4	yes	complemented
73	C₁₃×#449	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×#448	C₂²	1	4	yes	complemented
78	C₁₃×#447	C₂²	1	4	yes	complemented
79	C₁₃×#441	C₂²	1	2	yes	complemented
80	C₁₃×#440	C₂²	1	2	yes	complemented
81	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
83	C₁₃×#436	C₂²	1	2	yes	complemented
84	C₁₃×#435	C₂²	1	4	yes	complemented
85	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
86	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#417	C₂²	1	1	yes	characteristic
90	C₁₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
92	C₁₃×#408	C₂²	1	2	yes	complemented
93	C₄×C₁₃×M₁₆	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	4	yes	—
103	C₂×C₁₃×#41	C₂³	1	4	yes	—
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
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	2	no	—
110	C₂²×D₄×C₁₃	—	2	4	no	—
111	C₂²×D₄×C₁₃	—	2	2	no	—
112	C₂²×D₄×C₁₃	—	2	2	no	—
113	C₂²×D₄×C₁₃	—	2	1	no	—
114	C₂²×D₄×C₁₃	—	2	1	no	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₁₃×#137	—	2	16	no	—
118	C₁₃×#137	D₄	1	8	yes	complemented
119	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
120	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
121	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
122	C₁₃×#135	—	2	8	no	—
123	C₁₃×#135	—	2	16	no	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	—	2	8	no	—
127	C₂×C₁₃×SD₁₆	—	2	16	no	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	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	4	yes	—
134	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	2	yes	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₂×C₁₃×D₈	C₂³	1	4	yes	—
138	C₁₃×#131	—	2	8	no	—
139	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
141	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
143	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
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×#127	—	2	2	no	—
148	C₁₃×#127	—	2	2	no	—
149	C₁₃×#127	—	2	2	no	—
150	C₁₃×#127	—	2	2	no	—
151	C₁₃×#127	—	2	1	no	—
152	C₁₃×#127	—	2	1	no	—
153	C₁₃×#127	D₄	1	1	yes	characteristic
154	C₁₃×#127	C₂³	1	1	yes	characteristic
155	C₁₃×#127	C₂³	1	2	yes	—
156	C₁₃×#127	C₂³	1	2	yes	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	—	2	4	no	—
159	C₁₃×#124	D₄	1	2	yes	—
160	C₁₃×#124	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	4	no	—
163	C₁₃×C₂²⋊Q₈	—	2	4	no	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
165	C₁₃×#121	—	2	4	no	—
166	C₁₃×#121	—	2	4	no	—
167	C₁₃×#121	—	2	2	no	—
168	C₁₃×#121	—	2	1	no	—
169	C₁₃×#121	—	2	1	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	4	no	—
173	C₁₃×#121	—	2	4	no	—
174	C₁₃×#121	—	2	4	no	—
175	C₁₃×#121	D₄	1	2	yes	—
176	C₁₃×#121	D₄	1	2	yes	—
177	C₁₃×#121	C₂³	1	4	yes	—
178	C₁₃×#121	C₂³	1	4	yes	—
179	C₁₃×#121	C₂³	1	4	yes	—
180	C₁₃×#120	—	2	4	no	—
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	1	yes	characteristic
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	2	no	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	4	no	—
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	1	no	—
198	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#117	—	2	1	no	—
203	C₁₃×#117	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	—	2	1	no	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#61095	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	4	no	—
230	C₂⁴×C₁₃	—	2	2	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	2	8	no	—
235	C₁₃×#41	—	2	8	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	4	no	—
240	C₁₃×#41	—	4	16	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₁₃×#41	—	4	8	no	—
243	C₁₃×#41	C₂×D₄	1	4	yes	—
244	C₂×Q₈×C₁₃	—	2	1	no	—
245	C₂×Q₈×C₁₃	—	2	4	no	—
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	8	no	—
248	C₂×Q₈×C₁₃	—	4	4	no	—
249	C₂×Q₈×C₁₃	—	4	8	no	—
250	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
251	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
252	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
254	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	8	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	1	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	4	no	—
273	C₂×D₄×C₁₃	—	4	4	no	—
274	C₂×D₄×C₁₃	—	4	8	no	—
275	C₂×D₄×C₁₃	—	4	16	no	—
276	C₂×D₄×C₁₃	—	8	2	no	—
277	C₂×D₄×C₁₃	—	8	4	no	—
278	C₂×D₄×C₁₃	—	8	2	no	—
279	C₂×D₄×C₁₃	—	8	4	no	—
280	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
282	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	—	2	1	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	4	no	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	1	no	—
292	C₂²×C₄×C₁₃	—	2	1	no	—
293	C₂²×C₄×C₁₃	—	2	4	no	—
294	C₂²×C₄×C₁₃	—	2	4	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₁₃×Q₁₆	—	2	4	no	—
301	C₁₃×Q₁₆	C₂×D₄	1	8	yes	complemented
302	C₁₃×SD₁₆	—	2	8	no	—
303	C₁₃×SD₁₆	—	2	8	no	—
304	C₁₃×SD₁₆	—	2	4	no	—
305	C₁₃×SD₁₆	—	2	4	no	—
306	C₁₃×SD₁₆	—	2	8	no	—
307	C₁₃×SD₁₆	—	4	4	no	—
308	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
309	C₁₃×D₈	—	2	4	no	—
310	C₁₃×D₈	—	2	8	no	—
311	C₁₃×D₈	—	4	4	no	—
312	C₁₃×M₁₆	—	2	2	no	—
313	C₁₃×M₁₆	—	2	8	no	—
314	C₁₃×M₁₆	C₂×D₄	1	4	yes	complemented
315	C₂×C₈×C₁₃	—	2	4	no	—
316	C₂×C₈×C₁₃	—	2	8	no	—
317	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	—	2	4	no	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
334	C₁₃×C₂²⋊C₄	—	2	1	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	4	no	—
340	C₁₃×C₂²⋊C₄	—	2	4	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	4	no	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
344	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
345	C₄²×C₁₃	—	2	1	no	—
346	C₄²×C₁₃	—	2	1	no	—
347	C₄²×C₁₃	—	2	1	no	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂×#577	C₂×C₁₃	1	2	yes	complemented
355	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3287	C₂×C₁₃	1	2	yes	complemented
358	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
359	#3278	C₂×C₁₃	1	2	yes	complemented
360	#3274	C₂×C₁₃	1	2	yes	complemented
361	#3271	C₂×C₁₃	1	4	yes	complemented
362	#3265	C₂×C₁₃	1	4	yes	complemented
363	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3062	C₂×C₁₃	1	2	yes	complemented
365	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3012	C₂×C₁₃	1	2	yes	complemented
368	#3010	C₂×C₁₃	1	2	yes	complemented
369	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	2	4	no	—
374	C₂³×C₁₃	—	4	8	no	—
375	C₂³×C₁₃	—	4	4	no	—
376	C₂³×C₁₃	—	8	2	no	—
377	C₂³×C₁₃	—	8	2	no	—
378	C₂³×C₁₃	—	8	4	no	—
379	C₂³×C₁₃	—	8	4	no	—
380	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
381	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	Q₈×C₁₃	—	2	4	no	—
383	Q₈×C₁₃	—	2	4	no	—
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	2	1	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	4	8	no	—
389	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
390	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	8	no	—
393	D₄×C₁₃	—	2	4	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	4	no	—
397	D₄×C₁₃	—	2	1	no	—
398	D₄×C₁₃	—	2	2	no	—
399	D₄×C₁₃	—	2	4	no	—
400	D₄×C₁₃	—	4	2	no	—
401	D₄×C₁₃	—	4	8	no	—
402	D₄×C₁₃	—	4	8	no	—
403	D₄×C₁₃	—	4	8	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	4	no	—
409	D₄×C₁₃	—	8	1	no	—
410	D₄×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	8	2	no	—
412	D₄×C₁₃	—	8	4	no	—
413	D₄×C₁₃	—	8	4	no	—
414	D₄×C₁₃	—	8	4	no	—
415	D₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	—	2	4	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	4	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	4	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	4	1	no	—
428	C₂×C₄×C₁₃	—	4	8	no	—
429	C₂×C₄×C₁₃	—	4	8	no	—
430	C₂×C₄×C₁₃	—	4	8	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	8	1	no	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
443	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₁₃	—	2	2	no	—
445	C₈×C₁₃	—	2	2	no	—
446	C₈×C₁₃	—	2	2	no	—
447	C₈×C₁₃	C₂²×D₄	1	4	yes	—
448	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
449	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
450	#577	—	2	16	no	—
451	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
453	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
454	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
455	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
456	C₂×#135	C₂²×C₁₃	1	2	yes	—
457	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
458	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
459	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
461	#550	—	2	1	no	—
462	#550	C₂²×C₁₃	1	2	yes	—
463	#550	C₂²×C₁₃	1	2	yes	—
464	#550	C₂²×C₁₃	1	2	yes	complemented
465	D₄×Q₈	—	2	1	no	—
466	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
467	#548	—	2	2	no	—
468	#548	C₂²×C₁₃	1	4	yes	complemented
469	D₄²	—	2	2	no	—
470	D₄²	—	2	2	no	—
471	D₄²	C₂²×C₁₃	1	2	yes	—
472	D₄²	C₂²×C₁₃	1	2	yes	—
473	#537	—	2	2	no	—
474	#537	C₂²×C₁₃	1	2	yes	complemented
475	#535	—	2	2	no	—
476	#535	C₂²×C₁₃	1	2	yes	—
477	#532	—	2	1	no	—
478	#532	—	2	2	no	—
479	#532	C₂²×C₁₃	1	1	yes	characteristic
480	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂×#127	—	2	1	no	—
482	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
483	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	#496	C₂²×C₁₃	1	4	yes	complemented
486	#493	C₂²×C₁₃	1	2	yes	complemented
487	#492	C₂²×C₁₃	1	2	yes	complemented
488	#469	C₂²×C₁₃	1	4	yes	complemented
489	#468	C₂²×C₁₃	1	4	yes	complemented
490	#466	C₂²×C₁₃	1	4	yes	complemented
491	#465	C₂²×C₁₃	1	4	yes	complemented
492	#464	C₂²×C₁₃	1	2	yes	complemented
493	#463	C₂²×C₁₃	1	2	yes	complemented
494	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#460	C₂²×C₁₃	1	4	yes	complemented
497	#460	C₂²×C₁₃	1	2	yes	complemented
498	#460	C₂²×C₁₃	1	2	yes	complemented
499	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#452	C₂²×C₁₃	1	4	yes	complemented
502	#450	C₂²×C₁₃	1	4	yes	complemented
503	#449	C₂²×C₁₃	1	4	yes	complemented
504	#449	C₂²×C₁₃	1	4	yes	complemented
505	#449	C₂²×C₁₃	1	4	yes	complemented
506	#448	C₂²×C₁₃	1	4	yes	complemented
507	#448	C₂²×C₁₃	1	4	yes	complemented
508	#447	C₂²×C₁₃	1	4	yes	complemented
509	#441	C₂²×C₁₃	1	2	yes	complemented
510	#440	C₂²×C₁₃	1	2	yes	complemented
511	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
512	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
513	#436	C₂²×C₁₃	1	2	yes	complemented
514	#435	C₂²×C₁₃	1	4	yes	complemented
515	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
516	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#417	C₂²×C₁₃	1	1	yes	characteristic
520	#416	C₂²×C₁₃	1	2	yes	complemented
521	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
522	#408	C₂²×C₁₃	1	2	yes	complemented
523	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	C₂²×C₁₃	—	2	1	no	—
525	C₂²×C₁₃	—	2	1	no	—
526	C₂²×C₁₃	—	2	4	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	2	4	no	—
530	C₂²×C₁₃	—	4	1	no	—
531	C₂²×C₁₃	—	4	1	no	—
532	C₂²×C₁₃	—	4	4	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	4	4	no	—
536	C₂²×C₁₃	—	4	4	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	16	4	no	—
539	C₂²×C₁₃	—	16	8	no	—
540	C₂²×C₁₃	D₄²	1	2	yes	—
541	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₁₃	—	2	1	no	—
543	C₄×C₁₃	—	2	1	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	4	no	—
546	C₄×C₁₃	—	2	4	no	—
547	C₄×C₁₃	—	2	1	no	—
548	C₄×C₁₃	—	4	1	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	1	no	—
552	C₄×C₁₃	D₄²	1	2	yes	—
553	C₄×C₁₃	#577	1	2	yes	complemented
554	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	2₋¹⁺⁴	—	2	8	no	—
557	2₋¹⁺⁴	—	4	4	no	—
558	H(5,𝔽₂)	—	2	8	no	—
559	H(5,𝔽₂)	—	4	4	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	4	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	C₂³×C₁₃	1	2	yes	—
564	C₂×#41	C₂³×C₁₃	1	4	yes	—
565	C₂×#41	C₂³×C₁₃	1	4	yes	—
566	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×#41	C₂³×C₁₃	1	2	yes	—
568	C₂²×Q₈	—	2	2	no	—
569	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
570	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×D₄	—	2	2	no	—
572	C₂²×D₄	—	2	4	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
578	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
579	#137	—	2	16	no	—
580	#137	D₄×C₁₃	1	8	yes	complemented
581	AGL(1,ℤ/8)	—	2	16	no	—
582	AGL(1,ℤ/8)	—	2	8	no	—
583	AGL(1,ℤ/8)	—	4	4	no	—
584	#135	—	2	8	no	—
585	#135	—	2	16	no	—
586	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	—	2	8	no	—
589	C₂×SD₁₆	—	2	16	no	—
590	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
597	C₂×D₈	C₂³×C₁₃	1	2	yes	—
598	C₂×D₈	C₂³×C₁₃	1	4	yes	—
599	C₂×D₈	C₂³×C₁₃	1	4	yes	—
600	#131	—	2	8	no	—
601	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
602	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
605	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
606	C₄⋊Q₈	—	2	2	no	—
607	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
608	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
609	#127	—	2	2	no	—
610	#127	—	2	2	no	—
611	#127	—	2	2	no	—
612	#127	—	2	2	no	—
613	#127	—	2	1	no	—
614	#127	—	2	1	no	—
615	#127	D₄×C₁₃	1	1	yes	characteristic
616	#127	C₂³×C₁₃	1	2	yes	—
617	#127	C₂³×C₁₃	1	2	yes	—
618	#127	C₂³×C₁₃	1	1	yes	characteristic
619	#124	—	2	2	no	—
620	#124	—	2	4	no	—
621	#124	D₄×C₁₃	1	2	yes	—
622	#124	C₂³×C₁₃	1	2	yes	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	4	no	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
627	#121	—	2	4	no	—
628	#121	—	2	4	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	4	no	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	#121	D₄×C₁₃	1	2	yes	—
638	#121	D₄×C₁₃	1	2	yes	—
639	#121	C₂³×C₁₃	1	4	yes	—
640	#121	C₂³×C₁₃	1	4	yes	—
641	#121	C₂³×C₁₃	1	4	yes	—
642	#120	—	2	4	no	—
643	#120	—	2	4	no	—
644	#120	—	2	4	no	—
645	C₄×Q₈	—	2	1	no	—
646	C₄×Q₈	—	2	1	no	—
647	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
648	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
649	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
650	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	4	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	C₂³×C₁₃	1	2	yes	—
664	#117	—	2	1	no	—
665	#117	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
671	#107	C₂³×C₁₃	1	2	yes	—
672	#106	C₂³×C₁₃	1	2	yes	—
673	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
674	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
675	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
676	#103	C₂³×C₁₃	1	2	yes	—
677	#103	C₂³×C₁₃	1	2	yes	—
678	#103	C₂³×C₁₃	1	2	yes	—
679	#103	C₂³×C₁₃	1	2	yes	—
680	#103	C₂³×C₁₃	1	2	yes	—
681	#102	C₂³×C₁₃	1	4	yes	—
682	#102	C₂³×C₁₃	1	4	yes	—
683	#102	C₂³×C₁₃	1	2	yes	—
684	#102	C₂³×C₁₃	1	2	yes	—
685	#102	C₂³×C₁₃	1	2	yes	—
686	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
687	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
688	#97	C₂³×C₁₃	1	2	yes	—
689	C₄×C₈	C₂³×C₁₃	1	2	yes	—
690	C₂×C₁₃	—	2	2	no	—
691	C₂×C₁₃	—	4	4	no	—
692	C₂×C₁₃	—	4	2	no	—
693	C₂×C₁₃	—	8	2	no	—
694	C₂×C₁₃	—	8	4	no	—
695	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
696	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
697	C₂×C₁₃	#3585	1	1	yes	characteristic
698	C₂⁴	—	2	4	no	—
699	C₂⁴	—	2	2	no	—
700	#41	—	2	4	no	—
701	#41	—	2	2	no	—
702	#41	—	2	4	no	—
703	#41	—	2	8	no	—
704	#41	—	2	8	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	16	no	—
710	#41	—	4	8	no	—
711	#41	—	4	8	no	—
712	#41	C₂×D₄×C₁₃	1	4	yes	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	4	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	8	no	—
717	C₂×Q₈	—	4	4	no	—
718	C₂×Q₈	—	4	8	no	—
719	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
720	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	complemented
721	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
722	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
723	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	8	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	4	16	no	—
745	C₂×D₄	—	8	2	no	—
746	C₂×D₄	—	8	4	no	—
747	C₂×D₄	—	8	2	no	—
748	C₂×D₄	—	8	4	no	—
749	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
751	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
755	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	Q₁₆	—	2	4	no	—
770	Q₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
771	SD₁₆	—	2	8	no	—
772	SD₁₆	—	2	8	no	—
773	SD₁₆	—	2	4	no	—
774	SD₁₆	—	2	4	no	—
775	SD₁₆	—	2	8	no	—
776	SD₁₆	—	4	4	no	—
777	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
778	D₈	—	2	4	no	—
779	D₈	—	2	8	no	—
780	D₈	—	4	4	no	—
781	M₁₆	—	2	2	no	—
782	M₁₆	—	2	8	no	—
783	M₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
784	C₂×C₈	—	2	4	no	—
785	C₂×C₈	—	2	8	no	—
786	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
787	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
788	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
789	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
813	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
814	C₄²	—	2	1	no	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
821	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
822	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
823	C₁₃	#61095	1	1	yes	characteristic, direct product factor, Sylow
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	4	8	no	—
828	C₂³	—	4	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	—	8	2	no	—
831	C₂³	—	8	4	no	—
832	C₂³	—	8	4	no	—
833	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
834	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
835	Q₈	—	2	4	no	—
836	Q₈	—	2	4	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	1	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	4	8	no	—
842	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
843	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	8	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	4	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	2	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	1	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	D₄	—	8	4	no	—
868	D₄	C₂²×D₄×C₁₃	1	2	yes	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
892	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
896	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
897	C₈	—	2	2	no	—
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	C₂²×D₄×C₁₃	1	4	yes	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	4	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	4	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	4	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	4	no	—
915	C₂²	—	16	4	no	—
916	C₂²	—	16	8	no	—
917	C₂²	D₄²×C₁₃	1	2	yes	—
918	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	4	no	—
924	C₄	—	2	4	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	D₄²×C₁₃	1	2	yes	—
930	C₄	C₁₃×#577	1	2	yes	complemented
931	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
932	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂	—	2	2	no	—
934	C₂	—	4	4	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	4	no	—
937	C₂	—	8	2	no	—
938	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
939	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
940	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. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3497	C₂	semidirect
4. C₁₃×#3287	C₂	semidirect
5. D₄×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3278	C₂	semidirect
7. C₁₃×#3274	C₂	semidirect
8. C₁₃×#3271	C₂	semidirect
9. C₁₃×#3265	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3062	C₂	semidirect
12. C₁₃×#3035	C₂	semidirect
13. C₂×C₁₃×#460	C₂	semidirect
14. C₁₃×#3012	C₂	semidirect
15. C₁₃×#3010	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
17. C₁₃×#2935	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₂×C₁₃×#131	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
36. D₄×Q₈×C₁₃	C₂²	semidirect
38. C₁₃×#548	C₂²	semidirect
44. C₁₃×#537	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
54. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#493	C₂²	semidirect
57. C₁₃×#492	C₂²	semidirect
58. C₁₃×#469	C₂²	semidirect
59. C₁₃×#468	C₂²	semidirect
60. C₁₃×#466	C₂²	semidirect
61. C₁₃×#465	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#449	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#448	C₂²	semidirect
77. C₁₃×#448	C₂²	semidirect
78. C₁₃×#447	C₂²	semidirect
79. C₁₃×#441	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₄×C₁₃×Q₁₆	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
83. C₁₃×#436	C₂²	semidirect
84. C₁₃×#435	C₂²	semidirect
85. C₈×D₄×C₁₃	C₂²	semidirect
86. C₁₃×#428	C₂²	semidirect
87. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
88. C₁₃×#419	C₂²	semidirect
90. C₁₃×#416	C₂²	semidirect
91. C₂×C₁₃×#102	C₂²	semidirect
92. C₁₃×#408	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
118. C₁₃×#137	D₄	semidirect
228. #61095	C₁₃	direct (N × H)
251. C₂×Q₈×C₁₃	C₂×D₄	semidirect
301. C₁₃×Q₁₆	C₂×D₄	semidirect
308. C₁₃×SD₁₆	C₂×D₄	semidirect
314. C₁₃×M₁₆	C₂×D₄	semidirect
354. C₂×#577	C₂×C₁₃	semidirect
355. #3498	C₂×C₁₃	semidirect
356. #3497	C₂×C₁₃	semidirect
357. #3287	C₂×C₁₃	semidirect
358. D₄×SD₁₆	C₂×C₁₃	semidirect
359. #3278	C₂×C₁₃	semidirect
360. #3274	C₂×C₁₃	semidirect
361. #3271	C₂×C₁₃	semidirect
362. #3265	C₂×C₁₃	semidirect
363. #3151	C₂×C₁₃	semidirect
364. #3062	C₂×C₁₃	semidirect
365. #3035	C₂×C₁₃	semidirect
366. C₂×#460	C₂×C₁₃	semidirect
367. #3012	C₂×C₁₃	semidirect
368. #3010	C₂×C₁₃	semidirect
369. C₄×#137	C₂×C₁₃	semidirect
370. #2935	C₂×C₁₃	semidirect
448. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
452. C₂×#137	C₂²×C₁₃	semidirect
453. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
454. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
455. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
457. C₂×#135	C₂²×C₁₃	semidirect
458. C₂²×SD₁₆	C₂²×C₁₃	semidirect
459. C₂²×SD₁₆	C₂²×C₁₃	semidirect
460. C₂×#131	C₂²×C₁₃	semidirect
464. #550	C₂²×C₁₃	semidirect
466. D₄×Q₈	C₂²×C₁₃	semidirect
468. #548	C₂²×C₁₃	semidirect
474. #537	C₂²×C₁₃	semidirect
480. #532	C₂²×C₁₃	semidirect
484. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
485. #496	C₂²×C₁₃	semidirect
486. #493	C₂²×C₁₃	semidirect
487. #492	C₂²×C₁₃	semidirect
488. #469	C₂²×C₁₃	semidirect
489. #468	C₂²×C₁₃	semidirect
490. #466	C₂²×C₁₃	semidirect
491. #465	C₂²×C₁₃	semidirect
492. #464	C₂²×C₁₃	semidirect
493. #463	C₂²×C₁₃	semidirect
494. #462	C₂²×C₁₃	semidirect
495. #461	C₂²×C₁₃	semidirect
496. #460	C₂²×C₁₃	semidirect
497. #460	C₂²×C₁₃	semidirect
498. #460	C₂²×C₁₃	semidirect
499. #460	C₂²×C₁₃	semidirect
500. #459	C₂²×C₁₃	semidirect
501. #452	C₂²×C₁₃	semidirect
502. #450	C₂²×C₁₃	semidirect
503. #449	C₂²×C₁₃	semidirect
504. #449	C₂²×C₁₃	semidirect
505. #449	C₂²×C₁₃	semidirect
506. #448	C₂²×C₁₃	semidirect
507. #448	C₂²×C₁₃	semidirect
508. #447	C₂²×C₁₃	semidirect
509. #441	C₂²×C₁₃	semidirect
510. #440	C₂²×C₁₃	semidirect
511. C₄×Q₁₆	C₂²×C₁₃	semidirect
512. C₄×SD₁₆	C₂²×C₁₃	semidirect
513. #436	C₂²×C₁₃	semidirect
514. #435	C₂²×C₁₃	semidirect
515. C₈×D₄	C₂²×C₁₃	semidirect
516. #428	C₂²×C₁₃	semidirect
517. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
518. #419	C₂²×C₁₃	semidirect
520. #416	C₂²×C₁₃	semidirect
521. C₂×#102	C₂²×C₁₃	semidirect
522. #408	C₂²×C₁₃	semidirect
523. C₄×M₁₆	C₂²×C₁₃	semidirect
553. C₄×C₁₃	#577	semidirect
580. #137	D₄×C₁₃	semidirect
720. C₂×Q₈	C₂×D₄×C₁₃	semidirect
770. Q₁₆	C₂×D₄×C₁₃	semidirect
777. SD₁₆	C₂×D₄×C₁₃	semidirect
783. M₁₆	C₂×D₄×C₁₃	semidirect
823. C₁₃	#61095	direct (N × H)
930. 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×#3498	2
C₁₃×#3497	2
C₁₃×#3287	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3278	2
C₁₃×#3274	2
C₁₃×#3271	2
C₁₃×#3265	2
C₁₃×#3151	2
C₁₃×#3062	2
C₁₃×#3035	2
C₂×C₁₃×#460	2
C₁₃×#3012	2
C₁₃×#3010	2
C₄×C₁₃×#137	2
C₁₃×#2935	2
#61095	13

Subgroups — C13×#61095 #15747434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61095 #15747434