Subgroups — C₁₃×#24402 #15710741

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1785	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₁₃×#575	—	2	4	no	—
19	C₁₃×#575	—	2	4	no	—
20	C₂×C₁₃×#137	—	2	1	no	—
21	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	—	2	1	no	—
29	C₂×C₁₃×#135	—	2	1	no	—
30	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₁₃×#472	—	2	4	no	—
37	C₁₃×#471	—	2	4	no	—
38	C₁₃×#449	—	2	1	no	—
39	C₁₃×#449	—	2	1	no	—
40	C₁₃×#449	—	2	1	no	—
41	C₁₃×#449	—	2	1	no	—
42	C₁₃×#449	—	2	1	no	—
43	C₁₃×#449	—	2	1	no	—
44	C₁₃×#448	—	2	1	no	—
45	C₁₃×#447	—	2	1	no	—
46	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#408	—	2	1	no	—
59	C₁₃×#408	—	2	1	no	—
60	C₁₃×#408	C₂²	1	1	yes	characteristic
61	C₁₃×#408	C₂²	1	1	yes	characteristic
62	C₁₃×#407	—	2	1	no	—
63	C₁₃×#407	C₂²	1	1	yes	characteristic
64	C₁₃×#407	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	2	2	no	—
74	C₂×C₁₃×#41	—	2	2	no	—
75	C₂×C₁₃×#41	—	2	2	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	1	no	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	—	4	1	no	—
82	C₂×C₁₃×#41	—	4	1	no	—
83	C₂×C₁₃×#41	—	4	1	no	—
84	C₂×C₁₃×#41	—	4	1	no	—
85	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
86	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#137	—	2	8	no	—
101	C₁₃×#137	—	2	2	no	—
102	C₁₃×#137	—	2	2	no	—
103	C₁₃×#137	—	2	2	no	—
104	C₁₃×#137	D₄	1	4	yes	complemented
105	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
106	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
107	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
108	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
109	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
111	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
112	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
113	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
114	C₁₃×#135	—	2	8	no	—
115	C₁₃×#135	—	2	8	no	—
116	C₂×C₁₃×Q₁₆	—	2	1	no	—
117	C₂×C₁₃×Q₁₆	—	2	1	no	—
118	C₂×C₁₃×SD₁₆	—	2	1	no	—
119	C₂×C₁₃×SD₁₆	—	2	1	no	—
120	C₂×C₁₃×SD₁₆	—	2	1	no	—
121	C₂×C₁₃×SD₁₆	—	2	1	no	—
122	C₂×C₁₃×SD₁₆	—	2	1	no	—
123	C₂×C₁₃×SD₁₆	—	2	1	no	—
124	C₂×C₁₃×SD₁₆	—	2	2	no	—
125	C₂×C₁₃×SD₁₆	—	2	1	no	—
126	C₂×C₁₃×SD₁₆	—	2	1	no	—
127	C₂×C₁₃×SD₁₆	—	4	1	no	—
128	C₂×C₁₃×D₈	—	2	1	no	—
129	C₂×C₁₃×D₈	—	2	1	no	—
130	C₂×C₁₃×D₈	—	2	1	no	—
131	C₂×C₁₃×D₈	—	2	1	no	—
132	C₂×C₁₃×D₈	—	2	2	no	—
133	C₂×C₁₃×D₈	—	2	1	no	—
134	C₂×C₁₃×D₈	—	2	1	no	—
135	C₂×C₁₃×D₈	—	4	1	no	—
136	C₁₃×#131	—	2	2	no	—
137	C₁₃×#131	—	2	2	no	—
138	C₁₃×#131	—	4	1	no	—
139	C₁₃×#131	—	4	1	no	—
140	C₂×C₁₃×M₁₆	—	2	1	no	—
141	C₂×C₁₃×M₁₆	—	2	2	no	—
142	C₂×C₁₃×M₁₆	—	2	2	no	—
143	C₂×C₁₃×M₁₆	—	2	1	no	—
144	C₂×C₁₃×M₁₆	—	2	1	no	—
145	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₁₃	—	2	1	no	—
152	C₂²×C₈×C₁₃	—	2	1	no	—
153	C₂²×C₈×C₁₃	—	2	1	no	—
154	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₁₃×#108	—	2	2	no	—
163	C₁₃×#108	—	2	2	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#103	—	2	1	no	—
167	C₁₃×#103	—	2	1	no	—
168	C₁₃×#102	—	2	1	no	—
169	C₁₃×#102	—	2	1	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×#102	—	2	1	no	—
172	C₁₃×#101	—	2	2	no	—
173	C₁₃×#101	—	4	1	no	—
174	C₁₃×#100	—	2	2	no	—
175	C₁₃×#100	—	2	2	no	—
176	C₁₃×#100	—	2	2	no	—
177	C₁₃×#100	—	4	1	no	—
178	C₁₃×C₂²⋊C₈	—	2	1	no	—
179	C₁₃×C₂²⋊C₈	—	2	1	no	—
180	C₁₃×C₂²⋊C₈	—	2	1	no	—
181	C₁₃×C₂²⋊C₈	—	2	1	no	—
182	C₁₃×C₂²⋊C₈	—	2	1	no	—
183	C₁₃×C₂²⋊C₈	—	2	1	no	—
184	C₁₃×C₂²⋊C₈	—	2	1	no	—
185	C₁₃×C₂²⋊C₈	—	2	1	no	—
186	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
187	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
190	#24402	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂⁴×C₁₃	—	2	1	no	—
192	C₂⁴×C₁₃	—	2	1	no	—
193	C₂⁴×C₁₃	—	2	1	no	—
194	C₂⁴×C₁₃	#41	1	1	yes	characteristic
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	4	no	—
198	C₁₃×#41	—	2	4	no	—
199	C₁₃×#41	—	2	2	no	—
200	C₁₃×#41	—	2	2	no	—
201	C₁₃×#41	—	2	1	no	—
202	C₁₃×#41	—	2	1	no	—
203	C₁₃×#41	—	2	1	no	—
204	C₁₃×#41	—	2	1	no	—
205	C₁₃×#41	—	4	2	no	—
206	C₁₃×#41	—	4	2	no	—
207	C₁₃×#41	—	4	1	no	—
208	C₁₃×#41	—	4	1	no	—
209	C₁₃×#41	—	4	2	no	—
210	C₁₃×#41	—	4	2	no	—
211	C₁₃×#41	—	4	2	no	—
212	C₁₃×#41	—	4	2	no	—
213	C₁₃×#41	—	4	2	no	—
214	C₁₃×#41	—	4	2	no	—
215	C₁₃×#41	—	4	2	no	—
216	C₁₃×#41	—	4	2	no	—
217	C₁₃×#41	C₂×D₄	1	2	yes	—
218	C₁₃×#41	C₂×D₄	1	2	yes	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	4	1	no	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	4	1	no	—
248	C₂×D₄×C₁₃	—	4	2	no	—
249	C₂×D₄×C₁₃	—	4	2	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	1	no	—
253	C₂×D₄×C₁₃	—	4	1	no	—
254	C₂×D₄×C₁₃	—	4	1	no	—
255	C₂×D₄×C₁₃	—	4	1	no	—
256	C₂×D₄×C₁₃	—	8	2	no	—
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	1	no	—
276	C₂²×C₄×C₁₃	—	4	1	no	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₁₃×Q₁₆	—	2	4	no	—
284	C₁₃×Q₁₆	—	2	4	no	—
285	C₁₃×SD₁₆	—	2	4	no	—
286	C₁₃×SD₁₆	—	2	4	no	—
287	C₁₃×SD₁₆	—	2	4	no	—
288	C₁₃×SD₁₆	—	2	4	no	—
289	C₁₃×SD₁₆	—	4	2	no	—
290	C₁₃×SD₁₆	—	4	2	no	—
291	C₁₃×SD₁₆	—	4	2	no	—
292	C₁₃×SD₁₆	—	4	2	no	—
293	C₁₃×D₈	—	2	4	no	—
294	C₁₃×D₈	—	2	4	no	—
295	C₁₃×D₈	—	4	2	no	—
296	C₁₃×D₈	—	4	2	no	—
297	C₁₃×D₈	—	4	2	no	—
298	C₁₃×D₈	—	4	2	no	—
299	C₁₃×M₁₆	—	2	4	no	—
300	C₁₃×M₁₆	—	2	1	no	—
301	C₁₃×M₁₆	—	2	1	no	—
302	C₁₃×M₁₆	—	2	1	no	—
303	C₁₃×M₁₆	—	2	1	no	—
304	C₁₃×M₁₆	—	2	1	no	—
305	C₁₃×M₁₆	—	2	1	no	—
306	C₁₃×M₁₆	—	2	1	no	—
307	C₁₃×M₁₆	—	2	1	no	—
308	C₁₃×M₁₆	—	2	1	no	—
309	C₁₃×M₁₆	—	2	1	no	—
310	C₁₃×M₁₆	—	4	2	no	—
311	C₁₃×M₁₆	—	4	2	no	—
312	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
313	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
314	C₂×C₈×C₁₃	—	2	4	no	—
315	C₂×C₈×C₁₃	—	2	1	no	—
316	C₂×C₈×C₁₃	—	2	1	no	—
317	C₂×C₈×C₁₃	—	2	1	no	—
318	C₂×C₈×C₁₃	—	2	1	no	—
319	C₂×C₈×C₁₃	—	2	1	no	—
320	C₂×C₈×C₁₃	—	2	1	no	—
321	C₂×C₈×C₁₃	—	2	1	no	—
322	C₂×C₈×C₁₃	—	2	1	no	—
323	C₂×C₈×C₁₃	—	2	1	no	—
324	C₂×C₈×C₁₃	—	2	1	no	—
325	C₂×C₈×C₁₃	—	4	2	no	—
326	C₂×C₈×C₁₃	—	4	2	no	—
327	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	1	no	—
333	C₁₃×C₂²⋊C₄	—	4	1	no	—
334	C₁₃×C₂²⋊C₄	—	4	1	no	—
335	C₂×#575	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2018	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#1785	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	4	1	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	2	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	1	no	—
361	C₂³×C₁₃	—	4	1	no	—
362	C₂³×C₁₃	—	4	1	no	—
363	C₂³×C₁₃	—	4	1	no	—
364	C₂³×C₁₃	—	8	1	no	—
365	C₂³×C₁₃	—	8	1	no	—
366	C₂³×C₁₃	—	8	1	no	—
367	C₂³×C₁₃	—	8	1	no	—
368	C₂³×C₁₃	—	8	1	no	—
369	C₂³×C₁₃	#121	1	1	yes	characteristic
370	C₂³×C₁₃	#121	1	1	yes	characteristic
371	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
372	Q₈×C₁₃	—	2	1	no	—
373	Q₈×C₁₃	—	2	1	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	1	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	4	2	no	—
378	Q₈×C₁₃	—	4	1	no	—
379	Q₈×C₁₃	—	4	1	no	—
380	Q₈×C₁₃	#120	1	2	yes	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	1	no	—
384	D₄×C₁₃	—	2	2	no	—
385	D₄×C₁₃	—	2	1	no	—
386	D₄×C₁₃	—	2	1	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	2	no	—
390	D₄×C₁₃	—	4	2	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	1	no	—
394	D₄×C₁₃	—	4	1	no	—
395	D₄×C₁₃	—	4	1	no	—
396	D₄×C₁₃	—	4	1	no	—
397	D₄×C₁₃	—	4	1	no	—
398	D₄×C₁₃	—	4	1	no	—
399	D₄×C₁₃	—	4	1	no	—
400	D₄×C₁₃	—	4	1	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	—	8	2	no	—
403	D₄×C₁₃	#120	1	2	yes	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	1	no	—
425	C₂×C₄×C₁₃	—	4	1	no	—
426	C₂×C₄×C₁₃	—	4	1	no	—
427	C₂×C₄×C₁₃	—	4	1	no	—
428	C₂×C₄×C₁₃	—	4	1	no	—
429	C₂×C₄×C₁₃	—	8	1	no	—
430	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
431	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
438	C₈×C₁₃	—	2	2	no	—
439	C₈×C₁₃	—	2	2	no	—
440	C₈×C₁₃	—	2	1	no	—
441	C₈×C₁₃	—	2	1	no	—
442	C₈×C₁₃	—	2	1	no	—
443	C₈×C₁₃	—	2	1	no	—
444	C₈×C₁₃	—	4	1	no	—
445	C₈×C₁₃	—	4	1	no	—
446	C₈×C₁₃	—	4	1	no	—
447	C₈×C₁₃	—	4	1	no	—
448	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
450	#575	—	2	4	no	—
451	#575	—	2	4	no	—
452	C₂×#137	—	2	1	no	—
453	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×AGL(1,ℤ/8)	—	2	1	no	—
456	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#135	—	2	1	no	—
461	C₂×#135	—	2	1	no	—
462	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
468	#472	—	2	4	no	—
469	#471	—	2	4	no	—
470	#449	—	2	1	no	—
471	#449	—	2	1	no	—
472	#449	—	2	1	no	—
473	#449	—	2	1	no	—
474	#449	—	2	1	no	—
475	#449	—	2	1	no	—
476	#448	—	2	1	no	—
477	#447	—	2	1	no	—
478	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#417	C₂²×C₁₃	1	1	yes	characteristic
481	#417	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#408	—	2	1	no	—
491	#408	—	2	1	no	—
492	#408	C₂²×C₁₃	1	1	yes	characteristic
493	#408	C₂²×C₁₃	1	1	yes	characteristic
494	#407	—	2	1	no	—
495	#407	C₂²×C₁₃	1	1	yes	characteristic
496	#407	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₈	—	2	1	no	—
498	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
499	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	2	1	no	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	1	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	1	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	8	1	no	—
519	C₂²×C₁₃	—	8	1	no	—
520	C₂²×C₁₃	—	8	2	no	—
521	C₂²×C₁₃	—	8	2	no	—
522	C₂²×C₁₃	—	8	4	no	—
523	C₂²×C₁₃	—	8	1	no	—
524	C₂²×C₁₃	—	8	1	no	—
525	C₂²×C₁₃	—	8	1	no	—
526	C₂²×C₁₃	—	8	1	no	—
527	C₂²×C₁₃	—	8	1	no	—
528	C₂²×C₁₃	—	16	1	no	—
529	C₂²×C₁₃	—	16	1	no	—
530	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
531	C₂²×C₁₃	#546	1	1	yes	characteristic
532	C₂²×C₁₃	#546	1	1	yes	characteristic
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	8	1	no	—
539	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
540	C₄×C₁₃	#534	1	1	yes	characteristic
541	C₄×C₁₃	D₄²	1	1	yes	characteristic
542	C₄×C₁₃	D₄²	1	1	yes	characteristic
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	4	1	no	—
554	C₂×#41	—	4	1	no	—
555	C₂×#41	—	4	1	no	—
556	C₂×#41	—	4	1	no	—
557	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
558	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
559	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
561	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
572	#137	—	2	8	no	—
573	#137	—	2	2	no	—
574	#137	—	2	2	no	—
575	#137	—	2	2	no	—
576	#137	D₄×C₁₃	1	4	yes	complemented
577	AGL(1,ℤ/8)	—	2	8	no	—
578	AGL(1,ℤ/8)	—	2	2	no	—
579	AGL(1,ℤ/8)	—	2	2	no	—
580	AGL(1,ℤ/8)	—	2	2	no	—
581	AGL(1,ℤ/8)	—	2	2	no	—
582	AGL(1,ℤ/8)	—	2	2	no	—
583	AGL(1,ℤ/8)	—	4	1	no	—
584	AGL(1,ℤ/8)	—	4	1	no	—
585	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	complemented
586	#135	—	2	8	no	—
587	#135	—	2	8	no	—
588	C₂×Q₁₆	—	2	1	no	—
589	C₂×Q₁₆	—	2	1	no	—
590	C₂×SD₁₆	—	2	1	no	—
591	C₂×SD₁₆	—	2	1	no	—
592	C₂×SD₁₆	—	2	1	no	—
593	C₂×SD₁₆	—	2	1	no	—
594	C₂×SD₁₆	—	2	2	no	—
595	C₂×SD₁₆	—	2	1	no	—
596	C₂×SD₁₆	—	2	1	no	—
597	C₂×SD₁₆	—	2	1	no	—
598	C₂×SD₁₆	—	2	1	no	—
599	C₂×SD₁₆	—	4	1	no	—
600	C₂×D₈	—	2	1	no	—
601	C₂×D₈	—	2	1	no	—
602	C₂×D₈	—	2	2	no	—
603	C₂×D₈	—	2	1	no	—
604	C₂×D₈	—	2	1	no	—
605	C₂×D₈	—	2	1	no	—
606	C₂×D₈	—	2	1	no	—
607	C₂×D₈	—	4	1	no	—
608	#131	—	2	2	no	—
609	#131	—	2	2	no	—
610	#131	—	4	1	no	—
611	#131	—	4	1	no	—
612	C₂×M₁₆	—	2	1	no	—
613	C₂×M₁₆	—	2	2	no	—
614	C₂×M₁₆	—	2	2	no	—
615	C₂×M₁₆	—	2	1	no	—
616	C₂×M₁₆	—	2	1	no	—
617	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×C₈	—	2	1	no	—
624	C₂²×C₈	—	2	1	no	—
625	C₂²×C₈	—	2	1	no	—
626	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
628	#121	—	2	1	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	#108	—	2	2	no	—
635	#108	—	2	2	no	—
636	#103	—	2	1	no	—
637	#103	—	2	1	no	—
638	#103	—	2	1	no	—
639	#103	—	2	1	no	—
640	#102	—	2	1	no	—
641	#102	—	2	1	no	—
642	#102	—	2	1	no	—
643	#102	—	2	1	no	—
644	#101	—	2	2	no	—
645	#101	—	4	1	no	—
646	#100	—	2	2	no	—
647	#100	—	2	2	no	—
648	#100	—	2	2	no	—
649	#100	—	4	1	no	—
650	C₂²⋊C₈	—	2	1	no	—
651	C₂²⋊C₈	—	2	1	no	—
652	C₂²⋊C₈	—	2	1	no	—
653	C₂²⋊C₈	—	2	1	no	—
654	C₂²⋊C₈	—	2	1	no	—
655	C₂²⋊C₈	—	2	1	no	—
656	C₂²⋊C₈	—	2	1	no	—
657	C₂²⋊C₈	—	2	1	no	—
658	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
659	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
660	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
661	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₁₃	—	2	1	no	—
663	C₂×C₁₃	—	2	1	no	—
664	C₂×C₁₃	—	4	1	no	—
665	C₂×C₁₃	—	4	1	no	—
666	C₂×C₁₃	—	4	2	no	—
667	C₂×C₁₃	—	8	1	no	—
668	C₂×C₁₃	—	8	2	no	—
669	C₂×C₁₃	—	16	1	no	—
670	C₂×C₁₃	#2410	1	1	yes	characteristic
671	C₂×C₁₃	#3067	1	1	yes	characteristic
672	C₂×C₁₃	#3068	1	1	yes	characteristic
673	C₂⁴	—	2	1	no	—
674	C₂⁴	—	2	1	no	—
675	C₂⁴	—	2	1	no	—
676	C₂⁴	C₁₃×#41	1	1	yes	characteristic
677	#41	—	2	1	no	—
678	#41	—	2	1	no	—
679	#41	—	2	4	no	—
680	#41	—	2	4	no	—
681	#41	—	2	2	no	—
682	#41	—	2	2	no	—
683	#41	—	2	1	no	—
684	#41	—	2	1	no	—
685	#41	—	2	1	no	—
686	#41	—	2	1	no	—
687	#41	—	4	2	no	—
688	#41	—	4	2	no	—
689	#41	—	4	1	no	—
690	#41	—	4	1	no	—
691	#41	—	4	2	no	—
692	#41	—	4	2	no	—
693	#41	—	4	2	no	—
694	#41	—	4	2	no	—
695	#41	—	4	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	2	no	—
699	#41	C₂×D₄×C₁₃	1	2	yes	—
700	#41	C₂×D₄×C₁₃	1	2	yes	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	4	1	no	—
709	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
710	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	4	1	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	1	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	1	no	—
738	C₂×D₄	—	8	2	no	—
739	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
765	Q₁₆	—	2	4	no	—
766	Q₁₆	—	2	4	no	—
767	SD₁₆	—	2	4	no	—
768	SD₁₆	—	2	4	no	—
769	SD₁₆	—	2	4	no	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	4	2	no	—
772	SD₁₆	—	4	2	no	—
773	SD₁₆	—	4	2	no	—
774	SD₁₆	—	4	2	no	—
775	D₈	—	2	4	no	—
776	D₈	—	2	4	no	—
777	D₈	—	4	2	no	—
778	D₈	—	4	2	no	—
779	D₈	—	4	2	no	—
780	D₈	—	4	2	no	—
781	M₁₆	—	2	4	no	—
782	M₁₆	—	2	1	no	—
783	M₁₆	—	2	1	no	—
784	M₁₆	—	2	1	no	—
785	M₁₆	—	2	1	no	—
786	M₁₆	—	2	1	no	—
787	M₁₆	—	2	1	no	—
788	M₁₆	—	2	1	no	—
789	M₁₆	—	2	1	no	—
790	M₁₆	—	2	1	no	—
791	M₁₆	—	2	1	no	—
792	M₁₆	—	4	2	no	—
793	M₁₆	—	4	2	no	—
794	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
795	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
796	C₂×C₈	—	2	4	no	—
797	C₂×C₈	—	2	1	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	—	2	1	no	—
807	C₂×C₈	—	4	2	no	—
808	C₂×C₈	—	4	2	no	—
809	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
811	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
812	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	4	1	no	—
816	C₂²⋊C₄	—	4	1	no	—
817	C₁₃	#24402	1	1	yes	characteristic, direct product factor, Sylow
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	8	1	no	—
833	C₂³	—	8	1	no	—
834	C₂³	—	8	1	no	—
835	C₂³	—	8	1	no	—
836	C₂³	—	8	1	no	—
837	C₂³	C₁₃×#121	1	1	yes	characteristic
838	C₂³	C₁₃×#121	1	1	yes	characteristic
839	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
840	Q₈	—	2	1	no	—
841	Q₈	—	2	1	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	1	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	4	1	no	—
847	Q₈	—	4	1	no	—
848	Q₈	C₁₃×#120	1	2	yes	—
849	D₄	—	2	2	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	1	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	1	no	—
854	D₄	—	2	1	no	—
855	D₄	—	2	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	1	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	1	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	C₁₃×#120	1	2	yes	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
899	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
904	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
905	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	1	no	—
909	C₈	—	2	1	no	—
910	C₈	—	2	1	no	—
911	C₈	—	2	1	no	—
912	C₈	—	4	1	no	—
913	C₈	—	4	1	no	—
914	C₈	—	4	1	no	—
915	C₈	—	4	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	—	8	2	no	—
934	C₂²	—	8	2	no	—
935	C₂²	—	8	4	no	—
936	C₂²	—	8	1	no	—
937	C₂²	—	8	1	no	—
938	C₂²	—	8	1	no	—
939	C₂²	—	8	1	no	—
940	C₂²	—	8	1	no	—
941	C₂²	—	16	1	no	—
942	C₂²	—	16	1	no	—
943	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
944	C₂²	C₁₃×#546	1	1	yes	characteristic
945	C₂²	C₁₃×#546	1	1	yes	characteristic
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	8	1	no	—
952	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
953	C₄	C₁₃×#534	1	1	yes	characteristic
954	C₄	D₄²×C₁₃	1	1	yes	characteristic
955	C₄	D₄²×C₁₃	1	1	yes	characteristic
956	C₂	—	2	1	no	—
957	C₂	—	2	1	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	2	no	—
961	C₂	—	8	1	no	—
962	C₂	—	8	2	no	—
963	C₂	—	16	1	no	—
964	C₂	C₁₃×#2410	1	1	yes	characteristic
965	C₂	C₁₃×#3067	1	1	yes	characteristic
966	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#575	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₂×C₁₃×#471	C₂	semidirect
4. C₁₃×#3006	C₂	semidirect
5. C₂×C₁₃×#449	C₂	semidirect
6. C₁₃×#2880	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#2019	C₂	semidirect
10. C₁₃×#2018	C₂	semidirect
11. C₁₃×#1908	C₂	semidirect
12. C₁₃×#1907	C₂	semidirect
13. C₁₃×#1900	C₂	semidirect
14. C₁₃×#1855	C₂	semidirect
15. C₁₃×#1785	C₂	semidirect
30. C₂²×C₁₃×SD₁₆	C₂²	semidirect
31. C₂²×C₁₃×D₈	C₂²	semidirect
46. C₂×C₁₃×#108	C₂²	semidirect
47. C₂×C₁₃×#108	C₂²	semidirect
50. C₂×C₁₃×#103	C₂²	semidirect
51. C₂×C₁₃×#102	C₂²	semidirect
52. C₂×C₁₃×#101	C₂²	semidirect
53. C₂×C₁₃×#101	C₂²	semidirect
54. C₂×C₁₃×#100	C₂²	semidirect
55. C₂×C₁₃×#100	C₂²	semidirect
56. C₂×C₁₃×#100	C₂²	semidirect
57. C₂×C₁₃×#100	C₂²	semidirect
67. C₁₃×#343	C₂²	semidirect
68. C₁₃×#343	C₂²	semidirect
69. C₁₃×#341	C₂²	semidirect
70. C₁₃×#341	C₂²	semidirect
104. C₁₃×#137	D₄	semidirect
113. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
190. #24402	C₁₃	direct (N × H)
335. C₂×#575	C₂×C₁₃	semidirect
336. C₂×#472	C₂×C₁₃	semidirect
337. C₂×#471	C₂×C₁₃	semidirect
338. #3006	C₂×C₁₃	semidirect
339. C₂×#449	C₂×C₁₃	semidirect
340. #2880	C₂×C₁₃	semidirect
341. #2052	C₂×C₁₃	semidirect
342. #2051	C₂×C₁₃	semidirect
343. #2019	C₂×C₁₃	semidirect
344. #2018	C₂×C₁₃	semidirect
345. #1908	C₂×C₁₃	semidirect
346. #1907	C₂×C₁₃	semidirect
347. #1900	C₂×C₁₃	semidirect
348. #1855	C₂×C₁₃	semidirect
349. #1785	C₂×C₁₃	semidirect
462. C₂²×SD₁₆	C₂²×C₁₃	semidirect
463. C₂²×D₈	C₂²×C₁₃	semidirect
478. C₂×#108	C₂²×C₁₃	semidirect
479. C₂×#108	C₂²×C₁₃	semidirect
482. C₂×#103	C₂²×C₁₃	semidirect
483. C₂×#102	C₂²×C₁₃	semidirect
484. C₂×#101	C₂²×C₁₃	semidirect
485. C₂×#101	C₂²×C₁₃	semidirect
486. C₂×#100	C₂²×C₁₃	semidirect
487. C₂×#100	C₂²×C₁₃	semidirect
488. C₂×#100	C₂²×C₁₃	semidirect
489. C₂×#100	C₂²×C₁₃	semidirect
499. #343	C₂²×C₁₃	semidirect
500. #343	C₂²×C₁₃	semidirect
501. #341	C₂²×C₁₃	semidirect
502. #341	C₂²×C₁₃	semidirect
576. #137	D₄×C₁₃	semidirect
585. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
817. C₁₃	#24402	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#575	2
C₂×C₁₃×#472	2
C₂×C₁₃×#471	2
C₁₃×#3006	2
C₂×C₁₃×#449	2
C₁₃×#2880	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#2019	2
C₁₃×#2018	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1785	2
#24402	13

Subgroups — C13×#24402 #15710741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24402 #15710741